Numerical study and acceleration of LBM-RANS simulation of turbulent flow

The coupled models of LBM （Lattice Boltzmann Method） and RANS （Reynolds-Averaged Navier-Stokes） are more practical for the transient simulation of mixing processes at large spatial and temporal scales such as crude oil mixing in large-diameter storage tanks. To keep the efficiency of parallel computation of LBM, the RANS model should also be explicitly solved; whereas to keep the numerical stability the implicit method should be better for PANS model. This article explores the numerical stability of explicit methods in 2D cases on one hand, and on the other hand how to accelerate the computation of the coupled model of LBM and an implicitly solved RANS model in 3D cases. To ensure the numerical stability and meanwhile avoid the use of empirical artificial lim- itations on turbulent quantities in 2D cases, we investigated the impacts of collision models in LBM （LBGK, MRT） and the numerical schemes for convection terms （WENO, TVD） and production terms （FDM, NEQM） in an explic- itly solved standard k-e model. The combination of MRT and TVD or MRT and NEQM can be screened out for the 2D simulation of backward-facing step flow even at Re = 107. This scheme combination, however, may still not guarantee the numerical stability in 3D cases and hence much finer grids are required, which is not suitable for the simulation of industrial-scale processes.Then we proposed a new method to accelerate the coupled model of LBM with RANS （implicitly solved）. When implemented on multiple GPUs, this new method can achieve 13.5-fold accelera- tion relative to the original coupled model and 40-fold acceleration compared to the traditional CFD simulation based on Finite Volume （FV） method accelerated by multiple CPUs. This study provides the basis for the transient flow simulation of larger spatial and temporal scales in industrial applications with LBM-RANS methods.

Study of Tunnel Thruster Performance and Flow by Quasi-Steady Reynolds-Averaged Navier-Stokes Simulation

A numerical approach based on the solution of the Reynolds-averaged Navier-Stokes(RANS) equations using the shear-stress transport(SST) turbulence model has been employed to investigate the hydrodynamic performance and flow of tunnel thrusters.The flow passages between adjacent blades are discretized with prismatic cells so that the boundary layer flow is resolved down to the viscous sub-layer.The hydrodynamic performances predicted by the quasi-steady approach agree well with the experimental data for three impellers covering a range of blade area and pitch.Through analysis of the flow field,the reason why the hub of impeller also contributes to thrust which can amount to 40%—60% of the impeller thrust,and the mechanism of the impeller inducing an axial force on the hull are elucidated.

Hybrid Reynolds-averaged Navier-Stokes/large-eddy simulation of jet mixing in a supersonic crossflow

A sonic under-expanded transverse jet injection into a Ma 1.6 supersonic crossflow is investigated numerically using our hybrid RANS/LES (Reynolds-averaged Navier-Stokes/large eddy simulation) method. First, a calculation is carried out to validate the code, where both the instantaneous and statistical results show good agreement with the existing experimental data. Then the jet-mixing characteristics are analyzed. It is observed that the large-scale vortex on the windward portion of the jet boundary is formed mainly by the intermittent impingement of the incoming high-speed fluid on the relatively low-speed region of the upstream jet boundary, where the interaction between the upstream separated region and the jet supplies a favorable pressure condition for the sustaining acceleration of the high-speed fluid during the vortex forming, associated with which the incoming fluid is entrained into the jet boundary and large-scale mixing occurs. Meanwhile, the secondary recirculation zone between the upstream separated region and the jet is observed to develop evidently during the vortex forming, inducing the entrainment of jet fluid into the upstream separated region. Moreover, effects of the incoming boundary layer on the jet mixing are addressed.

Flow Dynamics of a Spiral-groove Dry-gas Seal

The dry-gas seal has been widely used in different industries. With increased spin speed of the rotator shaft, turbulence occurs in the gas film between the stator and rotor seal faces. For the micro-scale flow in the gas film and grooves, turbulence can change the pressure distribution of the gas film. Hence, the seal performance is influenced. However, turbulence effects and methods for their evaluation are not considered in the existing industrial designs of dry-gas seal. The present paper numerically obtains the turbulent flow fields of a spiral-groove dry-gas seal to analyze turbulence effects on seal performance. The direct numerical simulation （DNS） and Reynolds-averaged Navier-Stokes （RANS） methods are utilized to predict the velocity field properties in the grooves and gas film. The key performance parameter, open force, is obtained by integrating the pressure distribution, and the obtained result is in good agreement with the experimental data of other researchers. Very large velocity gradients are found in the sealing gas film because of the geometrical effects of the grooves. Considering turbulence effects, the calculation results show that both the gas film pressure and open force decrease. The RANS method underestimates the performance, compared with the DNS. The solution of the conventional Reynolds lubrication equation without turbulence effects suffers from significant calculation errors and a small application scope. The present study helps elucidate the physical mechanism of the hydrodynamic effects of grooves for improving and optimizing the industrial design or seal face pattern of a dry-gas seal.

Investigating the Performance of Twin Marine Propellers in Different Ship Wake Fields Using an Unsteady Viscous and Inviscid Solver

In this study,the performance of a twin-screw propeller under the influence of the wake field of a fully appended ship was investigated using a coupled Reynolds-averaged Navier–Stokes(RANS)/boundary element method(BEM)code.The unsteady BEM is an efficient approach to predicting propeller performance.By applying the time-stepping method in the BEM solver,the trailing vortex sheet pattern of the propeller can be accurately captured at each time step.This is the main innovation of the coupled strategy.Furthermore,to ascertain the effect of the wake field of the ship with acceptable accuracy,a RANS solver was developed.A finite volume method was used to discretize the Navier–Stokes equations on fully unstructured grids.To simulate ship motions,the volume of the fluid method was applied to the RANS solver.The validation of each solver(BEM/RANS)was separately performed,and the results were compared with experimental data.Ultimately,the BEM and RANS solvers were coupled to estimate the performance of a twin-screw propeller,which was affected by the wake field of the fully appended hull.The proposed model was applied to a twin-screw oceanography research vessel.The results demonstrated that the presented model can estimate the thrust coefficient of a propeller with good accuracy as compared to an experimental self-propulsion test.The wake sheet pattern of the propeller in open water(uniform flow)was also compared with the propeller in a real wake field.

AERODYNAMIC OPTIMIZATION FOR TURBINE BLADE BASED ON HIERARCHICAL FAIR COMPETITION GENETIC ALGORITHMS WITH DYNAMIC NICHE

A global optimization approach to turbine blade design based on hierarchical fair competition genetic algorithms with dynamic niche （HFCDN-GAs） coupled with Reynolds-averaged Navier-Stokes （RANS） equation is presented. In order to meet the search theory of GAs and the aerodynamic performances of turbine, Bezier curve is adopted to parameterize the turbine blade profile, and a fitness function pertaining to optimization is designed. The design variables are the control points＇ ordinates of characteristic polygon of Bezier curve representing the turbine blade profile. The object function is the maximum lift-drag ratio of the turbine blade. The constraint conditions take into account the leading and trailing edge metal angle, and the strength and aerodynamic performances of turbine blade. And the treatment method of the constraint conditions is the flexible penalty function. The convergence history of test function indicates that HFCDN-GAs can locate the global optimum within a few search steps and have high robustness. The lift-drag ratio of the optimized blade is 8.3% higher than that of the original one. The results show that the proposed global optimization approach is effective for turbine blade.

NUMERICAL STUDY OF AN OSCILLATORY TURBULENT FLOW OVER A FLAT PLATE

Oscillatory turbulent flow over a flat plate was studied by using large eddy simulation (LES) and Reynolds-average Navier-Stokes (RANS) methods. A dynamic subgrid-scale model was employed in LES and Saffman's turbulence model was used in RANS. The flow behaviors were discussed for the accelerating and decelerating phases during the oscillating cycle. The friction force on the wall and its phase shift from laminar to turbulent regime were also investigated for different Reynolds numbers. (Edited author abstract) 11 Refs.

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.

Characteristics of transonic moist air flows around butterfly valves with spontaneous condensation

Effects of spontaneous condensation of moist air on the shock wave dynamics around butterfly valves in transonic flows are investigated by experimental and numerical simulations.Two symmetric valve disk shapes namely-a flat rectangular plate and a mid-plane cross-section of a prototype butterfly valve have been studied in the present research.Results showed that in case with spontaneous condensation,the root mean square of pressure oscillation(induced by shock dynamics)is reduced significantly with those without condensation for both shapes of the valves.Moreover,local aerodynamic moments were reduced in case with condensation which is considered to be beneficial in torque requirement in case of on/off applications of valves as flow control devices.However,total pressure loss was increased with spontaneous condensation in both the valves.Furthermore,the disk shape of a prototype butterfly valve showed better aerodynamic performances compared to flat rectangular plate profile in respect of total pressure loss and vortex shedding frequency in the wake region.

一种改进的类DES湍流模拟方法

构造了一种基于一方程S-A(Spalart-Allmaras)模型和一方程Yoshizawa亚格子模型的混合RANS/LES(Reynolds-averaged Navier-Stokes/large eddy simulation)湍流模拟方法.在涡黏假设的基础上,将Yoshizawa亚格子湍动能方程转化为等效的亚格子湍流涡黏性输运方程,并采用混合函数将其与S-A模型方程进行混合,从而改进了DES(detached eddy simulation)模型的亚格子行为,同时克服了其依靠网格控制模型转换的缺点.模拟了超声速的带斜坡凹腔流动,并与相同网格下的LES及DES结果进行了比较,结果表明该混合RANS/LES方法在远离壁面的自由剪切流区域与LES行为一致,而在附着边界层区域表现优于LES和DES方法.

PREDICTION OF LOADING DISTRIBUTION AND HYDRODYNAMIC MEASUREMENTS FOR PROPELLER BLADES IN A RIM DRIVEN THRU-STER

This article presents an approach which employs a commercial Reynolds-Averaged Navier-Stokes（RANS）solver to predict the steady wake field and loading distributions for a rim driven thruster.Four different cases of propeller blades are chosen to be calculated with the presented method.The propeller blade radial circulation and chordwise circulation density distributions are analyzed.The maximum radial circulation is found at the blade tip,which is different from conventional shaft driven propeller.The numerical results indicate that there is no tip leakage vortex in rim driven propulors.But there exist the tip joint vortex and the root region vortex.Bollard characteristics are calculated by taking rim surface effect into account.From the predicted results the second case in this paper is selected as the final one to perform hydrodynamic experiment.The calculation results with empirical rim surface corrections are compared with the measurement.It shows that the developed numerical method can well predict hydrodynamic performances of the rim driven thruster.

Constrained large-eddy simulation and detached eddy simulation of flow past a commercial aircraft at 14 degrees angle of attack

With the development of computational power and numerical algorithms,computational fluid dynamics(CFD) has become an important strategy for the design of aircraft,which significantly reduces the reliance on wind-tunnel and flight tests.In this paper,we conducted a numerical investigation on the flow past a full commercial aircraft at Mach number 0.2 and 14 degrees angle of attack by means of Reynolds-averaged Navier-Stokes(RANS),detached-eddy simulation(DES) and our newly developed constrained large-eddy simulation(CLES).The objective of this paper is to study the capability of these models in simulating turbulent flows.To our knowledge,this is the first large-eddy simulation method for full commercial aircraft simulation.The results show that the CLES can predict the mean statistical quantities well,qualitatively consistent with traditional methods,and can capture more small-scale structures near the surface of the aircraft with massive separations.Our study demonstrates that CLES is a promising alternative for simulating real engineering turbulent flows.

NUMERICAL INVESTIGATION OF CAVITATION PERFORMANCE OF SHIP PROPELLERS

The cavitation performance of propellers is studied based on viscous multiphase flow theories. With a hybrid grid based on Navier-Stokes （N-S） and bubble dynamics equations, some recent validation results are presented in this paper in the predictions of the thrust, the torque and the vapor volume fraction on the back side of propeller blade for a uniform inflow. The numerical predictions of the hydrodynamic performance and the sheet cavitation under several operating conditions for two propellers agree with the corresponding measured data in general. The thrust and the torque are plotted with respect to the advance rate and the cavitation number. The cavitation performance breakdown is closely related to the strong sheet cavitation around propellers. The models with parameters modified are shown to predict the propeller cavitation well.

LARGE-EDDY AND DETACHED-EDDY SIMULATIONS OF THE SEPARATED FLOW AROUND A CIRCULAR CYLINDER

The separated turbulent flow around a circular cylinder is investigated using Large-Eddy Simulation （LES）, Detached-Eddy Simulation （DES, or hybrid RANS/LES methods）, and Unsteady Reynolds-Averaged Navier-Stokes （URANS）. The purpose of this study is to examine some typical simulation approaches for the prediction of complex separated turbulent flow and to clarify the capability of applying these approaches to a typical case of the separated turbulent flow around a circular cylinder. Several turbulence models, i.e. dynamic Sub-grid Scale （SGS） model in LES, the DES-based Spalart-Allmaras （S-A） and κ-ω Shear-Stress- Transport （SST） models in DES, and the S-A and SST models in URANS, are used in the calculations. Some typical results, e.g., the mean pressure and drag coefficients, velocity profiles, Strouhal number, and Reynolds stresses, are obtained and compared with previous computational and experimental data. Based on our extensive calculations, we assess the capability and performance of these simulation approaches coupled with the relevant turbulence models to predict the separated turbulent flow.

Numerical investigation of flow separation behavior in an over-expanded annular conical aerospike nozzle

A three-part numerical investigation has been conducted in order to identify the flow separation behavior––the progression of the shock structure, the flow separation pattern with an increase in the nozzle pressure ratio（NPR）, the prediction of the separation data on the nozzle wall,and the influence of the gas density effect on the flow separation behavior are included.The computational results reveal that the annular conical aerospike nozzle is dominated by shock/shock and shock/boundary layer interactions at all calculated NPRs, and the shock physics and associated flow separation behavior are quite complex.An abnormal flow separation behavior as well as a transition process from no flow separation at highly over-expanded conditions to a restricted shock separation and finally to a free shock separation even at the deign condition can be observed.The complex shock physics has further influence on the separation data on both the spike and cowl walls, and separation criteria suggested by literatures developed from separation data in conical or bell-type rocket nozzles fail at the prediction of flow separation behavior in the present asymmetric supersonic nozzle.Correlation of flow separation with the gas density is distinct for highly overexpanded conditions.Decreasing the gas density or reducing mass flow results in a smaller adverse pressure gradient across the separation shock or a weaker shock system, and this is strongly coupled with the flow separation behavior.The computational results agree well with the experimental data in both shock physics and static wall pressure distribution at the specific NPRs, indicating that the computational methodology here is advisable to accurately predict the flow physics.

Compressible flow characteristics around a biconvex arc airfoil in a channel

Shock wave-boundary layer interactions(SWBLI)are observed in several practical high-speed internal flows,such as compressor blades,turbine cascades,nozzles and so on.Shock induced oscillations(SIO),aerodynamic instabilities so-called buffet flows,flutter,aeroacoustic noise and vibration are the detrimental consequences of this unsteady shockboundary layer interactions.In the present study,a numerical computation has been performed to investigate the compressible flow characteristics around a 12%thick biconvex circular arc airfoil in a two dimensional channel.Reynolds averaged Navier-Stokes equations with two equation k-ωshear stress transport(SST)turbulence model have been applied for the computational analysis.The flow field characteristics has been studied from pressure ratio(ratio of back pressure,pb to inlet total pressure,p01)of 0.75 to 0.65.The present computational results have been compared and validated with the available experimental data.The results showed that the internal flow field characteristics such as shock wave structure,its behavior(steady or unsteady)and the corresponding boundary layer interaction are varied with pressure ratio.Self-excited shock oscillation was observed at certain flow conditions.Moreover,the mode of unsteady shock oscillation and its frequency are varied significantly with change of pressure ratio.

Turbulence modelling of the aerodynamic interaction ofOGV wakes and diffuser flow

Different turbulence closures were used to predict the flow interaction between the wakes created by compressor outlet guide vanes(OGVs) and a downstream annular pre-diffuser.Two statistical turbulence models were tested based on the classical Reynolds-averaged Navier-Stokes(RANS) approach.Both high-Re and low-Re(Launder-Sharma) versions of the k-ε model were applied to a selected test problem for OGV wake/diffuser flows.The test problem was specifically chosen because experimentally determined inlet conditions and both profile and performance data were available to validate predictions.A preliminary study was also reported of the more advanced large eddy simulation(LES) approach.The LES sub-grid-scale(SGS) model was the basic Smagorinsky eddy viscosity assumption,with a Van-Driest damping function for improved capture of near-wall viscous behaviour.Comparison between the two RANS models showed little difference in terms of velocity contours at OGV trailing edge and diffuser exit.In terms of overall diffuser performance(static pressure recovery and total pressure loss coefficients),the high-Re model was shown to agree well with experimental data.The preliminary LES study indicates the highly unsteady character of the OGV wake flow,but requires improved treatment of inlet conditions.

Computational Fluid Dynamics Uncertainty Analysis for Simulations of Roll Motions for a 3D Ship

The roll motions are influenced by significant viscous effects such as the flow separation.The 3D simulations of free decay roll motions for the ship model DTMB 5512 are carried out by Reynold averaged NavierStokes(RANS) method based on the dynamic mesh technique.A new moving mesh technique is adopted and discussed in details for the present simulations.The purpose of the research is to obtain accurate numerical prediction for roll motions with their respective numerical/modeling errors and uncertainties.Errors and uncertainties are estimated by performing the modern verification and validation(V&V) procedures.Simulation results for the free-floating surface combatant are used to calculate the linear,nonlinear damping coefficients and resonant frequencies including a wide range of forward speed.The present work can provide a useful reference to calculate roll damping by computational fluid dynamics(CFD) method and simulate a general ship motions in waves.

Nozzle geometry variations on the discharge coefficient

Numerical works have been conducted to investigate the effect of nozzle geometries on the discharge coefficient.Several contoured converging nozzles with finite radius of curvatures,conically converging nozzles and conical divergent orifices have been employed in this investigation.Each nozzle and orifice has a nominal exit diameter of 12.7x10^(-3)m.A 3rd order MUSCL finite volume method of ANSYS Fluent 13.0 was used to solve the Reynolds-averaged Navier-Stokes equations in simulating turbulent flows through various nozzle inlet geometries.The numerical model was validated through comparison between the numerical results and experimental data.The results obtained show that the nozzle geometry has pronounced effect on the sonic lines and discharge coefficients.The coefficient of discharge was found differ from unity due to the non-uniformity of flow parameters at the nozzle exit and the presence of boundary layer as well.

Numerical prediction of effective wake field for a submarine based on a hybrid approach and an RBF interpolation

A hybrid approach coupled with a surface panel method for the propeller and a Reynolds averaged Navier-Stokes（RANS） model for the hull with the propeller body forces are presented for predicting the self-propulsion performance and the effective wake field of underwater vehicles. To achieve a high accuracy and simplicity, a radial basis function（RBF） based approach is proposed for mapping the force field from the blade surface panels to the RANS model. The effective wake field is evaluated in two ways, i.e., by extrapolation from the flat planes upstream of the propeller disk, and by direct computation in a curved surface upstream of and parallel to the blade leading edges. The hull-propeller system of a real propeller geometry is further simulated with the sliding mesh model to numerically verify the hybrid approach. Numerical simulations are conducted for the fully appended SUBOFF submarine model. The high accuracy of the RBF-based interpolation scheme is confirmed, and the effective wake fraction predicted by the hybrid approach is found consistent with that obtained by the sliding mesh model. The effective wake fractions predicted by the two methods are, respectively, 4.6% and 3% larger than the nominal one.