The The Me Meaning a and Significance of of Heat Tran ansf sfer C Coeffic icie ient Ala lan Mu Mueller, C Chi hief T f Techn hnology O y Officer
The Me The Meaning of of Heat T Tra ransfer C Coe oefficient “I I know t the he m meaning of of HTC!” – Why should I waste my time listening to your presentation?” What i is t the d differe rence b between t the S STAR-CCM CCM+ F Field F d Functio ions? s? – Heat Transfer Coefficient – Local Heat Transfer Coefficient – Virtual Heat Transfer Coefficient – Specified Y+ Heat Transfer Coefficient 2
HTC is is not t the wh whole pic picture HTC e expresses a a li linear re relation b between t the he he heat flu flux a at the he wall a l and the d differe rence i in a “refere rence” t tempera rature re a and the he wall t l tempera rature re ( ) = − q h T T w ref w The The he heat flu flux i is, i in general, s som ome v very c y com omplicated fu function – The linear relation is only an approximation – Often referred to as Newton’s “law” of cooling 3
The m The meaning of of Reference T Temperature OK, I know the meaning of h OK heat at flux an and wall all temperature, what is is “ref efer erence t temper erature”? e”? Well d duh!, it its sim imply the temperature that at s sat atisfies q q = = + w h w T T − ref w T T h ref w – In textbooks often it is some far-field temperature, or some inlet temperature – For boiling heat often it is the boiling saturation temperature Heat transfer er coef efficien ent a and refer eren ence temper erature e come me in pairs – Can not define one without the other – Only wall heat flux and wall temperature are unambiguous
Tref is it is it im importan ant Some o of t the c confusion is is that at lit literat ature focuses on HT HTC b but lit little on it its relat ationship ip t to the Tref ef – Physical and Computational Aspects of Heat Transfer, Cebeci & Bradshaw, Springer-Verlag, 1991 – Developing Laminar Duct Flow ( ) q ( ) x D h x D ( ) = = w N x ( ) ( ) − u k T ( ) x T x k w m ( ) = ∫ ρ u x r T x r dA ( , ) , ( ) A T x ???? ??? ∫ m ρ u x r dA ( , ) A
Condu ductio ion H Heat at F Flux i x in a Boundar dary L Layer He Heat at flu lux in Boundary Layer ( ) ρ ρ − c u T T c u τ τ f w = = f p f , f p f , = q h , T T ( ) , + + + w ref f T T y + T and u τ All ll the phys ysics is is in in ( ) ( ) ( ) + + + + + > Pr u y P Pr / Pr , y y ( ) + + = T T T trans , T y + + + ≤ Pr y , y y , T trans 6
HTC F C Field F d Functio ions i s in STAR-CCM CCM+ q = w h ( ) − T T ref w “heat at t transf sfer c coeffic icie ient” – user specifies T ref “loc local he heat t tra ransfer c coe oefficient” & & loc local he heat t tra ransfer refere rence t temperature re” h – local law of wall – near wall cell temperature T ref 7
HTC F C Field F d Functio ions i s in STAR-CCM CCM+ “vi virtual loc local he heat t tra ransfer c coe oefficient” – local law of wall h – evaluated at near wall cell – need not solve energy transport – mute about the reference temperature 8
HTC F C Field F d Functio ions i s in STAR-CCM CCM+ “specifi fied y+ y+ he heat t tra ransfer c coe oefficient” & & ”specifi fied y+ y+ he heat transfer r r refere rence t tempera rature re” – user specifies y+ but uses properties at the cell adjacent to the wall ρ + ↑ c u τ ↓ − ↑ = y h T T c p c , h ( ) + ref w + T y q = + w T T ref w h 9
Pipe f Pipe flow e w exa xample spe specified q w =1e6 W =1e6 W/m 2 Description Value Pipe diameter (cm) 1 Pipe length (cm) 25 Reynolds number 50,000 Inlet temperature 300 K Uniform heat flux at the walls 1E6 W/m2 Density 1000 kg/m3 Specific heat 4200 J/kg-C Dynamic viscosity 0.001 Pa-s Thermal conductivity 0.6 W/m-K Laminar Pr number 7.0 Turbulent Pr number 0.9 10 10
High gh y y + mesh sh ( (near ar-wall c cell ll y + = 1 = 150 50) All Y+ High Y+ Wall Treatment All Y+ High Y+ % Error % Error RKE Turbulence Model RKE 2-layer Wall Temperature 359.39 359.22 Friction velocity u_tau 0.246 0.2465 Local HTC 19150 19202 Local HT Ref Temp 307.17 307.13 Heat Flux 1000013 0.0 1000232 0.0 HTC 16838 16888 Reference Temp for HTC 300 300 Heat Flux 1000009 0.0 1000107 0.0 Specified Y+ HTC 19154 19207 Specified Y+ HT Ref Temp 307.18 307.15 Specified Y+ 150 150 Heat Flux 99963 0.0 1000108 0.0 Virtual Local HTC 19150 19201 Reference Temp for 300 300 Virtual Local HTC Heat Flux 1137318 13.7 1137083 13.7 11 11 Dittus Boelter 18000 18000
low y y + mesh ( (near-wall c ll cell l y + = 2 = 2) All Y+ High High Low Y+ Low Y+ Wall Treatment All Y+ % Y+ % Y+ % Error Error Error RKE SKE Low Turbulence Model RKE 2-layer Re Wall Temperature 357.17 327.95 353.37 Friction velocity u_tau 0.239 0.314 0.258 Local HTC 89693 83570 85825 Local HT Ref Temp 346.0 316.0 341.7 Heat Flux 1001870 0.2 998662 -0.2 100415 -0.4 HTC 17492 35760 18739 Reference Temp for HTC 300 300 300 Heat Flux 1000018 0.0 999492 0.0 100098 -0.1 Specified Y+ HTC 18612 24460 NA Specified Y+ HT Ref Temp 303.44 287.1 NA Specified Y+ 150 150 NA Heat Flux 1000023 0.0 999191 0.1 NA Virtual Local HTC 89693 83570 NA Reference Temp for 300 300 NA Virtual Local HTC Heat Flux 5127749 -412.77 2335781 -133.6 NA Dittus Boelter 18000 18000 18000
Lesson Le ons Le Learned “Virtual al h heat t tran ansf sfer c coeffic icie ient” c can be misl sleadin ading – Not paired to any Reference Temperature – May not be near “textbook” HTC Best st P Prac actic ice: “ “Specif ifie ied y d y+ heat t transf sfer c coeffic icie ient” – For a good “guess of y+” then all is consistent with textbook – Not as sensitive to choice of reference temperature 13 13
Lesson Le ons Le Learned “Heat t tran ansfer c coefficient” is n is not saf safe – Poor choice of reference temperature can lead to negative HTC – Difficult to apply when temperature changes as the fluid cools down or heats up down the axis of the pipe. 14 14
Le Lesson ons le learned “Loc Local he heat t tra ransfer c coe oefficient” – Dangerous if not used with the “local heat transfer reference temperature” – For low Re meshes will give values not anywhere near “textbook” values. Specif ifie ied Y d Y+ HTC i C is good c d compromise mise – Likely the best option for cycle averaging q = + w T T ref w h 15 15
Lesson Le ons Le Learned At least st f for this c is constan ant p prope perty e exam ampl ple – Wall treatment models give reasonable surface temperatures when used properly • The default “all y+” is the best for all prism layer meshes size range 16 16
Heat at T Tran ansf sfer i in Expl plic icit it C Coupl pled P d Problems ms Couple t Co to Abaq aqus – Tw Abaqus => STAR-CCM+ – Option 1: (Best Practice) • HTC, Tref STAR-CCM+ => Abaqus, or – Option 2: • Heat flux STAR-CCM+ => Abaqus – Option 3: • Heat flux Abaqus => STAR-CCM+ • Tw STAR-CCM+ => Abaqus Unst nstabl ble becau because heat heat resi resistan ance in n flui uid Best est Pract ractice :Initial Tw Tw is s sam same e in n bot both code codes is s hi highe gher than han in sol n solid 17 17
Heat at T Tran ansf sfer i in a Exhau aust st M Manifold 18 18
HTC= C= “ “Local al H Heat at T Tran ansf sfer C Coeffic icie ient” HTC,Tref Steady HT ux, ∆ t=100s Hea eat Flux 100s Heat flux Steady Unstable!!! HTC,Tref ∆ t=10s ux, ∆ t=10s Hea eat Flux HT 10s 10s HTC,Tref ∆ t=100s HT 100s 19 19
HTC “ C “Specif ifie ied Y Y+ Heat at t tran ansf sfer C Coeffic icie ient” 200 ∆ t=100s HT HTC,Tref, y+=200 100s 1e6 ∆ t=100s HT HTC,Tref, y+=1e6 100s 20 20
Y+=1e6, +=1e6, a and still v ver ery a accu ccurate! e!?? 1e6 ∆ t=10s HT HTC,Tref, y+=1e6 10s 21 21
Steady ady-st stat ate S Solutio ion i in about 2 2 iterat atio ions HT HTC,Tref, y+=200 2000
Heat A Appl pplied in in Abaq aqus ( ) + + = − Linear f r form 1 1 n n n n q h T T w w ref ( ) ( ) + = − + + − n 1 n n n n n 1 n q h T T h T T What hat mus must be be ac accurate i is the hea he heat flux ux! w w ref w w ( ) + + = + − n 1 n n n 1 n q q h T T w w w w dqw dTw Heat at flux i x is linear ar e expan pansio sion a about w wall t temp Ref Heat efer eat Trans erence Tem ransfer Coef emper perature does oefficient is does not s more not appea ore num appear! numeri erical h = n Exchanging h heat at f flux o only is is sam same as as 0 in n nature ure – it stabi bilizes zes the solut ution on
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