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A novel numerical treatment of the near-wall regions in the k–ω class of RANS models

Journal Article · · International Journal of Heat and Fluid Flow
 [1];  [2];  [3];  [2];  [2];  [2]
  1. Aristotle Univ. of Thessaloniki (Greece); Argonne National Lab. (ANL), Argonne, IL (United States)
  2. Argonne National Lab. (ANL), Argonne, IL (United States)
  3. Univ. of Illinois at Urbana-Champaign, Urbana, IL (United States); Argonne National Lab. (ANL), Argonne, IL (United States)
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In this study, we discuss a novel approach to modeling the near-wall region in the class of k–ω to models. The proposed methodology obviates the need for ad hoc boundary conditions of to omega on the wall as typically required in the k–ω model. The primary motivation of this work is to provide a formulation equivalent to the standard k–ω to and k–ω to SST models, but which at the same time overcomes their limitations in the context of their implementation in high-order methods. This is achieved by subtracting the asymptotically known singular behavior of omega at walls. Imposing a grid-dependent value of omega at walls in high-order codes is not straightforward as is demonstrated below and it causes instability as well as accuracy issues. The mathematical formulation of the two novel approaches, termed as the "regularized k–ω model" and the "regularized k–ω OJ SST model", is discussed in detail. A consistency and verification study for these two approaches is performed by proving that the regularized models recover the results of the standard models in various canonical problems, such as turbulent channel and pipe flows, and a systematic investigation of convergence, using both p- (polynomial order) as well as h- (grid) refinement is reported. Furthermore, comparisons highlighting the performance of the proposed methods in more complex configurations such as flow over a backward facing step and the turbulent mixing of fluid streams of different temperatures in a T-junction are also presented.

Research Organization:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Organization:
USDOE Office of Nuclear Energy (NE), Nuclear Energy Advanced Modeling and Simulation (NEAMS)
Grant/Contract Number:
AC02-06CH11357
OSTI ID:
1472080
Alternate ID(s):
OSTI ID: 1564431
OSTI ID: 22807539
Journal Information:
International Journal of Heat and Fluid Flow, Journal Name: International Journal of Heat and Fluid Flow Journal Issue: C Vol. 72; ISSN 0142-727X
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

References (15)

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Direct numerical simulation of turbulent channel flow up to Reτ=590 journal April 1999
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Cited By (3)

Numerical errors at walls: on the sensitivity of RANS models to near-wall cell size journal March 2020
Numerical errors at walls: on the sensitivity of RANS models to near-wall cell size text January 2020
Numerical errors at walls: on the sensitivity of RANS models to near-wall cell size text January 2020

Figures / Tables (20)

Table 1(p. 9)table Table 1
Figure 1(p. 10)figure Figure 1
Figure 2(p. 11)figure Figure 2
Figure 3(p. 12)figure Figure 3
Figure 4(p. 13)figure Figure 4
Figure 5(p. 13)figure Figure 5
Figure 6(p. 13)figure Figure 6
Figure 7(p. 15)figure Figure 7
Figure 8(p. 16)figure Figure 8
Figure 9(p. 17)figure Figure 9
Figure 10(p. 18)figure Figure 10
Figure 11(p. 19)figure Figure 11
Figure 12(p. 20)figure Figure 12
Figure 13(p. 21)figure Figure 13
Figure 14(p. 22)figure Figure 14
Figure 15(p. 23)figure Figure 15
Figure 16(p. 24)figure Figure 16
Figure 17(p. 25)figure Figure 17
Figure 18(p. 26)figure Figure 18
Figure 19(p. 27)figure Figure 19

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Regularized
SST
k - w
uRANS