Full Reynolds Stress Model Research Articles

Linear logistic regression with weight thresholding for flow regime classification of a stratified wake

• Build a DNS database with O(100) realizations for stratified wake. • Develop a machine learning tool to classify the flow regimes in a stratified wake. • The physics governing stratified wake is universal with respect to Re and Fr. • The classifier captures the universal physics and generalize well. A stratified wake has multiple flow regimes, and exhibits different behaviors in these regimes due to the competing physical effects of momentum and buoyancy. This work aims at automated classification of the weakly and the strongly stratified turbulence regimes based on information available in a full Reynolds stress model. First, we generate a direct numerical simulation database with Reynolds numbers from 10000 to 50000 and Froude numbers from 2 to 50. Order (100) independent realizations of temporally evolving wakes are computed to get converged statistics. Second, we train a linear logistic regression classifier with weight thresholding for automated flow regime classification. The classifier is designed to identify the physics critical to classification. Trained against data at one flow condition, the classifier is found to generalize well to other Reynolds and Froude numbers. The results show that the physics governing wake evolution is universal, and that the classifier captures that physics.

Application of a Coupled Reynolds Stress Model to a Swirl-Driven Diffuser Flow

Swirling flow is a dominant feature in a significant number of technical applications. Hydraulic turbines at part-load are strongly affected by the related vortex rope phenomenon. Its dynamic behavior has a negative impact on the operating performance and durability of the machine.CFD can be used to get additional insight in this complex phenomenon but requires a valid simulation model able to capture the relevant flow physics, which is driven by highly anisotropic turbulent structures. The simulation results are therefore strongly affected by the turbulence modeling. A swirl apparatus (AC6-14), for which extensive experimental data is available, is used in this work for the assessment and validation of different turbulence models. The state-of-the-art SST k-ω model, with and without curvature correction, is compared to a coupled full Reynolds stress model. All models are integrated into a pressure-based coupled flow solver.The investigation revealed that both, SST k-ω with curvature correction and the full Reynolds stress model better predict the time-averaged velocity profiles in the diffuser compared to standard SST k-ω. The swirl component is thereby best captured with the Reynolds stress model. All models deliver a reasonable frequency spectrum for the dynamic behavior of the vortex rope. However, flow visualization shows that standard SST k-ω is not capable of predicting the shape and size of the vortex rope accordingly. Both, SST k-ω with curvature correction and the full Reynolds stress model, can be used in the future for more detailed flow investigations, which include also the assessment of flow control measures.

Modeling of Cube Array Roughness: RANS, Large Eddy Simulation, and Direct Numerical Simulation

AbstractFlow over arrays of cubes is an extensively studied model problem for rough wall turbulent boundary layers. While considerable research has been performed in computationally investigating these topologies using direct numerical simulation (DNS) and large eddy simulation (LES), the ability of sublayer-resolved Reynolds-averaged Navier–Stokes (RANS) to predict the bulk flow phenomena of these systems is relatively unexplored, especially at low and high packing densities. Here, RANS simulations are conducted on six different packing densities of cubes in aligned and staggered configurations. The packing densities investigated span from what would classically be defined as isolated, up to those in the d-type roughness regime, filling in the gap in the present literature. Three different sublayer-resolved turbulence closure models were tested for each case: a low Reynolds number k–ϵ model, the Menter k–ω SST model, and a full Reynolds stress model. Comparisons of the velocity fields, secondary flow features, and drag coefficients are made between the RANS results and existing LES and DNS results. There is a significant degree of variability in the performance of the various RANS models across all comparison metrics. However, the Reynolds stress model demonstrated the best accuracy in terms of the mean velocity profile as well as drag partition across the range of packing densities.

Influence of compressibility on the development of streamwise supersonic corner flow

The effect of compressibility on supersonic corner flow is numerically investigated by the Reynolds-averaged Navier–Stokes equations with a full Reynolds stress model. A grid sensitivity analysis is conducted in this paper to ensure the reliability of our conclusions. Then, a parametric study by changing the Mach number in the range of M∞=0.6−3.0 is carried out to investigate the effect of compressibility. The corner angle is also changed in the range of θ=45°−135° for each M∞ to see the effect of the corner angle. As a result, the Mach number was found to have a negligible effect on the propagation of vortex cores in this study. However, it has a positive effect on both the friction coefficient and the total pressure loss. The geometrical transformation for the position of the vortex center proposed in our recent paper has been proved to be valid in over wide range. Moreover, we further find that a unified formula can describe the distribution of the total pressure loss under different Mach numbers and corner angles. In engineering terms, these laws will play an important role in the initial design and evaluation of the project with streamwise corners.

Numerical investigation of flows around an axisymmetric body of revolution by using Reynolds-stress model based hybrid Reynolds-averaged Navier–Stokes/large eddy simulation

Flows around an axisymmetric body of revolution at a zero yaw angle were studied using a hybrid Reynolds-averaged Navier–Stokes (RANS)/large eddy simulation (LES) approach, which employed a full Reynolds stress model (RSM) in the RANS branch with the aim of accounting for the Reynolds stress anisotropy, streamline curvature, and flow separations in the boundary layer. The SUBOFF model without appendages was applied to conduct the simulations, and the Reynolds number based on the free-stream velocity and the length of the body is ReL=1.2×106. The results, including time-averaged Cp, Cf, and velocity statistics, were compared with the experimental data and wall-resolved LES results available in the literature, and the overall agreement of the comparisons was satisfactory. To assess the performance of the RSM-based hybrid RANS/LES approach, we carried out shear-stress transport-based hybrid RANS/LES approach simulations under identical free-stream conditions for comparison. The sensitivity of the hybrid RANS/LES approach to the RANS models was observed for separated flow with surface curvature and adverse pressure gradient-induced separation. The RSM-based hybrid RANS/LES approach was found to provide a better prediction for the unsteady flows near the stern. That is because the effects of the streamline curvature and the strong interactions between individual stresses can be captured by the exact production terms in the RSM-based hybrid RANS/LES approach. These effects are important for predicting the development of turbulent boundary layers along the stern.

Assessment of advanced RANS turbulence models for the stability analysis of low specific speed pump-turbines

Reversible pump-turbines, which can switch between pump and turbine operation, provide important support for the stabilization of the electrical grid. In order to fulfill their task, fast transition between the operation modes is required. This includes stable synchronization with the electrical grid during the process of turbine start at small guide vane openings (GVOs). However, the special geometry of pump-turbine impellers tends to produce unstable flow behavior, which can affect the synchronization process in a negative way.The prediction of the stability behavior with the help of CFD during the design process is not yet fully developed. The simulation of small specific speed pump-turbines operating at small GVOs sets high requirements on the underlying numerical model. To capture all relevant flow structures accordingly, 3-dimensional unsteady computation of the entire pump-turbine domain is required. Further, it has been shown that turbulence modeling is a key factor in order to reproduce the 4-quadrant characteristic in the unstable S-shape region. Vortex structures in the vaneless space and runner channels are considered the root-cause for the occurring instabilities. Standard two-equation models are not able to predict the stability behavior under these difficult circumstances (highly separated flows, small specific speed, small GVO angle). Models, which consider the anisotropic behavior of Reynolds-stresses have shown to produce better results.Considering the accurate prediction of mixing processes at off-design conditions, the focus was oriented to the anisotropy present in the turbulent structures. Standard models are often not sufficient to accurately predict vortices, which can have a huge impact on the performance, since based on the assumption of isotropic turbulence. Accordingly, they tend to dissipate and diffuse vortices too quickly. Improved models, which take the anisotropic nature of the Reynolds-stresses into account, can help in this context. The models can introduce the anisotropy via an explicit algebraic expression, or model directly the transport equations for the Reynolds-stresses. For this work the performance of a full Reynolds-stress model with improved coupling was investigated.In order to obtain the predictions using advanced turbulence models a particularly robust framework based on a pressure-based fully coupled approach was used. The goal of this work is the development and testing of an improved full Reynolds-stress model for the application in the stability analysis of pump-turbines. The focus lies thereby on separation behavior and mixing/vortex dissipation.

Influence of corner angle in streamwise supersonic corner flow

We use the Reynolds-averaged Navier–Stokes (RANS) equations with a full Reynolds stress model (RSM) to study the effect of the corner angle in supersonic corner flow. RANS data are compared to reference direct numerical simulation of fully developed a square duct flow, which support predictive capability of secondary flows from Stress-ω RSM. We then carry out a parametric study by changing the corner angle in the range θ=45°–135°, focusing on the effect on the mean streamwise and secondary flow. The maximum strength of the secondary flows of about 0.015u∞ occurs for θ=90°, which is similar to what is found in fully developed square ducts. Secondary eddies have approximately unit aspect ratio, and they maintain their shape for different corner angles by translating in the direction parallel to the closest wall. As a result, the position of the vortex center can be described by a simple geometrical transformation of the wall-parallel coordinate. We find that small corner angles are responsible for locally relaminarization flow at the corner, but otherwise the mean streamwise velocity profiles transformed according to van Driest following the canonical law-of-the-wall.

Unsteady shock front waviness in shock-buffet of transonic aircraft

The unsteady transonic aerodynamics of a wing-body configuration is investigated by solving the Unsteady Reynolds-averaged Navier-Stokes equations closed with the full Reynolds Stress Model. This work presents the prediction of flow field characteristics during deep shock-buffet penetration of a transport aircraft-representative geometry. Mach number of 0.85, and Reynolds number of 5 million based on the mean chord, are selected to reproduce experimental test conditions that serve as validating datasets. The results obtained give information about both surface and flow field shock-buffet dynamics. An unsteady shock front is observed on the suction side of the wing which gives birth to the so-called buffet cells. Flow field characteristics are dominated by the presence of lambda-shaped shocks and fully separated boundary layer over a significant part of the wing.

Using the Reynolds Stress Model to Predict Shock-Induced Separation on Transport Aircraft

Additional results about the wing-body of the NASA Common Research Model at flight conditions derived from those of the AIAA Computational Fluid Dynamics Drag Prediction Workshop are introduced in this Paper. An initial assessment compared the widely used shear stress transport model with the full Reynolds stress model as two possible closures for the Reynolds-averaged Navier–Stokes problem. The study, based on the 6th AIAA Computational Fluid Dynamics Drag Prediction Workshop, confirmed the limitations of linear eddy-viscosity turbulence models in highly anisotropic turbulent flows. A side-of-body separation larger than previous experiments was predicted by the shear stress transport model. By comparison, the study revealed that the Reynolds stress model is capable of simulating higher-incidence transonic flight as the trends observed in the results were in overall good agreement with the experiment. The aim herein was to investigate the high-incidence transonic aerodynamics about the Common Research Model. Using Reynolds-Averaged Navier–Stokes closed with the Reynolds stress model, the aeroelastically deformed Common Research Model was then simulated at incidences outside of the Drag Prediction Workshop remit. The evolution of shock-induced boundary-layer separation was observed. A separation bubble was first predicted at an incidence of 3.5 deg, then developed in the chordwise and spanwise directions, triggering the stall of the aircraft at an incidence of 5.75 deg. Using shear lines helps one understand the three-dimensionality of this phenomenon as large areas of crossflow are present, starting in the wing-kink region and extending toward the wing tip.

TWO-PHASE TURBULENT FLOW IN STRAIGHT HORIZONTAL CHANNELS WITH A SQUARE CROSS-SECTION TAKING INTO ACCOUNT THE INFLUENCE OF VERTICAL FORCES

The paper presents a numerical simulation of a two-phase turbulent flow in pneumatic transport through straight horizontal channels with a square cross-section. The transport of solid particles of ash and flour is taken as the two-phase flow, while air is chosen for the transporting fluid. The motion of solid particles occurs due to the aerodynamic forces of the transporting fluid. The paper considers the motion of solid particles by taking into account the influence of vertical forces, which act on the transported solid particles. In flow modelling, the transported solid particles are reduced to spherical shapes. The stress model of turbulence is corrected by taking into account the influence of the induction of secondary flows of the second kind in the gas phase. The full Reynolds stress model is used to model the turbulence, with the application of the complete model for turbulent stresses and turbulent temperature fluxes. The paper presents the results of the numerical grid with the highest resolution above which the increase of the mesh density does not affect the obtained results. The diagrams of the positions of the transported solid particles are provided for cross-sections normal and parallel to the flow direction.

Two-phase flow in channels with non-circular cross-section of pneumatic transport of powder material

The paper presents a numerical simulation of two-phase turbulent flow in straight horizontal channels of pneumatic transport with non-circular cross-section. For the granular flow simulation, we have chosen the flow of solid particles of quartz, flour, and ash in the flow of air, which is transporting fluid. During the modeling of the flow, the transported solid particles are reduced to spherical shapes. A correction of the stress model of turbulence is performed by taking into account the influences of the induction of secondary flows of the second order in the gas phase. The full Reynolds stress model was used for modeling the turbulence, and the complete model is used for the turbulent stresses and turbulent temperature fluxes. All numerical experiments were conducted for the same initial flow conditions and a single uniform grid was adopted for all numerical experiments. The flow is observed in a straight channel of a square cross-section and dimensions of sides of 200 mm and the length of 80 Dh. During the simulation, the fineness of the numerical grid was also tested, and the paper shows results of the numerical grid of the highest resolution beyond which the fineness does not influence the obtained results. The paper offers graphics of velocities of the solid particles transported by the transporting fluid (air) along the channel.

Euler–Euler multiphase CFD-simulation with full Reynolds stress model and anisotropic bubble-induced turbulence

In the present work, Euler–Euler modeling of bubbly flows is combined with a full Reynolds stress model for the turbulence in the liquid carrier phase. Reynolds stress models have only rarely been explored in this context, although effects requiring this level of description are frequently encountered in industrial applications towards which the Euler–Euler approach is geared. In particular, source terms describing the additional bubble-induced contribution to the liquid phase turbulence with proper account for its anisotropy have not firmly been established yet. A formulation based on the direction of bubble motion relative to the liquid is given here. Two well-known variants of Reynolds stress models due to Launder, Reece and Rodi and Speziale, Sarkar and Gatski are compared. Closure relations for the bubble forces are applied that have been shown previously to work well over a range of conditions. The model is validated by comparison with a set of pipe flow data that contains variations of liquid and gas flow rates as well as different pipe diameters. An important criterion for the selection of the data was to provide measurements of individual components of the Reynolds stress tensor.

On Application of EARSM Turbulence Model for Simulation of Flow Field behind Rack Station

This paper is interested in the mathematical modeling and approximation of the turbulent flow with strong anisotropy for the case of flow in a rack station. Turbulent models based on Boussinesq eddy viscosity assumption are traditionally employed for the solution of these types of flows. Linear eddy viscosity model and the assumption of isotropic Reynolds stress tensor are typically used in many cases. This leads to certain limitations in the cases of either separated flow or flow with significant curvature of the mean flow. The application of full Reynolds stress model is suitable for this case but it introduces at least seven additional equations and the model has much higher demand for computing time, grid parameters and discretization schemes. Therefore the Explicit Algebraic Reynolds Stress Model (EARSM) is used here. This model is based on two equations k – omega turbulence model with the nonlinear eddy viscosity model and explicit terms for anisotropic parts of the Reynolds stress tensor. The computational requirements are similar to the standard k – omega model. The numerical and experimental results from PIV measurement are compared.

A stress–strain lag Eddy viscosity model for unsteady mean flow

A new Eddy viscosity model is proposed to include stress–strain lag effects in the modelling of unsteady mean flows. A transport equation for the lag parameter, hereby denoted C as, is derived from a full Reynolds stress model (RSM), to be solved in conjunction with a standard two equation Eddy viscosity model (EVM). The performance of the new k– ε– C as model is assessed by applying it to the flow in a homogeneous irrotational cyclic strain; a channel flow driven by a pressure gradient oscillating around a non-zero mean, and a NACA0012 profile in deep stall. For the oscillating channel, results are compared with recent large Eddy simulations (LES) of the same flow and the addition of the lag parameter equation is shown to give improved results when compared to the standard EVM outside the near wall region.

Unsteady methods (URANS and LES) for simulation of combustion systems

A great variety of flows in practical engineering applications are inherently unsteady, and virtually all of Newtonian fluid flows in nature are turbulent. In order to better capture the dynamics of such complex flows, it is appropriate to use unsteady methods. The present overview is confined to single-phase turbulent flows. The first part provides an evaluation of the performance of the unsteady RANS (URANS) method. It could be confirmed that the U-RANS method employing a full Reynolds stress model is able to capture unsteady phenomena, such as precessing vortex core phenomenon both qualitatively and in parts also quantitatively. In the second part, some important features of combustion LES are recollected and some results for flames, that were already computed by RANS-based methods in the literature, are presented. Thereby a flamelet approach is used to relate the filtered mixture fraction to density, temperature and species concentrations. It is shown that LES is able to deliver good results very close to measured data, where the flow is governed by large, turbulent structures. Flamelet chemistry appears well able to reproduce experimental data for species, in particular with regard to kinetic effects prediction, whereas equilibrium chemistry strongly deviates. However, a good predictability could be achieved when appropriate choice of boundary and inflow conditions is made.

Calculation of turbulent fluid flow and heat transfer in ducts by a full Reynolds stress model

AbstractA computational method has been developed to predict the turbulent Reynolds stresses and turbulent heat fluxes in ducts by different turbulence models. The turbulent Reynolds stresses and other turbulent flow quantities are predicted with a full Reynolds stress model (RSM). The turbulent heat fluxes are modelled by a SED concept, the GGDH and the WET methods. Two wall functions are used, one for the velocity field and one for the temperature field. All the models are implemented for an arbitrary three‐dimensional channel.Fully developed condition is achieved by imposing cyclic boundary conditions in the main flow direction. The numerical approach is based on the finite volume technique with a non‐staggered grid arrangement. The pressure–velocity coupling is handled by using the SIMPLEC‐algorithm. The convective terms are treated by the van Leer scheme while the diffusive terms are handled by the central‐difference scheme. The hybrid scheme is used for solving the ε equation.The secondary flow generation using the RSM model is compared with a non‐linear k–ε model (non‐linear eddy viscosity model). The overall comparison between the models is presented in terms of the friction factor and Nusselt number. Copyright © 2003 John Wiley & Sons, Ltd.

Experimental studies and modelling of four-way coupling in particle-laden horizontal channel flow

Detailed measurements in a horizontal channel flow laden with solid particles with different size and loading ratio were performed using phase-Doppler anemometry. The data were required for the validation of numerical calculations based on the Euler/Lagrange approach. In this approach the Reynolds-averaged continuity and Navier–Stokes equations in connection with a full Reynolds-stress model constitute the basis. The conservation equations include appropriate source terms resulting from the dispersed phase (i.e., two-way coupling). For modelling the particle phase in the Lagrangian frame all relevant effects are accounted for, such as, turbulent dispersion, transverse lift forces, wall collisions with roughness, and inter-particle collisions (i.e., often called four-way coupling). Comparison of measurement and numerical calculation is presented for different particle diameters and mass loading. The agreement was found to be reasonable good for both mean and fluctuating velocities.

Turbulence Model Predictions of Strongly Curved Flow in a U-Duct

The ability of three types of turbulence models to accurately predict the effects of curvature on the flow in a U-duct is studied. An explicit algebraic stress model performs slightly better than one- or two-equation linear eddy viscosity models, although it is necessary to fully account for the variation of the production-to-dissipation-rate ratio in the algebraic stress model formulation. In their original formulations, none of these turbulence models fully captures the suppressed turbulence near the convex wall, whereas a full Reynolds stress model does. Some of the underlying assumptions used in the development of algebraic stress models are investigated and compared with the computed flowfield from the full Reynolds stress model. Through this analysis, the assumption of Reynolds stress anisotropy equilibrium used in the algebraic stress model formulation is found to be incorrect in regions of strong curvature. By the accounting for the local variation of the principal axes of the strain rate tensor, the explicit algebraic stress model correctly predicts the suppressed turbulence in the outer part of the boundary layer near the convex wall.

Turbulence model predictions of strongly curved flow in a U-duct

The ability of three types of turbulence models to accurately predict the effects of curvature on the flow in a U-duct is studied. An explicit algebraic stress model performs slightly better than one- or two-equation linear eddy viscosity models, although it is necessary to fully account for the variation of the production-to-dissipation-rate ratio in the algebraic stress model formulation. In their original formulations, none of these turbulence models fully captures the suppressed turbulence near the convex wall, whereas a full Reynolds stress model does. Some of the underlying assumptions used in the development of algebraic stress models are investigated and compared with the computed flowfield from the full Reynolds stress model. Through this analysis, the assumption of Reynolds stress anisotropy equilibrium used in the algebraic stress model formulation is found to be incorrect in regions of strong curvature. By the accounting for the local variation of the principal axes of the strain rate tensor, the explicit algebraic stress model correctly predicts the suppressed turbulence in the outer part of the boundary layer near the convex wall.

A Numerical Study of Vortex Breakdown in Turbulent Swirling Flows

Solutions to the incompressible Reynolds-averaged Navier–Stokes equations have been obtained for turbulent vortex breakdown within a slightly diverging tube. Inlet boundary conditions were derived from available experimental data for the mean flow and turbulence kinetic energy. The performance of both two-equation and full differential Reynolds stress models was evaluated. Axisymmetric results revealed that the initiation of vortex breakdown was reasonably well predicted by the differential Reynolds stress model. However, the standard K-ε model failed to predict the occurrence of breakdown. The differential Reynolds stress model also predicted satisfactorily the mean azimuthal and axial velocity profiles downstream of the breakdown, whereas results using the K-ε model were unsatisfactory. [S0098-2202(00)01601-1]