Using CTFs is tedious but not difficult. Finding them is difficult, and you have to use a program for that task.

Transcription

1 ME 44/54 HVAC Sysems Hea Balance Mehd The HBM requres a lad calculan prgram and hs mehd s n dscussed n ur ex. Dfferen peces f he clng lad prblem are lked a n slan. A prgram pus all hese peces geher fr us perfrm a cmplee clng lad analyss fr a srucure. Hence, engneers wrkng n HVAC are, n pracce, frced rely n cmmercal sfware packages fr a clng lad analyss. Bascally, he HBM cnsss f hea balances n he nerr and exerr surfaces f a sngle wall r rf elemen. Each f he hea fluxes slar, cnvecn, and radan - n an exerr surface vary hrughu he day as he sun changes pn n he and as he udr amben and radan emperaure changes. The me-varyng naure f he fluxes, cupled wh he hermal nera f he walls and rfs, creaes a ransen hea cnducn prblem. Slun mehds nclude:. lumped parameer small peces wh unfrm emperaure-me 2. frequency respnse perdc BCs (Furer seres) 3. numercal negran fne dfferences r fne elemens 4. Z-ransfrms he hery used n he HBM Z-ransfrms use eher respnse facrs r cnducn ransfer funcns. Respnse facrs and Cnducn ransfer funcns (CTF): me seres ceffcens ha relae curren hea flux pas and presen values f nerr and exerr emperaure (CTFs replace emperaure hsry wh hea flux hsry). Usng CTFs s edus bu n dffcul. Fndng hem s dffcul, and yu have use a prgram fr ha ask. Bascally, he hea balances expressed n erms f CTFs mus be slved fr each hur f he day. The slun prcedure may be erave (nal guess f he surface

2 emperaures and hea fluxes are updaed unl hey cnverge) r dne smulaneusly va marx nversn. A check n he slun valdy s baned by slvng a seady-sae prblem. The resul shuld agree wh he ransmssn equan frm Ch. 5: q U( ) EXTERIOR SURFACE HEAT FLUX The hree cmpnens f he exerr hea flux are slar, cnvecn and radan. Slar radan hgh emperaure surce, UV r shr wavelengh EMR q slar α G Where α surface absrpvy f shr wavelengh EMR G al slar rradan frm Chaper 6 (calculaed n he ½ hur) Exerr cnvecn Newn s Law f Clng q cnvecn hc ( ) where h c exerr cnvecve hea ransfer ceffcen usde ar emperaure usde surface emperaure In Tpc 5, we used abulaed values fr h c when we were calculang verall U values fr walls, rfs, ec. Here, a crrelan s gven fr usng a cmpuer: c 3 [ ] 2 b C Δ [ av ] 2 h + where C urbulen naural cnvecn cnsan Δ dfference beween exerr surface emperaure and exerr ar emperaure a, b V wnd speed n mph r m/s Exerr radan lw emperaure surce, IR r lng wavelengh EMR The surface exchanges hermal radan n he IR specra wh he grund and he : q [ F ( T T ) + F ( T T )] 4 " radan εσ s g g s The vew facrs F s-g and F s- are frm Tpc 6 wh α, he surface l angle. F s g 2 [ c( α )] 2

3 F [ + s c( α )] 2 The 4 h pwer erms are a nusance numercally, s he radan flux s lnearzed: q" Fs g hr, g εσ Fs hr, εσ h 4 4 ( T T ) g g 4 4 ( T T ) ( ) h ( ) radan r, g g r, The emperaure s apprxmaed as T 0.8 R (r T 6K). The crrecn fr a surface led a angle α s:, α α c 2 α + c 2 All f he exerr hea fluxes can be cmbned ge a smpler-lkng relanshp. FENESTRATIONS Drec, dffuse and refleced slar gan hrugh wndws and lghs s calculaed usng he mehds f Tpc 6. INTERIOR HEAT GAINS Peple, Lghs, Equpmen Peple Peple cnrbue sensble and laen hea. Tables are avalable fr dfferen ccupances and ccupan acves. N number f peple F u use facr (.0 fr fully ccuped rm) q s_peple N F u q s q la_peple N F u q la Sensble hea gan spl: 30% cnvecve, 70% radave Laen hea gan spl: 00% cnvecve, 0% radave The spl beween radave and cnvecve fracns s needed because cnvecve hea s par f he nsananeus hea lad whereas radave hea cnrbues he delayed lad. Lghs 3

4 q _lghs 3.4 W F u F s W al nsalled waage F u use facr (.0 f all nsalled lghs are n) F s fudge facr ( cmpensae fr less hea frm flurescen bulbs) Hea gan spl: Flurescen lamps: 4% cnvecve, 59% radave Incandescen lamps: 20% cnvecve, 80% radave Hea l he reurn ar plenum dependng n wheher r n he fxure s venlaed r unvenlaed. N all f he hea frm he lgh eners he cndned space. Equpmen q _mr C (P /E m ) F l F u q _mr hea equvalen f equpmen peran, BTU/hr r W P mr shaf pwer rang, hp r W E m mr effcency as decmal (n %) F l fracn f raed lad delvered F u mr use facr (.0 when he equpmen s runnng) C un cnversn cnsan, 2545 Buh/hp r W/W Mr usde cndned space, drven equpmen nsde: Mr nsde cndned space, drven u: q _mr C (P) F l F u q _mr C [ ( - E m ) / E m ] F l F u Equpmen hea gan spl: 30% cnvecve, 70% radave Elecrnc equpmen hea gan spl: Prner:89% cnvecve, % radave Cper: 86% cnvecve, 4% radave PCs: 74.5% cnvecve, 25.5% radave (average) Applances hded seam & elecrcal q applance 0.5 x 0.32 q Where 4

5 0.32 s he fracn f radave hea (cnvecve hea s remved frm he ccupancy by hds) q s he npu rang Applances hded fuel-fred Where q s he npu rang. INTERIOR OPAQUE SURFACES Cnvecn q cnvecn hc ( s ) q applance q where h c exerr cnvecve hea ransfer ceffcen s nsde surface emperaure, dfferen fr each surface and vares hrughu he day nsde ar emperaure, desgn cndn Radan exchange wh becs n he enclure Mdelng he deals f all he radan exchanges beween all f he surfaces walls, celng, flr and becs (furnure) s herecally psble bu mpraccal because f he deal nvlved. The ex descrbes he mean radan emperaure /balance mehd. Ths mdel uses a fcus surface represen he vew ha ne surface has f all her surfaces. Recall frm yur undergraduae hea ransfer class: The sum f he vews frm ne surface each surface n an enclure s. A planar surface cann see self. N F F 0 The ne radan exchange n an enclure s zer. N Q 0 Hence, fr ne surface n an enclure, he fcus surface area s he sum f he areas f all he her surfaces; he fcus surface emssvy s an area-weghed average; he fcus surface emperaure s an area-weghed average; he vew facr f he fcus 5

6 surface s calculaed usng he fcus emssvy and area; a radan ceffcen s calculaed usng he fcus vew facr and emperaures. The hermal radan calculaed frm all hs fcusness s n crrec and needs be crreced (balanced) s ha he ne exchange s zer. All f hese calculans are amenable a spreadshee apprach (see Example 8-5). Radan gans frm peple, lghs and equpmen We saw earler ha peple, lghs and equpmen nclude a radave lad. These cnrbuns are summed fr each hur and reaed as unfrm fluxes ver each nerr surface. All f he nerr hea fluxes can be cmbned ge a smpler-lkng relanshp. INTERIOR TRANSPARENT SURFACES Fenesrans The calculan f ransmed and absrbed rradan fllws he prcess ha we learned n Tpc 6. We can refne he calculan by cnsderng absrpance n each pane f a mul-pane wndw. The calculan prcedure s dencal ha T 6. Wha s new are he ceffcens separaely calculae absrpance n he uer pane and nner pane f a duble pane wndw. ZONE AIR Surface cnvecn- sum ver all surfaces: Q cnv A q cnvecn A h c ( s ) Inernal hea gan cnvecn add up he cnrbun frm peple, equpmen and lghs Inflran Sysem hea ransfer q& q& s, nf, θ s, la, θ m& m& a a C p ( ) C ( ) V& v V& v ( W W ) h fg ( W W ) h fg p q sysem a + b 6

7 IMPLEMENTATION. deermne all zne parameers (surface areas, hermal prperes, gemery) 2. fnd all mped fluxes (ransmed and ncden slar radan, nernal lads, nflran raes) 3. calculae exerr and nerr surface emperaures fr each hur f he day 4. calculae he requred sysem hea ransfer by usng he zne ar hea balance: Q& sysem A h c,, ( s, ) m& a,nf C p ( ) Q& n, cnv The dffculy, as we have seen, n hs decepvely smple lkng equan s fndng he nerr surface emperaure, s. All f he exerr hea lads (slar, cnvecn, ransmssn) and nerr hea lads (slar hrugh fenesrans, radan frm peple, equpmen and lghs) mus be ncluded and mdeled. 7