{"text_format":"1","workbook":"xlsx","n_sheets":14,"sheets":["Start","Quick Guide","Efficiency Map Fit (Curves)","Efficiency Map Fit (Points)","Efficiency Map","Efficiency Charts","Pressure Drop Fit","Pressure Drop","Leakage Fit","Leakage","SK Efficiency Curve","SAHC Calc.+Opt.","SAHC Model","History"],"not_rendered":{"charts":29,"images":12,"macros":1,"external_links":0,"defined_names":95,"comments":2,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Start","index":0,"n_rows":72,"n_cols":33,"rows_kept":72,"cut":false,"hidden":false,"merged":[]}
[]
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[]
[]
[]
[null,null,null,null,"AirCow"]
[null,null,null,null,"Solar Air Heating Collector Field Calculator and Optimizer for instantaneous Working Points"]
[]
[]
[null,null,null,null,"What it does basically"]
[null,null,null,null,"This workbook contains a thermal and hydraulic model to calculate air collectors with the following properties:"]
[null,null,null,null,null,"  ●","transparent cover"]
[null,null,null,null,null,"  ●","under-flown absorber"]
[null,null,null,null,null,"  ●","working in the turbulent flow range"]
[null,null,null,null,null,"  ●","measured with thermally preconditioned air"]
[null,null,null,null,"You can decide between the modes"]
[null,null,null,null,null,"A. - the guided pre-calculation for ScenoCalc and Solar KEYMARK and "]
[null,null,null,null,null,"B. - the complete features for system planning, scientific studies, and ScenoCalc."]
[]
[]
[]
[]
[]
[null,null,null,null,"What it does for Solar KEYMARK"]
[null,null,null,null,"This model considers the mass flow dependent thermal performance and pressure drop, the leakage, "]
[null,null,null,null,null,"and the system dependency of air collectors."]
[null,null,null,null,"The length and width of a collector field will be calculated, and the mass flow will be optimized for one "]
[null,null,null,null,null,"system configuration and one typical working point."]
[null,null,null,null,"The optimization maximizes the net primary power per collector area considering thermal and auxiliary power."]
[null,null,null,null,"The coefficients of the following efficiency curve model, which is usually used for liquid heating collectors, will "]
[null,null,null,null,null,"be determined considering the penalty by leakage, flow resistance, and mass flow dependent thermal "]
[null,null,null,null,null,"efficiency."]
[]
[]
[]
[null,null,null,null,"These coefficients gained from this pre-calculation are applicable in ScenoCalc for simulation of the Collector "]
[null,null,null,null,null,"Annual Output, CAO."]
[]
[]
[null,null,null,null,"What you need"]
[]
[null,null,null,null,"Mode A."]
[null,null,null,null,"To use this collector model, the model coefficients can be fitted within this file."]
[null,null,null,null,"For Solar KEYMARK, efficiency curves must be used for the thermal efficiency model. Leakage must be "]
[null,null,null,null,null,"considered, if present. The curves and measurement points must be gained according to DIN EN ISO 9806."]
[null,null,null,null,null,"Additionally to the standards requirements, the mean ambient pressure during leakage measurement "]
[null,null,null,null,null,"is needed."]
[]
[null,null,null,null,"Mode B."]
[null,null,null,null,"For the thermal efficiency, either measurement points with varied mass flows and inlet temperatures or the "]
[null,null,null,null,null,"coefficients of efficiency curves from different mass flows are necessary."]
[null,null,null,null,"The pressure drop and leakage coefficients need measurement points."]
[null,null,null,null,"Data from measurements of the test stand including connecting ducts can be entered once without and once "]
[null,null,null,null,null,"with the collector, to subtract the pressure drop and leakage of the test stand and the connecting ducts."]
[null,null,null,null,"If the collector is considered to be air tight, or if the influence of leakage will be neglected, no leakage data "]
[null,null,null,null,null,"are needed."]
[null,null,null,null,"Instead of measurement points, simulation points are sufficient as well."]
[null,null,null,null,"In the future, it is intended to provide all the necessary data in test reports of certified test labs if not yet "]
[null,null,null,null,null,"already provided nowadays."]
[]
[]
[null,null,null,null,"What is to do for the Solar KEYMARK pre-calculation"]
[null,null,null,null,"1.","Enter the data for thermal efficiency, pressure drop, and leakage."]
[null,null,null,null,"2.","Chose the coefficients for either the linear or the quadratic thermal efficiency model."]
[null,null,null,null,"3.","Fill out the cells with blue colored fond with the gross area and text information."]
[null,null,null,null,"4.","Press the button \"Perform Calculation\"."]
[null,null,null,null,"5.","Read out the three efficiency curve coefficients for direct use in ScenoCalc. "]
[null,null,null,null,"6.","Print the result document, if needed."]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"CONCATENATE(\"AirCow version:  \",History!A9)","v":"AirCow version:  3.00 (2016-09-30)"}]

{"sheet":"Quick Guide","index":1,"n_rows":61,"n_cols":34,"rows_kept":61,"cut":false,"hidden":true,"merged":[]}
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,"AirCow"]
[null,null,null,null,"Solar Air Heating Collector Field Calculator and Optimizer for instantaneous Working Points"]
[]
[null,null,null,null,"Quick guide"]
[]
[]
[null,null,null,null,"Determination of collector coefficients"]
[null,null,null,null,"1.","Enter your data points for efficiency, pressure drop and leakage or your efficiency curve coefficients into the"]
[null,null,null,null,null,"blue framed ranges"]
[null,null,null,null,"2.","Copy the determined coefficients and valid ranges to the sheet \"Input, Results\""]
[]
[]
[null,null,null,null,"Main steps for system planning"]
[null,null,null,null,"1.","Fill out the group \"Input\" of sheet \"Model\" including temperature rise and power"]
[null,null,null,null,"2.","Delete the upper mass flow choice-cell to optimize mass flow, if not deleted yet"]
[null,null,null,null,"3.","Check the group \"Error check\""]
[null,null,null,null,"4.","Copy the case column"]
[null,null,null,null,"5.","Take and round the results field length and width and enter them in the group \"Input\" of the new column"]
[null,null,null,null,"6.","Enter the optimal mass flow of the first case column to the manually set mass flow"]
[null,null,null,null,"7.","If interested, vary field dimensions, mass flow, and other input values in further case columns"]
[null,null,null,null,"8.","Possibly, optimize mass flow with given field length and width (pay attention on higher temperature rise)"]
[null,null,null,null,"9.","Select a fan from the market, and adapt the input for appropriate total pressure rise and volume flow"]
[null,null,null,null,"10.","If not done yet, design the remaining system, re-enter its flow resistance, and check results"]
[null,null,null,null,"11.","Check final results for errors"]
[]
[]
[null,null,null,null,"Usage of sheet \"SAHC Calc.+Opt.\""]
[]
[null,null,null,null,"Groups"]
[null,null,null,null,"  ●","Pressing on plus or minus symbols will expand or collapse "]
[null,null,null,null,"  ●","Above the plus and minus, pressing on level 3 will show all head lines"]
[null,null,null,null,"  ●","Level 4 will show all values"]
[null,null,null,null,"  ●","Level 1 will collapse all groups"]
[]
[null,null,null,null,"Multiplying the case column"]
[null,null,null,null,"  ●","Select a column and copy it by any means in an empty column"]
[null,null,null,null,"  ●",{"$f":"CONCATENATE(\"All columns with the word 'yes' in row \",ROW('SAHC Calc.+Opt.'!A71),\" will be instantly actualized by the model after each input change\")","v":"All columns with the word 'yes' in row 71 will be instantly actualized by the model after each input change"}]
[null,null,null,null,"  ●","The worksheet \"Input, Results\" can be copied also"]
[]
[null,null,null,null,"Further changes"]
[null,null,null,null,"  ●",{"$f":"CONCATENATE(\"Above row \",ROW('SAHC Calc.+Opt.'!A178),\" do not insert, delete, or move rows (the only restriction for communication with the model)\")","v":"Above row 178 do not insert, delete, or move rows (the only restriction for communication with the model)"}]
[null,null,null,null,"  ●","Fell free for any other changes, inserting diagrams, …"]
[]
[null,null,null,null,"Colors"]
[null,null,null,null,"  ●","Groups can be recognized by different cell frame colors"]
[null,null,null,null,"  ●","Feel free to fill cells of the whole worksheet with vivid colors for better orientation"]
[]
[]
[null,null,null,null,"Trouble shooting"]
[null,null,null,null,"  ●","Make shure, all input data go well together and characterise a realistic system"]
[null,null,null,null,"  ●","Pay attention to realistic results e.g. in the group \"Overview on results\""]
[null,null,null,null,"  ●","Pay attention to a positive cost function in the group \"Overview on results\" - \"Mass flow optimization\""]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"CONCATENATE(\"AirCow version:  \",History!A9)","v":"AirCow version:  3.00 (2016-09-30)"}]

{"sheet":"Efficiency Map Fit (Curves)","index":2,"n_rows":41,"n_cols":17,"rows_kept":41,"cut":false,"hidden":true,"merged":[]}
[null,"Data",null,null,null,null,null,null,null,null,null,"Results"]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,"Optimization"]
[null,null,null,null,null,null,null,null,null,null,null,"Model",null,null,"Linear","Quadratic"]
[null,null,null,null,null,null,null,null,null,null,null,"Iterative optimization did",null,null,{"$f":"'Efficiency Map'!LG9","v":""},{"$f":"'Efficiency Map'!LH9","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,"Quadratic efficiency map model"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"with",null,"and"]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,"Coefficients"]
[null,null,null,null,null,null,null,null,null,null,null,"Model",null,null,"Linear","Quadratic"]
[null,null,null,null,null,null,null,null,null,null,null,"Conversion factor","η0,max","-",{"$f":"'Efficiency Map'!LG13","v":""},{"$f":"'Efficiency Map'!LH13","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,"Linear heat loss coefficient","c1,max","W/(m²K)",{"$f":"'Efficiency Map'!LG14","v":""},{"$f":"'Efficiency Map'!LH14","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,"Quadratic heat loss coefficient","c2,max","W/(mK)²",{"$f":"'Efficiency Map'!LG15","v":""},{"$f":"'Efficiency Map'!LH15","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,"Mass flow dependent heat loss coefficient","cm","h/kg",{"$f":"'Efficiency Map'!LG16","v":""},{"$f":"'Efficiency Map'!LH16","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,"Statistics"]
[null,null,null,null,null,null,null,null,null,null,null,"Model",null,null,"Linear","Quadratic"]
[null,null,null,null,null,null,null,null,null,null,null,"Standard deviation","σ","%-points",{"$f":"'Efficiency Map'!LG19","v":""},{"$f":"'Efficiency Map'!LH19","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,"With coverage factor","k","-",{"$f":"'Efficiency Map'!LG21","v":""}]
[null,"Comments",null,null,null,null,null,null,null,null,null,"For conficence level","p","%",{"$f":"'Efficiency Map'!LG22","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,"Valid range"]
[null,null,null,null,null,null,null,null,null,null,null,"Minimum valid mass flow","ṁmin","kg/h",{"$f":"'Efficiency Map'!LG25","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,"Maximum valid mass flow","ṁmax","kg/h",{"$f":"'Efficiency Map'!LG26","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,"Valid range of efficiency map AND pressure drop model (after data of both are entered) for use in calculations"]
[null,null,null,null,null,null,null,null,null,null,null,"Minimum valid mass flow for efficiency, pressure drop","ṁmin","kg/h",{"$f":"IF(OR(O27=\"\",'Pressure Drop Fit'!R19=\"\"),\"\",\n     MAX(O27,     'Pressure Drop Fit'!R19))","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,"Maximum valid mass flow for efficiency, pressure drop","ṁmax","kg/h",{"$f":"IF(OR('Efficiency Map Fit (Curves)'!O28=\"\",'Pressure Drop Fit'!R20=\"\"),\"\",\n      MIN('Efficiency Map Fit (Curves)'!O28,     'Pressure Drop Fit'!R20))","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,"Please select model"]
[null,null,null,null,null,null,null,null,null,null,null,"Model",null,null,"Linear","Quadratic"]
[null,"Enter your data here",null,null,null,null,null,null,null,null,null,"Your selection"]
[null,"ṁ","η0","c1","c2"]
[null,"[kg/h]","[-]","[W/(Km²)]","[W/(Km)²]"]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,"Linear efficiency map model",null,null,null,null,"Quadratic efficiency map model"]

{"sheet":"Efficiency Map Fit (Points)","index":3,"n_rows":138,"n_cols":19,"rows_kept":138,"cut":false,"hidden":true,"merged":[]}
[null,"Data",null,null,null,null,null,null,null,null,null,null,null,"Results"]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Optimization"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Model",null,null,"Linear","Quadratic"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Iterative optimization did",null,null,{"$f":"'Efficiency Map'!LK9","v":""},{"$f":"'Efficiency Map'!LL9","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Quadratic efficiency map model"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"with",null,"and"]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Coefficients"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Model",null,null,"Linear","Quadratic"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Conversion factor","η0,max","-",{"$f":"'Efficiency Map'!LK13","v":""},{"$f":"'Efficiency Map'!LL13","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Linear heat loss coefficient","c1,max","W/(m²K)",{"$f":"'Efficiency Map'!LK14","v":""},{"$f":"'Efficiency Map'!LL14","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Quadratic heat loss coefficient","c2,max","W/(mK)²",{"$f":"'Efficiency Map'!LK15","v":""},{"$f":"'Efficiency Map'!LL15","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Mass flow dependent heat loss coefficient","cm","h/kg",{"$f":"'Efficiency Map'!LK16","v":""},{"$f":"'Efficiency Map'!LL16","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Statistics"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Model",null,null,"Linear","Quadratic"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Standard deviation","σ","%-points",{"$f":"'Efficiency Map'!LK19","v":""},{"$f":"'Efficiency Map'!LL19","v":""}]
[]
[null,"Comments",null,null,null,null,null,null,null,null,null,null,null,"With coverage factor","k","-",{"$f":"'Efficiency Map'!LK21","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"For conficence level","p","%",{"$f":"'Efficiency Map'!LK22","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Valid ranges"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Minimum valid mass flow","ṁmin","kg/h",{"$f":"'Efficiency Map'!LK25","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Maximum valid mass flow","ṁmax","kg/h",{"$f":"'Efficiency Map'!LK26","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Minimum valid reduced temperature difference","T*min","Km²/W",{"$f":"'Efficiency Map'!LK27","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Maximum valid reduced temperature difference","T*max","Km²/W",{"$f":"'Efficiency Map'!LK28","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Valid range of efficiency map AND pressure drop model (after data of both are entered) for use in calculations"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Minimum valid mass flow for efficiency, pressure drop","ṁmin","kg/h",{"$f":"IF(OR(Q28=\"\",'Pressure Drop Fit'!R19=\"\"),\"\",\n     MAX(Q28,     'Pressure Drop Fit'!R19))","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Maximum valid mass flow for efficiency, pressure drop","ṁmax","kg/h",{"$f":"IF(OR(Q29=\"\",'Pressure Drop Fit'!R20=\"\"),\"\",\n      MIN(Q29,     'Pressure Drop Fit'!R20))","v":""}]
[null,"Enter your data here"]
[null,"No.","Date","Time","G","ṁi","ṁe","ϑa","ϑi","ϑe","η"]
[null,null,"optional","optional","[W/m²]","[kg/h]","[kg/h]","[°C]","[°C]","[°C]","[-]"]
[null,{"$f":"IF(E39=\"\",\"\",1)","v":""},null,null,null,null,null,null,null,null,null,null,null,"Linear efficiency map model",null,null,null,null,"Quadratic efficiency map model"]
[null,{"$f":"IF(E40=\"\",\"\",B39+1)","v":""},null,null,null,null,null,null,null,null,null,null,null,"Within the valid range of reduced temperature difference (x-axis)",null,null,null,null,"Within the valid range of reduced temperature difference (x-axis)"]
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[null,"",null,null,null,null,null,null,null,null,null,null,null,"With extended range of reduced temperature difference (x-axis)",null,null,null,null,"With extended range of reduced temperature difference (x-axis)"]
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{"sheet":"Efficiency Map","index":4,"n_rows":141,"n_cols":324,"rows_kept":141,"cut":false,"hidden":true,"merged":[]}
["Input from efficiency curve",null,null,null,null,null,null,null,null,null,"Input from measurement",null,null,null,null,null,"Preparation",null,null,null,null,null,null,"1. Iteration",null,null,null,null,null,null,null,null,null,null,null,null,"2. Iteration",null,null,null,null,null,null,null,null,null,null,null,null,"3. Iteration",null,null,null,null,null,null,null,null,null,null,null,null,"4. Iteration",null,null,null,null,null,null,null,null,null,null,null,null,"5. Iteration",null,null,null,null,null,null,null,null,null,null,null,null,"6. Iteration",null,null,null,null,null,null,null,null,null,null,null,null,"7. Iteration",null,null,null,null,null,null,null,null,null,null,null,null,"8. Iteration",null,null,null,null,null,null,null,null,null,null,null,null,"9. Iteration",null,null,null,null,null,null,null,null,null,null,null,null,"10. Iteration",null,null,null,null,null,null,null,null,null,null,null,null,"11. Iteration",null,null,null,null,null,null,null,null,null,null,null,null,"12. Iteration",null,null,null,null,null,null,null,null,null,null,null,null,"13. Iteration",null,null,null,null,null,null,null,null,null,null,null,null,"14. Iteration",null,null,null,null,null,null,null,null,null,null,null,null,"15. Iteration",null,null,null,null,null,null,null,null,null,null,null,null,"16. Iteration",null,null,null,null,null,null,null,null,null,null,null,null,"17. Iteration",null,null,null,null,null,null,null,null,null,null,null,null,"18. Iteration",null,null,null,null,null,null,null,null,null,null,null,null,"19. Iteration",null,null,null,null,null,null,null,null,null,null,null,null,"20. Iteration",null,null,null,null,null,null,null,null,null,null,null,null,"Evaluation of Optimization",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Error check",null,null,null,null,null,"Results"]
[]
[null,null,null,null,null,"G",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Damping factor",null,"Starting coefficients",null,null,null,null,null,null,null,null,"New coefficients","SSQ",null,null,"Best coefficients",null,null,null,null,null,null,null,null,"New coefficients","SSQ",null,null,"Best coefficients",null,null,null,null,null,null,null,null,"New coefficients","SSQ",null,null,"Best coefficients",null,null,null,null,null,null,null,null,"New coefficients","SSQ",null,null,"Best coefficients",null,null,null,null,null,null,null,null,"New coefficients","SSQ",null,null,"Best coefficients",null,null,null,null,null,null,null,null,"New coefficients","SSQ",null,null,"Best coefficients",null,null,null,null,null,null,null,null,"New coefficients","SSQ",null,null,"Best coefficients",null,null,null,null,null,null,null,null,"New coefficients","SSQ",null,null,"Best coefficients",null,null,null,null,null,null,null,null,"New coefficients","SSQ",null,null,"Best coefficients",null,null,null,null,null,null,null,null,"New coefficients","SSQ",null,null,"Best coefficients",null,null,null,null,null,null,null,null,"New coefficients","SSQ",null,null,"Best coefficients",null,null,null,null,null,null,null,null,"New coefficients","SSQ",null,null,"Best coefficients",null,null,null,null,null,null,null,null,"New coefficients","SSQ",null,null,"Best coefficients",null,null,null,null,null,null,null,null,"New coefficients","SSQ",null,null,"Best coefficients",null,null,null,null,null,null,null,null,"New coefficients","SSQ",null,null,"Best coefficients",null,null,null,null,null,null,null,null,"New coefficients","SSQ",null,null,"Best coefficients",null,null,null,null,null,null,null,null,"New coefficients","SSQ",null,null,"Best coefficients",null,null,null,null,null,null,null,null,"New coefficients","SSQ",null,null,"Best coefficients",null,null,null,null,null,null,null,null,"New coefficients","SSQ",null,null,"Best coefficients",null,null,null,null,null,null,null,null,"New coefficients","SSQ",null,null,"Best coefficients",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Expected ranges of coefficients"]
[null,null,null,null,null,"[W/m²]",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"d",null,"ccur",null,null,null,null,null,null,null,"Δc","cmin",null,null,null,"cmin",null,null,null,null,null,null,null,"Δc","cmin",null,null,null,"cmin",null,null,null,null,null,null,null,"Δc","cmin",null,null,null,"cmin",null,null,null,null,null,null,null,"Δc","cmin",null,null,null,"cmin",null,null,null,null,null,null,null,"Δc","cmin",null,null,null,"cmin",null,null,null,null,null,null,null,"Δc","cmin",null,null,null,"cmin",null,null,null,null,null,null,null,"Δc","cmin",null,null,null,"cmin",null,null,null,null,null,null,null,"Δc","cmin",null,null,null,"cmin",null,null,null,null,null,null,null,"Δc","cmin",null,null,null,"cmin",null,null,null,null,null,null,null,"Δc","cmin",null,null,null,"cmin",null,null,null,null,null,null,null,"Δc","cmin",null,null,null,"cmin",null,null,null,null,null,null,null,"Δc","cmin",null,null,null,"cmin",null,null,null,null,null,null,null,"Δc","cmin",null,null,null,"cmin",null,null,null,null,null,null,null,"Δc","cmin",null,null,null,"cmin",null,null,null,null,null,null,null,"Δc","cmin",null,null,null,"cmin",null,null,null,null,null,null,null,"Δc","cmin",null,null,null,"cmin",null,null,null,null,null,null,null,"Δc","cmin",null,null,null,"cmin",null,null,null,null,null,null,null,"Δc","cmin",null,null,null,"cmin",null,null,null,null,null,null,null,"Δc","cmin",null,null,null,"cmin",null,null,null,null,null,null,null,"Δc","cmin",null,null,null,"cmin",null,null,null,"Absolute values",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Check of coefficients"]
[null,null,null,null,null,1000,null,null,null,null,null,null,null,null,null,null,null,"Set by macro",null,null,null,null,null,null,null,"(JTJ)-1",null,null,null,"JTΔy","d(JTJ)-1JTΔy","Δc+ccur,old",null,null,null,null,null,null,"(JTJ)-1",null,null,null,"JTΔy","d(JTJ)-1JTΔy","Δc+ccur,old",null,null,null,null,null,null,"(JTJ)-1",null,null,null,"JTΔy","d(JTJ)-1JTΔy","Δc+ccur,old",null,null,null,null,null,null,"(JTJ)-1",null,null,null,"JTΔy","d(JTJ)-1JTΔy","Δc+ccur,old",null,null,null,null,null,null,"(JTJ)-1",null,null,null,"JTΔy","d(JTJ)-1JTΔy","Δc+ccur,old",null,null,null,null,null,null,"(JTJ)-1",null,null,null,"JTΔy","d(JTJ)-1JTΔy","Δc+ccur,old",null,null,null,null,null,null,"(JTJ)-1",null,null,null,"JTΔy","d(JTJ)-1JTΔy","Δc+ccur,old",null,null,null,null,null,null,"(JTJ)-1",null,null,null,"JTΔy","d(JTJ)-1JTΔy","Δc+ccur,old",null,null,null,null,null,null,"(JTJ)-1",null,null,null,"JTΔy","d(JTJ)-1JTΔy","Δc+ccur,old",null,null,null,null,null,null,"(JTJ)-1",null,null,null,"JTΔy","d(JTJ)-1JTΔy","Δc+ccur,old",null,null,null,null,null,null,"(JTJ)-1",null,null,null,"JTΔy","d(JTJ)-1JTΔy","Δc+ccur,old",null,null,null,null,null,null,"(JTJ)-1",null,null,null,"JTΔy","d(JTJ)-1JTΔy","Δc+ccur,old",null,null,null,null,null,null,"(JTJ)-1",null,null,null,"JTΔy","d(JTJ)-1JTΔy","Δc+ccur,old",null,null,null,null,null,null,"(JTJ)-1",null,null,null,"JTΔy","d(JTJ)-1JTΔy","Δc+ccur,old",null,null,null,null,null,null,"(JTJ)-1",null,null,null,"JTΔy","d(JTJ)-1JTΔy","Δc+ccur,old",null,null,null,null,null,null,"(JTJ)-1",null,null,null,"JTΔy","d(JTJ)-1JTΔy","Δc+ccur,old",null,null,null,null,null,null,"(JTJ)-1",null,null,null,"JTΔy","d(JTJ)-1JTΔy","Δc+ccur,old",null,null,null,null,null,null,"(JTJ)-1",null,null,null,"JTΔy","d(JTJ)-1JTΔy","Δc+ccur,old",null,null,null,null,null,null,"(JTJ)-1",null,null,null,"JTΔy","d(JTJ)-1JTΔy","Δc+ccur,old",null,null,null,null,null,null,"(JTJ)-1",null,null,null,"JTΔy","d(JTJ)-1JTΔy","Δc+ccur,old",null,null,null,null,null,null,null,"Iteration",0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,null,null,"Min","Max",null,null,null,null,null,null,"Efficiency map from curves",null,null,null,"Efficiency map from points"]
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JM$42:INDEX(JP$42:JP$141,MAX($R$42:$R$141),1)))))","v":{"$error":"#VALUE!"}},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$f":"IF($T$7=1,\n       MMULT(\n          TRANSPOSE(JM$42:INDEX(JO$42:JO$141,MAX($R$42:$R$141),1)),\n          JL$42:INDEX(JL$42:JL$141,MAX($R$42:$R$141),1)),\n  IF($T$7=2,\n       MMULT(\n          TRANSPOSE(JM$42:INDEX(JP$42:JP$141,MAX($R$42:$R$141),1)),\n          JL$42:INDEX(JL$42:JL$141,MAX($R$42:$R$141),1))))","v":{"$error":"#VALUE!"}},{"$f":"IF($T$7=1,$U21*MMULT(JM21:JO23,JQ21:JQ23),\n  IF($T$7=2,$U21*MMULT(JM21:JP24,JQ21:JQ24)))","v":{"$error":"#VALUE!"}},{"$f":"IF($T$7=1,JR21:JR23+JJ$6:JJ$8,\n  IF($T$7=2,JR21:JR24+JJ$6:JJ$9))","v":{"$error":"#VALUE!"}},{"$f":"SUMXMY2($S$42:$S$141,JT$42:JT$141)","v":{"$error":"#DIV/0!"}},{"$f":"IF(ISERROR(JT21),\"\",JT21)","v":""},null,null,null,null,null,"SSQ improvement per iteration",null,{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},null,null,null,null,null,null,null,"With coverage factor","k","-",{"$f":"IF(LG7=0,\"\",\n       2)","v":""},null,null,null,{"$f":"IF(LK7=0,\"\",\n       2)","v":""},{"$f":"IF(LK7=0,\"\",\n       2)","v":""}]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"c1,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},null,null,null,null,null,"c1,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},null,null,null,null,null,"c1,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},null,null,null,null,null,"c1,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},null,null,null,null,null,"c1,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},null,null,null,null,null,"c1,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},null,null,null,null,null,"c1,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},null,null,null,null,null,"c1,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},null,null,null,null,null,"c1,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},null,null,null,null,null,"c1,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},null,null,null,null,null,"c1,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},null,null,null,null,null,"c1,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},null,null,null,null,null,"c1,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},null,null,null,null,null,"c1,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},null,null,null,null,null,"c1,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},null,null,null,null,null,"c1,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},null,null,null,null,null,"c1,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},null,null,null,null,null,"c1,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},null,null,null,null,null,"c1,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},null,null,null,null,null,"c1,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"c2,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#N/A"},null,null,null,null,null,"c2,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#N/A"},null,null,null,null,null,"c2,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#N/A"},null,null,null,null,null,"c2,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#N/A"},null,null,null,null,null,"c2,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#N/A"},null,null,null,null,null,"c2,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#N/A"},null,null,null,null,null,"c2,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#N/A"},null,null,null,null,null,"c2,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#N/A"},null,null,null,null,null,"c2,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#N/A"},null,null,null,null,null,"c2,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#N/A"},null,null,null,null,null,"c2,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#N/A"},null,null,null,null,null,"c2,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#N/A"},null,null,null,null,null,"c2,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#N/A"},null,null,null,null,null,"c2,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#N/A"},null,null,null,null,null,"c2,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#N/A"},null,null,null,null,null,"c2,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#N/A"},null,null,null,null,null,"c2,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#N/A"},null,null,null,null,null,"c2,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#N/A"},null,null,null,null,null,"c2,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#N/A"},null,null,null,null,null,"c2,max",{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#VALUE!"},{"$error":"#N/A"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Valid ranges"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Minimum valid mass flow","ṁmin","kg/h",{"$f":"IF(LG7=0,\"\",\n       MIN(C42:C65))","v":""},null,null,null,{"$f":"IF(LK7=0,\"\",\n       MIN(N42:N141))","v":""}]
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[]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"y(x)",null,null,null,"y(x,c)",null,"Δy","Jacobian matrix J",null,null,null,"y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,c)",null,"Δy","Jacobian matrix J",null,null,null,"y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,c)",null,"Δy","Jacobian matrix J",null,null,null,"y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,c)",null,"Δy","Jacobian matrix J",null,null,null,"y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,c)",null,"Δy","Jacobian matrix J",null,null,null,"y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,c)",null,"Δy","Jacobian matrix J",null,null,null,"y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,c)",null,"Δy","Jacobian matrix J",null,null,null,"y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,c)",null,"Δy","Jacobian matrix J",null,null,null,"y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,c)",null,"Δy","Jacobian matrix J",null,null,null,"y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,c)",null,"Δy","Jacobian matrix J",null,null,null,"y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,c)",null,"Δy","Jacobian matrix J",null,null,null,"y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,c)",null,"Δy","Jacobian matrix J",null,null,null,"y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,c)",null,"Δy","Jacobian matrix J",null,null,null,"y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,c)",null,"Δy","Jacobian matrix J",null,null,null,"y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,c)",null,"Δy","Jacobian matrix J",null,null,null,"y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,c)",null,"Δy","Jacobian matrix J",null,null,null,"y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,c)",null,"Δy","Jacobian matrix J",null,null,null,"y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,c)",null,"Δy","Jacobian matrix J",null,null,null,"y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,c)",null,"Δy","Jacobian matrix J",null,null,null,"y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,c)",null,"Δy","Jacobian matrix J",null,null,null,"y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,cmin)","y(x,c)",null,"y(x,c)-y(x)"]
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[null,null,"[kg/h]","[Km²/W]","[K²m²/W]","[-]",null,null,null,null,null,null,"[-]","[kg/h]","[Km²/W]","[K²m²/W]",null,null,"[-]","[kg/h]","[Km²/W]","[K²m²/W]",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"[-]"]
[null,{"$f":"IF(C42=\"\",\"\",1)","v":""},{"$f":"$B$9","v":""},{"$f":"TRANSPOSE(G9:J9)","v":""},{"$f":"IF(D42=\"\",\"\",\n     D42^2*$F$5)","v":""},{"$f":"IF(E42=\"\",\"\",\n     $C$9-$D$9*D42-$E$9*E42)","v":""},null,null,null,null,null,{"$f":"IF(M42=\"\",\"\",1)","v":""},{"$f":"IF('Efficiency Map Fit (Points)'!K39=\"\",\"\",\n      'Efficiency Map Fit (Points)'!K39)","v":""},{"$f":"IF('Efficiency Map Fit (Points)'!F39=\"\",\"\",\n     ('Efficiency Map Fit (Points)'!F39+'Efficiency Map Fit (Points)'!G39)/2)","v":""},{"$f":"IF('Efficiency Map Fit (Points)'!I39=\"\",\"\",\n    (('Efficiency Map Fit (Points)'!I39+'Efficiency Map Fit (Points)'!J39)/2-'Efficiency Map Fit (Points)'!H39)/'Efficiency Map Fit (Points)'!E39)","v":""},{"$f":"IF('Efficiency Map Fit (Points)'!I39=\"\",\"\",\n    (('Efficiency Map Fit (Points)'!I39+'Efficiency Map Fit (Points)'!J39)/2-'Efficiency Map Fit (Points)'!H39)^2/'Efficiency Map Fit (Points)'!E39)","v":""},null,{"$f":"IF(S42=\"\",\"\",1)","v":""},{"$f":"IF(AND($T$6=1,ISNUMBER(F42)),F42,\n  IF(AND($T$6=2,ISNUMBER(M42)),M42,\"\"))","v":""},{"$f":"IF(AND($T$6=1,C42<>\"\"),C42,\n  IF(AND($T$6=2,N42<>\"\"),N42,\"\"))","v":""},{"$f":"IF(AND($T$6=1,ISNUMBER(D42)),D42,\n  IF(AND($T$6=2,ISNUMBER(O42)),O42,\"\"))","v":""},{"$f":"IF(AND($T$6=1,ISNUMBER(E42)),E42,\n  IF(AND($T$6=2,ISNUMBER(P42)),P42,\"\"))","v":""},{"$f":"IF($S42=\"\",\"\",\n     IF($T$7=1,(1-EXP(-W$6*$T42))*(W$7-W$8*$U42),\n     IF($T$7=2,(1-EXP(-W$6*$T42))*(W$7-W$8*$U42-W$9*V42))))","v":""},null,{"$f":"IF($S42:$S141=\"\",\"\",\n      $S42:$S141-W42:W141)","v":""},{"$f":"IF($S42=\"\",\"\",\n     IF($T$7=1,$T42*EXP(-W$6*$T42)*(W$7-W$8*$U42),\n     IF($T$7=2,$T42*EXP(-W$6*$T42)*(W$7-W$8*$U42-W$9*$V42))))","v":""},{"$f":"IF($S42=\"\",\"\",\n     1-EXP(-W$6*$T42))","v":""},{"$f":"IF($S42=\"\",\"\",\n     $U42*(EXP(-W$6*$T42)-1))","v":""},{"$f":"IF($S42=\"\",\"\",\n     IF($T$7=1,0,\n     IF($T$7=2,$V42*(EXP(-W$6*$T42)-1))))","v":""},{"$f":"IF($S42=\"\",\"\",\n       IF($T$7=1,(1-EXP(-AF$6*$T42))*(AF$7-AF$8*$U42),\n       IF($T$7=2,(1-EXP(-AF$6*$T42))*(AF$7-AF$8*$U42-AF$9*$V42))))","v":""},{"$f":"IF($S42=\"\",\"\",\n       IF($T$7=1,(1-EXP(-AF$11*$T42))*(AF$12-AF$13*$U42),\n       IF($T$7=2,(1-EXP(-AF$11*$T42))*(AF$12-AF$13*$U42-AF$14*$V42))))","v":""},{"$f":"IF($S42=\"\",\"\",\n       IF($T$7=1,(1-EXP(-AF$16*$T42))*(AF$17-AF$18*$U42),\n       IF($T$7=2,(1-EXP(-AF$16*$T42))*(AF$17-AF$18*$U42-AF$19*$V42))))","v":""},{"$f":"IF($S42=\"\",\"\",\n       IF($T$7=1,(1-EXP(-AF$21*$T42))*(AF$22-AF$23*$U42),\n       IF($T$7=2,(1-EXP(-AF$21*$T42))*(AF$22-AF$23*$U42-AF$24*$V42))))","v":""},{"$f":"IF($S42=\"\",\"\",\n       IF($T$7=1,(1-EXP(-AF$26*$T42))*(AF$27-AF$28*$U42),\n       IF($T$7=2,(1-EXP(-AF$26*$T42))*(AF$27-AF$28*$U42-AF$29*$V42))))","v":""},{"$f":"IF($S42=\"\",\"\",\n       IF($T$7=1,(1-EXP(-AF$31*$T42))*(AF$32-AF$33*$U42),\n       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[null,"Enter your data here"]
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[null,"Comments"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Coefficients"]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Quadratic pressure drop coefficient","R2","Pa/(kg/h)²",{"$f":"'Pressure Drop'!S16","v":""}]
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[]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Statistics"]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"With coverage factor","k","-",{"$f":"'Pressure Drop'!Q21","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"For conficence level","p","%",{"$f":"'Pressure Drop'!Q22","v":""}]
[null,"Measurement without collector",null,null,null,null,null,"Measurement with collector"]
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{"sheet":"Pressure Drop","index":7,"n_rows":60,"n_cols":44,"rows_kept":60,"cut":false,"hidden":true,"merged":[]}
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{"sheet":"Leakage Fit","index":8,"n_rows":65,"n_cols":33,"rows_kept":65,"cut":false,"hidden":true,"merged":[]}
[null,"Data",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Results"]
[null,"Enter your data here"]
[]
[null,"Air properties",null,null,null,null,null,null,null,"Comments"]
[null,"Mean air temperature at flow meter",null,null,null,"ϑave","°C",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Coefficients"]
[null,"Mean ambient pressure",null,null,null,"pa,ave","Pa",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Linear outward leakage coefficient","Le1","kg/(h*Pa)",{"$f":"Leakage!AG23","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Quadratic outward leakage coefficient","Le2","kg/(h*Pa²)",{"$f":"Leakage!AG24","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Linear inward leakage coefficient","Li1","kg/(h*Pa)",{"$f":"Leakage!AG25","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Quadratic inward leakage coefficient","Li2","kg/(h*Pa²)",{"$f":"Leakage!AG26","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Curve models"]
[null,"Overpressure",null,null,null,null,null,"Underpressure",null,null,null,null,null,"Overpressure",null,null,null,null,null,"Underpressure"]
[null,"Without collector",null,null,null,null,null,"Without collector",null,null,null,null,null,"With collector",null,null,null,null,null,"With collector"]
[null,"No.","Date","Time","p","V̊",null,"No.","Date","Time","p","V̊",null,"No.","Date","Time","p","V̊",null,"No.","Date","Time","p","V̊"]
[null,null,"optional","optional","[Pa]","[m³/h]",null,null,"optional","optional","[Pa]","[m³/h]",null,null,"optional","optional","[Pa]","[m³/h]",null,null,"optional","optional","[Pa]","[m³/h]",null,null,"Statistics"]
[null,{"$f":"IF(E16=\"\",\"\",1)","v":""},null,null,null,null,null,{"$f":"IF(K16=\"\",\"\",1)","v":""},null,null,null,null,null,{"$f":"IF(Q16=\"\",\"\",1)","v":""},null,null,null,null,null,{"$f":"IF(W16=\"\",\"\",1)","v":""},null,null,null,null,null,null,"Standard deviation for outward leakage","σ","kg/h",{"$f":"Leakage!AG29","v":""}]
[null,{"$f":"IF(E17=\"\",\"\",B16+1)","v":""},null,null,null,null,null,{"$f":"IF(K17=\"\",\"\",H16+1)","v":""},null,null,null,null,null,{"$f":"IF(Q17=\"\",\"\",N16+1)","v":""},null,null,null,null,null,{"$f":"IF(W17=\"\",\"\",T16+1)","v":""},null,null,null,null,null,null,"Standard deviation for inward leakage","σ","kg/h",{"$f":"Leakage!AG30","v":""}]
[null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,null,"With coverage factor","k","-",{"$f":"Leakage!AG31","v":""}]
[null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,null,"For conficence level","p","%",{"$f":"Leakage!AG32","v":""}]
[null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,""]
[null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,null,"Valid range for use in calculations"]
[null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,null,"Minimum valid pressure for leakage coefficients","pmin","Pa",{"$f":"Leakage!AG35","v":""}]
[null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,null,"Maximum valid pressure for leakage coefficients","pmax","Pa",{"$f":"Leakage!AG36","v":""}]
[null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,""]
[null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,""]
[null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,""]
[null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,""]
[null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,null,"Chart, if the test stand leakage is considered",null,null,null,null,null,"Chart, if the test stand leakage is not considered"]
[null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,""]
[null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,""]
[null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,""]
[null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,""]
[null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,""]
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[null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,""]
[null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,""]
[null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,""]
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[null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,""]
[null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,""]
[null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,""]
[null,"",null,null,null,null,null,"",null,null,null,null,null,"",null,null,null,null,null,""]

{"sheet":"Leakage","index":9,"n_rows":60,"n_cols":76,"rows_kept":60,"cut":false,"hidden":true,"merged":[]}
["Data input",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Calculation/Results",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Chart"]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Model deviation"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Overpressure",null,"Underpressure"]
["Overpressure",null,null,null,null,null,"Underpressure",null,null,null,null,null,"Overpressure",null,null,null,null,null,"Underpressure",null,null,null,null,null,"Test stand","Test stand","Test stand","Test stand",null,null,null,null,null,null,null,null,null,null,null,"Overpressure",null,null,null,"Underpressure",null,null,null,"Overpressure",null,null,null,"Underpressure",null,null,null,null,null,null,null,null,null,null,null,null,"Overpressure",null,null,null,"Underpressure"]
["Without collector",null,null,null,null,null,"Without collector",null,null,null,null,null,"With collector",null,null,null,null,null,"With collector",null,null,null,null,null,null,"+ collector",null,"+ collector",null,null,null,null,"Overpressure",null,null,"Underpressure",null,null,null,"Without collector",null,null,null,"Without collector",null,null,null,"With collector",null,null,null,"With collector",null,null,null,null,null,null,null,null,null,null,null,null,"With collector",null,null,null,"With collector"]
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{"sheet":"SK Efficiency Curve","index":10,"n_rows":102,"n_cols":8,"rows_kept":102,"cut":false,"hidden":true,"merged":[[54,0,54,7],[98,6,98,7],[32,0,32,7],[7,2,7,3],[8,2,8,3],[9,2,9,3],[93,0,93,7],[7,5,7,7],[8,5,8,7],[9,5,9,7],[10,6,10,7],[12,4,12,7],[101,0,101,7],[98,2,98,3],[97,2,97,7],[96,2,96,7],[95,2,95,7],[99,0,99,7],[2,0,4,3],[5,2,5,3],[0,0,0,7],[2,6,2,7],[53,0,53,7],[3,6,3,7],[10,2,10,3]]}
["CERTIFICATION BODY HEADER\nfield available for logo etc."]
[null,null,null,null,null,null,null,"Page 1/2"]
["Determination of thermal efficiency curve coefficients of covered solar air heating collectors for usage in ScenoCalc for Solar KEYMARK Certificate",null,null,null,"Licence Number",null,"CERTNO-01C"]
[null,null,null,null,"Issued",null,"2015-07-20"]
[]
["Collector test standard",null,"EN ISO 9806"]
[]
["Licence holder",null,"Acompany",null,"Country","Acountry"]
["Brand (optional)",null,"Abrand",null,"Web","www.Acompany.Adomain"]
["Street, Number",null,"Astreet, 1",null,"E-mail","info@Acompany.Adomain"]
["Postcode, City",null,"A1111-1 Acity",null,"Tel","+99"," 999 999 999 /-999"]
[]
["Name of solar air heating collector",null,null,null,"Aname"]
[]
["Model coefficients of solar air heating collector (Input):"]
["Gross area",null,null,null,"Acoll","m²",null,2.222]
["Conversion factor",null,null,null,"η0,max","-",null,{"$f":"IF('Efficiency Map'!$LG$33=1,'Efficiency Map Fit (Curves)'!O14,\n  IF('Efficiency Map'!$LG$33=2,'Efficiency Map Fit (Curves)'!P14,\"\"))","v":""}]
["Linear heat loss coefficient",null,null,null,"c1,max","W/(m²K)",null,{"$f":"IF('Efficiency Map'!$LG$33=1,'Efficiency Map Fit (Curves)'!O15,\n  IF('Efficiency Map'!$LG$33=2,'Efficiency Map Fit (Curves)'!P15,\"\"))","v":""}]
["Quadratic heat loss coefficient",null,null,null,"c2,max","W/(m²K²)",null,{"$f":"IF('Efficiency Map'!$LG$33=1,'Efficiency Map Fit (Curves)'!O16,\n  IF('Efficiency Map'!$LG$33=2,'Efficiency Map Fit (Curves)'!P16,\"\"))","v":""}]
["Mass flow dependend heat loss coefficient",null,null,null,"cm","h/kg",null,{"$f":"IF('Efficiency Map'!$LG$33=1,'Efficiency Map Fit (Curves)'!O17,\n  IF('Efficiency Map'!$LG$33=2,'Efficiency Map Fit (Curves)'!P17,\"\"))","v":""}]
["Linear pressure drop coefficient",null,null,null,"R1","Pa/(kg/h)",null,{"$f":"'Pressure Drop Fit'!R6","v":""}]
["Quadratic pressure drop coefficient",null,null,null,"R2","Pa/(kg/h)²",null,{"$f":"'Pressure Drop Fit'!R7","v":""}]
["Linear outward leakage coefficient",null,null,null,"Le1","kg/(h·Pa)",null,{"$f":"'Leakage Fit'!AD6","v":""}]
["Quadratic outward leakage coefficient",null,null,null,"Le2","kg/(h·Pa²)",null,{"$f":"'Leakage Fit'!AD7","v":""}]
["Linear inward leakage coefficient",null,null,null,"Li1","kg/(h·Pa)",null,{"$f":"'Leakage Fit'!AD8","v":""}]
["Quadratic inward leakage coefficient",null,null,null,"Li2","kg/(h·Pa²)",null,{"$f":"'Leakage Fit'!AD9","v":""}]
["Minimum valid mass flow for efficiency and pressure drop coefficients",null,null,null,"ṁmin","kg/h",null,{"$f":"IF(OR('Efficiency Map Fit (Curves)'!O27=\"\",'Pressure Drop Fit'!R19=\"\"),\"\",\n     MAX('Efficiency Map Fit (Curves)'!O27,     'Pressure Drop Fit'!R19))","v":""}]
["Maximum valid mass flow for efficiency and pressure drop coefficients",null,null,null,"ṁmax","kg/h",null,{"$f":"IF(OR('Efficiency Map Fit (Curves)'!O28=\"\",'Pressure Drop Fit'!R20=\"\"),\"\",\n      MIN('Efficiency Map Fit (Curves)'!O28,     'Pressure Drop Fit'!R20))","v":""}]
["Minimum valid pressure for leakage coefficients",null,null,null,"pmin","Pa",null,{"$f":"'Leakage Fit'!AD22","v":""}]
["Maximum valid pressure for leakage coefficients",null,null,null,"pmax","Pa",null,{"$f":"'Leakage Fit'!AD23","v":""}]
[]
["Comments of testing laboratory:"]
["Example comment."]
[]
["Boundary conditions of air collector field"]
["Useful power",null,null,null,"Q̇e","W",null,{"$f":"'SAHC Calc.+Opt.'!D40","v":10000}]
["Temperature rise",null,null,null,"ΔTrise","K",null,{"$f":"'SAHC Calc.+Opt.'!D38","v":25}]
["Mean fluid temperature of field",null,null,null,"ϑm","°C",null,{"$f":"'SAHC Calc.+Opt.'!D149","v":32.5}]
[]
["Boundary conditions by system"]
["Hydraulic system configuration",null,null,null,null,null,null,{"$f":"IF(\n     'SAHC Calc.+Opt.'!D46=2,\n     \"Closed loop, field with underpressure\",\n     \"??? Here is no name for this system configuration yet!\")","v":"Closed loop, field with underpressure"}]
["Flow resistance before air collector field",null,null,null,"Rsys,before","Pa/(m³/h)²",null,{"$f":"'SAHC Calc.+Opt.'!D50","v":4.0000000000000003E-5}]
["Flow resistance after air collector field",null,null,null,"Rsys,after","Pa/(m³/h)²",null,{"$f":"'SAHC Calc.+Opt.'!D51","v":4.0000000000000003E-5}]
["Diameter at channel outlet into heating space",null,null,null,"dchan","mm",null,{"$f":"'SAHC Calc.+Opt.'!D53*1000","v":300}]
["Fan efficiency",null,null,null,"ηfan","%",null,{"$f":"'SAHC Calc.+Opt.'!D49","v":57.2}]
["Primary energy factor of electrical energy",null,null,null,"fp,aux","-",null,{"$f":"'SAHC Calc.+Opt.'!D60","v":3}]
["Primary energy factor of replaced thermal energy",null,null,null,"fp,therm","-",null,{"$f":"'SAHC Calc.+Opt.'!D61","v":1.1000000000000001}]
["Efficiency of system to replace",null,null,null,"ηsys,repl","%",null,{"$f":"'SAHC Calc.+Opt.'!D64","v":90}]
[]
["Boundary conditions by climate"]
["Global irradiance normal on collector plane",null,null,null,"Gb,d,coll","W/m²",null,{"$f":"IF(     'SAHC Calc.+Opt.'!D114=0,\n     'SAHC Calc.+Opt.'!D32,\n     CONCATENATE(\"An angle is given --> does not match with caption of this row! --> real insolation \",'SAHC Calc.+Opt.'!D116,\" differes from \",'SAHC Calc.+Opt.'!D32,\" !\"))","v":1000}]
["Ambient temperature",null,null,null,"ϑa","°C",null,{"$f":"'SAHC Calc.+Opt.'!D33","v":10}]
[]
["CERTIFICATION BODY FOOTER\naddress etc."]
[{"$f":"IF(A1=\"\",\"\",A1)","v":"CERTIFICATION BODY HEADER\nfield available for logo etc."}]
[null,null,null,null,null,null,null,"Page 2/2"]
["Results (coefficients of liquid heating collector model and further values for SK sheet in ScenoCalc):"]
["Conversion factor including leakage",null,null,null,"η0,L","-",null,{"$f":"'SAHC Calc.+Opt.'!D533","v":0.77213088467856883}]
["Linear heat loss coefficient",null,null,null,"c1","W/(m²K)",null,{"$f":"'SAHC Calc.+Opt.'!D534","v":7.7528099205030703}]
["Quadratic heat loss coefficient",null,null,null,"c2","W/(m²K²)",null,{"$f":"'SAHC Calc.+Opt.'!D535","v":7.7528099205030699E-3}]
[{"$f":"IF(\n     'SAHC Calc.+Opt.'!D46=2,\n     \"Efficient mass flow per row in relation to row gross area\",\n     \"??? Here is no name for this system configuration yet!\")","v":"Efficient mass flow per row in relation to row gross area"},null,null,null,"ṁe,opt,spec,row","kg/(sm²)",null,{"$f":"'SAHC Calc.+Opt.'!D536","v":2.3590240918342831E-2}]
[{"$f":"IF(\n     'SAHC Calc.+Opt.'!D46=2,\n     \"Efficient mass flow per row in relation to collector gross area\",\n     \"??? Here is no name for this system configuration yet!\")","v":"Efficient mass flow per row in relation to collector gross area"},null,null,null,"ṁe,opt,spec,coll","kg/(sm²)",null,{"$f":"'SAHC Calc.+Opt.'!D537","v":9.3463866907403478E-2}]
["Mean fluid temperature at zero efficiency (G = 1000 W/m², ϑa = 30 °C)",null,null,null,"ϑm(η=0)","°C",null,{"$f":"'SAHC Calc.+Opt.'!D538","v":121.26447707570554}]
[]
[null,"Table for diagramm"]
[null,"G","T*m","eta"]
[null,"[W/m²]","[Km²/W]","[-]"]
[null,{"$f":"H51","v":1000},{"$f":"($H$59-SQRT($H$59^2-4*(-$H$60*$B$68+0.0000000001)*$H$58))/(2*(-$H$60*$B$68+0.0000000001))\n/10\n*(ROW(C68)-ROW($C$68))","v":0},{"$f":"$H$58-$H$59*C68-$H$60*C68*ABS(C68)*$B$68","v":0.77213088467856883}]
[null,{"$f":"CONCATENATE(ROUND(B68,0),\" W/m²\")","v":"1000 W/m²"},9.1264477075796331E-3,0.70072952293812651]
[null,null,1.8252895415159266E-2,0.6280366663693514]
[null,null,2.7379343122738899E-2,0.55405231497224328]
[null,null,3.6505790830318532E-2,0.47877646874680241]
[null,null,4.5632238537898162E-2,0.40220912769302875]
[null,null,5.4758686245477799E-2,0.32435029181092212]
[null,null,6.3885133953057435E-2,0.24519996110048259]
[null,null,7.3011581660637065E-2,0.16475813556171026]
[null,null,8.2138029368216695E-2,8.3024815194605195E-2]
[null,null,9.1264477075796324E-2,-8.3280604634694555E-13]
[null,null,{"$f":"H89","v":2.2499999999999999E-2},0.59376780144499508]
[]
[]
["Additional results:"]
["Number of air collectors per row",null,null,null,"ncoll/row","coll",null,{"$f":"'SAHC Calc.+Opt.'!D124","v":3.9619716996925498}]
["Number of rows of field",null,null,null,"nrow","coll",null,{"$f":"'SAHC Calc.+Opt.'!D125","v":1.9130571014230651}]
["Fan mass flow of field",null,null,null,"ṁfan","kg/h",null,{"$f":"'SAHC Calc.+Opt.'!D143","v":1430.2706731378964}]
["Mass flow of Maximum primary Power (at outlet, per row), MMPprim",null,null,null,"ṁe,row,opt","kg/h",null,{"$f":"'SAHC Calc.+Opt.'!D68","v":747.63616416570187}]
["Pressure at field inlet",null,null,null,"pi,field","Pa",null,{"$f":"'SAHC Calc.+Opt.'!D133","v":-56.395271171006556}]
["Pressure drop of field",null,null,null,"Δpfield","Pa",null,{"$f":"'SAHC Calc.+Opt.'!D132","v":32.369156255092406}]
["Reduced temperature difference",null,null,null,"T*m","Km²/W",null,{"$f":"IF(     'SAHC Calc.+Opt.'!D114=0,\n     ('SAHC Calc.+Opt.'!D149-'SAHC Calc.+Opt.'!D33)/'SAHC Calc.+Opt.'!D32,\n     CONCATENATE(\"An angle is given --> real insolation \",'SAHC Calc.+Opt.'!D116,\" differes from \",'SAHC Calc.+Opt.'!D32,\" !\"))","v":2.2499999999999999E-2}]
["Instantaneous efficiency of field for final usage",null,null,null,"ηuse","%",null,{"$f":"'SAHC Calc.+Opt.'!D121","v":59.376780144499499}]
["Efficiency loss caused by mass flow",null,null,null,"Δηṁ","%-points",null,{"$f":"'SAHC Calc.+Opt.'!D118","v":-0.18624849332667592}]
["Efficiency loss caused by leakage at field",null,null,null,"ΔηL","%-points",null,{"$f":"'SAHC Calc.+Opt.'!D120","v":-0.31501073717381445}]
[]
["The efficiency curve coefficients of the liquid heating collector model are determined under consideration of the thermo-hydraulic mass flow and the leakage dependency by applying a solar air heating collector model. One static working point is considered within a system context (climate, auxiliary power of fan, system configuration, dynamic pressure loss, and temperature rise). The chosen system configuration causes significant leakage losses for better evaluation of this characteristic, although in other common system configurations the leakage losses can be very small or zero. The mass flow is optimized on the maximum net primary power output per field area, while the appropriate characteristic field length is calculated, to ensure a fair and repetitious air collector comparison. \nThese results are not appropriate to compare solar air heating collectors with liquid heating collectors."]
[]
["Testing Laboratory",null,"Atestlab"]
["Website",null,"www.Atestlab.Adomaine"]
["Test report number",null,123456]
["Date of test report",null,"2015-08-25",null,"AirCow version",null,{"$f":"History!A9","v":"3.00 (2016-09-30)"}]
["Stamp and signature of test body"]
[]
[{"$f":"IF(A54=\"\",\"\",A54)","v":"CERTIFICATION BODY FOOTER\naddress etc."}]

{"sheet":"SAHC Calc.+Opt.","index":11,"n_rows":538,"n_cols":4,"rows_kept":538,"cut":false,"hidden":true,"merged":[]}
["Input"]
[]
[]
[]
[]
[]
[]
["   Solar air collector"]
["Manufacturer",null,null,"Desert Wind"]
["Name of air collector",null,null,"Vitrine"]
["Area","Acoll","m²",2.222]
["Conversion factor","η0,max","-",0.77769999999999995]
["Linear heat loss coefficient","c1,max","W/(m²K)",7.7770000000000001]
["Quadratic heat loss coefficient","c2,max","W/(m²K²)",7.7770000000000001E-3]
["Mass flow dependent heat loss coefficient","cm","h/kg",7.7770000000000001E-3]
["Linear pressure drop coefficient","R1","Pa/(kg/h)",1.111E-3]
["Quadratic pressure drop coefficient","R2","Pa/(kg/h)²",1.3329999999999999E-5]
["Linear outward leakage coefficient","Le1","kg/(h*Pa)",3.5000000000000003E-2]
["Quadratic outward leakage coefficient","Le2","kg/(h*Pa²)",-6.9999999999999999E-6]
["Linear inward leakage coefficient","Li1","kg/(h*Pa)",3.5000000000000003E-2]
["Quadratic inward leakage coefficient","Li2","kg/(h*Pa²)",6.9999999999999999E-6]
["Minimum valid mass flow for efficiency, pressure drop","ṁmin","kg/h",250]
["Maximum valid mass flow for efficiency, pressure drop","ṁmax","kg/h",2500]
["Minimum valid pressure for leakage coefficients","pmin","Pa",-2500]
["Maximum valid pressure for leakage coefficients","pmax","Pa",2500]
["Ambrosetti parameter","r","-"]
["Incidence angle modifier for 50° of sun to normal of coll.","Khem(50°)","-",0.9]
[]
["   Climate"]
["Solar zenit angle (zenit = 0°, sun rise or sun set = 90°)","θs","°",45]
["Solar azimuth angle (east = -90°, south = 0°, west = 90°)","γs","°",0]
["Global radiation in direction of sun","Gb,d","W/m²",1000]
["Ambient temperature","ϑa","°C",10]
[]
["   Field"]
["Tilt angle ( horizontal collector surface = 0°, vertical = 90°)","βcoll","°",45]
["Azimut angle (east = -90°, south = 0°, west = 90°)","γcoll","°",0]
["Temperature rise","ΔTrise","K",25]
["Field length (number of air collectors per row)","ncoll/row","coll"]
["Power (at field outlet or at load)","Q̇e","W",10000]
["Field width (number of rows of field)","nrow","coll"]
["Inlet fluid temperature of field","ϑi","°C",20]
["Mean fluid temperature of field","ϑm","°C"]
[]
["   Air heating system"]
["Hydraulic system configuration:\nEnter: 1 - field with overpressure; 2 - field with \nunderpressure; 3 - field with over- , underpressure",null,null,2]
["Field with overpressure (considered for given power):\nEnter: 1 - open loop; 2 - closed loop without leakage of load; 3 - closed loop with leakage of load",null,null,1]
["Field with over- and underpressure (considered for fan volume flow): Enter: 1 - fan after load and before field; 2 - fan after field and before load",null,null,1]
["Fan efficiency (electric -> mechanic -> hydraulic)","ηfan","%",57.2]
["Flow resistance before air collector field","Rsys,before","Pa/(m³/h)²",4.0000000000000003E-5]
["Flow resistance after air collector field","Rsys,after","Pa/(m³/h)²",4.0000000000000003E-5]
["Blowing air into how many large volumes in series (e.g. building; for dynamic pressure losses and velocity):\nEnter: 0 - no; 1 - one; 2 - two large vol.; 3 - etc.",null,null,1]
["Channel diameter of circular cross-section before large volumes, if present (for consideration of dynamic pressure losses at mass flow opt. and for velocity)","dchan,circ,vol","m",0.3]
["Channel side length of square cross-section before large volumes, if present (for consideration of dynamic pressure losses at mass flow opt. and for velocity)","achan,square,vol","m"]
["Diameter of circular cross-section of regular channel (only for velocity calculation)","dchan,circ,reg","m",0.3]
["Side length of square cross-section of regular channel (only for velocity calculation)","achan,square,reg","m"]
[]
["   Global system for mass flow optimization"]
["Kind of optimization: 1 - primary energetic; 2 - monetary; \n3 - site energetic; 4 - system energetic",null,null,1]
["Primary energy factor of electrical energy for fan","fp,fan","-",3]
["Primary en. factor for heating energy carrier to replace","fp,sys,repl","-",1.1000000000000001]
["Price per unit electrical energy for fan","Cfan","cent/(kWh)",30]
["Price per unit heating energy carrier to replace","Csys,repl","cent/(kWh)",11]
["Efficiency of heating sys. to repl. (chemical -> thermal)","ηsys,repl","%",90]
[]
["   Mass flow"]
["Manually set outlet mass flow per row (enter or delete)","ṁe,row","kg/h"]
["Autom. optimized outlet mass flow p. row (do not enter)","MMP","kg/h",747.63616416570187]
[]
["   Calculation support"]
["Connection to model, only if \"yes\"",null,null,"yes"]
[]
["Error check"]
[]
["   Details"]
["      Choice-cells"]
["Fill out only one cell of incidence angle transparency parameters, the other leave empty.",null,null,"OK"]
["Fill out only one cell of the temperature rise and field length, the other leave empty.",null,null,"OK"]
["Fill out only one cell of the power and field width, the other leave empty.",null,null,"OK"]
["Fill out only one cell of the inlet and mean fluid temperature, the other leave empty.",null,null,"OK"]
["Fill out only one cell of the channel cross-section before large volumes, the other leave empty.",null,null,"OK"]
["Fill out only one cell of the cross-section of regular channels, the other leave empty.",null,null,"OK"]
[]
["      Mass flow optimization"]
["Give either temperature rise and power or field length and width. Do not give other parameter combinations.",null,null,"OK"]
["Optimization of mass flow is not possible with negative thermal efficiency",null,null,"OK"]
["Auxiliary demand is higher than thermal power (cost function is negative and has no maximum)",null,null,"OK"]
["Mass flow optimization could not be performed",null,null,"OK"]
["Relative range around the real MMP in which the MMP was found",null,"± %",0.01]
["MMP was not found within a relative range of ± 0.1 % of the real MMP",null,null,"OK"]
[]
["      Iterative calculation"]
["Number of iterations of circular references",null,"*10^6",3.9999999999999998E-6]
["Set max. iterations of circ. references is hit (divergency)\n-> efficiency is too low or do input field length and width",null,null,"OK"]
[]
["      Valid model ranges"]
["Mass flow is out of set valid mass flow range of efficiency and pressure drop coefficients",null,null,"OK"]
["Pressure is out of set valid pressure range of leakage coefficients",null,null,"OK"]
["Leakage mass flows have wrong algebraic sign -> check correct diagram quadrants of leakage curves",null,null,"OK"]
[]
["      Low thermal efficiency"]
["Calculation with negative efficiency only with given field length and width or negative temp. rise and field power",null,null,"OK"]
["Outlet temperature is above maximum possible mean temperature",null,null,"OK"]
[]
["   Summary"]
["Summary of error notices",null,null,"No errors found"]
[]
["Overview on results (for model communication)"]
[]
["Hydraulic system configuration (Field with …)",null,null,"underpress."]
["Hydraulic system config. (closed or probably open loop)",null,null,"closed loop"]
["Blowing into large volumes",null,null,"1 large vol."]
["Optimization on mass flow …",null,null,"MMPprim"]
["Total angle of sun to normal of collector plane","θ","°",0]
["Incidence angle modifier","Khem","-",1]
["Global irradiance on tilted collector plane","Gb,d,coll","W/m²",1000]
["Theor. inner effic. for gaining heat (extrapol. infinite flow)","ηinner,ṁ∞","%",59.878039374999993]
["Efficiency reduction by mass flow","Δηṁ","%-points",-0.18624849332667592]
["Inner efficiency (average mass flow, before leakage)","ηinner,ṁ_ave","%",59.691790881673313]
["Efficiency reduction by leakage","ΔηL","%-points",-0.31501073717381445]
["Usable efficiency (after leakage, at field outlet)","ηuse","%",59.376780144499499]
["Efficiency reduction by leakage of load","ΔηL,load","%-points","Not for this syst.!"]
["Usable efficiency (after leakage into load)","ηuse,load","%","Not for this syst.!"]
["Field length","ncoll/row","coll",3.9619716996925498]
["Field width","nrow","coll",1.9130571014230651]
["Number of air collectors of field","ncoll/field","coll",7.5794780957340437]
["Area of field","Afield","m²",16.841600328721047]
["Pressure drop of system before field","Δpsys1","Pa",56.395271171006556]
["Pressure drop of system after field","Δpsys2","Pa",68.221946658837552]
["Pressure drop of remaining system","Δpsys,rem","Pa",124.61721782984411]
["Dynamic pressure losses into large load volumes (sum)","pdyn,sum,sys","Pa",14.422830945794409]
["Pressure drop of field","Δpfield","Pa",32.369156255092406]
["Pressure at field inlet","pi,field","Pa",-56.395271171006556]
["Pressure at field outlet","pe,field","Pa",-88.764427426098962]
["Leakage mass flow (outward) as fraction of inlet mass flow","Rṁ,Le","%",0]
["Leakage mass flow (inward) as fraction of inlet mass flow","Rṁ,Li","%",1.3441489668438715]
["Leakage mass flow of field (outward)","ṁLe","kg/h",0]
["Leakage mass flow of field (inward)","ṁLi","kg/h",18.96998363698691]
["Substitution mass flow of field","ṁLe,subs","kg/h",0]
["Inlet mass flow of field","ṁi","kg/h",1411.3006895009096]
["Outlet mass flow of field","ṁe","kg/h",1430.2706731378964]
["Average mass flow along one row","ṁave,row","kg/h",742.31494505893011]
["Fan mass flow of field","ṁfan","kg/h",1430.2706731378964]
["Fan volume flow of field","V̇fan","m³/h",1305.9665640708183]
["Outlet volume flow of field","V̇e","m³/h",1305.9665640708183]
["Inlet temperature","ϑi","°C",20]
["Outlet temperature","ϑe","°C",45]
["Temperature rise","Δϑrise","K",25]
["Mean fluid temperature of field","ϑm","°C",32.5]
["Converted heat of field","Q̇inner","W",10053.052849347374]
["Power at field inlet","Q̇i","W",0]
["Power at field outlet","Q̇e","W",10000]
["Useful power after inward leakage into load","Q̇load","W","Not for this syst.!"]
["Leakage power loss (outward) as fraction of power","RQ̇,Le","%",0]
["Leakage power loss (inward) as fraction of power","RQ̇,Li","%",0.52772874212846754]
["Leakage power loss (into load) as fraction of power","RQ̇,Le,load","%","Not for this syst.!"]
["Power loss by outward leakage","Q̇Le","W",0]
["Power loss by inward leakage","Q̇Li","W",53.052849347370945]
["Power loss by inward leakage into load","Q̇Le,load","W","Not for this syst.!"]
["Auxiliary power demand for field","Paux,field","W",20.528863527745948]
["Auxiliary power demand for remaining system","Paux,sys","W",88.180679277272546]
["Auxiliary power demand for total system","Paux,sys,tot","W",108.70954280501849]
["Cash flow to spend for auxiliary power","CFaux","cent/h",3.2612862841505548]
["Cash flow to save by usable thermal energy","CFtherm","cent/h",122.22222222222221]
["Cash flow to save by thermal energy after load leakage","CFtherm,load","cent/h","Not for this syst.!"]
["Specific net primary power saving","q̇prim,net,spec","W/m²",706.35173389787701]
["Specific net cost saving per time by power","CFnet,spec","cent/h",7.0635173389787695]
["Specific net site power saving","q̇net,spec","W/m²",653.2871789828074]
["Specific net system power saving","q̇sys,net,spec","W/m²",587.31297882225238]
["Cost function","cost","-",706.35173389787701]
["Velocity before large load volumes (for dynamic pressure)","uchan,vol","m/s",5.1321243008545476]
["Velocity in cold regular channel","uchan,reg,cold","m/s",4.6661259512976816]
["Velocity in hot regular channel","uchan,reg,hot","m/s",5.1321243008545476]
["Factor for reduction by mass flow dependency","f(ṁave,row)","-",0.99688953587541085]
["Total efficiency reduction by leakage","ΔηL","%-points",-0.31501073717381445]
["Mean fluid temperature at zero efficiency (before leak.)","ϑm,h=0","°C",101.60797830996158]
[]
["Do not insert, delete, or move rows above this row!"]
["Results for system design"]
[]
["   Field dimensions"]
["Field length","ncoll/row","coll",{"$f":"D124","v":3.9619716996925498}]
["Field width","nrow","coll",{"$f":"D125","v":1.9130571014230651}]
["Number of air collectors of field","ncoll/field","coll",{"$f":"D126","v":7.5794780957340437}]
["   Thermal performance"]
["Power at field outlet","Q̇e","W",{"$f":"D152","v":10000}]
["Instantaneous efficiency at field outlet","ηuse","%",{"$f":"D121","v":59.376780144499499}]
["Outlet volume flow of field","V̇e","m³/h",{"$f":"D145","v":1305.9665640708183}]
["Outlet mass flow of field","ṁe","kg/h",{"$f":"D141","v":1430.2706731378964}]
["Inlet temperature","ϑi","°C",{"$f":"D146","v":20}]
["Outlet temperature","ϑe","°C",{"$f":"D147","v":45}]
["Temperature rise","ΔTrise","K",{"$f":"D148","v":25}]
["Mean fluid temperature of field","ϑm","°C",{"$f":"D149","v":32.5}]
["   Fan design"]
["Pressure drop of field","Δpfield","Pa",{"$f":"D132","v":32.369156255092406}]
["Pressure drop of remaining system","Δpsys","Pa",{"$f":"D130","v":124.61721782984411}]
["Dynamic pressure losses into large load volumes (sum)","pdyn,sum,sys","Pa",{"$f":"D131","v":14.422830945794409}]
["Total pressure rise of total system","psys,tot","Pa",{"$f":"D132+D130+D131","v":171.40920503073093}]
["Fan volume flow","V̇fan","m³/h",{"$f":"D144","v":1305.9665640708183}]
["Fan mass flow","ṁfan","kg/h",{"$f":"D143","v":1430.2706731378964}]
["   Air velocity in channels (no consideration of flow resistance here)"]
["Velocity before large load volumes (for dynamic pressure)","uchan,vol","m/s",{"$f":"D171","v":5.1321243008545476}]
["Velocity in cold regular channel","uchan,reg,cold","m/s",{"$f":"D172","v":4.6661259512976816}]
["Velocity in hot regular channel","uchan,reg,hot","m/s",{"$f":"D173","v":5.1321243008545476}]
["   Cost effectiveness"]
["Share of electric power for auxiliary","1/COPsyst","%",{"$f":"1/(D152/D162)*100","v":1.0870954280501848}]
["Share of money for auxiliary","1/COPcost","%",{"$f":"1/(D164/D163)*100","v":2.6683251415777267}]
[]
["Overview on results"]
[]
["   Working point"]
["Hydraulic system configuration (Field with …)",null,null,{"$f":"D110","v":"underpress."}]
["Hydraulic system config. (closed or probably open loop)",null,null,"closed loop"]
["Blowing into large volumes",null,null,"1 large vol."]
["Optimization on mass flow …",null,null,"MMPprim"]
["Total angle of sun to normal of collector plane","θ","°",0]
["Incidence angle modifier","Khem","-",1]
["Global irradiance on tilted collector plane","Gb,d,coll","W/m²",1000]
["Theor. inner effic. for gaining heat (extrapol. infinite flow)","ηinner,ṁ∞","%",59.878039374999993]
["Efficiency reduction by mass flow","Δηṁ","%-points",-0.18624849332667592]
["Inner effic. for gaining heat (ave. mass flow, before leak.)","ηinner,ṁ_ave","%",59.691790881673313]
["Efficiency reduction by leakage","ΔηL","%-points",-0.31501073717381445]
["Usable efficiency (after leakage, at field outlet)","ηuse","%",59.376780144499499]
["Efficiency reduction by leakage of load","ΔηL,load","%-points","Not for this syst.!"]
["Usable efficiency (after leakage into load)","ηuse,load","%","Not for this syst.!"]
["Field length","ncoll/row","coll",3.9619716996925498]
["Field width","nrow","coll",1.9130571014230651]
["Number of air collectors of field","ncoll/field","coll",7.5794780957340437]
["Area of field","Afield","m²",16.841600328721047]
["Pressure drop of system before field","Δpsys1","Pa",56.395271171006556]
["Pressure drop of system after field","Δpsys2","Pa",68.221946658837552]
["Pressure drop of remaining system","Δpsys,rem","Pa",124.61721782984411]
["Dynamic pressure losses into large load volumes (sum)","pdyn,sum,sys","Pa",14.422830945794409]
["Pressure drop of field","Δpfield","Pa",32.369156255092406]
["Pressure at field inlet","pi,field","Pa",-56.395271171006556]
["Pressure at field outlet","pe,field","Pa",-88.764427426098962]
["Leakage mass flow (outward) as fraction of inlet mass flow","Rṁ,Le","%",0]
["Leakage mass flow (inward) as fraction of inlet mass flow","Rṁ,Li","%",1.3441489668438715]
["Leakage mass flow of field (outward)","ṁLe","kg/h",0]
["Leakage mass flow of field (inward)","ṁLi","kg/h",18.96998363698691]
["Substitution mass flow of field","ṁLe,subs","kg/h",0]
["Inlet mass flow of field","ṁi","kg/h",1411.3006895009096]
["Outlet mass flow of field","ṁe","kg/h",1430.2706731378964]
["Average mass flow along one row","ṁave,row","kg/h",{"$f":"D142","v":742.31494505893011}]
["Fan mass flow of field","ṁfan","kg/h",1430.2706731378964]
["Fan volume flow of field","V̇fan","m³/h",1305.9665640708183]
["Outlet volume flow of field","V̇e","m³/h",1305.9665640708183]
["Inlet temperature","ϑi","°C",20]
["Outlet temperature","ϑe","°C",45]
["Temperature rise","ΔTrise","K",25]
["Mean fluid temperature of field","ϑm","°C",32.5]
["Converted heat of field","Q̇inner","W",10053.052849347374]
["Power at field inlet","Q̇i","W",0]
["Power at field outlet","Q̇e","W",10000]
["Useful power after inward leakage into load","Q̇load","W","Not for this syst.!"]
["Leakage power loss (outward) as fraction of power","RQ̇,Le","%",0]
["Leakage power loss (inward) as fraction of power","RQ̇,Li","%",0.52772874212846754]
["Leakage power loss (into load) as fraction of power","RQ̇,Le,load","%","Not for this syst.!"]
["Power loss by outward leakage","Q̇Le","W",0]
["Power loss by inward leakage","Q̇Li","W",53.052849347370945]
["Power loss by inward leakage into load","Q̇Le,load","W","Not for this syst.!"]
[]
["   Mass flow optimization"]
["Auxiliary power demand for field","Paux,field","W",{"$f":"D160","v":20.528863527745948}]
["Auxiliary power demand for remaining  system","Paux,sys","W",88.180679277272546]
["Auxiliary power demand for total system","Paux,sys,tot","W",108.70954280501849]
["Cash flow to spend for auxiliary power","CFaux","cent/h",3.2612862841505548]
["Cash flow to save by usable thermal energy","CFtherm","cent/h",122.22222222222221]
["Cash flow to save by thermal energy after load leakage","CFtherm,load","cent/h","Not for this syst.!"]
["Specific net primary power saving","q̇prim,net,spec","W/m²",706.35173389787701]
["Specific net cost saving per time by power","CFnet,spec","cent/h",7.0635173389787695]
["Specific net site power saving","q̇net,spec","W/m²",653.2871789828074]
["Specific net system power saving","q̇sys,net,spec","W/m²",587.31297882225238]
["Cost function","cost","-",706.35173389787701]
[]
["   Air velocity in channels (no consideration of flow resistance here)"]
["Velocity before large load volumes (for dynamic pressure)","uchan,vol","m/s",{"$f":"D171","v":5.1321243008545476}]
["Velocity in cold regular channel","uchan,reg,cold","m/s",{"$f":"D172","v":4.6661259512976816}]
["Velocity in hot regular channel","uchan,reg,hot","m/s",{"$f":"D173","v":5.1321243008545476}]
[]
["   ScenoCalc"]
["Factor for reduction by mass flow dependency","f(ṁave,row)","-",{"$f":"D174","v":0.99688953587541085}]
["Total efficiency reduction by leakage","ΔηL","%-points",{"$f":"D175","v":-0.31501073717381445}]
[]
["   Independent of working point"]
["Mean fluid temperature at zero efficiency (before leak.)","ϑm,η=0","°C",{"$f":"D176","v":101.60797830996158}]
[]
["Detailed results"]
[]
["   Values of total system"]
["      Labels"]
["Manufacturer",null,null,{"$f":"D9","v":"Desert Wind"}]
["Name of air collector",null,null,{"$f":"D10","v":"Vitrine"}]
["Hydraulic system configuration (Field with …)",null,null,{"$f":"D110","v":"underpress."}]
["Hydraulic system config. (closed or probably open loop)",null,null,{"$f":"D111","v":"closed loop"}]
["Blowing into large volumes",null,null,{"$f":"D112","v":"1 large vol."}]
["Optimization on mass flow …",null,null,{"$f":"D113","v":"MMPprim"}]
["      Efficiency"]
["Instantaneous efficiency for usage","ηuse","%",{"$f":"D121","v":59.376780144499499}]
["Instantaneous efficiency after leakage of load","ηuse","%",{"$f":"D123","v":"Not for this syst.!"}]
["Reduction of efficiency by leakage of load","ΔηL,load","%-points",{"$f":"D122","v":"Not for this syst.!"}]
["      Field dimensions"]
["Area","Afield","m²",{"$f":"D127","v":16.841600328721047}]
["Number of air collectors of field","ncoll/field","coll",{"$f":"D126","v":7.5794780957340437}]
["Field length","ncoll/row","coll",{"$f":"D124","v":3.9619716996925498}]
["Field width","nrow","coll",{"$f":"D125","v":1.9130571014230651}]
["      Air velocity in channels (no consideration of flow resistance here)"]
["Velocity before large load volumes (for dynamic pressure)","uchan,vol","m/s",{"$f":"D171","v":5.1321243008545476}]
["Velocity in cold regular channel","uchan,reg,cold","m/s",{"$f":"D172","v":4.6661259512976816}]
["Velocity in hot regular channel","uchan,reg,hot","m/s",{"$f":"D173","v":5.1321243008545476}]
["      Pressure"]
["Pressure drop","Δpsys,tot","Pa",{"$f":"D130+D132","v":156.98637408493653}]
["Dynamic pressure losses into large load volumes (sum)","pdyn,sys","Pa",{"$f":"D131","v":14.422830945794409}]
["      Mass flow"]
["Outlet mass flow","ṁe","kg/h",{"$f":"D141","v":1430.2706731378964}]
["Inlet mass flow","ṁi","kg/h",{"$f":"D140","v":1411.3006895009096}]
["Fan mass flow","ṁfan","kg/h",{"$f":"D143","v":1430.2706731378964}]
["      Temperatures"]
["Temperature rise","ΔTrise","K",{"$f":"D148","v":25}]
["Inlet temperature","ϑi","°C",{"$f":"D146","v":20}]
["Outlet temperature","ϑe","°C",{"$f":"D147","v":45}]
["      Thermal power"]
["Power delivered","Q̇use","W",{"$f":"D152","v":10000}]
["By power delivered saveable site power","Q̇use,site","W",{"$f":"D152/(D64/100)","v":11111.111111111111}]
["By power delivered saveable primary power","Q̇use,prim","W",{"$f":"D152/(D64/100)*D61","v":12222.222222222223}]
["Useful power after inward leakage into load","Q̇load","W",{"$f":"D153","v":"Not for this syst.!"}]
["By useful pow. a. inw. leak. into load saveable site power","Q̇load,site","W",{"$f":"IF(     ISNONTEXT(D153),\n     D153/(D64/100),\n     D153)","v":"Not for this syst.!"}]
["By useful pow. a. inw. leak. into load saveable prim. pow.","Q̇load,prim","W",{"$f":"IF(     ISNONTEXT(D153),\n     D153/(D64/100)*D61,\n     D153)","v":"Not for this syst.!"}]
["      Auxiliary power"]
["Hydraulic power","Paux,hydr,sys,tot","W",{"$f":"D162*D49/100","v":62.181858484470574}]
["Electric power","Paux,elec,sys,tot","W",{"$f":"D162","v":108.70954280501849}]
["Primary power","Paux,prim,sys,tot","W",{"$f":"D162*D60","v":326.12862841505546}]
["      Economic costs"]
["Cash flow to save by usable thermal energy","CFtherm","cent/h",{"$f":"D164","v":122.22222222222221}]
["Cash flow to save by thermal energy after load leakage","CFtherm,load","cent/h",{"$f":"D165","v":"Not for this syst.!"}]
["Cash flow to spend for auxiliary power","CFaux","cent/h",{"$f":"D163","v":3.2612862841505548}]
["      Performance, net energy or net cash flow"]
["Specific net primary power saving","q̇prim,net,spec","W/m²",{"$f":"D166","v":706.35173389787701}]
["Specific net cost saving per time by power","CFnet,spec","cent/h",{"$f":"D167","v":7.0635173389787695}]
["Specific net site power saving","q̇net,spec","W/m²",{"$f":"D168","v":653.2871789828074}]
["Specific net system power saving","q̇sys,net,spec","W/m²",{"$f":"D169","v":587.31297882225238}]
["      Performance, primary energetic"]
["Coefficient of primary energetic performance","COPprim","-",{"$f":"(D152/(D64/100)*D61)/(D162*D60)","v":37.476692192343556}]
["Share of primary power for auxiliary","1/COPprim","%",{"$f":"1/((D152/(D64/100)*D61)/(D162*D60))*100","v":2.6683251415777267}]
["Coefficient of primary energetic perf. after load leakage","COPprim,load","-",{"$f":"IF(     ISNONTEXT(D153),\n     (D153/(D64/100)*D61)/(D162*D60),\n     D153)","v":"Not for this syst.!"}]
["Share of primary power for auxiliary after load leakage","1/COPprim,load","%",{"$f":"IF(     ISNONTEXT(D153),\n     1/((D153/(D64/100)*D61)/(D162*D60))*100,\n     D153)","v":"Not for this syst.!"}]
["      Performance, monetary"]
["Coefficient of monetary performance","COPcost","-",{"$f":"D164/D163","v":37.476692192343556}]
["Share of money for auxiliary","1/COPcost","%",{"$f":"1/(D164/D163)*100","v":2.6683251415777267}]
["Coefficient of monetary performance after load leakage","COPcost,load","-",{"$f":"IF(     ISNONTEXT(D165),\n     D165/D163,\n     D165)","v":"Not for this syst.!"}]
["Share of money for auxiliary after load leakage","1/COPcost,load","%",{"$f":"IF(     ISNONTEXT(D165),\n     1/(D165/D163)*100,\n     D165)","v":"Not for this syst.!"}]
["      Performance, site energetic"]
["Coefficient of site energetic performance","COPsite","-",{"$f":"(D152/(D64/100))/D162","v":102.20916052457333}]
["Share of site power for auxiliary","1/COPsite","%",{"$f":"1/((D152/(D64/100))/D162)*100","v":0.97838588524516645}]
["Coefficient of site energetic perf. after load leakage","COPsite,load","-",{"$f":"IF(     ISNONTEXT(D153),\n     (D153/(D64/100))/D162,\n     D153)","v":"Not for this syst.!"}]
["Share of site power for auxiliary after load leakage","1/COPsite,load","%",{"$f":"IF(     ISNONTEXT(D153),\n     1/((D153/(D64/100))/D162)*100,\n     D153)","v":"Not for this syst.!"}]
["      Performance, system energetic"]
["Coefficient of performance","COPsyst","-",{"$f":"D152/D162","v":91.988244472116008}]
["Share of power for auxiliary","1/COPsyst","%",{"$f":"1/(D152/D162)*100","v":1.0870954280501848}]
["Coefficient of performance after load leakage","COPsyst,load","-",{"$f":"IF(     ISNONTEXT(D153),\n     D153/D162,\n     D153)","v":"Not for this syst.!"}]
["Share of power for auxiliary after load leakage","1/COPsyst,load","%",{"$f":"IF(     ISNONTEXT(D153),\n     1/(D153/D162)*100,\n     D153)","v":"Not for this syst.!"}]
[]
["   Values of system without field"]
["      Pressure"]
["Pressure drop of system before field","Δpsys1","Pa",{"$f":"D128","v":56.395271171006556}]
["Pressure drop of system after field","Δpsys2","Pa",{"$f":"D129","v":68.221946658837552}]
["Dynamic pressure losses into large load volumes (sum)","pdyn,sys","Pa",{"$f":"D131","v":14.422830945794409}]
["Total pressure of total system","psys,tot","Pa",{"$f":"D130\n     +IF(ISNONTEXT(D131),D131,0)","v":139.04004877563852}]
["      Thermal power"]
["Leakage power loss (into load) as fraction of power","RQ̇,Le,load","%",{"$f":"D156","v":"Not for this syst.!"}]
["Power loss by inward leakage into load","Q̇Le,load","W",{"$f":"D159","v":"Not for this syst.!"}]
["      Auxiliary power"]
["Hydraulic power","Paux,hydr,sys","W",{"$f":"D161*D49/100","v":50.439348546599895}]
["Electric power","Paux,elec,sys","W",{"$f":"D161","v":88.180679277272546}]
["Primary power","Paux,prim,sys","W",{"$f":"D161*D60","v":264.54203783181765}]
["      Economic costs"]
["Spent auxiliary power costs","Cdaux,sys","cent/h",{"$f":"D161*D62/1000","v":2.6454203783181764}]
[]
["   Values of field"]
["      Efficiency"]
["Instantaneous inner efficiency of field for gaining heat","ηinner","%",{"$f":"D119","v":59.691790881673313}]
["Instantaneous efficiency for usage","ηuse","%",{"$f":"D121","v":59.376780144499499}]
["Reduction of efficiency of field by leakage","ΔηL","%-points",{"$f":"D120","v":-0.31501073717381445}]
["      Dimensions"]
["Area","Afield","m²",{"$f":"D127","v":16.841600328721047}]
["Number of air collectors","ncoll/field","coll",{"$f":"D126","v":7.5794780957340437}]
["Field length","ncoll/row","coll",{"$f":"D124","v":3.9619716996925498}]
["Field width","nrow","coll",{"$f":"D125","v":1.9130571014230651}]
["      Pressure"]
["Pressure drop","Δpfield","Pa",{"$f":"D132","v":32.369156255092406}]
["Pressure at inlet","pi,field","Pa",{"$f":"D133","v":-56.395271171006556}]
["Pressure at outlet","pe,field","Pa",{"$f":"D134","v":-88.764427426098962}]
["      Mass flow"]
["Outlet mass flow","ṁe","kg/h",{"$f":"D141","v":1430.2706731378964}]
["Inlet mass flow","ṁi","kg/h",{"$f":"D140","v":1411.3006895009096}]
["Leakage mass flow (outward) as fraction of inlet mass flow","Rṁ,Le","%",{"$f":"D135","v":0}]
["Leakage mass flow (inward) as fraction of inlet mass flow","Rṁ,Li","%",{"$f":"D136","v":1.3441489668438715}]
["Leakage mass flow (outward)","ṁLe","kg/h",{"$f":"D137","v":0}]
["Leakage mass flow (inward)","ṁLi","kg/h",{"$f":"D138","v":18.96998363698691}]
["Average mass flow along field","ṁave","kg/h",{"$f":"D142*D125","v":1420.0908771374586}]
["      Temperatures"]
["Temperature rise","ΔTrise","K",{"$f":"D148","v":25}]
["Inlet temperature","ϑi","°C",{"$f":"D146","v":20}]
["Outlet temperature","ϑe","°C",{"$f":"D147","v":45}]
["      Thermal power"]
["Power gained","Q̇inner","W",{"$f":"D150","v":10053.052849347374}]
["Power delivered","Q̇use","W",{"$f":"D152","v":10000}]
["By power delivered saveable site power","Q̇use,site","W",{"$f":"D152/(D64/100)","v":11111.111111111111}]
["By power delivered saveable primary power","Q̇use,prim","W",{"$f":"D152/(D64/100)*D61","v":12222.222222222223}]
["Leakage power loss (outward) as fraction of power","RQ̇,Le","%",{"$f":"D154","v":0}]
["Leakage power loss (inward) as fraction of power","RQ̇,Li","%",{"$f":"D155","v":0.52772874212846754}]
["Leakage power loss as fraction of  power","RQ̇,L","%",{"$f":"D154+D155","v":0.52772874212846754}]
["Power loss by outward leakage","Q̇Le","W",{"$f":"D157","v":0}]
["Power loss by inward leakage","Q̇Li","W",{"$f":"D158","v":53.052849347370945}]
["Power loss by leakage","Q̇L","W",{"$f":"D157+D158","v":53.052849347370945}]
["      Auxiliary power"]
["Hydraulic power","Paux,hydr,field","W",{"$f":"D160*D49/100","v":11.742509937870683}]
["Electric power","Paux,elec,field","W",{"$f":"D160","v":20.528863527745948}]
["Primary power","Paux,prim,field","W",{"$f":"D160*D60","v":61.586590583237843}]
["      Economic costs"]
["Cash flow to save by usable thermal energy","CFtherm,field","cent/h",{"$f":"D152/(D64/100)*D63/1000","v":122.22222222222221}]
["Cash flow to spend for auxiliary power","CFaux,field","cent/h",{"$f":"D160*D62/1000","v":0.61586590583237844}]
[]
["   Values per row"]
["      Dimensions"]
["Area","Arow","m²",{"$f":"D127/D125","v":8.8035011167168467}]
["      Pressure"]
["Pressure drop","Δp","Pa",{"$f":"D132","v":32.369156255092406}]
["Pressure at inlet","pi","Pa",{"$f":"D133","v":-56.395271171006556}]
["Pressure at outlet","pe","Pa",{"$f":"D134","v":-88.764427426098962}]
["      Mass flow"]
["Outlet mass flow","ṁe,row","kg/h",{"$f":"D141/D125","v":747.63616416570187}]
["Inlet mass flow","ṁi,row","kg/h",{"$f":"D140/D125","v":737.72010696966959}]
["Leakage mass flow (outward)","ṁLe,row","kg/h",{"$f":"D137/D125","v":0}]
["Leakage mass flow (inward)","ṁLi,row","kg/h",{"$f":"D138/D125","v":9.9160571960323178}]
["Average mass flow along one row","ṁave,row","kg/h",{"$f":"D142","v":742.31494505893011}]
["      Temperatures"]
["Temperature rise","ΔTrise","K",{"$f":"D148","v":25}]
["Inlet temperature","ϑi","°C",{"$f":"D146","v":20}]
["Outlet temperature","ϑe","°C",{"$f":"D147","v":45}]
["      Thermal power"]
["Power gained","Q̇inner,row","W",{"$f":"D150/D125","v":5254.9674768563955}]
["Power delivered","Q̇use,row","W",{"$f":"D152/D125","v":5227.2355030915196}]
["By power delivered saveable site power","Q̇use,row,site","W",{"$f":"D152/D125/(D64/100)","v":5808.039447879466}]
["By power delivered saveable primary power","Q̇use,row,prim","W",{"$f":"D152/D125/(D64/100)*D61","v":6388.8433926674134}]
["Power loss by outward leakage","Q̇Le,row","W",{"$f":"D157/D125","v":0}]
["Power loss by inward leakage","Q̇Li,row","W",{"$f":"D158/D125","v":27.731973764874315}]
["Power loss by leakage","Q̇L,row","W",{"$f":"(D157+D158)/D125","v":27.731973764874315}]
["      Auxiliary power"]
["Hydraulic power","Paux,hydr,row","W",{"$f":"D160/D125*D49/100","v":6.138086484264262}]
["Electric power","Paux,elec,row","W",{"$f":"D160/D125","v":10.730920427035423}]
["Primary power","Paux,prim,row","W",{"$f":"D160/D125*D60","v":32.192761281106272}]
["      Economic costs"]
["Cash flow to save by usable thermal energy","CFtherm,row","cent/h",{"$f":"D164/D125","v":63.888433926674125}]
["Cash flow to spend for auxiliary power","CFaux,row","cent/h",{"$f":"D160/D125*D62/1000","v":0.32192761281106269}]
[]
["   Values per air collector"]
["      Dimensions"]
["Area","Acoll","m²",{"$f":"D127/D126","v":2.222}]
["      Pressure"]
["Pressure drop","Δpcoll","Pa",{"$f":"D132/D124","v":8.169961501139511}]
["      Mass flow"]
["Leakage mass flow (outward) (averaged along row)","ṁLe,coll","kg/h",{"$f":"D137/D126","v":0}]
["Leakage mass flow (inward) (averaged along row)","ṁLi,coll","kg/h",{"$f":"D138/D126","v":2.5028086891185533}]
["Average mass flow","ṁave,coll","kg/h",{"$f":"D142","v":742.31494505893011}]
["      Thermal power"]
["Power gained","Q̇inner,coll","W",{"$f":"D150/D126","v":1326.3515933907813}]
["Power delivered","Q̇use,coll","W",{"$f":"D152/D126","v":1319.3520548107788}]
["By power delivered saveable site power","Q̇use,coll,site","W",{"$f":"D152/D126/(D64/100)","v":1465.946727567532}]
["By power delivered saveable primary power","Q̇use,coll,prim","W",{"$f":"D152/D126/(D64/100)*D61","v":1612.5414003242854}]
["Power loss by outward leakage","Q̇Le,coll","W",{"$f":"D157/D126","v":0}]
["Power loss by inward leakage","Q̇Li,coll","W",{"$f":"D158/D126","v":6.9995385800020546}]
["Power loss by leakage","Q̇L,coll","W",{"$f":"(D157+D158)/D126","v":6.9995385800020546}]
["      Auxiliary power"]
["Hydraulic power","Paux,hydr,coll","W",{"$f":"D160/D126*D49/100","v":1.5492504615165676}]
["Electric power","Paux,elec,coll","W",{"$f":"D160/D126","v":2.7084798278261673}]
["Primary power","Paux,prim,coll","W",{"$f":"D160/D126*D60","v":8.1254394834785018}]
["      Economic costs"]
["Cash flow to save by usable thermal energy","CFtherm,coll","cent/h",{"$f":"D164/D126","v":16.125414003242852}]
["Cash flow to spend for auxiliary power","CFaux,coll","cent/h",{"$f":"D160/D126*D62/1000","v":8.1254394834785013E-2}]
[]
["   Values per square meter"]
["      Dimensions"]
["Area","Aspec","m²",{"$f":"D127/D126/D11","v":1}]
["      Mass flow"]
["Outlet mass flow","ṁe,spec","kg/(hm²)",{"$f":"D141/D127","v":84.924867306034173}]
["Inlet mass flow","ṁi,spec","kg/(hm²)",{"$f":"D140/D127","v":83.79849075827606}]
["Leakage mass flow (outward) (averaged)","ṁLe,spec","kg/(hm²)",{"$f":"D137/D127","v":0}]
["Leakage mass flow (inward) (averaged)","ṁLi,spec","kg/(hm²)",{"$f":"D138/D127","v":1.1263765477581247}]
["Average mass flow","ṁave,spec","kg/(hm²)",{"$f":"D142*D125/D127","v":84.320423797000331}]
["      Thermal power"]
["Power gained","q̇inner,spec","W/m²",{"$f":"D150/D127","v":596.91790881673319}]
["Power delivered","q̇use,spec","W/m²",{"$f":"D152/D127","v":593.76780144499492}]
["By power delivered saveable site power","q̇use,spec,site","W/m²",{"$f":"D152/D127/(D64/100)","v":659.74200160554994}]
["By power delivered saveable primary power","q̇use,spec,prim","W/m²",{"$f":"D152/D127/(D64/100)*D61","v":725.71620176610497}]
["Power loss by outward leakage","q̇Le,spec","W/m²",{"$f":"D157/D127","v":0}]
["Power loss by inward leakage","q̇Li,spec","W/m²",{"$f":"D158/D127","v":3.1501073717380983}]
["Power loss by leakage","q̇L,spec","W/m²",{"$f":"(D157+D158)/D127","v":3.1501073717380983}]
["      Auxiliary power"]
["Hydraulic power","Paux,hydr,spec","W/m²",{"$f":"D160/D127*D49/100","v":0.69723243092554799}]
["Electric power","Paux,elec,spec","W/m²",{"$f":"D160/D127","v":1.2189378163034055}]
["Primary power","Paux,prim,spec","W/m²",{"$f":"D160/D127*D60","v":3.6568134489102162}]
["      Economic costs"]
["Cash flow to save by usable thermal energy","CFtherm,spec","cent/h",{"$f":"D164/D127","v":7.2571620176610487}]
["Cash flow to spend for auxiliary power","CFaux,spec","cent/h",{"$f":"D160/D127*D62/1000","v":3.6568134489102164E-2}]
[]
["   Relative efficiency reduction at operating point"]
["Reduced temperature difference (= operating point)","T*m","Km²/W",{"$f":"(D149-D33)/D116","v":2.2499999999999999E-2}]
["Theor. inner effic. for gaining heat (extrapol. infinite flow)","ηinner,ṁ∞","%",{"$f":"D117","v":59.878039374999993}]
["Ratio of theor. inner effic. (infinite flow) / inner effic.","Rη_gain,ṁ∞/η_inner,ṁ_ave","-",{"$f":"D117/D119","v":1.0031201692992573}]
["Inner effic. for gaining heat (ave. mass flow, before leak.)","ηinner,ṁ_ave","%",{"$f":"D119","v":59.691790881673313}]
["Ratio of usable effic. (after leakage) / inner effic.","Rη_use/η_inner,ṁ_ave","-",{"$f":"D121/D119","v":0.99472271257871525}]
["Usable efficiency (after leakage, at field outlet)","ηuse","%",{"$f":"D121","v":59.376780144499499}]
["Ratio of us. eff. (after field + load leak.) / eff. f. gain. heat","Rη_use,load/η_gain,ṁ_ave","-",{"$f":"IF(     ISNONTEXT(D123),\n     D123/D119,\n     D123)","v":"Not for this syst.!"}]
["Usable efficiency (after leakage into load)","ηuse,load","%",{"$f":"D123","v":"Not for this syst.!"}]
["Usable efficiency (after leakage into load)","ηuse,load","%",{"$f":"D123","v":"Not for this syst.!"}]
[]
["   Absolute efficiency reduction at operating point"]
["Reduced temperature difference (= operating point)","T*m","Km²/W",{"$f":"(D149-D33)/D116","v":2.2499999999999999E-2}]
["Theor. inner effic. for gaining heat (extrapol. infinite flow)","ηinner,ṁ∞","%",{"$f":"D117","v":59.878039374999993}]
["Efficiency reduction by fan mass flow","Δηṁ_fan","%-points",{"$f":"(-EXP(-D15*D143/D125))\n     *(D12*D115     -D13*(D149-D33)/D116     -D14*(D149-D33)*ABS(D149-D33)/D116)\n     *100","v":-0.17869825313508689}]
["Efficiency reduction by average vs. fan mass flow","Δηṁ_ave","%-points",{"$f":"(EXP(-D15*D143/D125)     -EXP(-D15*D142))\n     *(D12*D115     -D13*(D149-D33)/D116     -D14*(D149-D33)*ABS(D149-D33)/D116)\n     *100","v":-7.5502401915890456E-3}]
["Inner effic. for gaining heat (ave. mass flow, before leak.)","ηinner,ṁ_ave","%",{"$f":"D119","v":59.691790881673313}]
["Efficiency reduction by leakage","ΔηL","%-points",{"$f":"-(D157+D158)/(D116*D127)*100","v":-0.31501073717380979}]
["Usable efficiency (after leakage, at field outlet)","ηuse","%",{"$f":"D121","v":59.376780144499499}]
["Efficiency reduction by leakage of load","ΔηL,load","%-points",{"$f":"IF(     ISNONTEXT(D159),\n     -D159/(D116*D127)*100,\n     D159)","v":"Not for this syst.!"}]
["Usable efficiency (after leakage into load)","ηuse,load","%",{"$f":"D123","v":"Not for this syst.!"}]
["Total efficiency reduction by mass flow and leakage","Δηṁ_ave,L","%-points",{"$f":"IF(     ISNONTEXT(D123),     D123,     D121)\n     -(D12*D115     -D13*(D149-D33)/D116     -D14*(D149-D33)*ABS(D149-D33)/D116)     *100","v":-0.50125923050049437}]
[]
["Efficiency curve for ScenoCalc"]
[]
["   Converted coefficient set for ScenoCalc (under consideration of thermo-hydraulic mass flow dependency and leakage)"]
["Conversion factor including leakage (use)","η0,L","-",{"$f":"D12*D174+D175/100","v":0.77213088467856883}]
["Linear heat loss coefficient","c1","W/(m²K)",{"$f":"D13*D174","v":7.7528099205030703}]
["Quadratic heat loss coefficient","c2","W/(m²K²)",{"$f":"D14*D174","v":7.7528099205030699E-3}]
["Efficient mass flow per row per row gross area","ṁe,row,spec,row","kg/(sm²)",{"$f":"D141/D125/(D11*D124)/3600","v":2.3590240918342831E-2}]
["Efficient mass flow per row per collector gross area","ṁe,row,spec,coll","kg/(sm²)",{"$f":"D141/D125/D11/3600","v":9.3463866907403478E-2}]
["Mean fluid temp. at zero eff. (G = 1000 W/m², ϑa = 30 °C)","ϑm(η=0)","°C",{"$f":"IF(D14<>0,\n       30     +(-(D13*D174)     +SQRT((D13*D174)^2     +4*(D12*D174+D175/100)*(D14*D174)*1000))     /(2*D14*D174),\n  IF(D14=0,\n       30     +(D12*D174+D175/100)*1000     /(D13*D174)))","v":121.26447707570554}]

{"sheet":"SAHC Model","index":12,"n_rows":463,"n_cols":4,"rows_kept":463,"cut":false,"hidden":true,"merged":[]}
["Input for macros (necessary only after inserting, deleting, or moving rows of sheets Model\" and \"Input, Results\")"]
[]
["Workbook_SheetChange()"]
["Variable: \"row_user_modelcolumn_exists\"",null,null,{"$f":"ROW('SAHC Calc.+Opt.'!A71)","v":71}]
[]
["SK_Optimization()"]
["Variable: \"row_user_Error\"",null,null,{"$f":"ROW('SAHC Calc.+Opt.'!A106)","v":106}]
["Variable: \"row_user_input_first\"",null,null,{"$f":"ROW('SAHC Calc.+Opt.'!A11)","v":11}]
["Variable: \"row_user_input_last\"",null,null,{"$f":"ROW('SAHC Calc.+Opt.'!A25)","v":25}]
["Variable: \"row_SK_input_first\"",null,null,{"$f":"ROW('SK Efficiency Curve'!H16)","v":16}]
["Variable: \"row_SK_input_last\"",null,null,{"$f":"ROW('SK Efficiency Curve'!H30)","v":30}]
["Variable: \"row_SKnew_boundery_first\"",null,null,{"$f":"ROW('SK Efficiency Curve'!H16)","v":16}]
["Variable: \"row_SKnew_boundery_last\"",null,null,{"$f":"ROW('SK Efficiency Curve'!H52)","v":52}]
["Variable: \"row_SKnew_results_fist\"",null,null,{"$f":"ROW('SK Efficiency Curve'!H58)","v":58}]
["Variable: \"row_SKnew_results_last\"",null,null,{"$f":"ROW('SK Efficiency Curve'!H92)","v":92}]
[]
["Exchange_InputModelResult()"]
["Variable: \"row_user_input_first\"",null,null,{"$f":"ROW('SAHC Calc.+Opt.'!A9)","v":9}]
["Variable: \"row_user_input_last\"",null,null,{"$f":"ROW('SAHC Calc.+Opt.'!A71)","v":71}]
["Variable: \"row_user_result_first\"",null,null,{"$f":"ROW('SAHC Calc.+Opt.'!A110)","v":110}]
["Variable: \"row_user_result_last\"",null,null,{"$f":"ROW('SAHC Calc.+Opt.'!A176)","v":176}]
["Variable: \"row_user_error_first\"",null,null,{"$f":"ROW('SAHC Calc.+Opt.'!A77)","v":77}]
["Variable: \"row_user_error_last\"",null,null,{"$f":"ROW('SAHC Calc.+Opt.'!A106)","v":106}]
["Variable: \"row_model_input_first\"",null,null,{"$f":"ROW(A56)","v":56}]
["Variable: \"row_model_input_last\"",null,null,{"$f":"ROW(A118)","v":118}]
["Variable: \"row_model_result_first\"",null,null,{"$f":"ROW(A362)","v":362}]
["Variable: \"row_model_result_last\"",null,null,{"$f":"ROW(A428)","v":428}]
["Variable: \"row_model_error_first\"",null,null,{"$f":"ROW(A434)","v":434}]
["Variable: \"row_model_error_last\"",null,null,{"$f":"ROW(A463)","v":463}]
["Variable: \"row_model_error_choicecell_first\"",null,null,{"$f":"ROW(A434)","v":434}]
["Variable: \"row_model_error_choicecell_last\"",null,null,{"$f":"ROW(A439)","v":439}]
["Variable: \"row_model_flow_manual\"",null,null,{"$f":"ROW(D114)","v":114}]
["Variable: \"row_model_flow_opt\"",null,null,{"$f":"ROW(D115)","v":115}]
["Variable: \"row_model_error_cost\"",null,null,{"$f":"ROW(D444)","v":444}]
["Variable: \"row_model_error_optmacro\"",null,null,{"$f":"ROW(D445)","v":445}]
["Variable: \"row_model_error_precis\"",null,null,{"$f":"ROW(D446)","v":446}]
[]
["QuadInterpolation()"]
["Variable: \"row_model_flow_min\"",null,null,{"$f":"ROW(D122)","v":122}]
["Variable: \"row_model_flow_max\"",null,null,{"$f":"ROW(D123)","v":123}]
["Variable: \"row_model_flow\"",null,null,{"$f":"ROW(D115)","v":115}]
["Variable: \"row_model_cost\"",null,null,{"$f":"ROW(D422)","v":422}]
[]
["ForAdmin_Protect_Hidden()"]
["Variable: \"row_user_result_hide_first\"",null,null,{"$f":"ROW('SAHC Calc.+Opt.'!A110)-2","v":108}]
["Variable: \"row_user_result_hide_last\"",null,null,{"$f":"ROW('SAHC Calc.+Opt.'!A176)+1","v":177}]
[]
["Input"]
[]
[]
[]
[]
[]
[]
["   Solar air collector"]
["Manufacturer",null,null,"Desert Wind"]
["Name of air collector",null,null,"Vitrine"]
["Area","Acoll","m²",2.222]
["Conversion factor","η0,max","-",0.77769999999999995]
["Linear heat loss coefficient","c1,max","W/(m²K)",7.7770000000000001]
["Quadratic heat loss coefficient","c2,max","W/(m²K²)",7.7770000000000001E-3]
["Mass flow dependent heat loss coefficient","cm","h/kg",7.7770000000000001E-3]
["Linear pressure drop coefficient","R1","Pa/(kg/h)",1.111E-3]
["Quadratic pressure drop coefficient","R2","Pa/(kg/h)²",1.3329999999999999E-5]
["Linear outward leakage coefficient","Le1","kg/(h*Pa)",3.5000000000000003E-2]
["Quadratic outward leakage coefficient","Le2","kg/(h*Pa²)",-6.9999999999999999E-6]
["Linear inward leakage coefficient","Li1","kg/(h*Pa)",3.5000000000000003E-2]
["Quadratic inward leakage coefficient","Li2","kg/(h*Pa²)",6.9999999999999999E-6]
["Minimum valid mass flow for efficiency, pressure drop","ṁmin","kg/h",250]
["Maximum valid mass flow for efficiency, pressure drop","ṁmax","kg/h",2500]
["Minimum valid pressure for leakage coefficients","pmin","Pa",-2500]
["Maximum valid pressure for leakage coefficients","pmax","Pa",2500]
["Ambrosetti parameter","r","-"]
["Incidence angle modifier for 50° of sun to normal of coll.","Khem(50°)","-",0.9]
[]
["   Climate"]
["Solar zenit angle (zenit = 0°, sun rise or sun set = 90°)","θs","°",45]
["Solar azimuth angle (east = -90°, south = 0°, west = 90°)","γs","°",0]
["Global radiation in direction of sun","Gb,d","W/m²",1000]
["Ambient temperature","ϑa","°C",10]
[]
["   Field"]
["Tilt angle ( horizontal collector surface = 0°, vertical = 90°)","βcoll","°",45]
["Azimut angle (east = -90°, south = 0°, west = 90°)","γcoll","°",0]
["Temperature rise","ΔTrise","K",25]
["Field length (number of air collectors per row)","ncoll/row","coll"]
["Power (at field outlet or at load)","Q̇e","W",10000]
["Field width (number of rows of field)","nrow","coll"]
["Inlet fluid temperature of field","ϑi","°C",20]
["Mean fluid temperature of field","ϑm","°C"]
[]
["   Air heating system"]
["Hydraulic system configuration:\nEnter: 1 - field with overpressure; 2 - field with \nunderpressure; 3 - field with over- , underpressure",null,null,2]
["Field with overpressure (considered for given power):\nEnter: 1 - open loop; 2 - closed loop without leakage of load; 3 - closed loop with leakage of load",null,null,1]
["Field with over- and underpressure (considered for fan volume flow): Enter: 1 - fan after load and before field; 2 - fan after field and before load",null,null,1]
["Fan efficiency (electric -> mechanic -> hydraulic)","ηfan","%",57.2]
["Flow resistance before air collector field","Rsys,before","Pa/(m³/h)²",4.0000000000000003E-5]
["Flow resistance after air collector field","Rsys,after","Pa/(m³/h)²",4.0000000000000003E-5]
["Blowing air into how many large volumes in series (e.g. building; for dynamic pressure losses and velocity):\nEnter: 0 - no; 1 - one; 2 - two large vol.; 3 - etc.",null,null,1]
["Channel diameter of circular cross-section before large volumes, if present (for consideration of dynamic pressure losses at mass flow opt. and for velocity)","dchan,circ,vol","m",0.3]
["Channel side length of square cross-section before large volumes, if present (for consideration of dynamic pressure losses at mass flow opt. and for velocity)","achan,square,vol","m"]
["Diameter of circular cross-section of regular channel (only for velocity calculation)","dchan,circ,reg","m",0.3]
["Side length of square cross-section of regular channel (only for velocity calculation)","achan,square,reg","m"]
[]
["   Global system for mass flow optimization"]
["Kind of optimization: 1 - primary energetic; 2 - monetary; \n3 - site energetic; 4 - system energetic",null,null,1]
["Primary energy factor of electrical energy for fan","fp,fan","-",3]
["Primary en. factor for heating energy carrier to replace","fp,sys,repl","-",1.1000000000000001]
["Price per unit electrical energy for fan","Cfan","cent/(kWh)",30]
["Price per unit heating energy carrier to replace","Csys,repl","cent/(kWh)",11]
["Efficiency of heating sys. to repl. (chemical -> thermal)","ηsys,repl","%",90]
[]
["   Mass flow"]
["Manually set outlet mass flow per row (enter or delete)","ṁe,row","kg/h",888]
["Autom. optimized outlet mass flow p. row (do not enter)","MMP","kg/h"]
[]
["   Calculation support"]
["Connection to model, only if \"yes\"",null,null,"yes"]
[]
["Optimization"]
[]
["Minimum of expected mass flow range","ṁe,row,min","kg/h",{"$f":"-LN(1-0.8)/D62","v":206.94842644131418}]
["Maximum of expected mass flow range","ṁe,row,max","kg/h",{"$f":"-LN(1-0.999)/D62","v":888.22878731929222}]
["Mass flow per row for calculation","ṁe,row","kg/h",{"$f":"IF(     NOT(D114=\"\"),\n     D114,\n     D115)","v":888}]
[]
["Calculation"]
[]
["   Coefficient manipulation to avoid #DIV/0!"]
["Linear pressure drop coefficient","R1","Pa/(kg/h)",{"$f":"IF(     AND(D63=0,D64=0),     0.00000001,     D63)","v":1.111E-3}]
["Quadratic pressure drop coefficient","R2","Pa/(kg/h)²",{"$f":"D64","v":1.3329999999999999E-5}]
["Linear outward leakage coefficient","Le1","kg/(h*Pa)",{"$f":"IF(     D65=0,     0.0000001,     D65)","v":3.5000000000000003E-2}]
["Quadratic outward leakage coefficient","Le2","kg/(h*Pa²)",{"$f":"IF(     D66=0,     -0.0000000001,     D66)","v":-6.9999999999999999E-6}]
["Linear inward leakage coefficient","Li1","kg/(h*Pa)",{"$f":"IF(     D67=0,     0.0000001,     D67)","v":3.5000000000000003E-2}]
["Quadratic inward leakage coefficient","Li2","kg/(h*Pa²)",{"$f":"IF(     D68=0,     0.0000000001,     D68)","v":6.9999999999999999E-6}]
[]
["   Solar irradiance"]
["Total angle of sun to normal of collector plane","θ","°",{"$f":"DEGREES(ACOS(COS(RADIANS(D77))     *COS(RADIANS(D83))\n     +SIN(RADIANS(D77))     *SIN(RADIANS(D83))     *COS(RADIANS(D78-D84))))","v":0}]
["Ambrosetti parameter","r","-",{"$f":"IF(\n     D73=0,\n     LN(TAN(RADIANS(50/2)))/LN(1-D74),\n     D73)","v":0.33132745208325876}]
["Incidence angle modifier","Khem","-",{"$f":"MAX(0,1-(TAN(RADIANS(D137/2)))^(1/D138))","v":1}]
["Factor for projected field area","-","-",{"$f":"MAX(0,COS(RADIANS(D137)))","v":1}]
["Global irradiance on tilted collector plane","Gb,d,coll","W/m²",{"$f":"D79*D140","v":1000}]
[]
["   Field with overpressure"]
["Mean fluid temperature of field (copy)","ϑm","°C",{"$f":"IF(D93=1,D166,22.2)","v":22.2}]
["Average mass flow along one row (copy)","ṁave,row","kg/h",{"$f":"IF(D93=1,MAX(D124,D167),77.7)","v":77.7}]
["Substitution mass flow per row (copy)","ṁLe,subs,row","kg/h",{"$f":"IF(D93=1,MAX(-1*10^-6,D168),5.55)","v":5.55}]
["Leakage mass flow per row (outward) (copy)","ṁLe,row","kg/h",{"$f":"IF(D93=1,MAX(-1*10^-6,D169),7.77)","v":7.77}]
["Theor. inner effic. for gaining heat (extrapol. infinite flow)","ηinner,ṁ∞","%",{"$f":"(D59*D139     -D60*(D144-D80)/D141     -D61*(D144-D80)*ABS(D144-D80)/D141)\n     *100","v":68.166307132}]
["Efficiency reduction by mass flow","Δηṁ","%-points",{"$f":"(-EXP(-D62*D145))\n     *(D59*D139     -D60*(D144-D80)/D141     -D61*(D144-D80)*ABS(D144-D80)/D141)\n     *100","v":-37.250952406321339}]
["Instantaneous inner efficiency of field for gaining heat","ηinner","%",{"$f":"(1-EXP(-D62*D145))\n     *(D59*D139     -D60*(D144-D80)/D141     -D61*(D144-D80)*ABS(D144-D80)/D141)\n     *100","v":30.915354725678668}]
["Specific heat capacity (mean temperature)","cp","J/(kgK)",{"$f":"MIN(1200,MAX(900,1005.89     +0.01475*D144     +0.00041*D144*ABS(D144)))","v":1006.4195144}]
["Temperature rise","ΔTrise","K",{"$f":"IF(     D85=0,\n     (D141*D150/100*D58*D86     -0/3600*D151*(D80-D144))     /((D124+D146+0/2)/3600*D151),\n     D85)","v":25}]
["Field length","ncoll/row","coll",{"$f":"IF(     D86=0,\n     ((D124+D146+0/2)/3600*D151*D85     +0/3600*D151*(D80-D144))     /(D141*D150/100*D58),\n     D86)","v":9.0911144991908905}]
["Power at field outlet","Q̇e","W",{"$f":"IF(     D87=0,\n     D124/3600*D88*D151*D152     -IF(D94=3,     D147/3600*D88*D151*(D144-D152/2-D80),     0),\n     D87)","v":10000}]
["Field width","nrow","coll",{"$f":"IF(     D88=0,\n     D87/(D124/3600*D151*D152     -IF(D94=3,     D147/3600*D151*(D144-D152/2-D80),     0)),\n     D88)","v":1.6112779993026947}]
["Number of air collectors of field","ncoll/field","coll",{"$f":"D155*D153","v":14.648312781688016}]
["Area of field","Afield","m²",{"$f":"D58*D156","v":32.54855100091077}]
["Inlet temperature","ϑi","°C",{"$f":"D144-D152/2","v":9.6999999999999993}]
["Outlet temperature","ϑe","°C",{"$f":"D144+D152/2","v":34.700000000000003}]
["Density (inlet temperature)","ρi","kg/m³",{"$f":"100000/(287*(273.15+D158))","v":1.2318616077395401}]
["Density (outlet temperature)","ρe","kg/m³",{"$f":"100000/(287*(273.15+D159))","v":1.1318241213224913}]
["Pressure drop of system after field","Δpsys2","Pa",{"$f":"D98*(D124*D155/D161)^2","v":63.924742398718003}]
["Pressure drop of field","Δpfield","Pa",{"$f":"D153     *(D129*D145     +D130*D145^2)","v":1.5164140415570568}]
["Pressure at field outlet","pe,field","Pa",{"$f":"D162","v":63.924742398718003}]
["Pressure at field inlet","pi,field","Pa",{"$f":"D164+D163","v":65.441156440275066}]
["Mean fluid temperature of field","ϑm","°C",{"$f":"IF(     NOT(ISERROR(D150)),\n     IF(     D90=\"\",\n          (D89+D159)/2,\n          D90),\n     22.2)","v":27.35}]
["Average mass flow along one row","ṁave,row","kg/h",{"$f":"IF(     NOT(ISERROR(D150)),\n     D124\n          -D156/(D155*D163)     *(D65/2*D164^2     +D66/3*D164^3)\n          +D156/(D155*D163^2)     *(D65/6*(D165^3-D164^3)     +D66/12*(D165^4-D164^4)),\n     77.7)","v":898.1184005271441}]
["Substitution mass flow per row","ṁLe,subs,row","kg/h",{"$f":"IF(     NOT(ISERROR(D150)),\n     D156/(D155*D163^2)\n          *(D65/2*D165*(D165^2-D164^2)     +(-D65/3+D66/3*D165)*(D165^3-D164^3)     -D66/4*(D165^4-D164^4)),\n     5.55)","v":10.118400527142386}]
["Leakage mass flow per row (outward)","ṁLe,row","kg/h",{"$f":"IF(     NOT(ISERROR(D150)),\n     D156/(D155*D163)\n          *(D65/2*(D165^2-D164^2)     +D66/3*(D165^3-D164^3)),\n     7.77)","v":20.315138105469927}]
["Inlet mass flow of field","ṁi","kg/h",{"$f":"     -D124*D155     -D147*D155","v":-1443.3344934353747}]
["Inlet Volume flow of field","V̇i","kg/h",{"$f":"D170/D160","v":-1171.6693534137219}]
["Fan mass flow of field","ṁfan","kg/h",{"$f":"-D170","v":1443.3344934353747}]
["Fan volume flow of field","V̇fan","m³/h",{"$f":"D172/D160","v":1171.6693534137219}]
["Outlet volume flow of field","V̇e","m³/h",{"$f":"D124*D155/D161","v":1264.1671408354}]
["Leakage mass flow (outward) as fraction of inlet mass flow","Rṁ,Le","%",{"$f":"D169*D155/-D170*100","v":2.2678966816783248}]
["Channel cross section before large volume","Achan,vol","m²",{"$f":"IF(D100<>\"\",\n     PI()/4*D100^2,\n     D101^2)","v":7.0685834705770348E-2}]
["Velocity before large load volume","uchan,vol","m/s",{"$f":"D174/3600/D176","v":4.9678629471185705}]
["Sum of dynamic pressure losses into large load volumes","pdyn,sum,sys","Pa",{"$f":"D99     *0.5*D161*D177^2","v":13.966518526746199}]
["Cross section of regular channel","Achan,reg","m²",{"$f":"IF(D102<>\"\",\n     PI()/4*D102^2,\n     D103^2)","v":7.0685834705770348E-2}]
["Velocity in cold regular channel","uchan,reg,cold","m/s",{"$f":"-D171/3600/D179","v":4.6043696114834249}]
["Velocity in hot regular channel","uchan,reg,hot","m/s",{"$f":"D174/3600/D179","v":4.9678629471185705}]
["Pressure drop of system before field","Δpsys1","Pa",{"$f":"D97*D171^2","v":54.912362949157163}]
["Pressure drop of remaining system","Δpsys,rem","Pa",{"$f":"D182+D162","v":118.83710534787517}]
["Converted heat of field","Q̇inner","W",{"$f":"D141*D157*D150/100","v":10062.5}]
["Power at field inlet","Q̇i","W",{"$f":"D170/3600*D151     *(D158-D158)","v":0}]
["Power at field outlet","Q̇e","W",{"$f":"D124/3600*D155*D151     *D152","v":10000}]
["By power at field outlet saveable site power","Q̇e,site","W",{"$f":"D186/(D111/100)","v":11111.111111111111}]
["By power at field outlet saveable primary power","Q̇e,prim","W",{"$f":"D187*D108","v":12222.222222222223}]
["Useful power after inward leakage into load","Q̇load","W",{"$f":"D186-D193","v":10001.049999999999}]
["By usef. pow. aft. inw. leak. into load saveable site pow.","Q̇load,site","W",{"$f":"D189/(D111/100)","v":11112.277777777777}]
["By usef. pow. aft. inw. leak. into load saveable prim. pow.","Q̇load,prim","W",{"$f":"D190*D108","v":12223.505555555555}]
["Power loss by outward leakage","Q̇Le","W",{"$f":"D146/3600*D155*D151     *D152","v":62.5}]
["Power loss by inward leakage into load","Q̇Le,load","W",{"$f":"D147/3600*D155*D151     *(D158-D80)","v":-1.0500000000000023}]
["Leakage power loss fraction (outward) of  power","RQ̇,Le","%",{"$f":"D192/(D186+D192)*100","v":0.6211180124223602}]
["Leakage power loss fraction (into load) of  power","RQ̇,Le,load","%",{"$f":"D193/(D186+D192)*100","v":-1.0434782608695674E-2}]
["Instantaneous efficiency of field after leakage for usage","ηuse","%",{"$f":"D186/D157/D141*100","v":30.72333388887321}]
["Reduction of efficiency of field by leakage","ΔηL","%-points",{"$f":"D196-D150","v":-0.19202083680545812}]
["Instantaneous efficiency of system after leak. into load","ηuse,load","%",{"$f":"D189/D157/D141*100","v":30.726559838931543}]
["Reduction of efficiency of system by leakage of load","ΔηL,load","%-points",{"$f":"D198-D196","v":3.225950058332927E-3}]
["Auxiliary power demand for field","Paux,field","W",{"$f":"D163*D173/3600/(D96/100)","v":0.86282821463609427}]
["Auxiliary power demand for remaining  system","Paux,sys,rem","W",{"$f":"(D183+D178)\n     *D173/3600/(D96/100)","v":75.564265790684118}]
["Auxiliary power demand for total system","Paux,sys,tot","W",{"$f":"D200+D201","v":76.427094005320214}]
["Primary auxiliary power demand for total system","Paux,prim,sys.tot","W",{"$f":"D202*D107","v":229.28128201596064}]
["Cash flow to spend for auxiliary power","CFaux","cent/h",{"$f":"D202*D109/1000","v":2.2928128201596065}]
["Cash flow to save by thermal energy at field outlet","CFtherm","cent/h",{"$f":"D187*D110/1000","v":122.22222222222221}]
["Cash flow to save by thermal energy after load leakage","CFtherm,load","cent/h",{"$f":"D190*D110/1000","v":122.23505555555555}]
["Primary energetic cost function","q̇prim,net,spec","W/m²",{"$f":"IF(     OR(D94=1,D94=2),\n     (D188-D203)/D157,\n     IF(     D94=3,\n          (D191-D203)/D157,))","v":368.46312881549403}]
["Monetary cost function","CFnet,spec","cent/h",{"$f":"IF(     OR(D94=1,D94=2),\n     (D205-D204)/D157,\n     IF(     D94=3,\n          (D206-D204)/D157,))","v":3.6846312881549399}]
["Site energetic cost function","q̇net,spec","W/m²",{"$f":"IF(     OR(D94=1,D94=2),\n     (D187-D202)/D157,\n     IF(     D94=3,\n          (D190-D202)/D157,))","v":339.02228141575398}]
["System energetic cost function","q̇sys,net,spec","W/m²",{"$f":"IF(     OR(D94=1,D94=2),\n     (D186-D202)/D157,\n     IF(     D94=3,\n          (D189-D202)/D157,))","v":304.88524376145034}]
["Cost function","cost","-",{"$f":"IF(     D106=1,\n     D207,\n     IF(     D106=2,\n          D208,\n          IF(     D106=3,\n               D209,\n               IF(     D106=4,\n                    D210,))))","v":368.46312881549403}]
[]
["   Field with underpressure"]
["Mean fluid temperature of field (copy)","ϑm","°C",{"$f":"IF(D93=2,D242,22.2)","v":32.5}]
["Average mass flow along one row (copy)","ṁave,row","kg/h",{"$f":"IF(D93=2,MIN(D124,D243),77.7)","v":880.60408967522869}]
["Leakage mass flow per row (inward) (copy)","ṁLi,row","kg/h",{"$f":"IF(D93=2,MIN(1*10^-6,D244),-7.7)","v":-13.382313294683774}]
["Theor. inner effic. for gaining heat (extrapol. infinite flow)","ηinner,ṁ∞","%",{"$f":"(D59*D139     -D60*(D214-D80)/D141     -D61*(D214-D80)*ABS(D214-D80)/D141)\n     *100","v":59.878039374999993}]
["Efficiency reduction by mass flow","Δηṁ","%-points",{"$f":"(-EXP(-D62*D215))\n     *(D59*D139     -D60*(D214-D80)/D141     -D61*(D214-D80)*ABS(D214-D80)/D141)\n     *100","v":-6.3536026407847709E-2}]
["Instantaneous inner efficiency of field for gaining heat","ηinner","%",{"$f":"(1-EXP(-D62*D215))\n     *(D59*D139     -D60*(D214-D80)/D141     -D61*(D214-D80)*ABS(D214-D80)/D141)\n     *100","v":59.81450334859214}]
["Specific heat capacity","cp","J/(kgK)",{"$f":"MIN(1200,MAX(900,1005.89     +0.01475*D214     +0.00041*D214*ABS(D214)))","v":1006.8024375}]
["Temperature rise","ΔTrise","K",{"$f":"IF(     D85=0,\n     (D141*D219/100*D58*D86     -D216/3600*D220*(D80-D214))     /((D124+0+D216/2)/3600*D220),\n     D85)","v":25}]
["Field length","ncoll/row","coll",{"$f":"IF(     D86=0,\n     ((D124+0+D216/2)/3600*D220*D85     +D216/3600*D220*(D80-D214))     /(D141*D219/100*D58),\n     D86)","v":4.6995283563428014}]
["Power at field outlet","Q̇e","W",{"$f":"IF(     D87=0,\n     D124/3600*D88*D220*D221,\n     D87)","v":10000}]
["Field width","nrow","coll",{"$f":"IF(     D88=0,\n     D87/(D124/3600*D220*D221),\n     D88)","v":1.610665172452586}]
["Number of air collectors of field","ncoll/field","coll",{"$f":"D224*D222","v":7.5693666505146959}]
["Area of field","Afield","m²",{"$f":"D58*D225","v":16.819132697443653}]
["Inlet temperature","ϑi","°C",{"$f":"D214-D221/2","v":20}]
["Outlet temperature","ϑe","°C",{"$f":"D214+D221/2","v":45}]
["Density (inlet temperature)","ρi","kg/m³",{"$f":"100000/(287*(273.15+D227))","v":1.1885794158251031}]
["Density (outlet temperature)","ρe","kg/m³",{"$f":"100000/(287*(273.15+D228))","v":1.0951816933808862}]
["Inlet mass flow of field","ṁi","kg/h",{"$f":"     -D124*D224     -D216*D224","v":-1408.7162471873}]
["Inlet volume flow of field","V̇i","kg/h",{"$f":"D231/D229","v":-1185.2100317666864}]
["Fan mass flow of field","ṁfan","kg/h",{"$f":"D124*D224","v":1430.2706731378964}]
["Fan volume flow of field","V̇fan","m³/h",{"$f":"D233/D230","v":1305.9665640708183}]
["Outlet volume flow of field","V̇e","m³/h",{"$f":"D124*D224/D230","v":1305.9665640708183}]
["Pressure drop of system before field","Δpsys1","Pa",{"$f":"D97*D232^2","v":56.188912776015592}]
["Pressure drop of system after field","Δpsys2","Pa",{"$f":"D98*D235^2","v":68.221946658837552}]
["Pressure drop of remaining  system","Δpsys,rem","Pa",{"$f":"D236+D237","v":124.41085943485314}]
["Pressure drop of field","Δpfield","Pa",{"$f":"D222     *(D129*D215     +D130*D215^2)","v":53.176481264832297}]
["Pressure at field inlet","pi,field","Pa",{"$f":"-D236","v":-56.188912776015592}]
["Pressure at field outlet","pe,field","Pa",{"$f":"D240-D239","v":-109.36539404084789}]
["Mean fluid temperature of field","ϑm","°C",{"$f":"IF(     NOT(ISERROR(D219)),\n     IF(     D90=\"\",\n          (D89+D228)/2,\n          D90),\n     22.2)","v":32.5}]
["Average mass flow along one row","ṁave,row","kg/h",{"$f":"IF(     NOT(ISERROR(D219)),\n     D124\n          -D225/(D224*D239)     *(D67/2*D241^2     +D68/3*D241^3)\n          +D225/(D224*D239^2)     *(D67/6*(D240^3-D241^3)     +D68/12*(D240^4-D241^4)),\n     77.7)","v":880.60408967522869}]
["Leakage mass flow per row (inward)","ṁLi,row","kg/h",{"$f":"IF(     NOT(ISERROR(D219)),\n     D225/(D224*D239)\n          *(D67/2*(D240^2-D241^2)     +D68/3*(D240^3-D241^3)),\n     -7.77)","v":-13.382313294683774}]
["Leakage mass flow (inward) as fraction of inlet mass flow","Rṁ,Li","%",{"$f":"D244*D224/-D231*100","v":-1.5300757688876532}]
["Channel cross section before large volume","Achan,vol","m²",{"$f":"IF(D100<>\"\",\n     PI()/4*D100^2,\n     D101^2)","v":7.0685834705770348E-2}]
["Velocity before large load volume","uchan,vol","m/s",{"$f":"D235/3600/D246","v":5.1321243008545476}]
["Sum of dynamic pressure losses into large load volumes","pdyn,sum,sys","Pa",{"$f":"D99     *0.5*D230*D247^2","v":14.422830945794409}]
["Cross section of regular channel","Achan,reg","m²",{"$f":"IF(D102<>\"\",\n     PI()/4*D102^2,\n     D103^2)","v":7.0685834705770348E-2}]
["Velocity in cold regular channel","uchan,reg,cold","m/s",{"$f":"-D232/3600/D249","v":4.6575811150066775}]
["Velocity in hot regular channel","uchan,reg,hot","m/s",{"$f":"D235/3600/D249","v":5.1321243008545476}]
["Converted heat of field","Q̇inner","W",{"$f":"D141*D226*D219/100","v":10060.280690516589}]
["Power at field inlet","Q̇i","W",{"$f":"D231/3600*D220     *(D227-D227)","v":0}]
["Power at field outlet","Q̇e","W",{"$f":"D124/3600*D224*D220     *D221","v":9999.9999999999982}]
["By power at field outlet saveable site power","Q̇e,site","W",{"$f":"D254/(D111/100)","v":11111.111111111109}]
["By power at field outlet saveable primary power","Q̇e,prim","W",{"$f":"D255*D108","v":12222.222222222221}]
["Power loss by inwards leakage","Q̇Li","W",{"$f":"D216/3600*D224*D220     *(D80-D227)","v":60.28069051659358}]
["Leakage power loss fraction (inward) of  power","RQ̇,Li","%",{"$f":"D257/(D254+D257)*100","v":0.59919491683187009}]
["Instantaneous efficiency of field after leakage for usage","ηuse","%",{"$f":"D254/D226/D141*100","v":59.456097884999167}]
["Reduction of efficiency of field by leakage","ΔηL","%-points",{"$f":"D259-D219","v":-0.35840546359297321}]
["Auxiliary power demand for field","Paux,field","W",{"$f":"D239*D234/3600/(D96/100)","v":33.725090582172335}]
["Auxiliary power demand for remaining  system","Paux,sys,rem","W",{"$f":"(D238+D248)\n     *D234/3600/(D96/100)","v":88.049804586094623}]
["Auxiliary power demand for total system","Paux,sys,tot","W",{"$f":"D261+D262","v":121.77489516826697}]
["Primary auxiliary power demand for total system","Paux,prim,sys,tot","W",{"$f":"D263*D107","v":365.32468550480087}]
["Cash flow to spend for auxiliary power","CFaux","cent/h",{"$f":"D263*D109/1000","v":3.6532468550480091}]
["Cash flow to save by usable thermal energy","CFtherm","cent/h",{"$f":"D255*D110/1000","v":122.2222222222222}]
["Primary energetic cost function","q̇prim,net,spec","W/m²",{"$f":"(D256-D264)/D226","v":704.96486055547655}]
["Monetary cost function","CFnet,spec","cent/h",{"$f":"(D266-D265)/D226","v":7.049648605554764}]
["Site energetic cost function","q̇net,spec","W/m²",{"$f":"(D255-D263)/D226","v":653.38304974626408}]
["System energetic cost function","q̇sys,net,spec","W/m²",{"$f":"(D254-D263)/D226","v":587.32071876293173}]
["Cost function","cost","-",{"$f":"IF(     D106=1,\n     D267,\n     IF(     D106=2,\n          D268,\n          IF(     D106=3,\n               D269,\n               IF(     D106=4,\n                    D270,))))","v":704.96486055547655}]
[]
["   Field with over- and underpressure"]
["Mean fluid temperature of field (copy)","ϑm","°C",{"$f":"IF(D93=3,D314,22.2)","v":22.2}]
["Average mass flow along one row (copy)","ṁave,row","kg/h",{"$f":"IF(D93=3,D315,77.7)","v":77.7}]
["Leak. mass flow per row, underpr. zone (inward) (copy)","ṁLi,row","kg/h",{"$f":"IF(D93=3,MIN(1*10^-6,D316),-7.77)","v":-7.77}]
["Substitution mass flow per row, overpr. zone (copy)","ṁLe,subs,row","kg/h",{"$f":"IF(D93=3,MAX(-1*10^-6,D317),7.77)","v":7.77}]
["Theor. inner effic. for gaining heat (extrapol. infinite flow)","ηinner,ṁ∞","%",{"$f":"(D59*D139     -D60*(D274-D80)/D141     -D61*(D274-D80)*ABS(D274-D80)/D141)\n     *100","v":68.166307132}]
["Efficiency reduction by mass flow","Δηṁ","%-points",{"$f":"(-EXP(-D62*D275))\n     *(D59*D139     -D60*(D274-D80)/D141     -D61*(D274-D80)*ABS(D274-D80)/D141)\n     *100","v":-37.250952406321339}]
["Instantaneous inner efficiency of field for gaining heat","ηinner","%",{"$f":"(1-EXP(-D62*D275))\n     *(D59*D139     -D60*(D274-D80)/D141     -D61*(D274-D80)*ABS(D274-D80)/D141)\n     *100","v":30.915354725678668}]
["Specific heat capacity","cp","J/(kgK)",{"$f":"MIN(1200,MAX(900,1005.89     +0.01475*D274     +0.00041*D274*ABS(D274)))","v":1006.4195144}]
["Temperature rise","ΔTrise","K",{"$f":"IF(     D85=0,\n     (D141*D280/100*D58*D86     -D276/3600*D281*(D80-D274))     /((D124+D277+D276/2)/3600*D281),\n     D85)","v":25}]
["Field length","ncoll/row","coll",{"$f":"IF(     D86=0,\n     ((D124+D277+D276/2)/3600*D281*D85     +D276/3600*D281*(D80-D274))     /(D141*D280/100*D58),\n     D86)","v":9.1127524810299594}]
["Power at field outlet","Q̇e","W",{"$f":"IF(     D87=0,\n     D124/3600*D88*D281*D282,\n     D87)","v":10000}]
["Field width","nrow","coll",{"$f":"IF(     D88=0,\n     D87/(D124/3600*D281*D282),\n     D88)","v":1.6112779993026947}]
["Number of air collectors of field","ncoll/field","coll",{"$f":"D283*D285","v":14.683177585774621}]
["Area of field","Afield","m²",{"$f":"D58*D286","v":32.626020595591207}]
["Inlet temperature","ϑi","°C",{"$f":"D274-D282/2","v":9.6999999999999993}]
["Outlet temperature","ϑe","°C",{"$f":"D274+D282/2","v":34.700000000000003}]
["Density (inlet temperature)","ρi","kg/m³",{"$f":"100000/(287*(273.15+D288))","v":1.2318616077395401}]
["Density (outlet temperature)","ρe","kg/m³",{"$f":"100000/(287*(273.15+D289))","v":1.1318241213224913}]
["Inlet mass flow of field","ṁi","kg/h",{"$f":"-D124*D285","v":-1430.8148633807928}]
["Inlet volume flow of field","V̇i","kg/h",{"$f":"D292/D290","v":-1161.5061743878282}]
["Fan mass flow of field","ṁfan","kg/h",{"$f":"D124*D285","v":1430.8148633807928}]
["Fan volume flow","V̇fan","m³/h",{"$f":"IF(     D95=1,\n     D294/D290,\n     IF(     D95=2,\n          D294/D291,))","v":1161.5061743878282}]
["Outlet volume flow of field","V̇e","m³/h",{"$f":"D124*D285/D291","v":1264.1671408354}]
["Pressure drop of system before field","Δpsys1","Pa",{"$f":"D97*D293^2","v":53.963863725641922}]
["Pressure drop of system after field","Δpsys2","Pa",{"$f":"D98*D296^2","v":63.924742398718003}]
["Pressure drop of remaining  system","Δpsys,rem","Pa",{"$f":"D297+D298","v":117.88860612435992}]
["Pressure drop of field","Δpfield","Pa",{"$f":"D283     *(D129*D275     +D130*D275^2)","v":1.5200232953503778}]
["Parameter for finding the root of a cubic function","a","kg/(hr*Pa²)",{"$f":"D132/3     -D134/3","v":-4.6666666666666663E-6}]
["Parameter for finding the root of a cubic function","b","kg/(hr*Pa)",{"$f":"D131/2     -D133/2     +D134*D300","v":1.0640163067452644E-5}]
["Parameter for finding the root of a cubic function","c","kg/hr",{"$f":"D133*D300     -D134*D300^2","v":5.3184642041534377E-2}]
["Parameter for finding the root of a cubic function","d","kg/hr*Pa",{"$f":"-D133/2*D300^2     +D134/3*D300^3","v":-4.0425044726713405E-2}]
["Parameter for finding the root of a cubic function","p'","Pa-2",{"$f":"(3*D301*D303     -D302^2)     /(3*D301^2)","v":-11398.44186201403}]
["Parameter for finding the root of a cubic function","q'","Pa-3",{"$f":"(2*D302^3     -9*D301*D302*D303     +27*D301^2*D304)     /(27*D301^3)","v":0}]
["Parameter for finding the root of a cubic function","cond","Pa-6",{"$f":"4*D305^3+27*D306^2","v":-5923746384755.2051}]
["Parameter for finding the root of a cubic function","tk","Pa",{"$f":"2*SQRT(-D305/3)\n*COS(1/3*\n     ACOS(3*D306/(2*D305)     *SQRT(-3/D305))\n     -2*PI()/3)","v":7.5518061524542597E-15}]
["Parameter for finding the root of a cubic function","t0,1","Pa",{"$f":"-2*ABS(D306)/D306*SQRT(-D305/3)\n*COSH(1/3*\n     ACOSH(-3*ABS(D306)/(2*D305)     *SQRT(-3/D305)))","v":{"$error":"#DIV/0!"}}]
["Parameter for finding the root of a cubic function","t0,2","Pa",{"$f":"-2*SQRT(D305/3)\n*SINH(1/3*\n     ASINH(3*D306/(2*D305)     *SQRT(3/D305)))","v":{"$error":"#NUM!"}}]
["Parameter for finding the root of a cubic function","t","Pa",{"$f":"IF(     AND(D305<0,D307<=0),     D308,\n     IF(     AND(D305<0,D307>0),     D309,\n     IF(     D305>0,     D310)))","v":7.5518061524542597E-15}]
["Pressure at field inlet","pi,field","Pa",{"$f":"D311     -D302/(3*D301)","v":0.76001164767519658}]
["Pressure at field outlet","pe,field","Pa",{"$f":"D312-D300","v":-0.76001164767518126}]
["Mean fluid temperature of field","ϑm","°C",{"$f":"IF(     NOT(ISERROR(D280)),\n     IF(     D90=\"\",\n          (D89+D289)/2,\n          D90),\n     22.2)","v":27.35}]
["Average mass flow along one row","ṁave,row","kg/h",{"$f":"IF(     NOT(ISERROR(D280)),\n     D124\n          +D286/(D285*D300^2)     *(-D65/3*D312^3     -D66/4*D312^4     +D67/3*D313^3     +D68/4*D313^4),\n     77.7)","v":887.95960411722979}]
["Leakage mass flow per row, underpressure zone (inward)","ṁLi,row","kg/h",{"$f":"IF(     NOT(ISERROR(D280)),\n     D286/(D285*D300)\n          *(D67/2*(-(D313^2))     +D68/3*(-(D313^3))),\n     -7.77)","v":-6.0594591776315744E-2}]
["Substitution mass flow per row, overpressure zone","ṁLe,subs,row","kg/h",{"$f":"IF(     NOT(ISERROR(D280)),\n     D286/(D285*D300^2)\n          *(D65/6*D312^3     +D66/12*D312^4),\n     7.77)","v":1.0099354503068375E-2}]
["Leakage mass flow per row, overpressure zone (outward)","ṁLe,row","kg/h",{"$f":"D286/(D285*D300)     *(D65/2*D312^2     +D66/3*D312^3)","v":6.0594591776318193E-2}]
["Leakage mass flow (inward) as fraction of inlet mass flow","Rṁ,Li","%",{"$f":"D316*D285/-D292*100","v":-6.8237152901256476E-3}]
["Leakage mass flow (outward) as fraction of inlet mass flow","Rṁ,Le","%",{"$f":"D318*D285/-D292*100","v":6.8237152901259234E-3}]
["Channel cross section before large volume","Achan,vol","m²",{"$f":"IF(D100<>\"\",\n     PI()/4*D100^2,\n     D101^2)","v":7.0685834705770348E-2}]
["Velocity before large load volume","uchan,vol","m/s",{"$f":"D296/3600/D321","v":4.9678629471185705}]
["Sum of dynamic pressure losses into large load volumes","pdyn,sum,sys","Pa",{"$f":"D99     *0.5*D291*D322^2","v":13.966518526746199}]
["Cross section of regular channel","Achan,reg","m²",{"$f":"IF(D102<>\"\",\n     PI()/4*D102^2,\n     D103^2)","v":7.0685834705770348E-2}]
["Velocity in cold regular channel","uchan,reg,cold","m/s",{"$f":"-D293/3600/D324","v":4.5644308416192558}]
["Velocity in hot regular channel","uchan,reg,hot","m/s",{"$f":"D296/3600/D324","v":4.9678629471185705}]
["Converted heat of field","Q̇inner","W",{"$f":"D141*D287*D280/100","v":10086.450000000001}]
["Power at field inlet","Q̇i","W",{"$f":"D292/3600*D281     *(D288-D288)","v":0}]
["Power at field outlet","Q̇e","W",{"$f":"D124/3600*D285*D281     *D282","v":10000}]
["By power at field outlet saveable site power","Q̇e,site","W",{"$f":"D329/(D111/100)","v":11111.111111111111}]
["By power at field outlet saveable primary power","Q̇e,prim","W",{"$f":"D330*D108","v":12222.222222222223}]
["Power loss by outward leakage","Q̇Le","W",{"$f":"D277/3600*D285*D281     *D282","v":87.499999999999986}]
["Power loss by inward leakage","Q̇Li","W",{"$f":"D276/3600*D285*D281     *(D80-D288)","v":-1.0500000000000023}]
["Leakage power loss fraction (outward) of  power","RQ̇,Le","%",{"$f":"D332/(D329+D332+D333)*100","v":0.86750045853595648}]
["Leakage power loss fraction (inward) of  power","RQ̇,Li","%",{"$f":"D333/(D329+D332+D333)*100","v":-1.0410005502431501E-2}]
["Instantaneous efficiency of field after leakage for usage","ηuse","%",{"$f":"D329/D287/D141*100","v":30.650382171803418}]
["Reduction of efficiency of field by leakage","ΔηL","%-points",{"$f":"D336-D280","v":-0.26497255387524987}]
["Auxiliary power demand for field","Paux,field","W",{"$f":"D300*D295/3600/(D96/100)","v":0.85737977989646319}]
["Auxiliary power demand for remaining  system","Paux,sys,rem","W",{"$f":"(D299+D323)\n     *D295/3600/(D96/100)","v":74.373806044549568}]
["Auxiliary power demand for total system","Paux,sys,tot","W",{"$f":"D338+D339","v":75.23118582444603}]
["Primary auxiliary power demand for total system","Paux,prim,sys,tot","W",{"$f":"D340*D107","v":225.6935574733381}]
["Cash flow to spend for auxiliary power","CFaux","cent/h",{"$f":"D340*D109/1000","v":2.2569355747333808}]
["Cash flow to save by usable thermal energy","CFtherm","cent/h",{"$f":"D330*D110/1000","v":122.22222222222221}]
["Primary energetic cost function","q̇prim,net,spec","W/m²",{"$f":"(D331-D341)/D287","v":367.6981883095479}]
["Monetary cost function","CFnet,spec","cent/h",{"$f":"(D343-D342)/D287","v":3.676981883095479}]
["Site energetic cost function","q̇net,spec","W/m²",{"$f":"(D330-D340)/D287","v":338.25393731216968}]
["System energetic cost function","q̇sys,net,spec","W/m²",{"$f":"(D329-D340)/D287","v":304.197957121277}]
["Cost function","cost","-",{"$f":"IF(     D106=1,\n     D344,\n     IF(     D106=2,\n          D345,\n          IF(     D106=3,\n               D346,\n               IF(     D106=4,\n                    D347,))))","v":367.6981883095479}]
[]
["   Calculation for ScenoCalc coefficients and error check"]
["Reduction of efficiency of field by leakage","ΔηL","%-points",{"$f":"IF(     D93=1,\n     D197,\n     IF(     D93=2,\n          D260,\n          IF(     D93=3,\n               D337,)))","v":-0.35840546359297321}]
["Reduction of efficiency of system by leakage of load","ΔηL,load","%-points",{"$f":"IF(     AND(D93=1,OR(D94=2,D94=3)),\n     D199,\n     \"Not for this syst.!\")","v":"Not for this syst.!"}]
["Average mass flow along one row","ṁave,row","kg/h",{"$f":"IF(     D93=1,\n     D145,\n     IF(     D93=2,\n          D215,\n          IF(     D93=3,\n               D275,)))","v":880.60408967522869}]
["Factor for reduction by mass flow depency","f(ṁave,row)","-",{"$f":"(1-EXP(-D62*D353))","v":0.99893890937193286}]
["Total efficiency reduction by leakage","ΔηL","%-points",{"$f":"D351+     IF(     AND(D93=1,D94=3),     D352,     0)","v":-0.35840546359297321}]
["Parameter for finding the root of a quadratic function","a","1/K²",{"$f":"-D61/D141","v":-7.7770000000000002E-6}]
["Parameter for finding the root of a quadratic function","b","1/K²",{"$f":"2*D61/D141*D80-D60/D141","v":-7.62146E-3}]
["Parameter for finding the root of a quadratic function","c","-",{"$f":"D59*D139+D60/D141*D80-D61/D141*D80^2","v":0.85469229999999996}]
["Mean fluid temperature at zero efficiency (before leak.)","ϑm,η=0","°C",{"$f":"IF(D61=0,\n     -D358/D357,\n     (-D357-SQRT(D357^2-4*D356*D358))/(2*D356))","v":101.60797830996158}]
[]
["   Values of selected hydraulic system configuration"]
["Hydraulic system configuration (Field with …)",null,null,{"$f":"IF(     D93=1,\n     \"overpress.\",\n     IF(     D93=2,\n          \"underpress.\",\n          IF(     D93=3,\n               \"over/underpr.\",)))","v":"underpress."}]
["Hydraulic system config. (closed or probably open loop)",null,null,{"$f":"IF(     AND(D93=1,ROUND(D158,4)<>D80),\n     \"closed loop\",\n     IF(     AND(D93=2,ROUND(D227,4)<>D80),\n          \"closed loop\",\n          IF(     D93=3,\n               \"closed loop\",\n               \"open loop\")))","v":"closed loop"}]
["Blowing into large volumes",null,null,{"$f":"IF(D99=0,\"no large vol.\",CONCATENATE(D99,\" large vol.\"))","v":"1 large vol."}]
["Optimization on mass flow …",null,null,{"$f":"IF(D114<>\"\",\"not optimiz.\",IF(AND(D115<>\"\",D106=1),\"MMPprim\",IF(AND(D115<>\"\",D106=2),\"MMPcost\",IF(AND(D115<>\"\",D106=3),\"MMPsite\",IF(AND(D115<>\"\",D106=4),\"MMPsyst\")))))","v":"not optimiz."}]
["Total angle of sun to normal of collector plane","θ","°",{"$f":"D137","v":0}]
["Incidence angle modifier","Khem","-",{"$f":"D139","v":1}]
["Global irradiance on tilted collector plane","Gb,d,coll","W/m²",{"$f":"D141","v":1000}]
["Theor. inner effic. for gaining heat (extrapol. infinite flow)","ηinner,ṁ∞","%",{"$f":"IF(     D93=1,\n     D148,\n     IF(     D93=2,\n          D217,\n          IF(     D93=3,\n               D278,)))","v":59.878039374999993}]
["Efficiency reduction by mass flow","Δηṁ","%-points",{"$f":"IF(     D93=1,\n     D149,\n     IF(     D93=2,\n          D218,\n          IF(     D93=3,\n               D279,)))","v":-6.3536026407847709E-2}]
["Inner efficiency (average mass flow, before leakage)","ηinner,ṁ_ave","%",{"$f":"IF(     D93=1,\n     D150,\n     IF(     D93=2,\n          D219,\n          IF(     D93=3,\n               D280,)))","v":59.81450334859214}]
["Efficiency reduction by leakage","ΔηL","%-points",{"$f":"IF(     D93=1,\n     D197,\n     IF(     D93=2,\n          D260,\n          IF(     D93=3,\n               D337,)))","v":-0.35840546359297321}]
["Usable efficiency (after leakage, at field outlet)","ηuse","%",{"$f":"IF(     D93=1,\n     D196,\n     IF(     D93=2,\n          D259,\n          IF(     D93=3,\n               D336,)))","v":59.456097884999167}]
["Efficiency reduction by leakage of load","ΔηL,load","%-points",{"$f":"IF(     AND(D93=1,OR(D94=2,D94=3)),\n     D199,\n     \"Not for this syst.!\")","v":"Not for this syst.!"}]
["Usable efficiency (after leakage into load)","ηuse,load","%",{"$f":"IF(     AND(D93=1,OR(D94=2,D94=3)),\n     D198,\n     \"Not for this syst.!\")","v":"Not for this syst.!"}]
["Field length","ncoll/row","coll",{"$f":"IF(     D93=1,\n     D153,\n     IF(     D93=2,\n          D222,\n          IF(     D93=3,\n               D283,)))","v":4.6995283563428014}]
["Field width","nrow","coll",{"$f":"IF(     D93=1,\n     D155,\n     IF(     D93=2,\n          D224,\n          IF(     D93=3,\n               D285,)))","v":1.610665172452586}]
["Number of air collectors of field","ncoll/field","coll",{"$f":"IF(     D93=1,\n     D156,\n     IF(     D93=2,\n          D225,\n          IF(     D93=3,\n               D286,)))","v":7.5693666505146959}]
["Area of field","Afield","m²",{"$f":"IF(     D93=1,\n     D157,\n     IF(     D93=2,\n          D226,\n          IF(     D93=3,\n               D287,)))","v":16.819132697443653}]
["Pressure drop of system before field","Δpsys1","Pa",{"$f":"IF(     D93=1,\n     D182,\n     IF(     D93=2,\n          D236,\n          IF(     D93=3,\n               D297,)))","v":56.188912776015592}]
["Pressure drop of system after field","Δpsys2","Pa",{"$f":"IF(     D93=1,\n     D162,\n     IF(     D93=2,\n          D237,\n          IF(     D93=3,\n               D298,)))","v":68.221946658837552}]
["Pressure drop of remaining  system","Δpsys,rem","Pa",{"$f":"IF(     D93=1,\n     D183,\n     IF(     D93=2,\n          D238,\n          IF(     D93=3,\n               D299,)))","v":124.41085943485314}]
["Dynamic pressure losses into large load volumes (sum)","pdyn,sum,sys","Pa",{"$f":"IF(     D93=1,\n     D178,\n     IF(     D93=2,\n          D248,\n          IF(     D93=3,\n               D323,)))","v":14.422830945794409}]
["Pressure drop of field","Δpfield","Pa",{"$f":"IF(     D93=1,\n     D163,\n     IF(     D93=2,\n          D239,\n          IF(     D93=3,\n               D300,)))","v":53.176481264832297}]
["Pressure at field inlet","pi,field","Pa",{"$f":"IF(     D93=1,\n     D165,\n     IF(     D93=2,\n          D240,\n          IF(     D93=3,\n               D312,)))","v":-56.188912776015592}]
["Pressure at field outlet","pe,field","Pa",{"$f":"IF(     D93=1,\n     D164,\n     IF(     D93=2,\n          D241,\n          IF(     D93=3,\n               D313,)))","v":-109.36539404084789}]
["Leakage mass flow (outward) as fraction of inlet mass flow","Rṁ,Le","%",{"$f":"IF(     D93=1,\n     D175,\n     IF(     D93=2,\n          0,\n          IF(     D93=3,\n               D320,)))","v":0}]
["Leakage mass flow (inward) as fraction of inlet mass flow","Rṁ,Li","%",{"$f":"IF(     D93=1,\n     0,\n     IF(     D93=2,\n          -D245,\n          IF(     D93=3,\n               -D319,)))","v":1.5300757688876532}]
["Leakage mass flow of field (outward)","ṁLe","kg/h",{"$f":"IF(     D93=1,\n     D147*D155,\n     IF(     D93=2,\n          0,\n          IF(     D93=3,\n               D318*D285,)))","v":0}]
["Leakage mass flow of field (inward)","ṁLi","kg/h",{"$f":"IF(     D93=1,\n     0,\n     IF(     D93=2,\n          -D216*D224,\n          IF(     D93=3,\n               -D276*D285,)))","v":21.554425950596375}]
["Substitution mass flow of field","ṁLe,subs","kg/h",{"$f":"IF(     D93=1,\n     D146*D155,\n     IF(     D93=2,\n          0,\n          IF(     D93=3,\n               D277*D285,)))","v":0}]
["Inlet mass flow of field","ṁi","kg/h",{"$f":"IF(     D93=1,\n     -D170,\n     IF(     D93=2,\n          -D231,\n          IF(     D93=3,\n               -D292,)))","v":1408.7162471873}]
["Outlet mass flow of field","ṁe","kg/h",{"$f":"IF(     D93=1,\n     D124*D155,\n     IF(     D93=2,\n          D124*D224,\n          IF(     D93=3,\n               D124*D285,)))","v":1430.2706731378964}]
["Average mass flow along one row","ṁave,row","kg/h",{"$f":"IF(     D93=1,\n     D145,\n     IF(     D93=2,\n          D215,\n          IF(     D93=3,\n               D275,)))","v":880.60408967522869}]
["Fan mass flow of field","ṁfan","kg/h",{"$f":"IF(     D93=1,\n     D172,\n     IF(     D93=2,\n          D233,\n          IF(     D93=3,\n               D294,)))","v":1430.2706731378964}]
["Fan volume flow of field","V̇fan","m³/h",{"$f":"IF(     D93=1,\n     D173,\n     IF(     D93=2,\n          D234,\n          IF(     D93=3,\n               D295,)))","v":1305.9665640708183}]
["Outlet volume flow of field","V̇e","m³/h",{"$f":"IF(     D93=1,\n     D174,\n     IF(     D93=2,\n          D235,\n          IF(     D93=3,\n               D296,)))","v":1305.9665640708183}]
["Inlet temperature","ϑi","°C",{"$f":"IF(     D93=1,\n     D158,\n     IF(     D93=2,\n          D227,\n          IF(     D93=3,\n               D288,)))","v":20}]
["Outlet temperature","ϑe","°C",{"$f":"IF(     D93=1,\n     D159,\n     IF(     D93=2,\n          D228,\n          IF(     D93=3,\n               D289,)))","v":45}]
["Temperature rise","Δϑrise","K",{"$f":"IF(     D93=1,\n     D152,\n     IF(     D93=2,\n          D221,\n          IF(     D93=3,\n               D282,)))","v":25}]
["Mean fluid temperature of field","ϑm","°C",{"$f":"IF(     D93=1,\n     D166,\n     IF(     D93=2,\n          D242,\n          IF(     D93=3,\n               D314,)))","v":32.5}]
["Converted heat of field","Q̇inner","W",{"$f":"IF(     D93=1,\n     D184,\n     IF(     D93=2,\n          D252,\n          IF(     D93=3,\n               D327,)))","v":10060.280690516589}]
["Power at field inlet","Q̇i","W",{"$f":"IF(     D93=1,\n     D185,\n     IF(     D93=2,\n          D253,\n          IF(     D93=3,\n               D328,)))","v":0}]
["Power at field outlet","Q̇e","W",{"$f":"IF(     D93=1,\n     D186,\n     IF(     D93=2,\n          D254,\n          IF(     D93=3,\n               D329,)))","v":9999.9999999999982}]
["Useful power after inward leakage into load","Q̇load","W",{"$f":"IF(     AND(D93=1,OR(D94=2,D94=3)),\n     D189,\n     \"Not for this syst.!\")","v":"Not for this syst.!"}]
["Leakage power loss (outward) as fraction of power","RQ̇,Le","%",{"$f":"IF(     D93=1,\n     D194,\n     IF(     D93=2,\n          0,\n          IF(     D93=3,\n               D334,)))","v":0}]
["Leakage power loss (inward) as fraction of power","RQ̇,Li","%",{"$f":"IF(     D93=1,\n     0,\n     IF(     D93=2,\n          D258,\n          IF(     D93=3,\n               D335,)))","v":0.59919491683187009}]
["Leakage power loss (into load) as fraction of power","RQ̇,Le,load","%",{"$f":"IF(     AND(D93=1,OR(D94=2,D94=3)),\n     D195,\n     \"Not for this syst.!\")","v":"Not for this syst.!"}]
["Power loss by outward leakage","Q̇Le","W",{"$f":"IF(     D93=1,\n     D192,\n     IF(     D93=2,\n          0,\n          IF(     D93=3,\n               D332,)))","v":0}]
["Power loss by inward leakage","Q̇Li","W",{"$f":"IF(     D93=1,\n     0,\n     IF(     D93=2,\n          D257,\n          IF(     D93=3,\n               D333,)))","v":60.28069051659358}]
["Power loss by inward leakage into load","Q̇Le,load","W",{"$f":"IF(     AND(D93=1,OR(D94=2,D94=3)),\n     D193,\n     \"Not for this syst.!\")","v":"Not for this syst.!"}]
["Auxiliary power demand for field","Paux,field","W",{"$f":"IF(     D93=1,\n     D200,\n     IF(     D93=2,\n          D261,\n          IF(     D93=3,\n               D338,)))","v":33.725090582172335}]
["Auxiliary power demand for remaining  system","Paux,sys","W",{"$f":"IF(     D93=1,\n     D201,\n     IF(     D93=2,\n          D262,\n          IF(     D93=3,\n               D339,)))","v":88.049804586094623}]
["Auxiliary power demand for total system","Paux,sys,tot","W",{"$f":"IF(     D93=1,\n     D202,\n     IF(     D93=2,\n          D263,\n          IF(     D93=3,\n               D340,)))","v":121.77489516826697}]
["Cash flow to spend for auxiliary power","CFaux","cent/h",{"$f":"IF(     D93=1,\n     D204,\n     IF(     D93=2,\n          D265,\n          IF(     D93=3,\n               D342,)))","v":3.6532468550480091}]
["Cash flow to save by usable thermal energy","CFtherm","cent/h",{"$f":"IF(     D93=1,\n     D205,\n     IF(     D93=2,\n          D266,\n          IF(     D93=3,\n               D343,)))","v":122.2222222222222}]
["Cash flow to save by thermal energy after load leakage","CFtherm,load","cent/h",{"$f":"IF(     AND(D93=1,OR(D94=2,D94=3)),\n     D206,\n     \"Not for this syst.!\")","v":"Not for this syst.!"}]
["Specific net primary power saving","q̇prim,net,spec","W/m²",{"$f":"IF(     D93=1,\n     D207,\n     IF(     D93=2,\n          D267,\n          IF(     D93=3,\n               D344,)))","v":704.96486055547655}]
["Specific net cost saving per time by power","CFnet,spec","cent/h",{"$f":"IF(     D93=1,\n     D208,\n     IF(     D93=2,\n          D268,\n          IF(     D93=3,\n               D345,)))","v":7.049648605554764}]
["Specific net site power saving","q̇net,spec","W/m²",{"$f":"IF(     D93=1,\n     D209,\n     IF(     D93=2,\n          D269,\n          IF(     D93=3,\n               D346,)))","v":653.38304974626408}]
["Specific net system power saving","q̇sys,net,spec","W/m²",{"$f":"IF(     D93=1,\n     D210,\n     IF(     D93=2,\n          D270,\n          IF(     D93=3,\n               D347,)))","v":587.32071876293173}]
["Cost function","cost","-",{"$f":"IF(     D93=1,\n     D211,\n     IF(     D93=2,\n          D271,\n          IF(     D93=3,\n               D348,)))","v":704.96486055547655}]
["Velocity before large load volumes (for dynamic pressure)","uchan,vol","m/s",{"$f":"IF(     D93=1,\n     D177,\n     IF(     D93=2,\n          D247,\n          IF(     D93=3,\n               D322,)))","v":5.1321243008545476}]
["Velocity in cold regular channel","uchan,reg,cold","m/s",{"$f":"IF(     D93=1,\n     D180,\n     IF(     D93=2,\n          D250,\n          IF(     D93=3,\n               D325,)))","v":4.6575811150066775}]
["Velocity in hot regular channel","uchan,reg,hot","m/s",{"$f":"IF(     D93=1,\n     D181,\n     IF(     D93=2,\n          D251,\n          IF(     D93=3,\n               D326,)))","v":5.1321243008545476}]
["Factor for reduction by mass flow dependency","f(ṁave,row)","-",{"$f":"D354","v":0.99893890937193286}]
["Total efficiency reduction by leakage","ΔηL","%-points",{"$f":"D355","v":-0.35840546359297321}]
["Mean fluid temperature at zero efficiency (before leak.)","ϑm,h=0","°C",{"$f":"D359","v":101.60797830996158}]
[]
["Error check"]
[]
["   Details"]
["      Choice-cells"]
["Fill out only one cell of incidence angle transparency parameters, the other leave empty.",null,null,{"$f":"IF(\n     AND(D73=\"\",D74=\"\"),\n     \"Enter one value!\",\n     IF(\n          AND(D73<>\"\",D74<>\"\"),\n          \"Delete one cell!\",\n          \"OK\"))","v":"OK"}]
["Fill out only one cell of the temperature rise and field length, the other leave empty.",null,null,{"$f":"IF(\n     AND(D85=0,D86=0),\n     \"Enter one value!\",\n     IF(\n          AND(D85<>0,D86<>0),\n          \"Delete one cell!\",\n          \"OK\"))","v":"OK"}]
["Fill out only one cell of the power and field width, the other leave empty.",null,null,{"$f":"IF(\n     AND(D87=0,D88=0),\n     \"Enter one value!\",\n     IF(\n          AND(D87<>0,D88<>0),\n          \"Delete one cell!\",\n          \"OK\"))","v":"OK"}]
["Fill out only one cell of the inlet and mean fluid temperature, the other leave empty.",null,null,{"$f":"IF(\n     AND(D89=\"\",D90=\"\"),\n     \"Enter one value!\",\n     IF(\n          AND(D89<>\"\",D90<>\"\"),\n          \"Delete one cell!\",\n          \"OK\"))","v":"OK"}]
["Fill out only one cell of the channel cross-section before large volumes, the other leave empty.",null,null,{"$f":"IF(\n     AND(D100=\"\",D101=\"\"),\n     \"Enter one value!\",\n     IF(\n          AND(D100<>\"\",D101<>\"\"),\n          \"Delete one cell!\",\n          \"OK\"))","v":"OK"}]
["Fill out only one cell of the cross-section of regular channels, the other leave empty.",null,null,{"$f":"IF(\n     AND(D102=\"\",D103=\"\"),\n     \"Enter one value!\",\n     IF(\n          AND(D102<>\"\",D103<>\"\"),\n          \"Delete one cell!\",\n          \"OK\"))","v":"OK"}]
[]
["      Mass flow optimization"]
["Give either temperature rise and power or field length and width. Do not give other parameter combinations.",null,null,{"$f":"IF(\n     D115<>\"\",\n     IF(\n          OR(AND(D85<>\"\",D87<>\"\"),AND(D86<>\"\",D88<>\"\")),\n          \"OK\",\n          \"Change input!\"),\n     \"\")","v":""}]
["Optimization of mass flow is not possible with negative thermal efficiency",null,null,{"$f":"IF(     D114<>\"\",\n     \"\",\n     IF(     D369<=0,\n          \"Change input!\",\n          \"OK\"))","v":""}]
["Auxiliary demand is higher than thermal power (cost function is negative and has no maximum)"]
["Mass flow optimization could not be performed"]
["Relative range around the real optimal mass flow in which the optimized mass flow was found",null,"± %"]
["Optimized mass flow was not found within a relative range of ± 0.1 % of the real optimal mass flow",null,null,{"$f":"IF(     D446=\"\",\n     \"\",\n     IF(\n          D446>0.1,\n          \"Change input or opt. manually!\",\n          \"OK\"))","v":""}]
[]
["      Iterative calculation"]
["Number of iterations of circular references",null,"*10^6",{"$f":"IF(     ISERROR(CircularReferenceIterationsCount(D450,2,1)),\n     D450,\n     CircularReferenceIterationsCount(D450,2,2))","v":6.9999999999999999E-6}]
["Set max. iterations of circ. references is hit (divergency)\n-> efficiency is too low or do input field length and width",null,null,{"$f":"IF(\n     0.0001=D450,\n     \"Change input!\",\n     \"OK\")","v":"OK"}]
[]
["      Valid model ranges"]
["Mass flow is out of set valid mass flow range of efficiency and pressure drop coefficients",null,null,{"$f":"IF(\n     OR(D124<=D69,D124>=D70),\n     \"Change input!\",\n     \"OK\")","v":"OK"}]
["Pressure is out of set valid pressure range of leakage coefficients",null,null,{"$f":"IF(\n     OR(     AND(     OR(D67<>0,D68<>0),     D386<D71),\n                  AND(     OR(D65<>0,D66<>0),     D385>D72)),\n     \"Change input!\",\n     \"OK\")","v":"OK"}]
["Leakage mass flows would have wrong algebraic sign -> check correct diagram quadrants of leakage curves",null,null,{"$f":"IF(\n     OR(D390<-0.0000001,D389<-0.0000001),\n     \"Change input!\",\n     \"OK\")","v":"OK"}]
[]
["      Low thermal efficiency"]
["Calculation with negative efficiency only with given field length and width or negative temp. rise and field power",null,null,{"$f":"IF(\n     AND(\n          D371<=0,\n          OR(D85>0,D87>0)),\n     \"Change input!\",\n     \"OK\")","v":"OK"}]
["Outlet temperature is above maximum possible mean temperature",null,null,{"$f":"IF(\n     AND(D398<D359,     D399>D359),\n     \"Unrealistic case!\",\n     \"OK\")","v":"OK"}]
[]
["   Summary"]
["Summary of error notices",null,null,{"$f":"IF(     OR(ISERROR(D443),     ISERROR(D455),     ISERROR(D459),     ISERROR(D460)),\n            \"Errors found!\",\n            IF(     OR(     D434<>\"OK\",     D435<>\"OK\",     D436<>\"OK\",     D437<>\"OK\",     D438<>\"OK\",     D439<>\"OK\",\n                                   D442=\"Change input!\",     D443=\"Change input!\",     D444=\"Change input!\",     D445=\"Change input!\",     D447=\"Change input or opt. manually!\",\n                                   D454<>\"OK\",     D455<>\"OK\",     D456<>\"OK\",     D459<>\"OK\",     D460<>\"OK\",     D451<>\"OK\"),\n                     \"Errors found!\",\n                     \"No errors found\"))","v":"No errors found"}]

{"sheet":"History","index":13,"n_rows":9,"n_cols":4,"rows_kept":9,"cut":false,"hidden":true,"merged":[]}
["Version","Comments, Changes","Institution","Person"]
[]
["1.00 (2015-08-17)","Building this worksheet \"AirCow\" is finished for circulation within the Solar KEYMARK Network.\nAirCow is built for the determination of the coefficients eta_0, c1 and c2 of the efficiency curve usable in ScenoCalc.\nThis efficiency curve considers the thermo-hydraulic mass flow depenendcy and leakage losses already, which are characteristical for solar air heating collectors.\nFor scientific use, the complete input and result area can be accessed.\nThe model is protected generally. For Solar KEYMARK, the input data except the collector coefficients are protected additionally, to avoid unauthorized changes.","Fraunhofer ISE","Christian Welz"]
["1.00.intern.01 (2015-08-28)","# Cost function evaluation added before loop in macro QuadInterpolation() to forecast mass flow optimization problems via error cell.\n# \"new_range_width = (x2 - x0)\" added before loop in macro QuadInterpolation() to allow optimization outside of initial range.\n# Text of sheet \"Quick Guide\" overworked.\n# Error cell for precisition of mass flow optimization added in group \"Error check\" and pop up window with the same info removed.\n# Error cell for checking of negative power for mass flow optimazation changed for better error detection.\n# Rows of group \"Error check\" rearranged, and manual overworked regarding the change.\n# Error cell for checking valid pressure range of leakage curve disabled in case of no given leakage coefficients.\n# Group \"Overview on results\" devided into sub groups.\n# Calculation of system flow resistance added.\n# Appearing order of field length and width at all places homogenized.\n# Conditional bold formatting of input data appearing in the results added.\n# Rows added stating open or closed loop.\n# Rows added with leakage mass flows and leakage power losses as fractions in percent.\n# Leakage mass flows and average mass flow prevented from wrong algebraic sign and wrong values due to extrapolation of leakage curves for better convergence of circular references and better mass flow optimization.","Fraunhofer ISE","Christian Welz"]
["1.00.intern.02 (2015-10-26)","# Formats of leakage mass flow, leakage power, and leakage fractions set on individual format \"0.000;-0.000\" to make visible negative sign of values near zero.\n# Group format removed from group \"Overview on results (for model communication)\" to enable expanding level 4 without expanding hidden rows of this former group.\n# Thermal efficiency of system of replaced energy added, and consequential mass flow optimization and COP calculation overworked.\n# Dynamic pressure of air blowed into a large volume considered for mass flow optimization. System pressure drop changed from mass flow to volume flow dependency.\n# Calculation of channel cross-section and flow velocity added. Thereby density calculation reorganized.","Fraunhofer ISE","Christian Welz"]
["2.00 (2015-11-26)","# Display of type of mass flow added in the results (MMP…).\n# Input for dynamic pressure changed from cross-sectional area or flow velocity to diameter or side length of circular or square cross-section.\n# Input of pressure drop before and after system removed.","Fraunhofer ISE","Christian Welz"]
["2.01 (2016-01-06)","# Net primary power, net site power, net system power, and net cost saving added in the results as evaluation criteria.\n# Error notice added to exclude optimization cases, which are not intensively examined yet.\n# Values (specific mass flow, mean fluid temperature at zero efficiency) added in SK data sheet neccesary for the SK data sheet in ScenoCalc (not for simulation).","Fraunhofer ISE","Christian Welz"]
["2.02 (2016-02-29)","# Nearly all unit symbols changed to an internal standard.\n# Protection of sheet \"SK Efficiency Curve\" changed to protection without password for allowing insertion of a logo picture.","Fraunhofer ISE","Christian Welz"]
["3.00 (2016-09-30)","# Sheets for coefficient optimization of models for thermal efficiency, pressure drop, and leakage added.\n# Calculation speed improoved.","Fraunhofer ISE","Christian Welz"]