Pressure Recovery for Missiles with Reaction Propulsion at High Supersonic Speeds (The Efficiency of Shock Diffusers)

The problem of the intake of air is treated for a missile flying at supersonic speeds and of changing the kinetic energy of the air into pressure with the least possible losses. Calculations are carried out concerning the results which can be attained. After a discussion of several preliminary experiments, the practical solution of the problem at hand is indicated by model experiments. The results proved very satisfactory in view of the results which had been attained previously and the values which were anticipated theoretically

Solvable vector nonlinear Riemann problems, exact implicit solutions of dispersionless PDEs and wave breaking

We have recently solved the inverse spectral problem for integrable PDEs in arbitrary dimensions arising as commutation of multidimensional vector fields depending on a spectral parameter $\lambda$. The associated inverse problem, in particular, can be formulated as a non linear Riemann Hilbert (NRH) problem on a given contour of the complex $\lambda$ plane. The most distinguished examples of integrable PDEs of this type, like the dispersionless Kadomtsev-Petviashivili (dKP), the heavenly and the 2 dimensional dispersionless Toda equations, are real PDEs associated with Hamiltonian vector fields. The corresponding NRH data satisfy suitable reality and symplectic constraints. In this paper, generalizing the examples of solvable NRH problems illustrated in \cite{MS4,MS5,MS6}, we present a general procedure to construct solvable NRH problems for integrable real PDEs associated with Hamiltonian vector fields, allowing one to construct implicit solutions of such PDEs parametrized by an arbitrary number of real functions of a single variable. Then we illustrate this theory on few distinguished examples for the dKP and heavenly equations. For the dKP case, we characterize a class of similarity solutions, a class of solutions constant on their parabolic wave front and breaking simultaneously on it, and a class of localized solutions breaking in a point of the $(x,y)$ plane. For the heavenly equation, we characterize two classes of symmetry reductions.Comment: 29 page

Energy Release on the Surface of a Rapidly Rotating Neutron Star during Disk Accretion: A Thermodynamic Approach

The total energy E of a star as a function of its angular momentum J and mass M in the Newtonian theory: E = E(J, M) [in general relativity, the gravitational mass M of a star as a function of its angular momentum J and rest mass m, M = M(J, m)], is used to determine the remaining parameters (angular velocity, equatorial radius, chemical potential, etc.) in the case of rigid rotation. Expressions are derived for the energy release during accretion onto a cool (with constant entropy), rapidly rotating neutron star (NS) in the Newtonian theory and in general relativity. A separate analysis is performed for the cases where the NS equatorial radius is larger and smaller than the radius of the marginally stable orbit in the disk plane. An approximate formula is proposed for the NS equatorial radius for an arbitrary equation of state, which matches the exact one at J = 0.Comment: 12 pages, 0 figures (Astronomy Letters in press

Analysis of preconditioning and multigrid for Euler flows with low-subsonic regions

For subsonic flows and upwind-discretized, linearized 1-D Euler equations, the smoothing behavior of multigrid-accelerated point Gauss-Seidel relaxation is analyzed. Error decay by convection across domain boundaries is also discussed. A fix to poor convergence rates at low Mach numbers is sought in replacing the point relaxation applied to unconditioned Euler equations, by locally implicit “time”-stepping applied to preconditioned Euler equations. The locally implicit iteration step is optimized for good damping of high-frequency errors. Numerical inaccuracy at low Mach numbers is also addressed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41714/1/10444_2005_Article_BF02123476.pd

Interaction between a normal shock wave and a turbulent boundary layer at high transonic speeds. Part I: Pressure distribution

Asymptotic solutions are derived for the pressure distribution in the interaction of a weak normal shock wave with a turbulent boundary layer. The undisturbed boundary layer is characterized by the law of the wall and the law of the wake for compressible flow. In the limiting case considered, for ‘high’ transonic speeds, the sonic line is very close to the wall. Comparisons with experiment are shown, with corrections included for the effect of longitudinal wall curvature and for the boundary-layer displacement effect in a circular pipe. Asymptotische Lösungen für den Druckverlauf bei der Wechselwirkung zwischen einem schwachen normalen Stoss und einer turbulente Grenzschicht werden hergeleitet. Das Wandgesetz und Geschwindigkeitsdefekt-Gesetz für kompressible Strömung kennzeichnen die ungestörte Grenzschicht. Der Grenzfall hoher transsonischen Strömung, in dem die Schallinie in der Nähe der Wand liegt, wird untersucht. Die theoretischen Ergebnisse werden mit Experimenten verglichen. Dabei wird die Wandkrümmung und im Fall der Rohrströmung die Verdrängungsdicke berücksichtigt.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43384/1/33_2005_Article_BF01590748.pd