Elliptic Blending with One-Equation Model

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M. M. Rahman
M. M. Rahman
σ
Xiaoqing Tian
Xiaoqing Tian
ρ
Huachen Pan
Huachen Pan
Ѡ
A. K. M. Sadrul Islam
A. K. M. Sadrul Islam

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Elliptic Blending with One-Equation Model

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Abstract

A wall-distance-free modification to Wray-Agarwal (WA) one-equation turbulence model is convoked using an elliptic relaxation approach to accurately accounting for non-local characteristics of near-wall turbulence. Model coefficients/functions are parameterized with the elliptic relaxation function to preserve the combined effects of near-wall turbulence and nonequilibrium. The characteristic length scale associated with the elliptic relaxation equation is formulated in terms of viscous and turbulent length scales in conjunction with the invariant of strain-rate tensor. Consequently, non-local effects are explicitly influenced by the mean flow and turbulent variables. A near-wall damping function is introduced to relax the viscous length-scale coefficient adhering to the elliptic relaxation model. Comparisons indicate that the new model improves the accuracy of flow simulations compared to the widely used Spalart-Allmaras model and remains competitive with the SST model. A good correlation is obtained between the current model and DNS/experimental data.

References

13 Cites in Article
  1. P Durbin (1991). Near-wall turbulence closure modeling without “damping functions”.
  2. M Rahman,T Siikonen (2006). Low-Reynolds Number k-epsilon Model with Elliptic Relaxation Function.
  3. M Rahman,T Siikonen (2007). A Simplified v2-f Model for Near-Wall Turbulence.
  4. M Rahman,T Siikonen (2008). Near-Wall Turbulence Modeling with Elliptic Relaxation Approach.
  5. M Rahman,T Siikonen (2009). An eddy viscosity model with elliptic relaxation approach.
  6. Tae Park,Hyung Sung (1997). A new low-Reynolds-number<i>k</i>-ϵ-<i>f</i><sub>μ</sub>model for predictions involving multiple surfaces.
  7. P Durbin,N Mansour,Z Yang (1994). Eddy viscosity transport model for turbulent flow.
  8. M Rahman,T Siikonen,R Agarwal (2011). Improved Low Re-number One-Equation Turbulence Model.
  9. Md Rahman,Stefan Wallin,Timo Siikonen (2012). Exploring k and ϵ with R–Equation Model Using Elliptic Relaxation Function.
  10. M Elkhoury (2017). On the eddy viscosity transport models with elliptic relaxation.
  11. Timothy Wray,Ramesh Agarwal (2015). Low-Reynolds-Number One-Equation Turbulence Model Based on k-ω Closure.
  12. T Wray (2016). Development of a One-Equation Eddy Viscosity Turbulence Model for Application to Complex Turbulent Flows.
  13. P Spalart,S Allmaras (1992). A One-Equation Turbulence Model for Aerodynamic Flows.

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

How to Cite This Article

M. M. Rahman. 2020. \u201cElliptic Blending with One-Equation Model\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 20 (GJSFR Volume 20 Issue F2): .

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Issue Cover
GJSFR Volume 20 Issue F2
Pg. 55- 64
Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords
Classification
GJSFR-F Classification: MSC 2010: 11G05
Version of record

v1.2

Issue date

March 23, 2020

Language
en
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Published Article

A wall-distance-free modification to Wray-Agarwal (WA) one-equation turbulence model is convoked using an elliptic relaxation approach to accurately accounting for non-local characteristics of near-wall turbulence. Model coefficients/functions are parameterized with the elliptic relaxation function to preserve the combined effects of near-wall turbulence and nonequilibrium. The characteristic length scale associated with the elliptic relaxation equation is formulated in terms of viscous and turbulent length scales in conjunction with the invariant of strain-rate tensor. Consequently, non-local effects are explicitly influenced by the mean flow and turbulent variables. A near-wall damping function is introduced to relax the viscous length-scale coefficient adhering to the elliptic relaxation model. Comparisons indicate that the new model improves the accuracy of flow simulations compared to the widely used Spalart-Allmaras model and remains competitive with the SST model. A good correlation is obtained between the current model and DNS/experimental data.

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Elliptic Blending with One-Equation Model

M. M. Rahman
M. M. Rahman Hajee Mohammad Danesh Science and Technology University
Xiaoqing Tian
Xiaoqing Tian
Huachen Pan
Huachen Pan
A. K. M. Sadrul Islam
A. K. M. Sadrul Islam

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