On the evolution of compression pulses in an exploding atmosphere: initial behaviour

1979 ◽  
Vol 94 (1) ◽  
pp. 195-208 ◽  
Author(s):  
J. F. Clarke
Keyword(s):  
Shock Wave ◽  
Present Theory ◽  
Sine Wave ◽  
Inert Atmosphere ◽  
Subsequent Evolution ◽  
Local Explosion ◽  
Wave Development ◽  
Amplifying Effect ◽  
Shock Fitting ◽  
Positive Half

The development in space and time of a plane initial disturbance to a spatially uniform exploding atmosphere is analysed on the assumption that the disturbance amplitude is comparable in magnitude with the inverse (dimensionless) activation energy of the explosion reaction. Particular attention is focused on the shock-fitting problem, which has features that distinguish it from its inert-atmosphere counterpart.Using the positive half of a sine wave to typify an isolated compression perturbation, it is found that the amplifying effect of the ambient reaction leads to very rapid shock wave development, which depends significantly on the spatial extent of the disturbance. The latter also influences the question of whether local explosion (local explosion is recognized here as a logarithmically unbounded growth of the disturbance amplitude; in other words as a local breakdown of the present approximations) occurs at the shock wave or some distance behind it. The subsequent evolution of these two states will no doubt be significantly different, but the answer to this speculation must await extension of the present theory to encompass the rapid events that ensue near the local explosion regions.

scholarly journals A study of the interaction of a travelling shock wave with a solid-propellant rocket motor head end

2021 ◽  
Author(s):  
Robert Elian Feteanu
Keyword(s):  
Shock Wave ◽  
Rocket Motor ◽  
Combustion Chambers ◽  
Cfd Simulations ◽  
Radial Wave ◽  
Flow Models ◽  
Numerical Studies ◽  
Solid Propellant Rocket ◽  
Wave Development ◽  
Solid Rocket

Experimental and numerical studies have been undertaken to examine various aspects pertaining to the interaction of an incident travelling shock wave with a solid rocket motor's head end (forward section), in order to identify any potential gasdynamic mechanism of wave reinforcement pertinent to combustion instability behaviour in these motors. A cold-flow experiment, based on a shock tube scheme tailored to the present application, has proved to be useful in providing information surrounding the interaction process. Both experimental and numerical results (CFD simulations) confirm the existence of substantial transient radial wave development superimposed on the base reflected axial shock wave. These results illustrate the potential weakness of one-dimensional flow models for certain engineering applications, where important multidimensional phenomena, such as those observed in this work, may not be captured. By analogy to actual propulsion system combustion chambers, the transverse wave activity is potentially a factor in supporting an augmentation of the local combustion rate in the head-end region of a rocket motor combustor.

scholarly journals ON THE INSTANTANEOUS SPECTRUM OF GAMMA-RAY BURSTS

2004 ◽  
Vol 13 (05) ◽  
pp. 843-851 ◽  
Author(s):  
REMO RUFFINI ◽  
CARLO LUCIANO BIANCO ◽  
SHE-SHENG XUE ◽  
PASCAL CHARDONNET ◽  
FEDERICO FRASCHETTI ◽  
...  
Keyword(s):  
Shock Wave ◽  
Gamma Ray ◽  
Thermal Emission ◽  
Equations Of Motion ◽  
Present Theory ◽  
Gamma Ray Bursts ◽  
Instantaneous Spectrum ◽  
Consistent Model ◽  
Past Light Cone

A theoretical attempt to identify the physical process responsible for the afterglow emission of Gamma-Ray Bursts (GRBs) is presented, leading to the occurrence of thermal emission in the comoving frame of the shock wave which gives rise to the bursts. The determination of the luminosities and spectra involves integration over an infinite number of Planckian spectra, weighted by appropriate relativistic transformations, each one corresponding to a different viewing angle in the past light cone of the observer. The relativistic transformations have been computed using the equations of motion of GRBs within our theory, giving special attention to the determination of the equitemporal surfaces. The only free parameter of the present theory is the "effective emitting area" in the shock wave front. A self-consistent model for the observed hard-to-soft transition in GRBs is also presented. When applied to GRB 991216 a precise fit (χ2≃1.078) of the observed luminosity in the 2–10 keV band is obtained. Similarly, detailed estimates of the observed luminosity in the 50–300 keV and in the 10–50 keV bands are obtained.

The Integrated Gas/Steam Nozzle With Steam Cooling: Part II — Design Considerations

1984 ◽  
Author(s):  
Ivan G. Rice
Keyword(s):  
Shock Wave ◽  
Film Cooling ◽  
Fat Body ◽  
Suction Side ◽  
Body Type ◽  
Trailing Edge ◽  
Cooling Effectiveness ◽  
Film Cooling Effectiveness ◽  
Wave Development ◽  
Gas Nozzle

The integration of multiple steam nozzles with the first-stage annular-gas nozzle to form a binary-flow system in a reheat-gas turbine is presented whereby steam is first used as an internal vane coolant before being expanded and accelerated for work extraction. Steam nozzles are located in “fat-body” type vanes. Trailing-edge impingement followed by reverse-serpentine-flow cooling takes place. Internal trailing-edge-steam nozzles produce either diffusion or shock-wave boundary-layer disturbance inside the trailing edge to enhance heat transfer. Externally, steam blanketing reduces nozzle-profile loss and improves film cooling effectiveness by reducing the surface viscosity and secondly by controlling suction-side aft-shock-wave development. A new vane shape coupled with a gas-turning-combustor system is suggested to improve vane-film cooling effectiveness further.

Asymptotic solution of shock tube flows with homogeneous condensation

1995 ◽  
Vol 287 ◽  
pp. 93-118 ◽  
Author(s):  
Can F. Delale ◽  
Günter H. Schnerr ◽  
Jürgen Zierep
Keyword(s):  
Shock Wave ◽  
Asymptotic Solution ◽  
Shock Tube ◽  
Complete Solution ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Droplet Growth ◽  
Homogeneous Condensation ◽  
Shock Fitting ◽  
Supercritical Flows

The asymptotic solution of shock tube flows with homogeneous condensation is presented for both smooth, or subcritical, flows and flows with an embedded shock wave, or supercritical flows. For subcritical flows an analytical expression, independent of the particular theory of homogeneous condensation to be employed, that determines the condensation wave front in the rarefaction wave is obtained by the asymptotic analysis of the rate equation along pathlines. The complete solution is computed by an algorithm which utilizes the classical nucleation theory and the Hertz–Knudsen droplet growth law. For supercritical flows four distinct flow regimes are distinguished along pathlines intersecting the embedded shock wave analogous to supercritical nozzle flows. The complete global solution for supercritical flows is discussed only qualitatively owing to the lack of a shock fitting technique for embedded shock waves. The results of the computations obtained by the subcritical algorithm show that most of the experimental data available exhibit supercritical flow behaviour and thereby the predicted onset conditions in general show deviations from the measured values. The causes of these deviations are reasoned by utilizing the qualitative global asymptotic solution of supercritical flows.

Propagation of Weak Shock Waves in a Vibrational Nonequilibrium, Nonuniform Gas

1975 ◽  
Vol 42 (3) ◽  
pp. 564-568 ◽  
Author(s):  
D. C. Chou ◽  
S. Y. Maa
Keyword(s):  
Shock Wave ◽  
Wave Propagation ◽  
Shock Waves ◽  
Vibrational Energy ◽  
Weak Shock ◽  
Present Theory ◽  
Shock Wave Propagation ◽  
Perturbation Scheme ◽  
Relaxation Rates ◽  
Vibrational Nonequilibrium

Problems concerned with the propagation of weak planar shock waves in a nonuniform, nonequilibrium gas is theoretically investigated. The medium under consideration is a diatomic thermally perfect gas with excited vibrational energy and is initially inhomogeneous with exponential density and temperature distributions. The systematic characteristic perturbation scheme is employed to render a first-order frozen shock expression. It is shown quantitatively that combined effects of nonequilibrium, nonlinearity, and stratification govern the nature of the shock wave propagation. The uniform gas limit of present theory agrees with previously known results of shock wave propagation in a general relaxing fluid. Numerical examples illustrate the variation of frozen shock strength and speed due to different magnitudes of relaxation rates and inhomogeneity. The interesting competition phenomenon between nonequilibrium effects and nonuniform effects on shock wave propagation is examined.

Shock wave development in couple stress fluid-filled thin elastic tubes

2015 ◽  
Vol 130 (6) ◽  
Author(s):  
Samuel O. Adesanya ◽  
Mostafa Eslami ◽  
Mohammad Mirzazadeh ◽  
Anjan Biswas
Keyword(s):  
Shock Wave ◽  
Couple Stress ◽  
Couple Stress Fluid ◽  
Elastic Tubes ◽  
Wave Development

Weakly nonlinear acoustic and shock-wave theory of the noise of advanced high-speed turbopropellers

1986 ◽  
Vol 164 ◽  
pp. 127-154 ◽  
Author(s):  
Christopher K. W. Tam ◽  
M. Salikuddin
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
High Speed ◽  
Wave Theory ◽  
Present Theory ◽  
Nonlinear Propagation ◽  
Weakly Nonlinear ◽  
Acoustic Disturbances ◽  
Propagation Effects ◽  
Shock Wave Theory

An acoustic and shock-wave theory of the noise generated by advanced turbo-propellers operating at supersonic tip helical velocity and high-subsonic cruise Mach number is developed. The theory includes the thickness and loading noise of the highly swept propeller blades. When operating at their design conditions these propellers radiate extremely intense sound waves. Because of the weakly nonlinear propagation effects these high-intensity acoustic disturbances steepen up quickly to form shock waves. In the present theory advantage is taken of the fact that in the blade fixed-rotating-coordinate system the acoustic and shock-wave fields are time independent. The problem is formulated in this coordinate system as a boundary-value problem. Weakly nonlinear propagation effects are incorporated into the solution following Whitham's nonlinearization procedure (Whitham 1974). The change in the disturbance-propagation velocity due to fluid-particle motion as well as the change in the speed of sound resulting from compression and rarefaction are all taken into account. It is found that the equal-area rule of Whitham's shock-fitting method is also applicable to the present problem. This method permits easy construction of the three-dimensional shock surfaces associated with the acoustic disturbances of these high-speed turbopropellers. Numerical results of the present theory are compared with the measurements of the JETSTAr flight experiment and the United Technology Research Center low-cruise Mach number open-wind-tunnel data. Very favourable overall agreements are found. The comparisons indicate clearly that, when these supersonic turbopropellers are operated at their high subsonic design-cruise Mach number, weakly nonlinear propagation effects must be included in the theory if an accurate prediction of the waveform of the sound wave incident on the design aircraft fuselage is to be obtained. This is especially true for noise radiated in the upstream or forward directions. In the forward directions the effective propagation velocity of the acoustic disturbances is greatly reduced by the convection velocity of the ambient flow. This allows more time for the cumulative nonlinear propagation effects to exert their influence, leading to severe distortion of the waveform and the formation of shock waves.

Shock Wave Development and Propagation in Automobile Exhaust Systems

1988 ◽  
Author(s):  
Noriaki Sekine ◽  
Shuji Matsumura ◽  
Kazuyoshi Takayama ◽  
Osamu Onodera ◽  
Katsuhiro Ito
Keyword(s):  
Shock Wave ◽  
Automobile Exhaust ◽  
Wave Development ◽  
Exhaust Systems
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