Modeling of Turbulence

Abstract

The accurate prediction of turbulence is of great importance in the design and optimization of rocket combustors and nozzles, while turbulence modeling is actually one key factor in the uncertainty of the whole numerical simulation (N-S) process. Turbulent flow is a complex multi-scale system. However, the Kolmogorov scale of turbulence is much larger than the molecule's free path, with the continuity hypothesis still working, and the N-S equations are effective in describing the behavior of turbulence. In recent decades, numerous turbulence modeling methods have been proposed for theoretical studies and industrial applications.Currently, the numerical simulation approaches on turbulence mainly include direct numerical simulation (DNS), large-eddy simulation (LES), Reynolds average method (RANS), and some other hybrid approaches. DNS based on the original N-S equation is expected to capture all scales contained in the turbulence field, which is capable of presenting all the flow information. However, the massive computational cost makes it only available for some theoretical studies; The RANS simulation approach starts from the Reynolds averaged N-S equation, with all kinds of turbulence models developed to enclose the high-order statistic terms in the governing equations. It is presently the most economical and popular approach for industrial applications [1]. The LES approach lies between the DNS and RANS simulations, with the large scale eddies resolved and small scale eddies modeled [2]. However, in the problems involving no-slip walls, the large computational cost is still a major challenge for industrial applications of LES; consequently, hybrid RANS/LES approaches have been developed. Aiming at industrial applications, we will mainly focus on the RANS and LES simulations in this chapter.Internal Combustion Processes of Liquid Rocket Engines: Modeling and Numerical Simulations, First Edition. Zhen-Guo Wang.