Menter's Shear Stress Transport Research Articles

Evaluating numerical models for the prediction of pollutant dispersion over Tokyo's Polytechnic University campus

This paper focuses on assessing how different Computational Fluid Dynamics (CFD) methodologies perform in modelling pollutant dispersion over extended urban areas. The case selected for evaluating the proposed methodologies is based on an extensive experimental study conducted by Tachibana et al. (2022), in which outdoor field measurements and wind tunnel experiments were carried out for monitoring tracer gas dispersion over the Atsugi Campus of Tokyo's Polytechnic University (TPU). Numerical results obtained by solving steady Reynolds Averaged Navier Stokes (RANS) governing equations, as well as using a scale resolving Large Eddy Simulation (LES) approach are compared against experimental data, in terms of both dimensionless local velocities and pollutant concentrations. The different meshing strategies that are employed for each methodology are also discussed in detail. The aim of the paper is to help gain further insights about the extent to which the Menter's Shear Stress Transport (SST) k-ω RANS model and LES can be used in the Architectural, Engineering and Construction (AEC) industry for pollutant dispersion modelling.

Mathematical modeling and performance evaluation of Ducted Horizontal-axis Helical Wind Turbines: Insights into aerodynamics and efficiency.

With the escalating demand for energy, there is a growing focus on decentralized, small-scale energy infrastructure. The success of new turbines in this context is notable. However, many of these turbines do not follow many of the basic ideas established to evaluate their performance, leaving no precise technique or mathematical model. This research developed a Ducted Horizontal-axis Helical Wind Turbine (DHAHWT). The DHAHWT is a duct-mounted helical savonius turbine with a venturi and diffuser to improve flow. Unlike a vertical axis helical savonius turbine, DHAHWT revolves roughly parallel to the wind, making it a horizontal turbine. This complicates mathematical and theoretical analysis. This study created a DHAHWT mathematical model. COMSOL simulations utilizing Menter's Shear Stress Transport model (SST) across an incoming velocity range of 1m/s to 4m/s were used to evaluate the turbine's interaction with the wind. MATLAB was used to train an artificial neural network (ANN) utilizing COMSOL data to obtain greater velocity data. The Mean Average Percentage Error (MAPE) and Root Mean Square Error (RMSE) of ANN data were found to be 3%, indicating high accuracy. Further, using advanced statistical methods the Pearson's correlation coefficient was calculated resulting in a better understanding of the relationship of between incoming velocity and velocity at different sections of the wind turbine. This study will shed light on the aerodynamics and working of DHAHWT.

An innovative modification to the Menter shear-stress transport turbulence model employing the symbolic regression approach

Drawing from the non-equilibrium link between the production Pk and dissipation ε of turbulent kinetic energy (TKE), we advocate for the introduction of a limiter to modulate the TKE production term within the Menter shear-stress transport (SST) model. The original SST model is made more sensitive to the adverse pressure gradient (APG) by Bradshaw's assumption. Bradshaw's assumption introduces the equilibrium condition Pk/ε = 1 in most regions of the turbulent boundary layer. In the APG flows with Pk≫ε, the equilibrium condition suppresses the magnitude of TKE (k) within the boundary layer, resulting in an early separation problem. To address this issue, we employ the symbolic regression (SR) to scrutinize the physical correlation between Pk/ε and local turbulence parameters, obtaining an approximate function FSR that encapsulates the relationship between Pk/ε, Sk/ε, and y+ in the APG flow. Following its incorporation into the original SST model in the form of a limiter, the FSR evolves into the SST-Symbolic Regression Evolution model. The SST-SRE is then applied to four cases with APGs. The modification leads to an increase in the skin-friction coefficient Cf in the APGs region and causes a downstream shift in the separation location, improving the consistency with high-accuracy data and experimental results. It is demonstrated that this correction can improve the early separation problem in the Menter SST turbulence model.

A modification of production term for the shear stress transport turbulence model based on a new wall-law for adverse pressure gradient

This paper presents an attempt to improve the predictive accuracy of the Menter shear stress transport (SST) turbulence model for adverse pressure gradient (APG) flows. The foundation of this work lies in the newly modified law of the wall and turbulent kinetic energy (TKE) transport equation within the APG turbulent boundary layer. The modification of the law of the wall is achieved through a newly proposed variable λ, which is derived theoretically and calibrated using direct numerical simulation data. Based on the new law of the wall, we analyze the TKE transport equation of the SST model at APG and demonstrate that the analytical solution satisfying the law of the wall cannot achieve equilibrium in the current SST model. Further theoretical analysis reveals that this imbalance is caused by the TKE production term Pk, and the decomposition of the wall friction coefficient Cf indicates that Pk directly affects the prediction of flow separation. Based on the analysis and the new law of the wall, an additional term for Pk is suggested to correct Pk and improve the model's predictive accuracy for APG flows. Numerical validation results show that the correction leads to an increase in Pk within the APG turbulent boundary layer, resulting in more accurate predictions of Cf and the mean velocity profile in the inner layer of the turbulent boundary layer.

Data Assimilation of Ideally Expanded Supersonic Jet Using RANS Simulation for High-Resolution PIV Data

Data assimilation using particle image velocimetry (PIV) and Reynolds-averaged Navier–Stokes (RANS) simulation was performed for an ideally expanded supersonic jet flying at a Mach number of 2.0. The present study aims to efficiently reconstruct all the physical quantities in the aeroacoustic fields that match well with a realistic, experimentally obtained flow field. The two-dimensional, two-component PIV measurement was applied to the jet axis plane, and the time-averaged velocity field was obtained using single-pixel ensemble correlation. Two-dimensional axisymmetric RANS simulation using the Menter shear stress transport (SST) model was also performed, and the parameters of the SST model were optimized via data assimilation using the ensemble Kalman filter. The standard deviation of the observation noise σ, which is a parameter of the ensemble Kalman filter, is estimated by the previously proposed method (Nakamura et al., Low-Grid-Resolution-RANS-Based Data Assimilation of Time-Averaged Separated Flow Obtained by LES. Int. J. Comp. Fluid. Dyn., 2022), and its effectiveness was investigated for the first time. This method effectively estimated the magnitude of σ at each generation without tuning the hyperparameters. The assimilated flow fields exhibited similar flow structures observed in PIV such as the potential core length or shear layer. Therefore, the present framework can be used to estimate time-averaged full flow fields that match well with experimentally observed flow fields, and has the potential to construct a database for the Navier-Stokes-based stability analysis that requires a full flow field.

Structural uncertainty quantification of Reynolds-Averaged Navier–Stokes closures for various shock-wave/boundary layer interaction flows

Accurate prediction of Shock-Wave/Boundary Layer Interaction (SWBLI) flows has been a persistent challenge for linear eddy viscosity models. A major limitation lies in the isotropic representation of the Reynolds stress, as assumed under the Boussinesq approximation. Recent studies have shown promise in improving the prediction capability for incompressible separation flows by perturbing the Reynolds-stress anisotropy tensor. However, it remains uncertain whether this approach is effective for SWBLI flows, which involve compressibility and discontinuity. To address this issue, this study systematically quantifies the structural uncertainty of the anisotropy for oblique SWBLI flows. The eigenspace perturbation method is applied to perturb the anisotropy tensor predicted by the Menter Shear–Stress Transport (SST) model and reveal the impacts of anisotropy on the prediction of quantities of interest, such as separation and reattachment positions, wall static pressure, skin friction, and heat flux. The results demonstrate the potential and reveal the challenges of eigenspace perturbation in improving the SST model. Furthermore, a detailed analysis of turbulent characteristics is performed to identify the source of uncertainty. The findings indicate that eigenspace perturbation primarily affects turbulent shear stress, while the prediction error of the SST model is more related to turbulent kinetic energy.

Turbulence Model Effects on Vortex Interaction Prediction on a Multiswept Delta Wing

In this study, vortical flows around a generic triple-delta wing geometry were investigated at transonic speeds. The focus of this work was the investigation of vortex interaction at medium to high angles of attack. To this end, numerical simulations were performed at two different Mach numbers, M=0.5 and M=0.85. To assess the performance of different turbulence models in predicting the complex flowfield, comparisons with experimental data were performed. In addition to the integral forces and moments, surface pressures from pressure-sensitive paint and velocity field data from particle image velocimetry were used. Across all investigated test cases, the best agreement with experimental results was achieved by the Menter shear stress transport turbulence model.

Numerical study of transverse hydrogen injection in high-speed reacting crossflow

A high-speed compressible solver capable of solving detailed chemical reaction mechanisms is developed by coupling the open-source computational fluid dynamic toolbox OpenFOAM® and Cantera 2.5.0. A sonic hydrogen jet discharging from a circular injector into a high enthalpy supersonic crossflow over a flat plate is selected as a test case for the developed solver. The incoming boundary layer is laminar, and an adverse pressure gradient-induced transition is expected due to transverse injection. The test case is selected to serve two purposes. First, to validate the developed solver. Second, to inspect the capability of Reynolds-Averaged Navier–Stokes (RANS) in predicting the flame characteristics in high-speed flows involving laminar to turbulent transition. The present study features three-dimensional RANS simulations with Shear Stress Transport (SST) k–ω and Langtry–Menter SST k–ω turbulence models, with three values of inlet turbulent intensity: I = 0.5, 1, and 2. Analysis showed that laminar to turbulent transition plays a significant role in the resulting flame structure. A fully turbulent SST k–ω model showed several discrepancies from the experiment, especially near the boundary layer. On the other hand, the Langtry–Menter SST k–ω model predicts transition onset and hence the flame structures accurately. Furthermore, the transition onset and the flame structure strongly depend on I. The low-velocity recirculation regions near the injector aid in flame stabilization upstream of the injector. At the same time, the horseshoe vortex dictates the flame spread in a spanwise direction. The reflected shock–boundary layer interaction helps in flame stabilization downstream of the injector.

Improvement of turbulence model for predicting shock-wave–boundary-layer interaction flows by reconstructing Reynolds stress discrepancies based on field inversion and machine learning

Reynolds-averaged Navier–Stokes (RANS) models have been the mainstay of engineering applications in recent years, and this trend will likely persist in the coming decades. However, the ability of RANS methods to predict complex flows, such as shock-wave/boundary-layer interaction (SWBLI) flows, is inadequate. In the absence of a breakthrough in traditional turbulence modeling, data-driven modeling has emerged as a new paradigm in turbulence research. In this study, a field-inversion and machine-learning framework based on the regularized ensemble Kalman filter (REnKF) was implemented to enhance the predictive ability of the Menter shear-stress transport (SST) model for SWBLI flows. This approach directly modifies the norm and eigenvalues of the Reynolds stress tensor obtained by RANS methods to overcome the limitations of the Boussinesq hypothesis. The spatial distributions of Reynolds stress discrepancies are initially obtained from experimental data using the REnKF method and a parameterization method based on geometric transformation for improved prediction of the training case. Then, a mapping function from local flow variables to discrepancy fields is constructed by selecting appropriate input features and combining them with a random forest algorithm. Our results verify the effectiveness of the framework for SWBLI flows of varying strengths and types. The results also demonstrate that the SST model's simulation ability for SWBLI flows has been significantly improved, providing more accurate predictions of separation and reattachment, considerably lowering the prediction errors for relevant flow variables, and verifying the generalization ability of the proposed framework.

Investigation of Aerodynamic Support Interference for Testing a Semispan T Tail Aircraft Model

High-fidelity computational fluid dynamics (CFD) flow simulations were carried out to assess the sources of aerodynamic support interference of an aircraft half-model with a T-tail empennage mounted in a wind tunnel in an attempt to improve how well a semispan model can represent the corresponding full-span aircraft. The Bombardier research aircraft configuration (BRAC) model was used, which consists of a fuselage, a fuselage to wing fairing, a cruise wing with flap fairings, an engine nacelle and pylon, a vertical tail, and a horizontal stabilizer (HSTAB). The standard half-model support used at the National Research Council of Canada’s 1.5 m trisonic wind tunnel consists of a wall-mounted splitter plate to remove a sizable portion of the upstream tunnel wall boundary layer and a two-dimensional peniche sandwiched between the model symmetry plane and the splitter plate. CFD simulations of the BRAC model mounted in the wind tunnel were performed using the Menter shear stress transport turbulence model at a Mach number of 0.2. The CFD results for the standard (baseline) mounting arrangement compared favorably well with the half-model experimental data. The BRAC CFD model was then modified to provide reference “full-span” data and to examine several alternate model mounting arrangements. All simulations were compared with the ideal full-span reference simulations. Significant disturbances were found to be induced by the reflection plane boundary layer and primary horseshoe vortex on the flowfield surrounding the HSTAB, which had a direct impact on the measured overall model forces and moments.

Investigating Pressure Fluctuations on Marine Vessel Rudders: Numerical Results from Propeller–Rudder–Hull Interactions

Yuan, H.; Li, F.; Yan, Q.; Zhang, W., and Hu, J., 2023. Investigating pressure fluctuations on marine vessel rudders: Numerical results from propeller–rudder–hull interactions. Journal of Coastal Research, 39(2), 284–295. Charlotte (North Carolina), ISSN 0749-0208. Severe pressure fluctuations induced by propeller wake enhance rudder vibrations. In the present study, the pressure fluctuations on the rudder are numerically investigated by using k-ω Menter's shear stress transport turbulence model. The pressure fluctuations on the port and starboard sides of the rudder are compared in time and frequency domains. Furthermore, the impact of the advance coefficient on the displacement of propeller wake and pressure fluctuations is also discussed. The numerical results indicate that the propeller wake displacement is oriented upward and downward at the port and starboard sides, respectively. The most intense pressure fluctuation occurs at the propeller blade passage frequency. As a result of vortex displacement, the suction-side fluctuations are weaker than those on the pressure side at frequencies of 100–300 Hz over an advance coefficient range of J = 0.75–0.925. The displacement of the propeller wake weakens when the advance coefficient decreases.

Two-equation turbulent viscosity model for simulation of transitional flows: An efficient artificial neural network strategy

Laminar-to-turbulent transition phenomena are ubiquitous in natural and industrial flows. As to the Reynolds-averaged Navier–Stokes (RANS) simulation method, the workhorse for accurate prediction of such flow regime boils down to the consideration of the transition effect in turbulence modeling. In this paper, an industrial–practical transition–turbulence model with excellent accuracy, robustness, and efficiency is established by the fully connected artificial neural network (ANN), which maps the relation between the RANS mean flow variables and an intermittency factor. A one-equation local correlation-based transition model coupled with Menter's shear stress transport (SST) model is taken as the benchmark. The present two-way coupling ANN model is trained with two National Advisory Committee for Aeronautics (NACA) airfoils, that is, NACA0012 and NACA2418, at various angles of attack and Mach numbers, while tested with the A-airfoil, NACA0015, and RAE 2822 supercritical airfoils in different flow states. The a posteriori test results manifest that the mean pressure coefficient, skin friction coefficient, size of laminar separation bubble, mean streamwise velocity, Reynolds shear stress, and lift/drag/moment coefficient predicted by the ANN model are all in good agreement with those given by the benchmark transition-based SST model. Furthermore, the ANN model exhibits higher calculation efficiency and convergence speed than the traditional transition-predictive SST model. The present work may pave a new way for machine learning methods to be used in integrated transition–turbulence modeling toward industrial applications.

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.

Uncertainty analysis of turbulence model in capturing flows involving laminarization and retransition

Flows experiencing laminarization and retransition are universal and crucial in many engineering applications. The objective of this study is to conduct an uncertainty quantification and sensitivity analysis of turbulence model closure coefficients in capturing laminarization and retransition for a rapidly contracting channel flow. Specifically, two commonly used turbulence models are considered: the Spalart-Allmaras (SA) one-equation model and the Menter Shear Stress Transport (SST) two-equation model. Thereby, a series of steady Reynolds Averaged Navier-Stokes (RANS) predictions of aero-engine intake acceleration scenarios are carried out with the purposely designed turbulence model closure coefficients. As a result, both SA and SST models fail to capture the retransition phenomenon though they achieve pretty good performance in laminarization. Using the non-intrusive polynomial chaos method, solution uncertainties in velocity, pressure, and surface friction are quantified and analyzed, which reveals that the SST model possesses much great uncertainty in the non-laminar regime, especially for the logarithmic law prediction. Besides, a sensitivity analysis is performed to identify the critical contributors to the solution uncertainty, and then the correlations between the closure coefficients and the deviations of the outputs of interest are obtained via the linear regression method. The results indicate that the diffusion-related constants are the dominant uncertainty contributors for both SA and SST models. Furthermore, the remarkably strong correlation between the critical closure coefficients and the outputs might be a good guide to recalibrate and even optimize the commonly used turbulence models.

Parametric uncertainty quantification of SST turbulence model for a shock train and pseudo-shock phenomenon

Computational fluid dynamics simulations are performed to identify the inadequacy of the Menter shear-stress transport (SST) turbulence model for the prediction of the shock train and pseudo-shock phenomenon in a square duct (Mr = 1.61, Re = 3 × 107 m−1), and the uncertainty of the SST model coefficients is quantified. Due to the underprediction of Reynolds stress and failures in predicting corner flow in a square duct, both two-dimensional and three-dimensional SST simulations tended to predict weaker first shock, more secondary shocks, and larger spacing between shocks. The static pressure of the wall fluctuates in the shock train region and suffers a greater loss after the shocks. Based on the two-dimensional simulations, parametric sensitivity analysis using Sobol indices is performed, and the SST model coefficients are classified into three groups according to their sensitivity and influence regions (before and within the shock train). Bayesian inference is conducted on three-dimensional simulations to quantify the uncertainty and calibrate the coefficients that mainly influence the shock train structure. After calibration using maximum a posteriori estimates, the eddy viscosity is greatly increased, and the prediction of the shock structures and the static pressure of the wall is significantly improved, while the prediction of the friction deteriorates.

The Effect of Curvature on the Heat Transfer Performance of Regenerative Cooling Passages for a High-Area-Ratio Nozzle

Abstract Numerical studies on the flow and heat transfer characteristics of rectangular regenerative cooling passages with lateral curvature for a high-area-ratio nozzle are presented. Unlike regular geometries of coolant paths used in various engineering applications, high-area-ratio rocket nozzles have steeply curved surfaces over which the cooling passages are provided. Though the inherent inward curvature benefits heat transfer enhancement in the throat region, it is insufficient to circumvent peak heat dissipation demand. Hence, the heat transfer enhancement due to lateral curvature of the coolant fluid passages provided near the throat region is explored in this study. Extensive numerical simulations have been performed to analyze the effect of the geometry of the cooling channel on its flow and heat transfer characteristics. The compressible turbulent flow field inside the nozzle has been resolved to understand the realistic local wall heat transfer characteristics of the typical high-area-ratio rocket nozzle using Advection Upstream Splitting Method (AUSM) scheme-based finite volume solver. Menter’s Shear Stress Transport k–ω turbulence model is used to model the turbulent flow inside the nozzle. Simulations of the incompressible coolant flow and conjugate heat transfer in regenerative cooling passages have been performed with realistic spatially varying local heat flux profiles, resulting due to compressible gas expansion in the convergent–divergent nozzle. Secondary flow structures are formed due to the lateral curvature of the coolant fluid passages and are found to enhance the heat transfer considerably. Further, the effect of coolant flowrate and channel curvature have been examined to explore its suitability to negotiate the peak heat flux dissipation demand at the throat region of the nozzle.

Adaptive Model Refinement Approach for Bayesian Uncertainty Quantification in Turbulence Model

The Bayesian uncertainty quantification technique has become well-established in turbulence modeling over the past few years. However, it is computationally expensive to construct a globally accurate surrogate model for Bayesian inference in a high-dimensional design space, which limits uncertainty quantification for complex flow configurations. Borrowing ideas from stratified sampling and inherited sampling, an adaptive model refinement approach is proposed in this work, which concentrates on asymptotically improving the local accuracy of the surrogate model in the high-posterior-density region by adaptively appending model evaluation points. To achieve this goal, a modification of inherited Latin hypercube sampling is proposed and then integrated into the Bayesian framework. The effectiveness and efficiency of the proposed approach are demonstrated through a two-dimensional heat source inversion problem and its extension to a high-dimensional design space. Compared with the prior-based method, the adaptive model refinement approach has the ability to obtain more reliable inference results using fewer evaluation points. Finally, the approach is applied to parametric uncertainty quantification of the Menter shear-stress transport turbulence model for an axisymmetric transonic bump flow and provides convincing numerical results.

Iterated discretization error transport equations for laminar and turbulent flows

AbstractThe focus of this work is on discretization error estimation for finite‐volume schemes using iterated forms of the linear and nonlinear error transport equations. The accuracy of the discretization error estimates is studied by applying the error estimates as corrections to the primal problem and calculating the observed order of accuracy of the corrected solution. The test cases used in this work include two‐dimensional Cross Term Sinusoidal manufactured solutions for laminar flow and turbulent flow modeled by the Spalart–Allmaras and Menter's Shear Stress Transport model and a boundary layer manufactured solution for the Spalart–Allmaras model. The discretization error estimates of the linearized error transport equations and the nonlinear error transport equations are compared. Higher‐order accurate corrected solutions have been obtained which shows that the discretization error estimates are sufficiently accurate.

Suitability of helium gas as surrogate fuel for hydrogen in H2-Air non-reactive supersonic mixing studies

Owing to the safety concerns associated with the usage of hydrogen (H 2 ) fuel in conducting experiments, the current study investigates the suitability of using helium (He) gas as a surrogate fuel for H 2 for supersonic mixing studies. The study adopts a steady state computational approach to compare the mixing performance between the two injection cases, where a wall-based pylon-cavity aided flameholder configuration is used for the investigation. A common fuel injection location at the cavity floor is used for He and H 2 injection cases with an injector hole diameter of 1 mm. An inflow Mach number of 2.2 with sonic transverse fuel injection is kept the same for all the cases. A steady Reynolds-averaged Navier–Stokes (RANS) based computational model for compressed real gas is used for the investigation. The governing equations are solved by an implicit, second-order upwind solver with a two-equation Menter's Shear Stress Transport (SST) turbulence model. The study shows a variation in near field mixing performance between He and H 2 injection cases due to the difference in the molecular mass. As a result, a 10%–11% variation in the mixing efficiency is observed between the two cases. This makes He not suitable for micro-level mixing studies as a surrogate to H 2 . However, it is possible to closely predict the trend in global mixing performance parameters as in the H 2 injection case. • H2 injection shows an enhanced near field mixing than He injection. • Trend in global mixing performance between He and H2 injection are similar. • He cannot be used as a surrogate fuel for H2 in micro-level mixing studies.

Numerical Investigation of the Shallow Water Effect on the Total Resistance, Vertical Motion and Wave Profile of a Container Ship Model

A ship sailing in shallow water is affected by the interaction between the moving hull and the seabed in different forms such as: significant increase in total resistance, increase in the sinkage and trim that may result in squatting effect, a change in wave pattern and increased wave amplitude, a change in the propeller wake field and an altered propeller and manoeuvring performance. In order to investigate the influence of shallow water on a container ship that is assumed to be subjected to work in different water depths, the KRISO container ship model is analysed in both deep and shallow water, with a special focus on the change in resistance, vertical motion and wave profile. A viscous flow simulation is performed first to predict the ship performance in deep water and the results are compared with the experimental data that are available in the public domain. Then, the critical shallow water condition is investigated and the obtained results are compared against those formerly obtained in deep water. The numerical simulations are performed using the viscous flow solver ISIS-CFD of the FINETM/Marine software provided by NUMECA. The solver is based on the finite volume method to build the spatial discretization of the transport equation in order to solve the Reynolds-Averaged Navier-Stokes (RANS) equations. Closure to turbulence is achieved using the Menter Shear Stress Transport (K-ω SST) model, while the free-surface is captured through an air-water interface based on the Volume of Fluid (VOF) method. The comparison between the numerically obtained results and the available EFD data showed a satisfactory congruence.