Critical comparison of second-order closures with direct numerical simulations of homogeneous turbulence

• Published in: AIAA journal 1993-04, Vol.31 (4), p.663-670
• Main Authors: Shih, Tsan-Hsing, Lumley, John L
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fluid dynamics; Fluid Mechanics And Heat Transfer; Fundamental areas of phenomenology (including applications); Physics; Turbulent flows, convection, and heat transfer
• ISSN: 0001-1452; 1533-385X
• DOI: 10.2514/3.11601

Recently, several models have been proposed for closing the second-moment equations, in which the velocity-pressure gradient tensor and the dissipation rate tensor are two of the most important terms. In the literature, these correlation tensors are usually decomposed into a so-called rapid term and a return-to-isotropy term. Models of these terms have been used in global flow calculations together with other modeled terms. However, their individual behaviors in different flows have not been fully examined because they are unmeasurable in the laboratory. Recently, the development of direct numerical simulation (DNS) of turbulence has given us the possibility to do this kind of study. With direct numerical simulation, we may use the solution to calculate exactly the values of these correlation terms and then directly compare them with the values from their modeled formulations. In this paper, we make direct comparisons of five representative rapid models and eight return-to-isotropy models using the DNS data of 45 homogeneous flows, which were done by Rogers et al. (1986) and Lee and Reynolds (1985). The purpose of these direct comparisons is to explore the performance of these models in different flows and identify the ones that give the best performance. The paper also describes the modeling procedure, model constraints, and the various evaluated models. The detailed results of the direct comparisons are discussed, and a few concluding remarks on turbulence models are given.