HEAT PERFORMANCE ANALYSIS OF MULTI-FLUID HEAT EXCHANGERS

Transcription

1 HEA PERFORANCE ANALYSIS OF ULI-FLUID HEA EXCHANGERS A hess Submtted to the Faulty Of Purdue Unversty By Sang Bae Par Advsor: Dr. S. S. Krshnan /3/2003

2 HEA EXCHANGERS Deves that provde flow of thermal energy between two or more fluds at dfferent temperatures. In a two-flud heat exhanger heat transfer ours between two fluds: one nternal and one external. ult-flud heat exhangers s a ombnaton of several two-flud heat exhangers. In a mult-flud heat exhanger heat transfer ours between more than two fluds: one external and several nternal fluds.

3 ULI-FLUID HEA EXCHANGERS Advantage ghter paage spae whle mantanng the proper temperature of vehle thermal management system. Great ost savng to ar manufaturers and automotve supplers. Dsadvantage In a mult-flud heat exhangers unfavorable thermal nteraton ours between two-flud heat exhangers operatng at dfferent temperatures. he thermal nteraton s the heat from tube walls that s not delvered to external stream but s transferred by onduton along the fns to adaent tubes.

4 PROBLE IDENIFICAION For mult-flud heat exhangers tube wall temperatures must frst be determned for heat performane analyss. However LD and e-ntu methods used for the analyss of two-flud heat exhangers are not apable of evaluatng tube wall temperatures. Neessary to develop a new method to predt the heat performane of mult-flud heat exhangers.

5 BASIC EQUAIONS FOR ULI- FLUID HEA EXCHANGER DESIGN wall temperature w + h + + b h h + h h h + h f f h h b w w h h h Fn Pth ( out h ( out ( n ( h n b f w ( h out ( h out h ( h n ( h n h h

6 HEA RANSFER RAE FRO HE th LAYER - I Negletng the very small wall-resstane the heat transfer rate from the th hot flud to the th tube wall s = ( hh Ah ( h b h A he heat transfer rate from the prme tube surfae: θ h = Insde tube permeter b = ( = A = h A w A b h / 2 b θ fn pth ( n ( h n Fn Pth ( h out ( h out h h ( out ( h out b ( h n f w ( h h n

7 HEA RANSFER RAE FRO HE th LAYER - II he fn effeny for the th layer η f = tanhm l m l + m l snh m l ( θ L / θb m l snh m L he heat transfer rate from the th fn to the th old stream f = (η f h Af f θ tanhml = h Af θ b + + ml ml snh m L A f : ( θ θ ( θ θ f = ( η h Af θ + ( η h Af + half of a fn surfae area

8 FIN EFFICIENCY? AND BY-PASS EFFICIENCY? When the fn onduton ( s very muh better than the wall- to-stream heat transfer (h the by-pass effeny s very hgh. hus all the heat from the tube walls s onduted from one tube to the other and very lttle heat s transferred to the old stream ?'?" When s relatvely poor the by- pass effeny s very low and hene all the heat from the tube walls s transferred to the old stream and very lttle heat s onduted from one tube to the other tanh ml η = m l ml η = m l snh m L m 5-5 hp A r

9 OVERALL HEA RANSFER OVERALL HEA RANSFER RAE FRO HE RAE FRO HE th th LAYER LAYER he total heat transfer of the old sde: he total heat transfer of the old sde: he overall surfae effeny he overall surfae effeny ( ( ( = f f b A h A A h θ θ η θ η b f A A A + = f b + = ( ( ( ( + + = f f A A A h A A A h θ θ η θ η ( ( ( + + = A h A h θ θ η θ η ( f A A = η η f A A = η η

10 ENERGY BALANCE ON HE th UBE LAYER - I he onservaton of energy reurement to the th tube: where h = ( h = ( hh Ah h w 0 ( + ( η h A ( = ( ηh A w w w + ( + ( η h A ( = ( ηh A w w w

11 ENERGY BALANCE ON HE th UBE LAYER - III he fnal form of the onservaton of energy reurement to the th tube: b = w + dw + aw + where a d = γ b = γ = ( α h + β + β = ( α + β + β + γ + γ

12 SYSE OF EQUAIONS FOR UBE WALL EPERAURES At the st tube: d w + aw 2 = At the 2 nd tube: b + d + a 2 w 2 w2 2w2 = 2 At the 3 rd tube: b + d + a 3 w 2 3 w3 3w4 = At the - th tube: b d w 2 + w + a w = At the th tube: b + d = w w tube

13 HE SYSE OF EQUAIONS HE SYSE OF EQUAIONS IN ARIX FOR IN ARIX FOR rdagonal rdagonal matrx form matrx form Soluton usng homas Soluton usng homas Algorthm Algorthm = w w w w w d b a d b a d b a d b a d

14 ZGP (ZERO-HERAL HERAL- GRADIEN POIN he boundary ondton for ZGP: dθ dx = 0 x* ml=2 ml=3 ml=5 ml=8 ml=0 he loaton to ZGP: x = osh ml θ snh m L + / θ m tanh * x osh m L θ + / θ x = = tanh L ml snh m L

15 HE DIRECION OF HERAL INERACION If? + >? the value of x* s smaller than 0.5 and the dreton of the thermal nteraton s from the + th tube to the th tube. If? + =? the value of x* s 0.5 and there s no thermal nteraton. If? + <? the value of x* s greater than 0.5 and the dreton s from the th tube to the + th tube.

16 EQUIVALEN SURFACE AND NODAL NEWORK Nodal networ n a heat exhanger Nodal networ n an euvalent surfae y z x (a = m = 2 = = 2 y z x (b = m = 2 = = 2 = = = 5 = = 5 = = n = n

17 HE SYSE OF HE SYSE OF EQUAIONS A NODES EQUAIONS A NODES he system of euatons for tube wall he system of euatons for tube wall temperatures at nodes temperatures at nodes = w w w w w d b a d b a d b a d b a d

18 HEA RANSFER RAE & HEA RANSFER RAE & FLUID EP. A NODES FLUID EP. A NODES he heat transfer rate at nodes he heat transfer rate at nodes he fluds temperature at nodes he fluds temperature at nodes ( ( h h h p h h m = & ( ( p m = & ( = h p h h h h m & p m ( + = &

19 OVERALL HEA RANSFER RAE Hot-sde = m n Q h h = = = y z x (b = m = 2 = = 2 Cold-sde + m Q = n = = = = 5 = = Q h = Q = n

20 FLOW CHAR FOR NEW EHODOLOGY Operatng ondtons ult-flud heat exhanger surfae geometry flow arrangement and materal Defne fn and overall surfae effenes for a mult-flud heat exhanger Convert a fn-tube surfae to an euvalent surfae based on the overall effeny Subdvde a heat exhanger nto a number of small regons and assgn to eah a referene pont that s at ts enter hermal propertes µ for Re C p for St Pr hermo-physal propertes of fluds homas' algorthm Apply the onservaton of energy reurements to a nodal regon of eah tube whh has the same and ndes. Develop a system of euatons for the tube wall temperatures at the nodes Solve the system of euatons (n a trdagonal matrx for the tube wall temperatures at the nodes Calulate the loal heat rate of the nodal regons Calulate the outlet temperatures of the old and hot fluds at the nodes Set the outlet flud temperatures as the nlet temperature of the next nodal regons n the flow dreton No =m and =n? Yes Integrate all the loal heat rates of eah flud to obtan the overall heat transfer rate End

21 SIULAION RESULS Features of the smulaton ore Operatng ondtons Assumptons Grd ndependent solutons Smulaton results Optmzaton of desgn

22 FEAURES OF HE SIULAION CORE Features of the smulaton ore 60 water tubes + 0 ol tubes 698 mm (W and 9 mm (d ol s d W ol H ommon fn ol h header water water ar water

23 OPERAING CONDIIONS Inflow ondtons Ar speed: 4 m/s Ar temperature: 20 C Water flow rate: 5000 l/hr Water temperature: 95 C Ol flow rate: 2 gal/mn Ol temperature: 40 C

24 ASSUPIONS - I he smulaton ore operates under steady-state state steady-flow ondtons. here s no heat generaton n the smulaton ore. he temperature of eah nternal flud (water or ol s unform over the flow ross seton. he nternal flow s fully developed at any flow ross seton. In a tube the wall-temperature dstrbuton s symmetr about the md plane whh dvdes the tube nto two eual parts along the tube wdth.

25 ASSUPIONS - II he outer fns are nsulated wth sde members; the fn heat transfer to the sde members s neglgble. he heat transfer resstane of tube walls s neglgble. he heat transfer resstane due to metall bondng between fn and tube s neglgble. he heat transfer from the headers s neglgble. he radaton effet from the ore surfae s neglgble.

26 HE DEGREE OF GRID INDEPENDENCE Depends on what we want out of the soluton. If we need extreme auray s reured we need to press the matter of grd ndependene n a very detaled fashon. If we an tolerate a lttle less prese soluton we an slghtly relax the rteron for extreme grd ndependene and use fewer grd ponts thus savng omputer tme. he grd ndependent-soluton s less senstve to a number of grd ponts.

27 GRID INDEPENEN SOLUIONS Crteron for the grd-ndependent ndependent soluton n the smulaton: e=0.02 (n: number of grd ponts Along tube wdth = n Q 2 Q Q n n ε Along tube length =400

28 IPAC OF UBE ASPEC RAIO ON HE HERAL INERACION ALONG HE COON FIN Impat of Aspet rato - Ol ube Impat of Aspet rato - Water ube f (W /2 /4 /6 f (W /6 /8 / x* x*

29 IPAC OF UBE ASPEC RAIO ON HE HERAL INERACION A EACH UBE LAYER Impat of Aspet rato - Ol ube Impat of Aspet rato - Water ube Q (W /2 /4 /6 Q (W /6 /8 / ube layer ube layer

30 IPAC OF INERNAL FLOW RAE ON HE HERAL INERACION ALONG HE COON FIN f (W gal/mn 2 gal/mn 3 gal/mn 4 gal/mn f (W l/h 4000 l/h 5000 l/h 6000 l/h 7000 l/h x* x*

31 IPAC OF INERNAL FLOW RAE ON HE HERAL INERACION A EACH UBE LAYER Q (W gal/mn 2 gal/mn 3 gal/mn 4 gal/mn Q (W l/h 4000 l/h 5000 l/h 6000 l/h 7000 l/h ube layer -00 ube layer

32 IPAC OF UBE ASPEC RAIO ON HE OVERALL HEA RANSFER RAE Impat of aspet rato - ol tube Impat of aspet rato - water tube Qwater (W water ooler ol ooler Qol (W Qwater (W water ooler ol ooler Qol (W 3.0 /2 /4 / /6 /8 /6 2.5 Aspet rato of ol tube Aspet rato of ol tube

33 IPAC OF INERNAL FLOW RAE ON HE OVERALL HEA RANSFER RAE Impat of ol flow rate Impat of water flow rate Qwater (W water ooler ol ooler Qol (W Qwater (W water ooler ol ooler Qol (W Ol flow rate (gal/mn Water flow rate (l/hr

34 IPAC OF FLOW DIRECION ON HE OVERALL HEA RANSFER RAE

35 UBE WALL EPERAURE DISRIBUION

36 AIR EPERAURE DISRIBUION

37 INERNAL FLUID EPERAURE DISRIBUION

38 OPIIZAION OF DESIGN In automotve applatons of mult-flud heat exhangers thermal nteratons between heat exhangers are not favorable and must be avoded or mnmzed f possble. he tube aspet rato has more mpat on the overall thermal nteraton than the flow arrangement or the flow ondtons of nternal and external fluds. However further reduton of the aspet rato of water tube wll results n the hgher nternal pressure drop and reure more pumpng power to rulate the water. It s sometmes not possble to nrease the pumpng power n vehular applatons. herefore the most effent way to redue the thermal nteraton s to optmze the surfae geometres of exhanger wthn an aeptable range of pressure drop.

39 IPORANCE OF ACCURACY EVALUAION he new method s ompletely dfferent from LD and e-ntu methods n that t frst determnes the temperatures of tube walls and alulates overall heat transfer rate usng the wall temperatures. Assumptons made for the smulaton model development may ntrodue some errors nto the alulatons. herefore the ueston about the auray of the smulaton model s nevtable. he auray of the smulaton model was defned by Auray = S where S and denote the smulaton and the experment respetvely.

40 AVERAGE ACCURACY he average auray of the smulaton model: Auray (l/hr 5000 (l/hr 6000 (l/hr 7000 (l/hr Ar speed (m/se

41 EVALUAION OF SIULAION ODEL he assumptons used for the smulaton model are reasonable. he smulaton model s apable of predtng the heat performane of heat exhangers that s aurate enough for the ntal produt development.

42 CONCLUSIONS he new method s apable of evaluatng he heat performane of mult-flud heat exhanger as well as two-flud heat exhangers. he heat transfer rate due to thermal nteraton. he dfferent flow arrangement (o- and ounter-flow. he error of the new method s less than 6% whh s aurate enough for ntal produt development. Wth nowledge of tube wall temperatures the exstene and the dreton of the thermal nteraton an readly be determned usng ZGP.

43 RECOENDAIONS - I he new method presents only the ratng problem that s onerned wth the determnaton of the heat transfer rates and the flow outlet temperatures. hs new method nvolves some assumptons and smplfatons and doesn t onsder all the fators that need to be onsdered for a omplete heat exhanger desgn.

44 RECOENDAIONS - II Reommended to onsder some other mportant fators: Pressure drop lmtaton of eah flud whh determnes the pumpng power. Influene of poor flow dstrbuton on exhanger performane. Optmum dstrbuton of thermal resstane and flow- frton power on surfaes. Unertanty of proper thermal ontat between the extended and prme surfaes. hermal stress and onstruton problems Allowane for foulng. Any or all of these fators may have a profound nfluene on the omplete desgn of a mult-flud heat exhanger.