TYPE 204: UNGLAZED TRANSPIRED COLLECTOR SYSTEM written by David Summers, Solar Energy Lab, University of Wisconsin - Madison for M.S. thesis, December 1995 Unglazed transpired collectors (UTCs) consist of a perforated, solar-absorbing plate mounted on a large south-facing wall. Air is drawn through the holes in the plate, into the plenum, and finally into the building. This component models a UTC system. The entire system includes the UTC plate and the building on which it is mounted. The basic energy balances are solved and the energy savings is calculated every time step for which the UTC system is operating. Nomenclature absor - collector plate absorptivity aircp - specific heat (kJ/kg-C) airden - density (kg/m3) area - total collector area (m2) d - hole diameter (m) effhx - heat exchanger effectiveness of collector emisc - collector plate emissivity emisw - outside wall surface emissivity flow1 - mass flow rate of air supply from UTC system (m3/hr) gamma - fraction of UTC system supply air that is outdoor air hdwall - coefficient for conduction through the wall (kJ/hr-m2-C) hvcol - coefficient for convection from the collector to the air (kJ/hr-m2-C) hvwall - coefficient for convection from the outside wall surface to the air (kJ/hr-m2-C) nud - Nusselt number where hole diameter is the characteristic length p - hole pitch (m) por - collector porosity qabs - absorbed solar heat rate (kJ/hr) qaux - auxiliary heat rate (kJ/hr) qdwall - conduction rate through the wall (kJ/hr) qrcol - radiation rate from the collector to the surroundings (kJ/hr) qrwall - radiation rate from the outside wall surface to the back of the collector (kJ/hr) qsave - saved energy rate (kJ/hr) qtrad - traditional heating system heat rate (kJ/hr) qu - useful energy rate (kJ/hr) qvcol - convection rate from the collector to the air (kJ/hr) qvwall - convection rate from the outside wall surface to the air (kJ/hr) rad - incident solar radiation on the collector surface (kJ/hr-m2) red - Reynolds number where hole diameter is the characteristic length sb - Stefan-Boltzmann constant (kJ/hr-m2-K4) surfa - collector surface area (m2) = (1-por)*area tamb - ambient air temperature (C) tcol - collector plate temperature (C) tmix - mixed air temperature (C) tout - collector outlet air temperature (C) tplen - plenum air temperature (C) troom - room air temperature (C) tsup - supply air temperature (C) tsur - radiative surroundings temperature (C) twall - outside wall surface temperature (C) The first step in predicting the thermal performance of the UTC system is to calculate the outlet air temperature from the collector, tout. There are four fundamental energy balance equations that are solved to find tout. gamma * flow1 * airden * aircp * (tplen - tamb) = qvcol gamma * flow1 * airden * aircp * (tout - tplen) = qvwall qdwall = qvwall + qrwall qabs + qrwall = qvcol + qrcol The rate equations for the energy flows are necessary to solve the energy balance equations. For convection from the collector to the air, an empirical heat transfer correlation is used [Kutscher, 1992]. nud = 2.75 * (p/d)**(-1.2) * red**0.43 This correlation determines the Nusselt number based on hole diameter that is used to find hvcol. The heat exchanger effectiveness of the collector is calculated. effhx = 1 - exp( (hvcol * surfa) / (gamma * flow1 * airden * aircp) ) This effectiveness is used in the relation between the plenum air temperature and the collector temperature. effhx = ( tplen - tamb ) / ( tcol - tamb ) This equation is effectively a rate equation for qvcol. The following rate equations are also used with the energy balances. qvwall = hvwall * area * ( twall - tplen ) qdwall = hdwall * area * ( troom - twall ) qrwall = sb * area * ( twall**4 - tcol**4 ) / ( 1/emisw + 1/emisc - 1 ) qabs = absor * rad * surfa qrcol = emisc * sb * surfa * ( tcol**4 - tsur**4 ) The outlet air from the collector is mixed with recirculated air from the building. tmix = gamma*tout + (1-gamma)*troom The mixed air is heated to the necessary supply temperature to meet the heating load. qaux = flow1 * airden * aircp * (tsup - tmix) The recirculation damper varies gamma, the fraction of the supply air that is drawn from the outside through the collector, such that the auxiliary energy is minimized. There are three energy savings mechanisms for a UTC system: active solar gain, recaptured wall loss, and reduced wall loss. However, the energy savings of the UTC system is not simply the sum of these three components. Fundamentally, the energy savings is the reduction in the heat required from a traditional system, which translates into a reduction of the heating bill. The heat required from an auxiliary unit of a UTC system is less than the heat required from a traditional heating system. qsave = qtrad - qaux The energy savings never exceeds the heating requirements of the building with a traditional system. The following 14 subroutines and functions are from LAPACK, a linear algebra package. They consist of DGESV, a general linear matrix solver, and all of its dependents. They are (in order): DGESV, DGETRF, DETRS, DGETF2, DGEMM, DGER, DLASWP, DTRSM, DSCAL, DSWAP, IDAMAX, ILAENV, LSAME, XERBLA DGESV is called once in the subroutine utcsolve. If the user has another matrix solver which performs faster, they may call it from utcsolve instead of DGESV without harming anything in the UTC system component. If the faster solver returns the solution in [x], make sure the lines [x]=[b] are commented out just after the call. Parameters: 1. Collector area (m2) 2. Collector height (m) 3. Collector hole diameter (m) 4. Collector hole pitch, distance between centers of holes (m) 5. Collector emissivity 6. Collector absorptivity 7. Plenum depth (m) 8. Emissivity of the wall behind the collector 9. R-value of the wall behind the collector (C-m2-hr/kJ) 10. Total UA-value of the building walls and roof (kJ/hr-C) 11. Room air temperature (C) 12. Ambient air temperature above which the summer bypass damper is opened (C) 13. Maximum auxiliary heat rate available (kJ/hr) 14. Night bypass = 0 if bypass not automatically opened at night = 1 if bypass automatically opened at night Inputs: 1. Month of year 2. Hour of month 3. Radiation incident on the collector (kJ/m2) 4. Ambient temperature (C) 5. Sky temperature (C) 6. Atmospheric pressure (kPa) 7. Internal gains due to people, equipment, etc. (kJ/hr) 8. Supply air flow rate from collector air-handling units (m3/hr) 9. Minimum outdoor air flow rate through collector/summer bypass damper (m3/hr) 10. Supply air flow rate from no-collector air-handling units (m3/hr) 11. Outdoor air flow rate through no collector (m3/hr) Outputs: 1. Plenum air temperature (C) 2. Collector outlet air temperature (C) 3. Mixed air temperature (C) 4. Supply air temperature (C) 5. Collector surface temperature (C) 6. Energy savings rate (kJ/hr) 7. Convection from collector (kJ/hr) 8. Convection from wall (kJ/hr) 9. Radiation from collector (kJ/hr) 10. Radiation from wall (kJ/hr) 11. Conduction through wall (kJ/hr) 12. Reduced conduction through wall because of collector (kJ/hr) 13. Absorbed energy rate (kJ/hr) 14. Auxiliary heating rate (kJ/hr) 15. Outdoor air flow rate through collector/summer bypass damper (m3/hr) 16. Heat exchanger effectiveness of collector (C) 17. Solar efficiency of the collector 18. Pressure drop across collector plate (kPa) 19. Bypass damper position = 0.0 if open = 1.0 if closed 20. Heat rate supplied by a traditional heating system (kJ/hr) 21. Additional fan power required (kJ/hr) Sample TRNSYS Deck: ASSIGN commer.lst 6 ASSIGN commer.out 11 ASSIGN commert.plt 12 ASSIGN commerq.plt 13 ASSIGN MADISN.WI 14 ASSIGN MADISN.ALL 15 ASSIGN COMMER.DAT 16 * LOGICAL UNIT 14 = SEL TMY DATA FILE. * LOGICAL UNIT 15 = FULL TMY DATA FILE. * LOGICAL UNIT 16 = HOURLY DATA ON INTERNAL GAINS AND AIR FLOW RATES. SIMULATION 1 8760 1 WIDTH 72 UNIT 9 TYPE 9 DATA READER PARAMETERS 26 *MODE N TD 21*(CONVERSION FACTORS) LOGICAL-UNIT FRMT -2 8 1 -1 1 0 -2 1 0 -3 1 0 -4 1 0 5 0.1 0 6 0.0001 0 8 10 0 14 -1 *OUTPUTS 8 *MONTH HR IDN I TDB HUMRAT WINDVEL WINDDIR UNIT 10 TYPE 9 DATA READER 2 PARAMETERS 35 *MODE N TD 30*(CONVERSION FACTORS) LOGICAL-UNIT FRMT -2 10 1 -1 1 0 -2 1 0 -3 1 0 -4 1 0 -5 1 0 -6 1 0 -7 1 0 -8 1 0 -9 1 0 -10 1 0 15 1 (72X, F4.0, 1X, 4F1.0, 17X, F5.0, 4X, F4.0, 7X, 2F2.0, F1.0) *OUTPUTS 10 *CEILING SC(1-4) PATM TDP NTOT NOPAQ SNOW UNIT 11 TYPE 9 DATA READER 3 PARAMETERS 5 *MODE N TD LOGICAL-UNIT FRMT -2 4 1 16 -1 *OUTPUTS 4 *HR LSENSIBLE FLOW1 MINOUT1 EQUATIONS 2 SNOW = [69,3] RHOG = 0.2 + SNOW * 0.5 UNIT 16 TYPE 16 RADIATION PROCESSOR PARAMETERS 9 *MODE TRACK-MODE SURF-MODE DAY LAT SC SHFT SMOOTH IE 7 1 1 1 43.1 4871 0 0 -1 INPUTS 7 *I IDN TD1 TD2 RHOG SLOPE AZIMUTH 9,4 9,3 9,19 9,20 RHOG 0,0 0,0 0.0 0.0 0.0 1.0 0.2 90.0 0.0 UNIT 69 TYPE 69 TSKY ESTIMATOR INPUTS 12 *CEILING SC(1-4) PATM TDP NTOT NOPAQ SNOW HOUR TAMB 10,1 10,2 10,3 10,4 10,5 10,6 10,7 10,8 10,9 10,10 9,2 9,5 7777.0 0.0 0.0 0.0 0.0 10125.0 0.0 0.0 0.0 0.0 0.0 0.0 *OUTPUTS 3 *TSKY PATM SNOW UNIT 71 TYPE 71 TRANSPIRED COLLECTOR PARAMETERS 14 *AREA HT DIAM PITCH EMISC ABSOR DEPTH EMISW RWALL UA *TROOM TBYPASS QMAX NITEBP 50.0 2.74 0.0009 0.01 0.9 0.9 0.08 0.9 0.489 7197.0 20.0 15.0 1000000000.0 1.0 INPUTS 11 *MONTH HR RAD TAMB TSKY PATM GAIN FLOW1 MINOUT1 FLOW2 *OUT2 9,1 9,2 16,6 9,5 69,1 69,2 11,2 11,3 11,4 0,0 0,0 0.0 0.0 0.0 0.0 0.0 101.3 0.0 0.0 0.0 30000.0 0.0 *OUTPUTS 21 *TPLENUM TOUT TMIX TSUP TCOL QSAVE QVCOL QVWALL QRCOL QRWALL *QDWALL QRED QABS QAUX OUTFLOW EFFHX SOLEFF DELP BYPASS QTRAD *FANPW UNIT 24 TYPE 24 INTEGRATOR PARAMETERS 1 *INTERVAL 8760 INPUTS 8 *QSAVE QVCOL QVWALL QRED QABS QAUX QTRAD HR 71,6 71,7 71,8 71,12 71,13 71,14 71,20 71,19 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 UNIT 25 TYPE 25 PRINTER PARAMETERS 5 *STEP START STOP LOGICAL-UNIT UNITS 8760 1 8760 11 1 INPUTS 8 24,1 24,2 24,3 24,4 24,5 24,6 24,7 24,8 QSAVE QVCOL QVWALL QRED QABS QAUX QTRAD HR KJ KJ KJ KJ KJ KJ KJ HR UNIT 26 TYPE 25 PRINTER 2 PARAMETERS 5 *STEP START STOP LOGICAL-UNIT UNITS 1 1 8760 12 2 INPUTS 10 9,5 69,1 71,1 71,2 71,4 71,5 71,15 71,16 71,17 16,6 TAMB TSKY TPLENUM TOUT TSUP TCOL OUTFLOW EFFHX SOLEFF RAD UNIT 27 TYPE 25 PRINTER 3 PARAMETERS 5 *STEP START STOP LOGICAL-UNIT UNITS 1 1 8760 13 2 INPUTS 10 71,6 71,7 71,8 71,9 71,10 71,11 71,12 71,13 71,14 71,18 QSAVE QVCOL QVWALL QRCOL QRWALL QDWALL QRED QABS QAUX DELP END References: 1. Summers, David N., Thermal Simulation and Economic Assessment of Unglazed Transpired Collectors, M.S. Thesis in Mechanical Engineering, University of Wisconsin-Madison, 1995. 2. Kutscher, Charles F., An Investigation of Heat Transfer for Air Flow Through Low Porosity Perforated Plates, Ph.D. Thesis in Mechanical Engineering, University of Colorado, 1992.