Chung-Gang Li

An Investigation of Compressible Turbulent Forced Convection by an Implicit Turbulence Model for Large Eddy Simulation

An investigation of compressible turbulent forced convection in a three-dimensional channel flow is studied numerically by an implicit turbulence model for large eddy simulation (LES). Because of a high temperature difference between two walls and turbulent flow, the compressibility and viscosity of fluid should be taken into consideration simultaneously. Methods of the Roe scheme, preconditioning, and dual time stepping coordinating an implicit turbulence model for LES are used for resolving the effect of the compressibility of fluid on a low speed flow field. The magnitudes of Re τ based on the friction velocity changing from 180 to 940, with the high temperature difference of two walls of 500 k are conducted. The results of the mean velocity profiles and turbulent intensities are in good agreement with the benchmark DNS data obtained by spectral codes from a low Reynolds number (Re τ = 180) to a high Reynolds number (Re τ = 940). Besides, the larger the Re τ is, with the exception of acquirement of larger average Nusselt number, the more drastic variation of local instantaneous Nusselt number is observed.

An implicit turbulence model for low-Mach Roe scheme using truncated Navier–Stokes equations

Abstract The original Roe scheme is well-known to be unsuitable in simulations of turbulence because the dissipation that develops is unsatisfactory. Simulations of turbulent channel flow for Re τ = 180 show that, with the ‘low-Mach-fix for Roe’ (LMRoe) proposed by Rieper [J. Comput. Phys. 230 (2011) 5263–5287], the Roe dissipation term potentially equates the simulation to an implicit large eddy simulation (ILES) at low Mach number. Thus inspired, a new implicit turbulence model for low Mach numbers is proposed that controls the Roe dissipation term appropriately. Referred to as the automatic dissipation adjustment (ADA) model, the method of solution follows procedures developed previously for the truncated Navier–Stokes (TNS) equations and, without tuning of parameters, uses the energy ratio as a criterion to automatically adjust the upwind dissipation. Turbulent channel flow at two different Reynold numbers and the Taylor–Green vortex were performed to validate the ADA model. In simulations of turbulent channel flow for Re τ = 180 at Mach number of 0.05 using the ADA model, the mean velocity and turbulence intensities are in excellent agreement with DNS results. With Re τ = 950 at Mach number of 0.1, the result is also consistent with DNS results, indicating that the ADA model is also reliable at higher Reynolds numbers. In simulations of the Taylor–Green vortex at Re = 3000 , the kinetic energy is consistent with the power law of decaying turbulence with −1.2 exponents for both LMRoe with and without the ADA model. However, with the ADA model, the dissipation rate can be significantly improved near the dissipation peak region and the peak duration can be also more accurately captured. With a firm basis in TNS theory, applicability at higher Reynolds number, and ease in implementation as no extra terms are needed, the ADA model offers to become a promising tool for turbulence modeling.

Feasibility investigation of compressible direct numerical simulation with a preconditioning method at extremely low Mach numbers

Compressible direct numerical simulation (DNS) with a preconditioning method is conducted for the turbulent channel flow of at an extremely low Mach number of 0.005. The turbulence statistics are in excellent agreement with incompressible DNS results, which indicates that the preconditioning method is able to accurately simulate the turbulence at an extremely low Mach number under the condition of sufficient resolution without any subgrid scale model or special treatment of numerical dissipation. In addition, the effects of the computational time step are investigated. It is shown that when the time step is shorter than 0.32 wall units, accurate results can be obtained and the total computational time is independent of the length of the time step. This study thus validates the feasibility of the compressible DNS with a preconditioning method for an extremely low Mach number and provides useful guidelines for simulating turbulence.

An investigation of the unstable phenomena of natural convection in parallel square plates by multi-GPU implementation

ABSTRACT Unstable phenomena induced by natural convection of parallel square plates are investigated numerically. The geometry belongs to the open boundary problem, and the compressibility of fluids is taken into consideration. The absorbing boundary condition and modified local one-dimensional inviscid relation method are adopted for open boundaries. Numerical methods of the Roe scheme, preconditioning, and dual time stepping matching the data-parallel lower-upper relaxation method are coordinated with multi-GPU implementation. Unstable phenomena of natural convection caused by the buoyancy force can be observed. Present results have good agreement with the experimental results in the overlap range of the existing study.