B13_31_1983_Aug_ZEROAIR Version 1.0 Uesr`s Manual_Public
Contents
1. ZEROAIR Version 1 0 User s Manual August 1983 Assistance and Information K Ford Design Aids Engineer Solar Programs Office Sir Charles Tupper Building Riverside Drive Ottawa K1A 0M2 613 998 3641 a E a a aa a a a a MM This document is not a departmental publication Do not cite as a reference or catalogue in a library 1 INTRODUCTION The ZEROAIR computer program was developed by Enermodal Engineering Limited to simulate the performance of solar space heating systems using air based solar collectors and no storage unit The program can accept data of all PUSH approved air based collectors Amherst 200 Solartech Solair and Watershed A 100 and any other parallel plate air based collector ZEROAIR is the only computer program capable of simulating zero storage air based solar space heating systems Performance calculations use a one hour time step to ensure maximum accuracy In general this type of system is best suited to buildings that can be allowed to fluctuate in temperature e g warehouses Buildings that require precise temperature control and have high internal heat gains during the day are not suited to this type of solar heating system Because there is no storage of heat other than in the building structure and its contents the solar heating system can supply very little of the nighttime heating load As such the system should be sized to meet under 40 of2. 1 Read Weather Data Calculate Space Heating Load Calculate New a a Building Tempt Ti Can solar energy be collected 18 Calculate Q and UE Calculate New Building Temp IS col y Calculate Aux bg min a Energy Calculate aux energy for existing building Add energy flows to old values N Is the simulation Go to 1 over Y Print system performance Go to 2 19 If there was no other energy input to the building the building temperature would become Tbg S Tog 8 Heil bg Provided that this new value is below the maximum allowable temperature and heat can be collected the solar heat delivered to the building can be calculated Q Faro K Hr FRU Ty T4 A where K is the incidence angle modifier factor 214 b 1 cose 1 The new building temperature is then T bg Th bg R Hr If this building temperature is greater than the maximum allowable temperature then all the solar heat for that hour is not usable The amount of solar heat that is usable is given by aq noQ Ti Qs d Trax Tog Th Th If the building temperature is below the minimum allowable temperature then auxiliary energy is used to raise the temperature The building heating load i e how much auxiliary energy is required to heat the building without the solar heating system is calculated in the same manner as above but without any solar gains It should be noted that the yea
3. After all the parameters have been entered the program calculates the collector heat removal factor for the test values of flow rate and flow path length using the method given in Section 5 2 This value is compared to the value of FR found from the collector Fata term The two values are printed at the terminal At the test condition the calculated value of FR will be either higher or lower than the test value If the difference between the values is greater than 207 the program prints a warning and returns to the input mode The collector heat removal factor is then adjusted for the system flow rate flow path length and duct air leakage The algorithm for adjusting the collector characteristics is given in Section 5 3 If the collector slope or azimuth is different from the value used to calculate the solar radiation in the scratch file then the solar radiation on a tilted surface is recalculated The algorithm for performing this calculation is given in Section 5 4 When the solar radiation and the input parameters are correct the program begins the simulation The first step is to calculate the building heat loss for that hour Obg UA Tog Ta Q g a ig Figure 2 ZEROAIR Program Flow Chart Read Default Data e Modify Input Data Correct Collector Characteristics Calculate solar radiation on tilted surface Is solar radiation on a tilted surface available Start Simulation
4. 1971 1971 1974 1971 1971 1971 1971 1971 1971 1971 1971 1971 1971 1971 1971 1971 1971 1971 o vv vo oO OO OO SF sa OO CO DO SZ OO OC O CO ce Oo amp 12 13 St John s Nfld 47 6 1971 M Gander Nfld 49 0 1971 D Stephenville Nfld 48 5 1971 D Goose Nfld 53 3 1971 M 3 3 Estimation of Building Heat Loss Coefficient For new homes the building heat loss coefficient can be estimated by adding up the heat loss from each building wall window and door and including an estimate of air infiltration The ASHRAE Handbook of Fundamentals and many heating textbooks show how this can be done This calculation is normally done for every house in order to size the furnace If heating bills are available it is easy to estimate the building heat loss coefficient UA using the formula 11600 FC De UA in W C DD HV where FC is the fuel consumption in litres of oil cubic metres of gas or kWhr of electricity Ne is the seasonal furnace efficient typically 0 6 for oil and natural gas and 1 0 for electricity HV is the heating value of fuel oil 25 1 GJ natural gas 27 m GJ electricity 278 kWhr GJ DD is the yearly total of degree days below 18 C in C days Vancouver 3000 Toronto 4000 Ottawa 4600 Fredericton 4600 Winnipeg 5900 Yellowknife 8600 Typical values for the building heat loss coefficient are 100 W C super insulated home 250 W
5. 3 Tutorial Session 3 SYSTEM INPUT PARAMETERS The following sections describe the parameters used in the ZEROAIR computer program The default value for each parameter is included with the definition 3 1 Definition of Input Parameters Cl C2 C3 c4 There are three separate sections of input data C collector data T collector test data L building heating load data The parameters for each of these sections are discussed below Collector Data NUMBER OF COLLECTORS 2 The number of collectors in the solar heating system NUMBER OF COLLECTORS IN SERIES 1 The number of collectors that are connected in series as opposed to parallel COLLECTOR SLOPE DEGREES 45 The angle that the collector is tilted from the horizontal in degrees This parameter must be between 0 and 90 If this parameter is different from the value on the scratch weather file the weather data will automatically be reprocessed COLLECTOR ORIENTATION SOUTH O EAST DEG 0 The number of degrees that the collector is oriented off due south east is positive west is negative This parameter must be between 90 and 90 If this parameter is different from the value on the scratch weather file then the weather data will automatically be reprocessed C5 C6 C7 COLLECTOR FLOW RATE PER UNIT AREA L SEC M2 10 The air flow rate per unit collector area through the collectors for the proposed system in litres per sec per sq
6. C average home 500 W C poorly insulated home 14 4 DESCRIPTION OF PROGRAM OUTPUT 4 1 Thermal Analysis Results The thermal analysis of the system is printed in monthly intervals with a yearly summary printed at the end The results are an estimate of the system performance of a properly designed and installed system The program cannot account for improperly insulated ductwork fan motor failure or other system faults The definition of the seven monthly output values follow SOLAR AVAIL GJ Total solar radiation incident on the collector over the time period in gigajoules SOLAR COLLECT GJ Solar energy converted to heat by the solar collector over the time period SOLAR DELIVER GJ Solar energy delivered to the building that reduces the auxiliary energy consumption SPACE HT LOAD GJ The auxiliary heat required over the time period to space heat the building if there was no solar heating system AUX HEATING GJ Auxiliary energy required to space heat the building over the time period when the solar heating system is used FAN POWER GJ The electrical energy required to operate the collector fan over the time period 15 MAX TEMP C The maximum building temperature over the time period If this value is equal to the maximum allowable building temperature then heat must have been dumped from the building After the monthly totals have been printed the yearly sum of the seven quan
7. collector air leaks out before collector air leaks out after collector Each of these cases is discussed below i Air Leaks In Before Collector In this case air leaks into the collector and out of the building The extra heat lost out the building can be included in the Fn term as follows L m Cp FAU 1 Lp E U R Leaks RL A F where Lp is the ratio of the leakage rate to the collector flow rate In this case the full air flow goes through the collector so there is no change in the Fp or the Feta term ii Air Leaks In After Collector This case is similar to case i except that some of the air does not flow thorugh the collector Thus the collector heat removal factor must be adjusted for this lower flow rate For small changes in mass flow rate 1 i L Ses 3 R Ech Folk R Lieaks R F A 26 Fara 8 Dui Be R Combining cases i and ii gives the collector characteristics for air leakage before and after the collector FU R Lieaks F FA 8 E a 22 EL p Des R c R Freaks Fata R where Lp is one half the ratio of the air leakage rate to collector flow rate and Fe is calculated based on one half the leakage rate iii Air Leaks Out Before Collector If air leaks out of the collector loop then air must leak into the building In this case a reduced flow rate goes through the collector and the air exhausted to the outdoors is at room temperatu
8. the heating load A larger system would be inefficient and therefore expensive The ZEROAIR computer program will provide an accurate estimate of the thermal performance of zero storage solar space heating systems provided that the user supplies system parameters within the program limitations All users should read and understand this manual before using the program 2 THE ZEROAIR COMPUTER PROGRAM 2 1 System Operation A zero storage air based solar space heating system is shown in Figure 1 The system consists of air based solar collectors supply and return ductwork fan and control system In many cases the collectors can be mounted directly on the south wall of a building with no need for collector support racks or supply and return ductwork If collector air is blown directly into the building it may be necessary to install a ceiling fan to mix the building air The control system for this type of system is quite simple There are only two modes of operation system on and system off If the temperature of the collector is greater than that of the building air is circulated through the collectors The fan would continue to operate unti the collector temperature drops below the building temperature or the maximum allowable building temperature is exceeded On spring and fall days when the solar gain exceeds the heating load the system will constantly cycle on and off so as not to exceed the maximum building temperature 2
9. 2 Using the ZEROAIR Program Using the ZEROAIR computer program is relatively easy The program has been written so that the user enters the system description interactively with the computer The program makes some fundamental checks on the suitability of the input parameters If a parameter appears unrealistic a warning is printed although the program accepts the value Before the program can be run hourly weather data solar radiation on a horizontal surface and ambient temperature must be available This data can be obtained from Atmospheric Environment Service The first step in the program execution is to calculate solar radiation on the collector surface and store it in a scratch file During the simulation the program accesses the scratch file If collector slope and orientation remain the same on successive runs the same scratch file is used If the values are changed the scratch file is automatically recalculated Return Duct Solar MN S Radiation ie oe Building Air Based Solar Collector Figure 1 Zero Storage Air Based Solar Space Heating System When the user accesses the program a series of questions concerning the program will have to be answered These questions are shown in Section 2 3 When the questions have been answered the user has the choice of several commands CHANGE DEFAULT LIST MODIFY RUN C or CHANGE D or DEFAULT L or LIST M or MODIFY R or RUN S or STOP T or T
10. CHART 4 0 User s Manual University of Wisconsin Madison EES Report 50 September 25 1980 Duffie and Beckman Solar Engineering of Thermal Processes John Wiley and Sons New York 1980 Orgill J F and Hollands K G T Solar Energy Vol 19 No 2 Correlation Equation for Hourly Diffuse Radiation on a Horizontal Surface Temps R C and Coulson K L Solar Energy Vol 19 No 2 Solar Radiation Incident upon Slopes of Different Orientation Klucher T M Solar Energy Vol 23 No 2 Evaluation of Models to Predict Insulation on Tilted Surfaces 8 34 NOMENCLATURE total collector area area of one collector surface area of fibre matrix collector channel height thermal capacitance of the building specific heat d A KR d collector heat removal factor collector transmission absorption coefficient collector heat loss coefficient measured hourly solar radiation beam hourly solar radiation beam hourly solar radiation on a tilted surface diffuse hourly solar radiation duffuse hourly solar radiation of a tilted surface extraterrestrial hourly solar radiation plate to fluid convective heat transfer coefficient radiative heat transfer coefficient reflected hourly solar radiation solar radiation on the tilted surface total incident solar radiation clearness index length of collector in flow direction ratio of collector loop air leakage to collector flow rate mass flow rate number of air flow p
11. ITLE The use of these commands is discussed below this command is used to change the program input data A list of the input data and their meanings is given in Section 3 1 The command is of the form C or CHANGE Parameter New Value e g C C3 50 Several changes can be made on one line with or without the equal sign e g C C4 0 0 T1 3 this command is used to re initialize all the input parameters to their default values There are no options with this parameter this command is used to list either all the input parameters all the parameters of one section or an individual parameter L or LIST ALL lists all parameters L C lists all collector parameters L C3 lists collector slope this command is used to modify the default collector characteristics i e to change the collector type this command is used to run the program If the option P is used a copy of the output will be sent to the printer If a simulation period other than one year is required the first day of the simulation followed by the length of the simulation should be entered e g RUN or R P 31 28 this would execute the program starting January 31st and run for 28 days A copy of the output would be sent to the printer STOP this command stops the program TITLE this command is used to insert a title into the program output The same title will be printed on every successive run unless it is changed e g TITLE or T THIS IS RUN NUMBER 1 2
12. OLLECTOR LOOF GIF LEAKAGE eee eee eee eee T QG FAN POWER CONSUMPTICIN PER UNIT AREA NAZZ 10 00 Du 30 1 74 Ch ID OH BRI fe E COLLECTOR TEST PATA i EGOS AREA OF ONE CO LECTOR CME ee wee ee re ee ee 2 NUMBER DC COLLECTORS IN SERIES WHEN TESTED sso z FR TALU AGLFHA TEST wc ccc er ee ee er et ee A FR LE W7 UME TEST ce ee ee ee as zo INCIDENT ANGLE MODIFIER 2 2 htt rm rms amp TALL TEST FLOW RATE FER UNIT GRES LA EECHER z TROEEMISSTON ABRSORE TION FRODLHTT 2 2 f 44 e D o RATIO CF APERTURE TO GROSS AREA 2 awa ee ee D o COLLECTOR CHANNEL HEIGHT MMi ee ee ee fy CHD i0 COLLECTOR FLOW CHANNEL LENGTH GP ee ee ee ae 1 00 L HEATING LOAD DATA Li BUILDING HEAT LOSS COEFFICIENT Wie L MINIMOM DAYTIME BUILDING TEMPERATURE Cl eee ne ee LZ MINIMUM NIGHTIME BUILDING TEMPERATURE Chess 4 MAXIMUM ALL OWSELE BUILDING TEMPERATURE CC ee BUILDING THERMAL CAFACITONCE R d 7 DAILY INTERNAL HEAT GAIN MJ DAY nn n S HOURLY INTERNAL HEAT GAIN PROFILE PERCENT i00 02 2 SS OD OO OO O OO 1 50 4 65 7 29 2 47 f 70 A Gr 3 60 5 10 z 70 z 40 z dQ 2 7D Gato 11 460 Fa GO 4 90 2 44 4 65 ZEROAIR Version 1 0 User s Manual August 1983 Assistance and Information K Ford Design Aids Engineer Solar Programs Office Sir Charles Tupper Building Riverside Drive Ottawa KIA 0M2 613 998 3641 a Sn d This document is not a departme
13. assage channels day number of the year Nusselt Number building heat loss internal heat gains due to lights people and windows solar heating contribution ratio of beam radiation on tilted surface to horizontal surface D be 0 w n3 t c a fi fo vi sl sl cl cl sl cl cl Lo om mx 35 Reynolds Number collector slope solar constant temperature of upper and lower plates of the air channel ambient temperature average temperature that collector losses heat from temperature of building collector fluid inlet temperature average collector fluid temperature collector fluid outlet temperature inlet temperature to the building average temperature of the collector absorber plate collector heat loss coefficient total plate to fluid heat transfer coefficient matrix constant matrix constant Greek Symbols Ado lt 0 R E Q o cr 1a solar absorptivity solar declination azimuth angle Tatitude 3 14159 absolute viscosity density Stefan Boltzman constant hour angle transmission absorption product effective transmission absorption product 9 INPUT DATA WORKSHEET Default Value COLLECTOR DATS n r NUMBER DF COLLECTORS cc ee eee euren EE BO Oo NUMBER nC COLLECTORS IN SERTED cece ee ee ee 1 62 COLLECTOR SLOPE DEGREES ea eee eene ntn rr AT GO COLLECTOR ORIENTATION SOLITHzO EAZTst DEZ Q0 COLLECTOR FLOW RATE FER LINTT AREA L EE 10 0 PERCENT C
14. ed using the radiation view factor from the collector to the sky with correction factors for non uniform distribution of diffuse radiation The correction factors for anisotropic diffuse radiation are taken from Temps and Coulson 4 and Klucher 5 The resulting equation is Hoe To 1 F sin s 2 1 F cos o sin e Hy where F 1 H H The reflected solar radiation on the tilted surface H is s H 5 0 92 mH where p is the ground reflectivity The total solar radiation on the tilted surface Hj is the sum of the beam diffuse and reflected solar radiation components Hourly values of total solar radiation on a tilted surface ambient temperature day number and hour number are written to the scratch file When all the data has been processed and written to the scratch file the file is rewound to be ready for the system simulation 3l 6 PROGRAM STRUCTURE The program structure is described in this section Only those individuals interested in modifying the program need read this section The program flow chart is shown in Figure 4 The program consists of a m inline and three subroutines 1 MAINLINE contains the interactive front end for reading and modification of system data 2 WEATH subroutine for converting measured horizontal solar radiation to the tilted surface 3 ZERO subroutine to calculate system performance on an hourly basis 4 FRCALC subroutine to calcu
15. ember 1981 Optimization of Flow Passage Geometry for Air Heating Plate Type Solar Collectors U sheth o pf pf i d At z hoe 21 where h is the radiative heat transfer coefficient between the upper and lower absorber plates if we assume that the inside of the air channel is painted black 2 hy d t To T T5 1 222 where T and T are the temperatures of the upper and lower absorber 1 2 plates e is the convective heat transfer coefficient between the plate and the air stream h d Nu k 2 b where K is the conductivity of air b is the spacing between the upper and lower absorber plates Nu is the Nusselt number for Re 2000 Reynolds number Nu 5 385 0 148 Re b n L where n is the number of air flow passage channels typically equal to 1 L is the collector flow path length for 2000 Re 10000 1 2 0 571 Nu 0 00044 Re 9 37 Re eb n L for 10000 lt Re lt 100000 0 74 O 74 Nu 0 03 Re 0 788 Re br n L L zi where Re 2 T if Re is greater than 100000 the program sets Re equal to 100000 ii Fp for Fibre Matrix Collectors see Figure 3 The estimation of Fp for fibre matrix collectors requires a different formulation for Fg FR can be though of as the ratio of the actual useful Solar Radiation I Nj e Ta Glazings Dee 15 d uu Air Flow In EE Air Flow Out Tei e eme a a Cine Za P i plat Back Insulation Fibre Matrix f
16. ent Service is of two types derived or measured Measured data isas recorded by their monitoring equipment with missing data estimated from the previous day s values Derived data is predicted by using other meteorological data such as rainfall cloud cover etc City Province Latitude Year Solar Rad Deg Derived Measured Victoria B C 48 7 1971 D Prince George B C 53 9 1974 M Vancouver B C 49 2 1971 M Summer land B C 49 6 1971 D Frobisher Bay N W T 63 8 1975 D Resolute N W T 74 7 1971 M Edmonton Alta 53 6 1971 M Medicine Hat Alta 50 0 1971 D Uranium City Sask 59 6 1971 D Swift Current Sask 50 3 1971 D Saskatoon Sask 52 2 1971 D Churchill Brandon Winnipeg The Pas Thunder Bay Sault Ste Marie Sudbury Kapuskasing Kingston Muskoka Windsor London Toronto Ottawa Montreal Sept Iles Quebec Sherbrooke Riviere du Loop Bagotville Val D Or Fredericton Charlo Chatham Moncton St John Charlottetown Truro Halifax Sydney Yarmouth Man Man Man Man Ont Ont Ont Ont Ont Ont Ont Ont Ont Ont Que Que Que Que Que Que Que N B N B N B N B N B P E I N S N S N S N S 58 8 49 9 49 9 53 8 48 4 46 5 46 5 49 4 44 2 45 0 42 3 43 0 43 7 45 4 45 5 50 2 46 8 45 4 47 8 48 3 48 0 45 9 48 0 47 0 46 1 45 3 46 3 45 4 44 7 46 2 43 8 1975 1971 1971 1971 1971 1971 1971 1966 1971 1971 1971 1971 1971
17. er coefficient Tem is the average fluid temperature 24 Estimating Uo for fibre matrix collectors is much more difficult than for parallel plate collectors The reference used for these equations is Kays W and London A L Compact Heat Exchangers Second Edition McGraw Hill New York 1964 pg 129 For fibre matrices Kays and London give equations of the form A Uy x tm SERA Bei pr j c where Pr is the Prandt number where x and y are constants dependent on the type and shape of the matrix For a similar type of fibre matrix Kays and London give x 1 3 y 0 45 By knowing the average fibre matrix diameter and the fibre matrix mass the ratio of heat transfer to collector area can be calculated For the Amherst collector A _fm ao Ac 5 3 Algorithm to Correct for Collector Loop Air Leakage All ductwork leaks air While air leakage is not critical for indoor ductwork it can seriously decrease performance for outdoor ductwork The collector performance characteristics can be modified to account for this decrease in performance The algorithm used in the program is taken from reference 1 with extensions for the case of air leaking out of the collector loop It will be assumed that air leaks are evenly divided between the ductwork 25 before the collector and the ductwork after the collector There are four possible cases for air leakage air leaks in before collector air leaks in after
18. g Load Data L1 L2 L3 L4 BUILDING HEAT LOSS COEFFICIENT W C 300 The heat loss coefficient or UA of the building Section 3 3 gives a method of estimating this parameter MINIMUM DAYTIME BUILDING TEMPERATURE C 20 The minimum allowable temperature of the building during the day i e the furnace thermostat set point MINIMUM NIGHTTIME BUILDING TEMPERATURE C 16 The minimum allowable temperature of the building during the night i e the furnace thermostat set point at night MAXIMUM ALLOWABLE BUILDING TEMPERATURE C 25 The maximum desired building temperature That is the temperature above which the building s occupants would be uncomfortable 11 L5 BUILDING THERMAL CAPACITANCE MJ C The thermal or heat capacitance of the building Most buildings have a thermal capacitance of 0 1 MJ C for every square metre of floor area although full warehouses would be slightly higher L6 DAILY INTERNAL HEAT GAIN KJ DAY 3000 The average daily internal heat gains from lights people and solar gains through windows in KJ L7 HOURLY INTERNAL HEAT GAIN PROFILE PERCENT 24 hourly values of the percent of the daily internal heat gain occurring within that hour The first value is for the hour 12 midnight to l a m 3 2 Weather Data At present there is weather data for 46 cities that can be used by the program These cities are tabulated below The solar radiation data as supplied by Atmospheric Environm
19. ient temperature in C The extraterrestrial solar radiation on a horizontal surface is calculated by LN 5c cos o where cos e_ is cosine of the zenith angle angle between the beam and the vertical cos e cos cos 8 cos w sine sins 29 is the latitude of the location w is the hour angle The diffuse solar radiation Hy can be estimated using a correlation by Orgill and Hollands 3 Ha 0 1769 H if 0 75 Ky Hy 1 55699 1 84013 Kr H if 0 35 lt Gd 0 75 Ha 1 0 248857 Ky H if 0 0 s Kr s 0 35 where H is the measured hourly solar radiation K is the ratio of measured solar radiation to the extraterrestrial solar radiation H Hex The beam radiation H is simply the tota measured solar radiation minus the diffuse radiation H H H b d The next step is to calculate the ratio of beam radiation on the tilted surface to that on the horizontal surface R R cos 07 cos e where cos 84 is the cosine of the angle of incidence of beam radiation between the beam and the normal to the surface cos o sin s sin cos s cos 8 cos cos s cos w cos 5 sin sin s cos y cos w cos s sin s sin y sin w y is the azimuth angle measured from south east is positive west is negative 30 Thus the beam solar radiation on the tilted surface is H R H bT b b The diffuse solar radiation component on the tilted surface is estimat
20. late the collector heat removal factor Fp for a given flow rate Six file definitions must be made before the program can be run Terminal Read Unit 5 is the device used for data input The program will send all questions and prompts to this device Printer Unit 7 is the device that receives the printed output i e a printer If a send and receive printer is being used unit 7 need not be defined Weather Data Unit 1 is the file containing the TRNSYS compatible weather data The data must be written in the format 2X I2 2X 12 2X I2 F3 1 I3 F6 1 and contain month number day number hour number ground reflectivity ambient temperature C and solar radiation on a horizontal surface W m Processed Data Unit 19 is the file that is created by the program containing the solar radiation on the tilted surface and ambient temperature Terminal Write Unit 6 is the device that receives questions from the program concerning the input of data Default Data Unit 4 is the file containing program default data The ZEROAIR program is written in FORTRAN 77 In order to compile this program on your system it must be able to handle this improved version of FORTRAN 32 Input from Terminal Weather Data FRCALC ERN ZERO nd WEATH Ga Processed Data Default Data MAINLINE Printer Figure 4 ZEROAIR Program Structure 33 REFERENCES Mitchell J C et al F
21. ntal publication Do not cite as a reference or catalogue in a library User Responsibility Users are responsible for the validity of the information generated by ZEROAIR Version 1 0 Consequently the program should not be used by those who do not comprehend the technical field to which this program applies Neither Public Works Canada nor any person acting on behalf of the department makes any warranty or assumes any responsibility for accuracy completeness or usefulness of any information generated by this program
22. o Figure 3 Schematic of Fibre Matrix Solar Collector 22 23 energy to the useful energy if the absorber plate were at the fluid inlet temperature Tei For a ventilation collector F is e ta l Ui Ta ve Tei zy U Tave y Tei r 1a I U Ces Teil ta l where T is the average temperature that the collector loses heat at This temperature is normally the average plate temperature however a fibre matrix collector has inlet air blowing across the lower glazing thus loses heat from a lower temperature For a fibre matrix collector ae is Tave S hy Tplate hor Te J h hoe where h is the convective heat transfer coefficient between the lower glazing and the air stream h is the radiative heat transfer coefficient between the fibre matrix and the lower glazing Because of the nature of the fibre matrix h is a weighted average of the value of h for each layer of fibres with the top layer having a weighting of 1 and the bottom layer having a weighting of 0 By integrating the values for h over the depth of the matrix bh can be approximated by h hu 3 h 9 6 where hey T4 To T T 1 222 h o T el Teo T5 1 222 r2 fo is the temperature of the top of the fibre matrix is the temperature of the lower glazing 1 T 1 2 The average fibre matrix plate temperature can be calculated by T Tem Qu U plate where Uo is the fibre matrix to air heat transf
23. ossible to estimate the amount of diffuse solar radiation from the ratio of the measured solar radiation to the extraterrestrial solar radiation If this ratio is low then the solar radiation must be mostly diffuse if this ratio is high the solar radiation must be mostly beam When the beam and diffuse solar radiation components are known standard geometric relations can be used to estimate the solar radiation components on a tilted surface When estimating solar radiation on a tilted surface a third component is introduced reflected radiation Reflected radiation can be estimated from the beam radiation and the ground albedo or reflectivity The program equations and execution procedure are given below 28 At the start of each day the solar constant and the earth s solar declination are calculated The solar constant is given by Sc 4871 0 1 0 33 cos 21N 365 in KJ hr m where N is the day number Jan 1 is 1 The earth s declination is given by 23 45 21 sin 2 284 N 365 in radians 360 360 These values are assumed constant for each day All other calculations are made on an hourly basis The first step is to read the measured weather values from the data file For each hour the weather data file contains six values in the following order 1 month number 1 12 2 day number 1 31 3 hour number 1 24 4 ground reflectivity 5 solar radiation on a horizontal surface in Watts m 6 amb
24. re This case has the same effect on collector characteristics as in case ii iv Air Leaks Out After Collector This case is similar to case i except that the air exhausted to the outdoors is at the collector outlet temperature as opposed to the building temperature The collector characteristics for this case are Feo z Faro 1 Lp leaks m Cp L 1 Lp R F U FU R Leaks RL 3 Combining cases iii and iv gives the case of equal air leaks out before and after the collector 27 FR 2Lp m Cp leaks F A r c 1 E R FR leaks 7 ile 1 Lp R where Lp is one half the ratio of the air leakage rate to collector flow rate and FR is calculated based on one half the leakage rate 5 4 Algorithm to Process Weather Data Most Canadian weather stations measure only total solar radiation on a horizontal surface Most solar collectors however are tilted toward the sun to increase the incident solar radiation The program determines hourly values of total solar radiation beam diffuse and reflected on a tilted surface and stores the values in a scratch file The algorithm for converting horizontal solar radiation to tilted solar radiation is similar to the method used in Solar Engineering of Thermal Processes by Duffie and Beckman 2 In order to estimate the solar radiation on a tilted surface it is necessary to split the total measured horizontal solar radiation into its two components beam and diffuse It is p
25. results are not available use 0 10 for single glazed collectors and 0 17 for double glazed collectors T6 T7 T8 T9 T10 10 COLL TEST FLOW RATE PER UNIT AREA L SEC M2 10 The air flow rate through the collector at test conditions in litres per second per square metre of collector TRANSMISSION ABSORPTION PRODUCT 0 9 The ta effective of the collector This can be estimated as 1 01 times ta for a single glazed collector where t is the glazing solar transmission and a is absorber solar absorptivity RATIO OF COLLECTOR APERTURE TO GROSS AREA 0 9 The ratio of the collector aperture area i e window area to the gross area Typically this value is usually close to 0 9 actual values can be obtained from collector data sheets COLLECTOR FLOW CHANNEL HEIGHT MM 6 The spacing between the upper and lower absorber plate in millimetres For a curved upper absorber use the average spacing In general decreasing the flow channel height increases the collector Fp although this will result in a higher collector pressure drop COLLECTOR FLOW CHANNEL LENGTH PER COLLECTOR M 1 The distance or length that the air stream is in contact with the absorber plate for one collector In most collectors this will be the length of collector in the flow direction In some cases however collectors are designed so that the contact length is much shorter than the collector such as in the overlapped glass plate collector Heatin
26. rly building heating load is not the sum of the hourly building heat losses from the solar heated building The solar building will be at a higher temperature and thus have higher heat losses than the building with no solar system Since we are interested in the energy savings as a result of installing 20 a solar heating system our base energy consumption should be that of the existing or non solar building The hourly values of the above energy flows are summed and monthly and yearly totals printed A full description of the output is given in Section 4 5 2 Algorithm for the Calculation of Fn Two separate algorithms are used for the calculation of Fp one for parallel plate solar collectors and one for fibre matrix solar collectors It is important to note that a correction on Fp for the number of collectors in series is not necessary provided that the mass flow per unit area is kept constant i Fp for Parallel Plate Solar Collectors is given by F MO 1 exp F U i Cp a where F HAD Ui All of the variables are constant except for m mass flow rate per unit area and Uo the total plate to fluid heat transfer coefficient m is given each hour by the air flow rate schedule thus a new value of Uo must be calculated for each hour H depends on the collector design The equations for Uo given below were taken from Hollands K G T and Shewen E C Journal of Solar Energy Engineering Vol 103 No 4 Nov
27. tities is printed A summary of energy use and savings is then printed in gigajoules The ENERGY SAVING is the percent reduction in auxiliary energy use attributable to the addition of the solar heating system i e percent solar It is defined as 100 Space Heating Load Aux Heating Fan Power Space Heating Load Energy Saving 42 AVERAGE SYSTEM EFFICIENCY Z is the solar contribution divided by the solar radiation over the simulation period It is important to note that if the daily air flow schedule is very short this value will be low regardless of the collector performance curve SOLAR CONTRIBUTION PER SQUARE METRE is the solar contribution divided by the collector area over the simulation period A good application of a zero storage solar space heating system would have a value of over 1 0 GJ m yr 16 5 PROGRAM ALGORITHM 5 1 Overview of Program Operation The ZEROAIR computer program calculates the performance of zero storage solar space heating systems on an hour by hour basis The basic assumption of the program is that for the purpose of calculating performance all variables including solar radiation ambient temperature and building heat loss can be considered constant for each hour The program calculation flow chart is shown in Figure 2 The first step in the program is the input and modification of the program parameters in an interactive manner Section 3 gives a full description of the input parameters
28. uare metre of collector PERCENT COLLECTOR LOOP AIR LEAKAGE 5 Percent of the collector flow rate that leaks into the collector loop i e collector under negative pressure For a collector loop under positive pressure air leaks out use a negative percentage A well designed and installed system should have a leakage rate of under 10 FAN POWER CONSUMPTION PER UNIT AREA W M2 10 The energy required to operate the collector fan in watts per square metre of collector Collector Test Data The program contains test results for three air based solar collectors effective Jan 24 1983 Amherst 200 Solartech Solair and Watershed A 100 These test results can be updated or other test results added H T2 T3 T4 T5 GROSS AREA OF ONE COLLECTOR M2 2 The gross or outside area of one collector in square metres NUMBER OF COLLECTORS IN SERIES WHEN TESTED 1 Number of collectors connected in series when it was tested typically one FR TAU ALPHA TEST 0 5 The Faro of the collector when tested by a certified laboratory based on gross collector area l FR UL W M C TEST 4 0 The Poli of the collector when tested by a certified laboratory based on gross collector area in W m C INCIDENT ANGLE MODIFIER 0 1 Coefficient that reduces collector solar transmission for incident angles off the normal The value for this coefficient bo is obtainable from collector data sheets and is usually negative If test
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