Eddy-viscosity Turbulence Model Research Articles

Transport-Based Transition Prediction for the Common Research Model Natural Laminar Flow Configuration

This paper presents the application of a new -based one-equation transition transport model to the Common Research Model Natural Laminar Flow Configuration (CRM-NLF), which was the central test case of the 1st AIAA CFD Transition Modeling and Prediction Workshop. The new model uses a simplified formulation of the Arnal, Habiballah, and Delcourt transition criterion that is stability based. The model is formulated in a grid-point-local manner and is coupled to the Menter shear stress transport eddy-viscosity turbulence model. The flow conditions applied are exactly those that were reported from the National Transonic Facility wind tunnel test campaign. The comparisons of the results yielded by the new model in terms of the transition fronts along the wing span show a very good match with the transition fronts derived from the temperature-sensitive paint images taken during the wind tunnel test and with computational result from an -based Two--factor strategy using critical -factors for Tollmien–Schlichting and crossflow instabilities and applying a local linear stability code.

Computation of viscous flow characteristics of a supersonic intake using eddy-viscosity turbulence models

Results of numerical investigation of flow and performance characteristics of a rectangular supersonic intake experimentally tested at Mach number of 4.03 are presented. The viscous flowfield has been obtained by solving Favre averaged Navier–Stokes equations with two eddy viscosity turbulence models, namely, Mentor’s baseline (BSL) k-ω and shear stress transport (SST) k-ω models. In addition, the effect of wall temperature conditions as well as several configurations of cowl and isolator are simulated to validate the computational methodology. The analysis has been carried out at a freestream Mach number of 4.03 and 0° angle-of-attack, corresponding to a unit Reynolds number of about 6.9×107 m−1. The predicted boundary-layer and the wall static pressure distribution using SST k-ω model shows better agreement with the experimental data compared to the BSL model and hence indicates superior capability to capture the onset and the amount of flow separation due to SWBLIs. Moreover, the terminal shock structure at different operating modes as well as the “unstart because of SWBLIs” is predicted quite accurately using the model. The wall temperature condition is found to have a strong effect on the amount of flow separation at the cowl and the subsequent interactions. Further, the results show that the sidewalls have a marginal effect on the centerline wall static pressure, though a three-dimensional flowfield with two stream-wise vortices are observed close to it as a result of the swept SWBLIs of the cowl shock with the sidewall boundary-layer leading to a higher loss in performance.

Investigations on Turbulence Model Uncertainty for Hypersonic Shock-Wave/Boundary-Layer Interaction Flows

Shock-wave/boundary-layer interaction (SWBLI) is a fundamental scientific problem that restricts the breakthrough of high-speed flight technology. Owing to the complex shock structure and boundary-layer separation in the interaction region, the widely used eddy-viscosity turbulence models have large uncertainties and model errors in the simulation of such flows. To make more reasonable aerodynamic/aerothermal predictions and identify the critical parameters affecting the prediction results, Bayesian uncertainty quantification and sensitivity analysis are conducted for the three turbulence models [Spalart–Allmaras (SA), SA with quadratic constitutive relation (SA-QCR), and shear-stress transport (SST) models] and the hypersonic SWBLI cases. First, the prior variances and Sobol indices are calculated to obtain a preliminary understanding of the parameter variability for turbulence models. Then, the posterior distributions of the model closure coefficients and posterior uncertainties of the wall pressure and thermal flux are systematically analyzed and compared. The results indicate that the prediction performances of the three models can be effectively enhanced by Bayesian estimation. The peak of the posterior uncertainty of the SST model is the largest among the three models, whereas that of the SA-QCR model is the smallest. The results of the Bayesian model evaluation demonstrate that the SA-QCR model has the highest reliability.

Calibration of an Extended Eddy Viscosity Turbulence Model Using Bayesian Update

The present work aims at improving the performance of the eddy viscosity-based Menter - Shear Stress Transport turbulence model for complex aircraft flows by adding physical extensions to the length-scale equation along with calibration aided by uncertainty quantification methods. Three different extensions based on rotation and curvature correction, wake flow correction, and irrotational strain correction are added to the original model, resulting in a parametric model, which is then calibrated using Bayesian updates. A series of test cases is employed to assess the model performance, whereby delta wings with deflected flaps and vortical flows are the predominant target application.

Numerical Evaluation of Riblet Drag Reduction on a MALE UAV

Flow control methods for aerodynamic drag reduction have been a field of interest to aircraft designers, who seek to minimize fuel consumption and increase the aircraft’s aerodynamic performance. Various flow control techniques, applied to aeronautical applications ranging from large airliners to small hand-launched unmanned aerial vehicles (UAVs), have been conceptualized, designed and tested in the past. Among others, the concept of riblets, inspired by the shark’s skin morphology, has been proposed and evaluated for airliners. In this work, the implementation of riblets on a medium-altitude long-endurance UAV (MALE) is investigated. The riblets can offer drag reduction due to the decrease in total skin friction, by altering the boundary layer characteristics in the near-wall region. The riblets are implemented on specific locations on the UAV (main wing, fuselage and empennage) and appropriately selected, on which the boundary layer becomes transitional from the laminar to the turbulent flow regime. For this reason, computational fluid dynamics modelling is performed by solving the Reynolds-averaged Navier–Stokes equations, incorporating the k-ω SST eddy viscosity turbulence model. The effect of the riblets in the near-wall region is modelled with the use of an appropriate wall boundary condition for the specific turbulence dissipation rate transport equation. It is shown that a drag reduction benefit, for both the loiter and the cruise flight segments of the UAV mission, can be obtained, and this is clearly presented by the drag polar diagrams of the air vehicle. Finally, the potential benefit to flight performance in terms of endurance and payload weight increase is also evaluated.

Flow and Heat Transfer Simulation in a Complete Pressurized Water Reactor Fuel Assembly Using Wall-Modeled RANS

Abstract Reproduction of turbulent flow and heat transfer inside a pressurized water reactor (PWR) fuel assembly is a challenging task due to the complex geometry and the huge computational domain. Capability of a wall-modeled Reynolds-averaged Navier–Stokes (RANS) simulation approach has been examined, which had already been validated against the measurements of the MATiS-H experiment. The method is here expanded to a larger computational domain aiming to reproduce flow and thermal field in the entire PWR fuel assembly. Namely, in the first part of this study, wall-modeled RANS is performed in a relatively short section of the representative PWR fuel assembly containing one single mixing grid with an array of 15 × 15 fuel rods. Linear and nonlinear eddy-viscosity turbulence models have been applied; however no significant difference is observed in the predicted pressure drop in the fuel assembly. The obtained predictions revealed an interesting pattern of swirl flow as well as diagonal cross flow downstream the mixing grid, which is driven by the applied design of split-type mixing vanes. In the second part, the computational model is extended to a domain representative of a complete PWR fuel assembly with ten mixing grids, inlet and outlet sections. Pressure drop and flow field are analyzed together with the predicted temperature and potential hot spots. In spite of a relatively coarse spatial resolution of the applied approach, the wall-modeled RANS provided promising results at least for the qualitative prediction of the pressure, flow field, and location of hot spots.

Analysis and validation of mathematical models of secondary velocities along vertical and transverse directions in wide open-channel turbulent flows

Cellular secondary flows are inevitably present in turbulent flows through ducts, natural or artificial channels, and compound channels. Secondary currents significantly modify the characteristics of turbulent quantities, the pattern of primary flow velocity by causing dip-phenomenon. To understand the detailed mechanism and hidden cause, modelling of secondary flow velocities is crucial. In this study, proper mathematical models of secondary flow velocities along vertical and transverse directions are proposed for steady and uniform turbulent flow through wide open channels with equal smooth and rough bed strips. Starting from the continuity and the Reynolds averaged Navier–Stokes equations, governing equation for secondary velocity is derived first and then using appropriate boundary conditions (no-slip boundary conditions at channel bottom and free surface, and maximum vertical velocity in magnitude at the interface of two cellular secondary cells and at mid-depth of the channel. All these conditions are consistent with several experimental observations). A new model of the streamwise Reynolds shear stress is proposed for the entire cross-sectional plane and using it, the analytical solutions are obtained. Proposed models include the effects of viscosity of the fluid and the eddy viscosity model of turbulence. All suggested models are validated with existing experimental data in rectangular open-channel flows, compound open channel flows, and duct flows, and satisfactory results are obtained. Furthermore, models are also compared with existing empirical models from literature to show the effectiveness and superiority of proposed models. Apart from these, the obtained results from this study are used to investigate the effects of vertical and transverse secondary flow velocities on the settling velocity vector in a cross-sectional plane. Effective alternative models for the settling velocity vector are suggested. The model of settling velocity vector is also compared with the existing model. Finally, all results are justified from physical viewpoints.

Aerodynamic Prediction of High-Lift Configuration Using Turbulence Model

The aerodynamic performance of the high-lift configuration greatly influences the safety and economy of commercial aircraft. Accurately predicting the aerodynamic performance of the high-lift configuration, especially the stall behavior, is important for aircraft design. However, the complex flow phenomena of high-lift configurations pose substantial difficulties to current turbulence models. In this paper, an eddy-viscosity turbulence model is used to compute the stall behavior of high-lift configurations. A separated shear layer fixed function is implemented in the turbulence model to better capture the nonequilibrium characteristics of turbulence. Different high-lift configurations, including the two-dimensional multi-element NLR7301 and Omar airfoils and a complex full-configuration model (JAXA Standard Model), are numerically tested. The simulations show engineering accurate results and indicate that the effect of the nonequilibrium characteristics of turbulence is significant in the free shear layer, which is key to accurately predicting the stall behavior of high-lift devices. The modified shear layer fixed model is more accurate in predicting stall behavior than the Spalart–Allmaras, shear stress transport, and original models for the full high-lift configuration. The relative errors in the predicted maximum lift coefficients are within 3% of the experimental data.

Assessment of Discretization Uncertainty Estimators Based on Grid Refinement Studies

Abstract This paper presents the assessment of the performance of nine discretization uncertainty estimates based on grid refinement studies including methods that use grid triplets and others that use a largest number of data points, which in this study was set to five. The uncertainty estimates are performed for the dataset proposed for the 2017 ASME Workshop on Estimation of Discretization Errors Based on Grid Refinement Studies including functional and local (boundary and interior) flow quantities from the two-dimensional flows of an incompressible fluid over a flat plate and the NACA 0012 airfoil. The data were generated with a Reynolds-averaged Navier–Stokes (RANS) solver using three eddy-viscosity turbulence models with double precision and sufficiently tight iterative convergence criteria to ensure that the numerical error is dominated by the discretization error. The use of several geometrically similar grid sets with different near-wall cell sizes for the same flow conditions lead to a wide range of convergence properties for the selected flow quantities, which enables the assessment of the numerical uncertainty estimators in conditions that are representative of the so-called practical applications.The evaluation of uncertainty estimates is based on the ratio of the uncertainty estimate over the “exact error” that is obtained from an “exact solution” obtained from extra grid sets significantly more refined than those used to generate the Workshop data. Although none of the methods tested fulfilled the goal of bounding the exact error 95 times out of 100 that was tested, the results suggest that the methods tested are useful tools for the assessment of the numerical uncertainty of practical numerical simulations even for cases where it is not possible to generate data in the “asymptotic range.”

Computational investigation of a novel hydrocyclone for fines bypass reduction

Hydrocylones offer a process intensified environment for rapid, high-throughput and relatively sharp particle classification or phase separation. One of the main performance limitations of hydrocyclone is bypassing of fines to the underflow. To address this limitation, a novel design modification of fitting thin concentric rings to the cylindro-conical section has been proposed. The Computational Fluid Dynamics (CFD) modeling based methodology has been adopted to validate the hypothesis. Predictions using Realizable k-ε, Reynolds Stress Model (RSM), and Large Eddy Simulation Wall Adopting Local Eddy viscosity (LES-WALE) turbulence models has revealed that LES-WALE matched better with the experimental observations. The experimental data included overall performance parameters and detailed observations of axial and tangential velocity profiles across the hydrocyclone. The validated CFD model and the methodology was then used to predict the behavior of the proposed designs. They established that the modifications held promise in reducing the bypass with additional benefits of sharper separation curve and finer D50.

Comparison of eddy viscosity turbulence models and stereoscopic PIV measurements for a flow past rectangular-winglet pair vortex generator

Vortex generators (VG) are widely used in enhancing the heat transfer coefficients in heat exchangers due to the development of longitudinal and transverse vortices. Therefore, understanding the development of these vortices has a high importance for the design and optimization of heat exchangers. When using numerical simulations, the choice of an appropriate turbulence model that can better predict the flow structure downstream a VG is fundamental. In the present study, three-dimensional numerical simulations, with two different commonly used eddy viscosity turbulence models, are performed for channel flow fitted with rectangular-winglet pairs (RWP) vortex generators. The numerical results are compared to experimental data obtained by stereoscopic particle image velocimetry (SPIV). The shear-stress transport (SST) κ-ω model and the re-normalization-group (RNG) κ-ε model are used for modeling turbulence. Validation is conducted by comparing the flow structure topology and velocity field obtained from numerical simulations to those obtained using the SPIV method. It is found that the SST κ-ω model is better than the RNG κ-ε turbulence model in predicting the flow characteristics downstream the RWP.

Assessment of a Two-Equation Eddy-Viscosity Turbulence Model in Crosswind Simulation of a Heavy Ground Vehicle

Assessment of a Two-Equation Eddy-Viscosity Turbulence Model in Crosswind Simulation of a Heavy Ground Vehicle

Numerical study of two-phase flow dynamics and atomization in an open-type liquid swirl injector

The three-dimensional, two-phase flow dynamics and underlying physics in an open-type liquid swirl injector are investigated using numerical simulations. The basis for this study is a validated multiphase flow solver, interFoam, in OpenFOAM. Turbulence closure is achieved by means of LES with a one-equation eddy-viscosity turbulence model. A volume-of-fluid method is used for tracking the interface between the gas and liquid phases. The detailed spatio-temporal evolution of the flow field is explored systematically, including the liquid surface wave motion and liquid film characteristics within the injector, the helical air core, and the formation and atomization of the liquid spray cone downstream of the injector. The spectral content of the pressure field is also examined, to reveal the characteristic frequencies and feedback mechanisms of gas-liquid interactions.

Wall-Modeled Large Eddy Simulations of Axial Turbine Rim Sealing

Abstract This paper presents wall-modeled large-eddy simulations (WMLES) of a chute-type turbine rim seal. Configurations with an axisymmetric annulus flow and with nozzle guide vanes fitted (but without rotor blades) are considered. The passive scalar concentration solution and WMLES are validated against available data in the literature for uniform convection and a rotor–stator cavity flow. The WMLES approach is shown to be effective, giving significant improvements over an eddy viscosity turbulence model, in prediction of rim seal effectiveness compared to research rig measurements. WMLES requires considerably less computational time than wall-resolved LES, and has the potential for extension to engine conditions. All WMLES solutions show rotating inertial waves in the chute seal. Good agreement between WMLES and measurements for sealing effectiveness in the configuration without vanes is found. For cases with vanes fitted, the WMLES simulation shows less ingestion than the measurements, and possible reasons are discussed.

Coupling Two Correlation-Based Transition Models to the Eddy Viscosity Turbulence Model

When dealing with flows at moderate Reynolds numbers, the laminar and transition regions are a key component of the flow solution. In applications such as wind turbines and unmanned aerial vehicles, an accurate prediction of the aerodynamic forces requires accounting for these effects. In Reynolds-averaged Navier–Stokes simulations, this is done by incorporating transition models because commonly used turbulence models are unable to predict a significant extent of laminar flow. In this paper, we present and study the coupling of the local correlation-based and transition models with the (KSKL) turbulence model, and we compare it to the original formulation using the shear-stress transport (SST) turbulence model. The coupling of the models is calibrated for the flow over a flat plate and subsequently tested for the flow around the S809 and NLF(1)-0416 airfoils, as well as around a 6:1 prolate spheroid. The results show that the combination of the transition model with the KSKL turbulence model leads to a reduction of the numerical uncertainty (discretization errors) when compared to its application with the SST model. On the other hand, the combination of the KSKL model with the transition model leads to the sharpest transition of the four combinations tested.

Steady and Unsteady Asymmetric Flow Regions Past an Axisymmetric Body

The theoretical solution of the flowfield past an axisymmetric body flying at a high angle of attack at subsonic flow conditions is a challenging problem since it entails large areas of boundary-layer separation and a complex vortex sheet structure. At high angles of attack, the flow is asymmetric and shows a dependence on the orientation angle, provided the body surface has sufficient roughness. Regarding theoretical simulations based on the unsteady Reynolds-averaged Navier–Stokes equations, eddy-viscosity turbulence models fail to simulate the unsteady flow structure in the rear zone of the body, yielding sectional side forces far different from those measured in experiments. Solutions obtained in this work by using Reynolds stress turbulence models combined with scale-adaptive simulation past an ogive-cylinder configuration show their ability to reproduce the essential features of the unsteady flow in the rear body. The model appears to be a suitable tool to investigate the complexities of this type of flow.

Experimental and numerical investigation of three-dimensional open channel with simulated partial ice-covers

This paper presents both experimental measurements and three-dimensional (3D) numerical simulations of turbulent flow in open channels with simulated partial ice-covers. The experiments were conducted with a particle image velocimetry system while the simulations were performed with five eddy-viscosity and second-moment closure turbulence models. Four coverage ratios based on the channel width were examined in each case: a reference fully open channel and 25%, 50% and 75% partially covered channels. The results showed that the influence of the partial ice-covers and secondary currents near the sidewall dramatically altered the distributions of the mean velocity, Reynolds stresses and turbulence production across the channel. Based on the 3D simulations, it was shown that the modifications to the turbulence quantities were largely influenced by strong counter-rotating secondary circulations in the core of the partially covered channels and eight smaller secondary cells at the corners. The core secondary circulations interact with adjacent corner cells to form a dynamic link between the open water and ice-covered sections of the channel.

An Accurate Model for Prediction of Turbulent Frictional Pressure Loss of Power-Law Fluids in Eccentric Geometries

SummaryThe effect of axial flow of power-law drilling fluids on frictional pressure loss under turbulent conditions in eccentric annuli is investigated. A numerical model is developed to simulate the flow of Newtonian and power-law fluids for eccentric annular geometries. A turbulent eddy-viscosity model based on the mixing-length approach is proposed, where a damping constant as a function of flow parameters is presented to account for the near-wall effects. Numerical results including the velocity profile, eddy viscosity, and friction factors are compared with various sets of experimental data for Newtonian and power-law fluids in concentric and eccentric annular configurations with diameter ratios of 0.2 to 0.8. The simulation results are also compared with a numerical study and two approximate models in the literature. The results of extensive simulation scenarios are used to obtain a novel correlation for estimation of the frictional pressure loss in eccentric annuli under turbulent conditions. Two new correlations are also presented to estimate the maximum axial velocity in the wide and narrow sections of eccentric geometries.

The continuous eddy simulation capability of velocity and scalar probability density function equations for turbulent flows

There is a well developed spectrum of computational methods for turbulent flows: modeling methods such as Reynolds-averaged Navier–Stokes (RANS) and probability density function (PDF) methods, and resolving methods such as large eddy simulation (LES) and filtered density function (FDF) methods. However, the applicability of RANS/PDF methods is limited to flows that do not essentially require the inclusion of resolved motion, and LES/FDF methods are well applicable if resolution criteria can be satisfied [which is often infeasible for very high Reynolds number (Re) wall-bounded turbulent flows]. A highly attractive approach to overcome these problems is the design of hybrid RANS–LES methods, which can be used with varying amounts of resolved and modeled motions. However, this approach faces the problem to ensure communication and balancing of resolved and modeled motions. A well working solution to this problem was presented recently for non-homogeneous flows with respect to velocity two-equation eddy viscosity turbulence models. Exact analytical results regarding the extension of these methods to velocity and passive scalar PDF/FDF methods and their implied RANS/LES equations are presented here. The latter matters with respect to the justification of the theoretical basis of new hybrid methods (realizability) and the availability of a hierarchy of simple and advanced simulation methods (including passive scalar transport). Based on the continuous mode redistribution mechanism, the new simulation methods are capable of providing reliable predictions of very high Re turbulent flows, which cannot be accomplished by using existing techniques.

Numerical investigation of marine propeller underwater radiated noise using acoustic analogy Part 2: The influence of eddy viscosity turbulence models

The present study focuses on the impact of eddy viscosity turbulence models on the benchmark INSEAN E779A marine propeller hydroacoustic performance under non-cavitating and open water conditions. In the numerical calculations, Realisable k-epsilon (k-ε), k-ω Shear Stress Transport (k-ω SST) and Spalart-Allmaras turbulence models, which are widely used in hydrodynamic fields, are selected. Hydroacoustic performance of the model propeller is predicted with the porous FW-H formulation coupled with Reynolds-averaged Navier Stokes (RANS) solver. This study aims to show the effects of different turbulence models on marine propeller hydroacoustic performance at high and low blade loading conditions both in the near and far-fields. The numerical results show that the underwater radiated noise (URN) levels, which are predicted by using different eddy viscosity turbulence models together with the porous FW-H formulation, are found to be similar at low blade loading conditions. The reason behind this similarity is due to the analogous wake structure and hydrodynamic field. However, when the propeller loading is high, the propeller's wake loses its stability; hence, the coherent vortex structures break-up and evolve into the far-field of the propeller's slipstream. The instability process of the propeller's wake is predicted in a different manner by eddy viscosity turbulence models, and these differences cause dissimilar prediction of the URN in the far-field. Consequently, the underwater pressure field is considerably affected by the instability of the vortex structures (as a non-linear noise source) for far-field noise estimations. As a result, vortex instability in the propeller's slipstream might be the main noise source of the URN for far-field noise estimations under non-cavitating and high blade loading conditions.