Numerical study of dynamic phase transitions in shock tube

Shock tube problem of a van der Waals fluid with a relaxation model was investigated.In the limit of relaxation parameter tending towards zero,this model yields a specific Riemann solver.Relaxing and relaxed schemes were derived.For an inci- dent shock in a fixed tube,numerical simulations show convergence toward the Riemann solution in one space dimension.Impact of parameters was studied theoretically and nu- merically.For certain initial shock profiles,nonclassical reflecting wave was observed.In two space dimensions,the effect of curved wave fronts was studied,and some interesting wave patterns were exposed.     

Instability theory of shock wave in a shock tube

The instability theory of shock wave in a shock tube including the effects of tube wall and contact surface is studied. The experimental data of unstable shock wave coincide with one of instability criteria derived in the present paper.     

Decay of shock waves in a dusty-gas shock tube

A numerical study is performed for the unsteady nonequilibrium flow of a gas-particle mixture in a shock tube, where a semi-empirical formula for a single particle is assumed to calculate the drag and heat transfer rate of the particle cloud. To simulate actual flows of the mixture in which the size of the particles is distributed over a finite range, the motion of the particles is analyzed by dividing them into several groups according to their different diameters. It is shown that the particles of diameter larger than the average value cause a significant delay in the relaxation of the gas-particle flow. Good agreement is obtained between the numerical and the experimental results of the decrease in the shock propagation velocity, except for strong shock waves transmitted into dusty gas with a high loading ratio.     

Interaction of a shock with a sphere suspended in a vertical shock tube

Shock wave interaction with a sphere is one of the benchmark tests in shock dynamics. However, unlike wind tunnel experiments, unsteady drag force on a sphere installed in a shock tube have not been measured quantitatively. This paper presents an experimental and numerical study of the unsteady drag force acting on a 80 mm diameter sphere which was vertically suspended in a 300 mm x 300 mm vertical shock tube and loaded with a planar shock wave of M _s = 1.22 in air. The drag force history on the sphere was measured by an accelerometer installed in it. Accelerometer output signals were subjected to deconvolution data processing, producing a drag history comparable to that obtained by solving numerically the Navier-Stokes equations. A good agreement was obtained between the measured and computed drag force histories. In order to interpret the interaction of shock wave over the sphere, high speed video recordings and double exposure holographic interferometric observations were also conducted. It was found that the maximum drag force appeared not at the time instant when the shock arrived at the equator of the sphere, but at some earlier time before the transition of the reflected shock wave from regular to Mach reflection took place. A negative value of the drag force was observed, even though for a very short duration of time, when the Mach stem of the transmitted shock wave relfected and focused at the rear stagnation point of the sphere.Received: 31 March 2003, Accepted: 7 July 2003, Published online: 2 September 2003     

A chemical shock tube driven by detonation

A chemical shock tube driven by a detonation driver is described in the present paper. This shock tube can produce a single controlled high-temperature pulse for studies of gas-phase reaction kinetics, but the difficulty associated with the timing for the rupture of diaphragms in the conventional chemical shock tube is overcome, because the detonation wave in the driver section can be predicted correctly and shows a good repeatability. In addition, this shock tube is capable of providing higher temperature conditions for the test gas than the conventional high-pressure shock tube, owing to the inherently high-driving capability of the detonation driver. The feasibility of this shock tube is examined by numerical simulations and preliminary experiments.     

A study on characteristics of shock train inside a shock tube

Shock tubes are devices which are used in the investigation of high speed and high temperature flow of compressible gas. Inside a shock tube, the interaction between the reflected shock wave and boundary layer leads to a complex flow phenomenon. Initially a normal shock wave is formed in the shock tube which migrates toward the closed end of the tube and that in turn leads to the reflection of shock. Due to the boundary layer interaction with the reflected shock, the bifurcation of shock wave takes place. The bifurcated shock wave then approaches the contact surface and shock train is generated. Till date only a few studies have been conducted to investigate this shock train phenomenon inside the shock tube. For the present study a computational fluid dynamics(CFD) analysis has been performed on a two dimensional axi-symmetric model of a shock tube using unsteady, compressible Navier–Stokes equations. In order to investigate the detailed characteristics of shock train, parametric studies have been performed by varying different parameters such as the shock tube length, diameter, pressure ratio used inside the shock tube.     

Pressure-sensitive paint measurements in a shock tube

 Surface pressures were measured in the short-duration, transient flow environment of a small-scale, low pressure-ratio shock tube using thin-film pressure-sensitive paint (PSP). Issues regarding coating formulation, measurement uncertainty, optical system design, and temperature and illumination compensation are discussed. The pressure measurements were acquired during steady flow conditions following the passage of normal shocks and expansion regions along a flat sidewall and a wedge sidewall. The PSP characteristic response time was 3 to 6 ms. Overall pressure uncertainty for the shock tube measurements ranged up to 5% over one atmosphere and compared well with theoretical estimates of uncertainty. Received: 20 April 1998 / Accepted: 9 September 1998     

The interaction between shock waves and foam in a shock tube

An experimental study and a numerical simulation were conducted to investigate the mechanical and thermodynamic processes involved in the interaction between shock waves and low density foam. The experiment was done in a stainless shock tube (80 mm in inner diameter, 10 mm in wall thickness and 5 360 mm in length). The velocities of the incident and reflected compression waves in the foam were measured by using piezo-ceramic pressure sensors. The end-wall peak pressure behind the reflected wave in the foam was measured by using a crystal piezoelectric sensor. It is suggested that the high end-wall pressure may be caused by a rapid contact between the foam and the end-wall surface. Both open-cell and closed-cell foams with different length and density were tested. Through comparing the numerical and experimental end-wall pressure, the permeability coefficients α and β are quantitatively determined.     

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     

Reflection of a blast-profile shock wave from the end wall of a shock tube

The flow in the shock tube, which models the flow conditions behind a blast wave, is calculated for an inviscid non-heat-conducting perfect gas with a constant value of the specific heat ratio. The results are compared with the authors' experimental data.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 141–148, May–June, 1992.The authors are grateful to V. A. Levin for assisting with the work and useful discussions.     

Precursor vacuum-ultraviolet radiation ahead of strong shock waves in a shock tube

The profile and excitation mechanism of vacuum-ultraviolet radiation emitted from shock wave is investigated in a shock tube. For shock wave in argon, the rdiation is due to resonant transition excited by argon-argon collision in the shock front with excitation cross section coefficientS ^*=1.0×10⁻¹⁷ cm²·ev⁻¹ and activation energyE ^*=11.4 ev. For shock wave in air the radition is emitted from a very thin shock layer in which the mechanism ofX ¹∑→b ¹∑ of N₂ is excited with excitation cross sectionQ=2×10⁻¹⁶cm² and activation energyE ^*=12.1 ev. Institute of Mechanics, Academia Sinica     

In vivo transdermal delivery using a shock tube

A shock tube was utilized for transdermal delivery in fuzzy rats. Rhodamine-B dextran, 10 kDa molecular weight, was used as the probe molecule. Shock waves were generated by a two-stage shock tube. A single shock wave was applied onto the skin to permeabilize the stratum corneum. Subsequently, the dextran solution diffused through the stratum corneum into the epidermis. Fluorescence microscopy of biopsies showed that the dextran was delivered to a depth of m into the skin. Thus, the shock tube could become an inexpensive device for transdermal drug delivery. Received 19 February 2000 / Accepted 29 June 2000     

Distortion of the shock front in a shock tube with a divergent conical transition section

The profile of the leading shock front in a gas has been experimentally investigated in shock tubes of variable cross section. It is shown that the presence of a conical transition section between the high-pressure and low-pressure chambers leads to the retention of inhomogeneities on the surface of the wave front (slopes, twists, and bends) over a length of 20–30 diameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 141–147, July–August, 1991.     

Acoustic wave propagation in a flowing liquid-vapour mixture

The two-fluid equations describing transient nonequilibrium liquid-vapour flow have been used to derive a general dispersion relation for acoustic waves. The analysis is valid in principle for both dispersed and separated flow regimes. In contrast to previous work, the predicted sound speeds and attenuations depend only on measurable properties of the flow. The model can apply over a wide range of angular frequencies (up to 1–10⁶ Hz for steam and water), under conditions where the scattering of waves by individual bubbles and droplets is unimportant. Predictions are made for sound speeds and attenuations in both bubbly and annular flow at low Mach numbers. Agreement of the theory with available data is shown to be reasonable.