No abstract

Despite constant progress in the development of upwind schemes, some failings still remain. Quirk recently reported (Quirk JJ. A contribution to the great Riemann solver debate. International Journal for Numerical Methods in Fluids 1994; 18: 555-574) that approximate Riemann solvers, which share the exact capture of contact discontinuities, generally suffer from such failings. One of these is the odd -even decoupling that occurs along planar shocks aligned with the mesh. First, a few results on some failings are given, namely the carbuncle phenomenon and the kinked Mach stem. Then, following Quirk's analysis of Roe's scheme, general criteria are derived to predict the odd -even decoupling. This analysis is applied to Roe's scheme (Roe PL, Approximate Riemann solvers, parameters vectors, and difference schemes,

The research and development efforts outlined in this paper address the aerodynamic design of micro air vehicles with hovering and vertical takeoff and landing capabilities. The tilt-body configuration of the vertical takeoff and landing micro air vehicle is proposed based on a propulsion system consisting of two coaxial contrarotating motors and propellers. Values of thrust, torque, power, and efficiency of this propulsion system were measured in pusher and tractor arrangements of propellers and compared against single motor-propeller propulsion. With comparable efficiency, the developed propulsion system has very little propeller torque. Hot-wire measurements have been conducted to investigate the velocity profile in slipstream. The lower average velocity and significant decrease in velocity in the core of the slipstream found in the tractor arrangement are mostly due to the parasite drag caused by the motors. It causes the decrease of the thrust force observed for the tractor arrangement in comparison with the pusher arrangement. Wind-tunnel testing was conducted for a motor, a wing, and an arrangement of a wing with a motor. The drag force on the wing is produced by two mixing airflows: freestream and propeller-induced pulsating slipstream. The zero-lift drag coefficient increases by about 4 times with propeller-induced speed increased from 0 to 7:5 m=s. The results of this study were realized in the design of a vertical takeoff and landing micro air vehicle prototype that was successfully flight tested. Nomenclature a = distance from propeller disk to the leading edge of the wing C D = drag coefficient C D 0 = zero-lift drag coefficient C D P = zero-lift drag coefficient on the part of the wing submerged into a propeller slipstream C L = lift coefficient c = chord F total = total force measured by a wind-tunnel balance P = electric power input P ind = induced power Q = torque R = propeller radius R m = maximum distance of velocity measurements from the z axis R s = radius of stream tube at distance s r = motor radius Re = mean aerodynamic chord Reynolds number S p = area of a part of the wing covered by propeller slipstream S S = area of the side wall S 0 = wing area T = thrust force T s = thrust force determined from air-velocity data V 0 = freestream velocity W = takeoff weight of an aircraft ws = induced velocity based on propeller momentum theory w e = measured propeller-induced velocity = air density

SUMMARYSince the development of shock-capturing methods, the carbuncle phenomenon has been reported to be a spurious solution produced by almost all currently available contact-preserving methods. The present analysis indicates that the onset of carbuncle phenomenon is actually strongly related to the shock wave numerical structure. A matrix-based stability analysis as well as Euler ÿnite volume computations are compared to illustrate the importance of the internal shock structure to trigger the carbuncle phenomenon.