Numerical-simulation of low supersonic-flow around a sphere

The controlled equations defined in a physical plane are changed into those in a computational plane with coordinate transformations suitable for different Mach number M(infinity). The computational area is limited in the body surface and in the vicinities of detached shock wave and sonic line. Thus the area can be greatly cut down when the shock wave moves away from the body surface as M(infinity) --> 1. Highly accurate, total variation diminishing (TVD) finite-difference schemes are used to calculate the low supersonic flowfield around a sphere. The stand-off distance, location of sonic line, etc. are well comparable with experimental data. The long pending problem concerning a flow passing a sphere at 1.3 greater-than-or-equal-to M(infinity) > 1 has been settled, and some new results on M(infinity) = 1.05 have been presented.

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.

Numerical study of bluff body flow structures

Our recent progress in numerical studies of bluff body flow structures and a new method for the numerical analysis of near wake flow field for high Reynolds number flow are introduced. The paper consists of three parts. In part one, the evolution of wake vortex structure and variation of forces on a flat plate in harmonic oscillatory flows and in in-line steady-harmonic combined flows are presented by an improved discrete vortex method, as the Keulegan-Carpenter number (KC) varies from 2 to 40 and ratios of U-m to U-0 are of O(10(-1)), O(10) and O(10), respectively. In part 2, a domain decomposition hybrid method, combining the finite-difference and vortex methods for numerical simulation of unsteady viscous separated flow around a bluff body, is introduced. By the new method, some high resolution numerical visualization on near wake evolution behind a circular cylinder at Re = 10(2), 10(3) and 3 x 10(3) are shown. In part 3, the mechanism and the dynamic process for the three-dimensional evolution of the Karman vortex and vortex filaments in braid regions as well as the early features of turbulent structure in the wake behind a circular cylinder are presented numerically by the vortex dynamics method.

Numerical simulation of hypersonic viscous flow around space shuttle with method of diffusion analogy

Hypersonic viscous flow around a space shuttle with M(infinity) = 7, Re = 148000 and angle of attack alpha = 5-degrees is simulated numerically with the special Jacobian matrix splitting technique and simplified diffusion analogy method. With the simplified diffusion analogy method the efficiency of computation and resolution of the shock can be improved.

Character of simplified Navier-Stokes (SNS) equations near separation point for two-dimensional laminar flow over a flat plate

It is proved that the simplified Navier-Stokes (SNS) equations presented by Gao Zhi[1], Davis and Golowachof-Kuzbmin-Popof (GKP)[3] are respectively regular and singular near a separation point for a two-dimensional laminar flow over a flat plate. The order of the algebraic singularity of Davis and GKP equation[2,3] near the separation point is indicated. A comparison among the classical boundary layer (CBL) equations, Davis and GKP equations, Gao Zhi equations and the complete Navier-Stokes (NS) equations near the separation point is given.

The kinetic-theory for dilute solid liquid 2-phase flow

On the basis of a brief review of the continuum theory for macroscopic descriptions and the kinetic theory for microscopic descriptions in solid/liquid two-phase flows, some suggestions are presented, i.e. the solid phase may be described by the Boltzmann equation and the liquid phase still be described by conservation laws in the continuum theory. Among them the action force on the particles by the liquid fluid is a coupling factor which connects the phases. For dilute steady solid/liquid two-phase flows, the particle velocity distribution function can be derived by analogy with the procedures in the kinetic theory of gas molecules for the equilibrium state instead of being assumed, as previous investigators did. This done, more detailed information, such as the velocity probability density distribution, mean velocity distribution and fluctuating intensity etc. can be obtained directly from the particle velocity distribution function or from its integration. Experiments have been performed for dilute solid/liquid two-phase flow in a 4 x 6 cm2 sized circulating square pipe system by means of laser Doppler anemometry so that the theories can be examined. The comparisons show that the theories agree very well with all the measured data.

Kinetic theory for particle concentration distribution in two phase flow

The results of experiments in open channels and closed pipelines show two kinds of patterns for the vertical distribution of particle concentration (i.e., pattern I and pattern II). The former shows a pattern of maximum concentration at some location above the bottom and the downward decay of the concentration below the location. The latter always shows an increase of the particle concentration downward over the whole vertical, with the maximum value at the bottom. Many investigations were made on the pattern II, but few were made on pattern I. In this paper, a particle velocity distribution function is first obtained in the equilibrium state or in dilute steady state for the particle in two-phase flows, then a theoretical model for the particle concentration distribution is derived from the kinetic theory. More attention is paid to the predictions of the concentration distribution of pattern I and comparisons of the present model are made with the data measured by means of laser doppler anemometry (LDA). Very good agreements are obtained between the measured and calculated results.

Principles of flow field diagnostics by laser-induced biacetyl phosphorescence

A new method for measuring the density, temperature and velocity of N2 gas flow by laser induced biacetyl phosphorescence is proposed. The characteristics of the laser induced phosphorescence of biacetyl mixed with N2 are investigated both in static gas and in one-dimensional flow along a pipe with constant cross section. The theoretical and experimental investigations show that the temperature and density of N2 gas flow could be measured by observing the phosphorescence lifetime and initial intensity of biacetyl triplet (3Au) respectively. The velocity could be measured by observing the time-of-flight of the phosphorescent gas after pulsed laser excitation. The prospect of this method is also discussed.