Differential Reynolds Stress Model Research Articles

Sensitized Reynolds stress modeling of a bubbly jet emerging into a water cross-flow

The present work is concerned with the computational study of an air–water mixture stream emanating from a nozzle submerged in a water cross-flow inside a rectangular open channel to form a curved, intensively dispersed, bubbly jet. The work focuses on evaluating the predictive performance of an eddy-resolving turbulence model applied to the described case of a multiphase gas-liquid flow system characterized by a variety of closely coupled phenomena, including: turbulence anisotropy-induced secondary motion, free surface flow, bubbly jet propagation, and the varying interaction dynamics of the carrier water flow with the air bubble dispersion. Correspondingly, an appropriately extended differential near-wall Reynolds stress model, which describes the dynamics of unresolved subscale structures within the Sensitized Reynolds-Averaged Navier–Stokes (RANS) computational framework, is currently used in conjunction with a two-way coupled Euler–Lagrange approach to simulate this gas-water bubbly flow, with the operating and boundary conditions following the experimental reference of Zhang and Zhu (2013). Accordingly, the conditions at the free surface are adequately derived for all components of the residual turbulence stress tensor and the corresponding length scale determining variable. It is shown that the statistics of the bubble phase can be accurately captured, and the proper-orthogonal-decomposition analysis of the dynamic properties of the flow reveals at least two large-scale transient effects associated with the bubbly jet. Furthermore, in the preliminary part of this work it is shown that the currently applied turbulence model can be successfully used to correctly capture the effects of Reynolds stress anisotropy in the single-phase open-channel configuration, representing the incoming flow field of the main two-phase flow configuration.

Separation and reattachment fixed Reynolds-stress model for iced airfoil and wing simulations

Differential Reynolds-stress models (RSMs) are the higher level of Reynolds-averaged Navier-Stokes (RANS) modeling and generally considered to have more potential than eddy viscosity models (EVMs) when applied to separated flows. Nevertheless, some peculiarities have been observed in simulating flows over iced wings. The first is the numerical stability problem caused by non-streamlined wall surfaces. To weaken this, a wall-boundary-natural scale λ=ω−1/8 is introduced into SSG/LRR RSM in this paper. The second is to remedy the problem of the unsatisfactory non-equilibrium characteristic in separating shear layer (SSL), a correction determined by anisotropy of Reynolds normal stresses is developed. The last focuses on the unphysical backbending of the streamlines near stagnation/reattachment (SR) points. Since the SSL correction will worsen this defect, a SR correction is carried out to blended with it. Four two-dimensional iced airfoils and a three-dimensional iced wing are simulated and then the above measures are confirmed to be the positive.

Large Eddy Simulation of a Low-Pressure Turbine Cascade with Turbulent End Wall Boundary Layers

We present results of implicit large eddy simulation (LES) and different Reynolds-averaged Navier–Stokes (RANS) models of the MTU 161 low pressure turbine at an exit Reynolds number of 90000\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$90\\,000$$\\end{document} and exit Mach number of 0.6. The LES results are based on a high-order discontinuous Galerkin method and the RANS is computed using a classical finite-volume approach. The paper discusses the steps taken to create realistic inflow boundary conditions in terms of end wall boundary layer thickness and freestream turbulence intensity. This is achieved by tailoring the input distribution of total pressure and temperature, Reynolds stresses and turbulence length scale to a Fourier series based synthetic turbulence generator. With this procedure, excellent agreement with the experiment can be achieved in terms of blade loading at midspan and wake total pressure losses at midspan and over the channel height. Based on the validated setup, we focus on the discussion of secondary flow structures emerging due to the interaction of the incoming boundary layer and the turbine blade and compare the LES to two commonly used RANS models. Since we are able to create consistent setups for both LES and RANS, all discrepancies can be directly attributed to physical modelling problems. We show that both a linear eddy viscosity model and a differential Reynolds stress model coupled with a state-of-the-art correlation-based transition model fail, in this case, to predict the separation induced transition process around midspan. Moreover, their prediction of secondary flow losses leaves room for improvement as shown by a detailed discussion of turbulence kinetic energy and anisotropy fields.

Calibration of a Near-Wall Differential Reynolds Stress Model Using the Updated Direct Numerical Simulation Data and Its Assessment

In the article, a differential Reynolds stress model is recalibrated using turbulent channel flow direct numerical simulation data in the range of friction Reynolds numbers 550–5200. The calibration aims to produce a RANS sublayer model for use within the hybrid RANS/LES framework. The model is designed to capture the average field of a thin near-wall part of a boundary layer as accurately as possible. An a posteriori procedure is employed in which one-dimensional channel flow calculations are performed for all variations of the model coefficients at each stage of the optimization procedure. The coefficients are initialized with their original values and then optimized by minimizing the appropriately chosen norm. An improved representation of the mean velocity profile and peak Reynolds stress values is demonstrated. Both models—baseline and recalibrated—are implemented in an in-house CFD code, and several simulations, including a channel flow, a flat plate boundary layer and a boundary layer separation from a rounded step, are performed. The latter benchmark flow is also simulated in hybrid RANS/LES mode. The updated model is compared to the original one, demonstrating improvements over the baseline model in the cases it was designed for.

Realizability-preserving time-stepping for the differential Reynolds stress turbulence models

In the context of incompressible turbulence modelling, differential Reynolds stress models allow a better representation of turbulence anisotropy than classical linear eddy viscosity models and are less expensive than large eddy simulations in terms of computational cost. They rely on a modelled transport equation for the Reynolds stress tensor, which is by definition a covariance tensor and must remain symmetric positive semi-definite. However, the solution of the modelled and discretized transport equation may not preserve these mathematical properties. In the present article, a methodology to time-split Reynolds stress R__ terms in the transport equation is proposed using a decomposition theorem which proves the realizability of R__ provided realizable initial conditions. Realizability-preserving time-steppings are designed for several differential Reynolds stress models. The numerical schemes are presented in a finite volume context but may be used with others space discretization schemes. The realizability, precision and robustness of the numerical scheme is verified through the anisotropy time evolution in homogeneous shear-flow simulations with various initial conditions.

Secondary flow and thermal field dynamics in a T-junction with an upstream elbow: A POD-aided, eddy-sensitized Reynolds-stress modeling study

The thermal mixing of the flow-crossing streams in a T-shaped pipe junction configuration with the main branch inflow forming an elbow is presently simulated by applying a RANS-based eddy-resolving model of turbulence. The low-temperature main stream enters the T-junction with a Reynolds number of Rem=107893 after passing through a 90o-turned elbow located upstream. The high temperature branch stream is injected perpendicularly into the main stream at a Reynolds number of Rem=5422. A significant difference between the flow velocities of the two streams leads to the formation of a characteristic mixing process resembling a reattached jet configuration. Of particular interest is the interference of the branch flow with the main flow characterized by secondary vortices – the so – called Dean vortices, that are convected from the curved main inlet generating a low-rank mixing structures in its wake. The reference LES-based (Large-Eddy Simulation) database is provided by Tunstall et al. (2016). The computational framework relying on the scale-adaptive turbulence modeling approach, introduced principally by Menter and Egorov (2010), is used to simulate the dynamics of large-scale turbulent structures with moderate spatial and temporal resolution requirements. The motion of unresolved subscale structures is described by an appropriately sensitized differential near-wall Reynolds stress model according to Jakirlić and Maduta (2015). In addition, Proper-Orthogonal Decomposition (POD) is used to analyze the prevailing flow and thermal field mechanisms. The results obtained show a reasonable level of agreement with the LES reference, both from the standpoint of first-order statistics and spectral reproduction of the dynamics of coherent structures.

Large-Amplitude Gusts on the NASA Common Research Model

To date, there is limited knowledge on the topic of unsteady nonlinear transonic flow caused by large-amplitude excitations. The Certification Specifications for Large Aeroplanes, however, demand loads computations for large-amplitude excitations, e.g., for gust encounters of an aircraft. In this paper, numerical solutions to the unsteady Reynolds-averaged Navier–Stokes equations will be used to analyze gust responses of a transport aircraft configuration for a variety of sinusoidal gusts with different lengths and amplitudes at different Mach numbers. On the one hand, it is shown that unsteady nonlinear responses can lead to lower maximum lift values compared to their time-linearized reference due to unsteady shock-induced flow separation. This nonlinear effect dominates for large gust lengths and higher Mach numbers. On the other hand, for the lowest Mach number considered, the coalescence of a double shock at medium gust lengths introduces nonlinear effects leading to an overprediction of the time-linearized maximum lift by the nonlinear computations. Though the turbulence model of Spalart and Allmaras shows completely different separation patterns than a differential Reynolds stress model, the variation of the turbulence model does not alter the overall qualitative findings, but has an effect on the quantitative values.

A dynamic version of the improved delayed detached-eddy simulation based on the differential Reynolds-stress model

A dynamic version of the improved delayed detached-eddy simulation (IDDES) based on the differential Reynolds-stress model (RSM), referred to as the RSM-DynIDDES, is developed by applying the dynamic Smagorinsky subgrid model to the large eddy simulation (LES) branch of the IDDES. The RSM-DynIDDES simulates the periodic hills flow after a basic numerical validation for the decaying isotropic turbulence simulation. Well-predicted velocity profiles and R eynolds stress distributions are obtained by the RSM-DynIDDES in the periodic hills flow. The simulation results indicate that the RSM-DynIDDES can capture more small-scale vortex structures in the LES region away from the wall than the original RSM-based IDDES (RSM-IDDES). The RSM-DynIDDES is also employed in simulating the transonic buffeting of a launch vehicle with a payload fairing. The numerical results have been compared with that of the RSM-IDDES. It is found that the RSM-DynIDDES can improve turbulence resolution in the off-wall region while retaining the advantages of the original RSM-IDDES in simulating the instability process of the free shear layer.

Assessment of the Flow Field and Heat Transfer in a Vane Cooling System Using Magnetic Resonance Velocimetry, Thermochromic Liquid Crystals, and Computational Fluid Dynamics

AbstractComputational fluid dynamics (CFD) is the standard tool in the turbomachinery industry to analyze and optimize internal cooling systems of turbine components, but the code applied has to be validated. This paper presents a combined experimental and numerical study on the flow field and heat transfer in a cooling system consisting of a three-pass serpentine with rib turbulators and trailing edge ejection. The cooling geometry is taken from a stator vane currently used in an industrial gas turbine and operates at a coolant inlet Reynolds number of 45,000. As an experimental technique, magnetic resonance velocimetry (MRV) was used to obtain the three-dimensional time-averaged velocity field of the isothermal flow. The measurements were conducted in a large-scale model and resulted in 3.2 million velocity vectors and measurement uncertainty of 6.1% of the bulk inlet velocity. The local wall heat transfer was measured in a separate experiment using thermochromic liquid crystals (TLC). These measurements yielded the distribution of the heat transfer coefficient on both the pressure and the suction side internal walls with a measurement uncertainty of 12%. The experimental data are used as a reference for the numerical study. In total, eight turbulence models are evaluated here, including one-equation, two-equation, algebraic and differential Reynolds stress models, and a scale adaptive simulation. The results show the differences between the velocity fields and the heat transfer coefficient distribution, allowing for the identification of the optimum turbulence model for this particular type of flow.

IDDES method based on differential Reynolds-stress model and its application in bluff body turbulent flows

A general construction approach for a class of detached-eddy simulation (DES) methods with the turbulent length-scale equation is presented in this study. It supports the rationality of the construction and provides a theoretical estimation of the model coefficients in DES simulation. By using the construction approach, a differential Reynolds-stress model (RSM), referred to as Speziale-Sarkar-Gatski (SSG)/Launder–Reece–Rodi (LRR)-ω RSM, is built into the improved delayed DES (IDDES) method. After calibration of the model parameters in the IDDES method and basic validation for decaying isotropic turbulence, the RSM-based IDDES approach is then applied to simulate the massively separated flows around the tandem cylinders and the transonic buffet flow over a hammerhead launch vehicle. The simulations are validated by the available experimental data, and the performance is evaluated by means of instantaneous, statistical, spectral analysis of the numerical data. It is found that the RSM-based IDDES method shows better performance comparing with the k-ω shear-stress transport (SST)-based IDDES method, especially for predicting the development of massively separated flows behind the bluff body.

Validation of transition modeling techniques for a simplified fuselage configuration

A Reynolds-averaged Navier-Stokes solver has been equipped with two different transition prediction and modeling techniques for automatic transition prediction on general three-dimensional geometrical configurations. The first technique is a streamline-based approach that applies an automated local linear stability code, the eN-method and a simplified two-N-factor strategy and is applicable with any kind of turbulence model. The second technique is a transition transport equation approach and uses the γ-Reθ,t model. The standard γ-Reθ,t model has been extended by a modeling approach that captures transition due to crossflow instabilities. The extended model can be applied to three-dimensional configuration exhibiting crossflow transition whereas the original γ-Reθ,t model only captures streamwise transition mechanisms. The paper focuses on a three-dimensional inclined 6:1 prolate spheroid which can be considered as a simplified fuselage configuration. For a number of years this configuration has become a standard basic three-dimensional test case for transition prediction approaches and has been used in a number of international workshops and research activities. The focus of the paper is the validation of the two transition modeling approaches for six different angles of attack using two different turbulence models, a standard two-equation eddy-viscosity model and a differential Reynolds-stress model. The simulation results from the two approaches have been compared against each other and to the available experimental data. The comparisons highlight as many qualitative and quantitative similarities and agreements as they reveal quantitative differences and deviations of specific details.

Numerical Simulation of the Streamwise Transport of a Delta Wing Leading-Edge Vortex

Longitudinal vortices are a common flow phenomenon in the flow around aircraft. They emerge wherever sharp edges are encountered and affect the stability of the boundary layers with which they interact. Hence, for an optimal aircraft design, it is necessary to accurately predict not only the formation of these vortices, but also their downstream evolution. This paper presents a numerical simulation approach for the formation and downstream transport of longitudinal vortices. The approach consists in a hybrid Reynolds-averaged Navier–Stokes/large eddy simulation (RANS/LES) method with synthetic turbulence forcing for which different RANS/LES interface locations are investigated. To provide a quantitative analysis, an isolated sharp-edged delta wing configuration is adopted that allows to get rid of unwanted uncertainties. The presented RANS/LES approach is validated against particle image velocimetry data and compared with a wall-modeled LES and to a differential Reynolds stress model simulation. The results show that the RANS simulation is able to accurately predict the formation of the bulk vortical structure. However, its downstream transport can be accurately predicted only by a scale-resolving simulation. The hybrid RANS/LES approach allows to achieve this while saving computational resources by modeling the roll-up of the vortex. Nevertheless, its predictive accuracy highly depends on the appropriate placement of the RANS/LES interface.

Computational and experimental study of 3D flow near the cube immersed in the turbulent free convection boundary layer on a vertical heated plate

Results of a coordinated computational and experimental study of time-averaged velocity and temperature fields in the vicinity of an adiabatic cube that is inserted into the turbulent free convection vertical-plate boundary layer are presented. The numerical simulation was based on the steady-state RANS approach using the k-ω SST turbulence model and a version of the differential Reynolds stress model (DRSM). The hot-wire technique was used for velocity measurements, simultaneously with temperature measurements by an accompanied “cold” wire. Two turbulence models produced similar vortex flow structures near the obstacle; however some important quantitative distinctions were observed. The velocity value profiles predicted for the middle vertical plane showed generally a good accordance with the hot-wire measurements carried out in this plane, especially in the DRSM case.

Explicit algebraic relation for calculating Reynolds normal stresses in flows dominated by bubble-induced turbulence

Two new algebraic turbulence models for flows dominated by bubble-induced turbulence (BIT) are presented. The first model, referred to as the algebraic Reynolds normal stress model, is derived from a differential Reynolds stress model for bubbly flows. The second model utilizes one two-equation turbulence model to achieve algebraic expressions for $k$ and $ϵ$ in the BIT dominated cases. If both models are combined, it results in a purely algebraic, explicit relation for the Reynolds normal stresses.

Prediction of flow and dispersion in cross–ventilated buildings

The present paper presents a detailed computational analysis of flow and dispersion in a generic isolated single–zone buildings. First, a grid generation strategy is discussed, that is inspired by a previous computational analysis and a grid independence study. Different turbulence models are appliedincluding two-equation turbulence models, the differential Reynolds Stress Model, Detached Eddy Simulation and Zonal Large Eddy Simulation. The mean velocity and concentration fields are calculated and compared with the measurements. A satisfactory agreement with the experiments is not observed by any of the modelling approaches, indicating the highly demanding flow and turbulence structure of the problem.

Towards the accurate prediction of the turbulent flow and heat transfer in low-Prandtl fluids

In the numerical simulation of turbulent heat transfer, a reliable representation of the turbulent flow field is a prerequisite in order to obtain an accurate prediction of the thermal field. In the framework of RANS modelling approach, classical two-equation eddy-viscosity models present intrinsic limitations for applications characterised by complex flow fields where significant turbulence anisotropy can be expected. In this respect, differential Reynolds stress models represent the natural choice for dealing with such highly anisotropic flows. On the other hand, the modelling of the turbulent heat flux term almost universally relies on the so-called Reynolds analogy, due to its simplicity and robustness. Nevertheless, this approach presents several well-known limitations, especially when dealing with low-Prandtl fluids. In this context, algebraic heat flux models are regarded as a promising approach to overcome the shortcomings of the Reynolds analogy. In particular, an implicit algebraic heat flux closure, called as AHFM-NRG, has been proposed for applications involving low-Prandtl fluids. In its original formulation, the algebraic turbulent heat flux closure was coupled with a low-Reynolds linear k-ε model for the closure of the Reynolds stress tensor. In the present work, the applicability of the AHFM-NRG model is extended to an advanced low-Reynolds differential Reynolds stress model. This new version of the model is validated against different planar channel flows at unity and low-Prandtl number; successively, the model is applied to two relatively complex flows, i.e. a planar impinging jet and a bare rod bundle configuration. It is shown that the coupling of the AHFM-NRG with an advanced closure for the Reynolds stresses gives encouraging results for these cases, where an accurate prediction of the anisotropy in the flow field results in a noticeable improvement in the prediction of the turbulent heat transfer.

Extension of a Reynolds-Stress-Based Transition Transport Model for Crossflow Transition

Two crossflow transition prediction approaches, the local C1-based approach and the local helicity-based approach, have been implemented into a Reynolds-stress-based transition transport model of the modeling framework. The differential Reynolds stress model is the model that has been coupled with the model. The whole framework of the coupled model, including the crossflow extensions, is presented in detail. A grid sensitivity study for crossflow transition prediction was conducted. In addition, the influence of the numerical scheme on the computational results is discussed. The new Reynolds-stress-based transition model is compared with the model coupled to the SST two-equation eddy-viscosity turbulence model including the two crossflow extensions for the NLF (2)-0415 infinite swept wing, the DLR prolate spheroid and the DLR-F4 wing-body geometry. The comparisons show that the Reynolds-stress-based transition model can yield very accurate results, which, in terms of the predicted transition onset, are sometimes better than those of the in conjunction with the eddy-viscosity model.

Coupling of a Reynolds Stress Model with the Transition Model

A transition transport model has been coupled with the SSG/LRR- differential Reynolds stress model to form a new transition and turbulence model containing nine transport equations. The aim is to handle complex turbulent flow together with wall-bounded transitional flow for industrial applications. Based on the difference between the Menter SST turbulence model and the SSG/LRR- model, special treatments are introduced for the length-scale determining equation of the turbulence model and the transition onset function of the intermittency transport equation of the transition model. The final transitional Reynolds stress model is calibrated based on zero-pressure-gradient flat plate flow. Additionally, a study on grid influences based on flat plate flow has been conducted. As a result, the presented model is able to predict transitional flows, including Tollmien-Schlichting transition, by-pass transition, and separation-induced transition, as well as considering complex turbulent flows. The model is validated for a number of test cases, including two-dimensional airfoils and the DLR prolate spheroid. The results are compared against transitional computations using the Langtry & Menter SST model and fully turbulent computations using the standard SSG/LRR- model. The comparisons show that the nine-equation transition model has equal or higher accuracy as the SST model for different types of flows.

Investigation of aerodynamic structure of isothermal swirl flow in a two-stage burner

The work is devoted to experimental and numerical study of aerodynamic structure of a swirl flow in isothermal model of a vortex burner device that is characterized by the fluid flow supply via two sequentially-mounted tangential swirlers. Depending on the way of the flow supply into the second-stage swirler, either co-swirl or counter-swirl of two flows can be realized. The effect of the second-stage supply direction on the resulting aerodynamic structure has been investigated. Using LDA measurement system the profiles of averaged axial and tangential velocity components were obtained. Experiments have shown that in the co-swirl case the flow inside the vortex burner model is characterized by strong non-uniformity, while in the counter-swirl regime a rapid mixing of the flows from the first and second stages occurs, resulting in a uniform distribution of the flow across the chamber section. Numerical simulation of 3D isothermal turbulent flow has been performed for the counter-swirl regime using the differential Reynolds stress model in the time-dependent formulation. Using the Q-criterion for the identification of vortices in numerical data arrays, the evolution of large-scale vortex structures of the swirl flow inside the vortex chamber has been visualized, indicating the presence of two spiral-shape vortex filaments in the vortex chamber. The periodic character of dynamics of these vortex structures has been revealed.

Combining the SSG/LRR-ω differential reynolds stress model with the detached eddy and laminar-turbulent transition models

The procedure of incorporating the detached eddy method and a model of laminar-turbulent transition into the SSG/LRR-ω turbulence model is presented. The approach proposed can be regarded as the generalization of the existing models intended to perform calculations with the SST turbulence model to the case of their use with the SSG/LRR-ω model. The advantage of the approach developed over the RANS turbulence models based on the Boussinesq hypothesis is demonstrated with respect to the problems of flow past an airfoil and cold jet outflow.