Explicit Algebraic Reynolds Stress Model Research Articles

Explicit Algebraic Reynolds-Stress Modeling of Pressure-Induced Separating Flows in the Presence of Sidewalls

AbstractReynolds-averaged Navier–Stokes (RANS) approach is used to simulate the steady-state of a family of pressure-induced turbulent separation bubbles in the presence of sidewalls. Different turbulence models are employed with a specific emphasis on the baseline explicit algebraic Reynolds stress model (BSL-EARSM) and the simulations are compared with experimental data. The separation and reattachment of a flat-plate turbulent boundary layer are generated through a combination of adverse and favorable pressure gradients (APG-FPG) by numerically reproducing the geometry of the wind-tunnel test section used for the experiments. Three cases are considered a large (LB) and a medium (MB) bubble presenting mean backflow, and a small bubble (SB) without mean-flow reversal. This is achieved by varying the streamwise position of the APG/FPG transition. Good agreement between the BSL-EARSM-computed solutions and the experimental results are obtained for wall-pressure and skin-friction distributions on the centerline plane of the test section as well as for the overall three-dimensional flow topology. However, both detachment and reattachment are predicted too early and the bubble length is slightly overestimated for cases LB and MB. For case LB, the streamwise Reynolds stress is estimated fairly well but its production is somewhat delayed. Normal and shear stresses are in good agreement with the experiments in the upstream part of the bubble but are significantly over-estimated in the reattachment region. The k−ω shear-stress transport (SST) model with the so-called reattachment modification performs better than the other tested linear-eddy-viscosity models but it is still unable to reproduce accurately the three-dimensional flow topology even for the “simplest” case SB. Overall, the results suggest that BSL-EARSM is the most suitable turbulence model for this flow configuration.

URANSE-Based Numerical Prediction for the Free Roll Decay of the DTMB Ship Model

In the present study, Computational Fluid Dynamics (CFD) is used to investigate the roll decay of the benchmark surface combatant DTMB-5512 ship model appended with bilge keels, sailing in calm water at different speeds (Fr = 0.0, 0.138, 0.2, 0.28 and 0.41) and with different initial roll angles. The numerical simulations are carried out using the viscous flow solver ISIS-CFD of the FINETM/Marine software provided by NUMECA. The solver uses the finite volume method to build the spatial discretization of the transport equation to solve the unsteady Reynolds-Averaged Navier–Stokes equations. Two-phase flow approach is applied to model the air–water interface, where the free surface is captured using the volume of fluid method. The closure to turbulence is achieved by making use of the blended Menter shear stress transport and the explicit algebraic Reynolds stress models. First, a systematic validation against the experimental data at medium speed and initial roll angle of 10° are performed; then, the effect of the initial roll angle and ship speed is later studied. Numerical errors and uncertainties are assessed using grid and time step convergence study based on Richardson Extrapolation method. A special focus on the flow in the vicinity of the bilge keels during the simulation is also investigated and presented in the form of velocity contours and vortical structure formations. The resemblance between the CFD results and experimental data for roll motion and flow characteristics are within a satisfactory congruence; however, some discrepancies are recorded for the over predicted roll amplitudes in the second and, sometimes, the third roll cycle, which appeared mostly in the cases with high initial roll angles.

Numerical simulation of separation induced laminar to turbulent transition over an airfoil

The article deals with the numerical simulation of flows with laminar to turbulent transition due to the separation of boundary layer. Mathematical model consists of the Reynolds averaged Navier–Stokes equations which are completed by the explicit algebraic Reynolds stress model (EARSM) of turbulence. The EARSM model is enhanced with algebraic model of bypass transition which is further modified by the additional source term for prediction of laminar boundary layer separation induced transition. Numerical solution is obtained by the finite volume method based on the second order HLLC scheme and explicit Runge–Kutta method. The proposed method is then tested on several cases of low-Reynolds subsonic transitional flows including flows over the SD 7003 airfoil with various angles of attack and flow past the NACA 0012 airfoil.

On the use of optimization techniques for turbulence model calibration

This article discusses the use of numerical optimization procedures to aid in the calibration of turbulence model coefficients. Such methods would increase the rigor and repeatability of the calibration procedure by requiring clearly defined and objective optimization metrics, and could be used to identify unique combinations of coefficient values for specific flow problems. The approach is applied to the re-calibration of an explicit algebraic Reynolds stress model for the incompressible planar mixing layer using the Nelder–Mead simplex algorithm and a micro-genetic algorithm with minimally imposed constraints. Three composite fitness functions, each based upon the error in the mixing layer growth rate and the normal and shear components of the Reynolds stresses, are investigated. The results demonstrate a significant improvement in the target objectives through the adjustment of three pressure-strain coefficients. Adjustments of additional coefficients provide little further benefit. Issues regarding the effectiveness of the fitness functions and the efficiency of the optimization algorithms are also discussed.

Simulation of the GOx/GCH4 Multi-Element Combustor Including the Effects of Radiation and Algebraic Variable Turbulent Prandtl Approaches

Multi-element thrusters operating with gaseous oxygen (GOX) and methane (GCH4) have been numerically studied and the results were compared to test data from the Technical University of Munich (TUM). A 3D Reynolds Averaged Navier–Stokes Equations (RANS) approach using a 60° sector as a simulation domain was used for the studies. The primary goals were to examine the effect of the turbulent Prandtl number approximations including local algebraic approaches and to study the influence of radiative heat transfer (RHT). Additionally, the dependence of the results on turbulence modeling was studied. Finally, an adiabatic flamelet approach was compared to an Eddy-Dissipation approach by applying an enhanced global reaction scheme. The normalized and absolute pressures, the integral and segment averaged heat flux were taken as an experimental reference. The results of the different modeling approaches were discussed, and the best performing models were chosen. It was found that compared to other discussed approaches, the BaseLine Explicit Algebraic Reynolds Stress Model (BSL EARSM) provided more physical behavior in terms of mixing, and the adiabatic flamelet was more relevant for combustion. The effect of thermal radiation on the wall heat flux (WHF) was high and was strongly affected by spectral models and wall thermal emissivity. The obtained results showed good agreement with the experimental data, having a small underestimation for pressures of around 2.9% and a good representation of the integral wall heat flux.

Numerical assessment of a very high pressure ratio centrifugal impeller

The paper focuses on studying the influence of mesh size, numerical discretization schemes and different turbulence models on radial impeller performances. The chosen impeller is a 14:1 pressure ratio novel design for use in the TIDE pulse detonation engine architecture. In preparation for the experimental research, numerical studies were performed for five steady-state analysis and one unsteady, single passage with a fully structured solver. A grid sensitivity study was conducted over four grid resolutions, starting from a coarse to dense mesh (0.7 mil, 1.5 mil, 5 mil and 9 mil), in order to determine the influence of mesh points, numerical stability and reduce interpolation errors. Another problem in a CFD study is the selection of a proper turbulence model, thus six RANS models were investigated: k-ε, v2-f, k-ω Shear Stress Transport (both steady and unsteady), Spalart – Allmaras and an Explicit Algebraic Reynolds Stress Model. Results show that global parameters such as pressure ratio and efficiency predictions remain unchanged above 1.5 mil cells/passage, while above 5 mil cells/passage, RANS models become unstable and lead to poor convergence. The most conservative model proved to be the SST with minimalistic values for both pressure ratio and isentropic efficiency.

Explicit algebraic Reynolds stress model for shock-dominated flows

Shock waves drastically alter the nature of Reynolds stresses in a turbulent flow, and conventional turbulence models cannot reproduce this effect. In the present study, we employ explicit algebraic Reynolds stress model (EARSM) to predict the Reynolds stress anisotropy generated by a shockwave. The model by Wallin and Johansson (2000) is used as the baseline model. It is found to over-predict the post-shock Reynolds stresses in canonical shock turbulence interaction. The budget of the transport equation of Reynolds stresses computed using linear interaction analysis shows that the unsteady shock distortion mechanism and the pressure–velocity correlations are important. We propose improvement to the baseline model using linear interaction analysis results and redistribute the turbulent kinetic energy between the principle Reynolds stresses. The new model matches DNS data for the amplification of Reynolds stresses across the shock and their post-shock evolution, for a range of Mach numbers. It is applied to oblique shock/boundary-layer interaction at Mach 5. Significant improvements are observed in predicting surface pressure and skin friction coefficient, with respect to experimental measurements.

Predicting turbulent flows in butterfly valves with the nonlinear eddy viscosity and explicit algebraic Reynolds stress models

The development of turbulence modeling is crucial for the numerical prediction of the flow behavior, especially for separation, stagnation, reattachment, recirculation, and streamline curvature of the flow through complex structures. In this study, the capability of turbulence models was estimated for predicting the flow in a butterfly valve. The explicit algebraic Reynolds stress model (EARSM) and nonlinear eddy viscosity model (NLEVM) were evaluated in terms of the velocity profile, turbulence intensity, and Reynolds stress, and their results were compared with those of the standard k–ε and renormalization group (RNG) models. A numerical validation was conducted with the flow past a backward-facing step as the benchmark test. Comparison with the validation test showed that the NLEVM accurately predicted the reattachment length. For the flow in a butterfly valve, the NLEVM and EARSM indicated a smaller velocity increase than the standard k–ε and RNG models in the recirculation area near the valve region. The NLEVM and EARSM demonstrated an ability to predict anisotropic stresses with a dominant stress value near the valve region.

Modelling of Stably Stratified Atmospheric Boundary Layers with Varying Stratifications

A recently developed explicit algebraic Reynolds-stress (EARS) model is validated for an idealized representation of the night-time high-latitude stably stratified atmospheric boundary layer. The simulations are made with four surface cooling rates that result in weakly to moderately stratified stable boundary layers. The predictions of the EARS model are compared to high-resolution large-eddy simulations (LES) of Sullivan et al. (J Atmos Sci 73(4):1815–1840, 2016). First- and second-order statistics are shown to be well predicted by the EARS model. The EARS model also predicts the horizontal turbulent fluxes and turbulence anisotropy and these compare well with the LES results. The sensitivity to the model coefficients is studied by comparing the EARS model results with LES results. Finally, we propose a new scaling for the production of turbulence kinetic energy and show that the EARS model captures the essential trends of the LES results for different cooling rates.

Turbulent closure analysis in heated separated and reattached flow using eddy-resolving data

In this study, we use Large-Eddy Simulations (LESs) to provide a platform to investigate the separated and reattached turbulent flow over a heated blunt plate at ReH = 21 600. The surface Nusselt number and flow field data show good agreement with the published experiments. The turbulence anisotropy resolved by the LES shows that, through the recirculation region, the anisotropy develops toward an axisymmetric contraction state in the near-wall profile. In the redeveloping region, profiles show progression toward the plane-strain state. Turbulent closures, providing simple models of the unknown turbulent correlations that arise from the Reynolds averaging of the Navier–Stokes equations, are routinely applied to complex flows, often with little known about their suitability. The eddy-resolved flow field is used to describe deficiencies in Reynolds-Averaged Navier–Stokes modeling using an LES informed turbulence transport a priori analysis. The explicit algebraic Reynolds stress model showed improved agreement, capturing the elevated turbulent stresses in the recirculation region. Closures describing the turbulent heat flux are compared, and the Higher-Order Generalized GDH (HOGGDH) closure is discovered to show good agreement with those resolved by the LES, capturing the correct ratio of the streamwise to normal turbulent heat flux across the redeveloping boundary layer. An explicit algebraic scalar flux model is examined and shows good predictions of the turbulent heat flux angle but underpredicts the magnitude across the recirculation region. An optimal coefficient for the HOGGDH is described to reproduce the turbulent heat flux magnitude from the LES, showing a range of optimal values across the flow.

Application of second-moment closure to statistically steady flows of practical interest

This work investigates the application of second-moment Reynolds-Averaged Navier-Stokes equations (RANS) closure to statistically steady flows of practical interest. Towards this end, the numerical and modelling accuracies of a Reynolds-Stress Model (RSM), Explicit Algebraic RSM (EARSM) and linear k−ω closure are quantified for various quantities of three representative ship hydrodynamics problems: the flows around a wing at 10o of angle of attack and Reynolds number Re=4.60×106, and the KVLCC2 tanker at Re=4.60×106 and 2.03×109. The results illustrate i) that all closures enable the reduction of the iterative error to negligible levels, and ii) the clear modelling advantages of using RSM. In comparison to the turbulent viscosity closures, RSM leads to a significant reduction of the modelling error. Yet, such computations require a larger number of iterations to achieve the specified iterative convergence criterion, along with finer grids to diminish discretization errors. This stems from the ability of RSM to better capture complex flow phenomena.

Heat Transfer in a Square Ribbed Channel: Evaluation of Turbulent Heat Transfer Models

This paper presents the results of integral heat transfer measurements taken in a square ribbed cooling channel configuration for evaluating heat transfer and turbulent flow characteristics in convective cooled gas turbine blades and draws a comparison with numerical results. The heated section of the channel is either smooth or equipped with 45 ∘ crossed ribs on two opposite walls. The first part of the paper describes the instrumentation and experimental setup in detail. The second part compares the numerical calculations with the experimentally determined results. The turbulent heat transfer is calculated using two common algebraic models and three implemented explicit algebraic models, each time in combination with an explicit algebraic Reynolds stress model. The numerical calculations show that the use of higher-order models for the turbulent heat flux provides a higher accuracy of the heat transfer prediction for both configurations. The best model is able to predict almost all results within the experimental uncertainties.

Coupling the algebraic model of bypass transition with EARSM model of turbulence

The article deals with numerical solution of the laminar-turbulent transition. A mathematical model consists of the Reynolds-averaged Navier-Stokes equations, which are completed by the explicit algebraic Reynolds stress model (EARSM) of turbulence. The algebraic model of laminar-turbulent transition, which is integrated to the EARSM, is based on the work of Kubacki and Dick (Int. J. Heat Fluid Flow 58, 68–83, 2016) where the turbulent kinetic energy is split in to the small-scale and large-scale parts. The algebraic model is simple and does not require geometry data such as wall-normal distance and all formulas are calculated using local variables. A numerical solution is obtained by the finite volume method based on the HLLC scheme and explicit Runge-Kutta method.

Development and Use of Machine-Learnt Algebraic Reynolds Stress Models for Enhanced Prediction of Wake Mixing in Low-Pressure Turbines

Nonlinear turbulence closures were developed that improve the prediction accuracy of wake mixing in low-pressure turbine (LPT) flows. First, Reynolds-averaged Navier–Stokes (RANS) calculations using five linear turbulence closures were performed for the T106A LPT profile at isentropic exit Reynolds numbers 60,000 and 100,000. None of these RANS models were able to accurately reproduce wake loss profiles, a crucial parameter in LPT design, from direct numerical simulation (DNS) reference data. However, the recently proposed kv2¯ω transition model was found to produce the best agreement with DNS data in terms of blade loading and boundary layer behavior and thus was selected as baseline model for turbulence closure development. Analysis of the DNS data revealed that the linear stress–strain coupling constitutes one of the main model form errors. Hence, a gene-expression programming (GEP) based machine-learning technique was applied to the high-fidelity DNS data to train nonlinear explicit algebraic Reynolds stress models (EARSM), using different training regions. The trained models were first assessed in an a priori sense (without running any RANS calculations) and showed much improved alignment of the trained models in the region of training. Additional RANS calculations were then performed using the trained models. Importantly, to assess their robustness, the trained models were tested both on the cases they were trained for and on testing, i.e., previously not seen, cases with different flow features. The developed models improved prediction of the Reynolds stress, turbulent kinetic energy (TKE) production, wake-loss profiles, and wake maturity, across all cases.

A theoretical, numerical and experimental analysis of S-shape instabilities in reversible pump-turbines: Resultant strategies for improving operational stability

In order to be able to draw conclusions on preventing S-shape instabilities in reversible pump-turbines during normal operation, it is important to fully understand their complex nature. In particular for the design, it is essential to predict occurring instabilities as accurate as possible and to fathom their underlying mechanisms properly. Therefore, the first section of this work incorporates a short CFD study based on the design of a reversible pump-turbine scale model. The numerical investigations are done according to the methodology represented in [7], comprising unsteady flow simulations under steady and transient operating conditions. The hydraulic machine is spatially discretized in model size. The turbulence modeling is based on the Explicit Algebraic Reynolds Stress Model. Related measurements are executed on a test rig at ASTROE (Hydraulic Engineering and Laboratory) in Graz, Austria, providing experimental data of integral quantities at different guide vane openings. Besides the CFD study, this work mainly aims at comprehensively analyzing underlying mechanisms of S-shape instabilities in reversible pump-turbines. An analytical description of flow phenomena is intended to provide a better understanding of mechanisms such instabilities are based on. A synthesis results in potential strategies for improving operational stability at individual operating points.

On the modelling turbulent transition in turbine cascades with flow separation

The work discusses performance, modification and implementation details of three intermittency based transition models. The intermittency is applied in the SST eddy viscosity turbulence model and in an explicit algebraic Reynolds stress model (EARSM). Experimental results of transonic flows through turbine cascades at different Reynolds numbers are used as test cases, where the interaction of shock wave with laminar or turbulent boundary layer can be distinguished and reproduced in simulations. Of the transition models tested, only the criteria based γ−ζ model captures well the influence of Reynolds number on the transition. The criterion for transition on separation bubble has been re-formulated so that the model is local in streamwise direction and applicable also in 3D flows. The model is still non-local in wall-normal direction but this is found acceptable considering its performance and the fact that its evaluation is made fully automatic in the framework of structured multi-block solver.

Consistent Boundary-Condition Treatment for Computation of the Atmospheric Boundary Layer Using the Explicit Algebraic Reynolds-Stress Model

Standard turbulence models for the atmospheric boundary layer (ABL) typically use boundary conditions based on the Monin–Obukhov similarity theory (MOST). This can lead to inconsistency between the boundary condition and the closure model. Here, we propose a new boundary-condition treatment of the stratified ABL, derived for the so-called explicit algebraic Reynolds-stress model. The boundary conditions correspond to the relations for vanishing buoyancy effects that are valid close to the ground. The solution for the stratified surface layer is in agreement with the surface scaling physics and MOST functions. This was validated in a simulation of an idealized diurnal cycle of the ABL based on the second Global Energy and Water cycle Experiment (GEWEX) Atmospheric Boundary Layer Study (GABLS2) case.

Investigation of turbulence model selection on the predicted flow behaviour in an industrial crystalliser — RANS and URANS approaches

An understanding of the flow behaviour in industrial crystallisers is critical to addressing mechanical design considerations such as impeller selection and off-bottom solids suspension. In the current study, Computational Fluid Dynamics (CFD) models were used to predict the flow field in a laboratory-scale alumina precipitator, with the objective of understanding which turbulence model can predict the time-averaged flow field in the vessel using the most efficient computational approach. The study focusses on RANS and URANS approaches using the k-ε, RNG k-ε, SST, SSG Reynolds Stress and explicit algebraic Reynolds Stress models (EARSM), with the predictions compared with high quality Laser Doppler Velocimetry (LDV) data from a laboratory-scale vessel. The best agreement with experimental data is achieved using the k-ε and k-ε EARSM models, with all other models either under or over-predicting the reattachment height of the flow in the annulus between the draft tube and the outer vessel wall. Of the models tested, the k-ε EARSM model is also found to give the best predictions of the RMS velocity fluctuations in the vessel. The use of turbulence production limiters, such as Kato-Launder, in conjunction with the k-ε model is found to result in worse agreement with the experimental data. The SST model significantly over-predicts the reattachment height and it is found that the high eddy viscosity generated in the separating shear layers exiting the draft tube, together with the recirculated turbulence in this geometry, suppresses the correct behaviour of the SST blending functions. The Reattachment Modification to the SST model is found to reduce the reattachment height, but the results still show significant deviation from the experimental data.

Effect of Hot Spot Location on Flow Structure in Nozzle Guide Vane

Interaction of a combustor and turbine in aircraft engines generates still a lot of open questions. Investigation of combustor and turbine separately have been done for a years by research institutes and aircraft engine companies, but there is lack of knowledge about the interaction effect. In the paper, numerical simulations results for combustor simulator and nozzle guide vane (NGV) of the first turbine stage are presented. No combustion is modelled, but the hot flow at the swirler inlet is applied. Geometry and flow conditions are defined according to the turbine stage designed for experimental investigations in FACTOR (Full Aerothermal Combustor-Turbine Interactions Research) project within a framework of European Commission 7th Framework Programme. The main objective of the presented investigations is an analysis of the location of the high temperature zone upstream of the nozzle guide vane and its effect on the wall temperature. Numerical simulations are carried out by means of Fine/Turbo Numeca with two turbulence models: Spalart-Allmaras and Explicit Algebraic Reynolds Stress Model. As a model validation, a comparison of total pressure, total temperature and flow angles downstream of combustor simulator with experimental data from University of Florence is also presented.

The Predictions of Common Turbulence Models in a Mature Vortex

A range of turbulence models is exercised in the problem of a mature two-dimensional isolated vortex with high circulation Reynolds number, mature meaning that the core size has grown to many times its initial value, and the vortex reaches a self-similar state in which all quantities scale with its outside circulation Γ and its age t. The reasoning closely follows the landmark papers of Govindaraju and Saffman (Phys. Fluids 14, 2074–2080, 1971) (GS) and Zeman (Phys. Fluids A 7, 135–143, 1995), and we call this the GSZ flow. The models produce radically different outcomes, and this simple problem clearly places each model into one of two classes, in terms of its predictions in vortices. Some reach a turbulent state, including the circulation overshoot first predicted by GS, whereas others reach a laminar state free of overshoot. We have no evidence of non-unique solutions or bifurcations for a given model. The overshoot consists in the circulation, as a function of radius r, rising from zero on the axis at r = 0 to values that exceed the outside circulation Γ, and then falling back down. This happens within the turbulent region, and it is associated with the creation by turbulence of mean vorticity of sign opposite to the core vorticity. We consider the second (i.e., the laminar) response as the correct one, the circulation overshoot appearing to us unphysical, a thought which was clear in both of the original papers and is supported by experimental and simulation results. The laminar state is given by eddy-viscosity models only when they include a rotation/curvature correction. A Reynolds-stress transport model and an Explicit Algebraic Reynolds-Stress Model return turbulent solutions but with weak turbulence, which we consider a positive result, although Zeman’s Reynolds-stress model prevented any overshoot and led to a laminar mature flow. We believe this flow can become a relevant, well-defined, standard test case for turbulence models.