Reynolds Stress Turbulence Closure Research Articles

Flow and thermal fields modeling in jet impingement configurations using a Reynolds stress turbulence closure within the RANS and Sensitized-RANS framework

The flow and thermal field characteristics underlying turbulent convective heat transfer in two reference configurations, representing a jet exiting a planar slot and a circular tube and impinging on a heated wall, are studied computationally. The performance of a conventional Reynolds Stress Model (RSM) and its scale-resolving variant, employed in the context of a time-accurate Reynolds-Averaged Navier–Stokes (RANS) simulation, is investigated in conjunction with different modeling approaches for the turbulent heat flux uj′θ′¯, whose gradient represents the turbulence-induced heat source in the temperature transport equation. In this so-called Sensitized-RANS modeling strategy, employing an improved eddy-resolving instability-sensitive Reynolds Stress Model (IISRSM, Jakirlić and Maduta (2015)), the unresolved ‘sub-scale’ turbulent correlations represent the solutions of a set of corresponding transport equations for the entire stress tensor ui′uj′¯. The turbulent scalar-flux models follow from the classical gradient-diffusion approach with the diffusion-like coefficients formulated as a function of both the scalar eddy-viscosity and the anisotropic Reynolds stress tensor. The latter model expressions also take into account various non-linear relationships in terms of turbulent stress components. The computational results of the fully-developed channel flow, featured only by the mean shear and constant wall heat flux, representing a preliminary investigated flow configuration, agree very well with the corresponding DNS (Direct Numerical Simulation) database for both RSM versions in conjunction with all the turbulent heat flux models adopted. However, the study of the two flow impingement cases with the different structure of the impinging jet and nozzle-to-wall distance variations, characterized by a much more complex flow straining, using the considered conventional Reynolds stress model shows significantly different results for the Reynolds stress and thermal fields compared to the available DNS data, especially in the immediate impact region manifested by a significant overprediction of the turbulence intensity. In contrast, the IISRSM-relevant results for the mean flow and temperature fields, the associated integral characteristics, and the corresponding turbulence quantities are in very good agreement with the reference DNS data, due to the much higher predictive capabilities of this eddy-resolving turbulence model compared to its baseline counterpart.

Multi-Fluid Computational Fluid Dynamic Predictions of Turbulent Bubbly Flows Using an Elliptic-Blending Reynolds Stress Turbulence Closure

The accurate prediction of bubbly flows is critical to many areas of nuclear reactor thermal hydraulics, mainly, but not only, in relation to the key role bubble behaviour plays in boiling flows. Large scale computations of flows with hundreds of thousands of bubbles are possible at a reasonable computational cost using computational fluid dynamic, multi-fluid Eulerian-Eulerian models. The main limitation of these models is the need to entirely model interfacial transfer processes with proper closure relations. Here, the capabilities and advantages provided by a model that includes an elliptic-blending Reynolds stress turbulence closure (EB-RSM), allowing fine resolution of the velocity field in the near-wall region, are tested over a large database. This database includes mostly monodispersed bubbly flows over a wide range of operating conditions and geometrical parameters, including upward and downward pipe flows, large diameter pipes and a square duct. The model shows encouraging accuracy and robustness, with good agreement over most void fraction distributions and accurate prediction of the magnitude and position of the near-wall void fraction peak. The model does not include any wall force, avoiding all the related uncertainties, and the prediction of the void fraction peak relies on the fine resolution of the near-wall pressure gradient induced by the turbulence field. Overall, the EB-RSM allows accurate resolution of the velocity and turbulence field near the wall, and the transition to this and similar turbulence closures is of value in assisting the ongoing quest for thermal hydraulic models that are accurate and of general applicability. Additional modifications to the near-wall modelling approach, which is still based on its single-phase counterpart, may be required to deal with high void fraction conditions and, in the overall model, additional improvements to momentum and, most importantly, bubble-induced turbulence closures are desirable.

A Representation Theory-Based Model for the Rapid Pressure Strain Correlation of Turbulence

In the presence of mean strain or rotation, the anisotropy of turbulence increases due to the rapid pressure strain term. In this paper, we consider the modeling of the rapid pressure strain correlation of turbulence. The anisotropy of turbulence in the presence of mean strain is studied and a new model is formulated by calibrating the model constants at the rapid distortion limit. This model is tested for a range of plane strain and elliptic flows and compared to direct numerical simulation (DNS) results. The present model shows agreement with DNS and improvements over the earlier models like those by Launder et al. (1975, “Progress in the Development of a Reynolds-Stress Turbulence Closure,” J. Fluid Mech., 68(3), pp. 537–566.) and Speziale et al. (1991, “Modelling the Pressure–Strain Correlation of Turbulence: An Invariant Dynamical Systems Approach,” J. Fluid Mech., 227(1), pp. 245–272.) that have been reported to give satisfactory performance for hyperbolic flows but not satisfactory for elliptic flows.

Numerical study of a wake-stabilized propane flame in a cross-flow of air

Predictions of flame structures, flame temperatures, and species concentrations have been numerically performed for a wake-stabilized propane flame in a cross-flow of air. The flow field has been modeled using the Reynolds-Averaged Navier-Stokes equation incorporating the Reynolds Stress turbulence closure Model (RSM) and the Large Eddy Simulation (LES) technique with the two methods compared. The combustion processes were modeled using the partially premixed and the non-premixed models and the two sets of results have also been compared. The CRECK reaction mechanism was used to model the kinetics of the propane reactions while soot in the flame was modeled with the Moss-Brookes-Hall model. Thermal radiation in the flame was modeled with the discrete ordinate method. The results of the simulation have been validated against experimental data and show that the partially premixed model performs better than the non-premixed model for wake-stabilized flames that are attached to the lee-side of the flare burner. Furthermore, the LES technique has been shown to perform better than the RSM.

Flow simulation over oblique cylindrical weirs

This paper presents a computational fluid dynamics (CFD) simulation to investigate the effects of the obliqueness of cylindrical weirs on the flow velocity distribution, the pressure distribution and the distribution of water depth over the weir crest. Three different cylindrical weirs with diameters of 0.114 m, 0.09 m, and 0.0635 m, with three dissimilar inclination angles of 90°, 135°, and 150° were used. The SSG Reynolds stress turbulence closure model was utilized in the analyses. The results show that the flow patterns are affected by the inclination angle with respect to the flow direction. It was noticed that inclination angle increment increases the velocity of flow at the downstream surface of the weir, thus increases the absolute value of the negative pressure, at the inward-moved end of the weir. The outward-moved end of the weir was observed not to be covered with water and extending with the increase of the inclination angle.

Numerical Simulation of Flow over a Semicylinder Weir

Laboratory experiments are conducted to measure the free-surface profile and the velocity field of an open channel flow over a semicylinder weir. The streamwise velocities of the flow are measured using a laser Doppler anemometer. The numerical simulation of the flow case having similar conditions with the experiment is performed. The basic equations of the problem are solved using the finite-volume method. A grid convergence analysis is applied to ensure the discretization error keeping within an acceptable limit for the predicted velocities. In the numerical modeling, the volume of fluid method is used to compute the free surface of the flow that interacts with the semicylindrical structure. In the numerical analysis, standard k-ε, renormalization group k-ε, realizable k-ε, modified k-ω, shear stress transport, and Reynolds stress turbulence closure models are employed. The computed results for the velocity field and free-surface profile of the flow are compared with the experimental data. The comparisons of the experimental and numerical results show that the numerical simulation using the Reynolds stress turbulence model provides better predictions for the horizontal velocities than the other turbulence models used herein.

Direct numerical simulations of turbulence subjected to a straining and destraining cycle

In many turbulent flows, significant interactions between fluctuations and mean velocity gradients occur in nonequilibrium conditions, i.e., the turbulence does not have sufficient time to adjust to changes in the velocity gradients applied by the large scales. The simplest flow that retains such physics is the time dependent homogeneous strain flow. A detailed experimental study of initially isotropic turbulence subjected to a straining and destraining cycle was reported by Chen et al. [“Scale interactions of turbulence subjected to a straining-relaxation-destraining cycle,” J. Fluid Mech. 562, 123 (2006)]. Direct numerical simulation (DNS) of the experiment of Chen et al. [“Scale interactions of turbulence subjected to a straining-relaxation-destraining cycle,” J. Fluid Mech. 562, 123 (2006)] is undertaken, applying the measured straining and destraining cycle in the DNS. By necessity, the Reynolds number in the DNS is lower. The DNS study provides a complement to the experimental one including time evolution of small-scale gradients and pressure terms that could not be measured in the experiments. The turbulence response is characterized in terms of velocity variances, and similarities and differences between the experimental data and the DNS results are discussed. Most of the differences can be attributed to the response of the largest eddies, which, even if are subjected to the same straining cycle, evolve under different conditions in the simulations and experiment. To explore this issue, the time evolution of different initial conditions parametrized in terms of the integral scale is analyzed in computational domains with different aspect ratios. This systematic analysis is necessary to minimize artifacts due to unphysical confinement effects of the flow. The evolution of turbulent kinetic energy production predicted by DNS, in agreement with experimental data, provides a significant backscatter of kinetic energy during the destraining phase. This behavior is explained in terms of Reynolds stress anisotropy and nonequilibrium conditions. From the DNS, a substantial persistency of anisotropy is observed up to small scales, i.e., at the level of velocity gradients. Due to the time dependent deformation, we find that the major contribution in the Reynolds stresses budget is provided by the production term and by the pressure/strain correlation, resulting in large time variation of velocity intensities. The DNS data are compared with predictions from the classical Launder–Reece–Rodi isoptropic production [B. E. Launder et al., “Progress in the development of a Reynolds stress turbulence closure,” J. Fluid Mech. 68, 537 (1975)] Reynolds stress model, showing good agreement with some differences for the redistribution term.

Aerodynamic effects of trees on pollutant concentration in street canyons

This paper deals with aerodynamic effects of avenue-like tree planting on flow and traffic-originated pollutant dispersion in urban street canyons by means of wind tunnel experiments and numerical simulations. Several parameters affecting pedestrian level concentration are investigated, namely plant morphology, positioning and arrangement. We extend our previous work in this novel aspect of research to new configurations which comprise tree planting of different crown porosity and stand density, planted in two rows within a canyon of street width to building height ratio W/ H = 2 with perpendicular approaching wind. Sulfur hexafluoride was used as tracer gas to model the traffic emissions. Complementary to wind tunnel experiments, 3D numerical simulations were performed with the Computational Fluid Dynamics (CFD) code FLUENT™ using a Reynolds Stress turbulence closure for flow and the advection–diffusion method for concentration calculations. In the presence of trees, both measurements and simulations showed considerable larger pollutant concentrations near the leeward wall and slightly lower concentrations near the windward wall in comparison with the tree-less case. Tree stand density and crown porosity were found to be of minor importance in affecting pollutant concentration. On the other hand, the analysis indicated that W/ H is a more crucial parameter. The larger the value of W/ H the smaller is the effect of trees on pedestrian level concentration regardless of tree morphology and arrangement. A preliminary analysis of approaching flow velocities showed that at low wind speed the effect of trees on concentrations is worst than at higher speed. The investigations carried out in this work allowed us to set up an appropriate CFD modelling methodology for the study of the aerodynamic effects of tree planting in street canyons. The results obtained can be used by city planners for the design of tree planting in the urban environment with regard to air quality issues.

Secondary flow and roll cells interaction in high-aspect-ratio rotating turbulent duct flows

End-wall effects for high aspect ratio (AR) turbulent duct flows under moderate spanwise rotation are investigated using Reynolds-Averaged Navier–Stokes (RANS) calculations with a Reynolds stress turbulence closure model. It is shown that despite an important uniformisation of the mean streamwise flow compared to the non-rotating case, the channel flow solution (AR = ∞) is not recovered in practical high AR ducts used in experiments. The unavoidable end-wall generated secondary flow causes transverse advection which is capable of altering the mean velocity profile, even for AR as high as 22. In addition, for Re = 40,000 and Ro = 0.22, persistent longitudinal roll cells are found in the RANS solutions. The results suggest that their interaction with the secondary flow may challenge the prospect of formally reaching a steady, streamwise invariant regime in actual rotating duct experiments.

Numerical and laboratory investigation of the hydrodynamic complexity of a river confluence

The paper deals with the hydrodynamic investigation of the junction of two rivers in north-west Hungary in an urban area. The goal of the investigation was to study the flow conditions by means of a 3D k-ε turbulence CFD model and hydraulic scale model. The project gave the opportunity to compare the outcome of the distorted scale model with the ones of the CFD model in field scale, in the distorted hydraulic model scale as well as in undistorted scale, converting all the results to real field scale by assuming Froude similarity. Overall flow patterns, the effect of distortion and the robustness of the k-ε turbulence model in such complex confluence conditions were analysed. Satisfactory agreement was found except for the region straight downstream of the confluence where significant differences between laboratory and numerical results were seen due most probably to the complex swirling and shearing character of the flow. Large scale vortex formation interacting with anisotropic local turbulence would certainly need differential Reynolds stress turbulence closure.

Observations and Modeling of Heavy Particle Deposition in a Windbreak Flow

Abstract This paper presents new observations of deposition of heavy particles (glass beads of gravitational settling velocity 8.7 cm s−1) within an undisturbed flow and within a flow disturbed by a porous windbreak fence. These data are then used to diagnose the capability of a Lagrangian stochastic (LS) particle trajectory model, which simulates heavy particle dispersion. The model is based on existing parameterizations and is coupled to a wind model based on a Reynolds stress turbulence closure that provides computed fields of wind statistics. The deposition rates, as simulated by the model, match the observation within E = 30% of accuracy, with E being the root-mean-square error normalized by the peak value on the deposition swath. These results suggest that the LS model handles properly the heterogeneities of the flow and that the heuristic adjustments made to account for the inertia of heavy particles are useful approximations. The model consequently proves to be a valuable tool to investigate the patterns of dispersion about an obstacle.

05/02714 Modelling of non-premixed swirl burner flows using a Reynolds-stress turbulence closure

05/02714 Modelling of non-premixed swirl burner flows using a Reynolds-stress turbulence closure

Advances in Rapid Distortion Theory: From Rotating Shear Flows to the Baroclinic Instability

Abstract The essentials of rapid distortion theory (RDT) are briefly recalled for homogeneous turbulence subjected to rotational mean flows, including its linkage to stability analysis. The latter “linkage” is of particular importance from our viewpoint, since it also attracted the attention of Charles Speziale, resulting in at least two papers [Speziale, C. G., Abid, R., and Blaisdell, G. A., 1996, “On the Consistency of Reynolds Stress Turbulence Closures With Hydrodynamic Stability Theory,” Phys. Fluids, 8, pp. 781–788 and Salhi, A., Cambon, C., and Speziale, C. G., 1997, “Linear Stability Analysis of Plane Quadratic Flows in a Rotating Frame,” Phys. Fluids, 9(8), pp. 2300–2309] with particular emphasis on rotating flows. New analytical solutions and related RDT results are presented for shear flows including buoyancy forces, with system rotation or mean density stratification. Finally, combining shear, rotation and stratification, RDT is shown to be pertinent to revisiting the baroclinic instability. This instability results from the tilting of mean isopycnal surfaces under combined effects of vertical shear and system rotation, in a vertically (stably) stratified medium rotating around the vertical direction. In addition, the challenge of reproducing RDT dynamics in single-point closure models is briefly discussed, from the viewpoint of structure-based modeling [Cambon C., Jacquin, L., and Lubrano, J.-L., 1992, “Towards a New Reynolds Stress Model for Rotating Turbulent Flows,” Phys. Fluids A, 4, pp. 812–824 and Kassinos, S. C., Reynolds, W. C., and Rogers, M. M., 2000, “One-Point Turbulence Structure Tensors,” J. Fluid Mech., 428, pp. 213–248.

Numerical Simulation of a Turbulent Lean, Premixed Combustion with an Explicit Algebraic Stress Model

A computational model is used in the present paper to study the influence of the turbulence modeling on the chemical species in a turbulent lean premixed flame. The simulated configuration is about a lean, premixed bluff-body-stabilized flame with a recirculation zone. To achieve the objectives, three different models were used for turbulence modeling as listed next: 1) standard k-e, 2) a Reynolds Stress Turbulence Closure and 3) a state of the art Explicit Algebraic Stress Model. Comparisons with experimental data are made in terms of velocities, temperatures, as well as major and minor species. As a result, predictions show that species such as CO and OH are strongly affected by the turbulence model; whereas other species such as NO are affected slightly. On the other hand the Explicit Algebraic Stress Model offers noticeable improvements over existing models.

Modelling of non-premixed swirl burner flows using a Reynolds-stress turbulence closure

In this computational study, the performance of a differential Reynolds-stress turbulence model has been assessed in predicting a turbulent, non-premixed combusting swirling flow of the type frequently found in practical combustion systems. Calculations are also performed using the widely employed eddy-viscosity based k– ε turbulence model in order to examine the relative performances of these two closure models. The predictions are compared against the experimental data of mean axial and tangential velocities, turbulence quantities, gas temperatures and oxygen concentration collected in a 400 kW semi-industrial scale combustor fired with coke-oven gas using an industry-type swirl burner at the International Flame Research Foundation [17]. Computations of a corresponding non-combusting flow are also carried out and the predictions are compared with limited data available. The overall agreement between the measurements and the predictions obtained with both the k– ε and Reynolds-stress turbulence models are reasonably good, in particular, the flame properties. However, some features of the isothermal and combusting flow fields, and the flame are better predicted by the Reynolds-stress model. The subcritical nature of the isothermal flow and the effects of combustion on the size and shape of the swirl-induced internal recirculation zone in the corresponding combusting flow are well simulated by this model. The k– ε model fails to reproduce the subcritical nature of the isothermal flow. The predictions of this model erroneously show a general trend of the mean tangential velocity distribution to assume a forced-vortex profile. The levels of gas temperature and oxygen concentration in the internal recirculation zone and the enveloping shear region are on the whole better predicted by the Reynolds-stress model.

Elliptic blending model: A new near-wall Reynolds-stress turbulence closure

A new approach to modeling the effects of a solid wall in one-point second-moment (Reynolds-stress) turbulence closures is presented. The model is based on the relaxation of an inhomogeneous (near-wall) formulation of the pressure–strain tensor towards the chosen conventional homogeneous (far-from-a-wall) form using the blending function α, for which an elliptic equation is solved. The approach preserves the main features of Durbin’s Reynolds-stress model, but instead of six elliptic equations (for each stress component), it involves only one, scalar elliptic equation. The model, called “the elliptic blending model,” offers significant simplification, while still complying with the basic physical rationale for the elliptic relaxation concept. In addition to model validation against direct numerical simulation in a plane channel for Reτ=590, the model was applied in the computation of the channel flow at a “real-life” Reynolds number of 106, showing a good prediction of the logarithmic profile of the mean velocity.

Assessment of reynolds stress turbulence closures in the calculation of a transonic separated flow

In this study, the performances of various turbulence closure models are evaluated in the calculation of a transonic flow over axisymmetric bump. k-e, explicit algebraic stress, and two Reynolds stress models, i. e., GL model proposed by Gibson & Launder and SSG model proposed by Speziale, Sarkar and Gatski, are chosen as turbulence closure models. SSG Reynolds stress model gives best predictions for pressure coefficients and the location of shock. The results with GL model also show quite accurate prediction of pressure coefficients downstream of shock wave. However, in the predictions of mean velocities and turbulent stresses, the results are not so satisfactory as in the prediction of pressure coefficients.

EARSM finite element solver for the study of turbulent 3-D compressible separated flows

A 3-D finite element solver, based on a semi-implicit formulation, that uses an algebraic Reynolds stress turbulence closure is presented. This solver aims to predict separated flow field behavior that typically appears in aerospace applications. In particular, analysis of control device efficiency and base flow/plume interaction of rocket-like configurations are the driving subjects behind this work. Concerning the organization of the paper, a limited review of Reynolds stress models is carried out in the introduction. Then, the numerical algorithm is described and details of the validation campaign are provided. Finally, an application case is presented that deals with the numerical re-building of some of the base flow/plume interaction experiments that have been carried out in the context of the ESA program: FESTIP technology developments in aerothermodynamics for reusable launch vehicles.

Development and calibration of algebraic nonlinear models for terms in the Reynolds stress transport equations

A simple and straightforward method is presented for the derivation and calibration of algebraic nonlinear models for terms in Reynolds stress turbulence closures. The method extensively utilizes data from direct numerical simulations to allow an investigation of the model performance over the entire Reynolds stress anisotropy-invariant map. The model constants are determined from the condition of minimizing the mean square error over the invariant map, in order to give good model behavior for as wide a class as possible of flow situations. A low Reynolds number closure is proposed based on the most general form for closing the Reynolds stress transport equations in terms of Reynolds stresses and total dissipation rate. It is shown that forcing the closure to satisfy realizability in a strict sense leads to a good model behavior even for the complicated flow situation near a wall, without any use of ad-hoc wall damping functions in the closure. The model behavior in homogeneous turbulent flow is analyzed by formulating equations for invariant measures, yielding several quite general results for the behavior of the present and other existing models. A new approach to the modeling effects of rotation in the context of Reynolds stress closures is presented and tested for some different homogeneous flows subjected to rotation.

Second-Moment Closure Model for IC Engine Flow Simulation Using Kiva Code1

The flow and turbulence in an IC engine cylinder were studied using the SSG variant of the Reynolds stress turbulence closure model. In-cylinder turbulence is characterized by strong turbulence anisotropy and flow rotation, which aid in air-fuel mixing. It is argued that solving the differential transport equations for each turbulent stress tensor component, as implied by second-moment closures, can better reproduce stress anisotropy and effects of rotation, than with eddy-viscosity models. Therefore, a Reynolds stress model that can meet the demands of in-cylinder flows was incorporated into an engine flow solver. The solver and SSG turbulence model were first successfully tested with two different validation cases. Finally, simulations were applied to IC-engine like geometries. The results showed that the Reynolds stress model predicted additional flow structures and yielded less diffusive profiles than those predicted by an eddy-viscosity model. [S0742-4795(00)00101-0]