Publication Date:
2014-11-07
Description:
In this study, we revisit the consequence of assuming equilibrium between the rates of production (P) and dissipation (∈) of the turbulent kinetic energy (k) in the highly anisotropic and inhomogeneous near-wall region. Analytical and dimensional arguments are made to determine the relevant scales inherent in the turbulent viscosity (ν〈inf〉t〈/inf〉) formulation of the standard k-∈ model, which is one of the most widely used turbulence closure schemes. This turbulent viscosity formulation is developed by assuming equilibrium and use of the turbulent kinetic energy (k) to infer the relevant velocity scale. We show that such turbulent viscosity formulations are not suitable for modelling near-wall turbulence. Furthermore, we use the turbulent viscosity (ν〈inf〉t〈/inf〉 formulation suggested by Durbin (Theor. Comput. Fluid Dyn., vol. 3, 1991, pp. 1-13) to highlight the appropriate scales that correctly capture the characteristic scales and behaviour of P/∈ in the near-wall region. We also show that the anisotropic Reynolds stress (u′¯v′¯) is correlated with the wall-normal, isotropic Reynolds stress (v′2¯) as -u′¯v′¯ = c′〈inf〉u〈/inf〉 (ST〈inf〉L〈/inf〉)(v′¯2), where S is the mean shear rate, T〈inf〉L〈/inf〉 =k/∈ is the turbulence (decay) time scale and c′〈inf〉u〈/inf〉 is a universal constant. 'A priori' tests are performed to assess the validity of the propositions using the direct numerical simulation (DNS) data of unstratified channel flow of Hoyas & Jiménez (Phys. Fluids, vol. 18, 2006, 011702). The comparisons with the data are excellent and confirm our findings. © 2014 Cambridge University Press.
Print ISSN:
0022-1120
Electronic ISSN:
1469-7645
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
