解不可压缩流体力学问题的降阶法——Ⅱ.空间V~h的基函数和误差估计

本文对于一大类数值求解二维Navier-Stokes方程边值问题的有限元格式给出了零散度空间V~h的一组简单基函数,讨论了速度的数值误差对压力的数值解的影响,并提出一个改进算法。

扩散型连续波HF化学激光器小信号增益的计算

应用层流边界层二维简化模型计算了扩散型连续波HF化学激光器的小信号增益。研究了气流速度、温度、组份对增益的影响,得到一些有用的结果。计算结果与二维Navier-Stokes方程组的计算结果相符,但计算方法较简单。

高温空气的热力学性质

<正> 自从第二次世界大战末德国发明V-2火箭,特别是1957年苏联发射第一个人造地球卫星以后,航空和宇航技术高速发展,现在,飞行体的速度已远远超过第一宇宙速度(7.8公里/秒)。随着速度剧增,带来了低速飞行时不曾出现的特殊问题:一是高M数效应,一是高温对飞行介质的影响。高M数效应使得通常的Navier-Stokes方程失效。研究这方面问题,属于高速空气动力学范围。在实际问题中,高速必然伴随着产生高温,这两方面的效应交织在一起。热效应比起单纯的速度效应更本质,这使得高速高温流动现象及其介质性质的研究成为高温气体物理力学的一个最重要方面。

利用有限差分法求解扩散混合化学反应二维平行流动

利用隐式有限差分方法,对两股平行流的扩散混合、化学反应问题进行了计算。计算中,使用了层流压缩边界层方程并考虑了HF化学激光器的化学反应。计算结果表明:HF(2)振动激发态的浓度要比HF(1),HF(3)、HF(0)的浓度都高,从而获得了粒子数反转条件。另外,在计算中不需要混合长度的假设,就可以求得主流(无化学反应区)与化学反应区的两条界面曲线。当然,本文的计算方法要比直接求解二维Navier-stokes方程要简单得多。

Numerical simulation of coherent structure in two-dimensional compressible mixing layers

The coherent structure in two-dimensional mixing layers is simulated numerically with the compressible Navier-Stokes equations. The Navier-Stokes equations are discretized with high-order accurate upwind compact schemes. The process of development of flow structure is presented: loss of stability, development of Kelvin-Helmholtz instability, rolling up and pairing. The time and space development of the plane mixing layer and influence of the compressibility are investigated.

Numerical study of bifurcation solutions of spherical Taylor-Couette flow

The steady bifurcation flows in a spherical gap (gap ratio sigma=0.18) with rotating inner and stationary outer spheres are simulated numerically for Re(c1)less than or equal to Re less than or equal to 1 500 by solving steady axisymmetric incompressible Navier-Stokes equations using a finite difference method. The simulation shows that there exist two steady stable flows with 1 or 2 vortices per hemisphere for 775 less than or equal to Re less than or equal to 1 220 and three steady stable flows with 0, 1, or 2 vortices for 1 220-or two-vortex flow depends mainly on the acceleratio n, but that of one-vortex flow also depends on the perturbation breaking the equatorial symmetry. The mechanism of development of a saddle point in the meridional plane at higher Re number and its role in the formation of two-vortex flow are analyzed.

Numerical simulation of axisymmetric unsteady incompressible flow by a vorticity-velocity method

A new numerical method for solving the axisymmetric unsteady incompressible Navier-Stokes equations using vorticity-velocity variables and a staggered grid is presented. The solution is advanced in time with an explicit two-stage Runge-Kutta method. At each stage a vector Poisson equation for velocity is solved. Some important aspects of staggering of the variable location, divergence-free correction to the velocity held by means of a suitably chosen scalar potential and numerical treatment of the vorticity boundary condition are examined. The axisymmetric spherical Couette flow between two concentric differentially rotating spheres is computed as an initial value problem. Comparison of the computational results using a staggered grid with those using a non-staggered grid shows that the staggered grid is superior to the non-staggered grid. The computed scenario of the transition from zero-vortex to two-vortex flow at moderate Reynolds number agrees with that simulated using a pseudospectral method, thus validating the temporal accuracy of our method.

Triple-region structure for turbulent-flow in a square duct - a finite-element approach

The Reynolds-averaged Navier-Stokes equations for describing the turbulent flow in a straight square duct are formulated with two different turbulence models. The governing equations are then expanded as a multi-deck structure in a plane perpendicular to the streamwise direction, with each deck characterized by its dominant physical forces as commonly carried out in analytical work using triple-deck expansion. The resulting equations are numerically integrated using higher polynomial (H-P) finite element technique for each cross-sectional plane to be followed by finite difference representation in the streamwise direction until a fully developed state is reached. The computed results using the two different turbulence models show fair agreement with each other, and concur with the vast body of available experimental data. There is also general agreement between our results and the recent numerical works anisotropic k-epsilon turbulence model.

Computation of turbulent-flow in a square duct - aspects of the secondary flow and its origin

A numerical study of turbulent flow in a straight duct of square cross-section is made. An order-of-magnitude analysis of the 3-D, time-averaged Navier-Stokes equations resulted in a parabolic form of the Navier-Stokes equations. The governing equations, expressed in terms of a new vector-potential formulation, are expanded as a multi-deck structure with each deck characterized by its dominant physical forces. The resulting equations are solved using a finite-element approach with a bicubic element representation on each cross-sectional plane. The numerical integration along the streamwise direction is carried out with finite-difference approximations until a fully-developed state is reached. The computed results agree well with other numerical studies and compare very favorably with the available experimental data. One important outcome of the current investigation is the interpretation analytically that the driving force of the secondary flow in a square duct comes mainly from the second-order terms of the difference in the gradients of the normal and transverse Reynolds stresses in the axial vorticity equation.

Upwind compact method and direct numerical-simulation of driven flow in a square cavity

A high-order accurate finite-difference scheme, the upwind compact method, is proposed. The 2-D unsteady incompressible Navier-Stokes equations are solved in primitive variables. The nonlinear convection terms in the governing equations are approximated by using upwind biased compact difference, and other spatial derivative terms are discretized by using the fourth-order compact difference. The upwind compact method is used to solve the driven flow in a square cavity. Solutions are obtained for Reynolds numbers as high as 10000. When Re less than or equal to 5000, the results agree well with those in literature. When Re = 7500 and Re = 10000, there is no convergence to a steady laminar solution, and the flow becomes unsteady and periodic.

Approximate theory of natural-convection with small grashof number

To gain some insight into the behaviour of low-gravity flows in the material processing in space, an approximate theory has been developed for the convective motion of fluids with a small Grashof number Gr. The expansion of the variables into a series of Gr reduces the Boussinesq equation to a system of weakly coupled linearly inhomogeneous equations. Moreover, the analogy concept is proposed and utilized in the study of the plate bending problems in solid mechanics. Two examples are investigated in detail, i. e. the 2-dimensional steady flows in either circular or square infinite closed cylinder, which is horizontally imposed at a specified temperature of linear distribution on the boundaries. The results for stream function ψ, velocity u and temperature T are provided. The analysis of the influences of some parameters such as the Grashof number Gr and the Prandtl number Pr, on motions will lead to several interesting conclusions. The theory seems to be useful for seeking for an analytical solutions. At least, it will greatly simplify the complicated problems originally governed by the Navier-Stokes equation including buoyancy. It is our hope that the theory might be applicable to unsteady or 3-dimensional cases in future.

Characteristics of a CW HF chemical-laser calculated from a simplified two-dimensional model

A two-dimensional simplified model of an HF chemical laser is introduced. Using an implicit finite difference scheme, the solution of two adjacent parallel streams with diffusion mixing and chemical reaction is generated. A contour of mixing and reaction boundary is obtained without presupposition. The distribution of the HF(v) concentrations, gas temperature and the optical small signal gain (alpha sub V, J) on the flowing plane (X, Y) are presented. Compared with the solution solved directly from a set of Navier-Stokes equations, the results of these two methods agree with each other qualitatively. The influences of the different velocity, temperature (T sub 0) and composition of the two streams on the small signal gain after the nozzle exit are investigated. It is interesting that for larger J with a fixed v, the peaks of alpha sub v-T sub 0 profiles move towards higher T sub 0. The computing method is simple and only a short computing time is needed.

Numerical experiments on one-dimensional model of turbulence

The initial-value problem of a forced Burgers equation is numerically solved by the Fourier expansion method. It is found that its solutions finally reach a steady state of 'laminar flow' which has no randomness and is stable to disturbances. Hence, strictly speaking, the so-called Burgers turbulence is not a turbulence. A new one-dimensional model is proposed to simulate the Navier-Stokes turbulence. A series of numerical experiments on this one-dimensional turbulence is made and is successful in obtaining Kolmogorov's (1941) k exp(-5/3) inertial-range spectrum. The (one-dimensional) Kolmogorov constant ranges from 0.5 to 0.65.

多孔介质中流体流动的细观-宏观模拟

阐述了如何用体积平均化方法推导具有非线性吸附效应的多孔介质中的 Forchhermer方程和对流 -扩散方程。这两个方程对分析多孔介质中质量输运有着极大的应用价值。在分析 Navier- Stokes方程中 ,我们发现非滑移条件在平均化过程中并不扮演重要的角色 ,而吸附边界条件对体积平均化输运方程作出了重要贡献。所以 ,在推导多相输运方程时对平均化方法和边界条件的处理必须非常小心。

激波-涡干扰声场的数值研究

采用高精度差分格式求解非定常可压缩Navier-Stokes方程,对激波-单涡/双涡相互干扰产生的声场进行了直接数值模拟。详细研究了波-涡干扰声场结构的早期发展阶段,将激波-单涡的计算结果和相应实验进行了对比,并给出近场声压的衰减规律。在此基础上模拟较为复杂的激波-双涡干扰,给出不同旋涡旋转方向下的声场结构。