A Dissipation Rate Equation for Low-Reynolds-Number and Near-Wall Turbulence

1997 ◽  
Vol 9 (1) ◽  
pp. 47-63 ◽  
Author(s):  
R.M.C. So ◽  
A. Sarkar ◽  
G. Gerodimos ◽  
J. Zhang
Keyword(s):  
Reynolds Number ◽  
Rate Equation ◽  
Dissipation Rate ◽  
Low Reynolds Number ◽  
Wall Turbulence ◽  
Low Reynolds ◽  
Near Wall Turbulence ◽  
Near Wall

On near-wall turbulent flow modelling

1990 ◽  
Vol 221 ◽  
pp. 641-673 ◽  
Author(s):  
Y. G. Lai ◽  
R. M. C. So
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Reynolds Stress ◽  
Rate Equation ◽  
Dissipation Rate ◽  
Wall Turbulence ◽  
Pressure Diffusion ◽  
Velocity Pressure ◽  
Near Wall Turbulence ◽  
Near Wall

The characteristics of near-wall turbulence are examined and the result is used to assess the behaviour of the various terms in the Reynolds-stress transport equations. It is found that all components of the velocity-pressure-gradient correlation vanish at the wall. Conventional splitting of this second-order tensor into a pressure diffusion part and a pressure redistribution part and subsequent neglect of the pressure diffusion term in the modelled Reynolds-stress equations leads to finite near-wall values for two components of the redistribution tensor. This, therefore, suggests that, in near-wall turbulent flow modelling, the velocity-pressure-gradient correlation rather than pressure redistribution should be modelled. Based on this understanding, a methodology to derive an asymptotically correct model for the velocity-pressure-gradient correlation is proposed. A model that has the property of approaching the high-Reynolds-number model for pressure redistribution far away from the wall is derived. A similar analysis is carried out on the viscous dissipation term and asymptotically correct near-wall modifications are proposed. The near-wall closure based on the Reynolds-stress equations and a conventional low-Reynolds-number dissipation-rate equation is used to calculate fully-developed turbulent channel and pipe flows at different Reynolds numbers. A careful parametric study of the model constants introduced by the near-wall closure reveals that one constant in the dissipation-rate equation is Reynolds-number dependent, and a preliminary expression is proposed for this constant. With this modification, excellent agreement with near-wall turbulence statistics, measured and simulated, is obtained, especially the anisotropic behaviour of the normal stresses. On the other hand, it is found that the dissipation-rate equation has a significant effect on the calculated Reynolds-stress budgets. Possible improvements could be obtained by using available direct simulation data to help formulate a more realistic dissipation-rate equation. When such an equation is available, the present approach can again be used to derive a near-wall closure for the Reynolds-stress equations. The resultant closure could give improved predictions of the turbulence statistics and the Reynolds-stress budgets.

Low-Reynolds-number k-epsilon-tilde model with enhanced near-wall dissipation introduction

AIAA Journal ◽  
2002 ◽  
Vol 40 ◽  
pp. 1462-1464
Author(s):  
M. Rahman ◽  
T. Siikonen
Keyword(s):  
Reynolds Number ◽  
Low Reynolds Number ◽  
Low Reynolds ◽  
Near Wall

Contribution towards a Reynolds-stress closure for low-Reynolds-number turbulence

1976 ◽  
Vol 74 (4) ◽  
pp. 593-610 ◽  
Author(s):  
K. Hanjalić ◽  
B. E. Launder
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Reynolds Stress ◽  
Dissipation Rate ◽  
Numerical Solutions ◽  
Low Reynolds Number ◽  
Transport Processes ◽  
Turbulent Shear ◽  
Turbulent Shear Stress ◽  
Low Reynolds

The problem of closing the Reynolds-stress and dissipation-rate equations at low Reynolds numbers is considered, specific forms being suggested for the direct effects of viscosity on the various transport processes. By noting that the correlation coefficient$\overline{uv^2}/\overline{u^2}\overline{v^2} $is nearly constant over a considerable portion of the low-Reynolds-number region adjacent to a wall the closure is simplified to one requiring the solution of approximated transport equations for only the turbulent shear stress, the turbulent kinetic energy and the energy dissipation rate. Numerical solutions are presented for turbulent channel flow and sink flows at low Reynolds number as well as a case of a severely accelerated boundary layer in which the turbulent shear stress becomes negligible compared with the viscous stresses. Agreement with experiment is generally encouraging.

scholarly journals Turbulent Flow Computations in Rotating Cavities Using Low-Reynolds-Number Models

1996 ◽  
Author(s):  
Hector Iacovides ◽  
Kostas S. Nikas ◽  
Marcel A. F. Te Braak
Keyword(s):  
Reynolds Number ◽  
Dissipation Rate ◽  
Correction Term ◽  
Low Reynolds Number ◽  
Moment Closure ◽  
Rotating Disc ◽  
Moment Coefficient ◽  
Second Moment Closure ◽  
Low Reynolds ◽  
Radial Outflow

This study is concerned with the use of low-Reynolds-number models of turbulence transport in the computation of flows through rotating cavities. The models tested are the Launder and Sharma low-Re k-ε (L-S) and a low-Re differential second-moment closure (DSM), first used by Iacovides and Toumpanakis, both with and without the Yap correction term to the dissipation rate equation. The cases examined include rotor-stator systems without throughflow, rotor-stator systems with radial outflow, contra-rotating disc systems without throughflow and also with radial outflow, co rotating discs with radial outflow and also rotor-stator systems with radial inflow. Earlier studies have shown that, when no throughflow or when radial outflow is involved, the L-S tends to over-estimate the size of the regions over which the boundary layers remain laminar, while the zonal k-ε/l-eqn model is unable to predict partially laminarized flows. A modification to the ε equation proposed here, which in regions of low turbulence reduces the dissipation rate when the fluid is in solid body rotation, provides a simple empirical way to significantly improve the L-S predictions of partially laminarized flows through rotating cavities, to acceptable levels. The DSM model used, in some cases led to some further predictive improvements and, for rotor-stator systems without throughflow, to a significant improvement in the predicted value of the moment coefficient. The Yap length scale correction term, while in most cases it has either a beneficial or a neutral effect on the flow predictions, in cases involving radial inflow it leads to poorer predictions. Models that do not rely on wall distance thus appear more likely to have a wider range of applicability.

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