Session D11: Turbulence Modeling I

Hybrid RANS/LES equations

The incompressible and compressible governing equations for the hybrid RANS/LES simulations have been recently formally derived by applying a hybrid filtering operator which linearly combines a LES average with the RANS statistical mean. These exact hybrid equations contain many additional terms that represent the interactions between RANS and LES formulations, and some preliminary simulations have shown their relevance in the correct representation of turbulence. Unfortunately the numerical implementation of these terms is not so easy, and a joint theoretical and numerical study is currently under work in order to overcome these difficulties and to develop simplified models for the hybrid contributions. New different procedures are explored and a new RANS-assisted LES that couples the additive hybrid procedure with an independent RANS computation is examined.   

Simulation of wall-bounded turbulent flow using ODTLES

Subgrid closure of coarse-grained simulations is challenging near walls and for multi-physics applications such as reacting flows. ODTLES [1] avoids coarse-grained advancement, yet is less costly than direct numerical simulation. In ODTLES, the smallest scales of motion are resolved on three arrays of sub-domains, such that each array fills the flow volume and provides full resolution in one coordinate direction. Within each sub-domain, one-dimensional turbulence (ODT) [2] simulates turbulent flow advancement in the resolved direction. A 3D advection step followed by pressure projection couples the sub-domains so as to capture large-scale 3D motion without requiring advancement of filtered flow variables. ODTLES has been used to simulate decaying homogeneous turbulence [1] and in the present study is extended to wall-bounded flows. The capability to capture 3D large-scale features while affordably resolving the wall-normal structure of near-wall flow is demonstrated. \\[4pt] [1] R. C. Schmidt, A. R. Kerstein, R. McDermott, Comput. Methods Appl. Mech. Eng. \textbf{199}, 865-880 (2010). \\[0pt] [2] A. R. Kerstein, Lect. Notes Phys. \textbf{756}, 291-333 (2009).   

A New Formulation For Coupling Turbulence in Hybrid LES-RANS Techniques

In order for the full potential of hybrid Large-Eddy Simulation (LES) - Reynolds-Averaged Navier-Stokes (RANS) computations to be realized, the turbulence in the RANS and LES regions must be coupled, permitting RANS-LES transitions to be set according to the physics of the problem rather than the requirements of the method. A formulation for doing this is proposed which clarifies the relationship between quantities computed from blended models and physical variables when the numerical resolution is varied from that of RANS to that of LES. This understanding may then be employed to show how the governing equations themselves must be modified in order to maintain physical validity when resolution varies. The formulation thus permits accuracy to be maintained throughout LES-RANS transitions, regardless of where they are placed, and all turbulence dynamics are consequently coupled between LES and RANS subdomains. The effectiveness of this formulation is demonstrated in hybrid simulations of plane channel flow, with the LES-RANS transition placed in the log layer. The unphysical shift in the log layer is largely eliminated, at the cost of some additional computation. Prospects for further improvements in accuracy and efficiency are discussed.   

Wall-modeling in large-eddy simulation at high Reynolds number: an approach to predict accurate skin friction

We present a new idea to address one of major sources of error in large-eddy simulation with wall-modeling where the wall shear stress is modeled directly: the inevitable presence of numerical and subgrid modeling errors in the first few grid points adjacent to the wall. By considering the behavior of turbulence length scales near the wall and the grid resolution, the cause of the error is diagnosed and a simple yet efficient approach to remove the impact of the error on the computed turbulence is proposed. The proposed approach allows us to feed accurate well-resolved information from the LES to the wall-model, thus allowing the wall-model to function as intended: this in turn leads to accurately predicted skin friction. The method is applied to zero-pressure-gradient attached and shock-induced separated supersonic turbulent boundary layers at very high Reynolds number, and compared with available experimental data.   

A wall model for large eddy simulation with complex geometries

Large eddy simulation of wall bounded flows is currently limited by the number of grid points required to resolve the inner part of the boundary layer at high Reynolds numbers. One possible solution is to compute approximate wall shear stresses through a separate-but-coupled RANS solver on a separate near-wall grid. This technique is implemented in an unstructured compressible solver. A fully structured grid is derived from the wall geometry to solve the RANS equations. The height of the RANS layer in relation to the boundary layer thickness is a critical parameter of the model and will be discussed. The capability of the model is assessed by computing several problems of both attached and separated flow at high Reynolds numbers, well beyond what is accessible to traditional LES.   

Experimental and Computational Investigations of Flow past Spinning Cylinders

Experiments are performed in a low speed subsonic wind tunnel to analyze flow past spinning cylinders. The sting-mounted cylinders are oriented such that their axis of rotation is aligned with the mean flow. Data from spinning cylinders with both rear-mounted and fore-mounted stings are presented for a Reynolds numbers of up to 260000 and rotation numbers of up to 1.2 (based on cylinder diameter). Computations are performed using a two-equation turbulence model that is capable of capturing the effects of swirl and curvature. The model performance was validated with benchmark experimental flows and implemented for analyzing the flow configuration used in the experimental study. The results are analyzed and the predictive capability of the model is discussed.   

Evaluation of low Reynolds number turbulence models for open channel flow over a rough wall using high-resolution large eddy simulation (LES) data

Quite some effort has been put into the development of low Reynolds number turbulence models to enhance predictions of the near wall flow over smooth walls. Despite the success of these models analogous models for the flow over rough walls are sparse. Based on a high resolution large-eddy simulation of the flow over a bed artificially roughened by hemispheres, we test the applicability of several low Reynolds number models to rough wall flow. The Reynolds number of the flow based on the channel depth is Re=13,680 at a relatively low submergence of h/k=3.42, with h being the water depth and k the roughness height. Similar to flows over smooth walls, the near wall turbulent eddy viscosity requires some damping and damping functions developed for flows over smooth and rough walls are tested and evaluated. Moreover, in the log-layer i.e. at some distance away from the rough wall, the turbulent eddy viscosity is found to be smaller than over the smooth wall, suggesting damping over the entire water depth.   

Uncertainty Quantification and Validation for RANS Turbulence Models

Uncertainty quantification and validation procedures for RANS turbulence models are developed and applied. The procedures used here rely on a Bayesian view of probability. In particular, the uncertainty quantification methodology requires stochastic model development, model calibration, and model comparison, all of which are pursued using tools from Bayesian statistics. Model validation is also pursued in a probabilistic framework. The ideas and processes are demonstrated on a channel flow example. Specifically, a set of RANS models---including Baldwin-Lomax, Spalart-Allmaras, $k$-$\epsilon$, $k$-$\omega$, and $\overline{v^2}$-$f$---and uncertainty representations are analyzed using DNS data for fully-developed channel flow. Predictions of various quantities of interest and the validity (or invalidity) of the various models for making those predictions will be examined. This work is supported by the Department of Energy [National Nuclear Security Administration] under Award Number [DE-FC52-08NA28615].   

A $k-\varepsilon$ Model for Flow through Submerged and Emergent Vegetation Accounting for Turbulence at the Stem Scale as Well as the Vertical Shear Scale(s)

Statistics of turbulence in and above vegetation are determined by the action and interaction of the turbulent wakes of plant stems (scaling with the stem diameter), the Kelvin-Helmholtz type vortices that form in regions of high vertical velocity gradient (scaling with the velocity gradient), and boundary layer turbulence (scaling with the flow depth). While turbulence from each of these sources is dissipated through the energy cascade, some shear-scale turbulence bypasses the lower wave numbers as shear-scale eddies do work against the form drag of the plant stems, converting shear-scale turbulence into wake-scale turbulence. We have developed a $k-\varepsilon$ model that accounts for all of these energy pathways. This is the first model of its kind to incorporate the stem diameter explicitly and thus predict the well-established relationship between stem diameter and turbulent kinetic energy in emergent vegetation. The model also performs well in submerged vegetation, where turbulent kinetic energy scales significantly, but to a lesser degree, with the stem diameter, and in real emergent aquatic vegetation, where multiple scales of vertical shear and stem diameter are equally important.   

The Oriented-Eddy Collision Model

A novel method of treating turbulence - as a collection of interacting fluid particles (eddies) which have inherent orientation - is employed to capture fast pressure-strain in rapid distortion as well as other canonical turbulent flows. The Oriented-Eddy Collision (OEC) model is cast in the form of a collection of Reynolds-stress transport models. Underlying this approach is a unique PDF collision model. The model returns unsteady-RANS-like results, contains no special provisions to satisfy realizability, and maintains both frame and coordinate invariance. Simple wall-bounded flows, such as pressure driven channel flow, are captured without the use of wall-functions. Although more expensive than standard RST models, the model's accuracy and cost fall between those of RST and LES.