Htc Explained Star Ccm

The Meaning and Significance of Heat Transfer Coefficient

Alan Mueller, Chief Technology Officer

I know the meaning of HTC! Why should I waste my time listening to your presentation?

What is the difference between the STAR-CCM+ Field Functions? Heat Transfer Coefficient Local Heat Transfer Coefficient Virtual Heat Transfer Coefficient Specified Y+ Heat Transfer Coefficient

The Meaning of Heat Transfer Coefficient

2

HTC expresses a linear relation between the heat flux at the wall and the difference in a reference temperature and the wall temperature

The heat flux is, in general, some very complicated function The linear relation is only an approximation Often referred to as Newtons law of cooling

HTC is not the whole picture

3

( )w ref wq h T T=

OK, I know the meaning of heat flux and wall temperature, what is reference temperature? Well duh!, its simply the temperature that satisfies 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 without the other Only wall heat flux and wall temperature are unambiguous

The meaning of Reference Temperature

wref w

qT Th

= + wref w

qhT T

=

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 & Bradshaw,

Springer-Verlag, 1991 Developing Laminar Duct Flow

Tref is it important

( )( )( )

( )( )( )

wu

w m

q x Dh x DN xk T x T x k

= =

???? ( )( )( , ) ,

( , )A

m

A

u x r T x r dAT x

u x r dA

=

Heat flux in Boundary Layer All the physics is in

Conduction Heat Flux in a Boundary Layer

6

( )( )

, ,, ,f p f f p fw ref f

f w c uc u T Tq h T TTT y

+

= ++ = =

( ) ( ) ( )( ) ,,

Pr Pr / Pr ,

Pr ,T T T trans

T trans

u y P y yT y

y y y

+ + + ++ +

+ + +

+ > =

and T u+

heat transfer coefficient user specifies

local heat transfer coefficient & local heat transfer reference temperature local law of wall near wall cell temperature

HTC Field Functions in STAR-CCM+

7

( )ref wwqh

T T=

refT

h

refT

virtual local heat transfer coefficient local law of wall evaluated at near wall cell need not solve energy transport mute about the reference temperature


8

h

specified y+ heat transfer coefficient & specified y+ heat transfer reference temperature user specifies y+ but uses properties at the cell adjacent to the wall


9

( ),c p cc uh

T y++=

wref w

qT Th

= +

ref wy h T T+

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

Pipe flow example specified qw =1e6 W/m2

10

Wall Treatment All Y+ All Y+ % Error High Y+ High Y+ % Error

Turbulence Model RKE 2-layer RKE

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 Virtual Local HTC 300 300

Heat Flux 1137318 13.7 1137083 13.7 Dittus Boelter 18000 18000

High y+ mesh (near-wall cell y+ = 150)

11

Wall Treatment All Y+ All Y+

% Error

High Y+

High Y+ % Error

Low Y+ Low Y+ % Error

Turbulence Model RKE 2-layer RKE SKE Low

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 Virtual Local HTC 300 300 NA

Heat Flux 5127749 -412.77 2335781 -133.6 NA Dittus Boelter 18000 18000 18000

low y+ mesh (near-wall cell y+ = 2)

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 with textbook Not as sensitive to choice of reference temperature

Lessons Learned

13

Heat transfer coefficient is not 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.

Lessons Learned

14

Local heat transfer coefficient Dangerous if not used with the local heat transfer reference

temperature For low Re meshes will give values not anywhere near textbook

values.

Specified Y+ HTC is good compromise Likely the best option for cycle averaging

Lessons learned

15

wref w

qT Th

= +

At least for this constant property example Wall treatment models give reasonable surface temperatures when

used properly The default all y+ is the best for all prism layer meshes size range

Lessons Learned

16

Couple to Abaqus 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

Heat Transfer in Explicit Coupled Problems

17

Unstable because heat resistance in fluid is higher than in solid

Best Practice :Initial Tw is same in both codes

Heat Transfer in a Exhaust Manifold

18

HTC= Local Heat Transfer Coefficient

19

Heat Flux, t=10s HTC,Tref t=10s HTC,Tref t=100s

Heat Flux, t=100s HTC,Tref Steady

Heat flux Steady Unstable!!!

HTC Specified Y+ Heat transfer Coefficient

20

HTC,Tref, y+=200 t=100s HTC,Tref, y+=1e6 t=100s

Y+=1e6, and still very accurate!??

21

HTC,Tref, y+=1e6 t=10s

Steady-state Solution in about 2 iterations

HTC,Tref, y+=2000

Linear form Heat flux is linear expansion about wall temp

Exchanging heat flux only is same as

Heat Applied in Abaqus

( )( ) ( )

( )

1

1 1

1 1

1n n nw ref

n n n n n n nw w ref w w

n n n n nw w w w

nw

dqwdTw

q h T

q h T T h T T

q q h T

T

T

+

+ +

+

+

+

=

= +

= +

0nh =Heat Transfer Coefficient is more numerical in nature it stabilizes the solution

What must be accurate is the heat flux!

Reference Temperature does not appear!

Can be used to give best estimate of the heat at the end of the time step 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

Specified Y+ HTC in Coupled Simulations

24

( )1 1n n n n nw w w wq q h T T+ += +

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 wall temperature Fluid passes HTC and Reference Temperature such that

Initial Wall temperatures same in both codes

Conclusions

wref w

qT Th

= +

The Meaning and Significance of Heat Transfer CoefficientAlan Mueller, Chief Technology OfficerThe Meaning of Heat Transfer CoefficientHTC is not the whole pictureThe meaning of Reference TemperatureTref is it importantConduction Heat Flux in a Boundary LayerHTC Field Functions in STAR-CCM+ HTC Field Functions in STAR-CCM+ HTC Field Functions in STAR-CCM+ Pipe flow example specified qw =1e6 W/m2High y+ mesh (near-wall cell y+ = 150)low y+ mesh (near-wall cell y+ = 2)Lessons LearnedLessons LearnedLessons learnedLessons LearnedHeat Transfer in Explicit Coupled ProblemsHeat Transfer in a Exhaust ManifoldHTC= Local Heat Transfer CoefficientHTC Specified Y+ Heat transfer CoefficientY+=1e6, and still very accurate!??Steady-state Solution in about 2 iterationsHeat Applied in AbaqusSpecified Y+ HTC in Coupled SimulationsConclusions

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Htc Explained Star Ccm