1、542 2010 ASHRAEThis paper is based on findings resulting from ASHRAE Research Project RP-1326.ABSTRACTThis paper provides an overview of recent refinements andimprovements to the Radiant Time Series Method (RTSM) aspart of 1326-RP. These refinements and improvements includeupdating the fenestration
2、model to be consistent with currentlyavailable manufacturers data, development of a correction forheat losses that can be significant in buildings with high percent-ages of single-pane glazing on the faade, and development ofcompact procedures for computing radiant time factors (RTF)and conduction t
3、ime series factors (CTSF). In addition, verifi-cation of the RTSM against the Heat Balance Method (HBM)with a large parametric study is also summarized. INTRODUCTIONThe Radiant Time Series Method (RTSM) is a simplifiedcooling load calculation procedure, originally developed (Spitleret al. 1997) to p
4、rovide a rigorously-derived approximation to theHeat Balance Method (HBM) (Pedersen et al. 1997). It effec-tively replaced all other simplified (non-heat-balance) methodssuch as the Cooling Load Temperature Difference/Solar CoolingLoad/Cooling Load Factor Method (CLTD/SCL/CLF), the TotalEquivalent T
5、emperature Difference/Time Averaging Method(TETD/TAM), and the Transfer Function Method (TFM.)Compared to the methods previously available, the RTSMis quite similar to the TFM. (Spitler and Fisher 1999) Like theTFM, the RTSM may be classified as a two-step method heatgains are computed first, then c
6、ooling loads. Both methodscompute loads for a 24-hour design day. In the TFM, conduc-tion heat gains were computed with conduction transfer func-tions (CTF) and cooling loads were computed with weightingfactors (WF); in both cases, iteration was needed to arrive atthe solution for a single day. The
7、most important differencebetween the two methods is that the RTSM eliminated theneed for iterative solutions of conduction heat gains and cool-ing loads by assuming steady periodic boundary conditionsand then deriving 24-term response factor series. For conduc-tion heat gains, a 24-term series of pe
8、riodic response factors(PRF) related the conduction heat gain to the 24 hourly sol-airtemperatures and a constant room air temperature. The peri-odic response factors were later replaced with conduction timeseries factors (CTSF), which non-dimensionalize the PRF bydividing by the U-factor. For deter
9、mination of cooling loadsfrom heat gains, a 24-term series of radiant time factors (RTF)were derived. Elimination of the need for iteration made theRTSM well-suited for spreadsheet application.For the TFM, CTF and WF were available from electronicdatabases (Falconer et al. 1993) and printed tables.
10、For theRTSM, the Cooling and Heating Load Calculation Principlesbook (Pedersen et al. 1998) (Pedersen, et al. 1998) was accom-panied by an HBM computer program that could calculate PRFand RTF. Printed tables of select PRF and RTF were later devel-oped (Spitler and Fisher 1999; ASHRAE 2001). For both
11、 theTFM and RTSM, pre-tabulated factors for conduction heat gainand cooling load calculations require the user to select walltypes or zone types that most closely match the actual wall typeor zone type. What “most closely matches” may not be clear inall cases, even to experienced designers. Use of a
12、 separatecomputer program to determine PRF, CTSF, and RTF, whichmust then be input to a spreadsheet is also less than desirable.Therefore, one improvement to the method has been develop-ment of compact procedures for computing CTSF and RTF.Refinements and Improvements to the Radiant Time Series Meth
13、od Jeffrey D. Spitler, PhD, PE Bereket A. Nigusse, PhDFellow ASHRAE Associate Member ASHRAEJeffrey D. Spitler is Regents Professor and C.M. Leonard Professor in the School of Mechanical and Aerospace Engineering, Oklahoma StateUniversity, Stillwater, OK. Bereket A. Nigusse is an associate at Florida
14、 Solar Energy Center, Cocoa, FL.OR-10-057 (RP-1326) 2010, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions 2010, Vol. 116, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either
15、 print or digital form is not permitted without ASHRAEs prior written permission. ASHRAE Transactions 543Since the original development of the RTSM, solar heatgain coefficients (SHGC) have replaced shading coefficients(SC) as the key figure of merit characterizing window perfor-mance. Therefore, the
16、 fenestration model of the RTSM wasupdated to utilize SHGC. Shading coefficients gave transmit-ted solar radiation and inward-flowing absorbed solar radia-tion as separate quantities; each of which in the RTSM haddifferent recommended values of radiant fraction. SinceSHGC give the total window heat
17、gain due to solar radiation,including both transmitted solar radiation and inward-flow-ing absorbed solar radiation in one quantity, a new recom-mendation for radiant fractions was developed based on alarge parametric study.As shown by Rees, et al. (1998), the RTSM, like the TFM,generally showed a s
18、mall amount of overprediction of peakcooling load compared to the HBM. As both the TFM and theRTSM are approximations to the HBM, it is generally desir-able that any inaccuracies result in overprediction rather thanunderprediction. However, for rooms with high percentages ofthe exterior faade covere
19、d with single-pane glass, the over-prediction can be significant, exceeding 40% in extreme cases,in cooler climates where the room geometry approaches thatof a vertical solar collector. Rees, et al. (1998) demonstratedfor one extreme case with 37% peak cooling load overpredic-tion that about 80% of
20、the overprediction was due to heat gainsthat entered the room but that were then lost through thesingle-pane glass. Therefore, one refinement to the RTSMdescribed here is a correction factor that can be applied forrooms where significant overprediction is possibility.Finally, performance of the RTSM
21、 performance is veri-fied against the HBM for a large number of cases with a para-metric study. The study and results are described briefly inthis paper.COMPACT CTSF AND RTF GENERATIONAll simplified cooling load calculation procedures rely onsome type of pre-calculated factors to compute conduction
22、heatgains and cooling loads. Prior to the advent of the RTSM, theCooling Load Temperature Difference / Solar Cooling Load /Cooling Load Factor Method (CLTD/SCL/CLFM) relied ontabulated CLTDs to determine the cooling load resulting fromconduction heat gain, tabulated CLFs to estimate cooling loadsres
23、ulting from internal heat gains, and SCLs to estimate cool-ing loads resulting from solar heat gains. The Transfer FunctionMethod (TFM) relied on tabulated conduction transfer func-tions (CTFs) to estimate conduction heat gain and weightingfactors to convert all types of heating gains to cooling loa
24、ds.The last ASHRAE load calculation manual to feature theCLTD/SCL/CLFM and TFM (McQuiston and Spitler 1992),was accompanied by software that could look up CTFs andWFs from a database developed by Falconer, et al. (1993). Soft-ware that could compute CLTDs, SCLs and CLFs, using thedatabase CTFs and W
25、Fs also accompanied the manual. Inevery case, some judgment is required on the part of the user tomatch actual wall constructions or actual room constructions tothose tabulated in the database.Although tabulated values may be useful for many cases,it is highly desirable to have the capability to com
26、pute wallresponse factors, CTSF, and room response factors, RTF,based on physical descriptions of the wall and room, respec-tively. As the RTSM is intended as a spreadsheet application,it is also desirable that the CTSF and RTF be computable bythe spreadsheet rather than an external program. As part
27、 of thisproject, the first approach that was attempted involved the useof Fortran programs, adapted from the ASHRAE Load Calcu-lations Toolkit (Pedersen et al. 2001), and compiled asdynamic linked libraries (DLLs) that could be called from thespreadsheet. Initial testing of this approach revealed th
28、at thespeed of computation was excellent, but occasional problemswith outside users of the software being unable to get the DLLsto work lead us to abandon this approach. Instead, compact procedures were developed and imple-mented in the macro language native to Microsoft Excel,Visual Basic for Appli
29、cations. These procedures are describedin detail by Nigusse (2007). A brief description follows here. Compact CTSF GenerationConduction time series factors (CTSF) are determinedwith a one-dimensional finite volume method (FVM) model.The user-provided layer-by-layer description is divided into agrid
30、with six volumes per layer. Time steps are fixed at 60seconds. The FVM model of the wall is pulsed with a unit heatgain triangular temperature pulse at the exterior surface. Thehourly conduction heat gain at the interior surface forms a setof response factors. These response factors are combined(Spi
31、tler et al. 1997) to give PRF, then divided by U to giveCTSF. As shown by Nigusse (2007), for 83 typical wall androof constructions, the maximum difference in peak conduc-tion heat gain computed with CTSF generated by this proce-dure and CTSF generated by the state space method (Seem etal. 1989) pro
32、vided with the ASHRAE Loads Toolkit is 2.2%;the average difference is 0.03%. More refined gridding proce-dures might be introduced to improve the accuracy of themethod, but the current accuracy is sufficient for cooling loadcalculation procedures, where conduction heat gains almostalways make up onl
33、y a small fraction of the peak cooling load.The 1-d FVM procedure has the further advantage ofbeing very compact. The procedure is implemented in about500 lines of VBA or F90 code, compared to about 2000 linesof F90 code used to implement the state-space method. Compact RTF GenerationSimilar to the
34、situation with CTSF, it is convenient to havea procedure for generating RTF within the spreadsheet. Inorder to make this a reality, a new RTF generation procedurewas developed that is much simpler than the full heat balancemethod (HBM) utilized in HBFORT. The so-called “reducedheat balance method” (
35、RHBM) requires only inside surfaceheat balance equations and takes advantage of the periodicityof the problem. The RHBM eliminates the following proce-dures that are part of the full heat balance method: outside 2010, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (w
36、ww.ashrae.org). Published in ASHRAE Transactions 2010, Vol. 116, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAEs prior written permission. 544 ASHRAE Transactionssurface heat balance, solar radiati
37、on calculations, shadingcalculations, infiltration and ventilation.A further simplification tested for the RHBM and foundto work well is the use of a fixed radiation heat transfer coef-ficient. The RHBM utilizes the Carroll (1980) MRT networkmethod for radiation interchange between surfaces. Carroll
38、defines a preliminary estimate of the radiation coefficientwhich may be calculated for each surface. Use of this estimate,without further iterative improvement, can be shown to giveexcellent results. Figure 1 shows peak cooling loads computedwith RTF based on fixed radiation coefficients compared to
39、peak cooling loads computed with RTF based on variable radi-ation coefficients for 13,440 zones of mixed construction typeand aspect ratio. The maximum difference error caused by thefixed radiation coefficient is 0.2% in peak cooling load and theaverage over all cases is 0.03%. The simplification co
40、nsider-ably speeds up the calculation of RTF, so use of this assump-tion is recommended.A procedure analogous to that described in the previoussection for obtaining CTSF is utilized to compute periodicresponse factors that give the conduction heat gain at the insidesurface due to a temperature pulse
41、 at the inside surface. Thismodel of conduction heat gain is coupled with fixed convectioncoefficients and the MRT network procedure with fixed radia-tion coefficients, the interior surface heat balance equations for24 hours can then be cast in matrix form and solved with a singlematrix inversion. A
42、 full derivation of the RHBM is given byNigusse (2007). A key feature is that the resulting code is verycompact about 500 lines in VBA or F90, compared to about4000 lines of F90 code for an implementation of the full HBMused to generate RTF. The compact coding made feasible by theRHBM has the advant
43、ages (all other things documentation,clarity, etc. being equal) of being easier to understand, main-tain, and port to other environments.UPDATING THE FENESTRATION MODELIn the original development of the RTSM, shading coef-ficients were utilized for fenestration heat gain and no proce-dure was recomm
44、ended for windows with interior shading,e.g. Venetian blinds. Since that time, the ASHRAE Handbook(2005) treatment of fenestration has shifted to the use of solarheat gain coefficients (SHGC) and, for interior shading, theinterior attenuation coefficient (IAC). Window manufacturershave also begun re
45、porting SHGC; these data are available fromthe National Fenestration Rating Council (NFRC). Accordingly, the RTSM has been revised to use solar heatgain coefficients instead of shading coefficients and has beenexpanded to include interior shading with the use of the IAC.Previously, with shading coef
46、ficients, the transmitted andabsorbed inward flowing components of solar radiation wereestimated separately. With solar heat gain coefficients, thetransmitted and absorbed components are lumped together.This, in turn, required further investigation of radiative/convective splits since the splits app
47、ropriate for transmittedradiation and absorbed radiation could not be readilycombined to form a single radiative/convective split. In addi-tion, with windows that have interior shading, the radiativefraction of the heat gain is reduced substantially, but this wasnot treated at all in the original de
48、velopment of the RTSM.Adoption of SHGC and incorporation of interior shadingrequired determination of additional recommended radiative/convective splits, which are summarized in Table 1. The recom-mended radiative/convective splits for windows were deter-mined with a large parametric study, describe
49、d below in thesection “Verification of the RTSM”. The parametric study wasused to find radiative/convective splits that minimized overpre-diction of cooling loads (compared to the HBM) without lead-ing to significant underprediction for a wide range of cases.OVERPREDICTION CORRECTIONThe radiant time series method (RTSM) generallyperforms as desired for a simplified cooling load calculationprocedure it has a small but acceptable amount of overprediction of peak cooling loads compared to the heat balancemethod (HBM). However, as shown previously by Rees, et al.(1998), for zone
