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.