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

Abstract

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.

Authors:
 [1];  [2];  [3];  [2];  [2];  [2]
+ Show Author Affiliations
  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)
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Nuclear Energy (NE), Nuclear Energy Advanced Modeling and Simulation (NEAMS); USDOE Office of Nuclear Energy (NE); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
OSTI Identifier:
1472080
Alternate Identifier(s):
OSTI ID: 1564431
Grant/Contract Number:  
AC02-06CH11357
Resource Type:
Accepted Manuscript
Journal Name:
International Journal of Heat and Fluid Flow
Additional Journal Information:
Journal Volume: 72; Journal Issue: C; Journal ID: ISSN 0142-727X
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; uRANS; k - w; Regularized; SST

Citation Formats

Tomboulides, A., Aithal, S. M., Fischer, P. F., Merzari, E., Obabko, A. V., and Shaver, D. R. A novel numerical treatment of the near-wall regions in the k–ω class of RANS models. United States: N. p., 2018. Web. doi:10.1016/j.ijheatfluidflow.2018.05.017.
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Tomboulides, A., Aithal, S. M., Fischer, P. F., Merzari, E., Obabko, A. V., & Shaver, D. R. A novel numerical treatment of the near-wall regions in the k–ω class of RANS models. United States. https://doi.org/10.1016/j.ijheatfluidflow.2018.05.017
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Tomboulides, A., Aithal, S. M., Fischer, P. F., Merzari, E., Obabko, A. V., and Shaver, D. R. Sat . "A novel numerical treatment of the near-wall regions in the k–ω class of RANS models". United States. https://doi.org/10.1016/j.ijheatfluidflow.2018.05.017. https://www.osti.gov/servlets/purl/1472080.
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@article{osti_1472080,
title = {A novel numerical treatment of the near-wall regions in the k–ω class of RANS models},
author = {Tomboulides, A. and Aithal, S. M. and Fischer, P. F. and Merzari, E. and Obabko, A. V. and Shaver, D. R.},
abstractNote = {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.},
doi = {10.1016/j.ijheatfluidflow.2018.05.017},
journal = {International Journal of Heat and Fluid Flow},
number = C,
volume = 72,
place = {United States},
year = {Sat Jun 23 00:00:00 EDT 2018},
month = {Sat Jun 23 00:00:00 EDT 2018}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1016/j.ijheatfluidflow.2018.05.017
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Citation Metrics:
Cited by: 15 works
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Figures / Tables:

Table 1 Table 1: Predicted friction velocity uτ for various formulations of the k-ω model.
All figures and tables (20 total)
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Works referenced in this record:

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journal, November 2013

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    Works referencing / citing this record:

    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

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

    • Lloyd, C. J.; Peakall, J.; Burns, A. D.
    • International Journal of Computational Fluid Dynamics, Vol. 34, Issue 3
    • DOI: 10.1080/10618562.2020.1732941
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      Figures / Tables found in this record:

      Table 1 (p. 9)table
      Figure 1 (p. 10)figure
      Figure 2 (p. 11)figure
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      Figure 18 (p. 26)figure
      Figure 19 (p. 27)figure
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