Eddy Viscosity Scheme Research Articles

Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES

The high order spectral element approximation of the Euler equations is stabilized via a dynamic sub-grid scale model (Dyn-SGS). This model was originally designed for linear finite elements to solve compressible flows at large Mach numbers. We extend its application to high-order spectral elements to solve the Euler equations of low Mach number stratified flows. The major justification of this work is twofold: stabilization and large eddy simulation are achieved via one scheme only.Because the diffusion coefficients of the regularization stresses obtained via Dyn-SGS are residual-based, the effect of the artificial diffusion is minimal in the regions where the solution is smooth. The direct consequence is that the nominal convergence rate of the high-order solution of smooth problems is not degraded. To our knowledge, this is the first application in atmospheric modeling of a spectral element model stabilized by an eddy viscosity scheme that, by construction, may fulfill stabilization requirements, can model turbulence via LES, and is completely free of a user-tunable parameter.From its derivation, it will be immediately clear that Dyn-SGS is independent of the numerical method; it could be implemented in a discontinuous Galerkin, finite volume, or other environments alike. Preliminary discontinuous Galerkin results are reported as well. The straightforward extension to non-linear scalar problems is also described. A suite of 1D, 2D, and 3D test cases is used to assess the method, with some comparison against the results obtained with the most known Lilly–Smagorinsky SGS model.

Assessment of the performance of different classes of turbulence models in a wide range of non-equilibrium flows

The performance of thirteen benchmark turbulence models within the RANS framework has been assessed in classical non-equilibrium flows. Linear and non-linear eddy-viscosity schemes, Reynolds stress transport models and single- and two-time-scale approaches have been considered in the investigation. Among the test cases studied are homogeneous shear and normally strained flows, adverse-pressure-gradient, favourable-pressure-gradient and oscillatory boundary layer flows, fully developed oscillatory and ramp up pipe flows and steady and pulsated backward-facing-step flows. The main advantages and drawbacks of the models in each of the test cases are discussed. These discussions provide a reasonably wide understanding of the expected behaviour of the models for future applications in non-equilibrium flows, and also result in suggestions on how the effectiveness of existing models can be further improved.

Investigation of model parameters for high-resolution wind energy forecasting: Case studies over simple and complex terrain

Wind power forecasting, turbine micrositing, and turbine design require high-resolution simulations of atmospheric flow. Case studies at two West Coast North American wind farms, one with simple and one with complex terrain, are explored using the Weather Research and Forecasting (WRF) model. Both synoptically and locally driven events that include some ramping are considered. The performance of the model with different grid nesting configurations, turbulence closures, and grid resolutions is investigated through comparisons with observation data. For the simple terrain site, no significant improvement in the simulation results is found when using higher resolution. In contrast, for the complex terrain site, there is significant improvement when using higher resolution, but only during the locally driven event. This suggests the possibility that computational resources could be spared under certain conditions, for example when the topography is adequately resolved at coarser resolutions. Physical parameters such as soil moisture have a very large effect, but mostly for the locally forced events for both simple and complex terrain. The effect of the PBL scheme choice varies significantly depending on the meteorological forcing and terrain. On average, prognostic TKE equation schemes perform better than non-local eddy viscosity schemes.

Comparison of turbulence schemes for prediction of wave-induced near-bed sediment suspension above a plane bed

Based on a wave bottom boundary layer model and a sediment advection-diffusion model, seven turbulence schemes are compared regarding their performances in prediction of near-bed sediment suspension beneath waves above a plane bed. These turbulence algorithms include six empirical eddy viscosity schemes and one standard two-equation k-ɛ model. In particular, different combinations of typical empirical formulas for the eddy viscosity profile and for the wave friction factor are examined. Numerical results are compared with four laboratory data sets, consisting of one wave boundary layer hydrodynamics experiment and three sediment suspension experiments under linear waves and the Stokes second-order waves. It is shown that predictions of near-bed sediment suspension are very sensitive to the choices of the empirical formulas in turbulence schemes. Simple empirical turbulence schemes are possible to perform equally well as the two-equation k-ɛ model. Among the empirical schemes, the turbulence scheme, combining the exponential formula for eddy viscosity and Swart formula for wave friction factor, is the most accurate. It maintains the simplicity and yields identically good predictions as the k-ɛ model does in terms of the wave-averaged sediment concentration.

Extension of Boussinesq turbulence constitutive relation for bridging methods

Bridging methods for turbulence simulation are adaptive eddy-viscosity schemes based on the accuracy-on-demand paradigm, much like hybrid approaches. The object is to resolve more scales of motion than Reynolds-averaged Navier–Stokes (RANS) by suitably reducing the eddy viscosity as a function of grid spacing. Currently, there are two proposals for extending the RANS two-equation model with Boussinesq constitutive relation to bridging methods. In the first approach, it is suggested that the coefficient in the Boussinesq relation be reduced and the transport equations for the length and velocity scales left unaltered for achieving the desired level of viscosity reduction. The second approach suggests that the viscosity reduction is better achieved by suitably modifying the transport equations rather than altering the Boussinesq coefficient. In this paper, we compare the merits of the two methods in two important benchmark cases: flows past circular cylinder and backward facing step. Three types of evaluations are performed. First, we verify if the requisite viscosity reduction is indeed achieved in the calculations. Then, we compare some crucial qualitative aspects of the solutions from the two methods. Finally, we evaluate the two solutions against experimental data for the same level of intended viscosity reduction.

On Modelling Periodic Motion with Turbulence Closures

In periodic flows near walls transport effects may be considerably larger than in a steady turbulent boundary layer. The question explored in this contribution is, therefore, whether providing separate transport equations for each of the Reynolds stresses consequently leads to a better modelling of a periodic flow's evolution than an eddy viscosity scheme whose constitutive equation is inherently linked to the generation and dissipation terms being in balance (local equilibrium). Our conclusion is that, while a stress-transport scheme is indeed better equipped to reproduce the phenomena, it does not consistently out-perform the EVM over the range of flows studied. In some cases it is suggested that more attention must be paid to modelling diffusive transport in order to secure the benefits of second-moment closure. To illustrate sensitivity to diffusive transport, two different diffusion models are tested, one of which leads to different effective transport coefficients in each stress component.

Simulation of a Round Jet and a Plume in a Regional Atmospheric Model

The mean flow characteristics of a turbulent round jet and a plume are simulated in a high-resolution regional atmospheric model. The model used for the study is the Advanced Regional Prediction System (ARPS). It is observed that the predicted flow characteristics are very sensitive to the turbulence closure scheme used. Among the three closure options in ARPS, namely, the constant eddy viscosity scheme, the Smagorinsky diagnostic closure, and the 1.5-order total kinetic energy scheme, the constant eddy viscosity scheme predicts the jet characteristics in better agreement with experiments. For the plume, all three schemes are unsatisfactory. It is shown that a modification of the constant eddy viscosity scheme incorporating a length-scale variation as suggested by theory predicts plume characteristics in good agreement with experiments. The simulations are carried out at one fixed grid-box size and flow inlet conditions; extending the present simulation results to other cases is discussed.

On a new nonlinear turbulence model for simulating flows around building-shaped structures

Numerical modelling of turbulence plays a crucial role in providing accurate wind fields, which are necessary to predict transport and dispersion of pollutants in the vicinity of buildings reliably. Although the standard k– ε has some well-known deficiencies and more elaborate turbulence models have been developed it is still by far the most widely applied in atmospheric flow and dispersion models. The large CPU time requirement of direct numerical simulation (DNS) and large eddy simulation (LES) still prohibits their application to wind engineering problems of practical interest. Many linear two-equation turbulence models have been proposed in recent years to overcome the deficiencies of the standard k– ε turbulence model. However, comparison shows that none achieves much greater accuracy in all regions of typical wind engineering flow fields. In this paper, a new nonlinear turbulence model is proposed which leads to improved results compared to a conventional eddy-viscosity scheme. The flows considered for the validation of the new model range from simple shear and boundary layer flows, to flows around arrays of cubic obstacles. The accuracy of the proposed turbulence model is assessed by comparing the numerical results with wind-tunnel measurements.

Prediction of turbulent transitional phenomena with a nonlinear eddy-viscosity model

Abstract This paper describes a new nonlinear eddy-viscosity model of turbulence designed with a view to predicting flow far from equilibrium, including transition. The scheme follows earlier UMIST practice in adopting a cubic relation between the stress and the strain/ vorticity tensors but broadens the range of flows to which the model applies by including a third transport equation for an anisotropy parameter of the stress field. Applications are shown for transition on a flat plate at different levels of free-stream turbulence, for the normal impingement of a turbulent jet on a flat plate, and for the flow around a turbine blade. The model is shown to generate much more realistic predictions than what is said to be the best of the linear eddy-viscosity schemes.

Development and application of a cubic eddy-viscosity model of turbulence

Many quadratic stress-strain relations have been proposed in recent years to extend the applicability of linear eddy-viscosity models at modest computational cost. However, comparison shows that none achieves much greater width of applicability. This paper, therefore, proposes a cubic relation between the strain and vorticity tensor and the stress tensor, which does much better than a conventional eddy-viscosity scheme in capturing effects of streamline curvature over a range of flows. The flows considered range from simple shear at high strain rates and pipe flow, to flows involving strong streamline curvature and stagnation.

Impinging jet studies for turbulence model assessment—II. An examination of the performance of four turbulence models

Four turbulence models are applied to the numerical prediction of the turbulent impinging jets discharged from a circular pipe measured by Cooper el al. [ Int. J. Heat Mass Transfer 36, 2675–2684 (1993)], Baughn and Shimizu [ ASME J. Heat Transfer 111, 1096–1098 (1986)] and Baughn el al. [ASME Winter Annual Meeting, November 1992]. They comprise one k-ε eddy viscosity model and three second-moment closures. In the test cases selected, the jet discharge was two and six diameters above a plane surface orthogonal to the jet's axis. The Reynolds numbers were 2.3 × 10 4 and 7 × 10 4 the flow being fully developed at the discharge plane. The numerical predictions, obtained with an extended version of the finite-volume TEAM code, indicate that the k-ε model and one of the Reynolds stress models lead to far too large levels of turbulence near the stagnation point. This excessive energy in turn induces much too high heat transfer coefficients and turbulent mixing with the ambient fluid. The other two second-moment closures, adopting new schemes for accounting for the wall's effect on pressure fluctuations, do much better though one of them is clearly superior in accounting for the effects of the height of the jet discharge above the plate. None of the schemes is entirely successful in predicting the effects of Reynolds number. It is our view, however, that the main cause of this failure is the two-equation eddy viscosity scheme adopted in all cases to span the near-wall sublayer rather than the outer layer models on which the present study has focused.