Testing a low-Reynolds number k-epsilon turbulence model based on direct simulation data

Abstract

T HE k-e model is mostly used in conjunction with the so-called wall functions, in which the viscosity-affected near-wall region is bridged with empirical relations based on the assumptions of a logarithmic velocity profile, local equilibrium of turbulence, and a constant near-wall stress layer. For a number of practically relevant flows, e.g., transitional, strongly accelerated (relaminarizing), and separating flows, these assumptions lose their validity. To allow a resoluton of the near-wall zone, Ipw-Reynolds-number versions of the k-e model have been developed by introducing damping functions arid extra terms to account for the observed near-wall effects.1 Because of a lack of reliable experimental data, these nearwall modifications have largely been based on dimensional reasoning, intuition, and indirect testing. A closer look reveals that even the more established models fail to reproduce the near-wall flow characteristics in detail, as will be shown later in this Note. Direct numerical simulation (DNS) data now available enable a direct and much more thorough assessment of near-wall models. Recently, Rodi and Mansour,2 hereafter referred to as RM, have evaluated the DNS channel flow data of Kirn et al. 3 and Kim4 and the zefo-pressure-gradient boundary-layer data of Spalart 5 and deduced new forms for the eddy-viscosity damping function and for the near-wall source/sink terms in the modeled e equation. The purpose of the present Note is to use and test these proposals in actual calculations of channel and boundary-layer flows and to fine tune the model functions by comparison with the DNS data. A more detailed account is given in Ref. 6. II. Low Reynolds Number k-e Modeling The k-e model employs the eddy-viscosity concept, and for the various low Re k-e models the relations determining the eddy viscosity vt can be written for 2£>o shear layers in the following form: Diffe where e — e - D and the various models differ through the use of different functions /M,/i, and/2 and different terms D and E. In Eq. (1), CM is a constant coefficient and/M is a damping function. Some models use as turbulence time scale k/e and solve an equation for e whereas others use k/e and solve an equation for the isotropic dissipation rate e, which, in contrast to e, goes to zero at the wall. In the latter case all e in Eq. (3) should be replaced by e. The function /2 in the e equation is effective only very close to the wall and is generally composed of two parts /2=/2'/2 (4)