Advanced Wall Treatment
Method for Turbulent Flow CFD
Simulations
STAR European Conference
Amsterdam, 22-23 March, 2011
Mika Nuutinen
Aalto University School of Science and Technology
NEAR WALL HEAT AND
MOMENTUM TRANSFER
Difficult to measure or simulate
18
Enormous gradients (T, U)
14
12
re a listic* profile
wa ll function profile
10
u+
Strong variation of (!
!, ", #, cp)
with T
16
8
la mina r−turbule nt switch point
6
Anisotropic near wall
turbulence
4
2
0
20
40
60
80
100
+
y or y*
120
140
160
180
200
HEAT (MOMENTUM) TRANSFER IN
CFD
Direct Numerical Simulation (DNS)
$ Accurate but too heavy for most engineering
simulations
Large Eddy Simulation (LES)
$ Still too heavy for accurate near wall modeling
Reynold Averad Navier-Stokes (RANS)
$ Economical but inaccurate with standard methods
NEAR WALL RANS MODELING
OPTIONS
 Low-Re/Two-layer models
$ require extensively fine mesh
 High-Re models with wall functions
$ huge property variations, e.g. !(T), impair
accuracy
 Advanced wall treatment/turbulence model $
$ Less restrictions, high accuracy!!!
ADVANCED WALL TREATMENT/
TURBULENCE MODEL
 Based on a Low-Re k-εε turbulence model
 Relevant profiles discretized in wall
adjacent cells, integrated numerically
 Discretization ADAPTIVE to local
conditions!!!
 Accounts for grad(T) induced property
variations (ρ
ρ, µ, k, cp)
ADVANCED WALL TREATMENT/
TURBULENCE MODEL
 Enhanced accuracy in near wall turbulence
source computation with any resolution
(utilizing the discrete profiles)
 Free from the usual High/Low Re model
grid spacing requirements
VALIDATION AGAINST MEAS. AND
DNS-DATA, WALL TEMPERATURE
2.8
2.6
2.4
2.2
T w /T i
 Pipe Flow
 Re=4300
 D=27.4mm
 L=0.96m
 q=3980W/m^2
 y+<1
3
2
1.8
1.6
pre se nt study
S he ha ta & McE ligot, me a s.
1.4
B a e , e t a l., D N S
1.2
low−R e k−ε + hybrid wa ll tr.
high−R e k−ε + wa ll func.
1
0
0.1
0.2
0.3
0.4
0.5
x[m]
0.6
0.7
0.8
0.9
1
VALIDATION AGAINST MEAS.,
T(r)
CI ENGINE HEAT TRANSFER
SIMULATIONS, 3D GRID
CI ENGINE HEAT TRANSFER
SIMULATIONS, SURFACE TEMP.
Advanced
T=787K
High-Re
T=717K
Low-Re hybr.
T=735K
TOTAL PISTON HEAT LOSS
Conjugate Heat Transfer
Const. Temp. B.C.
CONCLUSIONS & FUTURE GOALS
 Advanced model consistent with
measurements and DNS
 Advanced model adaptive to grid resolution
 Advanced model successfully implemented
on a commercial CFD code (Star-CD)
 Goals
$ Further model development
$ Piston temperature measurements
Near wall treatment equations
2
 ∂u 
∂ 2k
− µ 2 = µ t   − ρε
∂y
 ∂y 
∂2k
k
µ 2 = 2µ 2
∂y
y
C µ3 / 4 k 3 / 2
µ k
~
+2
=
ε = ε + ε wall =
κy
ρ y2
ρC µ k 2 f µ1  ∂u 
  = ρε~
ε~
 ∂y 
f µ1 = (1 − exp(− α µ Re y ))
C µ3 / 4 k 3 / 2  2κC µ−3 / 4
1 +
Re y
κy 

ε~1 +

α ε 
Re y 
(µ + µ t ) ∂u = τ w

=


y =0
2
y+ =
ρ w uτ y
µw
u+ =
u
uτ
µ µ
c p  + t
 Pr Prt
 ∂T

= qw
 ∂y
 (T − Tw )
y c+
c p,w µ w  c
=
+
Tc
 yc 
 (Tc − Tw ) 

 yc 
du +
=
dy + λ +
1
ρ w c p , w uτ (T − Tw )
uτ = τ w / ρ w
qw =
β + c p,w µ w 
∂y
T+ =
u − uw 
y c+
τ w = + µw  c
=
uc
 yc 
u − uw 
α +µw  c

 yc 
2
(λ + 4λ (κy ) f )
2
1
+ 2
4
Prw Prt
dT +
=
+
dy
λ2 Prt + λ3 Prw µ +
qw
µ+ =
2
µt
du +
= λ4 (κy + ) f µ31/ 2 +
µw
dy
3/ 2
µ1
Equations cont.
1/ 2
 yc* 2 f µ11/,2c

yc*
+

yc = λ1,c 
+
1/ 2 
 λ 4,c
λ4,c f µ1,cκ


( )
 ∂u
P wf = µ w µ +  +
 ∂y
+
(ρε )wf
 ∂u +
 +
 ∂y
  y uc − uw 
 

yc 
 u
+
c
+
c

 2κ 2
= µ w µ + + µ  1 / 2
C

 µ
2
  y c+ u c − u w 
  +

yc 
 uc
 y + ∂u +
= µ w µ  c+
+
 u c ∂y
+
 
 f µ1  ×
 
 
2
=
χ dissip
avg
χ dissip ,c
(ρε )c
χ dissip

 2κ 2
= µ w µ + + µ  1 / 2
C

 µ
Pavg ,tot

 ∂u t
=  P1 + P2 − µ t ,c  r

 ∂n
2
∂u
∂u rt
 
= n , ∇u rt = t i n j i
∂n
∂x j
uc − u w 


avg
 yc 
Pavg = χ prod
χ prod
2
(ρε )avg




2
2
  ∂u +
 f µ1 
  ∂y +
 



2




 + Pavg

2
THANK YOU!
QUESTIONS AND COMMENTS ARE
WELLCOME!