Session R2: CFD: Turbulence Modeling II

Modelling the cut-off resolution parameter in the PANS method for turbulence simulation

The Partially-Averaged Navier-Stokes (PANS) approach, designed to resolve a part of the turbulence spectrum, adjusts seamlessly from the Reynolds-Averaged Navier-Stokes (RANS) to the Direct Numerical Solution (DNS) of the Navier-Stokes equations. This turbulence closure, derived from a RANS model, supports any filter width or scale resolution. We choose the PANS model as the basis for the present analysis of options for the model resolution parameter, but the conclusions derived are applicable to other partially resolved closure methods. Namely, in the conventional well-established PANS, the resolution parameter is obtained from the grid spacing and the integral turbulence length scale. The latter is obtained usually by summing up the resolved turbulence, while the unresolved motion is computed from the modelled equation. Several formulations have been shown to provide reliable and accurate results for many test flows. However, serious impediments have been noted in some applications such as moving domains and transient boundaries because too long calculations of the average velocity make this approach impractical. We analysed some recent alternative approaches which use the turbulent-to-mean-strain-rate time scale aimed at avoiding the on-line calculations of the resolved kinetic energy required for calculations of the input resolution parameter. Comparisons of several approaches will be shown in detail and conclusions drawn on the merits of each method.   

A novel VLES model accounting for near-wall turbulence: physical rationale and applications

A novel VLES (Very Large Eddy Simulation) model whose non-resolved residual turbulence is modelled by using an advanced near-wall eddy-viscosity model accounting for the near-wall Reynolds stress anisotropy influence on the turbulence viscosity by modelling appropriately the velocity scale in the relevant formulation (Hanjalic et al., 2004) is proposed. It represents a variable resolution Hybrid LES/RANS (Reynolds-Averaged Navier--Stokes) computational scheme enabling a seamless transition from RANS to LES depending on the ratio of the turbulent viscosities associated with the unresolved scales corresponding to the LES cut-off and the `unsteady' scales pertinent to the turbulent properties of the VLES residual motion, which varies within the flow domain. The VLES method is validated interactively in the process of the model derivation by computing fully-developed flow in a plane channel (important representative of wall-bounded flows, underlying the log-law for the velocity field, for studying near-wall Reynolds stress anisotropy) and a separating flow over a periodic arrangement of smoothly-contoured 2-D hills. The model performances are also assessed in capturing the natural decay of the homogeneous isotropic turbulence. The model is finally applied to swirling flow in a vortex tube, flow in an IC-engine configuration and flow past a realistic car model.   

A new algebraic wall model for LES based on the momentum integral approach: formulation and sample applications

Inspired by the momentum integral boundary layer method of von Karman and Pohlhausen (VKP), we propose an integral Wall Model for LES (iWMLES). To capture near wall physics without assuming equilibrium conditions, a velocity profile with various parameters is proposed instead of numerical integration of the boundary layer equation in the near-wall zone. Since numerical solution of boundary layer equations on a refined mesh near the wall is not required, we preserve the essential simplicity of equilibrium-type wall models with a cost that is independent of Reynolds number. Two sets of test cases are presented here: (1) Fully developed half channel flows with a smooth wall at various Reynolds numbers, and with a rough wall in which roughness elements are numerically not resolved. The code we use for these cases is a pseudo-spectral code for fully developed channel flow with a Lagrangian dynamic subgrid model. (2) LES of flow over surface mounted cubes in a fully developed half channel for which detailed experimental data are available. A finite difference LES code with sharp immersed boundary method and dynamic Vreman eddy-viscosity model is used in this application. Results show that iWMLES provides a practical and accurate wall model for predicting the mean wall stress in LES.   

Parallel Optimization with Large Eddy Simulations

For design optimization results to be useful, the model used must be trustworthy. For turbulent flows, Large Eddy Simulations (LES) can capture separation and other phenomena that traditional models such as RANS struggle with. However, optimization with LES can be challenging because of noisy objective function evaluations. This noise is a consequence of the sampling error of turbulent statistics, or long time averaged quantities of interest, such as the drag of an airfoil or heat transfer to a turbine blade. The sampling error causes the objective function to vary noisily with respect to design parameters for finite time simulations. Furthermore, the noise decays very slowly as computational time increases. Therefore, robustness with noisy objective functions is a crucial prerequisite to optimization candidates for LES. One way of dealing with noisy objective functions is to filter the noise using a surrogate model. Bayesian optimization, which uses Gaussian processes as surrogates, has shown promise in optimizing expensive objective functions. The following talk presents a new approach for optimization with LES incorporating these ideas. Applications to flow control of a turbulent channel and the design of a turbine blade trailing edge are also discussed.   

Optimization of a Turbine Blade Trailing Edge using Large Eddy Simulations

As for many turbomachinery components, heat transfer and pressure loss are the key quantities influencing the design of turbine blades. To compute correct heat transfer and pressure loss data, flow features such as boundary layer transition and flow separation must be captured accurately. While traditional Computation Fluid Dynamics models such as Reynolds Averaged Navier-Stokes (RANS) struggle to capture these features accurately, Large Eddy Simulation (LES) is able to. This talk discusses an optimization study of a turbine blade trailing edge. The design of turbine blades involves two classical competing objectives: minimizing pressure loss and minimizing heat transfer to the blade. This trade-off is especially apparent for the design of the blade's trailing edge. The study was conducted using a novel Bayesian optimization technique developed by the authors. The optimization algorithm is combined with a massively parallel LES solver and the results for a number of trailing edge designs including the optimal geometry will be presented and their implications for turbine blade design will be discussed.   

Modeling of near-surface generated turbulence in large-eddy simulation of microscale atmospheric flows

Large-eddy simulation (LES) is often used in microscale atmospheric boundary layer (ABL) flows. As a wall-resolved LES is not relevant in actual ABL flows due to surface roughness and very high Reynolds numbers, LES with wall-modeling has been widely adopted. But special attention must be given to the near-surface treatment in LES of ABL flows as several of the more commonly applied methods, e.g. hybrid RANS/LES or models, can provide unrealistic accelerations leading to the log-layer mismatch problem. Numerous studies have focused on the smooth-wall turbulent channel flow to address the log-law mismatch problem. However, several of these studies have yet to be extended to LES of ABL flows where terrain surface is aerodynamically rough and arbitrarily complex. We investigate different near-surface treatments to ABL flow in our GPU-accelerated LES framework with an immersed boundary method for complex terrain. We consider the constrained LES approach of Chen et al. (2012), and the mean wall shear stress boundary condition proposal of Lee et al. (2013) that have shown promising results. Additionally, we investigate a hybrid RANS/LES approach. Our goal is to identify a suitable near-surface treatment and extend it to LES of complex terrain winds using the immersed boundary method.   

A DG-FDF Large Eddy Simulator

A new computational methodology is developed for large eddy simulation of turbulent flow in complex geometries. This is a hybrid methodology in which a discontinuous Galerkin (DG) base flow solver is combined with a Lagrangian Monte Carlo solver for the filtered density function (FDF). The advantage of the DG is that it provides high order accuracy with fewer degrees of freedom. It also provides flexibility of implementation on unstructured grids. The resulting DG-FDF solver is shown to be very useful for LES of turbulent flows.   

Implicit Large-Eddy Simulation of Transition and Turbulence Decay

In ILES, energy-containing large scales are resolved, and physics capturing numerics are used to spatially filter-out unresolved scales and implicitly model subgrid scale effects. Analysis of transition and decay in the ILES context are the focus of the present work. Euler based ILES is based on using the LANL RAGE code [1] with triple-periodic boundary conditions on evenly spaced grids involving 64, 128, 256, and 512 cells in each direction; Navier-Stokes based isotropic turbulence data generated with the CFDNS code [2] provided initial conditions for ILES. Effects of grid resolution on the ILES unsteady turbulence measures are examined in detail. \\[4pt] [1] Grinstein et al., PoF, 23, 034106, 2011.\\[0pt] [2] Livescu et al., LANL LA-CC-09-100, 2009.   

Scale resolving computation of submerged wall jets on flat wall with different roughness heights

Scale-adaptive simulation is used to investigate the response of velocity and turbulence in submerged wall jets to abrupt changes from smooth to rough beds. The submerged wall jets were experimentally investigated by Dey and Sarkar [JFM, V. 556, p. 337, 2006] at the Reynolds number of 17500 the Froude number of 4.09 and the submergence ratio of 1.12 on different rough beds that were generated by uniform sediments of different median diameters The SAS is carried out by means of a second-order-accurate finite volume method in space and time and the effect of bottom roughness is treated by the approach of Cebeci (2004). The evolution of free surface is captured by employing the two-phase volume of fluid (VOF) technique. The numerical results obtained by the SAS approach, incorporated with the VOF and the rough wall treatment, are in good agreement with the experimental measurements. The computed turbulent boundary layer grows more quickly and the depression of the free surface is more increased on the rough wall than those on smooth wall. The size of the fully developed zone shrinks and the decay rate of maximum streamwise velocity and Reynolds stress components are faster with increase in the wall roughness.   

Drag and drop simulation: from pictures to full three-dimensional simulations

We present a suite of methods to achieve ``drag and drop'' simulation, i.e., to fully automatize the process to perform thee-dimensional flow simulations around a bodies defined by actual images of moving objects. The overall approach requires a skeleton graph generation to get level set function from pictures, optimal transportation to get body velocity on the surface and then flow simulation thanks to a cartesian method based on penalization. We illustrate this paradigm simulating the swimming of a mackerel fish.