Towards a Unified Turbulence Simulation Approach for Wall-Bounded Flows

Abstract

A hybrid Reynolds-averaged Navier-Stokes/Large-Eddy Simulation (RANS/LES) methodology has received considerable attention in recent years, especially in its application to wall-bounded flows at high-Reynolds numbers. In the conventional zonal hybrid approach, eddy-viscosity-type RANS and subgrid scale models are applied in the RANS and LES zones, respectively. In contrast, the non-zonal hybrid approach uses only a generalized turbulence model, which provides a unified simulation approach that spans the continuous spectrum of modeling/simulation schemes from RANS to LES. A particular realization of the non-zonal approach, known as partially resolved numerical simulation (PRNS), uses a generalized turbulence model obtained from a rescaling of a conventional RANS model through the introduction of a resolution control function F R , where F R is used to characterize the degree of modeling required to represent the unresolved scales of turbulent motion. A new generalized functional form for F R in PRNS is proposed in this study, and its performance is compared with unsteady RANS (URANS) and LES computations for attached and separated wall-bounded turbulent flows. It is demonstrated that PRNS behaves similarly to LES, but outperforms URANS in general.

An efficient very large eddy simulation model for simulation of turbulent flow

“…On a coarse mesh, the new VLES model performs poorly in the buffer layer (see Figure ). It underpredicts the streamwise velocity while the velocity is generally overpredicted in this region by other simulation methods . This is because the standard k − ϵ model was used to accomplish the new VLES modeling in the present study, which is suitable only for high Reynolds number flow.…”

“…The present study focuses on the more important issue of formulating the control function F r . According to Hsieh et al , a generalized functional form of F r can be written based on the turbulence energy spectrum in the form of in which L c , L i , and L k are the turbulent cut off length scale, integral length scale, and Kolmogorov length scale, respectively, defined as where the definite integrals in Equation represent the turbulent kinetic energy between L k and L c , and between L k and L i , and therefore roughly resemble the ratio of the unresolved turbulent kinetic energy to the total turbulent kinetic energy. Following this idea, a new formulation of F r can be obtained based on the original Speziale model.…”

“…The present study focuses on the more important issue of formulating the control function F r . According to Hsieh et al [8], a generalized functional form of F r can be written based on the turbulence energy spectrum in the form of…”

The State of the Art of Hybrid RANS/LES Modeling for the Simulation of Turbulent Flows

“…These authors performed the wall jet flow that highlights the interaction between large structures developing in the free shear layer and the near wall boundary layer with encouraging results. This method was applied in its principle by Hsieh et al [116] to derive a variant of VLES model using a generalized function F R based on the turbulence energy spectrum E ( κ ) defined as where κ e and κ d are the wave numbers corresponding to the integral length-scale of turbulence L e = k 3/2 / 𝜖 and the Kolmogorov length-scale η K , respectively. This model was applied to simulate the flow over an array of cubes placed in a plane channel.…”

Numerical Simulation of Industrial Flows

“…In any event, DES still demands significant computer and software resources and, at the same time, suffers from a number of pitfalls like the already mentioned premature gridinduced separation and the more serious difficulties to demonstrate grid convergence and the absence of a theoretical order of accuracy (Spalart, 2009) together with the log-layer mismatch in channel flow simulation (Hamba, 2009 Liu & Shih (2006) and is motivated by the assertion that small-scale motions have small associated time scales, allowing for the use of temporal filtering for defining the resolved scales (see also Shih & Liu 2006, Shih & Liu, 2008, Shih & Liu 2009and Shih & Liu, 2010. Other methodologies for achieving PRNS, not necessarily relying on temporal filtering, have been proposed in the literature, such as that of Ruprecht et al (2003), that of Perot & Gadebusch (2007 or the one of Hsieh et al (2010), but the abovementioned approach of Liu & Shih is the most attractive due to its inherent simplicity. Temporal filtering has been demonstrated by Fadai-Ghotbi et al (2010) to offer a consistent formalism for a broad class of modeling methodologies that seamless unifies a URANS behavior of the simulation in some regions of the flow, e.g.…”