Session R3: CFD: Large Eddy Simulation II

Quantifying Numerical Dissipation due to Filtering in Implicit LES

Numerical dissipation plays an important role in LES and has given rise to the widespread use of implicit LES in the academic community. Recent results demonstrate that even with higher order codes, the use of stabilizing filters can act as a source of numerical dissipation strong enough to compare to an explicit subgrid-scale model (Cadieux et al, JFE 136-6). The amount of numerical dissipation added by such filtering operation in the simulation of a laminar separation bubble is quantified using a new method developed by Schranner et al, Computers \& Fluids 114 . It is then compared to a case where the filter is turned off, as well as the subgrid-scale dissipation that would be added by the $\sigma$ model. The sensitivity of the method to the choice of subdomain location and size is explored. The effect of different derivative approximations and integration methods is also scrutinized. The method is shown to be robust and accurate for large subdomains. Results show that without filtering, numerical dissipation in the high order code is negligible, and that the filtering operation at the resolution considered adds substantial numerical dissipation in the same regions and at a similar rate as the $\sigma$ subgrid-scale model would.   

Pressure-Velocity-Scalar Filtered Mass Density Function for Large Eddy Simulation of Compressible Turbulent Flow

A new model is developed which accounts for the effects of subgrid scale pressure in the context of the filtered density function (FDF) formulation. This results in a pressure-velocity-scalar filtered mass density function (PVS-FMDF), which is suitable for large eddy simulation of compressible turbulence. Following its mathematical definition, an exact transport equation is derived for the PVS-FMDF. This equation is modeled in a probabilistic manner by a system of stochastic differential equations (SDEs). The consistency and the predictive capability of the model are established by conducting LES of a three-dimensional compressible mixing layer, and comparison with direct numerical simulation (DNS) data.   

Large-eddy simulation of a spatially-evolving turbulent mixing layer

Large-eddy simulations of a spatially-evolving turbulent mixing layer have been performed. The flow conditions correspond to those of a documented experimental campaign (Delville, Appl. Sci. Res. 1994). The flow evolves downstream of a splitter plate separating two fully turbulent boundary layers, with Re$_\theta = 2900$ on the high-speed side and Re$_\theta = 1200$ on the low-speed side. The computational domain starts at the trailing edge of the splitter plate, where experimental mean velocity profiles are prescribed; white-noise perturbations are superimposed to mimic turbulent fluctuations. The fully compressible Navier-Stokes equations are solved by means of a finite-volume method implemented into the in-house code SPARK-LES. The results are mainly checked in terms of the streamwise evolution of the vorticity thickness and averaged velocity profiles. The combined effects of inflow perturbations, numerical accuracy and subgrid-scale model are discussed. It is found that excessive levels of dissipation may damp inlet fluctuations and delay the virtual origin of the turbulent mixing layer. On the other hand, non-dissipative, high-resolution computations provide results that are in much better agreement with experimental data.   

How Many Grid Points Are Required for Time Accurate Simulations?

Grid resolution is a key element in a numerical discretization scheme's ability to accurately capture complex fluid dynamics phenomena encountered in LES and DNS calculations. The fundamental question to be asked concerns the minimum number of points required to represent relevant flow phenomena such as vortex and acoustic wave propagation. The answer is naturally dependent upon the choice of numerical scheme,\footnote{Zingg, \textbf{SIAM J. Sci. Comput.}, 22, 476-502, 2000} but it is also influenced by the modal content of the fluid dynamics. Specifically, this study looks at high-order and optimized spatial stencils and their associated dispersion and dissipation characteristics coupled with several time integration schemes. Scheme stabilization is also addressed with respect to artificial dissipation and filtering techniques. \footnote{Edoh, Karagozian, Merkle and Sankaran, AIAA 2015-0284} The theoretical investigations based on von Neumann analysis are substantiated by calculations of pure mode and multiple mode wave propagation problems, isentropic vortex propagation and the DNS of Taylor Green vortex transition, all of which are used to establish the accuracy properties of the schemes.   

An improved numerical scheme for a dynamic LES model

Dynamic LES models are very popular nowadays. There are clear advantages in computing rather than prescribing the unknown coefficient that appear in a subgrid-scale model for Large Eddy Simulation (LES). Whatever is the origin of the model; these dynamic models usually impair the convergence rate when compared to the standard and well-known Smagorinski model. Although most of them provide physical bounds for the non-dimensional constant and with that numerically reasonable values for the unknown sub grid-scale stresses, strong gradients of these terms that can appear across the flow may introduce additional difficulties to the numerical simulations. In the present discretization scheme, we use a deferred-correction approach for the subgrid-scale stresses with the additional correction term, which all together ensure a more stable solution, but without negative effects on the accuracy. As a representative dynamic LES model, we choose the coherent structure model of Kobayashi (2005). Nevertheless, the conclusions derived here are applicable to other dynamic models as well.   

Unstructured finite element simulations of compressible phase change phenomena

Modeling interactions between compressible gas flow and multiple combusting solid objects, which may undergo large deformations, is a problem with several challenging aspects that include, compressible turbulent flows, shocks, strong interfacial fluxes, discontinuous fields and large topological changes. We have developed and implemented a mathematically consistent, computational framework for simulating such problems. Within our framework the fluid is modeled by solving the compressible Navier Stokes equations with a stabilized finite element method. Turbulence is modeled using large eddy simulation, while shocks are captured using discontinuity capturing methods. The solid is modeled as a hyperelastic material, and its deformation is determined by writing the constitutive relation in a rate form. Appropriate jump conditions are derived from conservations laws applied to an evolving interface, and are implemented using discontinuous functions at the interface. The mesh is updated using the Arbitrary Lagrangian Eulerian (ALE) approach, and is refined and adapted during the simulation. In this talk we will present this framework and will demonstrate its capabilities by solving canonical phase change problems.   

Large Eddy Simulation of Supersonic Cold Flow in Ramp-Cavity Combustor with Fuel Injector

Numerical simulation of supersonic flows is technologically important in efficient design and development of high-speed propulsion systems. The supersonic flow within the combustion chamber of scramjet is a prime example of multi-scale and multi-physics flow and is generally accompanied by concurrent presence of shock waves and turbulence. Developing a robust numerical method for such simulations leads to various technical challenges due to the presence of complex geometries, shocks, and turbulence, and normally requires massively parallel computation. In the present work, we employ the Discontinuous Spectral Element Method (DSEM) for high-fidelity simulation of supersonic and turbulent flows. The numerical code features an entropy-based artificial viscosity method for capturing shock waves and standard Smagorinsky-Lilly model for turbulence modeling. Two different turbulence sensors are also developed to improve the turbulent viscosity at the shocked areas and the inlet boundary layer. A supersonic cold flow within a ramp-cavity flame holder featuring a round fuel injector at the ramped side of the cavity is simulated. Results are provided and the physics of the flow is studied.   

Reynolds-constrained large-eddy simulation of compressible flow over a compression ramp

A novel large-eddy simulation (LES) method is introduced for numerical simulation of wall-bounded compressible turbulent flows. The subgrid-scale (SGS) model in this method is designed to be composed of two parts depending on the distance to the nearest wall. In the near-wall region, both the mean SGS stress and heat flux are constrained by external Reynolds stress and heat flux to ensure the total target quantities, while the fluctuating SGS stress and heat flux are closed in a traditional fashion but using residual model parameterizations. In the far-wall region, the conventional SGS model is directly employed with necessary smoothing operation in the neighborhood of the constrained-unconstrained interface, which might be different for the stress and heat flux depending on the flow configuration. Compressible flow over a compression ramp is numerically studied using the new LES technique. The results are compared with the available experimental and direct numerical simulation (DNS) data, and those from traditional LES and detached-eddy simulation (DES). It turns out that the Reynolds-constrained large-eddy simulation (RCLES) method can predict the size of the separation bubble, mean flow profile, and friction force, etc. more accurately than traditional LES and DES techniques. Moreover, the RCLES method proves to be much less sensitive to the grid resolution than traditional LES method, and makes pure LES of flows of engineering interest feasible with moderate grids.   

Energy based hybrid turbulence modeling

Traditional hybrid approaches exhibit deficiencies when used for fluctuating smooth-wall separation and reattachment necessitating ad-hoc delaying functions and model tuning making them no longer useful as a predictive tool. Additionally, complex geometries and flows often require high cell aspect-ratios and large grid gradients as a compromise between resolution and cost. Such transitions and inconsistencies in resolution detrimentally effect the fidelity of the simulation. We present the continued development of a new hybrid RANS/LES modeling approach specifically developed to address these challenges. In general, modeled turbulence is returned to resolved scales by reduced or negative model viscosity until a balance between theoretical and actual modeled turbulent kinetic energy is attained provided the available resolution. Anisotropy in the grid and resolved field are directly integrated into this balance. A viscosity-based correction is proposed to account for resolution inhomogeneities. Both the hybrid framework and resolution gradient corrections are energy conserving through an exchange of resolved and modeled turbulence.