A gas-kinetic scheme coupled with SST model for turbulent flows

Flow separation from a continuous surface under adverse pressure gradient remains one of the most challenging problems for turbulence modeling within the Reynolds-Averaged Navier–Stokes (RANS) framework. Although the Shear Stress Transport (SST) model performs well for a wide range of flows, its predictive capability deteriorates in wake regions dominated by complex turbulent structures. To enhance its accuracy, a modified SST model incorporating the Renormalization Group (RNG) theory of turbulence is proposed. The RNG correction is introduced as an additional source term in the dissipation equation and is limited to the reattachment region through a blending function to ensure computational efficiency and numerical stability. The model is validated using several canonical problems, including the curved backward-facing step, vertical and inclined backward-facing steps, and the periodic hills case at various Reynolds numbers. The effects of the inflow boundary condition are carefully examined to isolate the intrinsic performance of the modified model. For this purpose, an experimental campaign is performed. Comparisons with benchmark Large Eddy Simulation studies and experimental data show that the RNG-enhanced SST model substantially improves the prediction of mean velocity, turbulence kinetic energy, and wall quantities such as pressure coefficient, wall shear stress, and boundary-layer parameters. In particular, the prediction of the reattachment position is improved, yielding reduced relative errors that are nearly half of the SST model. These findings demonstrate that integrating RNG theory provides a computationally cost-effective, numerically robust, and physically consistent improvement to the SST model for separated flows from a continuous surface.

This study investigates the accuracy of Computational Fluid Dynamics (CFD) models to predict heat transfer in turbulent separated flows at low Reynolds numbers. A novel improvement of a Scale Adaptive technique is also presented. A spectrum of turbulence models is used to simulate flow and heat transfer of two geometries; fully developed flow through a staggered tube bank and a square prism in cross flow. Experimental data for both local heat transfer and velocity data are available in the literature for these cases and have been used extensively evaluate various CFD methods. Six unsteady models were used and the results show that the unsteady Shear Stress Transport (SST) model provided good overall accuracy relative to the mean Nusselt number for both cases. However, the SST model failed to accurately predict local variations. The Partially Averaged Navier-Stokes variant of the SST model showed a marked improvement for both cases. The Dynamic Smagorinsky Large Eddy Simulation (LES) showed a much-improved fidelity to the local Nusselt but under predicted the actual values. The computational cost for the LES model was significant. In general, it was found that the computationally expensive models with higher degrees of resolved turbulence did not necessarily return more accurate results. A Scale Adaptive Simulation (SAS) modification of the SST model (SAS-SST) is also used in this study. The SAS approach for the SST model adjusts the production term of the specific dissipation transport equation based on the second velocity derivative. This modification is intended to improve the SST model where local flow accelerations/ xx decelerations are detected, as occurs in separated flows. However, the local Nusselt number for the two cases considered were found to be generally less accurate than the baseline SST model. In this study a novel modification to this model was made to reduce the SAS contribution near stagnation points in the simulation. This was done through the Kato-Launder and production limiter modification in the SAS production term. The results showed only a slight improvement of the accuracy of the Nusselt number predictions. It is possible that further adjustments to the SAS terms and constants can be made to properly support and complement the stagnation point modification in this study and yield an overall better turbulence model.

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.

This article is focused on the choice of a suitable turbulence model for simulations of an industrial pump's intake, from the perspective of accuracy and, partially, also the CPU time. Twelve steady-state and transient simulations were made on a fine computational mesh, using turbulence models such as: the shear stress transport (SST), the scale-adaptive simulation (SAS), the Reynolds stress model, the explicit algebraic Reynolds-stress model, the detached eddy simulation and the large eddy simulation (LES). The curvature-correction (CC) option was assessed for the SST and SAS turbulence models. The results were compared with the LES and with published experimental results. Although all the models could predict the main floor vortex, there were still some substantial differences. It can be able to conclude that it is better to use either the SST-CC turbulence model, due to its low-computational resources and far better results than the SST model, or the SAS-CC turbulence model, since its predictions are quite similar to the LES results. In the final step, good agreement with experimental results was shown for a longer simulation with the SAS-CC turbulence model.

River bends and confluences are critical features in fluvial environments where complex flow patterns, including secondary currents, turbulence, and surface changes, strongly influence sediment transport, river morphology, and water quality. The accurate prediction of these flow characteristics is essential for hydraulic engineering applications. In this study, we present a numerical simulation of turbulent flow in river bends and confluences, with special consideration given to the dynamic interaction between free-surface variations and closed-surface constraints. The simulations were performed using OpenFOAM, an open-source computational fluid dynamics (CFDs) platform, with the k-ω SST (Shear Stress Transport) turbulence model, which is well-suited for capturing boundary layer behavior and complex turbulence structures. The finite volume method (FVM) is used to simulate and examine the behavior of the secondary current in channel bends and confluences. Two sets of experimental data, one with a sharply curved channel and the other with a confluent channel, were used to compare the numerical results and to evaluate the validity of the model. This study focuses on investigating to what extent the k-ω SST turbulence model can capture the effects of secondary flow and surface changes on flow hydrodynamics, analyzing velocity profiles and turbulence effects. The results are validated against experimental data, demonstrating the model’s ability to reasonably replicate flow features under both free- and closed-surface conditions. This study provides insights into the performance of the k-ω SST model in simulating the impact of geometrical constraints on flow regimes, offering a computationally robust and reasonable tool for river engineering and water resources management, particularly in the context of hydraulic structure design and erosion control in curved and confluence regions.

This work presents the comparison of newly developed numerical methods against earlier conventional numerical methods, used in the field of computational fluid dynamics (CFD) to model the boundary layer in turbulent flows with an adverse pressure gradient. The wall model used for comparison in this paper was developed by Manhart (2008). In the estimation of the flow field, the Manhart wall-model considers the contribution of the pressure gradient. The numerical simulations carried out in this paper are based on the Reynolds-averaged Navier Stokes (RANS) equations. The RANS-based numerical simulations were carried out using the k-ω turbulence model where the Shear Stress Transport (SST) was applied. The Manhart wall-model was implemented in the k-ω SST turbulence model. The results from the numerical simulations were validated against detailed experimental measurements. The experimental test case used for validation of the numerical simulation results consists in an asymmetric diffuser, in which a moderate adverse pressure gradient is present. The effects of the adverse pressure gradient were captured using the Laser Doppler Anemometry (LDA) technique, in two different sections of the asymmetric diffuser. The implementation procedure of the Manhart wall model was made using a free, open-source CFD software, Code_Saturne, developed by EDF. The velocity distribution estimated by the Manhart wall model is in good agreement with the experimental data for the viscous wall-layer, while the power computational requirement effort was reduced compared to the standard k-ω SST model.

Corner separation is one type of the three-dimensional (3D) separated flows which is commonly observed at the junction of the blade suction surface and endwall of an axial compressor. The commonly used Reynolds-Averaged Navier-Stokes (RANS) turbulence models, namely Spalart-Allmaras (SA) and Menter’s Shear Stress Transport (SST) models, have been found to overpredict the size of corner separation. The physical reason is partly attributed to the underestimation of turbulence mixing between the mainstream flow and the endwall boundary-layer flow. This makes the endwall boundary layer unable to withstand the bulk adverse pressure gradients, and in turn leads to its premature separation from the endwall surface during its migration towards the endwall/blade suction surface corner. The endwall flow characteristics within the compressor stator cascade are then studied to facilitate understanding the physical mechanisms that drive the formation of 3D flow structures, and the physical reasons that lead to RANS modelling uncertainties. It is found that the insufficient near-wall boundary layer mixing is partly due to the failure of both SA and SST models to reasonably model the non-equilibrium turbulence behaviors inside the endwall boundary layer, which is caused by the boundary layer skewness. Based on the understanding of the skew-induced turbulence characteristics and its effect on mixing, a detailed effort is presented towards the physical-based modelling of the skew-induced non-equilibrium wall-bounded turbulence. The source terms in the SA and SST models that control mixing are identified and modified, in order to enhance mixing and strengthen the endwall boundary layer. The improved turbulence models are then validated against the compressor corner separation flows under various operating conditions to prove that the location and extent of the corner separation are more realistically predicted.

Turbulent flow and heat transfer past a cube (L × L × L) mounted on one wall of a channel of height 2L have served as a benchmark problem to validate computational methods and turbulence models because of the richness in the flow features induced by an unassumingly simple geometry. These include an unstable bi-modal horse-shoe vertical structure upstream of the cube, vortex shedding from the two sides of the cube that extend to the aft of the cube, and periodic separation from the top of the cube. In this study, simulations based on steady and unsteady Reynolds-Averaged Navier-Stokes (RANS and URANS) and large-eddy simulations (LES) were performed to understand the nature of the flow and how that flow affects pressure, drag, and surface heat transfer distributions. For RANS and URANS, the following turbulence models were assessed: the realizable k−ε model, the shear-stress transport (SST) model with and without corrections for curvature, the Reynolds stress model with linear pressure strain (RSM-LPS), and the stress-omega Reynolds stress model. In this study, the RANS and URANS results were generated by using the ANYSYS Fluent code, and the LES results were generated by using the PowerFlow code. Results obtained show RANS to be unacceptable in predicting the reattachment of the separation bubble downstream of the cube. URANS by being able to resolve the oscillatory shedding from the two sides of the cube was able to predict the reattachment with reasonable accuracy. URANS with the SST model that has the curvature correction gave the best results for the reattachment length downstream of the cube (relative error within 5% of the experimental data). Also, this model was able to capture all details of the flow features revealed in the experimental oil-flow study with considerable accuracy. However even with this model, the predicted pressure just downstream of the cube is incorrect by up to 50%. This is because URANS was unable to predict the unstable bi-modal, horse-shoe vortex system upstream of the cube induced by interactions between the spanwise vortices in the turbulent boundary layer and the horsehoe vortex system. This interaction was found to cause the separation bubble on top of the cube to shed periodically. By being able to capture this interaction, LES was able to better predict the pressure just downstream of the cube. This shows why LES is needed and why RANS and URANS are inadequate unless those models can be modified to account for these unsteady interactions. Steady and unsteady RANS based on the SST model were also employed to study the heat transfer about the surface of the cube. Reasonably good results were obtained for the leading and trailing faces of the cube but not for the top and the two side faces. A parametric study on the effects of the turbulent Prandtl number show the connection between the turbulent eddy viscosity and the turbulent thermal conductivity cannot be represented by a simple algebraic equation, the Prandtl number. Thus, better RANS models are needed to capture the physics embedded in the correlations between the fluctuating velocities and temperatures. A paper on this work is being prepared. The order of authorship will be X. Chi, K, Adeel Ahmad, Surya Muthukannan Chinnamani, and T. I-P. Shih. The author of this abstract thanks his students who worked on the different parts of this problem.

This paper presents results from numerical simulations of a 3-bladed horizontal axis tidal stream turbine (TST). A two-equation transient Reynolds Averaged Navier Stokes (RANS) k-! Shear Stress Transport (SST)model was used for code validation and testing of a newly implemented sliding mesh technique for Code Saturne. Wall- and blade-resolved large-eddy simulations (LES) were then performed to study the complete geometry at various tip speed ratios (TSR). Thrust and power coefficients were compared to experimental measurements in a towing tank for a range of TSR (4, 5, 6, 7 & 8) at a fixed hub pitch angle. A strong flow meandering was observed with the wake recovery and velocity deficit showing a high sensitivity to upstream turbulence intensities. The mean thrust and power coefficients by RANS k-! SST model were found to be more sensitive to the upstream turbulence than the LES. A comparison of all models are also presented for the mean sectional blade pressures and mean wake velocity profiles. The paper also presents an overview of modelling and numerical issues relating to fine LES for such rotating geometries

Liquid microjet impingement cooling has shown the potential to be the solution for heat removal from electronic devices such as very-large-scale integration (VLSI) chips. The post-impingement dynamics of the jet, specifically the interaction between the liquid fronts on the surface engendered by the jets is a critical criterion improving the heat transfer characteristics. While some seminally important experimental studies have investigated this attribute, the amount of accurate data and analysis is limited by the shortcomings of real-life experiments. In this article, numerical investigations into the fluid dynamics and heat transfer in microjet cooling systems are carried out. Specifically, this paper addresses the question regarding the necessary fidelity of the simulations. Different Reynolds-averaged Navier–Stokes (RANS) models are compared to the Large Eddy Simulations (LES) simulation and the potential fidelity of different eddy-viscosity-based closures is clearly shown. Recommendations are made regarding the RANS closures that should give the best performance. It is demonstrated that the transition Shear Stress Transport (SST) model and k - ω SST model both show excellent ability to predict the local or average Nu, and also local level pressure coefficient f with less than 5% difference in the range of 30 < Red < 4000, compared with the reference LES model. For the experimental measurements in the range of 130 < Red < 1400, the LES model, transition SST model and k - ω SST model all show less than 25% prediction error. Moreover, it is shown that the validity of the unit cell assumption for the temperature and flow distribution depends on the flow rate.

Though the k–ω shear-stress transport (SST) turbulence model is widely used, it is developed based on incompressible flow and the analysis of simple flow characteristics such as boundary layer and free shear flows. Due to the lack of comprehensive consideration of important flow structures, such as shock wave and highly compressible zones, the k–ω SST turbulence model has inherent limitations in describing supersonic flows. A multi-physics improvement strategy is proposed to improve the prediction accuracy of the k–ω SST model for supersonic flows. This strategy leverages shock/turbulent boundary layer and shock/compressibility functions to accurately recognize areas with significant structures, enabling targeted improvement of the turbulence model. Five supersonic flow cases are tested and analyzed, and the results show that while the single-physics turbulence model can improve the prediction accuracy of flows with a single flow structure corresponding to the correction, its prediction ability is insufficient in other flows with different flow structures. In contrast, the multi-physics turbulence model exhibits good ability in flows with multiple flow structures, while also maintaining the performance of the single-physics turbulence model. The multi-physics turbulence model has higher accuracy and stronger universality, making it advantageous for modeling complex supersonic flows.

Rationality of the parameter settings in turbulence model is an important factor affecting the accuracy of conjugate heat transfer (CHT) prediction. On the basis of a developed CHT methodology and the experimental data of Mark// cooling turbine blade, influences of the turbulence model parameter settings and the selection of turbulence models on CHT simulation are investigated. Results and comparisons with experimental data indicate that the inlet setting of the $$\tilde{v}$$ in Spalart–Allmaras model has nearly no influence on flow and heat transfer in blade surface. The inlet turbulence length scale l T in the low-Reynolds number Chien k-e turbulence model and the blade surface roughness in shear stress transport (SST) k-ω SST model have relatively obvious effects on the blade surface temperature which increases with the increase of them. Both of the laminar Prandtl number and turbulent Prandtl number have slight influences on the prediction, and they only need to be constant in CHT simulation. The k-ω SST model has the best accuracy in the turbine blade CHT simulation compared with the other two models.

A numerical investigation of leading edge impingement is completed in this study. Impingement onto a half cylinder, concave surface is used to model the leading edge of a modern gas turbine airfoil. The temperature difference between the impinging jet and the target surface is varied from ΔT = 60°F (33.3°C) (typical of traditional laboratory experiments) to ΔT = 1000°F (555.6°C) (representative of temperature differences encountered in modern engines). Over this range of temperatures, the simulations are validated against experimental data and extended to engine-like conditions. In addition to the varying temperatures, the effect of jet Reynolds number is also investigated (Rejet = 5000–25000). The jet geometry is also varied in this investigation to model the effect of jet-to-jet spacing (s/d = 2–8), the effect of jet–to–target surface distance (ℓ/d = 2–8.5), and the effect of target surface diameter (D/d = 3.6 and 5.5). For all simulations the k-ω, Shear Stress Transport (SST) turbulence model is used to simulate the impingement flows. Over the range of flow conditions and geometry variations, the SST model is proven to be effective in predicting leading edge heat transfer coefficients. With multiple direct comparisons between the numerical simulations and existing experimental data, the simulations predict the surface Nusselt numbers within an average of 11% of the experimental data. Furthermore, the predictions indicate the existing correlations developed in low temperature laboratory experiments are sufficient for calculating stagnation region Nusselt numbers under engine-like temperatures.

The present author was asked to provide an update on the status and the more recent developments around the shear-stress transport (SST) turbulence model for this special issue of the journal. The article is therefore not intended as a comprehensive overview of the status of engineering turbulence modelling in general, nor on the overall turbulence modelling strategy for ANSYS computational fluid dynamics (CFD) in particular. It is clear from many decades of turbulence modelling that no single model – nor even a single modelling approach – can solve all engineering flows. Any successful CFD code will therefore have to offer a wide range of models from simple Eddy-viscosity models through second moment closures all the way to the variety of unsteady modelling concepts currently under development. This article is solely intended to outline the role of the concepts behind the SST model in current and future CFD simulations of engineering flows.

Implicit high-order gas kinetic scheme for turbulence simulation