289 research outputs found
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 . The associated inverse problem, in
particular, can be formulated as a non linear Riemann Hilbert (NRH) problem on
a given contour of the complex 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 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 âtimeâ-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 âhighâ 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 fĂŒr den Druckverlauf bei der Wechselwirkung zwischen einem schwachen normalen Stoss und einer turbulente Grenzschicht werden hergeleitet. Das Wandgesetz und Geschwindigkeitsdefekt-Gesetz fĂŒr kompressible Strömung kennzeichnen die ungestörte Grenzschicht. Der Grenzfall hoher transsonischen Strömung, in dem die Schallinie in der NĂ€he der Wand liegt, wird untersucht. Die theoretischen Ergebnisse werden mit Experimenten verglichen. Dabei wird die WandkrĂŒmmung und im Fall der Rohrströmung die VerdrĂ€ngungsdicke berĂŒcksichtigt.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43384/1/33_2005_Article_BF01590748.pd
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NACA Technical Memorandums
"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" (p. 1)
Measurements of density in flowing air by means of the double-slit interferometer
The present report begins with a description of the double-slit interferometer and a derivation of the interferometer formula, Following that the application of the interferometer to measurements of density in flows is discussed and the formula is modified forth is particular purpose, A calibration of the interferometer is essential. The possible sources of error are particularly stressed. The formulae given in this report are applicable to all interferometers. In conclusion measurements of density in a Laval nozzle are discussed. These measurements permit an insight into the accuracy of the measuring method.Peer reviewed: NoNRC publication: Ye
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