On the theory of a shock wave driven by a corrugated piston in a non-ideal fluid

2011 ◽  
Vol 691 ◽  
pp. 146-164 ◽  
Author(s):  
J. W. Bates
Keyword(s):  
Shock Wave ◽  
Ideal Gas ◽  
Mathematical Framework ◽  
Fluid Medium ◽  
Temporal Behaviour ◽  
Shock Stability ◽  
Linear Perturbations ◽  
Ripple Amplitude ◽  
The Stability ◽  
Appl Math

AbstractIn the context of an Eulerian fluid description, we investigate the dynamics of a shock wave that is driven by the steady impulsively initiated motion of a two-dimensional planar piston with small corrugations superimposed on its surface. This problem was originally solved by Freeman (Proc. Royal Soc. A, vol. 228, 1955, pp. 341–362), who showed that piston-driven shocks are unconditionally stable when the fluid medium through which they propagate is an ideal gas. Here, we generalize Freeman’s mathematical framework to account for a fluid characterized by an arbitrary equation of state. We find that a sufficient condition for shock stability is $\ensuremath{-} 1\lt h\lt {h}_{c} $, where $h$ is the D’yakov parameter and ${h}_{c} $ is a critical value less than unity. For values of $h$ within this range, linear perturbations imparted to the front by the piston at time $t= 0$ attenuate asymptotically as ${t}^{\ensuremath{-} 3/ 2} $. Outside of this range, the temporal behaviour of perturbations is more difficult to determine and further analysis is required to assess the stability of a shock front under such circumstances. As a benchmark of the main conclusions of this paper, we compare our generalized expression for the linearized shock-ripple amplitude with an independent Bessel-series solution derived by Zaidel’ (J. Appl. Math. Mech., vol. 24, 1960, pp. 316–327) and find excellent agreement.

scholarly journals Analysis of the Stability of the Riemann Problem for a Simplified Model in Magnetogasdynamics

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Yujin Liu ◽  
Wenhua Sun
Keyword(s):  
Shock Wave ◽  
Riemann Problem ◽  
Contact Discontinuity ◽  
Ideal Gas ◽  
Simplified Model ◽  
Characteristic Method ◽  
Small Perturbations ◽  
Riemann Solutions ◽  
One Dimensional ◽  
The Stability

The generalized Riemann problem for a simplified model of one-dimensional ideal gas in magnetogasdynamics in a neighborhood of the origin(t>0)in the(x,t)plane is considered. According to the different cases of the corresponding Riemann solutions, we construct the perturbed solutions uniquely with the characteristic method. We find that, for some case, the contact discontinuity appears after perturbation while there is no contact discontinuity of the corresponding Riemann solution. For most cases, the Riemann solutions are stable and the perturbation can not affect the corresponding Riemann solutions. While, for some few cases, the forward (backward) rarefaction wave can be transformed into the forward (backward) shock wave which shows that the Riemann solutions are unstable under such local small perturbations of the Riemann initial data.

Shock reflexion and shock-wave interaction in field-aligned flows

1975 ◽  
Vol 14 (1) ◽  
pp. 39-51 ◽  
Author(s):  
Manfred Natter
Keyword(s):  
Shock Wave ◽  
Wave Interaction ◽  
Flow Speed ◽  
Ideal Gas ◽  
Incident Shock ◽  
Reflected Shock Wave ◽  
Heat Conducting ◽  
Fluid Medium ◽  
Reflected Shock ◽  
Monatomic Gas

This paper considers the steady two-dimensional problem of regular reflexion and symmetric intersection of oblique magnetogasdynamic shock waves. It is assumed that the fluid medium is a non-viscous, non-heat-conducting, ideal gas of infinite electrical conductivity, and that the applied magnetic field is parallel to the velocity of the approaching stream. In view of the complexity of the shock relations, a graphical method is presented for determining the orientation and strength of the reflected shock wave in terms of the Laval number M*1 (flow speed divided by critical sound speed), the Alfvén number A1 (flow speed divided by Alfvén speed), and the shock angle ϑ 1 ahead of the incident shock. Moreover, the possible ranges of M*1, A1, and ϑ 1, for which regular reflexion may occur, are calculated and illustrated graphically for the case of a monatomic gas.

Analytical solution for unsteady flow behind ionizing shock wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field

2021 ◽  
Vol 76 (3) ◽  
pp. 265-283
Author(s):  
G. Nath
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Analytical Solution ◽  
Axial Magnetic Field ◽  
Order Approximation ◽  
Ideal Gas ◽  
Field Region ◽  
First Order ◽  
First Order Approximation ◽  
Flow Variables

Abstract The approximate analytical solution for the propagation of gas ionizing cylindrical blast (shock) wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field is investigated. The axial and azimuthal components of fluid velocity are taken into consideration and these flow variables, magnetic field in the ambient medium are assumed to be varying according to the power laws with distance from the axis of symmetry. The shock is supposed to be strong one for the ratio C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ to be a negligible small quantity, where C 0 is the sound velocity in undisturbed fluid and V S is the shock velocity. In the undisturbed medium the density is assumed to be constant to obtain the similarity solution. The flow variables in power series of C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ are expanded to obtain the approximate analytical solutions. The first order and second order approximations to the solutions are discussed with the help of power series expansion. For the first order approximation the analytical solutions are derived. In the flow-field region behind the blast wave the distribution of the flow variables in the case of first order approximation is shown in graphs. It is observed that in the flow field region the quantity J 0 increases with an increase in the value of gas non-idealness parameter or Alfven-Mach number or rotational parameter. Hence, the non-idealness of the gas and the presence of rotation or magnetic field have decaying effect on shock wave.

scholarly journals Equation of state studies at SILP by laser-driven shock waves

1996 ◽  
Vol 14 (2) ◽  
pp. 157-169 ◽  
Author(s):  
Yuan Gu ◽  
Sizu Fu ◽  
Jiang Wu ◽  
Songyu Yu ◽  
Yuanlong Ni ◽  
...  
Keyword(s):  
Shock Wave ◽  
High Pressure ◽  
Equation Of State ◽  
Shock Waves ◽  
Target Surface ◽  
Shock Adiabats ◽  
Pressure Shock ◽  
Aluminum Target ◽  
Laser Illumination ◽  
The Stability

The experimental progress of laser equation of state (EOS) studies at Shanghai Institute of Laser Plasma (SILP) is discussed in this paper. With a unique focal system, the uniformity of the laser illumination on the target surface is improved and a laser-driven shock wave with good spatial planarity is obtained. With an inclined aluminum target plane, the stability of shock waves are studied, and the corresponding thickness range of the target of laser-driven shock waves propagating steadily are given. The shock adiabats of Cu, Fe, SiO2 are experimentally measured. The pressure in the material is heightened remarkably with the flyer increasing pressure, and the effect of the increasing pressure is observed. Also, the high-pressure shock wave is produced and recorded in the experimentation of indirect laser-driven shock waves with the hohlraum target.

The Scattering of Shock Waves by Cylindrical Cavities in Liquids and Solids

1971 ◽  
Vol 38 (1) ◽  
pp. 190-196 ◽  
Author(s):  
E. Y. Harper
Keyword(s):  
Shock Wave ◽  
Asymptotic Expansion ◽  
Shielding Effect ◽  
Inviscid Fluid ◽  
Shadow Region ◽  
Shock Diffraction ◽  
Fluid Medium ◽  
Acoustic Shock Wave ◽  
Cylindrical Cavities ◽  
Logarithmic Decay

The scattering of a plane acoustic shock wave by a cylindrical cavity in an inviscid fluid medium is calculated numerically and compared with a recently obtained asymptotic expansion. In contrast to the scattering by a rigid cylinder, the cavity displays a distinctive shielding effect in the shadow region characterized by a peak exitation and an inverse logarithmic decay. Experimental results are presented which indicate a strong counterpart in plastic shock diffraction.

Influencing Factors of Chromium Ion Stability in Microbe Culture Media

2012 ◽  
Vol 610-613 ◽  
pp. 215-219
Author(s):  
Yun Xiao He ◽  
Xiao Ming Chen
Keyword(s):  
Ionic Liquid ◽  
Liquid Medium ◽  
Culture Media ◽  
Fluid Medium ◽  
Chromium Ion ◽  
Medium Components ◽  
Salt Ions ◽  
Ion Stability ◽  
The Stability ◽  
Ionic Liquid Medium

The stability factors for Cr6+ and Cr3+ in microbiological media, including temperature, preservation conditions and medium components were studied in this research project, through potassium permanganate oxidation and DPC (Diphenylcarbazide) spectrophotometry. It shows that the protein component mainly influences Cr6+ content changes at pre- and post- heat sterilization to the chromium ionic liquid medium, other than being impacted basically by inorganic salt ions. It also indicates that the method can be introduced into experiment researches for microbe dechromisation i.e. Chromium ion aqueous solution and fluid medium are sterilized separately, and then are made into the chrome ions liquid as per a certain concentration. The concentration of hexavalent chromium ions is affected by preservation time and temperature also. For this reason, chromium ionic liquid medium is kept at low temperature, and as quickly as possible for the test.

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