This study presents a new near-wall treatment for low-Reynolds number (LRN) turbulence models that maintains accuracy in ‘coarse’ mesh predictions. The method is based on a thorough examination of approximations made when integrating the discretized equations in the near-wall region. A number of modifications are proposed that counteract errors introduced when an LRN-model is used on meshes for which the first interior node is located at $y+≈5.$ Here the methodology is applied to the $k−ω$ turbulence model by Bredberg et al., although similar corrections are relevant for all LRN models. The modified model gives asymptotically, in the sense of mesh refinement, identical results to the baseline model. For coarser meshes $y+⩽10,$ the present method improves numerical stability with less mesh-dependency than the non-modified model. Results are included for fully developed channel flow, a backward-facing step flow and heat transfer in a periodic rib-roughened channel.

1.
Bredberg
,
J.
,
Peng
,
S-H.
, and
Davidson
,
L.
,
2002
,
An Improved k−ω Turbulence Model Applied to Recirculating Flows
.
Int. J. Heat Fluid Flow
,
23
,
731
743
.
2.
S. V. Patankar, and D. B. Spalding, 1970, Heat and Mass Transfer in Boundary Layers. Intertext Books, London.
3.
D. C. Wilcox, 1993, Turbulence Modeling for CFD. DCW Industries, Inc.
4.
Launder
,
B. E.
,
1984
,
Numerical Computation of Convective Heat Transfer in Complex Turbulent Flows: Time to Abandon Wall Functions?
Int. J. Heat Mass Transfer
,
27
,
1485
1491
.
5.
Launder
,
B. E.
, and
Spalding
,
D. B.
,
1974
,
The Numerical Computation of Turbulent Flows
.
Comput. Methods Appl. Mech. Eng.
,
3
,
269
289
.
6.
Chieng
,
C. C.
, and
Launder
,
B. E.
,
1980
,
On the Calculation of Turbulent Heat Transfer Transport Downstream an Abrupt Pipe Expansion
.
Numer. Heat Transfer
,
3
,
189
207
.
7.
Johnson
,
R. W.
, and
Launder
,
B. E.
,
1982
,
Discussion of: On the Calculation of Turbulent Heat Transfer Transport Downstream an Abrupt Pipe Expansion
.
Numer. Heat Transfer
,
5
,
493
496
.
8.
Ciofalo
,
M.
, and
Collins
,
M. W.
,
1989
,
k−ε Predictions of Heat Transfer in Turbulent Recirculating Flows Using an Improved Wall Treatment
.
Numer. Heat Transfer
,
15
,
21
47
.
9.
Amano
,
R. S.
,
Jensen
,
M. K.
, and
Goel
,
P.
,
1983
,
A Numerical and Experimental Investigation of Turbulent Heat Transport Downstream From an Abrupt Pipe Expansion
.
J. Heat Transfer
,
105
,
862
869
.
10.
Amano
,
R. S.
,
1984
,
Development of a Turbulence Near-wall Model and its Application to Separated and Reattached Flows
.
Numer. Heat Transfer
,
7
,
59
75
.
11.
Acharya
,
S.
,
Dutta
,
S.
, and
Myrum
,
T. A.
,
1998
,
Heat Transfer in Turbulent Flow Past a Surface-mounted Two-dimensional Rib
.
J. Heat Transfer
,
120
,
724
734
.
12.
Heyerichs
,
K.
, and
Pollard
,
A.
,
1996
,
Heat transfer in Separated and Impinging Turbulent Flows
.
Int. J. Heat Mass Transfer
,
39
,
2385
2400
.
13.
J. Bredberg, 2002, Turbulence Modelling for Internal Cooling of Gas-Turbine Blades. Ph.D. thesis, Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology, Gothenburg. Also available at www.tfd.chalmers.se/∼lada.
14.
Iacovides
,
H.
, and
Launder
,
B. E.
,
1984
,
PSL-an Economical Approach to the Numerical Analysis of Near-wall, Elliptic Flow
.
J. Fluids Eng.
,
106
,
241
242
.
15.
Choi
,
Y. D.
,
Iacovides
,
H.
, and
Launder
,
B. E.
,
1989
,
Numerical Computation of Turbulent Flow in a Square-sectioned 180 Deg Bend
.
J. Fluids Eng.
,
111
,
59
68
.
16.
Spalding
,
D. B.
,
1967
,
Heat Transfer from Turbulent Separated Flows
.
J. Fluid Mech.
,
27
,
97
109
.
17.
Wolfshtein
,
M.
,
1969
,
The Velocity and Temperature Distribution in One-dimensional Flow with Turbulence Augmentation and Pressure Gradient
.
Int. J. Heat Mass Transfer
,
12
,
301
318
.
18.
T. J. Craft, A. V. Gerasimov, H. Iacovides, and B. E. Launder, 2001, Progress in the Generalization of Wall-function Treatments. Report, Dept. of Mechanical Engineering, UMIST, Manchester.
19.
T. J. Craft, A. V. Gerasimov, H. Iacovides, B. E. Launder, and C. Robinson, 2001, A New Wall Function Strategy for Forced and Mixed Convection. In: 2nd Int. Symp. on Turbulent Shear Flow Phenomena, pages 1–20, Stockholm.
20.
Wilcox
,
D. C.
,
1988
,
Reassessment of the Scale-determining Equation for Advanced Turbulence Models
.
AIAA J.
,
26
,
1299
1310
.
21.
J. Bredberg, S-H. Peng, and L. Davidson, 2000, On the Wall Boundary Condition for Computing Heat Transfer with k−ω Models. In: J. H. Kim, editor, HTD-Vol. 366-5, ASME Heat Transfer Division-2000, 5, pages 243–250, Orlando. The American Society of Mechanical Engineers.
22.
J. Bredberg, 2000, On the Wall Boundary Condition for Turbulence Model. Report 00/4, Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology, Gothenburg. Also available at www.tfd.chalmers.se/∼lada.
23.
P. Rautaheimo, and T. Siikonen, 2000, Improved Solid-wall Boundary Treatment in Low-Reynolds Number Turbulent Models. AIAA Paper 2000–0136, Reno, NV, USA.
24.
H. Grotjans, and F. R. Menter, 1998, Wall Functions for General Application CFD Codes. In: CD-ROM Proceedings of ECCOMAS, pages 1112–1117, Athens.
25.
Kays
,
W. M.
,
1994
,
Turbulent Prandtl Number-where Are We?
J. Heat Transfer
,
116
,
284
295
.
26.
H. Tennekes, and J. L. Lumley, 1972, A First Course in Turbulence. Massachusetts Institute of Technology, Cambridge.
27.
Hanjalic´
,
K.
, and
Launder
,
B. E.
,
1976
,
Contribution Towards a Reynolds-stress Closure for Low-Reynolds-number Turbulence
.
J. Fluid Mech.
,
74
,
593
610
.
28.
R. D.
Moser
,
J.
Kim
, and
N. N.
Mansour
,
1999
,
Direct Numerical Simulation of Turbulent Channel Flow up to Re=590.
Physics of Fluids
,
11
:
943
945
. Data available at www.tam.uiuc.edu/Faculty/Moser/.
29.
Mansour
,
N. N.
,
Kim
,
J.
, and
Moin
,
P.
,
1988
,
Reynolds-stress and Dissipation-rate Budgets in a Turbulent Channel Flow
.
J. Fluid Mech.
,
194
,
15
44
.
30.
K. Hanjalic´, 2002, Near-wall behavior of ε and ω. Private Communication, Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology, Gothenburg.
31.
Huang
,
P. G.
, and
,
P.
,
1995
,
Law of the Wall for Turbulent Flows in Pressure Gradients
.
AIAA J.
,
33
,
624
632
.
32.
Abe
,
K.
,
Kondoh
,
T.
, and
Nagano
,
Y.
,
1994
,
A New Turbulence Model for Predicting Fluid Flow and Heat Transfer in Separating and Reattaching Flows-I. Flow Field Calculations
.
Int. J. Heat Mass Transfer
,
37
,
139
151
.
33.
Le
,
H.
,
Moin
,
P.
, and
Kim
,
J.
,
1997
,
Direct Numerical Simulation of Turbulent Flow Over a Backward-facing Step
.
J. Fluid Mech.
,
330
,
349
374
.
34.
Rau
,
G.
,
Cakan
,
M.
,
Moeller
,
D.
, and
Arts
,
T.
,
1998
,
The Effect of Periodic Ribs on the Local Aerodynamic and Heat Transfer Performance of a Straight Cooling Channel
.
J. Turbomach.
,
120
,
368
375
.
35.
L. Davidson, and B. Farhanieh, 1995, CALC-BFC. Report 95/11, Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology, Gothenburg.
36.
van Leer
,
B.
,
1974
,
Towards the Ultimate Conservative Difference Monotonicity and Conservation Combined in a Second-order Scheme
.
J. Comput. Phys.
,
14
,
361
370
.
37.
Rhie
,
C. M.
, and
Chow
,
W. L.
,
1983
,
Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation
.
AIAA J.
,
21
,
1525
1532
.
38.
W. B. George, 2001, Lecture notes, Turbulence Theory. Report, Dept. Thermo and Fluid Dynamics, Chalmers University of Technology, Gothenburg.
39.
Dittus
,
F. W.
, and
Boelter
,
L. M. K.
,
1930
,
Heat Transfer in Automobile Radiators of the Tubular Type
.
Univ. Calif. Publ. Eng.
,
2
,
443
461
.
40.
W. H. McAdams, 1942, Heat Transmission. McGraw-Hill, New York, 2nd edition.