Existence of traveling waves in compressible Euler equations with viscosity and capillarity

Given any Lax shock of the compressible Euler dynamics equations, we show that there exists the corresponding traveling wave of the system when viscosity and capillarity are suitably added. For a traveling wave corresponding to a given Lax shock, the governing viscous–capillary system is reduced to a system of two differential equations of first-order, which admits an asymptotically stable equilibrium point and a saddle point. We then develop the method of estimating attraction domain of the asymptotically stable equilibrium point for the compressible Euler equations and show that the saddle point in fact lies on the boundary of this set. Then, we establish a saddle-to-stable connection by pointing out that there is a stable trajectory leaving the saddle point and entering the attraction domain of the asymptotically stable equilibrium point. This gives us a traveling wave of the viscous–capillary compressible Euler equations.     

Analysis of shock wave reflection from fixed and moving boundaries using a stabilized particle method

In the present paper, the efficiency of an enhanced formulation of the stabilized corrective smoothed particle method （CSPM） for simulation of shock wave propagation and reflection from fixed and moving solid boundaries in compressible fluids is investigated. The Lagrangian nature and its accuracy for imposing the boundary conditions are the two main reasons for adoption of CSPM. The governing equations are further modified for imposition of moving solid boundary conditions. In addition to the traditional artificial viscosity, which can remove numerically induced abnormal jumps in the field values, a velocity field smoothing technique is introduced as an efficient method for stabilizing the solution. The method has been implemented for one- and two-dimensional shock wave propagation and reflection from fixed and moving boundaries and the results have been compared with other available solutions. The method has also been adopted for simulation of shock wave propagation and reflection from infinite and finite solid boundaries.     

On the pressure of cavitation bubbles

Shock wave emission upon the collapse of a cavitation bubble attached to a rigid wall is investigated using high-speed photography with 200 million frames/s and 5 ns exposure time. At a distance of 68 μm from the bubble wall, the shock pressure is 1.3 ± 0.3 GPa. The shock pressure decays proportionally to r^−1.5 with increasing distance from the bubble. An estimation of the peak pressure at the bubble wall reveals a pressure of about 8 GPa. A major part of the shock wave energy is dissipated within the first 100 μm from the bubble wall.     

Parametric investigation of particle acceleration in high enthalpy conical nozzle flows for coating applications

A modified cold gas-dynamic spray technique is under development by using shock tunnel technology, which can enhance the coating quality by increasing the solid particle velocity up to 1,500 m/s. The particle diameter typically amounts to 10 μm. A theoretical model based on gas-particle flows is employed to describe the behaviour of the flow and the solid particles. This quasi-1D model is capable to consider non-equilibrium effects of the gas phase due to high reservoir temperatures, and the influence of wall friction and heat transfer averaged over the nozzle cross section. This model is used for the design and optimization of the nozzle geometry by a parametric study, which results in a conical nozzle with a half opening angle of 2.8° and a length of 325 mm. Particles for coating are injected at about 55 mm downstream of the throat. A shock tunnel facility has been set up at the Shock Wave Laboratory for performing an experimental study of this new technique. The theoretical performance of this setup is evaluated by the KASIMIR simulation software and the quasi-1D method described in this paper. The high reservoir conditions required to achieve particle velocities of 1,500 m/s can be realized by using either a very high driver pressure of about 600 bar for air as driver gas or a relatively low driver pressure of about 200 bar for helium as driver gas.      

Numerical investigation of ethylene flame bubble instability induced by shock waves

In this paper, the ethylene/oxygen/nitrogen premixed flame instabilities induced by incident and reflected shock wave were investigated numerically. The effects of grid resolutions and chemical mechanisms on the flame bubble deformation process are evaluated. In the computational frame, the 2D multi-component Navier–Stokes equations with second-order flux-difference splitting scheme were used; the stiff chemical source term was integrated using an implicit ordinary differential equations (ODEs) solver. The two ethylene/oxygen/nitrogen chemical mechanisms, namely 3-step reduced mechanism and 35-step elementary skeletal mechanism, were used to examine the reliability of chemistry. On the other hand, the different grid sizes, Δx × Δy = 0.25 × 0.5mm and Δx × Δy = 0.15 × 0.2mm, were implemented to examine the accuracy of the grid resolution. The computational results were qualitatively validated with experimental results of Thomas et al. (Combust Theory Model 5:573–594, 2001). Two chemical mechanisms and two grid resolutions used in present study can qualitatively reproduce the ethylene spherical flame instability process generated by an incident shock wave of Mach number 1.7. For the case of interaction between the flame and reflected shock waves, the 35-steps mechanism qualitatively predicts the physical process and is somewhat independent on the grid resolutions, while the 3-steps mechanism fails to reproduce the instability of ethylene flame for the two selected grid resolutions. It is concluded that the detailed chemical mechanism, which includes the chain elementary reactions of fuel combustion, describes the flame instability induced by shock wave, in spite of the fact that the flame thickness (reaction zone) is represented by 1–2 grids only.      

Head on collision of a planar shock wave with a dusty gas layer

The head-on collision of a planar shock wave with a dust-air suspension is studied numerically. In this study the suspension is placed inside a conduit adjacent to its rigid end-wall. It is shown that as a result of this collision two different types of transmitted shock waves are possible, depending on the strength of the incident shock wave and the dust loading ratio in the suspension. One possibility is a partially dispersed shock wave, the other is a compression wave. The flow fields resulting in these two options are investigated. It is shown that in both cases, at late times after the head-on reflection of the transmitted shock wave from the conduit end-wall a negative flow (away from the end-wall) is evident. The observed flow behavior may suggest a kind of dust particle lifting mechanism that could shed new light on the complex phenomenon of dust entrainment behind sliding shock waves.      

A numerical study of oblique shock wave reflections over wedges in an ideal quantum gas

The various oblique shock wave reflection patterns generated by a moving incident shock on a planar wedge using an ideal quantum gas model are numerically studied using a novel high resolution quantum kinetic flux splitting scheme. With different incident shock Mach numbers and wedge angles as flow parameters, four different types of reflection patterns, namely, the regular reflection, simple Mach reflection, complex Mach reflection and the double Mach reflection as in the classical gas can be classified and observed. Both Bose–Einstein and Fermi–Dirac gases are considered.      

Nonideal effects behind reflected shock waves in a high-pressure shock tube

Abstract. Shock tubes often experience temperature and pressure nonuniformities behind the reflected shock wave that cannot be neglected in chemical kinetics experiments. Because of increased viscous effects, smaller tube diameters, and nonideal shock formation, the reflected-shock nonidealities tend to be greater in higher-pressure shock tubes. Since the increase in test temperature () is the most significant parameter for chemical kinetics, experiments were performed to characterize in the Stanford High Pressure Shock Tube using infrared emission from a known amount of CO in argon. From the measured change in vibrationally equilibrated CO emission with time, the corresponding ddt (or for a known time interval) of the mixture was inferred assuming an isentropic relationship between post-shock temperature and pressure changes. For a range of representative conditions in argon (24–530 atm, 1275–1900 K), the test temperature 2 cm from the endwall increased 3–8 K after 100 s and 15–40 K after 500 s, depending on the initial conditions. Separate pressure measurements using a shielded piezoelectric transducer confirmed the isentropic assumption. An analytical model of the reflected-shock gas dynamics was also developed, and the calculated 's agree well with those obtained from experiment. The analytical model was used to estimate the effects of temperature and pressure nonuniformities on typical chemical kinetics measurements. When the kinetics are fast (s), the temperature increase is typically negligible, although some correction is suggested for kinetics experiments lasting longer than 500 s. The temperature increase, however, has a negligible impact on the measured laser absorption profiles of OH (306 nm) and CH (216 nm), validating the use of a constant absorption coefficient. Infrared emission experiments are more sensitive to temperature and density changes, so nonuniformities should be taken into account when interpreting ir-emission data. Received 25 April 2000 / Accepted 8 September 2000     

多极板电流变阀应用于避震器之研究

以流动模式（flow mode)多极板之电流变阀（electrorheological valve)进行避震器阻尼力特性的研究。由于电极板的大小直接影响到流体流动的剪力及避雷器的阻尼力,因此使用多极板型式来探讨避震器的特性。设计有1－5个流道之并联及1－3个流道之串联多极板电流变阀的电流变避震器,并使用自制的电流变液进行实验。由研究结果显示,流动式并联极板之电流变避震器,一个流道之阻尼力最大,流道极板增加则阻尼力反而下降,而流动式串联多极板之电流变避震器之阻尼力则随极板数递增,故需要高阻尼力之避震器较适合使用串联多极板型式。