Comparison of the Reynolds-averaged Turbulence Models on Single Phase Flow Simulation in Agitated Extraction Columns

The flow field of liquid phase (water) of agitated extraction columns is simulated with the help of computational fluid dynamics (CFD). Four kinds of Reynolds-averaged turbulence models, i.e. the standard k-ε model, the RNG (renormalization group) k-s model, the realizable k-ε model and the Reynolds stress model, are compared in detail in order to judge which is the best model in terms of the accuracy, less CPU time and memory required. The performance of the realizable k-s model is obviously improved by reducing the model constant from C2 = 1.90 to C2 = 1.61. It is concluded that the improved realizable k-e model is the optimal model.

Performances of Different Turbulence Models for Simulating Shallow Water Sloshing in Rectangular Tank

Liquid sloshing is a common phenomenon in the transportation of liquid-cargo tanks.Liquid waves lead to fluctuating forces on the tank walls.If these fluctuations are not predicted or controlled,for example,by using baffles,they can lead to large forces and momentums.The volume of fluid(VOF)two-phase numerical model in Open FOAM open-source software has been widely used to model the liquid sloshing.However,a big challenge for modeling the sloshing phenomenon is selecting a suitable turbulence model.Therefore,in the present study,different turbulence models were studied to determine their sloshing phenomenon prediction accuracies.The predictions of these models were validated using experimental data.The turbulence models were ranked by their mean error in predicting the free surface behaviors.The renormalization group(RNG)k-ε and the standard k–ω models were found to be the best and worst turbulence models for modeling the sloshing phenomena,respectively;moreover,the SST k-ω model and v2-f k-ε results were very close to the RNG k-εmodel result.

Comparative Experimental and Numerical Study of Wave Loads on A Monopile Structure Using Different Turbulence Models

This study numerically and experimentally investigates the effects of wave loads on a monopile-type offshore wind turbine placed on a 1:25 slope at different water depths as well as the effect of choosing different turbulence models on the efficiency of the numerical model.The numerical model adopts a two-phase flow by solving Unsteady Reynolds-Averaged Navier−Stokes(URANS)equations using the Volume Of Fluid(VOF)method and three differentk-ωturbulence models.Typical environmental conditions from the East China Sea are studied.The wave run-up and the wave loads applied on the monopile are investigated and compared with relevant experimental data as well as with mathematical predictions based on relevant theories.The numerical model is well validated against the experimental data at model scale.The use of different turbulence models results in different predictions on the wave height but less differences on the wave period.The baseline k-ωturbulence model and Shear-Stress Transport(SST)k-ωturbulence model exhibit better performance on the prediction of hydrodynamic load,at a model-scale water depth of 0.42 m,while the laminar model provides better results for large water depths.The SST turbulence model performs better in predicting wave run-up for water depth 0.42 m,while the laminar model and standard k-ωmodel perform better at water depth 0.52 m and 0.62 m,respectively.

Numerical simulation of flow around square cylinder using different low-Reynolds number turbulence models

ABE-KONDOH-NAGANO,ABID,YANG-SHIH and LAUNDER-SHARMA low-Reynolds number turbulence models were applied to simulating unsteady turbulence flow around a square cylinder in different phases flow field and time-averaged unsteady flow field.Meanwhile,drag and lift coefficients of the four different low-Reynolds number turbulence models were analyzed.The simulated results of YANG-SHIH model are close to the large eddy simulation results and experimental results,and they are significantly better than those of ABE-KONDOH-NAGANO,ABID and LAUNDER-SHARMR models.The modification of the generation of turbulence kinetic energy is the key factor to a successful simulation for YANG-SHIH model,while the correction of the turbulence near the wall has minor influence on the simulation results.For ABE-KONDOH-NAGANO,ABID and LAUNDER-SHARMA models satisfactory simulation results cannot be obtained due to lack of the modification of the generation of turbulence kinetic energy.With the joint force of wall function and the turbulence models with the adoption of corrected swirl stream,flow around a square cylinder can be fully simulated with less grids by the near-wall.

End-to-end differentiable learning of turbulence models from indirect observations

The emerging push of the differentiable programming paradigm in scientific computing is conducive to training deep learning turbulence models using indirect observations.This paper demonstrates the viability of this approach and presents an end-to-end differentiable framework for training deep neural networks to learn eddy viscosity models from indirect observations derived from the velocity and pressure fields.The framework consists of a Reynolds-averaged Navier–Stokes(RANS)solver and a neuralnetwork-represented turbulence model,each accompanied by its derivative computations.For computing the sensitivities of the indirect observations to the Reynolds stress field,we use the continuous adjoint equations for the RANS equations,while the gradient of the neural network is obtained via its built-in automatic differentiation capability.We demonstrate the ability of this approach to learn the true underlying turbulence closure when one exists by training models using synthetic velocity data from linear and nonlinear closures.We also train a linear eddy viscosity model using synthetic velocity measurements from direct numerical simulations of the Navier–Stokes equations for which no true underlying linear closure exists.The trained deep-neural-network turbulence model showed predictive capability on similar flows.

Comparison of Reynolds average Navier-Stokes turbulence models in numerical simulations of the DC arc plasma torch

Five turbulence models of Reynolds average Navier-Stokes(RANS),including the standard k-ω model,the RNG k-e model taking into account the low Reynolds number effect,the realizable k-ω model,the SST k-ω model,and the Reynolds stress model(RSM),are employed in the numerical simulations of direct current(DC)arc plasma torches in the range of arc current from 80 A to 240 A and air gas flow rate from 10 m^3 h^-1 to 50 m^3 h^-1.The calculated voltage,electric field intensity,and the heat loss in the arc chamber are compared with the experiments.The results indicate that the arc voltage,the electric field,and the heat loss in the arc chamber calculated by using the standard k-ω model,the RNG k-ωmodel taking into account the low Reynolds number effect,and the realizable k-ω model are much larger than those in the experiments.The RSM predicts relatively close results to the experiments,but fails in the trend of heat loss varying with the gas flow rate.The calculated results of the SST k-ω model are in the best agreement with the experiments,which may be attributed to the reasonable predictions of the turbulence as well as its distribution.

Turbulence Models of Hydrodynamic Lubrication

The main theoretical turbulence models for application to hydrodynamic lubrication problems were briefly reviewed, and the course of their development and their fundamentals were explained. Predictions by these models on flow fields in turbulent Couette flows and shear-induced countercurrent flows were compared to existing measurements, and Zhang & Zhang's combined k-ε model was shown to have surpassingly satisfactory results. The method of application of this combined k-ε model to high speed journal bearings and annular seals was summarized, and the predicted results were shown to be satisfactory by comparisons with existing experiments of journal bearings and annular seals.

Nonlinear turbulence models for predicting strong curvature effects

Prediction of the characteristics of turbulent flows with strong streamline curvature, such as flows in turbomachines, curved channel flows, flows around airfoils and buildings, is of great importance in engineering applications and poses a very practical challenge for turbulence modeling. In this paper, we analyze qualitatively the curvature effects on the structure of turbulence and conduct numerical simulations of a turbulent Uduct flow with a number of turbulence models in order to assess their overall performance. The models evaluated in this work are some typical linear eddy viscosity turbulence models, nonlinear eddy viscosity turbulence models （NLEVM） （quadratic and cubic）, a quadratic explicit algebraic stress model （EASM） and a Reynolds stress model （RSM） developed based on the second-moment closure. Our numerical results show that a cubic NLEVM that performs considerably well in other benchmark turbulent flows, such as the Craft, Launder and Suga model and the Huang and Ma model, is able to capture the major features of the highly curved turbulent U-duct flow, including the damping of turbulence near the convex wall, the enhancement of turbulence near the concave wall, and the subsequent turbulent flow separation. The predictions of the cubic models are quite close to that of the RSM, in relatively good agreement with the experimental data, which suggests that these models may be employed to simulate the turbulent curved flows in engineering applications.

LONGITUDINAL VORTEX PAIR IMBEDDED IN A TURBULENT BOUNDARY LAYER:COMPARATIVE PERFORMANCES OF SEVERAL TURBULENCE MODELS

Four turbulence models, namely, the basic and nonlinear stress-transport models and the basic and anisotropic k- epsilon models, have been tested in the case of interaction between a longitudinal vortex pair and a flat-plate boundary layer. The results of their predictions were compared with Mehta and Bradshaw's measurements. Part of the results involving those of the nonlinear stress-transport model and anisotropic k- epsilon model are presented and discussed. (Edited author abstract) 13 Refs.

Assessment of advanced RANS turbulence models for prediction of complex flows in compressors

Reynolds-Averaged Navier-Stokes(RANS) Computational Fluid Dynamics(CFD) has been widely used in compressor design and analysis. However, reasonable prediction of compressor flow and its impact on compressor performance remains challenging. In this study, Menter’s Shear Stress Transport(SST) model and its variants, as well as the ω-based Reynolds stress model(Stress-BSL) are assessed. For a single rotor(Rotor 67), under the peak efficiency operating condition, all studied turbulence models predict its performance with reasonable accuracy;under the off-design conditions, SST with Helicity correction(SST-Helicity) shows superiority in predicting the effect of flow on the spanwise distribution of aerodynamic parameters. For Darmstadt’s 1.5-stage transonic axial compressor, SST-Helicity outperforms SST, SST with the Quadratic Constitutive Relation(SST-QCR) and Stress-BSL in predicting the performance as well as the spanwise distribution of aerodynamic parameters. At the design rotating speed, the stall margin given by SST-Helicity(20.90%) is the closest to the experimental measurement(24.81%), which is more than twice that by SST(8.71%) and 1.5 times that by SST-QCR(14.14%). This paper demonstrates that SSTHelicity model, together with a good quality and sufficiently refined grid, can capture the compressor flow features with reasonable accuracy, which results in a credible prediction of compressor performance and stage matching.

Constrained re-calibration of two-equation Reynolds-averaged Navier–Stokes models

Machine-learned augmentations to turbulence models can be advantageous for flows within the training dataset but can often cause harm outside.This lack of generalizability arises because the constants(as well as the functions)in a Reynolds-averaged Navier–Stokes(RANS)model are coupled,and un-constrained re-calibration of these constants(and functions)can disrupt the calibrations of the baseline model,the preservation of which is critical to the model's generalizability.To safeguard the behaviors of the baseline model beyond the training dataset,machine learning must be constrained such that basic calibrations like the law of the wall are kept intact.This letter aims to identify such constraints in two-equation RANS models so that future machine learning work can be performed without violating these constraints.We demonstrate that the identified constraints are not limiting.Furthermore,they help preserve the generalizability of the baseline model.

Numerical study of corner separation in a linear compressor cascade using various turbulence models

Three-dimensional corner separation is a common phenomenon that significantly affects compressor performance. Turbulence model is still a weakness for RANS method on predicting corner separation flow accurately. In the present study, numerical study of corner separation in a linear highly loaded prescribed velocity distribution （PVD） compressor cascade has been investigated using seven frequently used turbulence models. The seven turbulence models include Spalart Allmaras model, standard k-e model, realizable k-e model, standard k-to model, shear stress transport k co model, v2-fmodel and Reynolds stress model. The results of these turbulence models have been compared and analyzed in detail with available experimental data. It is found the standard k-1： model, realizable k-e model, v2-f model and Reynolds stress model can provide reasonable results for predicting three dimensional corner separation in the compressor cascade. The Spalart-Allmaras model, standard k-to model and shear stress transport k-w model overesti- mate corner separation region at incidence of 0°. The turbulence characteristics are discussed and turbulence anisotropy is observed to be stronger in the corner separating region.

Effect of turbulence models on predicting convective heat transfer to hydrocarbon fuel at supercritical pressure

A variety of turbulence models were used to perform numerical simulations of heat transfer for hydrocarbon fuel flowing upward and downward through uniformly heated vertical pipes at supercritical pressure. Inlet temperatures varied from 373 K to 663 K, with heat flux rang- ing from 300 kW/m2 to 550 kW/m2. Comparative analyses between predicted and experimental results were used to evaluate the ability of turbulence models to respond to variable thermophysical properties of hydrocarbon fuel at supercritical pressure. It was found that the prediction performance of turbulence models is mainly determined by the damping function, which enables them to respond differently to local flow conditions. Although prediction accuracy for experimental results varied from condition to condition, the shear stress transport （SST） and launder and sharma models performed better than all other models used in the study. For very small buoyancy-influenced runs, the thermal-induced acceleration due to variations in density lead to the impairment of heat transfer occurring in the vicinity of pseudo-critical points, and heat transfer was enhanced at higher temperatures through the combined action of four thermophysical properties： density, viscosity, thermal conductivity and specific heat. For very large buoyancy- influenced runs, the thermal-induced acceleration effect was over predicted by the LS and AB models.

Assessment of Two Turbulence Models and Some Compressibility Corrections for Hypersonic Compression Corners by High-order Difference Schemes

The Spalart-Allmaras （S-A） turbulence model, the shear-stress transport （SST） turbulence model and their compressibility corrections are revaluated for hypersonic compression comer flows by using high-order difference schemes. The compressibility effect of density gradient, pressure dilatation and turbulent Mach number is accounted. In order to reduce confusions between model uncertainties and discretization errors, the formally fifth-order explicit weighted compact nonlinear scheme （WCNS-E-5） is adopted for convection terms, and a fourth-order staggered central difference scheme is applied for viscous terms. The 15° and 34° compression comers at Mach number 9.22 are investigated. Numerical results show that the original SST model is superior to the original S-A model in the resolution of separated regions and predictions of wall pressures and wall heat-flux rates. The capability of the S-A model can be largely improved by blending Catris＇ and Shur＇s compressibility corrections. Among the three corrections of the SST model listed in the present paper, Catris＇ modification brings the best results. However, the dissipation and pressure dilatation corrections result in much larger separated regions than that of the experiment, and are much worse than the original SST model as well as the other two corrections. The correction of turbulent Mach number makes the separated region slightly smaller than that of the original SST model. Some results of low-order schemes are also presented. When compared to the results of the high-order schemes, the separated regions are smaller, and the peak wall pressures and peak heat-flux rates are lower in the region of the reattachment points.

Evaluation of Turbulence Models in Predicting Hypersonic and Subsonic Base Flows Using Grid Adaptation Techniques

The flows behind the base of a generic rocket, at both hypersonic and subsonic flow conditions, are numerically studied. The main concerns are addressed to the evaluation of turbulence models and the using of grid adaptation techniques. The investigation focuses on two configurations, related to hypersonic and subsonic experiments. The applicability tests of different turbu- lence models are conducted on the level of two-equation models calculating the steady state solution of the Reynolds-averaged Navier-Stokes（RANS） equations. All used models, the original Wilcox k-co, the Menter shear-stress transport （SST） and the ex- plicit algebraic Reynolds stress model（EARSM） formulation, predict an asymmetric base flow in both cases caused by the support of the models. A comparison with preliminary experimental results indicates a preference for the SST and EARSM results over the results from the older k-co model. Sensitivity studies show no significant influence of the grid topology or the location of the laminar to turbulent transition on the base flow field, but a strong influence of even small angles of attack is reported from the related experiments.

Two-phase turbulence models for simulating dense gas-particle flows

The two-fluid model is widely adopted in simulations of dense gas-particle flows in engineering facili- ties. Present two-phase turbulence models for two-fluid modeling are isotropic. However, turbulence in actual gas-particle flows is not isotropic. Moreover, in these models the two-phase velocity correlation is closed using dimensional analysis, leading to discrepancies between the numerical results, theoretical analysis and experiments. To rectify this problem, some two-phase turbulence models were proposed by the authors and are applied to simulate dense gas-particle flows in downers, risers, and horizontal channels; Experimental results validate the simulation results. Among these models the USM-O and the two-scale USM models are shown to give a better account of both anisotropic particle turbulence and particle-particle collision using the transport equation model for the two-phase velocity correlation.

The Influence of Advection Schemes and Turbulence Closure Models on Drag Coefficient Calculation Around a Circular Cylinder at High Reynolds Number

Different advection schemes and two-equation turbulence closure models based on eddy viscosity concept are used to compute the drag coefficient around a circular cylinder at high Reynolds number (106).The numerical results from these simulations are compared with each other and with experimental data in order to evaluate the performance of different combinations of advection scheme and two-equation turbulence model.The separate contributions from form drag and friction drag are also ana-lyzed.The computational results show that the widely used standard k-ε turbulence closure is not suitable for such kind of study,while the other two-equation turbulence closure models produce acceptable results.The influence of the different advection schemes on the final results are small compared to that produced by the choice of turbulence closure method. The present study serves as a reference for the choice of advection schemes and turbulence closure models for more complex numerical simulation of the flow around a circular cylinder at high Reynolds number.

Rotational Forms of Large Eddy Simulation Turbulence Models:Modeling and Mathematical Theory

In this paper the authors present a derivation of a back-scatter rotational Large Eddy Simulation model,which is the extension of the Baldwin&Lomax model to nonequilibrium problems.The model is particularly designed to mathematically describe a fluid filling a domain with solid walls and consequently the differential operators appearing in the smoothing terms are degenerate at the boundary.After the derivation of the model,the authors prove some of the mathematical properties coming from the weighted energy estimates,which allow to prove existence and uniqueness of a class of regular weak solutions.

THE APPLICATION AND DEVELOPMENT OF TURBULENCE MODELS IN BUOYANT RECIRCULATING FLOWS

In this paper, a modified κ-ε turbulence model, a simplified algebraic stress model and a developed two-fluid model have been presented based on numerical modeling of turbulent buoyant recirculating flows. The calculated results by these models are in good agreement with experiments. However, the last model is much better for simulating gravity-stratified flows.

APPLICATION OF TURBULENCE MODELS IN THERMOHYDRAULICS

The mathematical model of turbulent buoyant recirculating flows is applied in thermohydraulics and an algebraic stress model is proposed to simulate noniso- tropic turbulent buoyant recirculating flows in a shallow water channel.It can be shown that the buoyancy force is able to reduce the turbulence in vertical di- rection and the heat conduction in the thermocline layer is nonisotropic.At the same time,the stacked-up and separated arrangement of intake-outlet for thermal power stations have been predicted by such numerical models.The results are in good agreement with experiments(ref.1-3).