A high order accurate difference scheme for complex flow fields

A high order accurate finite difference method for direct numerical simulation of coherent structure in the mixing layers is presented. The reason for oscillation production in numerical solutions is analyzed, It is caused by a nonuniform group velocity of wavepackets. A method of group velocity control for the improvement of the shock resolution is presented. In numerical simulation the fifth-order accurate upwind compact difference relation is used to approximate the derivatives in the convection terms of the compressible N-S equations, a sixth-order accurate symmetric compact difference relation is used to approximate the viscous terms, and a three-stage R-K method is used to advance in time. In order to improve the shock resolution the scheme is reconstructed with the method of diffusion analogy which is used to control the group velocity of wavepackets. (C) 1997 Academic Press.

Drop migration of middle Reynolds number in a vertical temperature gradient

The experimental investigation of the thermocapillary drop migration in a vertical temperature gradient uns performed on ground. Silicon oil and pure soybean oil were used as experimental medium in drops and as continuous phases, respectively, in the present experiment. The drop migration, under the combined effects of buoyancy: and thermocapillarity, was studied for middle Reynolds numbers in order of magnitude O(10(1)). The drop migration velocities depending on drop diameters were obtained. The present experimental results show relatively small migration velocity in comparison with the one suggested by Young et nl. for linear theory of small Reynolds number. An example of flow patterns inside the drop was observed by PIV method.

Compact finite difference - Fourier spectral method for three-dimensional incompressible Navier-Stokes equations

A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported.

Effects of high-frequency vibration on critical marangoni number

The influence of vibration on thermocapillary convection and critical Marangoni number in liquid bridge of half floating zone was discussed for the low frequency range 0.4-1.5 Hz and the intermediate frequency range 2.5-15 Hz in our previous papers. This paper extends the study to high frequency range 15-100Hz. This ground based experiment was completed on the deck of an electromagnetic vibration machine. The results of our experiment shows when the frequency of the applied acceleration is high enough, the amplitude of the time varying part of the temperature response is disappear and the shape of the free surface of the liquid bridge exhibits no fluctuations due to inertia. The critical Marangoni number which is defined to describe the transitions from a peroidical convection in response to vibration to an oscillatory convection due to internal instability is nearly the same as the critical Marangoni number for oscillatory flow in the absence of vibration.

Numerical investigation of dynamic stall of an oscillating aerofoil

The flow structure around an NACA 0012 aerofoil oscillating in pitch around the quarter-chord is numerically investigated by solving the two-dimensional compressible N-S equations using a special matrix-splitting scheme. This scheme is of second-order accuracy in time and space and is computationally more efficient than the conventional flux-splitting scheme. A 'rigid' C-grid with 149 x 51 points is used for the computation of unsteady flow. The freestream Mach number varies from 0.2 to 0.6 and the Reynolds number from 5000 to 20,000. The reduced frequency equals 0.25-0.5. The basic flow structure of dynamic stall is described and the Reynolds number effect on dynamic stall is briefly discussed. The influence of the compressibility on dynamic stall is analysed in detail. Numerical results show that there is a significant influence of the compressibility on the formation and convection of the dynamic stall vortex. There is a certain influence of the Reynolds number on the flow structure. The average convection velocity of the dynamic stall vortex is approximately 0.348 times the freestream velocity.

Experimental-study of free-surface oscillations of a liquid bridge by optical diagnostics

A non-contact optical method, consisting of a projecting grating technique for the relative measurement of a surface, and a technique of absolute measurement at a fixed point on the surface, are applied to measure the free surface vibration in a liquid bridge of half floating zone with small typical scale of a few of mm for emphasizing the thermocapillary effect in comparison with the effect of buoyancy. The radii variations in both longitudinal and azimuthal directions are obtained, and, then, the feature of surface wave could be analyzed in detail. The results show that there are values of principal oscillatory frequencies at different positions of free surface. The amplitudes of surface waves in longitudinal and azimuthal directions are several mum and several tenths of mum in order of magnitude. The phase of two-dimensional surface waves is different at different height for fixed cross section or at different azimuthal angle for fixed height. The wave features are discussed for the cases of typical parameter ranges.

Effects of g-jitter on the critical marangoni number

A half floating zone is fixed on a vibrational deck, which supports a periodical applied acceleration to simulate the effect of g-jitter. This paper deals with the effects of g-jitter on the fluid fields and the critical Marangoni number, which describes the transition from a forced oscillation of thermocapillary convection into an instability oscillatory convection in a liquid bridge of half floating zone with top rod heated. The responses of g-jitter field on the temperature profiles and flow pattern in the liquid bridge were obtained experimentally. The results indicated that the critical Marangoni number decreases with the increasing of g-jitter effect and is slightly smaller for higher frequency of g-jitter with fixed strength of applied gravity.

Numerical-simulation of ac plasma-arc thermodynamics

A mathematical model and approximate analysis for the energy distribution of an ac plasma arc with a moving boundary is developed. A simplified electrical conductivity function is assumed so that the dynamic behavior of the arc may be determined, independent of the gas type. The model leads to a reduced set of non-linear partial differential equations which governs the quasi-steady ac arc. This system is solved numerically and it is found that convection plays an important role, not only in the temperature distribution, but also in arc disruptions. Moreover, disruptions are found to be influenced by convection only for a limited frequency range. The results of the present studies are applicable to the frequency range of 10-10(2) Hz which includes most industry ac arc frequencies. (C) 1994 Academic Press, Inc.

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.

Influence of low-gravity level on crystal-growth in floating-zone

The influence of low gravity level on crystal growth in the floating zone, which involves thermocapillary convection, phase change convection, thermal and solutal diffusion, is investigated numerically by a finite element method for the silicon crystal growth process. The velocity, temperature, concentration fields and phase change interfaces depending on heating temperature and growth rates are analyzed. The influence of low gravity level on the concentration is studied especially. The results show that the non-uniformities of concentration are about 10(-3) for growth rate nu(p) = 5.12 x 10(-8) m/s, 10(-2) for nu(p) = 5.12 x 10(-7) m/s and relatively larger for larger growth rate in the gravity level g = 0-9.8 m/s2. The thermocapillary effect is strong in comparison with the Bridgman system, and the level of low gravity is relatively insensitive for lower growth rates.

A study on stratification of concentration in crystal-growth of alpha-liio3 by holographic-interferometry

A new thermoplastic-photoconductor laser holographic recording system has been used for real-time and in situ observation of alpha-LiIO3 crystal growth. The influence of crystallization-driven convection on the concentration stratification in solution has been studied under gravity field. It is found that the stratification is closely related to the seed orientation of alpha-LiIO3 crystal. When the optical axis of crystal seed C is parallel to the gravity vector g, the velocity of the concentration stratification is two times larger than that in the case of C perpendicular-to g. It needs 40 h for the crystalline system of alpha-LiIO3 to reach stable concentration distribution (expressed as tau) at 47.6-degrees-C. The time tau is not sensitive to the seed orientation. Our results provide valuable data for designing the crystal growth experiments ia space.

H4 exponential finite-difference scheme for convective diffusion-equations

Perturbations are applied to the convective coefficients and source term of a convection-diffusion equation so that second-order corrections may be applied to a second-order exponential scheme. The basic Structure of the equations in the resulting fourth-order scheme is identical to that for the second order. Furthermore, the calculations are quite simple as the second-order corrections may be obtained in a single pass using a second-order scheme. For one to three dimensions, the fourth-order exponential scheme is unconditionally stable. As examples, the method is applied to Burgers' and other fluid mechanics problems. Compared with schemes normally used, the accuracies are found to be good and the method is applicable to regions with large gradients.

Crystal-growth in floating zone with phase-change and thermosolutal convections

Floating zone crystal growth in microgravity environment is investigated numerically by a finite element method for semiconductor growth processing, which involves thermocapillary convection, phase change convection, thermal diffusion and solutal diffusion. The configurations of phase change interfaces and distributions of velocity, temperature and concentration fields are analyzed for typical conditions of pulling rates and segregation coefficients. The influence of phase change convection on the distribution of concentration is studied in detail. The results show that the thermocapillary convection plays an important role in mixing up the melt with dopant. The deformations of phase change interfaces by thermal convection-diffusion and pulling rods make larger variation of concentration field in comparison with the case of plane interfaces.

Some theoretical aspects of the simplified Navier-Stokes(SNS) equations

This study deals with the formulation, mathematical property and physical meaning of the simplified Navier-Stokes (SNS) equations. The tensorial SNS equations proposed is the simplest in form and is applicable to flow fields with arbitrary body boundaries. The zones of influence and dependence of the SNS equations, which are of primary importance to numerical solutions, are expounded for the first time from the viewpoint of subcharacteristics. Besides, a detailed analysis of the diffusion process in flow fields shows that the diffusion effect has an influence zone globally windward and an upwind propagation greatly depressed by convection. The maximum upwind influential distance of the viscous effect and the relative importance of the viscous effect in the flow direction to that in the direction normal to the flow are represented by the Reynolds number, which illustrates the conversion of the complete Navier-Stokes (NS) equations to the SNS equations for flows with large Reynolds number.

地幔对流的数值实验研究

数值实验是地幔对流研究的基本方法。本文概述了近二十年地幔对流研究的主要进展,介绍并评价了每个研究阶段所提出的新概念和新思想。最后,着重讨论了上地幔与全地幔对流的论争。