Explicit Algebraic Reynolds Stress Model Research Articles

Comparison of Eddy Viscosity Models for High Turbulence Nozzle Guide Vane Flows

Abstract In this paper we investigate the performance of eddy viscosity turbulence models for high-pressure nozzle guide vane (NGV) flows with engine-realistic turbulence. Using metrics such as integrated kinetic energy (KE) loss and mixing rate, we compare simulation results using turbulence models with high-fidelity experimental data from fully-cooled NGVs, operating at engine-matched conditions of Reynolds number and Mach. For the widely-used k–ω shear stress transport (SST) model, the aerodynamic and thermal wakes of the NGVs were undermixed. We compare simulation results with those using other common turbulence models including the standard k–ω, baseline k–ω, Spalart–Allmaras, and baseline explicit algebraic Reynolds stress model. Alternative turbulence models formulations are explored, with an emphasis on modifications to the implementation of the shear stress limiter. We also investigate the sensitivity of models to the specified inlet turbulence intensity. We demonstrate that predictions of integrated KE loss, as well as the decay trends of the aerodynamic and thermal wakes are a closer match to experimental data for the baseline algebraic Reynolds stress model than for other turbulence models in more common use for NGV predictions.

Improvements in the Prediction of Steady and Unsteady Transition and Mixing in Low-Pressure Turbines by Means of Machine-Learnt Closures

Abstract In this article, novel machine-learnt transition and turbulence models are applied to the prediction of boundary-layer transition and wake mixing in a low-pressure turbine (LPT) cascade, including unsteady inflow cases with incoming wakes. A laminar kinetic energy (LKE) transport approach is employed as baseline transition framework. The application of the machine-learnt explicit algebraic Reynolds stress models (EARSMs) takes advantage of a zonal strategy based on a newly developed sensing function that allows automated wake demarcation. This work compares the performance of several approaches that are based on the application of improved transition models without machine learnt EARSMs, baseline transition model with EARSMs trained for improved wake mixing, and new transition and turbulence closures that are simultaneously developed in a fully coupled way and aimed at improving both transition and wake mixing predictions in LPTs. The investigation is carried out on a cascade of industrial footprint, representative of modern LPT bladings. First, the various modeling frameworks are evaluated, without bar wakes (steady conditions), over a wide range of Reynolds number values. Unsteady Reynolds-averaged Navier–Stokes (URANS) analyses have also been carried out to investigate the predictive capabilities of machine-learnt closures in the presence of incoming bar wakes. Reynolds-averaged Navier–Stokes (RANS)/URANS results are scrutinized against large eddy simulation (LES) calculations and experimental data. It will be demonstrated that machine-learnt EARSMs are capable of producing realistic wake mixing when simply applied on top of the baseline transition models. However, the most accurate predictions will be shown to be provided by fully integrated machine-learnt transition/turbulence closures.

Numerical Investigations of Turbulent Flow Through A 90-Degree Pipe Bend And Honeycomb Straightener

Abstract Pipe bends are commonly used in piping systems in offshore and subsea installations. The present study explores the design considerations for the honeycomb straightener inserted downstream of a 90-degree pipe bend. The objective of the study is to evaluate the effectiveness of the honeycomb in suppressing the flow swirling for different distances from the bend outlet (Lb) and different values of the honeycomb thickness (t). The turbulent flow through the 90-degree circular pipe bend with the honeycomb straightener is investigated by carrying out numerical simulations using the Reynolds-Averaged Navier-Stokes (RANS) turbulence modeling approach. The Explicit Algebraic Reynolds Stress Model (EARSM) is adopted to resolve the Reynolds stresses. The honeycomb thickness to pipe diameter ratio (t/D) is varied between 0.1 and 1. The normalized distance from the bend outlet to the honeycomb straightener (Lb/D) is varied between 1 and 5. The disturbance in the velocity field is generated by the pipe bend with the curvature radius to pipe diameter ratio (Rc/D) of 2 and Reynolds number (Re) of 2×105. It is found that both the increase in Lb/D and t/D improves the performance of the device in removing the swirl behind the bend outlet. The best performance is observed for the honeycomb straightener with the distance Lb/D=5 and thickness t/D=0.5.

Progressive augmentation of Reynolds stress tensor models for secondary flow prediction by computational fluid dynamics driven surrogate optimisation

Generalisability and the consistency of the a posteriori results are the most critical points of view regarding data-driven turbulence models. This study presents a progressive improvement of turbulence models using simulation-driven Bayesian optimisation with Kriging surrogates where the optimisation of the models is achieved by a multi-objective approach based on duct flow quantities. We aim for the augmentation of secondary-flow prediction capability in the linear eddy-viscosity model k−ω SST without violating its original performance on canonical cases e.g. channel flow. Progressively data-augmented explicit algebraic Reynolds stress models (PDA-EARSMs) for k−ω SST are obtained enabling the prediction of secondary flows that the standard model fails to predict. The new models are tested on channel flow cases guaranteeing that they preserve the successful performance of the original k−ω SST model. Subsequently, numerical verification is performed for various test cases. Regarding the generalisability of the new models, results of unseen test cases demonstrate a significant improvement in the prediction of secondary flows and streamwise velocity. These results highlight the potential of the progressive approach to enhance the performance of data-driven turbulence models for fluid flow simulation while preserving the robustness and stability of the solver.

On the application of statistical turbulence models to the simulation of airflow inside a car cabin

Computational fluid dynamics simulations of airflow inside a full-scale passenger car cabin are performed using the Reynolds averaged Navier–Stokes equations. The performance of a range of turbulence models is examined by reference to experimental results of the streamwise mean velocity and turbulence intensity profiles, obtained using the hot-wire anemometry technique at different locations inside the car cabin. The models include three linear eddy-viscosity-based variants, namely, the realizable k–ε, the renormalization group k–ε, and the shear-stress transport k–ω models. The baseline Reynolds stress model (BSL-RSM), a second-moment-closure variant, and an Explicit Algebraic Reynolds Stress Model (BSL-EARSM) are also investigated. Visualization of velocity vectors and streamlines in different longitudinal planes shows a similar airflow pattern. The flow topology is mainly characterized by jet flows developing from the dashboard air vents and extending to the back-seats compartment resulting in a large vortex structure. Additionally, a comparison between numerical and experimental results shows a relatively good agreement of the mean velocity profiles. However, all models exhibit some limitations in predicting the correct level of turbulence intensity. Moreover, the realizability of the modeled Reynolds stresses and the structure of turbulence are analyzed based on the anisotropy invariant mapping approach. All models reveal a few amounts of non-realizable solutions. The linear eddy-viscosity-based models return a prevailing isotropic turbulence state, while the BSL-RSM and the BSL-EARSM models display pronounced anisotropic turbulence states.

Generation of turbulent inflow data from realistic approximations of the covariance tensor

This study presents a novel synthetic inflow generator capable of producing a random field matching a realistic set of two-point statistics with minimal input. The method is based on two main elements. The first element is a procedure to infer realistic two-point covariance tensors from readily available data (e.g., freestream velocity, boundary layer thickness, and turbulence intensity) by a preliminary Reynolds-averaged Navier–Stokes simulation with an explicit algebraic Reynolds stress model closure. The second element is an efficient eigen-decomposition step of the two-point correlation tensor, which determines a set of modes. The modal decomposition guarantees the spatial correlation in transversal directions, while the temporal correlation/streamwise spatial correlation is obtained by digital filters based on longitudinal and transversal spectra of a realistic shape and Taylor's hypothesis. The instantaneous inlet flow field is obtained by a linear combination of the modes via uncorrelated random weights with unit variance. The modes are generated in a computationally inexpensive pre-processing step. Compared to existing inflow generation methods that try to match given two-point statistics, the proposed method relieves the burden of obtaining data from direct numerical simulation (DNS) or experiments, while the complexity of the eigenvalue problem that needs to be solved is reduced. The proposed method is shown to produce a realistic turbulent channel flow and a realistic turbulent boundary layer by the large-eddy simulation, which contains statistics that are in good agreement with results from DNS. The proposed inflow generator features, cost-effectiveness, robustness, and potential for generalization to complex geometries.

Sparse Bayesian Learning of Explicit Algebraic Reynolds-Stress models for turbulent separated flows

A novel Sparse Bayesian Learning (SBL) framework is introduced for generating stochastic Explicit Algebraic Reynolds Stress (EARSM) closures for the Reynolds-Averaged Navier–Stokes (RANS) equations from high-fidelity data. Building on the recently proposed SpaRTA (Sparse Regression of Turbulent Stress Anisotropy) algorithm of Schmelzer et al. (2020), corrections to an underlying Linear-Eddy-Viscosity Models (LEVM) (namely, the k−ω SST model) are formulated as physically-interpretable, frame-invariant tensor polynomials and built from a redundant dictionary of candidate functions. The SBL-SpaRTA algorithm yields a sparse model structure (which favors interpretability and reduces overfitting), while endowing model coefficients with a measure of uncertainty, namely, posterior probability distributions. The framework is used to learn customized stochastic closure models for three separated flow configurations, characterized by different geometries but similar Reynolds number. The resulting stochastic models are then propagated through a CFD solver for all three configurations by means of probabilistic chaos collocation (Loeven et al., 2007). SBL-SpaRTA predictions of velocity profiles and friction coefficient distributions outperform those of the baseline LEVM, for training as well as for test cases. Furthermore, the prediction uncertainty intervals encompass reasonably well the reference data and tend to become large in regions of large discrepancy between RANS and high-fidelity predictions, thus warning the user about model reliability. Finally, a global sensitivity analysis of the stochastic models is carried out, illustrating the role of the dominant corrective terms and providing insights for future improvement of data-driven turbulence models.

Wind turbine wake simulation with explicit algebraic Reynolds stress modeling

Abstract. Reynolds-averaged Navier–Stokes (RANS) simulations of wind turbine wakes are usually conducted with two-equation turbulence models based on the Boussinesq hypothesis; these are simple and robust but lack the capability of predicting various turbulence phenomena. Using the explicit algebraic Reynolds stress model (EARSM) of Wallin and Johansson (2000) can alleviate some of these deficiencies while still being numerically robust and only slightly more computationally expensive than the traditional two-equation models. The model implementation is verified with the homogeneous shear flow, half-channel flow, and square duct flow cases, and subsequently full three-dimensional wake simulations are run and analyzed. The results are compared with reference large-eddy simulation (LES) data, which show that the EARSM especially improves the prediction of turbulence anisotropy and turbulence intensity but that it also predicts less Gaussian wake profile shapes.

Numerical Simulations of Turbulent Flow Through a 90-Deg Pipe Bend

Abstract The turbulent flow through a 90-deg circular pipe bend is investigated by carrying out the numerical simulations using the Reynolds-averaged Navier–Stokes (RANS) turbulence model in the present study. The objective of the present study is to evaluate the effects of different values of the curvature radius (Rc) and different Reynolds numbers (Re) on the flow development in the circular pipe bend by employing the explicit algebraic Reynolds stress model (EARSM) to resolve the Reynolds stresses, unlike the research carried out so far where the turbulence anisotropy has not been considered. The curvature ratio defined as the curvature radius to pipe diameter (Rc/D) is varied between 1 and 4 and the investigated Re range is from 10,000 to 60,000. The numerical model is validated by comparing the axial velocity profiles with the previous published experimental data. It is found that for the fixed Re and decreasing Rc/D, the axial velocity, the velocity perturbation, and the pressure difference in the cross section increase and vorticity becomes stronger. When the curvature ratio gets smaller than 2, the flow velocity profile becomes highly distorted. For the fixed Rc/D, the influence of the Re on the flow behavior is small for the investigated range of Re.

Reynolds-averaged stress and scalar-flux closures via symbolic regression for vertical natural convection

Turbulent natural convection is characterised by mutual coupling effects between velocity and thermal fields. This inter-coupling induces simulation errors with linear and non-coupled turbulence closures commonly used in many Reynolds–averaged Navier–Stokes (RANS) approaches. In this paper, we re-examine the buoyancy-accounting algebraic scalar-flux model proposed by Kenjereš et al., Int. J. Heat Fluid Flow, Vol. 26, pp. 569–586 (2005). Using a term-by-term analysis on the model with the aid of high-fidelity datasets for natural convection flow between two differentially heated vertical plates, it is demonstrated that there are significant discrepancies in the predicted turbulent heat fluxes once the model is combined with the existing algebraic Reynolds stress models. As a result, we suggest including the quadratic terms in buoyancy-extended explicit algebraic Reynolds stress models, and have developed non-linear Reynolds-stress and heat-flux closure models via an in–house symbolic regression tool based on gene expression programming (GEP). The evaluation of these GEP-developed models shows significant improvements in the prediction of mean quantities and second-moments in an a priori stage and in an a posteriori stage, with the latter being realized by embedding the new models into the elliptic relaxation v2‾/k-f-k-ε-θ2‾ equations, for vertical natural convection with Rayleigh numbers in the range of 106 to 109.

CFD-driven symbolic identification of algebraic Reynolds-stress models

A CFD-driven deterministic symbolic identification algorithm for learning explicit algebraic Reynolds-stress models (EARSM) from high-fidelity data is developed building on the frozen-training SpaRTA algorithm of [1]. Corrections for the Reynolds stress tensor and the production of transported turbulent quantities of a baseline linear eddy viscosity model (LEVM) are expressed as functions of tensor polynomials selected from a library of candidate functions. The CFD-driven training consists in solving a blackbox optimization problem in which the fitness of candidate EARSM models is evaluated by running RANS simulations. The procedure enables training models against any target quantity of interest, computable as an output of the CFD model. Unlike the frozen-training approach, the proposed methodology is not restricted to data sets for which full fields of high-fidelity data, including second flow order statistics, are available. However, the solution of a high-dimensional expensive blackbox function optimization problem is required. Several steps are then undertaken to reduce the associated computational burden. First, a sensitivity analysis is used to identify the most influential terms and to reduce the dimensionality of the search space. Afterwards, the Constrained Optimization using Response Surface (CORS) algorithm, which approximates the black-box cost function using a response surface constructed from a limited number of CFD solves, is used to find the optimal model parameters. Model discovery and cross-validation is performed for three configurations of 2D turbulent separated flows in channels of variable section using different sets of training data to show the flexibility of the method. The discovered models are then applied to the prediction of an unseen 2D separated flow with higher Reynolds number and different geometry. The predictions of the discovered models for the new case are shown to be not only more accurate than the baseline LEVM, but also of a multi-purpose EARSM model derived from purely physical arguments. The proposed deterministic symbolic identification approach constitutes a promising candidate for building accurate and robust RANS models customized for a given class of flows at moderate computational cost.

Clocking and Potential Effects in Combustor–Turbine Stator Interactions

Investigations of combustors and turbines separately have been carried out for years by research institutes and aircraft engine companies, but there are still many questions about the interaction effect. In this paper, a prediction of a turbine stator’s potential effect on flow in a combustor and the clocking effect on temperature distribution in a nozzle guide vane are discussed. Numerical simulation results for the combustor simulator and the nozzle guide vane (NGV) of the first turbine stage are presented. The geometry and flow conditions were defined according to measurements carried out on a test section within the framework of the EU FACTOR (full aerothermal combustor–turbine interactions research) project. The numerical model was validated by a comparison of results against experimental data in the plane at a combustor outlet. Two turbulence models were employed: the Spalart–Allmaras and Explicit Algebraic Reynolds Stress models. It was shown that the NGV potential effect on flow distribution at the combustor–turbine interface located at 42.5% of the axial chord is weak. The clocking effect due to the azimuthal position of guide vanes downstream of the swirlers strongly affects the temperature and flow conditions in a stator cascade.

Local flow assessment of the Japan Bulk Carrier using different turbulence models

Ship resistance and powering represent the most important aspects in the initial design stage of the ship. Based on their estimation the basic milestone for selecting the main engine and the propulsion system is established. The majority of ships in the international fleet nowadays rely on the screw propeller working in the wake zone behind the ship. The wake flow of the ship has a direct impact on the propeller performance and the propulsion efficiency. Accurate prediction of the nominal and effective wake is crucially important to provide a proper understanding of the flow where the propeller will perform. From this point of view, the wake flow of the Capesize Japan Bulk Carrier (JBC) is assessed using a viscous flow Computational Fluid Dynamics (CFD) method. Numerical simulations are performed to predict the nominal and effective wake of the ship by making use of the viscous flow solver ISIS_CFD of the FINETM/Marine software provided by NUMECA. The solver is based on the finite volume method to build the spatial discretization of the transport equation to resolve the Reynolds-Averaged Navier-Stokes (RANS) equations. Closure to turbulence is achieved using different turbulence models in order to investigate their accuracy in predicting the complex wake flow of the ship. Two-phase flow approach is used to model the air-water interface where the Volume of Fluid method is implemented to capture the free-surface. The results for both nominal and effective wake are assessed against the experimental data provided by the National Maritime Research Institute (NMRI) and Yokohama National University in Japan that were presented in the seventh Workshop on CFD in ship hydrodynamics (Tokyo2015). The results validation showed a reasonable agreement compared to the experimental data for both nominal and effective wake. As it was expected, some turbulence models showed to be more accurate in predicting ship wake, especially the Shear Stress Transport (K-ω SST) and Explicit Algebraic Reynolds Stress (EASM) Models. A special investigation of the flow vortices is also taken into consideration.

Capturing the S-Shape of Pump-Turbines by Computational Fluid Dynamics Simulations Using an Anisotropic Turbulence Model

Abstract Pump-turbines cope very well with modern electricity-market demand, having high operational flexibility and storage capabilities. Nevertheless, dynamic operation of these machines can lead to very challenging transient conditions, depending on the shape of the characteristic. Mechanical integrity can be correspondingly affected. Therefore, assessment of the characteristic during the design phase is of crucial importance. In the past years, different attempts to accurately compute the characteristic under steady and transient conditions have been undertaken using Reynolds-averaged Navier–Stokes (RANS) computational fluid dynamics. While the k–ω shear stress transport (SST) turbulence model has become the reference for machine design, it often fails for conditions close to or around instabilities. Under unstable conditions, which are characterized by continuous unsteady vortex formation, turbulence isotropy as assumed by linear two equation models is no longer the right choice. Accordingly, a turbulence model able to capture anisotropy, explicit algebraic Reynolds stress model (EARSM), has been implemented in an in-house code and used for the computation of the characteristic of various machines, stable and unstable, to assess the model performance. In this paper, computations of three different dynamic pump-turbine operating conditions are presented. Results using steady boundary conditions (BC) in the unstable region as well as transient BC like load-rejection and runaway are computed with EARSM, showing its superiority compared to linear two equation models. The model's capability to capture anisotropic effects—such as the influence of corners—produces more physical flow structures in the vaneless space, which lead to an overall improvement of the predicted stability characteristics.

Anisotropic SST turbulence model for shock-boundary layer interaction

Menter SST k-ω is a Reynolds-averaged Navier–Stokes based two-equation turbulence model routinely used in industry for predicting aerodynamic flows. It shows excellent performance for low-speed flows, but gives inconsistent predictions for high-speed shock-induced separated flows. The model assumption of using a constant value of 0.31 for the structure parameter contradicts experimental observations. The model is also unable to predict Reynolds stress anisotropy generated by shock waves. In this work, we augment the SST model with quadratic eddy viscosity formulation of an explicit algebraic Reynolds stress model. A new relation for the structure parameter is proposed, making it a function of the local strain-rates and is no longer a constant in the regions of shock/turbulent boundary layer interaction (SBLI). Additional shock-physics is introduced using (Sinha et al., 2003) shock-unsteadiness model and an upper limit to the value of structure parameter is set in regions of shock waves. The new model, termed as SUQ-SST, is validated using a number of SBLI test cases ranging from supersonic to hypersonic speeds and near-incipient to fully-separated flows. Results show that the modifications do not alter the boundary layer prediction capability of the SST model. On the other hand, the new model gives significant improvement in predicting Reynolds stress anisotropy, flow separation, and surface properties in a wide range of SBLI flows.

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.