Algebraic Reynolds Stress Model Research Articles

Effect of Jet Vortex Generators on Shock Wave Induced Separation on Gas Turbine Profile

The interaction between a shock wave and a boundary layer on a suction side of gas turbine profile, namely Transition Location Effect on Shock Wave Boundary Layer Interaction, was one of main objectives of TFAST project. A generic test section in a transonic wind tunnel was designed to carry out such investigations. The design criteria were to reproduce flow conditions on the profile in wind tunnel as the one existing on the suction side of the turbine guide vane. In this paper, the effect of film cooling and jet vortex generators on the shock wave boundary layer interaction and shock induced separation is presented. Numerical results for Explicit Algebraic Reynolds Stress Model with transition modeling are compared with experimental data.

Data assimilation of flow-acoustic resonance.

A data assimilation (DA) strategy was developed for accurate prediction of the flow-acoustic resonant fields within a channel-branch system. The challenges of numerical simulation of such internal aeroacoustic systems are primarily associated with determination of the transfer loss between the acoustic waves and the shear layer vortices. Thus, a data-assimilated momentum loss model that comprises a viscous loss item and an inertial loss item was established and embedded into the Navier-Stokes equations. During the DA, the acoustic pressure pulsations measured from a dynamic pressure array served as the observational data, the ensemble Kalman filter served as the optimization algorithm, and a three-dimensional transient computational fluid dynamics method comprising an explicit algebraic Reynolds stress model (EARSM) served as the predictive model system. EARSM was used because its ability to predict internal flow-acoustic resonances was superior to that of other eddy viscosity models and Reynolds stress models. The data-assimilated flow-acoustic resonant fields were then comprehensively validated in terms of their acoustic fields, time-averaged flow fields, and phase-dependent flow fields. The time-averaged flow fields were obtained from planar particle-image velocimetry (PIV) measurements, and the phase-dependent flow fields were obtained from field programmable gate array-based phase-locking PIV measurements. The results demonstrate that the use of DA afforded an optimal simulation that efficiently decreased the numerical errors in the frequencies and amplitudes of the acoustic pressure pulsations, thereby achieving better agreement between time-averaged flow distributions and fluctuations. In addition, the data-assimilated numerical simulation completely reproduced the spatiotemporal evolution of the shear layer vortices, that is, their formation, developing, transport, and collapsing regions.

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.

Continuous and discontinuous gravity currents in open-channel embayments.

Embayments, as major storage zones in riverine environments, could be surrounded by gravity currents associated with industrial pollution, heavy impurities, and sewage. The accumulated contaminated matter in embayments significantly impairs aquatic habitats and influences the embayment performance. In this study, the three-dimensional vortical structures of continuous and discontinuous gravity currents in channels connected to an embayment are investigated by solving unsteady Reynolds-averaged Navier-Stokes with algebraic Reynolds stress model (ASM) which has been improved by the buoyancy effects. The lateral embayment with different configurations is simulated to investigate the exchange processes of the dense fluid between the lateral embayment and main stream. The accuracy and consistency of the developed model are checked using the experimental data of continuous and discontinuous gravity currents in the straight channel and mass exchange in the lateral embayment. The findings have revealed that the agreement between measured and simulated flow and concentration fields is reasonable. The current head propagation of the continuous gravity current inside the embayment is similar to the discontinuous gravity current head propagation. At early time, the continuous gravity current leads to rapid diffusion of the concentration in the embayment and main channel downstream. In the discontinuous gravity current with the embayment aspect ratio equal to 1.0, the dense fluid firstly fills the lateral embayment as the most volume of the dense fluid is trapped and then it flushes out into the main channel. The geometric aspect ratio of the lateral cavity slightly affects the exchange coefficient between the main channel and lateral cavity. The time-averaged exchange coefficient is 0.33 in the continuous gravity current.

Numerical simulation study of offshore heavy oil desanding by hydrocyclones

Sand production often occurs in offshore heavy oil production. Sand particles enter offshore platform processing systems with heavy oil, easily causing pipeline sand deposition, valve and separator erosion and blockage, and pump and other equipment wear and damage, resulting in various oilfield production safety risks. Due to the high viscosity of heavy oil, it exerts a strong viscous drag on sand particles. They easily adhere to heavy oil and move with its flow, which also leads to the extremely difficult separation of heavy oil and sand. Due to the desanding difficulty of highly viscous oil, this work proposes a desanding scheme combining water blending for viscosity reduction with hydrocyclone separation and focuses on hydrocyclone separation in the heavy oil desanding process. Based on algebraic slip mixture, Reynolds stress and discrete-phase models, the hydrocyclone desanding characteristics of heavy oil with the water cut were studied by computational fluid dynamics (CFD) numerical simulations. Flow field, sand removal rate (SSR) and pressure drop differences under different oil viscosities, oil contents and hydrocyclone geometries were studied via single-factor sensitivity analysis, and the essence of these differences was comprehensively analysed. Through high-precision response surface prediction model establishment, the influence of the interaction between hydrocyclone structures on the pressure drop was analysed, and the influence of the pairwise interaction between the main hydrocyclone structures on the hydrocyclone pressure drop is mutual inhibition. The hydrocyclone structure is optimized with pressure drop minimization as the objective, and the pressure drop of the optimized hydrocyclone is 23.3% lower than that at the lowest pressure in response surface experiments, indicating that the optimization effect of the response surface method (RSM) is extremely significant. Moreover, the research methods and conclusions in this work provide a basis for subsequent experimental prototype development and experimental verification steps.

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.

Higher-order realizable algebraic Reynolds stress modeling based on the square root tensor

In this study, realizable algebraic Reynolds stress modeling based on the square root tensor [Phys. Rev. E \textbf{92}, 053010 (2015)] is further developed for extending its applicability to more complex flows. In conventional methods, it was difficult to construct an algebraic Reynolds stress model satisfying the realizability conditions when the model involves higher-order nonlinear terms on the mean velocity gradient. Such higher-order nonlinear terms are required to predict turbulent flows with three-dimensional mean velocity. The present modeling based on the square root tensor enables us to make the model always satisfy the realizability conditions, even when it involves higher-order nonlinearity. To construct a realizable algebraic Reynolds stress model applicable to turbulent flows with three-dimensional mean velocity, a quartic-nonlinear eddy-viscosity model is proposed. The performance of the model is numerically verified in a turbulent channel flow, a homogeneous turbulent shear flow, and an axially rotating turbulent pipe flow. The present model gives a good result in each turbulent flow. Note that the mean swirl flow in an axially rotating turbulent pipe flow is reproduced because the present model involves cubic nonlinearity. Such a higher-order realizable algebraic Reynolds stress model, involving quartic nonlinearity on the mean velocity, is expected to be useful in numerically stable predictions of turbulent flows with three-dimensional mean velocity.

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.

Investigation of a stable boundary layer using an explicit algebraic model of turbulence

Using the recently developed explicit anisotropic algebraic Reynolds-stress model, calculations were performed to study the stable boundary layer dynamics according to the well-known test case of the GABLS1 (Global Energy and Water Cycle Experiment Atmospheric Boundary Layer Study) project, where the Richardson number Ri > 1. The model includes the effect of gravity waves, which allows taking into account the momentum maintenance under strong stability conditions. The model shows good agreement with the results of LES simulation. The study aims at obtaining a much more realistic boundary layer, shallower in depth than in traditional first-order models. The case of a constant surface cooling rate is considered. Some interesting features of the model are related to its deduction based on physical principles. In particular, the use of a larger number of prognostic equations in the model makes it possible to obtain more realistic dynamic behavior.

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.