A compressible finite volume formulation for large eddy simulation of turbulent pipe flows at low Mach number in Cartesian coordinates

A finite volume formulation for large eddy simulation (LES) of turbulent pipe flows based on the compressible time-dependent three-dimensional Navier–Stokes equations in Cartesian coordinates with non-Cartesian control volumes is presented. The small scale motions are modeled by a dynamic subgrid-scale (SGS) model. A dual-time stepping approach with time derivative preconditioning is employed to enable the simulations to run efficiently at low Mach numbers. The equations with primitive variables, (p, u, v, w, T), are solved with an implicit lower-upper-symmetric-Gauss–Seidel (LU-SGS) scheme. An isothermal turbulent pipe flow at two Reynolds numbers, and a turbulent pipe flow with a low heat transfer are simulated to evaluate this compressible LES finite volume formulation. The results agree very well with the experimental data and DNS results, verifying the accuracy of the present scheme.