Second-moment Closure Model Research Articles

Application of Extended Eddy-viscosity and Elliptic-Relaxation Approaches to Turbulent Convective Flow in a Partially Divided Cavity

The paper reports on the numerical turbulence model in predicting mass, momentum and heat transfer in a partially divided cavity heated from the side using buoyancy-extended eddy-viscosity and elliptic relaxation approach with the algebraic expressions for the Reynold stress tensor and turbulent heat flux vector. The CDS (central differencing scheme) and LUDS (linear upwind differencing scheme) were used as the discretization method and the governing equations were solved using the finite volume method and Navier-Stokes solver. Validation of the model has been carried out by experimental data of convective flow in the cavity as well as by numerical data DNS (direct numerical simulation). The model agrees very well with the experiment and DNS and it is also able to demonstrate the performance which is comparable to that of the previous advanced second-moment closure model (SMC) in the literature. The results show that the model is suitable for use in simulations of the turbulent convective flow in a cavity with partition and it has the potential to be applied to more complex cavities and a wide range of turbulence levels.

Nonhydrostatic simulation of internal lee wave-induced turbulence mixing: A comparative study of second-moment closure mixing schemes for an idealized marginal sea sill topography

To further understand the processes of wave-turbulence interactions under nonhydrostatic conditions and to gain insight into the selection of second-moment closure models in subsequent nonhydrostatic ocean models, a newly developed nonhydrostatic ocean model is coupled with the General Ocean Turbulence Model (GOTM) to form a robust version of the Marine Environment Research and Forecasting Model (MERF). On this basis, internal lee wave simulation with various turbulent mixing schemes is investigated for an idealized two-dimensional supercritical sea slope topography with high-resolution (100 m). First, the LES-type simulation based on a 3D Smagorinsky diffusivity scheme can reproduce well the characteristics of lee waves, serving as a benchmark for comparison. Second, the Mellor and Yamada (MY) scheme and the quasi-equilibrium scheme are able to effectively simulate the effects of internal waves on large-scale structures, while small-scale dynamic processes are partially suppressed by turbulent mixing. However, the K-ε model and the one-equation model further suppress the small-scale dynamic processes and weaken the propagation of internal lee waves due to overly strong turbulence mixing. Finally, the generation of a lee wave changes the instantaneous temperature field, and the use of the second-moment closure models converts more energy into irreversible mixing. Enhancing the model resolution can slightly improve the accuracy of the simulation in exchange for paying considerable computation.

On an Improved Second‐Moment Closure Model for Langmuir Turbulence Conditions and Its Application

AbstractRecently, a k‐ω second‐moment closure (SMC) model including the Langmuir turbulence effects was proposed by Yu et al. (2018, https://doi.org/10.1029/2018jc013878), however, the equations for determining the stability functions in it are very complicated. In this study, the equations of the stability functions are derived in more detail and a new explicit version is proposed. In the meantime, a new constant cω4 = 0.15 is introduced into the turbulent frequency transport equation to manifest the role of the shear generating term caused by the Stokes drift. And then the performance of the new SMC model is investigated by one‐dimensional Papa Ocean Station simulation and three‐dimensional global climate model simulation. The results show that the use of the new SMC model produces significant changes in the results of the ocean surface boundary layer simulations at the Papa Ocean Station, especially for the summer and autumn sea surface temperature (SST) simulations, and for the mixed layer depth (MLD) and mixed layer temperature (MLT) in the mixed layer deepening process. In the three‐dimensional simulation, the new SMC model resulted in a decrease of more than 34% in the annual root mean square error of SST in the northern extratropical region compared to the non‐LT effects model. The simulated MLD for tropical regions in winter and summer has also improved by 61.9% and 53.6%, respectively. The effect of the new SMC model on the MLT is mainly found in the regions beyond the tropical in summer and the tropical and northern extratropical regions in winter.

Second Moment Closure Modeling and Direct Numerical Simulation of Stratified Shear Layers

AbstractBuoyant shear layers encountered in many engineering and environmental applications have been studied by researchers for decades. Often, these flows have high Reynolds and Richardson numbers, which leads to significant/intractable space–time resolution requirements for direct numerical simulation (DNS) or large eddy simulation (LES). On the other hand, many of the important physical mechanisms, such as stress anisotropy, wake stabilization, and regime transition, inherently render eddy viscosity-based Reynolds-averaged Navier–Stokes (RANS) modeling inappropriate. Accordingly, we pursue second-moment closure (SMC), i.e., full Reynolds stress/flux/variance modeling, for moderate Reynolds number nonstratified, and stratified shear layers for which DNS is possible. A range of submodel complexity is pursued for the diffusion of stresses, density fluxes and variance, pressure strain and scrambling, and dissipation. These submodels are evaluated in terms of how well they are represented by DNS in comparison to the exact Reynolds-averaged terms, and how well they impact the accuracy of full RANS closure. For the nonstratified case, SMC model predicts the shear layer growth rate and Reynolds shear stress profiles accurately. Stress anisotropy and budgets are captured only qualitatively. Comparing DNS of exact and modeled terms, inconsistencies in model performance and assumptions are observed, including inaccurate prediction of individual statistics, non-negligible pressure diffusion, and dissipation anisotropy. For the stratified case, shear layer and gradient Richardson number growth rates, and stress, flux and variance decay rates, are captured with less accuracy than corresponding flow parameters in the nonstratified case. These studies lead to several recommendations for model improvement.

A new K-profile parameterization for the ocean surface boundary layer under realistic forcing conditions

In this study, we present a new parameterization for the enhancement of vertical mixing brought by the inclusion of the Stokes drift for the turbulent mixing schemes in ocean circulation models. The new scheme (KPP-LT) uses the K-Profile Parameterization (Large et al., 1994) as a template, and attempts to include the effect of the penetration decay scale of the Stokes drift (δ) and the misalignment between the wind stress and Stokes drift (θww). The effect of the wind–wave angle of misalignment is guided by a set of idealized Large Eddy Simulations (LES) and the Langmuir Turbulence (LT) parameterization is developed based on LES of the ocean surface boundary layer at Ocean Weather Station Papa, for a period of 20 days under observed atmospheric and oceanic conditions. The KPP-LT model is implemented in the Navy Coastal Ocean Model (NCOM) and compared to in situ oceanographic measurements, LES and other Second Moment Closure (SMC) schemes available in NCOM, namely the model of Kantha and Clayson (2004) and Harcourt (2013, 2015). Comparisons with temperature observations suggest better performance of the KPP-LT model over SMC models within the boundary layer, which are supported by comparisons of inertially averaged eddy viscosity profiles estimated from LES.

Lateral edge effects on heat/mass transfer on a finite width surface within a turbulent boundary layer

Numerical simulations of the local heat/mass transfer on a finite width surface within a turbulent boundary layer are presented. Different approaches to the RANS modelling of the turbulent heat/mass flux are compared to Large Eddy Simulations (LES). Mass transfer experiments conducted with the naphthalene sublimation technique are used as validation. The isotropic eddy viscosity model, Simple Gradient Diffusion Hypothesis (SGDH), is shown to underestimate the span-wise effects. Its anisotropic extension, Generalized Gradient Diffusion Hypothesis (GGDH), improves the prediction, but still does not account for near-wall contribution in strongly dissimilar velocity and temperature/concentration fields, even in combination with a wall-sensitive second-moment closure model such as the Elliptic Blending Reynolds Stress Model (EB-RSM). A more complete turbulent heat flux model based on the elliptic blending approach, the Elliptic Blending GGDH (EB-GGDH) presents very good agreement with LES and with the experiments, confirming the need for more advanced turbulent heat flux modelling in applications with strong three-dimensional effects.

Impact of Langmuir Turbulence on the Thermal Response of the Ocean Surface Mixed Layer to Supertyphoon Haitang (2005)

AbstractLangmuir turbulence (LT) due to the Craik–Leibovich vortex force had a clear impact on the thermal response of the ocean mixed layer to Supertyphoon Haitang (2005) east of the Luzon Strait. This impact is investigated using a 3D wave–current coupled framework consisting of the Princeton Ocean Model with the generalized coordinate system (POMgcs) and the Simulating Waves Nearshore (SWAN) wave model. The Coriolis–Stokes forcing (CSF), the Craik–Leibovich vortex forcing (CLVF), and the second-moment closure model of LT developed by Harcourt are introduced into the circulation model. The coupled system is able to reproduce the upper-ocean temperature and surface mixed layer depth reasonably well during the forced stage of the supertyphoon. The typhoon-induced “cold suction” and “heat pump” processes are significantly affected by LT. Local LT mixing strengthened the sea surface cooling by more than 0.5°C in most typhoon-affected regions. Besides LT, Lagrangian advection of temperature also modulates the SST cooling, inducing a negative (positive) SST difference in the vicinity of the typhoon center (outside of the cooling region). In addition, CLVF has the same order of magnitude as the horizontal advection in the typhoon-induced strong-vorticity region. While the geostrophy is broken down during the forced stage of Haitang, CLVF can help establish and maintain typhoon-induced quasigeostrophy during and after the typhoon. Finally, the effect of LT on the countergradient turbulent flux under the supertyphoon is discussed.

Experimental and numerical investigation of developing turbulent flow over a wavy wall in a horizontal channel

Turbulent flow over a wavy bottom wall in a horizontal channel is investigated by experimental and numerical methods. The ratio between wave length and wave amplitude is 10. This work assesses the predictive accuracy of the seven turbulence models and provides an experimental benchmark dataset suitable for numerical validation in both the developing and fully periodic regions of the wavy wall flow. The experiments are conducted using a particle image velocimetry system at a Reynolds number of 10700. The influences of the recirculation region and the shear layer region on the flow mean quantities are studied experimentally. Three Reynolds stresses (streamwise, wall-normal, and shear) are examined to assess the development of the turbulence quantities along the wavy channel. There are significant differences between the flow characteristics at the first wave compared to others. Flow periodicity is found at Wave 8. Computational fluid dynamics simulations are performed to predict the turbulent flow using four eddy viscosity turbulence models: standard k-epsilon, Realizable k-epsilon, standard k-omega, and SST; and three Second Moment Closure (SMC) turbulence models: LRR-IP, LPS, and SMC-omega. The standard k-epsilon, Realizable k-epsilon, and LPS models have the best overall agreement compared to the experiments. The eddy viscosity models predict similar results for the mean velocity and recirculation location. The LPS and SMC-omega models are also in good agreement with experimental data for the mean velocity. The wall treatment is shown to be critically important in the capability of the model to predict the flow separation. The results indicate no notable benefit of the SMC models compared to the eddy viscosity models in capability of predicting the mean flow and the separation and re-attachment locations.

An Improved Second-Moment Closure Model of Langmuir Turbulence

AbstractA prior second-moment closure (SMC) model of Langmuir turbulence in the upper ocean is modified by introduction of inhomogeneous pressure–strain rate and pressure–scalar gradient closures that are similar to the high Reynolds number, near-wall treatments for solid wall boundaries. This repairs several near-surface defects in the algebraic Reynolds stress model (ARSM) of the prior SMC by redirecting Craik–Leibovich (CL) vortex force production of turbulent kinetic energy out of the surface-normal vertical component and into a horizontal one, with an associated reduction in near-surface CL production of vertical momentum flux. A surface-proximity function introduces a new closure parameter that is tuned to previous results from large-eddy simulations (LES), and a numerical SMC model based on stability functions from the new ARSM produces improved comparisons with mean profiles of momentum and TKE components from steady-state LES results forced by aligned wind and waves. An examination of higher-order quasi-homogeneous closures and a numerical simulation of Langmuir turbulence away from the boundaries both show the near-surface inhomogeneous closure to be both necessary for consistency and preferable for simplicity.

On Near-Wall Treatment in (U)RANS-Based Closure Models

The present work is concerned with computational evaluation of a recently formulated near-wall relationship providing the value of the dissipation rate e of the kinetic energy of turbulence k through its exact dependence on the Taylor microscale λ: e = 10νk/λ 2, (Jakirlic and Jovanovic, J. Fluid Mech. 656:530–539, 2010). Dissipation rate determination benefits from the asymptotic behavior of the Taylor microscale resulting in its linear variation in terms of the wall distance (λ ∝ y) being valid throughout entire viscous sublayer. Accordingly, it can be applied as a unified near-wall treatment in all computational frameworks relying on a RANS-based model of turbulence (including also hybrid LES/RANS schemes) independent of modeling level—both main modeling concepts eddy-viscosity and Reynolds stress models can be employed. Presently, the feasibility of the proposed formulation was demonstrated by applying a conventional near-wall second-moment closure model based on the homogeneous dissipation rate e h ( ${\varepsilon_h =\varepsilon -0.5\partial \left( {{\nu \partial k}/ {\partial x_j }} \right)} / {\partial x_j }$ ; Jakirlic and Hanjalic, J. Fluid Mech. 539:139–166, 2002) and its instability-sensitive version, modeled in terms of the inverse turbulent time scale ω h (ω h = e h /k; Maduta and Jakirlic, 2011), to a fully-developed channel flow with both flat walls and periodic hill-shaped constrictions mounted on the bottom wall in a Reynolds number range. The latter configuration is subjected to boundary layer separation from a continuous curved wall. The influence of the near-wall resolution lowering with respect to the location of the wall-closest computational node, coarsened even up to the viscous sublayer edge situated at $y_P^+ \approx 5$ in equilibrium flows, is analyzed. The results obtained follow closely those pertinent to the conventional near-wall integration with the wall-next node positioned at $y_P^+ \le 0.5$ .

A Second-Moment Closure Model of Langmuir Turbulence

Abstract The Reynolds stress equation is modified to include the Craik–Leibovich vortex force, arising from the interaction of the phase-averaged surface wave Stokes drift with upper-ocean turbulence. An algebraic second-moment closure of the Reynolds stress equation yields an algebraic Reynolds stress model (ARSM) that requires a component of the vertical momentum flux to be directed down the gradient of the Stokes drift, in addition to the conventional component down the gradient of the ensemble-averaged Eulerian velocity. For vertical and horizontal component fluctuations, the momentum flux must be closed using the form , where the coefficient is generally distinct from the eddy viscosity or eddy diffusivity . Rational expressions for the stability functions , , and are derived for use in second-moment closure models where the turbulent velocity and length scales are dynamically modeled by prognostic equations for and . The resulting second-moment closure (SMC) includes the significant effects of the vortex force in the stability functions, in addition to source terms contributing to the and equations. Additional changes are made to the way in which is limited by proximity to boundaries or by stratification. The new SMC model is tuned to, and compared with, a suite of steady-state large-eddy simulation (LES) solutions representing a wide range of oceanic wind and wave forcing conditions. Comparisons with LES show the modified SMC captures important processes of Langmuir turbulence, but not without notable defects that may limit model generality.

Experimental and computational study of the flow induced by a plasma actuator

A complementary experimental and computational study of the flow field evoked by a plasma actuator mounted on a flat plate was in focus of the present work. The main objective of the experimental investigation was the determination of the vector force imparted by the plasma actuator to the fluid flow. The force distribution was presently extracted from the Navier–Stokes equations directly by feeding them with the velocity field measured by a PIV technique. Assuming a steady-in-mean, two-dimensional flow with zero-pressure gradient, the imbalance between the convective term and the momentum equation’s right-hand-side terms reveals the desired resulting force. This force-distribution database was used afterwards as the source term in the momentum equation. Furthermore, an empirical model formulation for the volume-force determination parameterized by the underlying PIV-based model is derived. The model is tested within the RANS framework in order to predict a wall jet-like flow induced by a plasma actuator. The Reynolds equations are closed by a near-wall second-moment closure model based on the homogeneous dissipation rate of the kinetic energy of turbulence. The computationally obtained velocity field is analysed along with the experimental data focussing on the wall jet flow region in proximity of the plasma actuator. For comparison purposes, different existing phenomenological models were applied to evaluate the new model’s accuracy. The comparative analysis of all applied models demonstrates the strength of the new empirical model, particularly within the plasma domain. In addition, the presently formulated empirical model was applied to the flow in a three-dimensional diffuser whose inflow was modulated by a pair of streamwise vortices generated by the present plasma actuator. The direct comparison with existing experimental data of Grundmann et al. (2011) demonstrated that the specific decrease of the diffuser pressure corresponding to the continuous forcing was predicted correctly.

On the Performance of Various Reynolds Stress Models in Resolving Non-equilibrium Features of Turbulent In-cylinder Engine Flows

In highly transient turbulent flows, the energy cascade and related dissipation rate of energy are key factors which must be modeled precisely to obtain the accurate computational predictions. The flow in diesel engines specifically during compression stroke is quite transient, so most commonly used eddy viscosity based turbulence models fail to predict the transitional characteristics of these types of flow. This paper focuses on performance appraisal of three versions of Reynolds stress turbulence models in resolving non-equilibrium features and transitional characteristics of turbulent in-cylinder engine flows. Results indicate that although these turbulence models give the same prediction of averaged quantities of turbulent flows (i.e. mean flow kinetic energy), their results are totally different in calculating non-equilibrium features and the turbulent length scales. According to calculated results, incompressible Launder–Reece–Rodi and Naot second-moment closure models give unreal estimations of the turbulent integral length scale during compression stroke, while the modified Launder–Reece–Rodi model predictions have more similarity with physical trends.

Diapycnal Transport and Mixing Efficiency in Stratified Boundary Layers near Sloping Topography

Abstract The interaction of shear, stratification, and turbulence in boundary layers on sloping topography is investigated with the help of an idealized theoretical model, assuming uniform bottom slope and homogeneity in the upslope direction. It is shown theoretically that the irreversible vertical buoyancy flux generated in the boundary layer is directly proportional to the molecular destruction rate of small-scale buoyancy variance, which can be inferred, for example, from microstructure observations. Dimensional analysis of the equations shows that, for harmonic boundary layer forcing and no rotation, the problem is governed by three nondimensional parameters (slope angle, roughness number, and ratio of forcing and buoyancy frequencies). Solution of the equations with a second-moment closure model for the turbulent fluxes reveals the periodic generation of gravitationally unstable boundary layers during upslope flow, consistent with available observations. Investigation of the nondimensional parameter space with the help of this model illustrates a systematic increase of the bulk mixing efficiencies for (i) steep slopes and (ii) low-frequency forcing. Except for very steep slopes, mixing efficiencies are substantially smaller than the classical value of Γ = 0.2.

Application of a second-moment closure model to mixing processes involving multicomponent miscible fluids

A second-moment closure model is proposed for describing turbulence quantities in flows where large density fluctuations can arise due to mixing between different density fluids, in addition to compressibility or temperature effects. The turbulence closures used in this study are an extension of those proposed by Besnard et al., which include closures for the turbulence mass flux and density-specific-volume covariance. Current engineering models developed to capture these extended effects due to density variations are scarce and/or greatly simplified. In the present model, the density effects are included and the results are compared to direct numerical simulations (DNS) and experimental data for flow instabilities with low to moderate density differences. The quantities compared include Reynolds stresses, turbulent mass flux, mixture density, density-specific-volume covariance, turbulent length scale, turbulence and material mix time scales, turbulence dissipation, and mix widths and/or growth rates. These comparisons are made within the framework of three very different classes of flows: shear-driven, Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Overall, reasonable agreement is seen between experiments, DNS, and averaging models.

Wingtip Vortex Simulation by Using Nonequilibrium Eddy Viscosity Model

W INGTIP vortex is an important subject in fluid mechanics, as it is involved inmany practical engineering problems that can be found, for example, in [1–4]. Thus, it has long been the subject of numerous experimental and/or numerical investigations. Chigier and Corsiglia [5] pioneered the experimental study of thewingtip vortex. Theymeasured, by using hot-wire anemometry, thewingtip vortex of a square-tipped rectangular wing up to a 12c downstream distance. The maximum axial velocity at the vortex core at x0=c 0:25 was 1:4U1. They showed that themaximum tangential velocity increases with the angle of attack, while the vortex core radius remains unchanged. Green [6] and Green and Acosta [7] used double-pulsed holography to measure the instantaneous velocity distribution in trailing vortices of a round-tipped rectangular wing. At a 10 deg angle of attack, the axial velocity at the vortex core was 1:6U1 at x0=c 2:0. Chow et al. [8] used hot-wire and seven-hole probes to measure the flow over and immediately downstream of a roundtipped rectangular wing with a NACA0012 section at Rec 4:6 10 and a 10 deg angle of attack. The measurement data of this study will be used as reference data in this work. Numerical studies began to appear in the late 1980s. Srinivasan et al. [9] used a thin-layer Navier–Stokes solver with the Baldwin– Lomax turbulence model [10] to examine the influence of the tip-cap shape and tip planform on the wingtip vortex. Their results showed good agreement with the experimental data of Spivey and Moorehouse [11] for the surface pressures, except for the surface pressure suction peak induced by the vortex in the vicinity of the wingtip. The computed vorticity contours of the tip vortex, however, were rather poor in the sense that theywere highly distorted andmore diffusive with the downstream distance. Dacles-Mariani and Zilliac [12] studied, both numerically and experimentally, the wingtip vortex in the nearfield in conjunctionwithChowet al.’s experimental study [8]. The Baldwin–Barth turbulence model [13] was used with the modified production term suggested by Spalart through private communication [12] to reduce the eddy viscosity at the vortex core. The predicted velocity profile was in good agreement with the measured data, but the core static pressure was underpredicted up to 25%at the downstreamboundary. Craft et al. [14] recently performed a numerical simulation of the experiment of Chow et al. [8]. Three turbulence models, the eddy viscosity model, the nonlinear eddy viscosity model of Suga [15], and the two-component-limit (TCL) second-moment closure model [16], were adopted in their simulation. The results obtained using linear and nonlinear eddy viscosity models showed a far too rapid decay of the vortex core. Only the TCL model successfully reproduced the principal features of the vortex flowfield. The TCL model is a Reynolds stress transport model, which is much more complicated for application to practical flows than the two-equation models in spite of its distinguished merits. It is well known that conventional two-equation models perform rather poorly for flows that are not in near-equilibrium flow. To remedy this situation, Yoshizawa et al. [17] suggested a nonequilibrium eddy viscosity model, which works well for swirling (or strong vorticity) flows. The motivation of the present work is to investigate whether this nonequilibrium model performs well for wingtip vortex flow in comparison with the TCL model, which is a first attempt to the authors’ knowledge. It is found that the model performs almost as good as the TCL model; hence, it is strongly recommended for practical flow computations of wingtip vortex flow.

Calculations of heat transfer in stagnation flow regions by using second-moment closure models in conjunction with the new general wall treatment

The general wall treatment adopted and extended in this work, was previously derived for the eddy viscosity model based on the elliptic relaxation approach. The main target is to provide the wall approach which combines the integration up to the wall with wall functions, and with that, to provide the optimum solution for any computational mesh. In this paper, such general wall treatment is further adjusted in order to be efficiently used with the Second-Moment Closure (SMC) models as well. The results show that the near-wall SMC can be efficiently used in conjunction with the general wall treatment.

Implicit algebraic model for predicting turbulent heat flux in film cooling flow

AbstractThe present study addresses a new effort to improve the prediction of turbulent heat flux in the film cooling flow by applying the implicit algebraic flux (IAF) model of Rogers et al. A three‐dimensional symmetry case is investigated using a film hole length‐to‐diameter ratio of 1.75 and an injection angle of 35∘. The low Reynolds number second moment closure (SMC) model with a wall‐reflection term is employed for simulating the turbulent flow field right up to the wall. Results obtained from the IAF model are compared with two other algebraic turbulent heat flux models, namely, the simple eddy diffusivity (SED) with a constant turbulent Prandtl number and the generalized gradient diffusion hypothesis (GGDH). Comparisons of the turbulent heat flux components calculated by these models show that the major difference appears in the streamwise turbulent heat flux. These models demonstrate a significant effect on the prediction of film cooling effectiveness. The SED model with a constant prescribed value for the turbulent Prandtl number fails to predict the cooling air spreading in the lateral direction while by employing the GGDH and IAF models, the spreading of the cooling air and the decay of the effectiveness in the core region are reasonably predicted. A combination of the SMC and IAF models for simulating the turbulent flow and heat transfer is capable of predicting the streamwise and lateral film cooling effectiveness in very good agreement with the available experimental data. Copyright © 2009 John Wiley & Sons, Ltd.

A stress transport equation model for simulating turbulence at any mesh resolution

Prior work has demonstrated the effectiveness of using two-equation closures as the basis for universal, self-adapting turbulence models that are effective at any mesh resolution (Perot and Gadebusch in Phys. Fluids 19:115105, 2007). In order to demonstrate the broad applicability of the fundamental approach, the same behavior is now demonstrated for a second-moment closure (SMC). The SMC has the advantage over the earlier two-equation universal closure of being more accurate in the coarse mesh limit and of having a natural mechanism for backscattering energy from the modeled to the resolved turbulent fluctuations. The mathematical explanation for why Reynolds averaged (RANS) transport equation closures are applicable at any mesh resolution, including the large eddy simulation (LES) regime, is reviewed. It is demonstrated that for the problem of isotropic decaying turbulence, the SMC model produces good predictions at any mesh resolution and with arbitrary initial conditions. In addition, it is shown that the proposed model automatically adapts to the mesh resolution provided. The self-adaptive nature of the method is clearly observed when different initial conditions are used. It is shown that classic RANS models (often thought to produce steady and smooth solutions) can produce three-dimensional, unsteady, and chaotic solutions when generalized correctly and when provided with sufficient mesh resolution. The implications of these observations on the fundamental theories of RANS and LES turbulence modeling are discussed.

Near-wall, Reynolds-stress model calculations of transonic flow configurations relevant to aircraft aerodynamics

The present work focuses on the application of two near-wall, wall-normal free, second-moment closure (SMC) models in the RANS ( Reynolds-Averaged Navier–Stokes) framework in computing the (compressible) transonic flow past aircraft configurations and their elements (airfoils and wings). The flow geometries considered in this work include the transonic RAE 2822 profiles (cases 9 and 10), the ONERA M6 wing and the DLR-ALVAST wing-body configuration. The model results are analysed and discussed in conjunction with an available experimental database and the results of two widely used eddy-viscosity-based models, the one-equation Spalart–Allmaras model [Spalart, P.R., Allmaras, S.R., 1994. A one-equation turbulence model for aerodynamic flows. La Recherche Aérospatiale 1, 5–21] and the two-equation k– ω model of Wilcox [Wilcox, D.C., 1988. Reassessment of the scale-determining equation for advanced turbulence models. AIAA Journal 26, 1299–1310]. The SMC predictions show encouraging results with respect to the shock position, shock-affected flow structure and the strength of the wing-tip vortex.