Shock-wave reflexion in a relaxing gas
Plane normal shock wave reflection in relaxing gas for shock tube endwall upstream and downstream dynamic pressures, using method of characteristics
Hanson, R. K.↗
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Numerical solutions of several reflected shock-wave flow fields with nonequilibrium chemical reactions
The method of characteristics for a chemically reacting gas is used in the construction of the time-dependent, one-dimensional flow field resulting from the normal reflection of an incident shock wave at the end wall of a shock tube. Nonequilibrium chemical reactions are allowed behind both the incident and reflected shock waves. All the solutions are evaluated for oxygen, but the results are generally representative of any inviscid, nonconducting, and nonradiating diatomic gas. The solutions clearly show that: (1) both the incident- and reflected-shock chemical relaxation times are important in governing the time to attain steady state thermodynamic properties; and (2) adjacent to the end wall, an excess-entropy layer develops wherein the steady state values of all the thermodynamic variables except pressure differ significantly from their corresponding Rankine-Hugoniot equilibrium values.
Hanson, R. K.↗
Fabrication of (U, Zr) C-fueled/tungsten-clad specimens for irradiation in the Plum Brook Reactor Facility
Fuel samples, 90UC - 10 ZrC, and chemically vapor deposited tungsten fuel cups were fabricated for the study of the long term dimensional stability and compatibility of the carbide-tungsten fuel-cladding systems under irradiation. These fuel samples and fuel cups were assembled into the fuel pins of two capsules, designated as V-2E and V-2F, for irradiation in NASA Plum Brook Reactor Facility at a fission power density of 172 watts/c.c. and a miximum cladding temperature of 1823 K. Fabrication methods and characteristics of the fuel samples and fuel cups prepared are described.
Source record↗
Longitudinal impact of cylindrical shells.
The transient response due to longitudinal impact of three aluminum cylindrical shells of different thickness-to-radius ratios is studied both analytically and experimentally. The analyses were obtained from method of characteristics' solutions of two sets of equations: one which includes the transverse shear, radial inertia, and rotary inertial effects; and the other set is from a modified membrane theory. Experimentally, longitudinal and circumferential strains are monitored along the length of each of the shells; the velocity of the impacter ring is also measured. The experimental results of this study indicate that the wave front, after traveling three diameters from the impacted end, propagates at essentially the plate velocity, in agreement with the theory. In addition, the longitudinal and circumferential strain calculated from the two theories are in good agreement with the experimental results.
Mortimer, R. W.↗
The earth's bow shock in an oblique interplanetary field.
The pressure, magnetic field, temperature, particle density, and stream velocity throughout the magnetosheath have been calculated in the plane containing the interplanetary field and solar wind velocity vector for various orientations of the interplanetary magnetic field and various assumed ratios of specific heats of the compressed solar wind. Jump conditions at the bow shock gave initial conditions in the shocked plasma from which the appropriate hydromagnetic equations (for blunt bodies in the subsonic region near the subsolar point and for the method of characteristics in the supersonic region back in the tail) were integrated numerically back to the surface of the magnetosphere. Explicit consideration of the magnetic field shows that a net asymmetrical force on the magnetopause produces a side force, or 'lift' in addition to the well-known drag on the magnetosphere.
Shen, W.-W.↗
Transient axisymmetric motions of a conical bar.
Three bar of revolution theories are developed. The most inclusive theory is equivalent to the Mindlin-McNiven theory for circular bars in that it includes radial, axial shear, and longitudinal modes. By removing the axial shear mode in the foregoing, a theory equivalent to the Mindlin-Herrmann theory for circular bars is obtained. Finally, by eliminating all the radial effects in this latter theory, a simple theory incorporating only longitudinal effects is obtained. Each of these three theories is then specialized for a conical geometry and solved by the method of characteristics for the case of a longitudinal impact. The solutions for each of these theories are then compared to published surface meridional strain and internal strain data. In addition, the importance of impact pulse duration in establishing the validity of the approximate bar theories for impact problems is analytically indicated.
Mortimer, R. W.↗
Strongly coupled stress waves in heterogeneous plates.
Consideration of coupled stress waves generated by an impulsive load applied at one end of a semiinfinite plate. For the field equations governing the one-dimensional coupled waves a hyperbolic system of equations is obtained in which a strong coupling in the second derivatives exists. The method of characteristics described by Chou and Mortimer (1967) is extended to cover the case of strong coupling, and a study is made of the transient stress waves in a semiinfinite plate subjected to an initial step input. Coupled discontinuity fronts are found to propagate at different velocities. The normal plate stress and the bending moment at different time regimes are illustrated by graphs.
Wang, A. S. D.↗
Finite-amplitude pressure waves in the radial mode of a cylinder
A numerical study of finite-strength, isentropic pressure waves transverse to the axis of a circular cylinder was made for the radial resonant mode. The waves occur in a gas otherwise at rest, filling the cylinder. A method of characteristics was used for the numerical solution. For small but finite amplitudes, calculations indicate the existence of waves of permanent potential form. For larger amplitudes, a shock is indicated to occur. The critical value of the initial amplitude parameter in the power series is found to be 0.06 to 0.08, under various types of initial conditions.
Kubo, I.↗
Studies for determining rapid thrust response requirements and techniques for use in a long range transport aircraft
Propulsion systems proposed for the next generation of long-range transport aircraft will utilize advanced technology to reduce the noise to levels that will be inoffensive to the community. Additional reductions can be realized by adopting steeper glide slopes during the landing approach. The aircraft dynamic characteristics and methods of obtaining rapid engine response during the go-around maneuver from an aborted landing approach are identified and discussed. The study concludes that the present levels of flight safety will not be compromised by the steeper approach.
Newirth, D. M.↗
Nonlinear analysis of a shock-loaded membrane.
Results from a computer method for analyzing the unsteady interaction of a fluid stream and a flat circular elastic membrane are presented. The loading on the membrane is assumed to be caused by the firing of a shock tube. The fluid pressures and velocities are determined from a scheme based on the numerical method of characteristics, and the membrane is analyzed using exact relations for membrane strain. The interactive solution is found to give peak stresses 40% lower than a solution which assumes a pressure invariant in space and time.
Madden, R.↗
Investigations of Air-Cooled Turbine Rotors for Turbojet Engines. 1: Experimental Disk Temperature Distribution in Modified J33 Split-Disk Rotor at Speeds up to 6000 RPM
An experimental investigation is being conducted at the Lewis laboratory to establish general principles for the design of noncritical turbine rotor configurations. This investigation includes evaluation of cooling effectiveness, structural stability, cooling-air flow distribution characteristics, and methods of supplying cooling air to the turbine rotor blades. Prior to design of a noncritical rotor, a standard turbine rotor of a commerical turbojet engine was split in the plane of rotation and machined to provide a passage for distributing cooling air to the base of each blade. The rotor was fitted with nontwisted, hollow, aircooled blades containing nine tubes in the coolant passage. In the investigation reported herein, the modified turbine rotor operated successfully up to speeds of 6000 rpm with ratios of cooling-air to combustion-gas flow as low as 0.02. The disk temperatures observed at these conditions were below 450 0 F when cooling air at 100 F was used from the laboratory air system. The calculated disk temperatures based on the correlation method presented for rated engine conditions were well below 1000 F at a cooling-air flow ratio of 0.02, which is considered adequate for a noncritical rotor. An appreciable difference in temperature level existed between the forward and rear disks. This temperature difference probably introduced undesirable disk stress distributions as a result of the relative elongations of the two disks. This investigation was terminated at 6000 rpm so that slight changes in the engine configuration could be made to relieve this condition.
Schramm, Wilson B.↗
Analysis and design of three dimensional supersonic nozzles. Volume 1: Nozzle-exhaust flow field analysis by a reference plane characteristics technique
A second order numerical method employing reference plane characteristics has been developed for the calculation of geometrically complex three dimensional nozzle-exhaust flow fields, heretofore uncalculable by existing methods. The nozzles may have irregular cross sections with swept throats and may be stacked in modules using the vehicle undersurface for additional expansion. The nozzles may have highly nonuniform entrance conditions, the medium considered being an equilibrium hydrogen-air mixture. The program calculates and carries along the underexpansion shock and contact as discrete discontinuity surfaces, for a nonuniform vehicle external flow.
Dash, S.↗
Transient analysis using conical shell elements
The use of the NASTRAN conical shell element in static, eigenvalue, and direct transient analyses is demonstrated. The results of a NASTRAN static solution of an externally pressurized ring-stiffened cylinder agree well with a theoretical discontinuity analysis. Good agreement is also obtained between the NASTRAN direct transient response of a uniform cylinder to a dynamic end load and one-dimensional solutions obtained using a method of characteristics stress wave code and a standing wave solution. Finally, a NASTRAN eigenvalue analysis is performed on a hydroballistic model idealized with conical shell elements.
Yang, J. C. S.↗
Modification of a three-dimensional supersonic nozzle analysis and comparison with experimental data
A computer program previously developed to analyze three-dimensional supersonic nozzles by the method of characteristics has been modified to study less restrictive nozzle geometries and nonuniform inlet conditions. An example indicates that a one-dimensional calculation that uses an averaged initial profile may be significantly in error. A comparison between the analysis and the data from a three-dimensional experiment shows generally good agreement between the two.
Bishop, A. R.↗
One-Dimensional Shock Wave Formation by an Accelerating Piston
The formation of a shock wave by a solid accelerating piston was studied. A theoretical solution using the method of characteristics for a perfect gas showed that a complex wave system exists, and that the compressed gas can have large gradients in temperature, density and entropy. Experiments were performed with a piston tube where piston speed, shock speed and pressure were measured. The comparison of theory and experiment was good.
Mann, M. J.↗
Boundary-layer transition and displacement thickness effects on zero-lift drag of a series of power-law bodies at Mach 6
Wave and skin-friction drag have been numerically calculated for a series of power-law bodies at a Mach number of 6 and Reynolds numbers, based on body length, from 1.5 million to 9.5 million. Pressure distributions were computed on the nose by the inverse method and on the body by the method of characteristics. These pressure distributions and the measured locations of boundary-layer transition were used in a nonsimilar-boundary-layer program to determine viscous effects. A coupled iterative approach between the boundary-layer and pressure-distribution programs was used to account for boundary-layer displacement-thickness effects. The calculated-drag coefficients compared well with previously obtained experimental data.
Ashby, G. C., Jr.↗
Trace element geochemistry of Archean volcanic rocks
The K, Rb, Sr, Ba and rare-earth-element contents of some Archean volcanic rocks from the Vermilion greenstone belt, northeast Minnesota, were determined by the isotopic dilution method. The characteristics of trace element abundances, supported by the field occurrences and major element chemistry, suggest that these volcanic rocks were formed in an ancient island arc system.
Jahn, B.-M.↗
Prediction of pressure and flow transients in a gaseous bipropellant reaction control rocket engine
An analytic model is developed to predict pressure and flow transients in a gaseous hydrogen-oxygen reaction control rocket engine feed system. The one-dimensional equations of momentum and continuity are reduced by the method of characteristics from partial derivatives to a set of total derivatives which describe the state properties along the feedline. System components, e.g., valves, manifolds, and injectors are represented by pseudo steady-state relations at discrete junctions in the system. Solutions were effected by a FORTRAN IV program on an IBM 360/65. The results indicate the relative effect of manifold volume, combustion lag time, feedline pressure fluctuations, propellant temperature, and feedline length on the chamber pressure transient. The analytical combustion model is verified by good correlation between predicted and observed chamber pressure transients. The developed model enables a rocket designer to vary the design parameters analytically to obtain stable combustion for a particular mode of operation which is prescribed by mission objectives.
Markowsky, J. J.↗