Numerical simulation of fluid dynamics in the stirred tank by the SSG Reynolds Stress Model

The Speziale,Sarkar and Gatski Reynolds Stress Model(SSG RSM)is utilized to simulate the fluid dynamics in a full baffled stirred tank with a Rushton turbine impeller.Four levels of grid resolutions are chosen to determine an optimised number of grids for further simulations.CFD model data in terms of the flow field,trailing vortex,and the power number are compared with published experimental results.The comparison shows that the global fluid dynamics throughout the stirred tank and the local characteristics of trailing vortices near the blade tips can be captured by the SSG RSM.The predicted mean velocity components in axial,radial and tangential direction are also in good agreement with experiment data.The power number predicted is quite close to the designed value,which demonstrates that this model can accurately calculate the power number in the stirred tank.Therefore,the simulation by using a combination of SSG RSM and MRF impeller rotational model can accurately model turbulent fluid flow in the stirred tank,and it offers an alternative method for design and optimisation of stirred tanks.

High-order discretization of the Reynolds stress model with anε_(β)-adaptive algorithm

The Reynolds stress model(RSM)outperforms the eddy viscosity model(EVM)when simulating complex flows and has increased demand for high-order discretization.However,the complexity of the RSM equations results in poor numerical stability and weak convergence performance.One of the reasons is that the properties of Reynolds stresses are not fully considered in the design of the numerical scheme.In response to this issue,this study develops an adaptive algorithm to adjustε_(β)values(an empirical parameter in nonlinear weights)according to the magnitude and smoothness of the Reynolds stresses.This algorithm is introduced into the fifth-order weighted compact nonlinear scheme(WCNS)and is applied to the high-order discretization of the RSM.Three aeronautic test cases are simulated to investigate the performance of the algorithm.The numerical results show that,the adaptive algorithm can reduce the residual by up to 3 orders of magnitude and predict the correct weights for gradient reversals.These results confirm that the application of theε_(β)-adaptive algorithm to the high-order discretization of the RSM is beneficial both for enhancing convergence and improving resolution.

Modeling and Numerical Simulation of Wings Effect on Turbulent Flow between Two Contra-Rotating Discs

Turbulence is a fundamentally interesting physical phenomenon which is of fundamental interest. Indeed, it is at the origin of several industrial applications, the control of energy in these industrial applications pass by the comprehension and the modelling of turbulent flows. Several factors are at the origin of turbulence in the complex flows, among these factors, we can quote the effect of wings in the rotating flows. The interest of this work is to model and to simulate numerically the effect of wings on the level of turbulence in the flow between two contra-rotating discs. We have fixed on these two discs eight wings uniformly distributed and we have varied the height of the wings to have eleven values from 0 to 18 mm by maintaining the same Reynolds number of rotation. The numerical tool is based on a statistical model in a point using the closing of the second order of the transport equations of the Reynolds stresses （Reynolds Stress Model： RSM）. We have modelled wings effect on the flow by a source term added to the equation tangential speed. The results of the numerical simulation showed that all the average and fluctuating variables are affected the value of the kinetic energy of turbulence as those of Reynolds stresses increase with the height of the wings.

Extended intrinsic mean spin tensor for turbulence modelling in non-inertial frame of reference

We investigate the role of extended intrinsic mean spin tensor introduced in this work for turbulence modelling in a non-inertial frame of reference. It is described by the Euclidean group of transformations and, in particular, its significance and importance in the approach of the algebraic Reynolds stress modelling, such as in a nonlinear K-ε model. To this end and for illustration of the effect of extended intrinsic spin tensor on turbulence modelling, we examine several recently developed nonlinear K-ε models and compare their performance in predicting the homogeneous turbulent shear flow in a rotating frame of reference with LES data. Our results and analysis indicate that, only if the deficiencies of these models and the like be well understood and properly corrected, may in the near future, more sophisticated nonlinear K-ε models be developed to better predict complex turbulent flows in a non-inertial frame of reference.

Second-order modeling of non-premixed turbulent methane-air combustion

The main purpose of this research is the second-order modeling of flow and turbulent heat flux in nonpremixed methane-air combustion.A turbulent stream of non-premixed combustion in a stoichiometric condition,is numerically analyzed through the Reynolds averaged Navier-Stokes(RANS) equations.For modeling radiation and combustion,the discrete ordinates(DO) and eddy dissipation concept model have been applied.The Reynolds stress transport model(RSM) also was used for turbulence modeling.For THF in the energy equation,the GGDH model and high order algebraic model of HOGGDH with simple eddy diffusivity model have been applied.Comparing the numerical results of the SED model(with the turbulent Prandtl 0.85) and the second-order heat flux models with available experimental data follows that applying the second-order models significantly led to the modification of predicting temperature distribution and species mass fraction distribution in the combustion chamber.Calculation of turbulent Prandtl number in the combustion chamber shows that the assumption of Pr_(t) of 0.85 is far from reality and Pr_(t) in different areas varies from 0.4 to 1.2.

Linear logistic regression with weight thresholding for flow regime classification of a stratified wake

A stratified wake has multiple flow regimes,and exhibits different behaviors in these regimes due to the competing physical effects of momentum and buoyancy.This work aims at automated classification of the weakly and the strongly stratified turbulence regimes based on information available in a full Reynolds stress model.First,we generate a direct numerical simulation database with Reynolds numbers from 10,000 to 50,000 and Froude numbers from 2 to 50.Order(100)independent realizations of temporally evolving wakes are computed to get converged statistics.Second,we train a linear logistic regression classifier with weight thresholding for automated flow regime classification.The classifier is designed to identify the physics critical to classification.Trained against data at one flow condition,the classifier is found to generalize well to other Reynolds and Froude numbers.The results show that the physics governing wake evolution is universal,and that the classifier captures that physics.

Assessment of alternative scale-providing variables in a Reynolds-stress model using high-order methods

This paper is set in the high-order finite-difference discretization of the Reynolds-averaged Navier-Stokes(RANS)equations,which are coupled with the turbulence model equations.Three alternative scale-providing variables for the specific dissipation rate(o)are implemented in the framework of the Reynolds stress model(RSM)for improving its robustness.Specifically,g(=1/√ω)has natural boundary conditions and reduced spatial gradients,and a new numerical constraint is imposed on itω(=lnω)can preserve positivity and also has reduced spatial gradients;the eddy viscosity v,also has natural boundary conditions and its equation is improved in this work.The solution polynomials of the mean-flow and turbulence-model equations are both reconstructed by the weighted compact nonlinear scheme(WCNS).Moreover,several numerical techniques are introduced to improve the numerical stability of the equation system.A range of canonical as well as industrial turbulent flows are simulated to assess the accuracy and robustness of the scale-transformed models.Numerical results show that the scale-transformed models have significantly improved robustness compared to the w model and still keep the characteristics of RSM.Therefore,the high-order discretization of the RANS and RSM equations,which number 12 in total,can be successfully achieved.

Numerical Study on the Unsteady Characteristics of the Propeller Cavitation in Uniform and Nonuniform Wake Flows

Propeller cavitation is a problematic issue because of its negative effects, such as performances losses, noise,vibration and erosion. Numerical methodology is an effective and efficient technical tool for the study of propeller cavitation, however, it is hard to capture tip-vortex cavitation in the previous work by using common turbulence models based on turbulent-viscosity hypothesis. In this work, the Reynolds-Averaged Naiver-Stokes(RANS)approach, adopting the Reynolds stress turbulence model(RSM), is taken to study the unsteady characteristics of the cavitation on the four-bladed INSEAN E779 A model propeller. The numerical simulation was carried out using the commercial CFD software ANSYS Fluent 14.0. One kind of uniform wake flow and two kinds of nonuniform wake flows are considered here. The results in the uniform flow show a good agreement with previous experimental results on both the sheet cavitation and the tip vortex cavitation and prove the ability of the RSM on capturing the tip vortex cavitation. Two kinds of nonuniform wake flows are designed based on the previous experimental researches and the unsteady characteristics of the propeller cavitation are analyzed by comparing the results in the uniform and two nonuniform wake flows together.

Assessment of advanced RANS turbulence models for prediction of complex flows in compressors

Reynolds-Averaged Navier-Stokes(RANS) Computational Fluid Dynamics(CFD) has been widely used in compressor design and analysis. However, reasonable prediction of compressor flow and its impact on compressor performance remains challenging. In this study, Menter’s Shear Stress Transport(SST) model and its variants, as well as the ω-based Reynolds stress model(Stress-BSL) are assessed. For a single rotor(Rotor 67), under the peak efficiency operating condition, all studied turbulence models predict its performance with reasonable accuracy;under the off-design conditions, SST with Helicity correction(SST-Helicity) shows superiority in predicting the effect of flow on the spanwise distribution of aerodynamic parameters. For Darmstadt’s 1.5-stage transonic axial compressor, SST-Helicity outperforms SST, SST with the Quadratic Constitutive Relation(SST-QCR) and Stress-BSL in predicting the performance as well as the spanwise distribution of aerodynamic parameters. At the design rotating speed, the stall margin given by SST-Helicity(20.90%) is the closest to the experimental measurement(24.81%), which is more than twice that by SST(8.71%) and 1.5 times that by SST-QCR(14.14%). This paper demonstrates that SSTHelicity model, together with a good quality and sufficiently refined grid, can capture the compressor flow features with reasonable accuracy, which results in a credible prediction of compressor performance and stage matching.

Numerical Simulation of Aspect Ratio Effect on Turbulent Annular Flows

The control of energy in various industrial applications passes by the comprehension of the phenomena of transfers especially in complex flows. The structure of the turbulent flow in the cavities in rotation depends on several parameters like the Reynolds number of rotation Ra and the aspect ratio of the cavity. The purpose of this work is to simulate numerically the effect of the aspect ratio on the level of turbulence in the annular steady flow with an incompressible fluid for three different configurations. In the first, the interior cylinder is fixed and the external is moving. The second configuration is the reverse. The third is the contra-rotating cylinders. For all these configurations, we varied the aspect ratio from 0.5 to 2.5. The numerical tool is based on a statistical model in a point using the closing of the second order of the transport equations of the Reynolds stresses （Reynolds Stress Model： RSM）. The results of our numerical simulation show that this geometrical parameter can be an interesting factor to increase the level of turbulence that is often required in several industrial applications where the economy and the control of energy are always required.

Numerical simulation of flows around long-span flat roof

Long-span roof with span larger than height always has a complicated three-dimensional curve. Wind pressure on the roof is often influenced not only by the atmospheric turbulence, but also by the “signature” turbulence provoked in the wind by the structure itself. So it is necessary to study characteristics of flows around the roof. In this paper, three-dimensional numerical simulation of wind-induced pressure has been periormed on a long-span flat roof by means of Computational Fluid Dynamics （CFD） software ——FLUENT. The flow characteristics are studied by considering some parameters, such as wind direction, span-height ratio, roof pitch, flow characteristics, roughness of terrain. The simulation is based upon the Reynolds-averaged equations, in which Reynolds stress equation model （RSM） and SIMPLE technology, （Semi-Implieit Method for Pressure-Linked Equations） have been used. Compared with wind tunnel tests, the computational results have good agreement with the experimental data. It is proved that the results are creditable and the method is feasible.

Mathematical Modeling of Flow Field in CeramicCandle Filter

Integrated gasification combined cycle (IGCC) is one of the candidates to achieve stringent environmental regulation among the clean coal technologies. Advancing the technology of the hot gas cleanupsystems is the most critical component in the development of the IGCC. Thus the aim of this study isto understand the flow field in the ceramic filter and the influence of ceramic filter in removal of theparticles contained in the hot gas flow. The numerical model based on the Reynolds stress turbulencemodel with the Darcy’s law in the porous region is adopted. It is found that the effect of the porosityin the flowfield is negligibly small while the effect of the filter length is significant. It is also found asthe permeability decreases, the reattachment point due to the flow separation moves upstream. Thisis because the fluid is sucked into the filter region due to the pressure drop before the flow separationoccurs. The particle follows well with the fluid stream and the particle is directly sucked into the filterdue to the pressure drop even in the flow separation region.

Long-Time Turbulence Model Deduced from the Navier-Stokes Equations

The author shows the existence of long-time averages to turbulent solutions of the Navier-Stokes equations and determines the equations satisfied by them, involving a Reynolds stress that is shown to be dissipative.

Numerical investigation of flow with floating vegetation island

Floating vegetation island(FVI)provides an effective way to remove excessive nutrition and pollutants in rivers.The Reynolds stress model(RSM)is employed to investigate the hydrodynamic characteristics induced by varied canopy densities of FVI in an open channel.In longitudinal direction,four regions are subdivided according to the flow development process:upstream adjustment region(LUD),diverging flow region(LDF),shear layer growth region(LSD),and flilly developed region.The increasing canopy density accelerates the flow adjustment in the diverging flow region and shear layer growth region,signaling a shorter distance to reach an equilibrium stage,while LUD keeps a constant.The vertical profiles of the normalized velocity are found to be self-similar downstream of the diverging flow region.In the vertical direction,the streamwise velocity profiles in the mixing layer collapse for all densities and obey the hyperbolic tangent law.Normalized penetration depth into the canopy was fitted as a function of dimensionless canopy density given by δc/hc=0.404(CDahc)^-0.316.This finding indicates a large space for rapid water renewal between the canopy region and the underlying water driven by the shear-scale vortices.In the lateral direction,the intensification of secondary current and the increasing number of secondary current cells with increasing canopy density reveal that dense floating canopies contribute to strong momentum exchange.The centers of vortices move as canopy density increases,while the vortices in canopy region do not merge with those in the gap region,as limited by the height and width of the canopy region.The distribution of longitudinal velocity in the transects is significantly influenced by secondary current.

NUMERICAL SIMULATION OF SWIRLING FLOWS IN OXIDATION REACTORS FOR TiO_2 MANUFACTURE

The oxidation reactor plays a key role in producing rutile titanium dioxide （TiO2） from vapor-phase titanium tetrachloride （TiCl4） by employing a swirling flow operation for enhanced gas mixing. This work aims to understand the effect of reactor configuration on the 3-D swirling flow field using computational fluid dynamics （CFD） simulation. Considering the anisotropic turbulence involved, the Reynolds stress model is applied to describe the complex swirling flow together with the cross-flow mixing of gases. The results show significant effect of the flow angle between the wall jet of air stream （representing TiCl4 in practice） and the axial direction on the initial flow field of cross-flow mixing, where 60° gives smooth profiles of axial velocity development while 90° may provide the fastest mixing between the jet and the axial bulk flow. The pipe shape for the reaction and developing zone, i.e., straight, expanding and shrinking, shows slight influence on the hydrodynamics.

NUMERICAL INVESTIGATION OF TURBULENT COUNTER-GRADIENT-TRANSPORT IN ASYMMETRIC FLOW WITH A JET

By using the Reynolds Stress Closure Model (RSM), turbulentCounter-Gradient-Transport (CGT) phenomenon was numerically investigated in asymmetric flow with ajet, and the computational results were compared with experimental data. The computational resultsshow that the negative turbulent energy production only appears at some certain stations in CGTregion, this fact indicates that the CGT phenomenon exists more widely than the negative turbulentenergy production; while the CGT region exists all along, it gradually shrinks in the favorablepressure gradient zone until the position of the wing central part is reached, where it vanishes,but it appears in the adverse pressure gradient region; in addition, the location in the flow whereuv = 0 switched sides, relative to where partial deriv U/partial deriv y = 0, from favorablepressure gradient to adverse pressure gradient. The pressure gradient takes an important effect onthe region of negative turbulent energy production and CGT.

Influence of Turbulence Schmidt Number on Exit Temperature Distribution of an Annular Gas Turbine Combustor using Flamelet Generated Manifold

The Reynolds analogy concept has been used in almost all turbulent reacting flow RANS(Reynoldsaveraged Navier–Stokes)simulations,where the turbulence scalar transfers in flow fields are calculated based on the modeled turbulence momentum transfer.This concept,applied to a lean premixed combustion system,was assessed in this paper in terms of exit temperature distribution.Because of the isotropic assumption involved in this analogy,the prediction in some flow condition,such as jet cross flow mixing,would be inaccurate.In this study,using Flamelet Generated Manifold as reaction model,some of the numerical results,obtained from an annular combustor configuration with the turbulent Schmidt number varying from 0.85 to 0.2,were presented and compared with a benchmark atmospheric test results.It was found that the Schmidt numberσt in mean mass fraction f transport equation had significant effect on dilution air mixing process.The mixing between dilution air and reaction products from the primary zone obviously improved asσt decreased on the combustor exit surface.Meanwhile,the sensitivity ofσt in three turbulence models including Realizable k-ε,SST(Shear Stress Transport)and RSM(Reynolds Stress Model)has been compared as well.Since the calculation method of eddy viscosity was different within these three models,RSM was proved to be less sensitive than another two models and can guarantee the best prediction of mixing process condition.On the other hand,the results of dilution air mixing were almost independent of Schmidt number Sct in progress variable c transport equation.This study suggested that for accurate prediction of combustor exit temperature distribution in steady state reacting flow simulation,the turbulent Schmidt number in steady state simulation should be modified to cater to dilution air mixing process.

NUMERICAL SIMULATION AND EXPERIMENTAL INVESTIGATION OF THE GUIDE-VANE FLOW AND THE INFLUENCE FROM THE LEAKAGE FLOW

This paper presents numerical and experimental results of the flow in the tipclearance region of the guide vane row in hydraulic turbine. The 3-D Navier-Stokes equations wereemployed to model the flow in end clearance region of guide vane cascade, the Reynolds stressdifferential model was used for turbulence closure, and the body-fitted curvilinear coordinates andthe SIMPLE! algorithm were adopted. The governing equations were discretized with the non-staggeredgrids by means of the finite volume method. Detailed comparison of hydrodynamical characteristics ofguide vane in hydraulic turbine with or without tip gap was made. Special attention was paid to theinfluence of leakage flow on the main flow and to the movement of tip leakage flow in the end guidevane. The position and strength of the roll-vortex on the sides of guide vane in were determined.The numerical solutions agree with the experimental results obtained by particle image ve-locimetry.The results help to clarify the loss, wear and cavi-tation erosion between the guide vane andrings, especially for those used in the Yellow River which has a high sediment content.