Navier—Stokes Computations of the Supersonic Ejector—Diffuser System with a Second Throat

The supersonic ejector-diffuser system with a second throat was simulated using CFD.An explicit finite volume scheme was applied to solve two-dimensional Navier-Stokes equations with standard κ-εturbulence model.The vacuum performance of the supersonic ejector-diffuser system was investigated by changing the ejector throat area ration and the operating pressure ratio.Two convergent-divergent nozzles with design Mach number of 2.11 and 3.41 were selected to give the supersonic operation of the ejector-diffuser system.The presence of a second throat strongly affected the shock wave structure inside the mixing tube as well as the spreading of the under-expanded jet discharging from the primary nozzle.There were optimum values of the operating pressure ratio and ejector throat area ratio for the vacuum performance of the system to maximize.     

A κ-ε Turbulence Model Considering Compressibility in Three-Dimensional Transonic Turbulent Flow Calculation

Based on the standark κ-ε turbulence model,a new compressible κ-ε model considering the pressure expansion influence due to the compressibility of fluid is developed and aplied to the simulation of 3D transonic turbulent flows in a nozzle and a cascade.The Reynolds averaged N-S equations in generalized curvilinear coordinates are solved with implementation of the new model,the high resolution TVD scheme is used to discretize the convective terms.The numerical results show that the compressible κ-ε odel behaves well in the simulation of transonic internal turbulent flows.     

Application and comparison of SST model in numerical simulation of the axial compressors

<正>The shear-stress transport(SST)turbulence model is incorporated into Navier-Stokes equations to simulate a turbomachinery flowfield.A staggered finite volume method is used to make the mean flow equations and turbulence model equations strongly coupled and enhance the stability of the numerical computation.The implicit treatment of the source terms is applied to the SST model.A steady state solution is obtained using five-stage Runge-Kutta time-stepping scheme with local time stepping and residual smoothing to accelerate convergence. The wall distance d,a key parameter in the SST model,is solved by a partial differential equation.The validations of the code are conducted on rotor 37,wp11 at design and off-design conditions by comparison with measurements and the Spalart-Allmaras(SA)turbulence model.The flow within the tip is calculated with a multi-block grid.     

An Analysis of Flow in a Centrifugal Impeller by FEM with k—ε Model

In this study,we attempt the analysis of the passage flow in the centrifugal impeller using FEM with/without the turbulence model,and compare this result with the experimental result.The turbulence model is the low Reynolds k-ε model proposed by Chien.We use the GSMAC method for the Reynolds averaged Navier-Stokes equations,the Euler explicit method for the transport equations of the turbulent kinetic energy and the dissipation rate.All equations are discretized by the Galerkin‘s method.At the midpassage of the centrifugal impeller,the passagewise velocity component tends to increase in the pressure-to-suction direction,and the other component toward the pressure surface tends to be large in the region of the middle blade-to-blade to the hub side.The tip leakages appear around the region of the middle blade-to-blade near the casing together with the secondary flow toward the suction surface.These phenomena correspond with the experimental result,qualitatively.     

Study of Spiral Flow Generated through an Annular Slit

The effect of pressurized air inlets in the reservoir upstream of the annular slit on characteristics of the axial and tangential velocity components is investigated numerically, and the mechanism of occurrence of spiral nozzle flow is clarified. In simulations, Unified Platform for Aerospace Computational Simulation (UPACS) is used. The governing equations under consideration are the unsteady compressible Navier - Stokes. A second-order finite volume scheme with MUSCL (Roe scheme) is used to discretize the spatial derivatives, and a second order-central difference scheme for the viscous terms, and a MFGS (Matrix Free Gauss Seidel) is employed for time integration. Spalart-Allmaras model was used as a turbulence model. The results obtained are compared with velocity distributions in the experiment measured by the two-component fiber optic laser Doppler velocimeter system. The existence of discrete pressurized air inlets that leads to the occurrence of asymmetrical characteristics is a very important factor for the formation of spiral flow.     

Computational research on rotating channel by a modified anisotropic turbulence model

Based on the simplified format of the Reynolds stress equations,a fire-new rotational-modification method for the anisotropic turbulence model has been presented.A three-dimensional Navier-Stokes code with this new rotational modified k-ω turbulence models(β=0.1 and β=1) and the standard k-ω turbulence model have been used for the prediction of flow and heat transfer characteristics in a rotating smooth square channel.The Reynolds number Re based on the inlet velocity of the cooling air and hydraulic diameter is 6000.The rotating speed are 300,600,900,1200rpm respectively.The calculations results of using three turbulence models have been compared with the experimental data.The research results show that(1) the rotational modification coefficient Rf13 used in the new anisotropic k-ω model would increased/decreased the predictions of heat transfer on the trailing surface/leading surface compared to the standard k-ω model.And this tendency would be increased with the increased β.(2) The simulation performance of the standard k-ω model was well on the leading surface.However,on the trailing surface it under-predicted the heat transfer at high rotating speed.(3) The calculation results of the new anisotropic k-ω model with β=0.1 proposed by the present paper agreed well with experimental data,both on the leading and trailing surfaces.Besides,compared to 1,0.1 is a more appropriate magnitude of β at conditions in the present paper.     

Numerical Study of Forced Convection Lid-Driven Cavity Flows Using LES （Large Eddy Simulation）

This study presents the LES （large eddy simulation） of forced convection in laminar and two dimensional turbulent flows when the flow reaches the steady state. The main purpose is the evaluation of a developed numerical methodology for the simulation of forced convection flows at various Reynolds numbers （100 _〈 Rex 〈_ 10,000） and for a fixed Prandtl number （Pr = 1.0）. The hexahedral eight-node FEM （finite element method） with an explicit Taylor-Galerkin scheme is used to obtain the numerical solutions of the conservation equations of mass, momentum and energy. The Smagorinsky model is employed for the sub-grid treatment. The time-averaged velocity and temperature profiles are compared with results of literature and a CFD （computational fluid dynamics） package based on finite volume method, leading to a highest deviation of nearly 6%. Moreover, characteristics of the forced convection flows are properly obtained, e.g., the effect of the Reynolds number over the multiplicity of scales.     

Shape Optimization of Inclined Ribs as Heat Transfer Augmentation Device

This work presents numerical optimization techniques for the design of a rectangular channel with inclined ribs toenhance turbulent heat transfer.The response surface method with Reynolds-averaged Navier-Stokes analysis isused for optimization.Shear stress transport turbulence model is used as a turbulence closure.Computational re-sults for local heat transfer rate show a reasonable agreement with the experimental data.Width-to-rib height ratioand attack angle of the rib are chosen as design variables.The objective function is defined as a linear combina-tion of heat-transfer and friction-loss related terms with the weighting factor.Full-factorial experimental designmethod is used to determine the data points.Optimum shapes of the channel have been obtained in a range of theweighting factor.     

Assessment of Linear and Non-Linear Two-Equation Turbulence Models for Aerothermal Turbomachinery Flows

Three linear two-equation turbulence models k -ε, k -ωand k -1 and a non-linear k -1 model are used for aerodynamic and thermal turbine flow prediction. The pressure profile in the wake and the heat transfer coefficient on the blade are compared with experimental data. Good agreement is obtained with the linear k -1 model. No significant modifications are observed with the non-linear model. The balance of transport equation terms in the blade wake is also presented. Linear and non-linear k -1 models are evaluated to predict the three-dimensional vortices characterising the turbine flows. The simulations show that the passage vortex is the main origin of the losses.     

Optimization of Mass Bleed Control for Base Drag Reduction of Supersonic Flight Bodies

The minimization of base drag using mass bleed control is examined in consideration of various base to orifice exit area ratios for abody of revolution in the Mach 2.47 fieestream.Axisymmetric,compressible,mass-averaged Navier-Stokes equations are solvedusing the standard k-ω turbulence model,a fully implicit finite volume scheme,and a second order upwind scheme.Base flowcharacteristics are explained regarding the base configuration as well as the injection parameter which is defined as the mass flow rateof bleed jet non-dimensionalized by the product of tile base area and freestream mass flux.The results obtained through the presentstudy show that for a smaller base area,the optimum mass bleed condition leading to minimum base drag occurs at relatively largermass bleed,and a larger orifice exit can offer better drag control.     

Unsteady shock-flow characteristics in an over-expanded rocket nozzle

<正>A numerical investigation of transient side-loads in an axisymmetric over-expanded thrust optimized contour nozzle is presented.These nozzles experience side-loads during start-up and shut-down operations,because of the flow separation at nozzle walls.Two types of flow separations such as FSS and RSS shock structure occur.A two-dimension numerical simulation has been carried out over an axisymmetric TOC nozzle to validate present results and investigate oscillatory flow characteristics for start-up processes.Reynolds Averaged Navier-Stokes equations are numerically solved using a fully implicit finite volume scheme.Governing equations are solved by coupled implicit scheme.Reynolds Stress turbulence model is selected.Present computed pressure at the nozzle wall closely matched with experiment data.A hysteresis phenomenon has been observed between these two shock structures.The transition from FSS to RSS pattern during start-up process has shown maximum nozzle wall pressure.Nozzle wall pressure and shear stress values have shown fluctuations during the FSS to RSS transition. The oscillatory pressure has been observed on the nozzle wall for high pressure ratio.Present results have shown that magnitude of the nozzle wall pressure variation is high for the oscillatory phenomenon.     

Experimental Study on Jet Blast at Laboratory Scale

The flow field of 3D （three-dimensional） wall-jet is investigated. Jet-blast from airplane is simulated by wall-jet setup using a sonic nozzle at a laboratory scale. Farfield velocity and fluctuation distributions are measured by using X-type hot wire anemometer at four measurement planes. As a result, the flow properties of streamwise component are consistent with data which are obtained in previous researches. The secondary flow is also measured on each measurement plane. Reynolds stresses, v＇v＇ and w＇ w＇, are analyzed from the fluctuation of the secondary flow. The law of similarity is observed in the dimensionless distributions of mean velocity and fluctuation. However, the distributions in nearer field （i.e., in the measurement plane at X/D = 100） tend to disobey the similarity law, especially in the cases of fluctuation. It seems that jet-blast is not fully developed by reaching X/D = 100. The experimental results are compared with computational results which are obtained by CFD （computational fluid dynamics） with SST （shear-stress transport） turbulence model. And it is shown that the results by the simulation with SST turbulence model do not follow the similarity law. The present database of the Reynolds stresses is critically important for development of a new turbulence model of RANS （reynolds-averaged navier-atokes） simulations on wall-jet.     

Turbulent Mixed Convection—Radiation Interactions in a Cavity

Two-dimensional turbulent mixed convection-surface radiation interaction phenomenon in a back-wall-heated open square cavity is numerically investigated. The flow medium is air, and the turbulence model used is the Low-Reynolds-Number κ-ε Scheme. Calculations have been performed for Grashof numbers Gr up to 10~(10). And the Richardson number Ri covers a range of 4×10~(-3)-45. It is shown that within a rather extensive range of Ri, the effects of radiation on the heat transfer and fluid flow in the cavity are significant, should not be neglected and become stronger with the increase of Ri and Gr.     

Theoretical and computational analyses of LNG evaporator

Theoretical and numerical analysis on the fluid flow and heat transfer inside a LNG evaporator is conducted in this work.Methane is used instead of LNG as the operating fluid.This is because;methane constitutes over 80％ of natural gas.The analytical calculations are performed using simple mass and energy balance equations.The analytical calculations are made to assess the pressure and temperature variations in the steam tube.Multiphase numerical simulations are performed by solving the governing equations (basic flow equations of continuity,momentum and energy equations) in a portion of the evaporator domain consisting of a single steam pipe.The flow equations are solved along with equations of species transport.Multiphase modeling is incorporated using VOF method.Liquid methane is the primary phase.It vaporizes into the secondary phase gaseous methane.Steam is another secondary phase which flows through the heating coils.Turbulence is modeled by a two equation turbulence model.Both the theoretical and numerical predictions are seen to match well with each other.Further parametric studies are planned based on the current research.     

Natural Convection of Nanofluid in Cylindrical Enclosure Filled with Porous Media

A numerical study has been carried out to investigate the effect of aspect ratio on heat transfer by natural convection of nanofluid taking Cu nano particles and the water as based fluid. The flow is laminar, steady state, axisymmetric two-dimensional in a vertical cylindrical channel filled with porous media. Heat is generated uniformly along the center of the channel with its vertical surface remain with cooled constant wall temperature and insulated horizontal top and bottom surfaces. The governing equations which used are continuity, momentum and energy equations using Darcy law and Boussinesq＇s approximation which are transformed to dimensionless equations. The finite difference approach is used to obtain all the computational results using the MATLAB-7 program. The parameters affected on the system are Rayleigh number ranging within （10≤ Ra ≤ 103）, aspect ratio （1 ≤ As 〈 5） and the volume fraction （0 ≤0 〈 0.2）. The results obtained are presented graphically in the form of streamline and isotherm contour plots and the results show that as ~ increase from 0.01 to 0.2 the value of the mean Nusselt number increase 50.4% for Ra = 1,000.     

A Study of 2D Separated Cascade Flow at Large Angles of Attack Using Euler Equations

This paper presents a numerical simulation method developed for separated flow in cascades using the Eulerequations and demonstrates the feasibility of this method.MacCormack's two-steps explicit finite differencescheme is used to discretize the equations in conservation form,and the artificial viscosity is added to the dis-cretized inviscid equations by means of the self-adapted filter technique.The initial separation boundary is givenaccording to simple experimental results.The numerical simulation results including subsonic and transonicturbine cascades flow with or without separation show that the fundamental idea of this numerical method isreasonable and simple.The present study indicates that for solving certain engineering problems it is a simpleand effective tool for adding some viscosity corrections to inviscid flow model,especially the current when theNavier-Stokes equations have not been solved very effectively for various complicated flows in turbomachinery.     

Magnetohydrodynamic Effect on Free Convection of Three Dimensional Laminar Flow in Porous Annulus

A numerical study has been carried out to investigate heat transfer by free convection under the effect of MHD （magnetohydrodynamic） for steady state three-dimensional laminar flow in horizontal and vertical cylindrical annulus filled with saturated porous media （sand silica） with fins attached to the inner cylinder. A single electric coil placed around the inner cylinder to generate a magnetic field. The governing equations which used are continuity, momentum （using Darcy＇s law） and energy equations which are transformed to dimensionless equations. The finite difference approach is used to obtain all the computational results using Fortran 90 program. The parameters affected on the system are Rayleigh number ranging within （102 ~ Ra＊ 〈 104）, and MHD （Mn） （0 〈_ Mn 〈_ 100） and radius ratio Rr （0.225, 0.338 and 0.435）. The results obtained are presented graphically in the form of streamline and isotherm contour plots and the results show that heat transfer decrease with the increase of magnetohydrodynamic. It was found that the average Nusselt number increase with Ra＊ and decrease with H~ Mn and Rr. A correlation for the average Nusselt number in terms of Ra＊ and Mn, has been developed for the inner cylinder.     

Theoretical and numerical stability analysis of the liquid metal pinch using the shallow water approximation

The pinch instability for a cylindrical jet of liquid metal passed through by an axial electrical current is investigated. Besides the pinch effect originating from surface tension, the Lorentz force, created by the axial current density and the corresponding azimuthal magnetic field, causes an electromagnetic pinch effect. This effect has drawn attention in electrical engineering, because it can be used in the construction of liquid metal current limit- ers with self-healing properties. In this paper a simple model is derived using the shallow water approximation： the equations describing the full system are reduced to two one-dimensional evolution equations for the axial velocity and the radius of the jet. A stability analysis for this reduced system is carried out yielding critical current density and the growth rate for the instability. To investigate the nonlinear behaviour of the pinch instability for finite perturbations simulations, the shallow water model are performed.     

An Improved k-Equation Turbulence Model

LRN （low-Reynolds number） modifications to the NR （Norris-Reynolds） k-equation turbulence model are proposed and evaluated. The k and e that render the hybrid time scale are determined using the k-transport equation together with the Bradshaw and other algebraic relations. The eddy-viscosity coefficient Cμ and the empirical damping function are constructed such as to preserve the anisotropic characteristics of turbulence for application to non-equilibrium turbulent flows. The MNR （modified NR） model is applied to calculate two well-documented flows, yielding predictions in good agreement with the DNS （direct numerical simulation） and experimental data. Comparisons demonstrate that the MNR model offers a significant improvement over the original NR model and competitiveness with the Spalart-Allmaras one-equation turbulence model. The performance evaluation dictates that unlike the original NR model, the MNR model can be employed as a single-equation model instead of associating it with the two-layer model of turbulence.     

Thermal Performance of Elliptical Fin-and-Tube Heat Exchangers with Vortex Generator under Various Inclination Angles

Elliptical fin-and-tube heat exchangers are commonly used in air conditioning,heating,refrigeration industries,and ventilation.This study numerically investigates the effect of vortex generators on the performance of elliptical fin-and-tube heat exchanger under different inclination angles.In this study,air flow that is in the transitional regime is selected as the working fluid.Reynolds numbers at the inlet are varied in a range of 1300 to 2100,and the shear stress transport k-ωturbulence model is selected to solve the non-closure of basic turbulence equations.The ellipticity ratios of the tubes which are used for the analysis are between 0.6 and 1.0,and the inclination angles are varied from 15°to 75°.The effects of different inclination angles of vortex generators on the Colburn factor j,friction factor f,and efficiency index j/f are analyzed.The friction and Colburn factors are observed to increase with increasing vortex generator inclination angles.It is found that the efficiency factors for a 15°vortex generator inclination angle at 0.6,0.7,0.8,and 0.9 ellipticity ratios improve compared to the corresponding cases with no vortex generator.However,the vortex generator cannot improve the efficiency factor of the circular tube heat exchanger.The 3 D CFD method employed by this study has great potential for use in optimally designing the arrangement of the vortex generators to enhance the performance of heat exchangers.