scholarly journals Normal Reflection Characteristics of One-Dimensional Unsteady Flow Shock Waves on Rigid Walls from Pulse Discharge in Water

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Dong Yan ◽  
Jinchang Zhao ◽  
Shaoqing Niu
Keyword(s):  
Shock Wave ◽  
Hydrostatic Pressure ◽  
Shock Waves ◽  
Pulse Discharge ◽  
Weak Shock ◽  
Rigid Wall ◽  
Wave Source ◽  
One Dimensional ◽  
Normal Reflection ◽  
Rigid Walls

Strong shock waves can be generated by pulse discharge in water, and the characteristics due to the shock wave normal reflection from rigid walls have important significance to many fields, such as industrial production and defense construction. This paper investigates the effects of hydrostatic pressures and perturbation of wave source (i.e., charging voltage) on normal reflection of one-dimensional unsteady flow shock waves. Basic properties of the incidence and reflection waves were analyzed theoretically and experimentally to identify the reflection mechanisms and hence the influencing factors and characteristics. The results indicated that increased perturbation (i.e., charging voltage) leads to increased peak pressure and velocity of the reflected shock wave, whereas increased hydrostatic pressure obviously inhibited superposition of the reflection waves close to the rigid wall. The perturbation of wave source influence on the reflected wave was much lower than that on the incident wave, while the hydrostatic pressure obviously affected both incident and reflection waves. The reflection wave from the rigid wall in water exhibited the characteristics of a weak shock wave, and with increased hydrostatic pressure, these weak shock wave characteristics became more obvious.

On the interaction between shock waves and boundary layers

1951 ◽  
Vol 47 (3) ◽  
pp. 545-553 ◽  
Author(s):  
K. Stewartson
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Reynolds Number ◽  
Shock Waves ◽  
Boundary Layers ◽  
Weak Shock ◽  
Boundary Layer Separation ◽  
Weak Shock Wave ◽  
Layer Separation ◽  
Boundary Layer Equations

AbstractThe effect on the boundary-layer equations of a weak shock wave of strength ∈ has been investigated, and it is shown that ifRis the Reynolds number of the boundary layer, separation occurs when ∈ =o(R−i). The boundary-layer assumptions are then investigated and shown to be consistent. It is inferred that separation will occur if a shock wave meets a boundary and the above condition is satisfied.

scholarly journals An Analytical Method for the Response of Coated Plates Subjected to One-Dimensional Underwater Weak Shock Wave

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Zeyu Jin ◽  
Caiyu Yin ◽  
Yong Chen ◽  
Xiuchang Huang ◽  
Hongxing Hua
Keyword(s):  
Shock Wave ◽  
Analytical Method ◽  
Weak Shock ◽  
Wave Theory ◽  
Time Sequence ◽  
Weak Shock Wave ◽  
One Dimensional ◽  
Coated Plate ◽  
Pressure Increment ◽  
Good Agreement

An analytical method based on the wave theory is proposed to calculate the pressure at the interfaces of coated plate subjected to underwater weak shock wave. The method is carried out to give analytical results by summing up the pressure increment, which can be calculated analytically, in time sequence. The results are in very good agreement with the finite element (FE) predictions for the coating case and Taylor’s results for the noncoating case, which validate the method that is suitable for underwater weak shock problem. On the other hand, Taylor’s results for the coating case are invalid, which indicates a potential application field for the method. The extension of the analytical method to q-layer systems and dissipation case is also outlined.

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.

Precursor shock waves at a slow—fast gas interface

1976 ◽  
Vol 76 (1) ◽  
pp. 157-176 ◽  
Author(s):  
A. M. Abd–El–Fattah ◽  
L. F. Henderson ◽  
A. Lozzi
Keyword(s):  
Experimental Data ◽  
Carbon Dioxide ◽  
Shock Wave ◽  
Shock Waves ◽  
Plane Shock ◽  
One Dimensional ◽  
Irregular Wave ◽  
Irregular Systems ◽  
Theory And Experiment ◽  
Good Agreement

This paper presents experimental data obtained for the refraction of a plane shock wave at a carbon dioxide–helium interface. The gases were separated initially by a delicate polymer membrane. Both regular and irregular wave systems were studied, and a feature of the latter system was the appearance of bound and free precursor shocks. Agreement between theory and experiment is good for regular systems, but for irregular ones it is sometimes necessary to take into account the effect of the membrane inertia to obtain good agreement. The basis for the analysis of irregular systems is one-dimensional piston theory and Snell's law.

Direct numerical simulation of isotropic turbulence interacting with a weak shock wave

1993 ◽  
Vol 251 ◽  
pp. 533-562 ◽  
Author(s):  
Sangsan Lee ◽  
Sanjiva K. Lele ◽  
Parviz Moin
Keyword(s):  
Shock Wave ◽  
Kinetic Energy ◽  
Shock Waves ◽  
Shock Front ◽  
Numerical Simulations ◽  
Turbulent Kinetic Energy ◽  
Isotropic Turbulence ◽  
Weak Shock ◽  
Linear Analysis ◽  
Weak Shock Wave

Interaction of isotropic quasi-incompressible turbulence with a weak shock wave was studied by direct numerical simulations. The effects of the fluctuation Mach number Mt of the upstream turbulence and the shock strength M21 — 1 on the turbulence statistics were investigated. The ranges investigated were 0.0567 ≤ Mt ≤ 0.110 and 1.05 ≤ M1 ≤ 1.20. A linear analysis of the interaction of isotropic turbulence with a normal shock wave was adopted for comparisons with the simulations.Both numerical simulations and the linear analysis of the interaction show that turbulence is enhanced during the interaction with a shock wave. Turbulent kinetic energy and transverse vorticity components are amplified, and turbulent lengthscales are decreased. The predictions of the linear analysis compare favourably with simulation results for flows with M2t < a(M21 — 1) with a ≈ 0.1, which suggests that the amplification mechanism is primarily linear. Simulations also showed a rapid evolution of turbulent kinetic energy just downstream of the shock, a behaviour not reproduced by the linear analysis. Investigation of the budget of the turbulent kinetic energy transport equation shows that this behaviour can be attributed to the pressure transport term.Shock waves were found to be distorted by the upstream turbulence, but still had a well-defined shock front for M2t < a(M21— 1) with a ≈ 0.1). In this regime, the statistics of shock front distortions compare favourably with the linear analysis predictions. For flows with M2t > a(M21— 1 with a ≈ 0.1, shock waves no longer had well-defined fronts: shock wave thickness and strength varied widely along the transverse directions. Multiple compression peaks were found along the mean streamlines at locations where the local shock thickness had increased significantly.

One-dimensional spherical shock waves in an interstellar dusty gas clouds

2021 ◽  
Vol 76 (5) ◽  
pp. 417-425
Author(s):  
Astha Chauhan ◽  
Kajal Sharma
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Differential Equations ◽  
Shock Propagation ◽  
Dusty Gas ◽  
Shock Strength ◽  
Efficient System ◽  
One Dimensional ◽  
Arbitrary Strength ◽  
Spherical Shock

Abstract A system of partial differential equations describing the one-dimensional motion of an inviscid self-gravitating and spherical symmetric dusty gas cloud, is considered. Using the method of the kinematics of one-dimensional motion of shock waves, the evolution equation for the spherical shock wave of arbitrary strength in interstellar dusty gas clouds is derived. By applying first order truncation approximation procedure, an efficient system of ordinary differential equations describing shock propagation, which can be regarded as a good approximation of infinite hierarchy of the system. The truncated equations, which describe the shock strength and the induced discontinuity, are used to analyze the behavior of the shock wave of arbitrary strength in a medium of dusty gas. The results are obtained for the exponents from the successive approximation and compared with the results obtained by Guderley’s exact similarity solution and characteristic rule (CCW approximation). The effects of the parameters of the dusty gas and cooling-heating function on the shock strength are depicted graphically.

scholarly journals Modern infinitesimals and the entropy jump across an inviscid shock wave

2018 ◽  
Vol 17 (4-5) ◽  
pp. 502-520
Author(s):  
Roy S Baty ◽  
Len G Margolin
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Euler Equations ◽  
Nonstandard Analysis ◽  
Generalized Solutions ◽  
Perfect Gas ◽  
One Dimensional ◽  
Number Systems ◽  
Shock Thickness ◽  
Modern Mathematics

This article applies nonstandard analysis to study the generalized solutions of entropy and energy across one-dimensional shock waves in a compressible, inviscid, perfect gas. Nonstandard analysis is an area of modern mathematics that studies number systems that contain both infinitely large and infinitely small numbers. For an inviscid shock wave, it is assumed that the shock thickness occurs on an infinitesimal interval and that the jump functions for the field variables are smoothly defined on this interval. A weak converse to the existence of the entropy peak is derived and discussed. Generalized solutions of the Euler equations for entropy and energy are then derived for both theoretical and realistic normalized velocity profiles.

scholarly journals Triangular Gross-Pitaevskii breathers and Damski-Chandrasekhar shock waves

2021 ◽  
Vol 10 (5) ◽  
Author(s):  
Maxim Olshanii ◽  
Dumesle Deshommes ◽  
Jordi Torrents ◽  
Marina Gonchenko ◽  
Vanja Dunjko ◽  
...  
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Initial Conditions ◽  
Broad Class ◽  
Hydrodynamic Equations ◽  
Nonlinear Transport ◽  
One Dimensional ◽  
Nonlinear Transport Equation ◽  
Bosonic Case ◽  
The One

The recently proposed map [5] between the hydrodynamic equations governing the two-dimensional triangular cold-bosonic breathers [1] and the high-density zero-temperature triangular free-fermionic clouds, both trapped harmonically, perfectly explains the former phenomenon but leaves uninterpreted the nature of the initial (t=0) singularity. This singularity is a density discontinuity that leads, in the bosonic case, to an infinite force at the cloud edge. The map itself becomes invalid at times t<0t<0. A similar singularity appears at t = T/4t=T/4, where T is the period of the harmonic trap, with the Fermi-Bose map becoming invalid at t > T/4t>T/4. Here, we first map—using the scale invariance of the problem—the trapped motion to an untrapped one. Then we show that in the new representation, the solution [5] becomes, along a ray in the direction normal to one of the three edges of the initial cloud, a freely propagating one-dimensional shock wave of a class proposed by Damski in [7]. There, for a broad class of initial conditions, the one-dimensional hydrodynamic equations can be mapped to the inviscid Burgers’ equation, which is equivalent to a nonlinear transport equation. More specifically, under the Damski map, the t=0 singularity of the original problem becomes, verbatim, the initial condition for the wave catastrophe solution found by Chandrasekhar in 1943 [9]. At t=T/8t=T/8, our interpretation ceases to exist: at this instance, all three effectively one-dimensional shock waves emanating from each of the three sides of the initial triangle collide at the origin, and the 2D-1D correspondence between the solution of [5] and the Damski-Chandrasekhar shock wave becomes invalid.

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