Jinsheng Cai

Unsteady Flow Calculations with a Parallel Multiblock Moving Mesh Algorithm

A novel parallel dynamic moving mesh algorithm designed for multiblock parallel unsteady flow calculations using body-fitted grids is presented. The moving grid algorithm within each block uses a method of arc-length-based transfinite interpolation, which is performed independently on local processors where the blocks reside. A spring network approach is used to determine the motion of the corner points of the blocks, which may be connected in an unstructured fashion in a general multiblock method. A smoothing operator is applied to the points of the block face boundaries and edges to maintain grid smoothness and grid angles. A multiblock parallel Euler/Navier-Stokes solver using multigrid and dual-time stepping is developed along with the moving mesh method. Computational results are presented for the unsteady flow calculations of airfoils and wings with deforming shapes as found in flutter simulations

Stability of symmetric vortices in two dimensions and over three-dimensional slender conical bodies

Ag eneral stability condition for vortices in a two-dimensional incompressible inviscid flow field is presented. This condition is first applied to analyse the stability of symmetric vortices behind elliptic cylinders and circular cylinders with a splitter plate at the rear stagnation point. The effect of the size of the splitter plate on the stability of the vortices is studied. It is also shown that no stable symmetric vortices exist behind two-dimensional bodies based on the stability condition. The two-dimensional stability condition is then extended to analyse the absolute (temporal) stability of as ymmetric vortex pair over three-dimensional slender conical bodies. The threedimensional problem is reduced to a vortex stability problem for a pair of vortices in tw od imensions by using the conical flow assumption, classical slender-body theory, and postulated separation positions. The bodies considered include circular cones and highly swept flat-plate wings with and without vertical fins, and elliptic cones of various eccentricities. There exists an intermediate cone with a finite thickness ratio between the circular cone and the flat-plate delta wing for which the symmetric vortices change from being unstable to being stable at a given angle of attack. The effects of the fin height and the separation position on the stability of the vortices are studied. Results agree well with known experimental observations.

Stability of symmetric and asymmetric vortex pairs over slender conical wings and bodies

Theoretical analyses are presented for the stability of symmetric and asymmetric vortex pairs over slender conical wings and bodies under small perturbations in an inviscid incompressible flow at high angles of attack and sideslip. The three-dimensional problem of a pair of vortices over slender conical wings and bodies is reduced to a problem in two dimensions by using the conical flow assumption and classical slender-body theory. The stability of symmetric and asymmetric vortex pairs over flat-plate delta wings, slender circular cones, and elliptic cones of various thickness ratios are examined. Results are compared with available experimental data.

Stability of Vortex Pairs over Slender Conical Bodies: Analysis and Numerical Computation

DOI: 10.2514/1.33498 Analytical studies and computational fluid dynamics simulations are presented to study the formation and stability of stationary symmetric and asymmetric vortex pairs over slender conical bodies in an inviscid incompressible flow at high angles of attack. The analytical method is based on an eigenvalue analysis on the motion of the vortices under small perturbations. A three-dimensional time-accurate Euler code is used to compute five typical flowsstudiedbythe analytical methodon extraordinarily finegrids withstrict convergence criteria. Both the theory and the computation show that the vortices over a delta wing are stable and those over a wing–body configuration at the low angle of attack are symmetric and stable, but become asymmetric and bistable at higher angles of attack; that is, the vortices shift to one of two stable mirror-imaged asymmetric configurations. The computational results agree well with the analytical predictions, demonstrating the existence of a global inviscid hydrodynamic instability mechanism responsible for the asymmetry of separation vortices over slender conical bodies.

On vortical flows shedding from a bluff body with a wavy trailing edge

Studies have shown that shaping the trailing edge of a quasistreamlined bluff body in the form of a sinusoidal wave can result in substantial base pressure recovery. In this paper, direct numerical simulations at a Reynolds number based on base height of 2500 are used to understand the flow characteristics associated with the observed drag reduction. In particular, the effects of the wavelength of the sinusoidal disturbance on the drag coefficient, vortex shedding mechanism, and frequency selection are examined. Numerical flow visualizations compare favorably to previous experimental observations and the results confirm that there is a range of wavelengths where significant drag reduction is possible. A sinusoidal trailing edge with fixed amplitude and a wavelength which is five times the base height produces the largest reduction of more than 30% in the mean drag coefficient compared to a straight trailing edge. The drag reduction is associated with known observations such as a lengthening of the mean re...

Stability of Symmetric and Asymmetric Vortices over Slender Conical Wing-Body Combinations

Theoretical analyses of the stability of symmetric and asymmetric vortex pairs over slender conical wing-body combinations consisting of a slender circular or elliptic cone and a flat-plate delta wing under small perturbations in an inviscid incompressible steady flow at high angles of attack with or without sideslip are presented. The three-dimensional flow problem is reduced to a problem in two dimensions, for which a general stability condition for vortex pairs can be applied. The stationary positions of symmetric and asymmetric vortex pairs and their stabilities are examined for various geometric configurations, angles of attack, and sideslip. Results of the analyses are compared with available experimental data and used to help gain insight into the flow behavior.

An Overset Grid Solver for Viscous Computations with Multigrid and Parallel Computing

We describe an approach to simulate accurately viscous flows around complex configurations using overset grids. A combination of patched multi-block and overlapping grids is used to discretize the flow domain. A hierarchical grid system with different layers of grids of varying resolution ensures inter-grid connectivity within a multigrid solution acceleration framework. At each stage of the numerical computation, the block boundaries maintain a regular information exchange between neighboring blocks be it patched or overlapping boundaries. Coarse-grain parallel processing is facilitated by the multi-blocking system. Numerical results of flows over multi-element airfoils and three-dimensional turbulent flows around wingbody aerodynamic configurations show the feasibility and efficiency of the method for large-scale numerical computations.

Stability of Vortex Pairs over Slender Conical Bodies - Theory and Numerical Computations

Theoretical analyses and computational fluid dynamics (CFD) simulations are presented to study the formation and stability of stationary symmetric and asymmetric vortex pairs over slender conical bodies in an inviscid incompressible flow at high angles of attack with and without sideslip. The theoretical analysis is based on an eigenvalue analysis on the motion of the vortices under small perturbations. A three-dimensional time-accurate Euler code is used to compute five typical flows studied by the theoretical method on extraordinarily fine and overset grids with strict convergence criteria. The computational results agree well with the theoretical predictions and corroborate on the conclusion that an absolute type of hydrodynamic instability can be the mechanism for breaking of symmetry of the vortex flow over slender conical bodies at high angles of attack. The presented results demonstrate the usefulness of CFD for stability studies of vortex flow over slender bodies at high angles of attack.

Numerical Study on Choked Flow over Grid-Fin Configurations

An improved configuration, which we term a swept-back grid fin, is proposed in the present study to reduce the detrimental effects of high drag caused by the flow choking within the transonic regime. Viscous computational fluid dynamics simulationswere performed to investigateflows over amissilewith baseline and swept-back gridfins under supersonic and transonic conditions at zero incidence. The computed drag coefficients for the baseline missile agree well with those in the literature. Our numerical results indicate that flow choking can be reduced by using the sweptback gridfin.As a result, the drag coefficient on thefins is decreased by approximately 13% for all theMachnumbers investigated in the present study.

Numerical Study on Drag Reduction for Grid-Fin Configurations

A grid fin, or lattice fin, consists of an outer frame supporting an inner grid of intersecting planar surfaces of small chord. At transonic Mach numbers normal shocks form at the back of the lattice cells thus choking the flow through the cells and causing a significant increase in drag force. In order to reduce the transonic flow choking, an improved, sweptback grid fin configuration is proposed in the present study. Viscous computational fluid dynamic (CFD) simulations were performed to investigate the flow characteristics of a vehicle with baseline and sweptback grid fins at transonic and supersonic Mach numbers in the range 0.817- 2.0, at zero angle of attack. Good agreement (within the error of 4%) is observed for the computed drag coefficients with data available in literature. The present numerical results indicate the sweptback grid fins reduce the flow chocking. This translates in a grid-fin drag reduction of about 12% for all the Mach numbers investigated in the present study.