Determination of ϵ at inlet boundaries

Abstract

Different methods for the determination of accurate values for the dissipation rate ϵ at the inlet boundary of a computational domain, are studied. With DNS data for a fully developed channel flow and pipe flow, it is shown that the method suggested by Rhee and Sung (2000), in which the k–ϵ turbulence model is used to compute both k and ϵ from a given velocity profile, is not reliable and can result in very poor results. The method is found to be extremely sensitive to the details of the imposed velocity profile. An alternative procedure is proposed, in which only the ϵ transport equation is employed, with given profiles for the mean velocity and the turbulence kinetic energy. This way, accurate and reliable profiles are obtained for ϵ. Another procedure, based on the turbulent mixing length, was suggested by Jones (1994). The problem. The problem is then shifted towards the determination of the mixing length at the inlet boundary of the computational domain. An expression for this mixing length is proposed in this paper, based on the mentioned DNS data. Finally, the method proposed by Rodi and Scheuerer (1985) is included for comparison reasons. The different procedures are first validated on the fully developed channel and pipe flow. Next, the turbulent flow over a backward‐facing step is considered. Finally, the influence of the inlet boundary condition for ϵ is illustrated in the application of a turbulent piloted jet diffusion flame.

Citation

Merci, B., Dick, E., Vierendeels, J. and De Langhe, C. (2002), "Determination of ϵ at inlet boundaries", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 12 No. 1, pp. 65-80. https://doi.org/10.1108/09615530210413172