Interaction of a singular surface with a strong shock in the interstellar gas clouds

We investigate the interaction between a singular surface and a strong shock in the self-gravitating interstellar gas clouds with the assumption of spherical symmetry. Using the method of the Lie group of transformations, a particular solution of the flow variables and the cooling–heating function for an infinitely strong shock is obtained. This paper explores an application of the singular surface theory in the evolution of an acceleration wave front propagating through an unperturbed medium. We discuss the formation of an acceleration, considering the cases of compression and expansion waves. The influence of the cooling–heating function on a shock formation is explained. The results of a collision between a strong shock and an acceleration wave are discussed using the Lax evolutionary conditions. doi:10.1017/S1446181121000328

INTERACTION OF A SINGULAR SURFACE WITH A STRONG SHOCK IN THE INTERSTELLAR GAS CLOUDS

We investigate the interaction between a singular surface and a strong shock in the self-gravitating interstellar gas clouds with the assumption of spherical symmetry. Using the method of the Lie group of transformations, a particular solution of the flow variables and the cooling–heating function for an infinitely strong shock is obtained. This paper explores an application of the singular surface theory in the evolution of an acceleration wave front propagating through an unperturbed medium. We discuss the formation of an acceleration, considering the cases of compression and expansion waves. The influence of the cooling–heating function on a shock formation is explained. The results of a collision between a strong shock and an acceleration wave are discussed using the Lax evolutionary conditions.

The Complete Performance Map of Gas Wave Ejector and Analysis on the Variation Laws and Limitation of Performance

The gas wave ejector (GWE) is an efficient gas wave equipment using pressure waves to realize energy exchange. In this paper, a theoretical analysis of the limitation of application range and the factors affecting the performance of GWE was carried out by numerical simulation. And a complete experimental system including an adjustable GWE was employed to obtain the specific performance values in various working conditions. Such theoretical analysis showed that the device became inapplicable with a relatively high driving pressure ratio, resulting from the generation of supersonic flow at the outlet end of the passages. A relatively high supercharging ratio also limited the equipment application because of the weakening of the reflected expansion waves and the enhancement of the reversed compression wave. Furthermore, the mixing, vortex, viscosity, and other flow losses could also affect the equipment performance. Then, a complete performance map indicating the specific performance values in the application range was obtained by plenty of experiments. The performance map proved that GWE had excellent efficiency and broad applicability especially as the driving pressure ratio was lower than 2.6. The results are significant for practical application and performance improvement of GWE.

Uncertainty Analysis of Supersonic Biplane's Aerodynamic Characteristics

Utilizing the interference of shock and expansion waves, supersonic biplane can reduce the wave drag remarkably. However, the supersonic biplane is only designed at special conditions, so that it has poor performance at off-design conditions. To analyze supersonic biplane's aerodynamic characteristics at off-design conditions, the non-instructive probabilistic collocation method has been employed to achieve uncertainty quantification. Besides, Sobol global sensitivity is adopted to accurately evaluate the influence of the input uncertainty parameters. The uncertainty parameters are Mach number and the angle of attack which both satisfy special normal distributions. Aerodynamic coefficients and pressure distribution from the biplane's surface as well as flow filed are studied. The results of uncertainty quantification show that the main reason for aerodynamic characteristics fluctuations is the pressure pulsation from the maximum thickness of the lower airfoil's upper surface. The results of global sensitivity show that Mach number is the most important factor for the variation of aerodynamic performance.

Interaction of linear modulated waves and unsteady dispersive hydrodynamic states with application to shallow water waves

A new type of wave–mean flow interaction is identified and studied in which a small-amplitude, linear, dispersive modulated wave propagates through an evolving, nonlinear, large-scale fluid state such as an expansion (rarefaction) wave or a dispersive shock wave (undular bore). The Korteweg–de Vries (KdV) equation is considered as a prototypical example of dynamic wavepacket–mean flow interaction. Modulation equations are derived for the coupling between linear wave modulations and a nonlinear mean flow. These equations admit a particular class of solutions that describe the transmission or trapping of a linear wavepacket by an unsteady hydrodynamic state. Two adiabatic invariants of motion are identified that determine the transmission, trapping conditions and show that wavepackets incident upon smooth expansion waves or compressive, rapidly oscillating dispersive shock waves exhibit so-called hydrodynamic reciprocity recently described in Maiden et al. (Phys. Rev. Lett., vol. 120, 2018, 144101) in the context of hydrodynamic soliton tunnelling. The modulation theory results are in excellent agreement with direct numerical simulations of full KdV dynamics. The integrability of the KdV equation is not invoked so these results can be extended to other nonlinear dispersive fluid mechanic models.

The speed, reflection and intensity of waves propagating in flexible tubes with aneurysm and stenosis: Experimental investigation

A localized stenosis or aneurysm is a discontinuity that presents the pulse wave produced by the contracting heart with a reflection site. However, neither wave speed ( c) in these discontinuities nor the size of reflection in relation to the size of the discontinuity has been adequately studied before. Therefore, the aim of this work is to study the propagation of waves traversing flexible tubes in the presence of aneurysm and stenosis in vitro. We manufactured different sized four stenosis and four aneurysm silicone sections, connected one at a time to a flexible ‘mother’ tube, at the inlet of which a single semi-sinusoidal wave was generated. Pressure and velocity were measured simultaneously 25 cm downstream the inlet of the respective mother tube. The wave speed was measured using the PU-loop method in the mother tube and within each discontinuity using the foot-to-foot technique. The stenosis and aneurysm dimensions and c were used to determine the reflection coefficient ( R) at each discontinuity. Wave intensity analysis was used to determine the size of the reflected wave. The reflection coefficient increased with the increase and decrease in the size of the aneurysm and stenosis, respectively. c increased and decreased within stenosis and aneurysms, respectively, compared to that of the mother tube. Stenosis and aneurysm induced backward compression and expansion waves, respectively; the size of which was related to the size of the reflection coefficient at each discontinuity, increases with smaller stenosis and larger aneurysms. Wave speed is inversely proportional to the size of the discontinuity, exponentially increases with smaller stenosis and aneurysms and always higher in the stenosis. The size of the compression and expansion reflected wave depends on the size of R, increases with larger aneurysms and smaller stenosis.