Eddy-viscosity Turbulence Model Research Articles

Performance assessment of a non-linear eddy-viscosity turbulence model applied to the anisotropic wake flow of a low-pressure turbine blade

The wake flow produced by a low-pressure turbine blade is modeled using a non-linear eddy-viscosity turbulence model. The theoretical benefit of using a non-linear eddy-viscosity model is strongly related to the capability of resolving highly anisotropic flows in contrast to the linear turbulence models, which are unable to correctly predict anisotropy. The main aim of the present work is to practically assess the performance of the model, by examining its ability to capture the anisotropic behavior of the wake-flow, mainly focusing on the measured velocity and Reynolds-stress distributions and to provide accurate results for the turbulent kinetic energy balance terms. Additionally, the contribution of each term of its non-linear constitutive expression for the Reynolds stresses is also investigated, in order to examine their direct effect on the modeling of the wake flow. The assessment is based on the experimental measurements that have been carried-out by the same group in Thessaloniki, Sideridis et al. (2011). The computational results show that the non-linear eddy viscosity model is capable to predict, with a good accuracy, all the flow and turbulence parameters while it is easy to program it in a computer code thus meeting the expectations of its originators.

Manufactured solutions for steady-flow Reynolds-averaged Navier–Stokes solvers

This paper presents manufactured solutions (MS's) for code verification of incompressible flow solvers based on the Reynolds-averaged Navier–Stokes (RANS) equations. The proposed solutions mimic statistically steady, two-dimensional or three-dimensional near-wall turbulent flows in a simple domain (rectangle or rectangular box) at a given Reynolds number. The proposed analytical functions cover the mean flow quantities and the dependent variables of several eddy-viscosity turbulence models. Namely, the undamped eddy-viscosity of the Spalart and Allmaras and Menter one-equations models, from the one (SKL) and two-equation (KSKL) models proposed by Menter, the turbulence kinetic energy and the turbulence frequency included in two-equation k − ω models. A basic flow field resembling a turbulent flat plate flow is constructed with the turbulence quantities defined from ‘automatic wall functions’ that are supposed to reproduce more or less the normal behaviour of these variables. Alternative flow fields are constructed superposing a perturbation flow field that creates a ‘recirculation zone’. However, the near-wall solution of the basic flow is kept to avoid zero friction at the wall. Three-dimensional MS's are obtained from the blending of the basic two-dimensional MS's in the transverse direction. All flow fields satisfy mass conservation, i.e. mean velocity fields are divergence-free. The source functions required for the balancing of momentum and turbulence quantities transport equations and all the dependent variables and their derivatives are available in Fortran 90 modules.

Assessing the predictive capabilities of isotropic, eddy viscosity Reynolds‐averaged turbulence models in a natural‐like meandering channel

The predictive capabilities of an isotropic, eddy viscosity turbulence model for closing the unsteady Reynolds‐averaged Navier‐Stokes (RANS) equations are systematically investigated by simulating turbulent flow through a field‐scale meandering channel and comparing the computed results with the large‐eddy simulation (LES) of the same flow recently reported by Kang and Sotiropoulos (2011). To facilitate the comparison of the two turbulence models, both RANS simulation and LES are carried on exactly the same grid with the same numerical method. The comparisons show that while the RANS model captures the curvature‐driven secondary flow within the bend, it fails completely to predict other key flow features in the channel, which are predicted by the LES and also observed in flow visualization experiments. These features include the inner and outer bank shear layers, the outer bank secondary cell, and the inner bank horizontal recirculation zone. By analyzing the results of the LES, we conclusively show that flow features not predicted by the RANS calculation are located in regions of the flow with high levels of turbulence anisotropy. The extent of these regions and, consequently, the degree of disagreement between the RANS and LES predictions are shown to depend on the stream geometry and the flow rate. Our results underscore the major challenges confronting the computationally expedient, isotropic RANS models, which are widely used today in three‐dimensional hydrodynamic and morphodynamic simulations.

Application of smart flap for race car wings

A pressure-based implicit procedure is due to solve Navier-Stokes equations. A non-orthogonal mesh with collocated finite volume formulation is used to simulate flow around the smart and conventional flaps of airfoil under the ground effect. Cantilever beam with uniformly varying load with roller support at the free end is considered for smart flaps. The boundedness criteria for this procedure are determined by a normalised variable diagram (NVD) scheme. The procedure incorporates the k – e eddy-viscosity turbulence model. The method is first validated against experimental data. Then, the SIMPLE algorithm is applied for turbulent aerodynamic flows around airfoil with smart and conventional flaps for different attack angle, flap angle and ground clearance where the results of two flaps are compared. It is found that the pressure coefficient distribution in a smart flap is smoother than a conventional one. The comparisons show that the quality of the solution is considerable.

Bayesian uncertainty quantification applied to RANS turbulence models

A Bayesian uncertainty quantification approach is developed and applied to RANS turbulence models of fully-developed channel flow. The approach aims to capture uncertainty due to both uncertain parameters and model inadequacy. Parameter uncertainty is represented by treating the parameters of the turbulence model as random variables. To capture model uncertainty, four stochastic extensions of four eddy viscosity turbulence models are developed. The sixteen coupled models are calibrated using DNS data according to Bayes' theorem, producing posterior probability density functions. In addition, the competing models are compared in terms of two items: posterior plausibility and predictions of a quantity of interest. The posterior plausibility indicates which model is preferred by the data according to Bayes' theorem, while the predictions allow assessment of how strongly the model differences impact the quantity of interest. Results for the channel flow case show that both the stochastic model and the turbulence model affect the predicted quantity of interest. The posterior plausibility favors an inhomogeneous stochastic model coupled with the Chien k-ϵ model. After calibration with data at Reτ = 944 and Reτ = 2003, this model gives a prediction of the centerline velocity at Reτ = 5000 with uncertainty of approximately ± 4%.

A new turbulence model for separated flows

In this study, the classical eddy viscosity turbulence models are analysed from a new standpoint. Based on this standpoint, a new, two-equation model that aims at separated flows is presented. This new turbulence model is directly derived from the standard k−ϵ and k−ω models and tested against flow in a plane, asymmetric diffuser and against NACA 4412 aerofoil flow. The results of numerical simulation of the two different types of flow compared to experimental data show that the new model is good at prediction of separated flows. The results are very encouraging, but further verification and extensive application of this new model are needed.

Evaluation of Turbulence Models Using Direct Numerical and Large-Eddy Simulation Data

The performance of some commonly used eddy-viscosity turbulence models has been evaluated using direct numerical simulation (DNS) and large-eddy simulation (LES) data. Two configurations have been tested, a two-dimensional boundary layer undergoing pressure-driven separation, and a square duct. The DNS and LES were used to assess the k−ε, ζ−f, k−ω, and Spalart–Allmaras models. For the two-dimensional separated boundary layer, anisotropic effects are not significant and the eddy-viscosity assumption works well. However, the near-wall treatment used in k−ε models was found to have a critical effect on the predictive accuracy of the model (and, in particular, of separation and reattachment points). None of the wall treatments tested resulted in accurate prediction of the flow field. Better results were obtained with models that do not require special treatment in the inner layer (ζ−f, k−ω, and Spalart–Allmaras models). For the square duct calculation, only a nonlinear constitutive relation was found to be able to capture the secondary flow, giving results in agreement with the data. Linear models had significant error.

Aerodynamics of smart flap under ground effect

Aerodynamic characteristics of two-dimensional smart flap under the ground effect have been assessed by a numerical simulation. In this process, a pressure-based implicit procedure to solve Navier–Stokes equations on a nonorthogonal mesh with collocated finite volume formulation is used. The boundedness criteria for this procedure are determined from the Normalized Variable Diagram (NVD) scheme. The procedure incorporates the k – ε eddy–viscosity turbulence model. Cantilever beam with uniformly varying load with roller support at the free end is considered for the configuration of the smart flap. The method is first validated against experimental data. Then, the algorithm is applied for turbulent aerodynamic flows around airfoil with smart and conventional flaps for different attack angle, flap angle and ground clearance where the results of two flaps are compared. The comparisons show that the quality of the solution is considerable.

ICONE19-44132 SIX DIFFERENT TURBULENCE MODELS AND EXPERIMENTS COMPARISONS ON THERMAL MIXING PHENOMENON IN A TEE PIPING

The fluctuating stresses on a piping system in reactor cooling systems of nuclear power plants are potential causes of thermal fatigue failures. These stresses are generated due to temperature fluctuations in regions where hot and cold flows are intensively mixed together. The main focus of this study shows that the application of eddy-viscosity (EVM) and Reynolds stress (RSM) turbulence models to solving flow and heat transfer in mixing piping. The present paper describes three Reynolds-Stress Models(BSL-RSM, ω-RSM, SSG-RSM)and three Eddy-Viscosity Models(SST, k-ε, k-ω) simulation data of temperature fluctuations in a mixing piping compared with results from experimental data proposed by the Laboratory for Nuclear Energy Systems, Institute for Energy Technology, ETHZ, Zurich, Switzerland. The experimental measurements ( concentration of de-ionized water)have been carried out by the use of the 16×16 electrode WMS on the basis of difference in liquid electrical conductivities. To verify the analogy between electrical conductivity of de-ionized water and temperature of water, the inlet temperatures of the hot and cold water are set to 80℃ and 15℃ separately in the simulation process. The computational results are in qualitative good agreement with experimental data and the correlation between electrical conductivity of de-ionized water and temperature of water is good. The purpose of this paper is to analyze which turbulent model is suit for the mixing phenomenon.

Quadratic and cubic eddy-viscosity models in turbulent supercavitating flow computation

Quadratic and cubic non-linear eddy-viscosity turbulence models (NLEVM) with low Reynolds number (Re) correction were presented to provide better description of anisotropic turbulence stresses in the numerical prediction of supercavitating flows, which are accompanied with large density ratio and large-scaled swirling flow structures. The applications of the NLEVM were carried out through a self-developed cavitation codes, coupled with a cavitation model based on the transport equation of liquid phase. These NLEVM were verified capable of capturing more accurate macroscopic shape and hydrodynamic property of supercavity by the benchmark problems of supercavities over simple objects. Finally, the cubic NLEVM was further applied to the numerical prediction of supercavitating flow around a complex submerged vehicle. The corresponding cavitation behaviors were explored in detail to provide beneficial experience for further research.

Numerical aspects of including wall roughness effects in the SST k– ω eddy-viscosity turbulence model

This paper presents a study on the numerical requirements of including sand-grain wall roughness effects in the SST k– ω eddy-viscosity model. Three implementations are tried: two retain the direct application of the no-slip condition at the wall, the third is based on a wall function formulation. In the first two options the roughness effect is introduced via a change in wall boundary conditions, either for ω only or for k and ω. The two-dimensional flow along a finite flat plate is adopted to assess the numerical accuracy of the three approaches. The computed results are also compared with semi-empirical formula available in the open literature. It is demonstrated that sand-grain roughness effects can be simulated with acceptable numerical uncertainties with all three options, but the numerical settings to achieve that goal differ significantly.

Performance assessment limits in transonic 3D turbine stage blade rows using a mixing-plane approach

Numerical computation of gas turbine flowfields demands high computing power. In the present work, we present a detailed analysis of 3D computations for a highly loaded transonic blade and for a gas turbine stage. Comparison between experimental results and numerical computations reveals the precision limits of current modeling assumptions. Computations are performed using a time-marching approach coupled with a mixing-plane model for the exchange of flowfields between stator and rotor domains. Eddy viscosity turbulence models are applied to compute the flow with and without wall functions. Limitations in performance assessment are presented regarding the level of detail used for the geometry definition, the mixing-plane approach, and the near wall turbulence model employed.

Numerical study of the cavitating flows over underwater vehicle with large angle of attack

A Homogenous-Equilibrium-Model based cavitation code was developed to numerically analyze the three-dimensional cavitating flows over underwater vehicle navigating with large angle of attack. Rayleigh-Plesset equation based cavitation model was used together with non-linear eddy-viscosity turbulence model. The computed cavity shapes and pressure distributions along the vehicle body were found to generally accord with experimental results at different cavitation numbers and angles of attack. The forces acting on the vehicle body was studied qualitatively to explain why the body may get damaged during navigation. It was also discovered interestingly that, the variation trend of drag-force along with cavitation number at the conditions of large angle was completely opposite to that at zero angle.

Unsteady RANS simulations of flow around a bridge section

This paper presents the results of unsteady Reynolds-averaged Navier–Stokes (URANS) simulations of flow around a common bridge deck geometry. Computations are performed with a noncommercial unstructured flow solver using two-dimensional hybrid meshes with fine near-wall resolution. The influence of different simulation parameters (grid refinement, time-step size, turbulence modelling) is analyzed, in particular in order to obtain flow solutions independent of spatial and temporal discretization. Results given by a one-equation eddy-viscosity turbulence model and a two-equation explicit algebraic Reynolds stress model are compared. Despite the limits imposed by the URANS approach and the relatively inexpensive two-dimensional computations, satisfactory agreement is found with the experimentally measured forces and pressures. These simulations help to explain the discrepancy between the results of two wind-tunnel test campaigns and show the dramatic influence of non-perfectly sharp edges on the global flow field development. The capability of the numerical approach to capture complex Reynolds number effects is also discussed.

Numerical Study of Flow Past a Circular Cylinder Using Hybrid Turbulence Formulations

Two multiscale-type turbulence models are implemented in the PAB3D solver. The models are based on modifying Reynolds-averaged Navier―Stokes equations. The first scheme is a hybrid Reynolds-averaged Navier―Stokes and large eddy simulation model using the two-equation ke model with a Reynolds-averaged Navier―Stokes and large eddy simulation transition function dependent on grid spacing and the computed turbulence length scale. The second scheme is a modified version of the partially averaged Navier―Stokes model, where the unresolved kinetic energy parameter f k is allowed to vary as a function of grid spacing and the turbulence length scale. Solutions from these models are compared to Reynolds-averaged Navier―Stokes results and experimental data for a stationary and rotating cylinder. The parameter f k varies between zero and one and has the characteristic to be equal to one in the viscous sublayer, and when the Reynolds-averaged Navier―Stokes turbulent viscosity becomes smaller than the large eddy simulation viscosity. The formulation, usage methodology, and validation example are presented to demonstrate the enhancement of PAB3D's time-accurate and turbulence modeling capabilities. The models are compared to Reynolds-averaged Navier―Stokes results and experimental data for turbulent separated flows and laminar separated flows around stationary and rotating cylinders. For a stationary cylinder, the turbulent separated case is accurately simulated using the general two-equation ke turbulence model (eddy-viscosity model). PAB3D accurately predicts the drag coefficient C D , lift coefficient C L , and the Strouhal number St. The laminar separated case was a challenge for the Reynolds-averaged Navier―Stokes computation with an eddy-viscosity turbulence model. The Reynolds-averaged Navier―Stokes with large eddy simulation and partially averaged Navier―Stokes performed well and showed marked improvements over the Reynolds-averaged Navier―Stokes solution. The modified partially averaged Navier―Stokes model was the most accurate. For the rotating cylinder, the spin ratio varied from zero to one, and the partially averaged Navier―Stokes results were in good agreement with published experimental data. Reynolds-averaged Navier―Stokes with large eddy simulation and partially averaged Navier― Stokes capture both temporal and spatial fluctuations and produce large-scale structures that do not occur in the Reynolds-averaged Navier―Stokes simulation. The current results show promise for the capability of partially averaged Navier―Stokes in simulating unsteady and complex flow phenomena.

Experimental and numerical study of convection heat transfer of CO 2 at super-critical pressures during cooling in small vertical tube

Convection heat transfer of CO 2 at super-critical pressures during cooling in a vertical small tube with inner diameter of 2.00 mm was investigated experimentally and numerically. The local heat transfer coefficients were determined through a combination of experimental measurements and numerical simulations. This study investigated the effects of pressure, cooling water mass flow rate, CO 2 mass flow rate, CO 2 inlet temperature, flow direction, properties variation and buoyancy on convection heat transfer in small tube. The results show that the local heat transfer coefficients vary significantly along the tube when the CO 2 bulk temperatures are in the near-critical region. The increase of specific heat and turbulence kinetic energy due to the density variation leads to the increase of the local heat transfer coefficients for upward flow. The buoyancy effect induced by density variation leads to a different variation trend of the local heat transfer coefficients along the tube for upward and downward flows. The numerical simulations were conducted using several k–ε turbulence models including the RNG k–ε model with a two-layer near wall treatment and three low-Reynolds number eddy viscosity turbulence models. The simulations using the low-Reynolds number k–ε model due to Yang–Shih has been found to be able to reproduce the general features exhibited in the experiments, although with a relatively large overestimation of measured wall temperatures. A better understanding of the mechanism of properties variation and buoyancy effects on convection heat transfer of CO 2 at super-critical pressures in a vertical small tube during cooling has been developed based on the information generated by the simulation on the detailed flow and turbulence fields.

Explicit algebraic Reynolds stress and non-linear eddy-viscosity models

This article reviews explicit algebraic Reynolds stress models and other non-linear eddy-viscosity turbulence models utilised in the context of Reynolds-Averaged Navier-Stokes simulations of turbulent flows. Since the 1990s, these modelling classes have become important intermediate classes between the linear eddy viscosity models and full Reynolds stress transport models. The derivation of explicit algebraic Reynolds stress models from the Reynolds stress transport models, and the required simplifications are discussed. The most important simplification is the weak-equilibrium assumption. Properties of the basic weak-equilibrium assumption and its extended form are discussed. Differences between explicit solutions based on complete tensor representation and those based on reduced representation as well as other non-linear eddy-viscosity models are pointed out. The scale-determining models are also discussed briefly.

Prediction of Boundary Layer Transition Based on Modeling of Laminar Fluctuations Using RANS Approach

This article presents a linear eddy-viscosity turbulence model for predicting bypass and natural transition in boundary layers by using Reynolds-averaged Navier-Stokes (RANS) equations. The model includes three transport equations, separately, to compute laminar kinetic energy, turbulent kinetic energy, and dissipation rate in a flow field. It needs neither correlations of intermittency factors nor knowledge of the transition onset. Two transition tests are carried out: flat plate boundary layer under zero and non-zero pressure gradients with different freestream turbulence intensities, and transitional flow over a wind turbine blade at a chord Reynolds number of 3×106. Results are presented in terms of skin friction coefficients. Comparison with the experimental data from both tests evidences a good agreement there is between them.

Applications of URANS on predicting unsteady turbulent separated flows

Accurate prediction of unsteady separated turbulent flows remains one of the toughest tasks and a practical challenge for turbulence modeling. In this paper, a 2D flow past a circular cylinder at Reynolds number 3,900 is numerically investigated by using the technique of unsteady RANS (URANS). Some typical linear and nonlinear eddy viscosity turbulence models (LEVM and NLEVM) and a quadratic explicit algebraic stress model (EASM) are evaluated. Numerical results have shown that a high-performance cubic NLEVM, such as CLS, are superior to the others in simulating turbulent separated flows with unsteady vortex shedding.

A Three-Equation Eddy-Viscosity Model for Reynolds-Averaged Navier–Stokes Simulations of Transitional Flow

An eddy-viscosity turbulence model employing three additional transport equations is presented and applied to a number of transitional flow test cases. The model is based on the k-ω framework and represents a substantial refinement to a transition-sensitive model that has been previously documented in the open literature. The third transport equation is included to predict the magnitude of low-frequency velocity fluctuations in the pretransitional boundary layer that have been identified as the precursors to transition. The closure of model terms is based on a phenomenological (i.e., physics-based) rather than a purely empirical approach and the rationale for the forms of these terms is discussed. The model has been implemented into a commercial computational fluid dynamics code and applied to a number of relevant test cases, including flat plate boundary layers with and without applied pressure gradients, as well as a variety of airfoil test cases with different geometries, Reynolds numbers, freestream turbulence conditions, and angles of attack. The test cases demonstrate the ability of the model to successfully reproduce transitional flow behavior with a reasonable degree of accuracy, particularly in comparison with commonly used models that exhibit no capability of predicting laminar-to-turbulent boundary layer development. While it is impossible to resolve all of the complex features of transitional and turbulent flows with a relatively simple Reynolds-averaged modeling approach, the results shown here demonstrate that the new model can provide a useful and practical tool for engineers addressing the simulation and prediction of transitional flow behavior in fluid systems.