钝锥绕流流动稳定性分析与转捩预报

研究了超音速钝锥绕流的稳定性和转捩点预报的数值计算方法,首先采用Euler方程求解钝锥绕流基本流场,用所得到的物面压力分布作为粘性边界层的外缘压力分布,给出了基本流场的初值;然后应用反迭代法与边界层渐近匹配的方法求解了钝锥边界层的稳定性方程,得到了钝锥边界层转捩数据.该方法可提高计算精度,节约计算时间.     

Accurate Solutions of the Navier-Stokes Equations Despite Unknown Outflow Boundary Data

A very common procedure when constructing boundary conditions for the time-dependent Navier-Stokes equations at artificial boundaries is to extrapolate the solution from grid points near the boundary to the boundary itself. For supersonic outflow, where all the characteristic variables leave the computational domain, this leads to accurate results. In the case of subsonic outflow, where one characteristic variable enters the computational domain, one cannot in general expect accurate solutions by this procedure. The problem with outflow boundary operators of extrapolation type at artificial boundaries with errors in the boundary data of order one will be investigated. Both the problem when the artificial outflow boundary is located in essentially uniform flow and the situation when the artificial outflow boundary is located in a flow field with large gradients are discussed. It will be shown, that in the special case when there are large gradients tangential to the boundary, extrapolation methods can be used even in the subsonic case.     

Investigation of the pseudo-shock wave in a two-dimensional supersonic inlet

Abstract  

This paper describes experimental and numerical investigations into the multiple shock waves/turbulent boundary layer interaction in a supersonic inlet. The test model has a rectangular shape with an asymmetric subsonic diffuser of 5°. Experiments were conducted to obtain the visualization images and static pressure data by using supersonic wind tunnel. Numerical simulation was performed by solving the RANS equations with the Menter’s SST turbulent model. The inflow condition was a free-stream Mach number of 2.5 and a unit Reynolds number of 7.6 × 10⁷/m. Numerical results showed good agreement with the experimental results. Based on this agreement, the flow characteristics which are often very difficult to obtain experimentally alone were analyzed with the aid of numerical simulation. The structures, pressure and velocity distributions, and total pressure loss of the pseudo-shock wave in the supersonic inlet were presented in detail from flow visualization images and static pressures.     

High-order non-uniform grid schemes for numerical simulation of hypersonic boundary-layer stability and transition

The direct numerical simulation of receptivity, instability and transition of hypersonic boundary layers requires high-order accurate schemes because lower-order schemes do not have an adequate accuracy level to compute the large range of time and length scales in such flow fields. The main limiting factor in the application of high-order schemes to practical boundary-layer flow problems is the numerical instability of high-order boundary closure schemes on the wall. This paper presents a family of high-order non-uniform grid finite difference schemes with stable boundary closures for the direct numerical simulation of hypersonic boundary-layer transition. By using an appropriate grid stretching, and clustering grid points near the boundary, high-order schemes with stable boundary closures can be obtained. The order of the schemes ranges from first-order at the lowest, to the global spectral collocation method at the highest. The accuracy and stability of the new high-order numerical schemes is tested by numerical simulations of the linear wave equation and two-dimensional incompressible flat plate boundary layer flows. The high-order non-uniform-grid schemes (up to the 11th-order) are subsequently applied for the simulation of the receptivity of a hypersonic boundary layer to free stream disturbances over a blunt leading edge. The steady and unsteady results show that the new high-order schemes are stable and are able to produce high accuracy for computations of the nonlinear two-dimensional Navier–Stokes equations for the wall bounded supersonic flow.     

Boundary data immersion method for Cartesian-grid simulations of fluid-body interaction problems

A new robust and accurate Cartesian-grid treatment for the immersion of solid bodies within a fluid with general boundary conditions is described. The new approach, the Boundary Data Immersion Method (BDIM), is derived based on a general integration kernel formulation which allows the field equations of each domain and the interfacial conditions to be combined analytically. The resulting governing equation for the complete domain preserves the behavior of the original system in an efficient Cartesian-grid method, including stable and accurate pressure values on the solid boundary. The kernel formulation allows a detailed analysis of the method, and it is demonstrated that BDIM is consistent, obtains second-order convergence relative to the kernel width, and is robust with respect to the grid and boundary alignment. Formulation for no-slip and free slip boundary conditions are derived and numerical results are obtained for the flow past a cylinder and the impact of blunt bodies through a free surface. The BDIM predictions are compared to analytic, experimental and previous numerical results confirming the properties, efficiency and efficacy of this new boundary treatment for Cartesian grid methods.     

Influence of the opening angle of a conical supersonic nozzle on the structure of initial interval of non-isobaric jet

The ideal gas exhaustion from an infinite volume into a gas at rest through a supersonic conical Laval nozzle is considered. The problem was solved numerically by steadying in time in a unified formulation for the regions inside the nozzle and in the ambient environment. In such a statement, the nozzle outlet section is no internal boundary of the region under consideration, and there is no need of specifying the boundary conditions here. Local subsonic zones arising in the flow lie inside the region under consideration, which eliminates the possibility of using a marching technique along one of the coordinates. The numerical solution is constructed by a unified algorithm for the entire flow region, which gives a possibility of obtaining a higher accuracy. The computations are carried out in the jet initial interval, where, according to monograph [1], the wave phenomena predominate over the viscous effects. The exhaustion process is described by the system of gas dynamics equations. Their solution is constructed with the aid of a finite difference Harten’s TVD (Total Variation Diminishing) scheme [2], which has the second approximation order in space. The second approximation order in time is achieved with the aid of a five-stage Runge-Kutta method. The solution algorithm has been parallelized in space and implemented on the multi-processor computer systems of the ITAM SB RAS and the MVS-128 of the Siberian Supercomputer Center of SB RAS. The influence of the semi-apex angle of the nozzle supersonic part and the pressure jump between the nozzle outlet section and the ambient environment on the flow in the initial interval of a non-isobaric jet is investigated in the work. A comparison with experimental data is presented. The computations are carried out for the semi-apex angles of the nozzle supersonic part from 0 (parallel flow) to 20 degrees. For all considered nozzles, the Mach number in the nozzle outlet section, which was computed from the one-dimensional theory, equaled three. Computations showed that in the case of flow acceleration in a conical supersonic nozzle, its geometry is one of the main factors determining the formation of the jet initial interval in ambient environment.     

超声速等离子体射流的数值模拟

基于可压缩的全Naiver-Stokes方程，利用PHOENICS程序对由会聚 辐射阳极形状等离子体炬产生的超声速等离子体射流进行了数值模拟.考虑了等离子体的黏性、可压缩性以及变物性对等离子体射流特性影响.研究了超声速等离子体射流的流场结构特性以及不同环境压力对等离子体射流产生激波结构的影响.结果表明，超声速等离子体射流在喷口附近形成的周期性激波结构是其和环境气体相互作用的结果. 关键词： 等离子体炬 超声速等离子体射流 PHOENICS     

高超声速层流绕三维压缩拐角的数值模拟

通过数值模拟研究了高超声速来流绕过压缩拐角的层流分离三维流动特性.数值方法采用三维N-S方程,结合2阶精度Roe格式以及分区结构网格有限体积法进行离散.数值模拟的空间激波结构与实验纹影结果符合较好;激波/边界层干扰区内3条纵向线上的计算压力分布与实验结果进行了对比分析,计算获得在三维楔侧面存在低压力区,与实验结果反映的规律一致,计算结果表明低压力区是由楔体侧缘尖端发起的二次涡的抽吸作用造成的.此外,在楔体后端尾流区的低压沿边界层内的亚声速区往上游传递了一定距离.      

Supersonic flows with small perturbations in the presence of external effects on the flow. II. Slender wing profile

An analytic theory of a supersonic flow past a slender profile of an arbitrary shape in the presence of local energy release zones and an external force acting on the flow near the surface is developed. Main results are obtained using the linear approximation, which is valid in a wide range of external conditions. Analytic expressions are derived for calculating the spatial distributions of pressure perturbations near the surfaces of a slender profile at a small angle of attack. The results of analytic calculations are compared with the numerical simulation data based on the Euler equations for a wedge at a zero angle of attack. The comparison reveals good agreement between numerical and analytic calculations. The results make it possible to formulate and solve optimization problems for a supersonic aerodynamic flow with the help of external effects on the supersonic flow.     

Open and traction boundary conditions for the incompressible Navier–Stokes equations

We present numerical schemes for the incompressible Navier–Stokes equations (NSE) with open and traction boundary conditions. We use pressure Poisson equation (PPE) formulation and propose new boundary conditions for the pressure on the open or traction boundaries. After replacing the divergence free constraint by this pressure Poisson equation, we obtain an unconstrained NSE. For Stokes equation with open boundary condition on a simple domain, we prove unconditional stability of a first order semi-implicit scheme where the pressure is treated explicitly and hence is decoupled from the computation of velocity. Using either boundary condition, the schemes for the full NSE that treat both convection and pressure terms explicitly work well with various spatial discretizations including spectral collocation and C⁰ finite elements. Moreover, when Reynolds number is of O(1) and when the first order semi-implicit time stepping is used, time step size of O(1) is allowed in benchmark computations for the full NSE. Besides standard stability and accuracy check, various numerical results including flow over a backward facing step, flow past a cylinder and flow in a bifurcated tube are reported. Numerically we have observed that using PPE formulation enables us to use the velocity/pressure pairs that do not satisfy the standard inf–sup compatibility condition. Our results extend that of Johnston and Liu [H. Johnston, J.-G. Liu, Accurate, stable and efficient Navier–Stokes solvers based on explicit treatment of the pressure term. J. Comp. Phys. 199 (1) (2004) 221–259] which deals with no-slip boundary conditions only.     

Kr-PLIF for scalar imaging in supersonic flows

Experiments were performed to explore the use of two-photon planar laser-induced fluorescence (PLIF) of krypton gas for applications of scalar imaging in supersonic flows. Experiments were performed in an underexpanded jet of krypton, which exhibited a wide range of conditions, from subsonic to hypersonic. Excellent signal-to-noise ratios were obtained, showing the technique is suitable for single-shot imaging. The data were used to infer the distribution of gas density and temperature by correcting the fluorescence signal for quenching effects and using isentropic relations. The centerline variation of the density and temperature from the experiments agree very well with those predicted with an empirical correlation and a CFD simulation (FLUENT). Overall, the high signal levels and quantifiable measurements indicate that Kr-PLIF could be an effective scalar marker for use in supersonic and hypersonic flow applications.     

Supersonic Laminar Flow Past a Blunt Fin: Duality of the Numerical Solution

Technical Physics - The results of a numerical solution of the problem of supersonic flow past a blunt fin mounted on a plate with a developing boundary layer are presented. Generally, the case...     

Flow turbulization in a pseudo-shock forming in an axisymmetric duct with a frontal inlet

The results of the numerical modeling of the supersonic flow in an axisymmetric duct in which a pseudo-shock arises are presented. The duct includes the frontal inlet with a funnel-shaped part of initial compression of the supersonic flow and with a cylindrical throat part as well as the subsequent (cylindrical or diverging) diffuser where the flow slows down to a subsonic velocity. The flow conditions at the freestream Mach number M = 6 have been considered. Numerical computations of the flow have been done using a Navier–Stokes equations code and the k-ω SST turbulence model. As a result of computations, such flow parameters have been determined as the location of the pseudo-shock beginning, the length of the pseudo-shock supersonic part, the pressure distribution on the duct wall, the total pressure losses as well as the characteristics of flow turbulence. In particular, the variation of the turbulence intensity and turbulent viscosity along the pseudo-shock length have been examined and, based on these characteristics, the possibility of determining the location of a cross section, in which the pseudo-shock can be treated as completed, have been considered.     

Pressure based finite volume method for calculation of compressible viscous gas flows

A pressure based, iterative finite volume method is developed for calculation of compressible, viscous, heat conductive gas flows at all speeds. The method does not need the use of under-relaxation coefficient in order to ensure a convergence of the iterative process. The method is derived from a general form of system of equations describing the motion of compressible, viscous gas. An emphasis is done on the calculation of gaseous microfluidic problems. A fast transient process of gas wave propagation in a two-dimensional microchannel is used as a benchmark problem. The results obtained by using the new method are compared with the numerical solution obtained by using SIMPLE (iterative) and PISO (non-iterative) methods. It is shown that the new iterative method is faster than SIMPLE. For the considered problem the new method is slightly faster than PISO as well. Calculated are also some typical microfluidic subsonic and supersonic flows, and the Rayleigh–Bénard convection of a rarefied gas in continuum limit. The numerical results are compared with other analytical and numerical solutions.     

Entropy considerations in numerical simulations of non-equilibrium rarefied flows

Non-equilibrium rarefied flows are encountered frequently in supersonic flight at high altitudes, vacuum technology and in microscale devices. Prediction of the onset of non-equilibrium is important for accurate numerical simulation of such flows. We formulate and apply the discrete version of Boltzmann’s H-theorem for analysis of non-equilibrium onset and accuracy of numerical modeling of rarefied gas flows. The numerical modeling approach is based on the deterministic solution of kinetic model equations. The numerical solution approach comprises the discrete velocity method in the velocity space and the finite volume method in the physical space with different numerical flux schemes: the first-order, the second-order minmod flux limiter and a third-order WENO schemes. The use of entropy considerations in rarefied flow simulations is illustrated for the normal shock, the Riemann and the two-dimensional shock tube problems. The entropy generation rate based on kinetic theory is shown to be a powerful indicator of the onset of non-equilibrium, accuracy of numerical solution as well as the compatibility of boundary conditions for both steady and unsteady problems.     

High-pressure subsonic mode operation of chemical oxygen-iodine laser

A new regime of chemical oxygen-iodine laser (COIL), high-pressure subsonic mode operation, was demonstrated using a jet-type singlet oxygen generator (SOG). The laser output power of 342 W with chemical efficiency of 20.9% was obtained at the Cl₂ flow rate of 18 mmol/s and the operating pressure of 6.4 Torr in the laser cavity. The specific energy was 3.1 J/l which was four times higher than our supersonic device, and was comparable to the highest value for the supersonic regime. The experimental results were in good agreement with the numerical simulation results. Received: 26 February 1999 / Revised version: 13 July 1999 / Published online: 30 November 1999     

解双曲型方程组的分离系数矩阵差分法

分离系数矩阵(SCM)差分方法是近年来发展的一种基于特征理论的数值方法,该方法将双曲型方程组系数矩阵,利用相似变换,按照特征值的正负构造成SCM方程,然后,合理地选择适合于SCM方法的二阶单向差分格式,能显示出流场中每点的特征值的方向和大小,也就是对于含正特征值的项用向后差分算子,并乘以正特征值,而含负特征值的项用向前差分算子,乘以负特征值,这比以往的差分计算具有合理的物理意义。本文参考文献[1]导得了三维非对称头部绕流的分离系数矩阵方法,不论内点或特殊点都是分离系数矩阵形式,除此之外,还将SCM方法推广于后身的超音速区域。通过计算表明,在头部区采用局部Δt步长,能加速非定常流的收敛,对于后身超音速区,该方法用较少的网格点,仍获得较高的精度。     

发动机喷流对火箭气动特性影响

开展了考虑底部发动机喷流影响的火箭气动特性CFD仿真设计,比较了有/无喷流时火箭附近流场结构、表面压力分布、整体气动力/力矩特性在亚/超声速段的差异,结果显示,发动机喷流对火箭亚声速段的轴向力、法向力和俯仰力矩特性均有较为显著的影响,且有减小尾部空气舵气动控制力矩的影响,而超声速段的影响仅限于轴向力。该仿真结果与飞行试验气动辨识结果较为一致。基于仿真分析结果,可建立一种折中考虑喷流影响的气动特性设计方法,供火箭精细化气动特性设计参考使用。      

Implicit preconditioned WENO scheme for steady viscous flow computation

A class of lower–upper symmetric Gauss–Seidel implicit weighted essentially nonoscillatory (WENO) schemes is developed for solving the preconditioned Navier–Stokes equations of primitive variables with Spalart–Allmaras one-equation turbulence model. The numerical flux of the present preconditioned WENO schemes consists of a first-order part and high-order part. For first-order part, we adopt the preconditioned Roe scheme and for the high-order part, we employ preconditioned WENO methods. For comparison purpose, a preconditioned TVD scheme is also given and tested. A time-derivative preconditioning algorithm is devised and a discriminant is devised for adjusting the preconditioning parameters at low Mach numbers and turning off the preconditioning at intermediate or high Mach numbers. The computations are performed for the two-dimensional lid driven cavity flow, low subsonic viscous flow over S809 airfoil, three-dimensional low speed viscous flow over 6:1 prolate spheroid, transonic flow over ONERA-M6 wing and hypersonic flow over HB-2 model. The solutions of the present algorithms are in good agreement with the experimental data. The application of the preconditioned WENO schemes to viscous flows at all speeds not only enhances the accuracy and robustness of resolving shock and discontinuities for supersonic flows, but also improves the accuracy of low Mach number flow with complicated smooth solution structures.     

临近声速气流条件下电子束空气等离子体特性

为了研究高速动态气流中的电子束等离子体特性,建立了一个由蒙特卡罗模型、多组分等离子体模型与计算流体力学模型组成的多阶段耦合数值模型,在临近声速气流条件下,对1.33×104 Pa空气电子束等离子体特性进行了研究。结果表明,电子束能量沉积具有极强的空间不均性,电子束激发下的风洞流场呈现不同的性质,亚声速流场下游边界区密度减小,而在超声速流场中可诱发弱激波;相比于静止气体,在动态气流中等离子体密度下降,且存在额外的输运行为,使其向气流下游输运,但在临近声速条件下,气流速度大小对气流下游等离子体分布的影响不大;电子束入射角对等离子体空间分布和大小均有影响。