0
Special Section Articles

The Effect of a Pressure-Containing Correlation Model on Near-Wall Flow Simulations With Reynolds Stress Transport Models

[+] Author and Article Information
Svetlana V. Poroseva

Assistant Professor
Department of Mechanical Engineering,
The University of New Mexico,
Albuquerque, NM 87131-0001
e-mail: poroseva@unm.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 22, 2013; final manuscript received October 28, 2013; published online April 28, 2014. Assoc. Editor: Ye Zhou.

J. Fluids Eng 136(6), 060909 (Apr 28, 2014) (8 pages) Paper No: FE-13-1256; doi: 10.1115/1.4025936 History: Received April 22, 2013; Revised October 28, 2013

It is accustomed to think that turbulence models based on solving the Reynolds-averaged Navier–Stokes (RANS) equations require empirical functions to accurately reproduce the behavior of flow characteristics of interest, particularly near a wall. The current paper analyzes how choosing a model for pressure-strain correlations in second-order closures affects the need for introducing empirical functions in model equations to reproduce the flow behavior near a wall correctly. An axially rotating pipe flow is used as a test flow for the analysis. Results of simulations demonstrate that by using more physics-based models to represent pressure-strain correlations, one can eliminate wall functions associated with such models. The higher the Reynolds number or the strength of imposed rotation on a flow, the less need there is for empirical functions regardless of the choice of a pressure-strain correlation model.

FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Monin, A. S., and Yaglom, A. M., 1979, Statistical Fluid Mechanics: Mechanics of Turbulence, Vol. 1, The MIT Press, Cambridge, MA, Chap. 4.
Lumley, J. L., 1975, “Introduction,” Lecture Series 76, Prediction Methods for Turbulent Flows, von Kármán Institute for Fluid Dynamics, Rhode-St-Genese, Belgium.
Rumsey, C. L., Gatski, T. B., SellersIII, W. L., Vatsa, V. N., and Viken, S. A., 2004, “Summary of the 2004 CFD Validation Workshop on Synthetic Jets and Turbulent Separation Control,” Proc. 2nd AIAA Flow Control Conference, AIAA-2004-2217,.
Johansson, T. G., and Davidson, L., 2006, “The 11th ERCOFTAC Workshop on Refined Turbulence Modelling,” the Czestochowa University of Technology, Czestochowa, Poland, ERCOFTAC Bulletin, 69-2006.
Thiele, F., and Jakirlic, S., 2007, “The 12th ERCOFTAC/IAHR/COST Workshop on Refined Turbulence Modelling,” the Czestochowa University of Technology, Czestochowa, Poland, ERCOFTAC Bulletin, 75-2007.
Torii, S., and Yang, W., 1995, “Numerical Prediction of Fully Developed Turbulent Swirling Flows in an Axially Rotating Pipe by Means of a Modified k-ε Turbulence Model,” Int. J. Numer. Meth. Heat Fluid Flow, 5, pp. 175–183. [CrossRef]
Hanjalić, K., and Launder, B., 2011, Modelling Turbulence in Engineering and the Environment, Cambridge University Press, Cambridge, UK.
Kurbatskii, A. F., Poroseva, S. V., and Yakovenko, S. N., 1995, “Calculation of Statistical Characteristics of a Turbulent Flow in a Rotating Cylindrical Pipe,” High Temp., 33(5), pp. 738–748.
Kurbatskii, A. F., and Poroseva, S. V., 1997, “A Model for Calculating the Three Components of the Excess for the Turbulent Field of Flow Velocity in a Round Pipe Rotating About Its Longitudinal Axis,” High Temp., 35(3), pp. 432–440.
Kurbatskii, A. F., and Poroseva, S. V., 1999, “Modelling Turbulent Diffusion in a Rotating Cylindrical Pipe Flow,” Int. J. Heat Fluid Flow, 20(3), pp. 341–348. [CrossRef]
Daly, B. J., and Harlow, F. H., 1970, “Transport Equations in Turbulence,” Phys. Fluids, 13, pp. 2634–2649. [CrossRef]
So, R. M. C., and Yoo, G. J., 1986, “On the Modeling of Low-Reynolds-Number Turbulence,” NASA CR 3994.
Poroseva, S. V., Kassinos, S. C., Langer, C. A., and Reynolds, W. C., 2002, “Structure-Based Turbulence Model: Application to a Rotating Pipe Flow,” Phys. Fluids, 14(4), pp. 1523–1532. [CrossRef]
Kassinos, S. C., Langer, C. A., Haire, S. L., and Reynolds, W. C., 2000, “Structure-Based Turbulence Modeling for Wall–Bounded Flows,” Int. J. Heat Fluid Flow, 21, pp. 599–605. [CrossRef]
Rotta, J. C., 1951, “Statistische Theorie Nichthomogener Turbulenz,” Z. Phys., 129, pp. 547–572; 131, pp. 51–77. [CrossRef]
Poroseva, S. V., 2001, “Modeling the “Rapid” Part of the Velocity/Pressure-Gradient Correlation in Inhomogeneous Turbulence,” Annual Research Brief 2001, Center for Turbulence Research, NASA-Ames/Stanford University, pp. 367–374.
Poroseva, S. V., 2000, “New Approach to Modeling the Pressure-Containing Correlations,” Proc. of the 3rd Inter. Symposium on Turbulence, Heat and Mass Transfer, Nagoya, Japan, pp. 487–493.
Poroseva, S. V., and Iaccarino, G., 2001, “Simulating Separated Flows Using the k-ε Model,” Annual Research Brief 2001, Center for Turbulence Research, NASA-Ames/Stanford Univ., pp. 375–384.
Launder, B. E., Reece, G. J., and Rodi, W., 1975, “Progress in Development of a Reynolds-Stress Turbulent Closure,” J. Fluid Mech., 68, pp. 537–566. [CrossRef]
Gatski, T. B., and Speziale, C. G., 1993, “On Explicit Algebraical Stress Models for Complex Turbulent Flow,” J. Fluid Mech., 254, pp. 59–78. [CrossRef]
Speziale, C. G., Sarkar, S., and Gatski, T. B., 1991, “Modeling the Pressure-Strain Correlation of Turbulence: An Invariant Dynamical System Approach,” J. Fluid Mech., 227, pp. 245–272. [CrossRef]
Kassinos, S. C., Reynolds, W. C., and Rogers, M. M., 2001, “One-Point Turbulence Structure Tensors,” J. Fluid Mech., 428, pp. 213–248. [CrossRef]
Spalding, D. B., 1977, GENMIX: A General Computer Program for Two-Dimensional Parabolic Phenomena, Pergamon, New York.
Kikuyama, K., Murakami, M., Nishibori, K., and Maeda, K., 1983, “Flow in an Axially Rotating Pipe (a Calculation of Flow in the Saturated Region),” Bull. JSME, 26, pp. 506–513. [CrossRef]
Zaets, P. G., Safarov, N. A., and SafarovR. A.1985, “Experimental Study of the Behavior of Turbulence Characteristics in a Pipe Rotating Around Its Axis,” Modern Problems of Continuous Medium Mechanics, Moscow Physics and Technics Institute, Moscow, Russia, pp. 136–142 (in Russian).
Nishibori, K., Kikuyama, K., and Murakami, M., 1987, “Laminarization of Turbulent Flow in the Inlet Region of an Axially Rotating Pipe,” Bull. JSME, 30, pp. 255–262.
Imao, S., Itoh, M., and Harada, T., 1996, “Turbulent Characteristics of the Flow in an Axially Rotating Pipe,” Int. J. Heat Fluid Flow, 17, pp. 444–451. [CrossRef]
Laufer, J., 1954, “The Structure of Turbulence in Fully Developed Pipe Flow,” NASA Report 1174.

Figures

Grahic Jump Location
Fig. 1

Test flow geometry

Grahic Jump Location
Fig. 2

The axial mean velocity component of the IP-model at (a) Re=2×104 and (b) Re=4×104. Notations: IP model: —-; experiments: (a) ◻ N = 0, ▪ N = 0.5 [27] and (b) ⋄ N = 0, ♦ N = 0.6 [25].

Grahic Jump Location
Fig. 3

The IP-model profiles of (a) shear stress and (b) turbulent kinetic energy calculated at Re=4×104 (see notations in Fig. 2(b))

Grahic Jump Location
Fig. 4

The axial mean velocity components for LRR —-, LSSG - - - -, SSG ········, and Q- -··- models calculated at (a) Re=2×104 and (b) Re=4×104. Experiments: (a) ◻ N = 0, ▪ N = 0.5, ▼ N = 1 [27] and (b) ⋄ N = 0, ○ N = 0.15, ♦ N = 0.6 [25].

Grahic Jump Location
Fig. 5

The circumferential mean velocity components at (a) Re=2×104 and (b) Re=4×104 (see notations in Fig. 4)

Grahic Jump Location
Fig. 6

Shear stress at (a) Re=2×104 and (b) Re=4×104 (see notations in Fig. 4)

Grahic Jump Location
Fig. 7

Turbulent kinetic energy (a) Re=2×104 and (b) Re=4×104 (see notations in Fig. 4)

Grahic Jump Location
Fig. 8

The individual components of turbulent kinetic energy at the exit of the stationary pipe section at Re=4×104 for: (a) 〈u2〉/uτo2 (upper lines), 〈v2〉/uτo2 (lower lines) and (b) 〈w2〉/uτo2. Notations: —- LRR model, - - - - LSSG model, ········ SSG model, -··- Q-model; experiments: ¯ [25], r [28].

Grahic Jump Location
Fig. 9

Individual components of the turbulent kinetic energy at the exit of the stationary pipe section at Re=2×104 for: (a) 〈u2〉/Um (upper lines), 〈v2〉/Um (lower lines) and (b) 〈w2〉/Um. Notations: —- LRR model, - - - - LSSG model, ········ SSG model, -··- Q-model; experiments: ◻ [27].

Grahic Jump Location
Fig. 10

Effect of rotation on the individual components of turbulent kinetic energy at Re=4×104 (see notations in Fig. 4)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In