Algebraic Reynolds Stress Model Research Articles

The Explicit Algebraic Reynolds Stress Models for Turbulent Flows

The explicit algebraic Reynolds stress models are obtained from second-order closure models that are valid for three-dimensional turbulent flows in non-inertial frames. The purpose of this present research is to simplify the development of the Reynolds stress anisotropy tensor. This anisotropy stress tensor has seven scalar coefficients and has seven tensor polynomial groups that are the integrity basis for the functions of both symmetric and antisymmetric tensors. This research will also explicitly determine the six independent invariants of the mean strain rate tensor and of the mean rotation rate tensor. The resulting algebraic equation for the anisotropy tensor depends on the choice of the model that is used to determine the dissipation rate and pressure-strain correlation. These equations also represent the slow pressure strain rate and an isotropic dissipation rate tensor of the Rotta model. The results of present research can be compared with the results of Gatski and Speziale that give the complete expression for a traceless symmetric second order tensor which depended on the symmetric and the antisymmetric tensor that involved ten tensor polynomial groups with five independent invariants. The present work reduces the ten tensor polynomial groups down to seven groups which drastically decreases computational time.

Interaction of shrouded stator flow and main flow and its influence on performances of a three-stage high pressure compressor

The prediction of the complex flows within a turbomachinery remains a challenging issue for computational fluid dynamics (CFD). The real features of a turbomachinery must be taken into account in the simulation but they increase its complexity. One of these features is the leakage flow due to the axial gap between the fixed and rotating parts of the hub. This article focuses on this flow within the scope of a high-pressure compressor. The results are compared with experimental data obtained in the main flow path. The leakage flow is characterized by several vortices, especially near the hub and between the seal-teeth. It interacts with the main flow: the hub separation is quite wider while the casing one is reduced in comparison with the smooth case. In this article, the smooth case is related to the simulation without any shrouded stator cavity. The leakage flow influences strongly on compressor performances. Taking into account the leakage flow in the CFD improves the agreement between CFD and experimental values. Due to the vortex prediction, the influence of the turbulence modelling is also assessed. The explicit algebraic Reynolds stress model improves the flow prediction while the presently investigated differential Reynolds stress model predicts too wide hub corner separation which leads to high underestimation of compressor performances.

Numerical simulation of separated flows in channels

The work deals with numerical modelling of turbulent flows in channels with an expansion of the cross-section where flow separation and reattachment occur. The performance of several eddy viscosity models and an explicit algebraic Reynolds stress model (EARSM) is studied. The used test cases are flows in channels with various backward facing steps where the step is perpendicular or inclined and the top wall is parallel or deflected. Furthermore, a channel with the circular ramp is considered. The numerical solution is achieved by the finite volume method or by the finite element method. The results of both numerical approaches are compared.

J054033 壁面近傍に設置された三角柱周りの乱流解析

Numerical analysis has been performed for turbulent flow with heat transfer in a rectangular duct with triangular cylinder placed near a wall by using an algebraic Reynolds stress model and the turbulent Prandtl number assumed to be constant in temperature field. Calculated results are compared with the experiment in order to confirm the validity of the presented model. It has been found that the calculation can reproduce reasonably the phase-averaged velocity profiles including vorticity. And calculation also predicts that the vortex affects the flow near the top and bottom walls. Adding to this, although the presented method underestimates Nusselt number in the region behind the triangular cylinder, two characteristic peaks of Nusselt number profile are predicted as well as the experiment. The compared results with the experimental and numerical data suggest that an algebraic Reynolds stress model has the potentiality to reproduce the turbulent flow with vortex.

J054034 流れ方向に円柱を有する矩形断面管路内の乱流解析

Numerical analysis has been performed for three-dimensional developing turbulent flow in a rectangular duct containing straight cylinder placed near a bottom wall by using an algebraic Reynolds stress model. Calculated results of streamwise velocity and Reynolds stresses are compared with the experimental data in order to examine the validity of the presented numerical method and an algebraic Reynolds stress model. Comparisons with the experimental result suggest that the present method is able to predict velocity profiles correctly and reproduce the secondary flow of the second kind. Adding to this, calculated results show clearly the generation of pulsation flow near the narrow region between cylinder and bottom wall.

Nonlinear Algebraic Reynolds Stress Model for Two-Phase Turbulent Flows Laden with Small Heavy Particles in Circular Tube

The purpose of the study is to present an explicit algebraic Reynolds stress (nonlinear turbulent viscosity) model combined with modified k – ε turbulence model taking into account particles effect on turbulence for calculating the main turbulent characteristics of two-phase flows. For calculating particles distribution in space we used diffusion-inertia model (DIM). The turbulence attenuating in the presence of particles is clearly observed, investigated and compared with the experimental data. The developed model adequately described turbulence anisotropy and the influence of particles inertia and concentration on the turbulence intensity.

Simulation of fine-dispersed turbulent flow in a pipe on the basis of the nonlinear model of turbulent viscosity

A nonlinear model of turbulent viscosity (the explicit algebraic Reynolds stress model) for gas-dispersed flow with small heavy particles has been presented. The calculations have been checked by comparison with the experimental data on the effect of the fine-dispersed admixture on turbulent flow of air in a pipe.

Nonlinear algebraic Reynolds stress model for two-phase turbulent flows laden with small heavy particles

The purpose of the study is to present an explicit self-consistent algebraic Reynolds stress model (ARSM) for two-phase turbulent flows combined with diffusion-inertia model (DIM). The modulation of turbulence by small heavy particles whose diameter is not greater than the Kolmogorov length scale is considered. The volume concentration of dispersed phase is assumed to be sufficiently small so that inter-particle collisions can be neglected; however, the mass concentration is fairly large (ρp≫ρf). Calculations were performed for turbulent flow in a vertical tube and turbulent flow past a backward-facing step. It was shown that the suggested turbulence model correctly predicts anisotropy of velocity fluctuations and the turbulence modulation by particles. In the presence of small particles turbulence of the flow in a vertical tube is attenuated. The level of turbulence attenuation is increased with increasing particles mass loading and decreased with increasing particle response time. In turbulent flow past the backward-facing step regions with attenuating and enhancing turbulence are observed.

DNS and RANS modelling of a turbulent plane impinging jet

The main objective of this paper is to study in detail the fluid flow and the heat transfer in plane impinging jets. Mean and fluctuating velocities and global parameters, i.e. the local Nusselt number, are analysed. The study is focused on a Reynolds number 20,000 (based on the bulk inlet velocity and the nozzle width, B) and dimensionless jet-to-surface spacing 4. As a first step, a reliable direct numerical simulation (DNS) has been performed. Then, the DNS results have been used as reference solution to assess the performance of several Reynolds-averaged Navier–Stokes (RANS) models. Namely, explicit algebraic Reynolds stress models and both non-linear and linear eddy viscosity models in conjunction with k − ϵ and k − ω platforms. Moreover, an overview of the numerical methods and the methodology used to verify the code and the simulations is also presented. Time-averaged DNS results have revealed that the main recirculating flow cannot be captured well unless the outflow is placed at least at 40 B from the jet centreline approximately. This suggests that previous experimental data may not be adequate to study the flow configuration far from the jet. Consequently, conclusions previously published by the authors on the performance of the tested RANS models have been necessarily revised.

Unsteady numerical simulations of the single-phase turbulent mixing between two channels connected by a narrow gap

This paper focuses on the unsteady numerical simulation of the turbulent flow in two types of geometry containing a narrow gap with the explicit algebraic Reynolds stress model. The model was first validated through the comparison of simulation results inside a rectangular channel containing a cylinder and the corresponding experimental data. The structures of the oscillation were correctly reproduced. Simulation of turbulent mixing between circular channels connected by a narrow gap was carried out with the validated model. Because of the influence of the strong anisotropic turbulent flow in the gap region, the mixing rate was dramatically enhanced by the cyclic and almost periodic flow pulsation. The calculation results of the turbulent mixing rate showed good agreement with the experiment and the maximum error was less than 15%.

Choice of a turbulence model for pump intakes

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.

Numerical simulation with a DES approach for automotive flows

A Detached Eddy Simulation (DES) approach is used to investigate the main flow features of the Ahmed body. The flow around the Ahmed body exhibits basic features which are characteristic of real ground vehicles. This work presents unsteady flow simulations at the rear slant angle 25° using the ISIS-CFD flow solver which is developed by the CFD Department of the Fluid Mechanics Laboratory of Ecole Centrale de Nantes. Several versions of the DES models which are based on the k - ω SST turbulence model are used. An Explicit Algebraic Reynolds Stress Model for the turbulence modeling is also used to compare the DES approaches with a Reynolds-Averaged Navier–Stokes (RANS) solution. The flow on the slanted surface and in the wake is discussed. Averaged velocities and turbulent kinetic energy profiles are compared with the experimental data. This work shows that the DES approaches, and particularly the DES-SST model, give a better solution compared with the RANS solution. However, the bubble in the rear slant is not predicted by the DES approaches.

ICONE19-43177 Experimental Study of Airflow-Mixture by Using PIV

In this paper, it was reported that simulation design study about gas process unit, such as process gas reactor, heat exchangers and heat conditioner, for one of the heat utilization system components development of High Temperature Gas-cooled Reactor (HTGR). In simulating precisely the heat transfer control characteristics of the gas-mixing unit, a good model for turbulent mixing process of some velocity ratios is a key issue. Therefore, we have been proceeding to develop the newly CFD code. This code using algebraic Reynolds stress model has been reasonably predicted about complex turbulent flows such as flow separation in a rectangular duct with 90-degree sharp turn and strong anisotropic flow in straight duct with roughened walls. However, it has not enough been validated for gas-mixing turbulent flow. We have a lack of detailed knowledge and experimental data on the turbulent gas process in the unit. Hence, as the first step to make the air mixing process in gas unit clear, we have made an preliminary experimental study on turbulent mixing using the equipment with flow control door arranged some velocity ratios and a heating core. Flow visualization was carried out by using particle image velocimetry (PIV). As a result of this study, it was obtained representative velocity distribution data and turbulent kinetic energy distributions about separation and gas mixing section in the equipment, which is important for unit performance. Furthermore, it was found that production of turbulence in the unit were strongly formed by unsteadily long separation flow between velocity ratios and small scale vortices induced to the tip of door.

Numerical Simulation of 3D Density Flow by an Improved EASM Model

Reynolds stress turbulence models are still an effective method to solve thermal density flow in reservoir. Presently, these turbulence models have extensive research and play an important role in the project. However, the pursuit of a more general, economic and accurate Reynolds stress model is still necessary for buoyant turbulent flow. In this paper, an improved explicit algebraic Reynolds stress model was established accounting for buoyancy. The tensor representation of the Reynolds stresses are divided into two parts, the former is composed of EASM derived by Wallin & Johansson (2000) and latter is the formulations of buoyant stress. In the derivation of explicit algebraic active scalar flux model, WWJ (Wikström, Wallin and Johansson, 2000) model only for explicit tensor representation of passive scalar flux is improved by affiliating external buoyancy effects terms. The current EASM is discretized on three-dimensional unstructured grids and compared with experimental data of 3D thermal density flow. The calculations show that the model yields better results than LAHM and LARM. In addition, EASM model also has good stability and relative economic calculation CPU time-consuming. The current model would be promising in hydraulic engineering and environmental engineering.

CFD analysis of inlet chamber body profile effects on de-oiling hydrocyclone efficiency

In this study the effect of inlet chamber design on de-oiling hydrocyclone efficiency has been investigated numerically with the aim of minimizing the energy loss. To this aim, effects of four different inlet chamber designs (exponential, conical, quadratic polynomial body profile and standard design) on efficiency have been considered. Algebraic slip mixture model and Reynolds Stress Model (RSM) have been employed for prediction of multiphase flow behavior and simulation of turbulent flow through the cyclone respectively. The simulation results for efficiency of standard design demonstrate a proper agreement with reported experimental data. The results show that the separation efficiency can be improved approximately 8% using exponential body shape. The recirculation eddies that exists in the upper section prevents inward radial flow, consequently the efficiency reduces; the simulations illustrate that inlet chamber shape affects on the size of these eddies. More recirculation in hydrocyclone inlet chamber with quadratic polynomial body profile causes minimum separation efficiency.

Numerical analysis of turbulent flow in a rotating U-bend with roughened walls

A numerical analysis has been performed for a developing turbulent flow in a rotating U-bend of strong curvature with rib-roughened walls using an anisotropic turbulent model. In this calculation, an algebraic Reynolds stress model is used to precisely predict Reynolds stresses, and a boundary-fitted coordinate system is introduced as a method of coordinate transformation to set the exact boundary conditions along the complicated shape of U-bend with rib-roughened walls. Calculated results for mean velocity and Reynolds stresses are compared to the experimental data in order to validate the proposed numerical method and the algebraic Reynolds stress model. Although agreement is certainly not perfect in all details, the present method can predict characteristic velocity profiles and reproduce the separated flow generated near the outer wall, which is located just downstream of the curved duct. The Reynolds stresses predicted by the proposed turbulent model agree well with the experimental data, except in regions of flow separation.

Unsteady RANS simulations of flow around a bridge section

This paper presents the results of unsteady Reynolds-averaged Navier–Stokes (URANS) simulations of flow around a common bridge deck geometry. Computations are performed with a noncommercial unstructured flow solver using two-dimensional hybrid meshes with fine near-wall resolution. The influence of different simulation parameters (grid refinement, time-step size, turbulence modelling) is analyzed, in particular in order to obtain flow solutions independent of spatial and temporal discretization. Results given by a one-equation eddy-viscosity turbulence model and a two-equation explicit algebraic Reynolds stress model are compared. Despite the limits imposed by the URANS approach and the relatively inexpensive two-dimensional computations, satisfactory agreement is found with the experimentally measured forces and pressures. These simulations help to explain the discrepancy between the results of two wind-tunnel test campaigns and show the dramatic influence of non-perfectly sharp edges on the global flow field development. The capability of the numerical approach to capture complex Reynolds number effects is also discussed.

A propos d'un modèle de relaxation pour des écoulements turbulents hors équilibre

In this work, we started with the development of an algebraic Reynolds stress model designed for a turbulent mixing layer. By comparison with the second-order models of L.R.R. and S.S.G., this model makes clear improvements as for the prediction of a mixing layer developing towards an asymptotic state. Thereafter, and in order to improve the performance of the algebraic model for turbulent flows that are far from equilibrium, we proposed a relaxation model similar to that proposed by Speziale and Xu. Using the relaxation model, we simulated numerically the time evolution of a rapid axisymmetric contraction. The obtained results bring a manifest confirmation of the validity of the model for non-equilibrium turbulent flows.

Variable Turbulent Schmidt and Prandtl Number Modeling

:This paper describes variable turbulent Schmidt and Prandtl number formulations, based on Rodi’s (1980) algebraic Reynolds stress model adapted to velocity-scalar correlations. Since the approach is algebraic in nature, it does not introduce transport equations beyond the ones already existing to compute the flow, rendering it a viable engineering tool. The method is scrutinized against several test cases, including a 3D Scramjet combustor problem. Results are encouraging and lend confidence in the proposed approach.

Explicit algebraic subgrid stress models with application to rotating channel flow

New explicit subgrid stress models are proposed involving the strain rate and rotation rate tensor, which can account for rotation in a natural way. The new models are based on the same methodology that leads to the explicit algebraic Reynolds stress model formulation for Reynolds-averaged Navier–Stokes simulations. One dynamic model and one non-dynamic model are proposed. The non-dynamic model represents a computationally efficient subgrid scale (SGS) stress model, whereas the dynamic model is the most accurate. The models are validated through large eddy simulations (LESs) of spanwise and streamwise rotating channel flow and are compared with the standard and dynamic Smagorinsky models. The proposed explicit dependence on the system rotation improves the description of the mean velocity profiles and the turbulent kinetic energy at high rotation rates. Comparison with the dynamic Smagorinsky model shows that not using the eddy-viscosity assumption improves the description of both the Reynolds stress anisotropy and the SGS stress anisotropy. LESs of rotating channel flow at Reτ = 950 have been carried out as well. These reveal some significant Reynolds number influences on the turbulence statistics. LESs of non-rotating turbulent channel flow at Reτ = 950 show that the new explicit model especially at coarse resolutions significantly better predicts the mean velocity, wall shear and Reynolds stresses than the dynamic Smagorinsky model, which is probably the result of a better prediction of the anisotropy of the subgrid dissipation.