The Meaning and Significance of Heat Transfer Coefficient. Alan Mueller, Chief Technology Officer

Transcription

1 The Meaning and Significance of Heat Transfer Coefficient Alan Mueller, Chief Technology Officer

2 The Meaning of Heat Transfer Coefficient I kno the meaning of HTC! Why should I aste my time listening to your presentation? What is the difference beteen the STAR-CCM+ Field Functions? Heat Transfer Coefficient Local Heat Transfer Coefficient Virtual Heat Transfer Coefficient Specified Y+ Heat Transfer Coefficient 2

3 HTC is not the hole picture HTC expresses a linear relation beteen the heat flux at the all and the difference in a reference temperature and the all temperature ( ) q = ht T ref The heat flux is, in general, some very complicated function The linear relation is only an approximation Often referred to as Neton s la of cooling 3

4 The meaning of Reference Temperature OK, I kno the meaning of heat flux and all temperature, hat is reference temperature? Well duh!, its simply the temperature that satisfies T ref = T + q h h = 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 coefficient and reference temperature come in pairs Can not define one ithout the other Only all heat flux and all temperature are unambiguous T ref q T

5 Tref is it important Some of the confusion is that literature focuses on HTC but little on its relationship to the Tref Physical and Computational Aspects of Heat Transfer, Cebeci & Bradsha, Springer-Verlag, 1991 Developing Laminar Duct Flo N u ( x) hxd ( ) q( xd ) = = k T x T x k ( ( ) m( )) T m ( x) = A ( ) ρuxrt (, ) xr, da A ρu( x, r) da????

6 Conduction Heat Flux in a Boundary Layer Heat flux in Boundary Layer ρ c u ( Tf T) ρ c u q = τ + h= T T T T + = f p, f τ f p, f,, ref f ( + y ) All the physics is in T + and u τ T ( y ) + + ( + ( + u y ) P( )) y > y, Pr Pr / Pr, T T T trans = Pr y, y yt, trans 6

7 HTC Field Functions in STAR-CCM+ heat transfer coefficient user specifies T ref h = ( T T ) ref q local heat transfer coefficient & local heat transfer reference temperature local la of all near all cell temperature h T ref 7

8 HTC Field Functions in STAR-CCM+ virtual local heat transfer coefficient local la of all h evaluated at near all cell need not solve energy transport mute about the reference temperature 8

9 HTC Field Functions in STAR-CCM+ specified y+ heat transfer coefficient & specified y+ heat transfer reference temperature user specifies y+ but uses properties at the cell adjacent to the all h = ρ c T c + pc, u τ ( + y ) y + h T T ref T ref = T + q h 9

10 Pipe flo example specified q =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 alls 1E6 W/m2 Density 1000 kg/m3 Specific heat 4200 J/kg-C Dynamic viscosity Pa-s Thermal conductivity 0.6 W/m-K Laminar Pr number 7.0 Turbulent Pr number

11 High y + mesh (near-all cell y + = 150) Wall Treatment All Y+ All Y+ % Error High Y+ High Y+ % Error Turbulence Model RKE 2-layer RKE Wall Temperature Friction velocity u_tau Local HTC Local HT Ref Temp Heat Flux HTC Reference Temp for HTC Heat Flux Specified Y+ HTC Specified Y+ HT Ref Temp Specified Y Heat Flux Virtual Local HTC Reference Temp for Virtual Local HTC Heat Flux Dittus Boelter

12 lo y + mesh (near-all cell y + = 2) Wall Treatment All Y+ All Y+ % Error High Y+ High Y+ % Error Lo Y+ Lo Y+ % Error Turbulence Model RKE SKE Lo RKE 2-layer Re Wall Temperature Friction velocity u_tau Local HTC Local HT Ref Temp Heat Flux HTC Reference Temp for HTC Heat Flux Specified Y+ HTC NA Specified Y+ HT Ref Temp NA Specified Y NA Heat Flux NA Virtual Local HTC NA Reference Temp for Virtual Local HTC NA Heat Flux NA Dittus Boelter

13 Lessons Learned Virtual heat transfer coefficient can be misleading Not paired to any Reference Temperature May not be near textbook HTC Best Practice: Specified y+ heat transfer coefficient For a good guess of y+ then all is consistent ith textbook Not as sensitive to choice of reference temperature 13

14 Lessons Learned Heat transfer coefficient is not safe Poor choice of reference temperature can lead to negative HTC Difficult to apply hen temperature changes as the fluid cools don or heats up don the axis of the pipe. 14

15 Lessons learned Local heat transfer coefficient Dangerous if not used ith the local heat transfer reference temperature For lo Re meshes ill give values not anyhere near textbook values. Specified Y+ HTC is good compromise Likely the best option for cycle averaging T ref = T + q h 15

16 Lessons Learned At least for this constant property example Wall treatment models give reasonable surface temperatures hen used properly The default all y+ is the best for all prism layer meshes size range 16

17 Heat Transfer in Explicit Coupled Problems Couple to Abaqus T 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+ T STAR-CCM+ => Abaqus Best Unstable Practice because :Initial T heat is resistance same in both in fluid codes is higher than in solid 17

18 Heat Transfer in a Exhaust Manifold 18

19 HTC= Local Heat Transfer Coefficient HTC,Tref Steady Heat flux Steady Heat Unstable!!! Flux, t=100s Heat HTC,Tref Flux, t=10s HTC,Tref t=100s 19

20 HTC Specified Y+ Heat transfer Coefficient HTC,Tref, y+=200 t=100s HTC,Tref, y+=1e6 t=100s 20

21 Y+=1e6, and still very accurate!?? HTC,Tref, y+=1e6 t=10s 21

22 Steady-state Solution in about 2 iterations HTC,Tref, y+=2000

23 Heat Applied in Abaqus Linear form ( n+ 1 T ) ref q = h T n+ 1 n n ( ) ( ) q = h T T + h T T n+ 1 n n n n n+ 1 n ref What must be accurate is the heat flux! q = q + h T ( + T ) n+ 1 n n n 1 n dq dt Heat flux is linear expansion about all temp Reference Heat Transfer Temperature Coefficient does is more not appear! numerical Exchanging heat flux only is same as n in nature it stabilizes the solution h = 0

24 Specified Y+ HTC in Coupled Simulations Can be used to give best estimate of the heat at the end of the time step ( ) q = q + h T T n+ 1 n n n+ 1 n The actual physics of the choice of HTC using boundary layer theory is not as important as getting the heat flux correct HTC is not important at all if time step is small 24

25 Conclusions HTC and Reference Temp come in pairs HTC choices may not be satisfactory if not paired to the proper Reference Temperature Specified Y+ HTC recommended Coupling to other codes Solid passes all temperature Fluid passes HTC and Reference Temperature such that T ref = T + Initial Wall temperatures same in both codes q h