Extension and Exploration of a Hybrid Turbulence Model on Unstructured Grids

Abstract

M OST fluid flows of engineering interest are turbulent, and while numerous advances have been made in the numerical solution of the Navier–Stokes equations, known as computational fluid dynamics (CFD), turbulent flows still present challenges for today’s methods. Turbulent flows are characterized by a very wide range of scales in both time and space.Most of the kinetic energy of a turbulent flow is stored in the large-scale structures of the flow. In contrast, kinetic energy is dissipated as heat at the smallest scales. Although the much more computationally intensive large eddy simulations (LES) and direct numerical simulations (DNS) are performed in research environments, simulations that resolve the Reynolds-averaged Navier–Stokes (RANS) equations are still required for rapid engineering results. The size of the smallest length scales, and therefore the maximum allowable CFD grid spacing to completely resolve all turbulence, is inversely proportional to Re. So for a three-dimensional simulation, the number of grid points must scale with Re [1]. Because such fine grids and small time steps are not practical with today’s computers, compromises must be made that approximate certain aspects of the physics. Most CFD methods solve the steady or unsteady RANS (URANS) equations, as illustrated in Fig. 1. Essentially, only the mean flow is solved on the computational mesh, and the turbulent physics are replaced by closure models of varying sophistication. URANS–based methods include simple algebraic models like Baldwin–Lomax, one-equation models like Baldwin–Barth and Spalart–Allmaras, and two-equation models such as k-! and k-! shear stress transport (SST). These turbulence models tend to be heuristic and rely on nonphysical constants that are “tuned” to specific flows, such as airfoils at low angles of attack. That is, the results from the model are iteratively compared against experimental data, and the constants are adjusted until the computational results agree with the experiment. Although they perform well for those cases, they fail to accurately predict unsteady flows dominated by viscous effects, as in the case of static and dynamic stall [2,3] or bluffbody flows. Hybrid RANS/LESmethods provide away to achieve some of the advantages of LES for separated and highly vortical flowfields while retaining the computational efficiency of URANS methods. Baurle et al. [4] developed the idea that URANS and LES methods can be linearly blended by some smooth function to form a hybrid model. This idea of blending was used in 2006 by Sanchez-Rocha et al. [5], who used the k-! SST RANSmodel as the basis for a hybrid method within an existing LES code to resolve wall-bounded turbulence. Sanchez-Rocha et al. demonstrated this capability with simulations of a NACA 0015 airfoil in static and dynamic stall at a Reynolds number of 1 10. A more common approach is to incorporate an LES model into a URANS code to capture subgrid scales, so that where grid resolution permits, LES-like results are obtained. Strictly speaking, LES requires that the resolved scales extend into the inertial subrange. These scales, and those smaller, are more universal, meaning that their physics depends less on the particular geometry. Such universal scales are more amenable to modeling, since even when heuristics are used, they should be valid for a larger range of flows. The drawback of LES is that in order to directly solve for the larger turbulent scales, it requiresmuch finer grids and smaller time steps than URANS computations. In most engineering applications, LES remains far too computationally expensive for routine use.On coarse grids that are usually only suitable forURANS applications, hybrid methods of this variety can capture larger turbulent eddies in the interior of the flow (away from boundaries), thus providing a better approximation of the true physics than URANS alone. Detached eddy simulation (DES) is a commonhybrid formulation, inwhich the turbulence near walls ismodeledwithMenter’s k-!SST [6] or Spalart–Allmaras [7] URANS turbulence models. However, it must be noted that DESmodels are separate and distinct from hybrid methods like those of Sanchez-Rocha et al. [5] in that they lack a dedicated subgrid-scale model. Instead, the URANS equations perform “double-duty” as theLESmodel bymodifying a length scale used in the destruction terms [8,9]. For this effort, the RANS–LES hybrid model developed by Sanchez-Rocha et al. [5,10] has been extended and evaluated within an unstructured CFD methodology. Comparisons with experimental data, as well as published LES and structured CFD simulations, were used to verify and expand the base of knowledge of unstructured hybrid RANS–LES methods. Emphasis is placed on the improvement of the aerodynamic performance quantities (forces and moments) through more accurate prediction of the pressure distribution and separation location on the cylinder.