Two-equation Eddy-viscosity Models Research Articles

Effects of Reynolds Number on the Wake Characteristics of a Notchback Ahmed Body

Abstract This paper investigates the effects of Reynolds number on the wake characteristics of a notchback Ahmed body with effective backlight angle, βe=17.8 deg. The Reynolds number based on the body height was varied from 5×103 to 5×104. Prior to the Reynolds number investigation, a Reynolds-averaged Navier–Stokes (RANS) model assessment was performed using nine turbulence models consisting of one- and two-equation eddy-viscosity models and second moment closure models. The standard Spalart–Allmaras model was the only model that accurately predicted the asymmetric time-averaged wake topology, as reported in previous studies, for the βe=17.8 deg notchback Ahmed body at Re=5×104. The drag coefficient decreased with increasing Reynolds number, while the lift coefficient remained constant for Re≥1×104. The wake structure exhibited three regimes: symmetric (Re≤1×104), transitionally asymmetric (1×104<Re≤3.5×104), and fully asymmetric (Re>3.5×104) states. The wake asymmetry was attributed to an imbalance in entrainment from the sides and asymmetric separation from the roof and the C-pillars of the body. The tilting and stretching terms in the vorticity transport equation were used to provide insight into the source of asymmetry in the vorticity field around the body.

Assessment of solving the RANS equations with two-equation eddy-viscosity models using high-order accurate discretization

A challenge that faces high-order methods for industrial applications generally is turbulence modeling at high Reynolds numbers. Large eddy simulation is studied extensively for high-order methods, nevertheless, its computational cost is enormous for industrial applications. The hybrid LES/RANS compromises the computational cost and the modeling error, however, solving the Reynolds-averaged Navier-Stokes equations is a resilient task for high-order methods, due to the non-smooth profiles of the turbulence quantities. Taking into account the complexity with high-order methods and the fairly large modeling errors of the RANS modeling, low-order methods has proved to be more pragmatic. For instance, in the discontinuous Galerkin framework, the polynomial approximation for these quantities leads to large oscillations that obstructs the non-linear solver. To use the high-order methods for industrial cases it is essential to have reliable implementations of two-equation turbulence models in RANS formulations. In this paper, a RANS discretization based on hybridizable discontinuous Galerkin is presented for the standard, TNT, BSL and SST versions of the k−ω model for applications at Reynolds numbers up to 109. A particular focus is given to the treatment of the specific rate of turbulence dissipation ω in the high-order framework. The complexity increases with these types of models as the value of ω goes to infinity at solid walls. Additionally, with minor modifications to the numerical flux definition, the turbulence model formulation can be solved by discontinuous Galerkin method as well. The results show remarkable improvements regarding the error magnitudes and non-linear convergence rate (iterative error) compared to second-order finite volume based solvers.

Thermohydraulic analysis of covalent and noncovalent functionalized graphene nanoplatelets in circular tube fitted with turbulators

Covalent and non-covalent nanofluids were tested inside a circular tube fitted with twisted tape inserts with 45° and 90° helix angles. Reynolds number was 7000 ≤ Re ≤ 17,000, and thermophysical properties were assessed at 308 K. The physical model was solved numerically via a two-equation eddy-viscosity model (SST k-omega turbulence). GNPs-SDBS@DW and GNPs-COOH@DW nanofluids with concentrations (0.025 wt.%, 0.05 wt.% and 0.1 wt.%) were considered in this study. The twisted pipes' walls were heated under a constant temperature of 330 K. The current study considered six parameters: outlet temperature, heat transfer coefficient, average Nusselt number, friction factor, pressure loss, and performance evaluation criterion. In both cases (45° and 90° helix angles), GNPs-SDBS@DW nanofluids presented higher thermohydraulic performance than GNPs-COOH@DW and increased by increasing the mass fractions such as 1.17 for 0.025 wt.%, 1.19 for 0.05 wt.% and 1.26 for 0.1 wt.%. Meanwhile, in both cases (45° and 90° helix angles), the value of thermohydraulic performance using GNPs-COOH@DW was 1.02 for 0.025 wt.%, 1.05 for 0.05 wt.% and 1.02 for 0.1 wt.%.

A comprehensive model for analysis of turbulent natural convection flow in rectangular and trapezoidal enclosures at high Rayleigh numbers > 109

Turbulent natural convection is dominant mechanism of heat transfer in enclosed cavities. The simulation of transport phenomena in different enclosures is of paramount importance in industrial design and operation. The present research aimed to find the proper model for prediction of heat transfer mechanisms in rectangular and trapezoidal enclosures filled with air (Pr 0.71) in wide range of Five Reynolds averaged Navier-Stokes equations (SA, standard k-ɛ, RNG k-ɛ, standard k-ω, SST k-ω) were solved numerically with finite volume method. The simulation results were fitted to the experimental data so as to reach the proper model for analysis of turbulent natural convection. It was concluded that the kε and kω models can well describe the heat transfer at low and high Ra numbers, respectively, for both enclosures. For prediction of transport phenomena in the entire range of Ra, it is proposed to develop two-equation eddy-viscosity models.

Numerical investigation of wave-induced loads on an offshore monopile using a viscous and a potential-flow solver

Wave-induced loads on an offshore monopile were investigated using a viscous-flow solver and a potential-flow solver. Considered were only two steep regular wave trains, with the same height but different periods. The potential-flow approach relied on a weakly nonlinear time-domain solver (i.e., Green function). The viscous-flow solver used three solution schemes, namely, an Euler scheme that neglected the flow viscosity, a Laminar scheme that numerically integrated the full Navier–Stokes equations without a model accounting for the fluctuating portion of the velocity field, and a Reynolds-averaged Navier–Stokes scheme that modeled turbulent flow via a two-equation eddy-viscosity model. Numerical uncertainties of viscous-flow simulations were quantified, and computed results were validated against model test measurements. Overall, the main characteristics of wave-induced forces and bending moments were well predicted by all adopted numerical schemes. In terms of higher harmonic components, predictions only from the viscous-flow solver compared favorably to the experimental measurements, including the local free surface elevations, higher harmonic forces/moments, and the secondary wave load cycles. The effect of strong nonlinear motion of free surface on the wave-induced total loading was secondary, and the contribution from the associated viscous and turbulent effects was also very limited. Nevertheless, they attribute to the generation of higher harmonic forces/moments as well as the secondary load cycle. In addition, the effects of wave steepness on the global, first- and higher harmonic forces were addressed.

Assessment of Solving the Rans Equations with Two-Equation Eddy-Viscosity Models Using High-Order Accurate Discretization

Assessment of Solving the Rans Equations with Two-Equation Eddy-Viscosity Models Using High-Order Accurate Discretization

Validation of transition modeling techniques for a simplified fuselage configuration

A Reynolds-averaged Navier-Stokes solver has been equipped with two different transition prediction and modeling techniques for automatic transition prediction on general three-dimensional geometrical configurations. The first technique is a streamline-based approach that applies an automated local linear stability code, the eN-method and a simplified two-N-factor strategy and is applicable with any kind of turbulence model. The second technique is a transition transport equation approach and uses the γ-Reθ,t model. The standard γ-Reθ,t model has been extended by a modeling approach that captures transition due to crossflow instabilities. The extended model can be applied to three-dimensional configuration exhibiting crossflow transition whereas the original γ-Reθ,t model only captures streamwise transition mechanisms. The paper focuses on a three-dimensional inclined 6:1 prolate spheroid which can be considered as a simplified fuselage configuration. For a number of years this configuration has become a standard basic three-dimensional test case for transition prediction approaches and has been used in a number of international workshops and research activities. The focus of the paper is the validation of the two transition modeling approaches for six different angles of attack using two different turbulence models, a standard two-equation eddy-viscosity model and a differential Reynolds-stress model. The simulation results from the two approaches have been compared against each other and to the available experimental data. The comparisons highlight as many qualitative and quantitative similarities and agreements as they reveal quantitative differences and deviations of specific details.

Assessment of turbulence models for single phase CFD computations of a liquid-liquid hydrocyclone using OpenFOAM

ABSTRACT Hydrocyclones are widely used in industry and CFD has been used to compute them. Reynolds stress turbulence models (RSM), which are computationally costly and oftentimes hard to converge, are often recommended in these computations. The present work has selected a liquid-liquid separation hydrocyclone for which single-phase experimental tangential and axial velocity profiles are available. CFD has been employed to test simpler turbulence models than the RSM and results have been compared with experimental data. The turbulence models assessed in the present work were: standard k-ε, standard k-ε with a curvature correction term, RNG k-ε, realizable k-ε, k-ω, SST, a two-time-scale linear eddy viscosity model, nonlinear quadratic and cubic k-ε eddy viscosity models and the Gibson and Launder and LRR Reynolds stress models. Computations have been carried out with OpenFOAM 2.2.2. Results using the Gibson and Launder turbulence model have been compared to some obtained with Ansys Fluent and these were in agreement. Results have shown that all turbulence models, apart from the RSM, returned basically the same tangential velocity profiles as the standard model. All turbulence models have failed in predicting axial velocity. Assessment of the Reynolds stresses has indicated that the internal flow field in hydrocyclones might be shear dominant and that the Reynolds shear stress component is the most relevant to correctly predict tangential velocity. Geometric proportions of hydrocyclones may affect significantly the intensity of rotational and streamline curvature effects. Two-equation eddy-viscosity models are likely to be able to attend such condition, since appropriate levels of eddy viscosity are predicted at free and forced vortexes regions, however further investigation is still needed.

Progress in the second-moment closure for bubbly flow based on direct numerical simulation data

Data from direct numerical simulations (DNS) of disperse bubbly flow in an upward vertical channel are used to develop a new second-moment closure for bubble-induced turbulence (BIT) in the Euler–Euler framework. The closure is an extension of a BIT model originally proposed by Ma et al. (Phys. Rev. Fluids, vol. 2, 2017, 034301) for two-equation eddy-viscosity models and focuses on the core region of the channel, where the interfacial term and dissipation term are in balance. Particular attention in this study is given to the treatment of the pressure–strain term for bubbly flows and the form of the interfacial term to account for BIT. For the latter, the concept of an effective BIT source is proposed, which leads to a significant simplification of the modelling work for both the pressure–strain correlation and the interfacial term itself. The anisotropy of bubbly flow is analysed with the aid of the anisotropy-invariant map obtained from the DNS data, and a parameter governing this issue is established. The complete second-moment closure is tested against reference data for different bubbly channel flows and a case of a bubble column. The agreement achieved with the DNS data is very good and the performance of the new model is better than obtained with the standard procedure. Furthermore, the model is shown to be robust and to fulfil the requirements of realizability.

A study of thermo-fluid characteristics of Czochralski melt using rotation and curvature corrected Partially-Averaged Navier-Stokes (PANS) turbulence models

A Czochralski melt flow encounters the effects of anisotropic body forces owing to the system rotation as well as significant streamline curvature due to inherent vortical structures and flow past curved surfaces. Two-equation eddy-viscosity models lack the ability to capture the flow anisotropy and curvature effects. Here we present the first study on the thermo-fluid characteristics of Czochralski melt using rotation and streamline curvature corrected Partially-Averaged Navier-Stokes (PANS) adaptations of the low-Re k-ε and SST k-ω models. The paper presents physical insights to the new PANS turbulence modelling approach highlighting improvements in the predicting capability of PANS models with the incorporation of rotation and curvature corrections. The PANS models showed good agreement with the results available in the literature (both experimental and computational). In addition for the PANS low-Re k-ε model it was observed that the prediction of the typical Czochralski melt flow structure in terms of shape, relative size and orientation of the characteristic cells improved with rotation and curvature corrections. Further thermal fluctuations and vortex cores also reduced in the melt in the case of the PANS low-Re k-ε model showing stabilization of flow. The corresponding rotation and curvature modification to the PANS SST k-ω model corrected the flow dynamics from a buoyancy dominated to rotationally driven along with an increase in the thermal fluctuations and vortex cores in the Czochralski melt resulting in a destabilization of the melt flow.

Towards the accurate prediction of the turbulent flow and heat transfer in low-Prandtl fluids

In the numerical simulation of turbulent heat transfer, a reliable representation of the turbulent flow field is a prerequisite in order to obtain an accurate prediction of the thermal field. In the framework of RANS modelling approach, classical two-equation eddy-viscosity models present intrinsic limitations for applications characterised by complex flow fields where significant turbulence anisotropy can be expected. In this respect, differential Reynolds stress models represent the natural choice for dealing with such highly anisotropic flows. On the other hand, the modelling of the turbulent heat flux term almost universally relies on the so-called Reynolds analogy, due to its simplicity and robustness. Nevertheless, this approach presents several well-known limitations, especially when dealing with low-Prandtl fluids. In this context, algebraic heat flux models are regarded as a promising approach to overcome the shortcomings of the Reynolds analogy. In particular, an implicit algebraic heat flux closure, called as AHFM-NRG, has been proposed for applications involving low-Prandtl fluids. In its original formulation, the algebraic turbulent heat flux closure was coupled with a low-Reynolds linear k-ε model for the closure of the Reynolds stress tensor. In the present work, the applicability of the AHFM-NRG model is extended to an advanced low-Reynolds differential Reynolds stress model. This new version of the model is validated against different planar channel flows at unity and low-Prandtl number; successively, the model is applied to two relatively complex flows, i.e. a planar impinging jet and a bare rod bundle configuration. It is shown that the coupling of the AHFM-NRG with an advanced closure for the Reynolds stresses gives encouraging results for these cases, where an accurate prediction of the anisotropy in the flow field results in a noticeable improvement in the prediction of the turbulent heat transfer.

Numerical and experimental analyses of the characteristics of burning jets of base bleed ignited in the atmospheric environment

ABSTRACTThe characteristics of burning jets of magnesium/polytetrafluoroethylene (MT) pyrotechnic base bleed igniter in the atmosphere are studied by a high-speed camera (HSC) combined with the infrared thermal imager (ITI) for MT igniters with different mass ratios. A 3D steady combustion model is established based on the simplified three-step chemical kinetic mechanism. Finite volume method (FVM) is applied to the numerical simulation of the time-averaged combustion field using a RANS two-equation eddy viscosity model coupled with the eddy dissipation concept (EDC) model. The results indicate that the highest temperature region in the combustion field is located above the potential core of each single jet, corresponding to the most intense chemical reaction region, whereas the maximum velocity region is located on the perimeter side of the potential core. In the converging region, the momentum, heat, and components Mg, MgF2, and C2 transfer and diffuse rapidly from each burning jet to the centerline of the combustion field, except that the component C2F4 is consumed completely in and around the potential core. However, in the combined region, the temperature, velocity, and concentration of each component all reach the maximum on the central axis of the combustion field. Simultaneously, the similarity of cross sections is shown. An increase in the concentration of Mg in the range of 0.45–0.61 occurs, and the reaction rate and reaction heat decrease, so that the temperature and velocity of the combustion flow decay and the gradient are also reduced. In addition, the mass fractions of C2F4, MgF2, and C2 decrease.

Comparison of turbulent models in the case of a constricted tube

The validation of a proper solution is an indispensable phase of every numerical simulation. Nowadays, many turbulent models are available, whose application leads to slightly different solution of flow behaviour depending on the boundary conditions of a specific problem. It is essential to select the proper turbulence model appropriate for the given situation. The aim of this study is to select the most suitable two-equation eddy-viscosity model, which can be further used during calculations of airflow in human airways. For this purpose, geometry of a constricted tube with well-documented experimental measurements was chosen. The flow in the constricted tube was calculated using Spallart-Almaras, k-omega, k-epsilon and SST model approach using commercial software. The outcome of the comparison is a choice of the suitable model which is capable of simulating the transition of the boundary layer from laminar to turbulent flow. This transition typically arises in the upper part of the respiratory system, where the airways are constricted, specifically in the area, where the oral cavity continues through the glottis to trachea. The simulations were performed in a commercial solver Star-CCM+.

Two-equation eddy viscosity models based on the Monin–Obukhov similarity theory

The present study is devoted for the development of two equation Reynolds-Averaged Navier–Stokes (RANS) closures for computational fluid dynamics (CFD) modelling of the atmospheric boundary layer. By using the inflow conditions based on the Monin–Obukhov similarity theory, the closure coefficients of the proposed models are derived from the analytical solutions of simplified turbulent transport equations. Modifications are conducted for three different turbulence models, which are standard k−ϵ,k−ω and Re-Normalisation Group (RNG) k−ϵ. Numerical experiments are performed for the homogeneous atmospheric boundary layer and the results are compared with the theoretical values in comparison to the standard versions of modified turbulence models. Developed models are implemented to open source CFD toolbox OpenFOAM.

A gas-kinetic scheme coupled with SST model for turbulent flows

In order to simulate the compressible and incompressible turbulent flows, a gas-kinetic scheme (GKS) based on the Bhatnagar–Gross–Krook (BGK) model coupled with the shear stress transport (SST) two-equation turbulence model is developed. The SST model is a two-equation eddy-viscosity model based on the k−ω and k−ε models, which is one of the most common turbulence models and widely used in Reynolds averaged Navier–Stokes (RANS) modeling for turbulent flows. In this study, we implement GKS–SST coupling model by (a) solving the GKS and SST models in vertex-based finite volume method on hybrid grids; (b) incorporating the SST model into the GKS based on the eddy viscosity hypothesis and using the eddy viscosity to modify the collision time in gas-kinetic scheme; (c) using a modified Venkatakrishnan limiter for hybrid and highly stretched grids during the initial reconstruction stage; (d) applying the boundary conditions adopted from vertex-based solvers for Navier–Stokes equations in present GKS solver. The original gas-kinetic scheme has been proved to be an accurate and effective approach for incompressible and compressible laminar flows, and the SST turbulence model is incorporated here for the turbulent flow. The eddy viscosity at the cell centers is obtained by solving SST model, and then the eddy viscosity on the cell interface can be interpolated from cell centers around. Numerical experiments performed on high Reynolds number turbulent flows around the 2D zero pressure gradient flat plate and a RAE2822 airfoil demonstrate the applicability of the GKS–SST model presented in this study for simulations of high Reynolds number turbulent flows.

V2-F 난류 모델의 터보기계 유동 해석 적용

Since a turbomachine has complex flow characteristics, which are caused by adverse pressure gradient and high speed motion, an elaborate turbulence model is needed to accurately predict the flow. Some turbulence models such as an algebraic or a two-equation eddy viscosity model have been used for in-house RANS-code, but it is difficult to obtain good result for several complex flows. In this study, Durbin‘s V2-F turbulence model, which has been known for better prediction for severe flow separation, is applied to T-Flow. It was validated for simple cases such as channel and compressor cascade, and its applicability to turbomachinery was shown by analyzing internal flow of a single rotor. As a result, the V2-F turbulence model shows better blade surface pressure distribution than the one-and-two equation turbulence model. Corresponding Author, jhbaek@postech.ac.kr 2016 The Korean Society of Mechanical Engineers C

Comparison of turbulence closures for optimized active control

Active flow control strategies, such as oscillatory blowing/suction, have proved their efficiency to modify flow characteristics for various purposes (e.g. skin friction reduction, separation delay, etc.) in case of rather simple configurations. To extend this approach to industrial cases, the simulation of a large number of devices at real scale and the optimization of parameters are required. In this perspective, numerical simulations based on Reynolds-Averaged Navier–Stokes (RANS) equations seem to be the most appropriate framework, despite the well known limitations of turbulence closures in the context of unsteady separated flows. Thus, the objective of this work is to evaluate the ability of RANS models for the optimization of control devices and compare the results obtained using different turbulence closures. In this perspective, an incompressible RANS solver for unstructured grids is coupled with a surrogate-based global optimizer. The resulting tool is applied to derive an optimal actuation, based on an oscillatory blowing/suction device, for a set of turbulence closures including two-equation eddy-viscosity models and an explicit algebraic Reynolds stress model. As test-case, the reduction of the separation length for a backward facing step is targeted. Results are finally compared and analyzed, in terms of flow characteristics and optimal actuation parameters found.

On numerical modelling of conjugate turbulent natural convection and radiation in a differentially heated cavity

Turbulent natural convection with and without radiation transfer in two-dimensional (2D) and three-dimensional (3D) air-filled differentially heated cavities is numerically investigated using various RANS (Reynolds Averaged Navier–Stokes) turbulence models and the Discrete Ordinates radiation model. Five different two-equation eddy-viscosity models including the standard k–ε model, the renormalization group (RNG) k–ε model, the realisable k–ε model, the standard k–ω model and the shear-stress transport (SST) k–ω model are selected for comparison. Qualitative and quantitative data are presented to demonstrate the effects of three-dimensionality, radiation transfer and the thermal boundary conditions on the horizontal surfaces on the numerical solution of the convective flow in the cavity. The present numerical results are compared against published experimental and direct numerical simulation data. It is found that the predicted thermal stratification in the interior of the cavity is improved when the simulation is extended from 2D to 3D and when the effect of radiation transfer is accounted for. The discrepancy with regard to the interior stratification between the experiment and numerical simulation is mainly caused by the negligence of radiation transfer. The thermal boundary conditions on the horizontal surfaces also have a significant impact on the numerical solution, especially when the radiation transfer is not accounted for. Further, the present results show that all the RANS models are capable of capturing the main features of the flow and the overall performance of these turbulence models in terms of predicting time-averaged quantities is acceptable. It is found that the variation of the numerical results obtained with the three k–ε models is very small, whereas the discrepancy between the two k–ω models is significant. The SST k–ω model has the best overall performance and the standard k–ω model has the worst overall performance.

On turbulence criteria and model requirements for numerical simulation of turbulent flows above offshore helidecks

Turbulence criteria for CFD of helideck flows in the Norwegian Norsok standard are reviewed and discussed. It is argued that the turbulence energy has benefits compared to the standard deviation of the vertical velocity component when used in criteria for turbulence in CFD. Revised expressions for the criteria are proposed, based on the turbulence energy. On the background of Norsok Standard C-004, requirements for turbulence modeling for helideck flow simulations are discussed. It is demonstrated that a requirement alone for using a Reynolds stress equation model, with no other specific requirements to the modeling, will not ensure improved CFD results compared to two-equation eddy-viscosity models. In addition, some issues of the turbulence terminology in Norsok Standard C-004 are discussed.

Solid-liquid mixing analysis in stirred vessels

AbstractThis review evaluates computational fluid dynamic applications to analyze solid suspension quality in stirred vessels. Most researchers typically employ either Eulerian-Eulerian or Eulerian-Lagrangian approach to investigate multiphase flow in stirred vessels. With sufficient computational resources, the E-L approach simulates flow structures with higher spatial resolution for dispersed multiphase flows. Common turbulence models such as the two-equation eddy-viscosity models (