UNSTEADY/STEADY NUMERICAL SIMULATION OF THREE-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS ON ARTIFICIAL COMPRESSIBILITY

A mixed algorithm of central and upwind difference scheme for the solution of steady/unsteady incompressible Navier-Stokes equations is presented. The algorithm is based on the method of artificial compressibility and uses a third-order flux-difference splitting technique for the convective terms and the second-order central difference for the viscous terms. The numerical flux of semi-discrete equations is computed by using the Roe approximation. Time accuracy is obtained in the numerical solutions by subiterating the equations in pseudotime for each physical time step. The algebraic turbulence model of Baldwin-Lomax is ulsed in this work. As examples, the solutions of flow through two dimensional flat, airfoil, prolate spheroid and cerebral aneurysm are computed and the results are compared with experimental data. The results show that the coefficient of pressure and skin friction are agreement with experimental data, the largest discrepancy occur in the separation region where the lagebraic turbulence model of Baldwin-Lomax could not exactly predict the flow.

Discussion of Direct Numerical Simulation Method for Supercritical Carbon Dioxide Jet Flow

A kind of direct numerical simulation method suitable for supercritical carbon dioxide jet flow has been discussed in this paper. The form of dimensionless nonconservative compressible Navier-Stokes equations in a two-dimensional cartesian coordinate system is derived in detail. High accurate finite difference compact schemes based on non-uniform grid system are introduced to solve the equations. The simulation results of the three vortex pairing phenomenon of plane mixing layer and a compressible axisymmetric jet flow field show that the discussed numerical simulation method is feasible to calculate the supercritical carbon dioxide jet fluid. And it is found that the difficulties of splitting the convective terms in conservation Navier-Stokes equations, which are brought by the supercritical carbon dioxide fluid pressure state equation, can be avoided by solving the nonconservative compressible Navier-Stokes equations.

AN INTEGRATION METHOD WITH FITTING CUBIC SPLINE FUNCTIONS TO A NUMERICAL MODEL OF 2ND-ORDER SPACE-TIME DIFFERENTIAL REMAINDER——FOR AN IDEAL GLOBAL SIMULATION CASE WITH PRIMITIVE ATMOSPHERIC EQUATIONS

In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the spherical coordinates.The Spline Model,which adopted the Navier-Stokes primitive equations and quasi-Lagrangian time-split integration scheme,provides an initial ideal case of global atmospheric circulation.In addition,considering the essentially non-linear atmospheric motions,the Spline Model could judge reasonably well simple points of any smoothed variable field according to its fitting spline curvatures that must conform to its physical interpretation.

BGK-EQUATION SIMULATION OF THE EXHAUST PLUME FORMED BY A MANOEUVRE THRUSTER IN OUTER SPACE

The general principle of utilizing the BGK equation to simulate a macroscopic gas flow is illustrated. Two typical examples, i.e., a low-speed axisymmetric submerged jet and the Prandtl-Meyer expansion to a vacuum, are presented for validating the feasibility and accuracy of the BGK-equation simulation in continuum and non-continuum flow regimes. This approach is then used to simulate the exhaust plume formed by a small manoeuvre thruster of an artificial satellite in the outer space. The plume impingement on a flat surface perpendicular to the nozzle axis is also simulated by the same method. In the latter case the impingement force acting on the flat surface is calculated. When the flow reaches to the steady state the calculated impingement force is reasonably compared with the theoretical value of the nozzle thrust.

A New Finite Volume Element Formulation for the Non-Stationary Navier-Stokes Equations

A semi-discrete scheme about time for the non-stationary Navier-Stokes equations is presented firstly,then a new fully discrete finite volume element(FVE)formulation based on macroelement is directly established from the semi-discrete scheme about time.And the error estimates for the fully discrete FVE solutions are derived by means of the technique of the standard finite element method.It is shown by numerical experiments that the numerical results are consistent with theoretical conclusions.Moreover,it is shown that the FVE method is feasible and efficient for finding the numerical solutions of the non-stationary Navier-Stokes equations and it is one of the most effective numerical methods among the FVE formulation,the finite element formulation,and the finite difference scheme.

NUMERICAL SIMULATION OF THREE DIMENSIONAL INTERACTING TURBULENCE FLOW FIELD OVER PROJECTILE WITH LATERAL JETS

In order to study complicated interacting flow field over projectile with lateral jets. External interacting turbulence flow over projectile with lateral jets was numerically simulated firstly in supersonic speed and zero attack angle. The three dimensional Reynolds averaged Navier Stokes equations and implicit finite volume TVD scheme were applied. In order to avoid zonal method, ’O’ type grid of single zone including projectile base was produced by algebraic arithmetic. Body fitted grid was generated for the lateral nozzle exit successfully so that the nozzle exit can be simulated more accurately. The high Reynolds number two equation κ ε turbulence models were used. The main features of the complex flow are captured. The two kinds of flow field over projectile with and without lateral jets are compared from shock structure, pressure of body and base, etc . It shows that lateral jets not only can provide push force, but also change aerodynamics characteristic of projectile significantly. The results are very important for the study of projectile with lateral rocket boosters.

Vibration analysis of hydropower house based on fluid-structure coupling numerical method

By using the shear stress transport （SST） model to predict the effect ot random now motion in a fluid zone, and using the Newmark method to solve the oscillation equations in a solid zone, a coupling model of the .powerhouse and its tube water was developed. The effects of fluid-structure interaction are considered through the kinematic and dynamic conditions applied to the fluid-structure interfaces （FSI）. Numerical simulation of turbulent flow through the whole flow passage of the powerhouse and concrete structure vibration analysis in the time domain were carried out with the model. Considering the effect of coupling the turbulence and the powerhouse structure, the time history response of both turbulent flows through the whole flow passage and powerhouse structure vibration were generated. Concrete structure vibration analysis shows that the displacement, velocity, and acceleration of the dynamo floor respond dramatically to pressure fluctuations in the flow passage. Furthermore, the spectrum analysis suggests that pressure fluctuation originating from the static and dynamic disturbances of hydraulic turbine blades in the flow passage is one of the most important vibration sources.

A Preconditioned Multigrid Method for Efficient Simulation of Three-dimensional Compressible and Incompressible Flows

To develop an efficient and robust aerodynamic analysis method for numerical optimization designs of wing and complex configuration, a combination of matrix preconditioning and multigrid method is presented and investigated. The time derivatives of three-dimensional Navier-Stokes equations are preconditioned by Choi-Merkle preconditioning matrix that is originally designed for two-dimensional low Mach number viscous flows. An extension to three-dimensional viscous flow is implemented, and a method improving the convergence for transonic flow is proposed. The space discretizaition is performed by employing a finite-volume cell-centered scheme and using a central difference. The time marching is based on an explicit Rtmge-Kutta scheme proposed by Jameson. An efficient FAS multigrid method is used to accelerate the convergence to steady-state solutions. Viscous flows over ONERA M6 wing and M100 wing are numerically simulated with Mach numbers ranging from 0.010 to 0.839. The inviscid flow over the DLR-F4 wing-body configuration is also calculated to preliminarily examine the performance of the presented method for complex configuration. The computed results are compared with the experimental data and good agreement is achieved. It is shown that the presented method is efficient and robust for both compressible and incompressible flows and is very attractive for aerodynamic optimization designs of wing and complex configuration.

Generation of linear and nonlinear waves in numerical wave tank using clustering technique-volume of fluid method

A two-dimensional （2D） numerical model is developed for the wave sim- ulation and propagation in a wave flume. The fluid flow is assumed to be viscous and incompressible, and the Navier-Stokes and continuity equations are used as the governing equations. The standard k-e model is used to model the turbulent flow. The Navier- Stokes equations are discretized using the staggered grid finite difference method and solved by the simplified marker and cell （SMAC） method. Waves are generated and propagated using a piston type wave maker. An open boundary condition is used at the end of the numerical flume. Some standard tests, such as the lid-driven cavity, the constant unidirectional velocity field, the shearing flow, and the dam-break on the dry bed, are performed to valid the model. To demonstrate the capability and accuracy of the present method, the results of generated waves are compared with available wave theories. Finally, the clustering technique （CT） is used for the mesh generation, and the best condition is suggested.

NUMERICAL SIMULATION OF TURBULENT SPOTS IN INCLINED OPEN-CHANNEL FLOW

The generation and evolution of turbulent spots in the open-channel flow are simulated numerically by using the Navier-Stokes equations. An effective numerical method with high accuracy and high resolution is developed. The fourth-order time splitting methods with high accuracy is proposed. Three-dimensional coupling difference methods are presented for the spatial discretization of the Poisson equation of pressure and Hemholtz equations of velocity, therefore, the fourth-order three-dimensional coupling central difference schemes are constituted. The fourth-order explicit upwind-biased compact difference schemes are designed to overcome the difficulty for the general higher-order central difference scheme which is inadaptable in the boundary neighborhood. The iterative algorithm and overall time marching is used to enhance efficiency. The method is applied in the numerical simulation of turbulent spots at various complex boundary conditions and flow domains. The generation and the developing process of turbulent spots are given, and the basic characteristics of turbulent spots are shown by simulating the evolution of the wall pulse in inclined open-channel flow.

带有含时组合源项的输运方程的黎曼问题

求解带有含时组合源项的输运方程的黎曼问题.首先,引入某个较一般的含时变量替换将非齐次含源系统转化为守恒律系统,并在守恒律框架下构造了包含δ-激波和真空的黎曼解.其次,借助适当的广义Rankine-Hugoniot条件和熵条件,建立了δ-激波解的存在唯一性.结果表明,受源项影响,系统的黎曼解不再自相似,且所有的特征线均变为曲线.数值模拟证实了理论分析.

喷管流场和羽流场的N－S数值模拟

利用时间推进的方法，通过求解可压缩的、雷诺平均的Ｎ－Ｓ方程，并利用Ｂａｌｄｗｉｎ－Ｌｏｍａｘ两层代数湍流模型和Ｐｒａｎｄｔｌ混合长度模型，数值模拟了飞机和火箭发动机喷管的内流和羽流，获得了喷管内流场和羽流场的参数分布，计算结果与试验结果及国外研究成果一致。网格划分采用了自适应网格技术。

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.

圆柱绕流近壁面处气动噪声源识别研究

对物体高速行驶下的气动噪声现象的认识和描述一直以来都是气动声学领域探索的基本问题和难点问题,尤其对物体近壁面处声源的产生及其声辐射缺乏有效的描述手段。该研究以圆柱绕流为研究对象,结合数值仿真手段,基于涡声方程的声源项描述圆柱绕流近壁面处的声源特性,建立声源识别方法。研究表明,该方法描述的声源存在不该有声源的位置出现声源的现象。研究进一步基于质点振速的矢量波动方程,将不能辐射噪声的源分离,较为准确地识别出了圆柱绕流气动噪声源的大小和位置。该研究在探索识别圆柱绕流气动噪声源方法的同时,也为准确识别气动噪声源特征提供了有效的方法。

自由项对交通流双曲型方程组数值解影响研究

该文以交通流模型中不同平衡函数表达式为例,对一阶非线性双曲型方程组的自由项形式与数值解的色散性、耗散性之间关系,进行了数值模拟研究。结果发现:自由项对方程组数值解的色散性和耗散性影响都是比较有规律的,这种规律性在不同初始密度条件下是不一样的;自由项导致方程组数值解色散或耗散强弱,与方程组的离散方式也有关,尤其在中等密度条件下。就Payne-W h itham模型方程,建议了能够对不同初始密度下扰动的传播和发展进行合理数值模拟的自由项和离散方式。

Numerical study of high-pressure GO_2/GH_2 combustion of a single-element injector

A single-element shear-coaxial combustor using gaseous hydrogen(GH2) and oxygen(GO2) was designed and hot-tested.The wall temperature was measured.The combustion flowfield of this GH2 /GO2 single-element combustor was modeled by RANS(Reynolds Averaged Navier-Stokes) and LES(Large Eddy Simulation) methods respectively.The impact of using various turbulence and turbulent combustion models was investigated to obtain the model combination which best represented the experimental data in the RANS modeling.The flamelet model was used in the LES modeling and the validity of its application to the GH2 /GO2 combustion in the combustor was carefully examined.The combustor wall heat flux distributions of both RANS and LES results show good agreement with the experimental data.The experimental wall temperature distribution can be clearly explained through analyzing the inner flowfield structure.The results indicate that both RANS and LES used in this paper can give good predictions of the development of the whole flowfield and the combustion completion length.LES can resolve large-scale flow motions in the combustor and accurately predict the influence of the wall heat loss on the combustion efficiency.

A preliminary study of 3D difference scheme with energy dynamic equilibrium

In this paper, a difference scheme with energy dynamic equilibrium (DS-EDE) is presented, which can be used for the simulation of long-term atmosphere and sea motion. Based on three dimensional nonlinear evolution equations for atmosphere and sea motion, a three dimensional compact upwind scheme (CUWS) is constructed, as the basis of the DS-EDE. The DS-EDE satisfies the following condition of energy dynamic equilibrium (EDE): the total work of external forces on the region boundary is equal to the sum of the total effective variation of the kinetic energy and the energy dissipation in the average flow motion and the effective variation of the potential energy per unit time within the region of interest. It really reflects the basic mechanism of the action of external forces and dissipation in atmosphere and sea movement. Therefore, the DS-EDE developed in this paper is a suitable model for simulating long-term atmosphere and sea movement with forcing and dissipation.

Analysis on Aerodynamic Performance of Finite Swept Wing with Glaze Ice Accretions

A computational investigation was performed to predict the effects of aerodynamic performance degradation on aircraft swept taper wing with and without 10 minutes and 22.5 minutes glaze ice accretions. In this study, the three-dimensional simulated glaze ice shapes were defined from a series of two-dimensional ice sections. The aerodynamic performances of glaze iced swept wings with C-H structure multi-block grid were analyzed and evaluated. The steady Reynolds- Averaged Navier-Stokes （RANS） equations are employed to compute solutions with implementation of two equation Shear-Stress Transport （SST） turbulence model and second-order upwind differencing for entire iced wing flow field. Computed results were compared with available experimental data. The CFD computation can also accurately predict the aerodynamic performance degradation of lift, drag and pressure coefficients of finite swept wing with glaze ice accretions which have two big upper and lower horn.

一类平衡大气边界层边界条件研究

基于标准k-ε湍流模型,首先利用湍流粘度方程和剪切应力在整个边界层内恒定的假设,推导出一类耗散率表达式,并根据常用的湍动能入口剖面方程以及平均风速剖面方程,计算获得相应的耗散率方程;然后在输运方程中添加自定义源项,通过已经确定的平均速度方程、湍动能方程、耗散率方程计算得到相应输运方程的自定义源项表达式,并进行空风洞数值模拟,从而得到了一类满足平衡大气边界层的来流边界条件.通过将这种边界条件与由湍流平衡条件得到的边界条件进行比较,表明本方法获得的边界条件更适用.并且,本方法无需考虑修正壁面函数和修正湍流模型常数,因而计算更为简单,可为平衡大气边界层的研究提供一种新的思路.

Control of Karman Vortex Street By Using Plasma Actuators

A mathematical model for unsteady electro-and aerodynamic processes in the presence of a plasma actuator has been elaborated through physical modeling of the dielectric barrier discharge.A specialized computational fluid dynamics package has been developed accordingly in order to calculate steady and unsteady laminar and turbulent flows.For the numerical simulation of the dielectric barrier discharge,in particular,two equations have been added to the Navier-Stokes equations and solved.They describe the distribution of the applied voltage and the charged particles density.The impact of the plasma actuator on air has been accounted for through the Lorentz force,included as a source term in the momentum balance equation.The system of governing equations for the considered hydrodynamics and electrodynamics has been written in an arbitrary curvilinear coordinate system in dimensionless form and integrated in the framework of a finite volume method.A TVD scheme with a third-order ISNAS flow limiter has been chosen for the convective terms approximation.The obtained block-matrix system of linear algebraic equations has been solved by the generalized minimal residual(GMRES)method with ILU(k)preconditioning.Using this approach,the occurrence of a propulsion force,emerging as a result of the action of plasma actuators on a cylinder in quiescent air,has been investigated.The possibility to mitigate the cylinder drag coefficient with the help of the plasma actuators,due to the ensuing suppression of the Karman vortex street,has been demonstrated.