SLIDE 1 The The Me Meaning a and Significance of
Tran ansf sfer C Coeffic icie ient Ala lan Mu Mueller, C Chi hief T f Techn hnology O y Officer
SLIDE 2 “I I know t the he m meaning of
– 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
The The Me Meaning of
Tra ransfer C Coe
2
SLIDE 3 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 The The he heat flu flux i is, i in general, s som
very c y com
function
– The linear relation is only an approximation – Often referred to as Newton’s “law” of cooling
HTC is is not t the wh whole pic picture
3
( )
w ref w
q h T T = −
SLIDE 4 OK OK, I know the meaning of h 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
– 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
The The m meaning of
Temperature
w ref w
q T T h = +
w ref w
q h T T = −
SLIDE 5 Some o
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
Tref is it is it im importan ant
( ) ( )
( )
( ) ( ) ( )
w u w m
q x D h x D N x k T x T x k = = −
??? ????
( ) ( )
( , ) , ( , )
A m A
u x r T x r dA T x u x r dA ρ ρ = ∫
∫
SLIDE 6 He Heat at flu lux in Boundary Layer All ll the phys ysics is is in in
Condu ductio ion H Heat at F Flux i x in a Boundar dary L Layer
6
( )
( )
, ,
,
,
f p f f p f w ref f
f w
c u c u T T q h T T T T y
τ
τ
ρ ρ
+
− =
+ +
= =
( ) ( )
( )
( )
, ,
Pr Pr / Pr , Pr ,
T T T trans T trans
u y P y y T y y y y
+ + + + + + + + +
+ > = ≤
and T uτ
+
SLIDE 7 “heat at t transf sfer c coeffic icie ient”
– user specifies
“loc local he heat t tra ransfer c coe
& loc local he heat t tra ransfer refere rence t temperature re”
– local law of wall – near wall cell temperature
HTC F C Field F d Functio ions i s in STAR-CCM CCM+
7
( )
ref w w
q h T T = −
ref
T
h
ref
T
SLIDE 8 “vi virtual loc local he heat t tra ransfer c coe
– local law of wall – evaluated at near wall cell – need not solve energy transport – mute about the reference temperature
HTC F C Field F d Functio ions i s in STAR-CCM CCM+
8
h
SLIDE 9 “specifi fied y+ y+ he heat t tra ransfer c coe
& ”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
HTC F C Field F d Functio ions i s in STAR-CCM CCM+
9
( )
, c p c
c u h T y
τ
ρ
+
+
=
w ref w
q T T h = +
ref w
y h T T
+ ↑
↓ − ↑
SLIDE 10
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 Pipe f flow e w exa xample spe specified qw =1e6 W =1e6 W/m2
10 10
SLIDE 11 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 gh y y+ mesh sh ( (near ar-wall c cell ll y+ = 1 = 150 50)
11 11
SLIDE 12 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
100415
HTC 17492 35760 18739 Reference Temp for HTC 300 300 300 Heat Flux 1000018 0.0 999492 0.0 100098
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
2335781
NA Dittus Boelter 18000 18000 18000
low y y+ mesh ( (near-wall c ll cell l y+ = 2 = 2)
SLIDE 13 “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
Le Lesson
Learned
13 13
SLIDE 14 “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
- r heats up down the axis of the pipe.
Le Lesson
Learned
14 14
SLIDE 15 “Loc Local he heat t tra ransfer c coe
– 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
Le Lesson
learned
15 15 w ref w
q T T h = +
SLIDE 16 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
Le Lesson
Learned
16 16
SLIDE 17 Co Couple t 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
Heat at T Tran ansf sfer i in Expl plic icit it C Coupl pled P d Problems ms
17 17
Unst nstabl ble becau because heat heat resi resistan ance in n flui uid is s hi highe gher than han in sol n solid Best est Pract ractice :Initial Tw Tw is s sam same e in n bot both code codes
SLIDE 18
Heat at T Tran ansf sfer i in a Exhau aust st M Manifold
18 18
SLIDE 19
HTC= C= “ “Local al H Heat at T Tran ansf sfer C Coeffic icie ient”
19 19 Hea eat Flux ux, ∆t=10s 10s HT HTC,Tref ∆t=10s 10s HT HTC,Tref ∆t=100s 100s Hea eat Flux ux, ∆t=100s 100s HT HTC,Tref Steady Heat flux Steady Unstable!!!
SLIDE 20
HTC “ C “Specif ifie ied Y Y+ Heat at t tran ansf sfer C Coeffic icie ient”
20 20 HT HTC,Tref, y+=200 200 ∆t=100s 100s HT HTC,Tref, y+=1e6 1e6 ∆t=100s 100s
SLIDE 21
Y+=1e6, +=1e6, a and still v ver ery a accu ccurate! e!??
21 21 HT HTC,Tref, y+=1e6 1e6 ∆t=10s 10s
SLIDE 22
Steady ady-st stat ate S Solutio ion i in about 2 2 iterat atio ions
HT HTC,Tref, y+=200 2000
SLIDE 23 Linear f r form Heat at flux i x is linear ar e expan pansio sion a about w wall t temp Exchanging h heat at f flux o
is sam same as as Heat A Appl pplied in in Abaq aqus
( ) ( ) ( )
(
)
1 1 1 1 1 1 n n n w ref n n n n n n n w w ref w w n n n n n w w w w n w
dqw dTw
q h T q h T T h T T q q h T T T
+ + + + + +
= − = − + − = + −
n
h =
Heat eat Trans ransfer Coef
s more
numeri erical in n nature ure – it stabi bilizes zes the solut ution
What hat mus must be be ac accurate i is the hea he heat flux ux!
Ref efer erence Tem emper perature does does not not appea appear!
SLIDE 24 Can b be used t to
best e estimate of
he he heat a at the he e end of
the t time s step The The a actual p phys ysics of
he c choi hoice of
using b bou
layer theory is is not as as im impo portant as as getting t the h heat at f flux c correct HTC is is not im impo portant at at al all if if time st step is smal is small Specif ifie ied Y d Y+ HTC i C in Coupl pled S d Simu mulat atio ions
24 24
( )
1 1 n n n n n w w w w
q q h T T
+ +
= + −
SLIDE 25 HTC an and d Reference T Temp c come me in in pair pairs
– HTC choices may not be satisfactory if not paired to the proper Reference Temperature
Specif ifie ied Y d Y+ HTC r C recomm mmende ded Co Coupling t to other c code des
– Solid passes wall temperature – Fluid passes HTC and Reference Temperature such that – Initial Wall temperatures same in both codes
Conclusio sions
w ref w
q T T h = +
