Eddy-viscosity Turbulence Model Research Articles

Simulation of a conventionally neutral boundary layer with two-equation URANS

Simulating conventionally neutral boundary layers (CNBLs) with the unsteady Reynolds-Averaged Navier-Stokes (URANS) technique is investigated in this paper using a modified two-equation linear eddy viscosity turbulence model. For CNBLs over a flat and uniform surface, as typically used as the inflow to wind farm simulations, the governing equations of URANS can be solved with a one-dimensional solver, which makes the simulation of a typical CNBL five to six orders of magnitude faster than with large-eddy simulation (LES) approaches. However, URANS on the other hand requires more modelling than LES, and its accuracy is heavily dependent on the turbulence model employed. Through a cross-code study of a CNBL case with data from five different LES codes, it is found that the length-scale limiter of the employed turbulence model should be removed to correctly predict the atmospheric boundary layer (ABL) height evolution and the qualitative shape of various atmospheric profiles. A parametric study of simulations with varying initial ABL height further demonstrates the prediction capabilities of URANS, although a comparison with LES data shows that modelling of turbulence anisotropy and near-surface turbulence could be improved.

A tensor basis neural network-based turbulence model for transonic axial compressor flows

Traditional turbulence models encounter limitations when simulating intricate flows within transonic axial compressors. In contrast, recent advancements in machine learning turbulence models have demonstrated enhanced potential in refining the precision of turbulence modeling. Notably, the tensor basis neural network (TBNN) methodology has successfully developed non-linear eddy viscosity turbulence models. These models possess the capability to capture the anisotropic characteristic of Reynolds stress. However, applying machine learning non-linear eddy viscosity models to aircraft turbomachinery remains relatively infrequent. Current research mainly focuses on linear eddy viscosity turbulence models based on the Boussinesq hypothesis that presupposes isotropy in Reynolds stress. In this work, we introduce a non-linear eddy viscosity turbulence model, denoted as the k-ω-SST-TBNN model based on the TBNN framework. This model has been employed to simulate the transonic axial compressor NASA Rotor 37. The TBNN is trained using large eddy simulation (LES) results datasets. The importance of input scalar features is analyzed using the random forest method, from which significant and low-degree variables are selected as inputs for the TBNN. Furthermore, this study proposes including the turbulent Mach number as one of the extra features, representing fluid compressibility, thereby extending the computational mass flow rate range of compressor. Additionally, this paper proposes a method involving the weighted average of Reynolds stress, combining the high-precision but less robust TBNN predictions with results based on the Boussinesq assumption to enhance the turbulence model's robustness. The trained k-ω-SST-TBNN model undergoes validation on Rotor 37, where it exhibits a marked improvement in the prediction of overall performance, tip-gap vortex, and radial distribution of flow parameters. The model also displays a commendable capacity for generalization.

Comparison of Eddy Viscosity Models for High Turbulence Nozzle Guide Vane Flows

Abstract In this paper we investigate the performance of eddy viscosity turbulence models for high-pressure nozzle guide vane (NGV) flows with engine-realistic turbulence. Using metrics such as integrated kinetic energy (KE) loss and mixing rate, we compare simulation results using turbulence models with high-fidelity experimental data from fully-cooled NGVs, operating at engine-matched conditions of Reynolds number and Mach. For the widely-used k–ω shear stress transport (SST) model, the aerodynamic and thermal wakes of the NGVs were undermixed. We compare simulation results with those using other common turbulence models including the standard k–ω, baseline k–ω, Spalart–Allmaras, and baseline explicit algebraic Reynolds stress model. Alternative turbulence models formulations are explored, with an emphasis on modifications to the implementation of the shear stress limiter. We also investigate the sensitivity of models to the specified inlet turbulence intensity. We demonstrate that predictions of integrated KE loss, as well as the decay trends of the aerodynamic and thermal wakes are a closer match to experimental data for the baseline algebraic Reynolds stress model than for other turbulence models in more common use for NGV predictions.

Ensemble variational method with adaptive covariance inflation for learning neural network-based turbulence models

This work introduces an ensemble variational method with adaptive covariance inflation for learning nonlinear eddy viscosity turbulence models where the Reynolds stress anisotropy is represented with tensor-basis neural networks. The ensemble-based method has emerged as an important alternative to data-driven turbulence modeling due to its merit of non-derivativeness. However, the training accuracy of the ensemble method can be affected by the linearization assumption and sample collapse issue. Given these difficulties, we introduce the hybrid ensemble variational method, which inherits the merits of the ensemble method in non-derivativeness and the variational method in nonlinear analysis. Moreover, a covariance inflation scheme is proposed based on convergence states to alleviate the detrimental effects of sample collapse. The capability of the ensemble variational method in model learning is tested for flows in a square duct, flows over periodic hills, and flows around the S809 airfoil, with increasing complexity in the training data from direct observation to sparse indirect observation. Our results show that the ensemble variational method can learn relatively accurate neural network-based turbulence models in scenarios of small ensemble size and sample variances, compared to the ensemble Kalman method. It highlights the superiority of the ensemble variational method in practical applications, since small ensemble sizes can reduce computational costs, and small sample variance can ensure the training robustness by avoiding nonphysical samples of Reynolds stresses.

Assessment of the DDES-γ Model for the Simulation of a Highly Loaded Turbine Cascade

Abstract The flow over the linear low-pressure turbine cascade MTU-T161 at Re = 90,000 is analyzed using delayed detached eddy simulations (DDES). At this operating point, the low Reynolds number and the high loading of the blade result in a separation bubble and a separation-induced transition of the flow over the suction side. The utilized DDES method is based on a vorticity-based formulation to calculate the subgrid length scales, and it incorporates the one-equation γ-transition model. The computational model of the MTU-T161 cascade consists of one blade passage, including the diverging viscous sidewalls. To reproduce realistic operating conditions and to mimic the experiments, synthetic turbulence is prescribed at the inlet of the computational domain. Several studies are performed to assess the accuracy and performance of the DDES one-equation γ-transition model against experimental data and a benchmark large eddy simulations (LES). The primary focus is on the prediction of the separation and the separation-induced transition mechanism. First of all, a systematic grid convergence study is conducted and grid criteria are derived in order to ensure a satisfactory agreement of the flow metrics, such as isentropic Mach number, friction coefficient distribution, and total pressure wake losses at mid-span with experimental data. Furthermore, a detailed analysis of the DDES model parameters, such as shielding function and subgrid length scale, is presented and the effect of these parameters on the prediction accuracy of the separation bubble region is analyzed. The analysis of the suction side boundary layer indicates that the turbulent kinetic energy should be resolved and modeled properly in order to represent the separation bubble correctly. In particular, the correct prediction of the separated shear layer above the separation bubble is of utmost importance. The results of the simulations reveal higher demands on grid resolution for such transitional flows than typically have been reported in the literature for turbulent boundary layers. This higher demand on grid resolution results in more expensive simulations than Reynolds-averaged Navier–Stokes (RANS). Nevertheless, DDES requires less computing time than wall-resolved LES. Additionally, the results of the transitional DDES model are compared to DDES without a transition model, an RANS eddy viscosity model, and a reference LES. The results show that the DDES approach needs to be coupled with a transition model, such as the one-equation γ-transition model, in order to capture the flow topology over a highly loaded turbine blade correctly. The benefit of the DDES one-equation γ-transition model becomes particularly evident when predicting the separated shear layer, the transition process, and the subsequent reattachment. The RANS eddy viscosity turbulence and transition models applied within our study are not able to predict the aforementioned mechanisms accurately. For highly loaded turbine blades in particular, the accurate prediction of flow separation and potential reattachment is crucial for the aerodynamic design of turbines, since large parts of the total pressure loss are generated in the separated region. For this reason, the DDES one-equation γ-transition model can be a good compromise in terms of predictive accuracy and computational costs.

Experimental and Numerical Dynamic Investigation of a Swirling Jet: Application to Improve the Efficiency of Air Diffusion in an Occupied Zone

When reducing the energy prerequisites of buildings, the correct distribution of fresh air flows injected into the living rooms poses a problem. If the problem of mixing the injected air in the ambient air is not effectively solved, there will be a strong deterioration in air quality and comfort. In this research, a new design of swirling diffuser is investigated experimentally and numerically using large eddy simulations. The influence of fins is studied for the improvement of air diffusion and jet mixing with ambient air. The study was carried out for a fins angle of 30° with the jet's axis and 60° with the blowing orifice's plane with the condition of uniform heat flux of the air. The working fluid used is air. It has been validated that using fins leads to a greater spreading of the jet and good air mixing compared to those obtained from smooth tubes (circular nozzle). To enhance the accuracy of the turbulence models' predictions, three turbulence models are tested: the wall-adapting local eddy-viscosity turbulence model (LES/WALEVM), Smagorinski-Lilly (LES/S-LM) model and the kinetic-energy transport model (LES/K-ETM). It is worth highlighting that the LES/K-ETM model is well established in the prediction of swirling flows, which have been successfully compared with experimental results.

Amplification factor transport transition model for high-speed flows

A fully local amplification factor transport model is developed for high-speed transitional flows. On the basis of the approximate eN envelope method of linear stability theory, two transport equations are established to describe the evolution of amplification factors for first- and second-mode instabilities in high-speed boundary layers. An intermittency factor transport equation is then constructed based on the transported amplification factors and is coupled with Menter’s k−ω shear-stress transport eddy-viscosity turbulence model. The new model is validated through several test cases under different flow conditions, including flat plates, straight and flared cones, and a double ramp configuration. Comparisons with linear stability theory and experimental data demonstrate the ability of the model to predict the transition behavior induced by first- or second-mode instabilities. The model provides a reasonable reflection of the effects of different parameters that influence transitions, including the Mach number, temperature, nose bluntness, and pressure gradient.

Assessment of Turbulence Models for Unsteady Separated Flows Past an Oscillating NACA 0015 Airfoil in Deep Stall

This paper provides 2D Computational Fluid Dynamics (CFD) investigations, using OpenFOAM package, of the unsteady separated fully turbulent flows past a NACA 0015 airfoil undergoing sinusoidal pitching motion about its quarter-chord axis in deep stall regime at a reduced frequency of 0.1, a free stream Mach number of 0.278, and at a Reynolds number, based on the airfoil chord length, , of . First, eighteen 2D steady-state computations coupled with the SST model were carried out at various angles of attack to investigate the static stall. Then, the 2D Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations of the flow around the oscillating airfoil about its quarter-chord axis were carried out. Three eddy viscosity turbulence models, namely the Spalart-Allmaras, Launder-Sharma , and SST were considered for turbulence closure. The results are compared with the experimental data where the boundary layer has been tripped at the airfoil’s leading-edge. The findings suggest that the SST performs best among the other two models to predict the unsteady aerodynamic forces and the main flow features characteristic of the deep stall regime. The influence of moving the pitching axis downstream at mid chord was also investigated using URANS simulations coupled with the SST model. It was found that this induces higher peaks in the nose-down pitching moment and delays the stall onset. However, the qualitative behavior of the unsteady flow in post-stall remains unchanged. The details of the flow development associated with dynamic stall were discussed

Numerical Study of Velocity and Mixture Fraction Fields in a Turbulent Non-Reacting Propane Jet Flow Issuing into Parallel Co-Flowing Air in Isothermal Condition through OpenFOAM

This research employs computational methods to analyze the velocity and mixture fraction distributions of a non-reacting Propane jet flow that is discharged into parallel co-flowing air under iso-thermal conditions. This study includes a comparison between the numerical results and experimental results obtained from the Sandia Laboratory (USA). The objective is to improve the understanding of flow structure and mixing mechanisms in situations where there is no involvement of chemical reactions or heat transfer. In this experiment, the Realizable k-ε eddy viscosity turbulence model with two equations was utilized to simulate turbulent flow on a nearly 2D plane (specifically, a 5-degree partition of the experimental cylinder domain). This was achieved using OpenFOAM open-source software and swak4Foam utility, with the reactingFoam solver being manipulated carefully. The selection of this turbulence model was based on its superior predictive capability for the spreading rate of both planar and round jets, as compared to other variants of the k-ε models. Numerical axial and radial profiles of different parameters were obtained for a mesh that is independent of the grid (mesh B). These profiles were then compared with experimental data to assess the accuracy of the numerical model. The parameters that are being referred to are mean velocities, turbulence kinetic energy, mean mixture fraction, mixture fraction half radius (Lf), and the mass flux diagram. The validity of the assumption that w߰ = v߰ for the determination of turbulence kinetic energy, k, seems to hold true in situations where experimental data is deficient in w߰. The simulations have successfully obtained the mean mixture fraction and its half radius, Lf, which is a measure of the jet’s width. These values were determined from radial profiles taken at specific locations along the X-axis, including x/D = 0, 4, 15, 30, and 50. The accuracy of the mean vertical velocity fields in the X-direction (Umean) is noticeable, despite being less well-captured. The resolution of mean vertical velocity fields in the Y-direction (Vmean) is comparatively lower. The accuracy of turbulence kinetic energy (k) is moderate when it is within the range of Umean and Vmean. The absence of empirical data for absolute pressure (p) is compensated by the provision of numerical pressure contours.

Fineness Ratio Effects on the Flow Past an Axisymmetric Body at High Incidence

The flow past an axisymmetric body at a sufficiently high angle of attack becomes asymmetric and unsteady. Several authors identified three different flow regions for bodies of large fineness ratio at low subsonic flow and high incidence: a steady region in the forebody and two unsteady regions in the rear body. Unsteady Reynolds Averaged Navier–Stokes (URANS) codes with eddy viscosity turbulence models or Reynolds stress turbulence models fail to capture the unsteady flow region. These methods are overly dissipative and resolve only frequencies far lower than turbulent fluctuations. Scale-Adaptive-Simulation (SAS) provides an alternative method to afford the problem of these massively separated flows at high Reynolds numbers without addressing the problem to Large Eddy Simulation (LES). This paper applies SAS to study the effect of slenderness on the flow. The numerical solutions show that the flow becomes more unstable as the fineness ratio increases, and the three flow regions are clearly recognizable. For low fineness ratios, only one of the two unsteady regions is visible. The good agreement between the sectional forces and pressure coefficients with their corresponding experimental data for an ogive-cylinder configuration allows an analysis of the flow structure with a fair degree of confidence.

Robust Eddy Viscosity Turbulence Modeling with Elliptic Relaxation and Compound Wall Treatment

This paper presents a holistic Reynolds-averaged Navier–Stokes (RANS) turbulence modeling framework for the computational fluid dynamics (CFD) simulations of complex wall-bounded turbulent flows. Based on the elliptic relaxation idea, the deployed eddy viscosity turbulence model reconstructs the near-wall stress anisotropy and nonviscous effects. The appropriate selection of the turbulent quantities that are being solved for, together with the zero value wall boundary condition for the related turbulent quantities, renders the model less sensitive to the near-wall grid nonuniformities and resolution. The unified near-wall velocity profile, obtained based on the boundary layer theory, is used to devise the compound near-wall treatment that ensures the robustness of the numerical simulation. The proposed turbulence modeling framework is implemented into the general-purpose open-source CFD code and validated against the generic test cases with satisfactory agreement.

RANS-Based Modelling of Turbulent Flow in Submarine Pipe Bends: Effect of Computational Mesh and Turbulence Modelling

Pipe bend is a critical integral component, widely used in slurry pipeline systems involving various engineering applications, including natural gas hydrate production. The aim of this study is to assess the capability of RANS-based CFD models to capture the main features of the turbulent single-phase flow in pipe bends, in view of the future investigation of the hydrate slurry flow in the same geometry. This is different from the available literature in which only a few accounted for the effects of a combination of computational mesh, turbulence model, and near-wall treatment approach. In this study, three types of mesh configuration were adopted to carry out the computations, namely unstructured mesh and two structured meshes with a uniform and nonuniform inflation layer, respectively. To explore the influence of the turbulence model, standard k-ε, low-Reynolds k-ε, and nonlinear eddy viscosity turbulence model were selected to close RANS equations. Pressure coefficient, mean axial velocity, turbulence intensity, secondary flow velocity, and magnitude of secondary flow were regarded as the critical variables to make a comprehensive sensitivity analysis. Predicted results suggest that turbulent kinetic energy is the most sensitive variable to the computational mesh while others tend to stabilize. The largest difference of turbulence kinetic energy was around 26% between unstructured mesh and structured mesh with a nonuniform inflation layer. Additionally, a fully resolved boundary layer can reduce the sensitivity of mesh on turbulent kinetic energy, especially for a nonlinear turbulence model. However, the large gradient and peak value of turbulence intensity near the inner wall of the bend was not captured by the case with a fully resolved boundary layer, compared with that of the wall function used. Furthermore, it has been confirmed that the same rule was detected also for different curvature ratios, Reynolds numbers, and dimensionless wall distance y+.

CFD Calculations of Average Flow Parameters around the Rotor of a Savonius Wind Turbine

The geometry of a conventional two-bladed Savonius rotor was used in this study based on a report available in the literature. A two-dimensional rotor model consisting of two buckets and an overlap ratio of 0.1 was prepared. The unsteady Reynolds averaged Navier-Stokes (URANS) equations and the eddy-viscosity turbulence model SST k-ω were employed in order to solve the fluid motion equations numerically. Instantaneous velocities and pressures were calculated at defined points around the rotor and then averaged. The research shows that the operating rotor significantly modifies the flow on the downwind part of the rotor and in the wake, but the impact of the tip speed ratio on the average velocity distribution is small. This parameter has a much greater influence on the characteristics of the aerodynamic moment and the distribution of static pressure in the wake. In the upwind part of the rotor, the average velocity parallel to the direction of undisturbed flow is 29% lower than in the downwind part.

The Influence of Turbulence Models on the Numerical Modelling of a 3D Wing in Ground Effect

This paper deals with the influence of different RANS turbulence models on the numerical modelling of a 3D rectangular symmetrical wing in ground effect. Travelling near a solid surface, so-called ground effect, considerably alters the aerodynamic characteristics of a wing. This paper aims to investigate the performance of the widely used eddy viscosity turbulence models while predicting the changing aerodynamic behavior due to the ground effect. Three different RANS turbulence models, realizable , SST and Spalart-Allmaras models are taken into consideration. The effectiveness of the turbulence models were tasted in comparison with the experimental data in different angles of attack and ground heights. Results reveals that, the effect of the turbulence models on the numerical accuracy of the ground effect aerodynamics calculations are related to the altitude and the angle of attack. The choice of the turbulence model becomes important when the wing travels in very close proximity to the ground and the angle of attack is low or negative. The discrepancy of the calculated results mainly comes from the pressure distribution variations on the lower side of the wing. For high angles of attack, or relatively larger ground heights, the difference between the predictions of the turbulence models become negligible.

Three-dimensional modeling and investigation of the flow around a troposkein vertical axis wind turbine at different operating conditions

Vertical axis wind turbines of troposkein architecture are among the most attractive technologies for harvesting wind energy off-shore. In this paper, a high-fidelity Computational Fluid-Dynamics model of the flow around troposkein rotors is presented, experimentally validated, and applied to analyze the complex aerodynamics of this machine considering both operation and design aspects. At first, a set of two-dimensional simulations of the machine equatorial section was carried out to compare multiple spatial resolutions and three eddy-viscosity turbulence models, including Spalart–Allmaras, k-ω SST, and k-ω SST in low-Reynolds formulation, using as reference wind-tunnel experimental data. Then, the results of fully three-dimensional simulations for peak power and high TSR conditions are discussed, to further assess the models against experiments and to investigate the turbine aerodynamics and its spanwise variability, the flow around and downstream of the rotor, with particular emphasis on the peculiar character of troposkein rotor wake and the related tip vortices. Finally, the paper proposes an analysis about the impact of blade design on the machine aerodynamics, showing that rotors obtained with the simplest and most economic blade bending procedure outperforms configurations obtained by manufacturing the blades with plane airfoil sections along the troposkein curve.

Sensitivity analysis of a swirling flow to the GEKO model

Accurate numerical models for hydraulic turbine applications are highly coveted. They must be able to correctly capture the swirling flow found at off-design operating conditions in the turbine draft tube. The GEKO model is a relatively fast and flexible eddy viscosity turbulence model with adjustable coefficients to tune the model to different flow scenarios. In this study, the GEKO model is tested on a swirling flow inside a diffusor similar to the flow conditions found at part-load operation of a propeller turbine. The diffusor investigated corresponds to the Porjus U9 draft tube cone section, including the runner cone. Results showed that the near-wall coefficient, with a value of 2, increased the wall shear stress and moved the separation point from the runner cone further downstream. Moreover, with a value of 0.7, the separation coefficient increased the eddy viscosity, which also moved the separation point from the runner cone further downstream. Both coefficients gave velocity profiles closer to experimental values and increased the swirl number at the outlet of the diffusor by up to 36.9 % compared to the GEKO default model. Overall, the near-wall coefficient with a value of 2 gave the best results. The GEKO model provides an opportunity to tweak numerical models to swirling flow.

Comparative evaluation of RANS eddy-viscosity turbulence models for calculating the silicon melt convection in crystal growth systems

Comparative evaluation of RANS eddy-viscosity turbulence models for calculating the silicon melt convection in crystal growth systems

RANS-based numerical simulation of shock wave/turbulent boundary layer interaction induced by a blunted fin normal to a flat plate

Results of refined RANS-based numerical simulation of shock wave/turbulent boundary layer interaction induced by a blunted fin mounted on a flat plate are presented. The RANS equations for compressible viscous gas flow closed by a (varied) eddy-viscosity turbulence model were solved using the finite volume method implemented in the unstructured-grid parallelized in-house code SINF/Flag-S developed at the SPbPU. Detailed numerical data concerning time-averaged characteristics of the separation region and the shock wave/turbulent boundary layer interaction are acquired, including identification of the horse-shoe vortices and their influence on the pressure and shear stress distributions on the streamlined surfaces. A thorough comparison with measurements presented in literature were conducted. Methodical data on the influence of grid resolution and turbulence model on the predicted structure of the viscous-inviscid interaction are obtained and recommendations for achieving a high-quality resolution of the viscous effects and the complex shock-wave pattern of the flow are worked out.

Transport-Based Transition Prediction for the Common Research Model Natural Laminar Flow Configuration

This paper presents the application of a new -based one-equation transition transport model to the Common Research Model Natural Laminar Flow Configuration (CRM-NLF), which was the central test case of the 1st AIAA CFD Transition Modeling and Prediction Workshop. The new model uses a simplified formulation of the Arnal, Habiballah, and Delcourt transition criterion that is stability based. The model is formulated in a grid-point-local manner and is coupled to the Menter shear stress transport eddy-viscosity turbulence model. The flow conditions applied are exactly those that were reported from the National Transonic Facility wind tunnel test campaign. The comparisons of the results yielded by the new model in terms of the transition fronts along the wing span show a very good match with the transition fronts derived from the temperature-sensitive paint images taken during the wind tunnel test and with computational result from an -based Two--factor strategy using critical -factors for Tollmien–Schlichting and crossflow instabilities and applying a local linear stability code.

Computation of viscous flow characteristics of a supersonic intake using eddy-viscosity turbulence models

Results of numerical investigation of flow and performance characteristics of a rectangular supersonic intake experimentally tested at Mach number of 4.03 are presented. The viscous flowfield has been obtained by solving Favre averaged Navier–Stokes equations with two eddy viscosity turbulence models, namely, Mentor’s baseline (BSL) k-ω and shear stress transport (SST) k-ω models. In addition, the effect of wall temperature conditions as well as several configurations of cowl and isolator are simulated to validate the computational methodology. The analysis has been carried out at a freestream Mach number of 4.03 and 0° angle-of-attack, corresponding to a unit Reynolds number of about 6.9×107 m−1. The predicted boundary-layer and the wall static pressure distribution using SST k-ω model shows better agreement with the experimental data compared to the BSL model and hence indicates superior capability to capture the onset and the amount of flow separation due to SWBLIs. Moreover, the terminal shock structure at different operating modes as well as the “unstart because of SWBLIs” is predicted quite accurately using the model. The wall temperature condition is found to have a strong effect on the amount of flow separation at the cowl and the subsequent interactions. Further, the results show that the sidewalls have a marginal effect on the centerline wall static pressure, though a three-dimensional flowfield with two stream-wise vortices are observed close to it as a result of the swept SWBLIs of the cowl shock with the sidewall boundary-layer leading to a higher loss in performance.