Extending the bounds of ‘steady’ RANS closures: Toward an instability-sensitive Reynolds stress model

The incapability of the conventional Unsteady RANS (Reynolds–Averaged Navier Stokes) models to adequately capture turbulence unsteadiness presents the prime motivation of the present work, which focuses on formulating an instability-sensitive, eddy-resolving turbulence model on the Second-Moment Closure level. The model scheme adopted, functioning as a ‘sub-scale’ model in the Unsteady RANS framework, represents a differential near-wall Reynolds stress model formulated in conjunction with the scale-supplying equation governing the homogeneous part of the inverse turbulent time scale ω_h (ω_h = ɛ_h/k). The latter equation was straightforwardly obtained from the model equation describing the dynamics of the homogeneous part of the total viscous dissipation rate ɛ, defined as ɛ_h = ɛ − 0.5ν∂²k/(∂x_j∂x_j) (Jakirlic and Hanjalic, 2002), by applying the derivation rules to the expression for ω_h. The model capability to account for vortex length and time scales variability was enabled through an additional term in the corresponding length-scale determining equation, providing a selective enhancement of its production, pertinent particularly to the highly unsteady separated shear layer region, modeled in terms of the von Karman length scale (comprising the second derivative of the velocity field) in line with the SAS (Scale-Adaptive Simulation) proposal (Menter and Egorov, 2010). The present model formulation, termed as SRANS model (Sensitized RANS), does not comprise any parameter depending explicitly on grid spacing. The predictive capabilities of the newly proposed length-scale determining model equation, solved in conjunction with Jakirlic and Hanjalic’s (2002) Reynolds stress model equation, are presently demonstrated by computing the flow configurations of increasing complexity featured by boundary layer separation from sharp-edged and continuous curved surfaces: backward-facing step flow, flow over a wall-mounted fence, flow over smoothly contoured periodically arranged hills and flow in a 3-D diffuser. The model performances are also assessed in capturing the natural decay of the homogeneous isotropic turbulence and the near-wall Reynolds stress anisotropy in a plane channel. In most cases considered the fluctuating velocity field was obtained starting from steady RANS results.     

Investigation of the sensitivity of turbulent closures and coupling of hybrid RANS‐LES models for predicting flow fields with separation and reattachment

Hybrid models have found widespread applications for simulation of wall‐bounded flows at high Reynolds numbers. Typically, these models employ Reynolds‐averaged Navier–Stokes (RANS) and large eddy simulation (LES) in the near‐body and off‐body regions, respectively. A number of coupling strategies between the RANS and LES regions have been proposed, tested, and applied in the literature with varying degree of success. Linear eddy‐viscosity models (LEVM) are often used for the closure of turbulent stress tensor in RANS and LES regions. LEVM incorrectly predicts the anisotropy of Reynolds normal stress at the RANS‐LES interface region. To overcome this issue, use of non‐linear eddy‐viscosity models (NLEVM) have started receiving attention. In this study, a generic non‐linear blended modeling framework for performing hybrid simulations is proposed. Flow over the periodic hills is used as the test case for model evaluation. This case is chosen due to complex flow physics with simplified geometry. Analysis of the simulations suggests that the non‐linear hybrid models show a better performance than linear hybrid models. It is also observed that the non‐linear closures are less sensitive to the RANS‐LES coupling and grid resolution. Copyright © 2016 John Wiley & Sons, Ltd.     

Non-zonal detached eddy simulation coupled with a steady RANS solver in the wall region

Xiao and Jenny (2012) proposed an interesting hybrid LES/RANS method in which they use two solvers and solve the RANS and LES equations in the entire computational domain. In the present work this method is simplified and used as a hybrid RANS-LES method, a wall-modeled LES. The two solvers are employed in the entire domain. Near the walls, the flow is governed by the steady RANS solver; drift terms are added to the DES equations to ensure that the time-averaged DES fields agree with the steady RANS field. Away from the walls, the flow is governed by the DES solver; in this region, the RANS field is set to the time-averaged LES field. The disadvantage of traditional DES models is that the RANS models in the near-wall region – which originally were developed and tuned for steady RANS – are used as URANS models where a large part of the turbulence is resolved. In the present method – where steady RANS is used in the near-wall region – the RANS turbulence models are used in a context for which they were developed. In standard DES methods, the near-wall accuracy can be degraded by the unsteady agitation coming from the LES region. It may in the present method be worth while to use an accurate, advanced RANS model. The EARSM model is used in the steady RANS solver. The new method is called NZ S-DES . It is found to substantially improve the predicting capability of the standard DES. A great advantage of the new model is that it is insensitive to the location of the RANS-LES interface.     

End-to-end differentiable learning of turbulence models from indirect observations

The emerging push of the differentiable programming paradigm in scientific computing is conducive to training deep learning turbulence models using indirect observations. This paper demonstrates the viability of this approach and presents an end-to-end differentiable framework for training deep neural networks to learn eddy viscosity models from indirect observations derived from the velocity and pressure fields. The framework consists of a Reynolds-averaged Navier–Stokes(RANS) solver and a neuralnetwork-represented turbulence model, each accompanied by its derivative computations. For computing the sensitivities of the indirect observations to the Reynolds stress field, we use the continuous adjoint equations for the RANS equations, while the gradient of the neural network is obtained via its built-in automatic differentiation capability. We demonstrate the ability of this approach to learn the true underlying turbulence closure when one exists by training models using synthetic velocity data from linear and nonlinear closures. We also train a linear eddy viscosity model using synthetic velocity measurements from direct numerical simulations of the Navier–Stokes equations for which no true underlying linear closure exists. The trained deep-neural-network turbulence model showed predictive capability on similar flows.     

On the simulation of the flow around a circular cylinder at Re=140,000

The flow around a circular cylinder at Reynolds number of 1.4 × 10⁵ is examined with Reynolds-Averaged Navier–Stokes equations (RANS) and Scale-Resolving Simulation (SRS) methods. Such problem is in the upper limit of the flow regime where turbulent transition occurs in the free shear-layers and so the flow dynamics is dominated by the spatial development of vortex-shedding structure, and in particular by the Kelvin–Helmholtz rollers and turbulence onset. The objectives of this investigation are threefold: (i) determine the aptitude of distinct RANS and SRS models to simulate the correct flow regime; (ii) compare the predictions of selected methods with available experimental measurements; and (iii) examine key modelling and flow features that contribute to the observed results. The evaluated models range from RANS supplemented with linear, transition, and non-linear turbulent viscosity closures, to hybrid and bridging SRS methods. Bridging computations are conducted at various constant degrees of physical resolution (range of resolved scales). The results illustrate the complexity of predicting the present flow problem. It is shown that RANS and SRS formulations modelling turbulence in boundary-layers with the selected linear turbulent viscosity closures lead to a premature onset of turbulence which alters the flow regime of the simulations. Although the transition and non-linear RANS closures can predict the correct flow regime, the outcome of this study indicates that solely the bridging model at constant physical resolution is able to achieve an accurate and physics-based prediction of the flow dynamics. Nonetheless, the necessary degree of physical resolution makes the numerical requisites of such computations demanding.     

A manufactured solution for a two-dimensional steady wall-bounded incompressible turbulent flow

This paper presents a manufactured solution (MS), resembling a two-dimensional, steady, wall-bounded, incompressible, turbulent flow for RANS codes verification. The specified flow field satisfies mass conservation, but requires additional source terms in the momentum equations. To also allow verification of the correct implementation of the turbulence models transport equations, the proposed MS exhibits most features of a true near-wall turbulent flow. The model is suited for testing six eddy-viscosity turbulence models: the one-equation models of Spalart and Allmaras and Menter; the standard two-equation k–ε model and the low-Reynolds version proposed by Chien; the TNT and BSL versions of the k–ω model.     

Application of the PITM Method Using Inlet Synthetic Turbulence Generation for the Simulation of the Turbulent Flow in a Small Axisymmetric Contraction

We investigate the turbulence modeling of second moment closure used both in RANS and PITM methodologies from a fundamental point of view and its capacity to predict the flow in a low turbulence wind tunnel of small axisymmetric contraction designed by Uberoi and Wallis. This flow presents a complex phenomenon in physics of fluid turbulence. The anisotropy ratio of the turbulent stresses τ ₁₁/τ ₂₂ initially close to 1.4 returns to unity through the contraction, but surprisingly, this ratio gradually increases to its pre-contraction value in the uniform section downstream the contraction. This point constitutes the interesting paradox of the Uberoi and Wallis experiment. We perform numerical simulations of the turbulent flow in this wind tunnel using both a Reynolds stress model developed in RANS modeling and a subfilter scale stress model derived from the partially integrated transport modeling method. With the aim of reproducing the experimental grid turbulence resulting from the effects of the square-mesh biplane grid on the uniform wind tunnel stream, we develop a new analytical spectral method of generation of pseudo-random velocity fields in a cubic box. These velocity fields are then introduced in the channel using a matching numerical technique. Both RANS and PITM simulations are performed on several meshes to study the effects of the contraction on the mean velocity and turbulence. As a result, it is found that the RANS computation using the Reynolds stress model fails to reproduce the increase of anisotropy in the centerline of the channel after passing the contraction. In the contrary, the PITM simulation predicts fairly well this turbulent flow according to the experimental data, and especially, the “return to anisotropy” in the straight section of the channel downstream the contraction. This work shows that the PITM method used in conjunction with an analytical synthetic turbulence generation as inflow is well suited for simulating this flow, while allowing a drastic reduction of the computational resources.     

Evaluations of SGS Combustion,Scalar Flux and Stress Models in a Turbulent Jet Premixed Flame

A newly developed fractal dynamic SGS (FDSGS) combustion model and a scale self-recognition mixed (SSRM) SGS stress model are evaluated along with other SGS combustion, scalar flux and stress models in a priori and a posteriori manners using DNS data of a hydrogen-air turbulent plane jet premixed flame. A posteriori tests reveal that the LES using the FDSGS combustion model can predict the combustion field well in terms of mean temperature distributions and peak positions in the transverse distributions of filtered reaction progress variable fluctuations. A priori and a posteriori tests of the scalar flux models show that a model proposed by Clark et al. accurately predicts the counter-gradient transport as well as the gradient diffusion, and introduction of the model of Clark et al. into the LES yields slightly better predictions of the filtered progress variable fluctuations than that of a gradient diffusion model. Evaluations of the stress models reveal that the LES with the SSRM model predicts the velocity fluctuations well compared to that with the Smagorinsky model.     

A Priori Assessment of Prediction Confidence for Data-Driven Turbulence Modeling

Although Reynolds-Averaged Navier–Stokes (RANS) equations are still the dominant tool for engineering design and analysis applications involving turbulent flows, standard RANS models are known to be unreliable in many flows of engineering relevance, including flows with separation, strong pressure gradients or mean flow curvature. With increasing amounts of 3-dimensional experimental data and high fidelity simulation data from Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS), data-driven turbulence modeling has become a promising approach to increase the predictive capability of RANS simulations. However, the prediction performance of data-driven models inevitably depends on the choices of training flows. This work aims to identify a quantitative measure for a priori estimation of prediction confidence in data-driven turbulence modeling. This measure represents the distance in feature space between the training flows and the flow to be predicted. Specifically, the Mahalanobis distance and the kernel density estimation (KDE) technique are used as metrics to quantify the distance between flow data sets in feature space. To examine the relationship between these two extrapolation metrics and the machine learning model prediction performance, the flow over periodic hills at Re = 10595 is used as test set and seven flows with different configurations are individually used as training sets. The results show that the prediction error of the Reynolds stress anisotropy is positively correlated with Mahalanobis distance and KDE distance, demonstrating that both extrapolation metrics can be used to estimate the prediction confidence a priori. A quantitative comparison using correlation coefficients shows that the Mahalanobis distance is less accurate in estimating the prediction confidence than KDE distance. The extrapolation metrics introduced in this work and the corresponding analysis provide an approach to aid in the choice of data source and to assess the prediction performance for data-driven turbulence modeling.     

A Bayesian Calibration–Prediction Method for Reducing Model-Form Uncertainties with Application in RANS Simulations

Model-form uncertainties in complex mechanics systems are a major obstacle for predictive simulations. Reducing these uncertainties is critical for stake-holders to make risk-informed decisions based on numerical simulations. For example, Reynolds-Averaged Navier-Stokes (RANS) simulations are increasingly used in the design, analysis, and safety assessment of mission-critical systems involving turbulent flows. However, for many practical flows the RANS predictions have large model-form uncertainties originating from the uncertainty in the modeled Reynolds stresses. Recently, a physics-informed Bayesian framework has been proposed to quantify and reduce model-form uncertainties in RANS simulations for flows by utilizing sparse observation data. However, in the design stage of engineering systems, when the system or device has not been built yet, measurement data are usually not available. In the present work we extend the original framework to scenarios where there are no available data on the flow to be predicted. In the proposed method, we first calibrate the model discrepancy on a related flow with available data, leading to a statistical model for the uncertainty distribution of the Reynolds stress discrepancy. The obtained distribution is then sampled to correct the RANS-modeled Reynolds stresses for the flow to be predicted. The extended framework is a Bayesian calibration–prediction method for reducing model-form uncertainties. The merits of the proposed method are demonstrated on two flows that are challenging to standard RANS models. By not requiring observation data on the flow to be predicted, the present calibration–prediction method will gain wider acceptance in practical engineering design and analysis compared to the original framework. While RANS modeling is chosen to demonstrate the merits of the proposed framework, the methodology is generally applicable to other complex mechanics models involving solids, fluids flows, or the coupling between the two (e.g., mechanics models for the cardiovascular systems), where model-form uncertainties are present in the constitutive relations.     

A Gas-Kinetic Scheme for Turbulent Flow

RANS simulations may not provide accurate results for all flow conditions. The interaction between a shock wave and a turbulent boundary layer is an example which may still be difficult to simulate accurately. Beside the inability to reproduce physical phenomena such as shock unsteadiness, the argument is put forward that the conventional numerical schemes, based on the Navier-Stokes equations, may be unable to generate a physically consistent turbulent stress tensor in the presence of large unresolved scales of motion. A large ratio between unresolved and resolved scales of motion, a sort of Knudsen number based on turbulent fluctuations, might introduce inaccuracies for which the turbulence model is not accountable. In order to improve the accuracy of RANS simulations, researchers have suggested various ad-hoc modifications to standard turbulence models which limit eddy viscosity or the turbulent stress tensor in the presence of strong gradients. Gas-kinetic schemes might be able to improve RANS predictions in shocklayers by removing or limiting the errors caused by the large scales ratio. These schemes are a class of their own; in the framework of a finite-volume or finite-elements discretizations, they model the numerical fluxes on the basis of the Boltzmann equation instead of the Navier-Stokes equations as is conventionally done. In practical terms, these schemes provide a higher accuracy and, more importantly, an in-built “multiscalar” mechanism, i.e. the ability to adjust to the size of unresolved scales of motion. This property makes them suitable for shock-capturing and rarefied flow. Gas-kinetic scheme may be coupled to a conventional RANS turbulence model; it is shown that the turbulent stress tensor is naturally adjusted as a function of the unresolved-to-resolved scales ratios and achieves a higher physical consistency than conventional schemes. The simulations shown - well-known benchmark cases with strong shock-boundary layer interactions - have been obtained with a standard two-equation turbulence model (k- ω). It is shown that the gas-kinetic scheme provides good quality predictions, where conventional schemes with the same turbulence model are known to fail.     

Two‐dimensional prediction of time dependent,turbulent flow around a square cylinder confined in a channel

This paper presents two‐dimensional and unsteady RANS computations of time dependent, periodic, turbulent flow around a square block. Two turbulence models are used: the Launder–Sharma low‐Reynolds number k–ε model and a non‐linear extension sensitive to the anisotropy of turbulence. The Reynolds number based on the free stream velocity and obstacle side is Re=2.2×10⁴. The present numerical results have been obtained using a finite volume code that solves the governing equations in a vertical plane, located at the lateral mid‐point of the channel. The pressure field is obtained with the SIMPLE algorithm. A bounded version of the third‐order QUICK scheme is used for the convective terms. Comparisons of the numerical results with the experimental data indicate that a preliminary steady solution of the governing equations using the linear k–ε does not lead to correct flow field predictions in the wake region downstream of the square cylinder. Consequently, the time derivatives of dependent variables are included in the transport equations and are discretized using the second‐order Crank–Nicolson scheme. The unsteady computations using the linear and non‐linear k–ε models significantly improve the velocity field predictions. However, the linear k–ε shows a number of predictive deficiencies, even in unsteady flow computations, especially in the prediction of the turbulence field. The introduction of a non‐linear k–ε model brings the two‐dimensional unsteady predictions of the time‐averaged velocity and turbulence fields and also the predicted values of the global parameters such as the Strouhal number and the drag coefficient to close agreement with the data. Copyright © 2009 John Wiley & Sons, Ltd.     

Hybrid RANS/LES of flow and heat transfer in round impinging jets

Fluid flow and convective heat transfer predictions are presented of round impinging jets for several combinations of nozzle-plate distances H/D = 2, 6 and 13.5 (where D is the nozzle diameter) and Reynolds numbers Re = 5000, 23,000 and 70,000 with the newest version of the k-ω model of Wilcox (2008) and three hybrid RANS/LES models. In the RANS mode of the hybrid RANS/LES models, the k-ω model is recovered. Three formulations are considered to activate the LES mode. The first model is similar to the hybrid models of Davidson and Peng (2003) and Kok et al. (2004). The turbulent length scale is replaced by the grid size in the destruction term of the k-equation and in the definition of the RANS eddy viscosity. As grid size, a maximum measure of the hexahedral grid cell is used. The second model has the same k-equation, but the eddy viscosity is the minimum of the k-ω eddy viscosity and the Smagorinsky eddy viscosity, following a proposal by Batten et al. (2004). The Smagorinsky eddy viscosity is formed with the cube root of the cell volume. The third model has, again, the same k-equation, but has an eddy viscosity which is an intermediate between the eddy viscosities of the first and second models. This is reached by using the cube root of the cell volume in the eddy viscosity formula of the first model.The simulation results are compared with experimental data for the high Reynolds number cases Re = 23,000 and Re = 70,000 and LES data for the low-Reynolds number case Re = 5000. The Reynolds numbers are defined with the nozzle diameter and the bulk velocity at nozzle outlet. At low nozzle-plate distance (the impingement plate is in the core of the jet), turbulent kinetic energy is overpredicted by RANS in the stagnation flow region. This leads to overprediction of the heat transfer rate along the impingement plate in the impact zone. At high nozzle-plate distance (the impingement plate is in the mixed-out region of the jet), the turbulence mixing is underpredicted by RANS in the shear layer of the jet which gives a too high length of the jet core. This also results in overprediction of the heat transfer rate in the impingement zone caused by too big temperature gradients at impingement.All hybrid RANS/LES models are able to correct the heat transfer overprediction of the RANS model. For good predictions at low nozzle-plate distance, it is necessary to sufficiently resolve the formation and development of the near-wall vortices in the jet impingement region. At high nozzle-plate distance, the essence is to capture the evolution and breakup of the flow unsteadiness in the shear layer of the jet, so that accurate mean and fluctuating velocity profiles are obtained in the impingement region. Although the models have a quite different theoretical justification and generate a quite different eddy viscosity in some flow regions, their overall results are very comparable. The reason is that in zones that are crucial for the results, the models behave similarly.     

Scrutinizing URANS in Shedding Flows: The Case of Cylinder in Cross-Flow in the Subcritical Regime

To unravel the widespread perception that the RANS (Reynolds-averaged Navier-Stokes) concept is unreliable in predicting the dynamics of separated flows, we assessed the performance of two RANS closure levels, the linear eddy-viscosity (LEVM) and the second-moment (Reynolds stress, RSM) approaches in a massively separated generic flow over a bluff body. Considered is the canonical, zero-turbulence, cross-flow over an infinite cylinder with reference to our LES and the available DNS and experiments at two Reynolds numbers, Re = 3.9 × 10³ and 1.4 × 10⁵, both within the sub-critical regime with laminar separation. Both models capture successfully the vortex shedding frequency, but the low frequency modulations are detected only by the RSM. At high Reynolds numbers the RSM is markedly superior to the LEVM showing very good agreement with the LES and experimental data. The RSM, accounting naturally for the stress anisotropy and phase lag between the stress and strain eigenvectors, is especially successful in reproducing the growth rate of the turbulent kinetic energy in the initial shear layer which proved to be crucial for accurate prediction of the separation-induced transition. A scrutiny of the unsteady RANS (URANS) stress terms based on the conditional phase-averaged LES data shows a remarkable similarity of the normalized coherent and stochastic (modeled) stress components for the two Reynolds numbers considered. The mixed (cross) correlations, while non-negligible at the low Re number, diminish fast relative to the stochastic ones with increasing Reynolds number and, in the whole, are not significant to undermine the URANS concept and its applicability to high Re flows of industrial relevance.     

A least square extrapolation method for the a posteriori error estimate of the incompressible Navier Stokes problem

A posteriori error estimators are fundamental tools for providing confidence in the numerical computation of PDEs. To date, the main theories of a posteriori estimators have been developed largely in the finite element framework, for either linear elliptic operators or non‐linear PDEs in the absence of disparate length scales. On the other hand, there is a strong interest in using grid refinement combined with Richardson extrapolation to produce CFD solutions with improved accuracy and, therefore, a posteriori error estimates. But in practice, the effective order of a numerical method often depends on space location and is not uniform, rendering the Richardson extrapolation method unreliable. We have recently introduced (Garbey, 13th International Conference on Domain Decomposition, Barcelona, 2002; 379–386; Garbey and Shyy, J. Comput. Phys. 2003; 186 :1–23) a new method which estimates the order of convergence of a computation as the solution of a least square minimization problem on the residual. This method, called least square extrapolation, introduces a framework facilitating multi‐level extrapolation, improves accuracy and provides a posteriori error estimate. This method can accommodate different grid arrangements. The goal of this paper is to investigate the power and limits of this method via incompressible Navier Stokes flow computations. Copyright © 2005 John Wiley & Sons, Ltd.     

On the Modelling of the Electro-Hydrodynamic Flow Field in Electrostatic Precipitators

Electro-hydrodynamic (EHD) flows are investigated theoretically and numerically in this paper and results are presented for the flow field in model electrostatic precipitators (EPs). The resulting flow fields are shown in various representations and explained qualitatively. Numerical calculations with different flow models (non-turbulent and RANS) were conducted to investigate the influence of the flow model on the resulting secondary flows. Furthermore, a perturbation analysis is presented, leading to a simple differential equation of the Helmholtz type. This allows a more detailed view of the important mechanisms forming the secondary flows as well as being able to obtain a very fast estimation of the resulting flow field. The calculations reveal a strong influence of a vortex formation at the beginning of the precipitation zone on the whole flow field. Furthermore, a strong effect of the boundary conditions of the electric field and the operating parameters is shown. This revised version was published online in July 2006 with corrections to the Cover Date.     

Turbulent flow and loading on a tidal stream turbine by LES and RANS

This paper presents results from numerical simulations of a 3-bladed horizontal axis tidal stream turbine. Initially, Reynolds Averaged Navier Stokes (RANS) k–ω Shear Stress Transport eddy-viscosity and Launder–Reece–Rodi models were used for code validation and testing of a newly implemented sliding mesh technique for an unstructured finite volume code. Wall- and blade-resolved large-eddy simulations (LES) were then performed to study the complete geometry at various tip speed ratios (TSR). Thrust and power coefficients were compared to published experimental measurements obtained from a towing tank for a range of TSR (4, 5, 6, 7, 8, 9 and 10) at a fixed hub pitch angle. A strong meandering is observed downstream of the supporting tower due to interaction between the detached tip vortices and vortex shedding from the support structure. The wake profiles and rate of recovery of velocity deficit show high sensitivity to the upstream turbulence intensities. However, the mean thrust and power coefficients were found to be less sensitive to the upstream turbulence. Comparisons between RANS and LES are also presented for the mean sectional blade pressures and mean wake velocity profiles. The paper also presents an overview of modelling and numerical issues relating to simulations for such rotating geometries.     

Simulation of the Flow in a Ribbed Rotating Duct with a Hybrid k-ω RANS/LES Model

The objective of this work is to verify the capabilities of a hybrid k-ω RANS/LES model for simulation of the unsteady three-dimensional flow in a ribbed duct subjected to system rotation. The Reynolds number is 15,000 and the rotation number is 0.3, both based on hydraulic diameter and bulk velocity. A correction term for system rotation is introduced into the originating k-ω RANS model. Simulation results in the mid-span section are compared with experimental data by Coletti et al. (Exp. Fluids 52:1043–1061, 2012). The comparison is complemented by analysis of the flow features in cross-sections. It is demonstrated that the hybrid k-ω RANS/LES model produces an accurate simulation of the rotating ribbed duct flow. Results are compared with those by the originating time-accurate k-ω RANS model. The k-ω RANS model is not accurate concerning secondary features in the longitudinal mean flow recirculation patterns and the secondary flow in cross-sections, but it reproduces quite well the time-averaged longitudinal flow.     

Computational and experimental analysis of supersonic air ejector: Turbulence modeling and assessment of 3D effects

Numerical and experimental analyses are performed on a supersonic air ejector to evaluate the effectiveness of commonly-used computational techniques when predicting ejector flow characteristics. Three series of experimental curves at different operating conditions are compared with 2D and 3D simulations using RANS, steady, wall-resolved models. Four different turbulence models are tested: k–ε, k–ε realizable, k–ω SST, and the stress–ω Reynolds Stress Model. An extensive analysis is performed to interpret the differences between numerical and experimental results. The results show that while differences between turbulence models are typically small with respect to the prediction of global parameters such as ejector inlet mass flow rates and Mass Entrainment Ratio (MER), the k–ω SST model generally performs best whereas ε-based models are more accurate at low motive pressures. Good agreement is found across all 2D and 3D models at on-design conditions. However, prediction at off-design conditions is only acceptable with 3D models, making 3D simulations mandatory to correctly predict the critical pressure and achieve reasonable results at off-design conditions. This may partly depend on the specific geometry under consideration, which in the present study has a rectangular cross section with low aspect ratio.     

Implementation and Evaluation of an Embedded LES-RANS Solver

In the current work, we present the development and application of an embedded large-eddy simulation (LES) - Reynolds-averaged Navier Stokes (RANS) solver. The novelty of the present work lies in fully embedding the LES region inside a global RANS region through an explicit coupling at the arbitrary mesh interfaces, exchanging flow and turbulence quantities. In particular, a digital filter method (DFM) extracting mean flow, turbulent kinetic energy and Reynolds stress profiles from the RANS region is used to provide meaningful turbulent fluctuations to the LES region. The framework is developed in the open-source computational fluid dynamics software OpenFOAM. The embedding approach is developed and validated by simulating a spatially developing turbulent channel flow. Thereafter, flow over a surface mounted spanwise-periodic vertical fence is simulated to demonstrate the importance of the DFM and the effect of the location of the RANS-LES interface. Mean and second-order statistics are compared with direct numerical simulation (DNS) data from the literature. Results indicate that feeding synthetic turbulence at the LES interface is essential to achieve good agreement for the mean flow quantities. However, in order to obtain a good match for the Reynolds stresses, the LES interface needs to be placed sufficiently far upstream, which in the present case was six spoiler heights before the fence. Further, a realistic spoiler configuration with finite-width in the spanwise direction and inclined at 30 degrees was simulated using the embedding approach. As opposed to the vertical fence case this is a genuinely (statistically) three-dimensional case and a very good match with mean and second-order statistics was obtained with the experimental data. Finally, in order to test the present solver for high sub-sonic speed flows the flow over an open cavity was simulated. A good match with reference data is obtained for mean and turbulence profile comparisons. Tones in the pressure spectra were predicted reasonably well and an overall sound pressure level with a maximum deviation of 2.6 d B was obtained with the present solver when compared with the experimental data.