One‐dimensional turbulence investigation of incompressible and low Mach number variable density pipe‐flow

Abstract

AbstractCylindrical pipe‐flow is evaluated by means of the One‐Dimensional Turbulence (ODT) model applying both an incompressible and a low Mach number variable density framework. In the variable density formulation, the velocity field is decomposed into density‐related (non‐divergence‐free) and density‐unrelated (divergence‐free) contributions, as detailed in Medina et al. [Combust. Flame 190 (2018) 388‐401]. Both contributions to the velocity field are subject to the effects of diffusion and turbulent transport, as it is normally the case for the incompressible velocity field in traditional ODT formulations. The turbulent transport is implemented by means of stochastic eddy events. These are influenced by the available kinetic energy given by the divergence‐free velocity contribution. An eddy may arise from the different regions of shear caused by varying velocity gradients in the 1‐D domain, but also as a consequence of the temperature‐varying dynamic viscosity. The cylindrical low Mach number variable density formulation is tested in a very low heat transfer regime and compared to the passive scalar results of the incompressible pipe‐flow formulation. ODT model parameters are assumed equal for both formulations. ODT results are compared to DNS results from Satake and Kunugi [Int. J. Numer. Methods Heat Fluid Flow 12 (2002) 958‐1008]. The passive scalar and variable density results show very good agreement with each other as well as with DNS data, respectively, thus suggesting new possible applications for ODT.