A computational technique for high enthalpy shock tube and shock tunnel flow simulation

A contact discontinuity tracking method with a specially designed moving grid is developed to eliminate the interface smearing completely. In order to precisely locate the contact surface, an updated Riemann solver for unsteady one-dimensional inviscid flows is also developed to allow consideration of the specific heat ratio change across the shock wave. These two new computational techniques are illustrated in a high Mach number shock tube flow field computation. Received 30 October 1997 / Accepted 6 December 1997     

Comparison with experiment for TVD calculations of blast waves from a shock tube

Harten's second-order-accurate total-variation-diminishing (TVD) scheme is applied to calculation of flow from the open end of a shock tube. Comparison of numerical results with available experimental data for overpressure at selected points around the shock tube exit shows good agreement. Numerically indicated positions of the moving shock front and Mach stem also compare well with flow shadowgraph data. Where the problem geometry is sufficiently simple and rectangular gridding can be used, Harten's method affords a good choice for blast wave calculations.     

Solution of Riemann problem for dusty gas flow

A direct approach is used to solve the Riemann problem for a quasilinear hyperbolic system of equations governing the one dimensional unsteady planar flow of an isentropic, inviscid compressible fluid in the presence of dust particles. The elementary wave solutions of the Riemann problem, that is, shock waves, rarefaction waves and contact discontinuities are derived and their properties are discussed for a dusty gas. The generalised Riemann invariants are used to find the solution between rarefaction wave and the contact discontinuity and also inside rarefaction fan. Unlike the ordinary gasdynamic case, the solution inside the rarefaction waves in dusty gas cannot be obtained directly and explicitly; indeed, it requires an extra iteration procedure. Although the case of dusty gas is more complex than the ordinary gas dynamics case, all the parallel results for compressive waves remain identical. We also compare/contrast the nature of the solution in an ordinary gasdynamics and the dusty gas flow case.     

Performance of a shock tube facility for impact response of structures

This paper presents a numerical approach to compute the performance of a double diaphragm shock tube facility for structural response investigations. To assess the influence of different sources of dissipation, including partial diaphragm opening and shock tube vibration, numerical simulations are carried out using several different finite element models of increasing complexity to compute shock tube performance. The numerical model accounting for tearing and partial opening of the diaphragms is the one that best reproduces the results of the experiment, thus indicating that the diaphragm non-ideal opening process is the most relevant cause of losses. Both the numerical and the experimental results agree in predicting shock tube efficiency in terms of intensity of the reflected shock of about 50–60% with respect to ideal, one-dimensional conditions.     

Reflection of shock wave from a compression corner in a particle-laden gas region

We investigated in this paper the progression of a shock-wave reflected from a compression corner in a particle-laden gas medium using a TVD class numerical technique and a MacCormack scheme. For a gas-only flow, the numerical results agreed well with the existing experimental data, suggesting that the gas phase is correctively solved. The effect of particle size and mass fraction ratio is investigated for a dilute gas-particle flow. It has been shown that the shock-wave diffraction and the flow configuration after the shock can become remarkably different from the gas-only flow depending on the particle parameters. Relaxation phenomenon due to the momentum drag and the heat exchange between the gas and the particle phases is explained.Graduate Student of Korea Advanced Institute of Science and TechnologyThis article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

A new, friction controlled, piston actuated diaphragmless shock tube driver

A new friction operated single piston shock tube driver design that is capable of generating shock waves of Mach number 1.1 to 2 is presented. By using different test gases and evacuating the driven section Mach 5 shock waves can easily be produced. The driver is efficient with shock wave Mach numbers within 9% of that predicted by ideal shock tube theory and the non-dimensional formation length lies between 20 and 40. The brake pad mechanism, that restrains the piston until tests commence, removes the necessity of venting an auxiliary chamber rapidly, thus speeding up the displacement of the piston. It is believed that the design is a practical, simple and cost effective way of generating reproducible shock tube tests with very short test turn around times, while removing the necessity of using a diaphragm and exposing the test gases to the atmosphere. Results for three pistons with masses of 4.4, 0.71 and 0.38 kg (brass, PVC and hollow aluminium respectively) with driver gauge pressures of between 2 and 50 bar (Mach 1.2 to 2) are given. Received 27 February 1998 / Accepted 8 July 1998     

Investigation of high-speed combustible gas ignited by a hot gas jetproduced in the shock tube

The high-speed combustible gas ignited by a hot gas jet, which is induced by shock focusing, was experimentally investigated. By use of the separation mode of shock tube, the test section of a single shock tube is split into two parts, which provide the high-speed flow of combustible gas and pilot flame of hot gas jet, respectively. In the interface of two parts of test sections the flame of jet was formed and spread to the high-speed combustible gas. Two kinds of the ignitions, 3-D “line-flame ignition” and 2-D “plane-flame ignition”, were investigated. In the condition of 3-D “line-flame ignition” of combustion, thicker hot gas jet than pure air jet, was observed in schlieren photos. In the condition of 2-D “plane-flame ignition” of combustion, the delay time of ignition and the angle of flame front in schlieren photos were measured, from which the velocity of flame propagation in the high-speed combustible gas is estimated in the range of 30–90m/s and the delay time of ignition is estimated in the range of 0.12–0.29ms. PACS 47.40.Nm; 82.40.FpPart of this paper was presented at the 5th International Workshop on Shock/Vortex Interaction, Kaohsiung, October 27–31, 2003.     

Advances in detonation driving techniques for a shock tube/tunnel

Early works on the detonation driven shock tube are reviewed briefly. High initial pressure detonable mixture can be used in backward-detonation driver when the buffer tube is attached to the end of the driver for eliminating the excessive reflected peak pressure. Experimental data showed that an improvement on attenuation of the incident shock wave generated by the forward driver can be obtained, provided the diameter of the driver is larger than that of the driven section and an abrupt reduction of cross-section area is placed just beyond the diaphragm. Also, it is clearly verified by a numerical analysis. An additional backward-detonation driver is proposed to attach to the primary detonation driver and on condition that the ratios of initial pressure in the additional driver to that in the primary driver exceed the threshold value, the Taylor wave behind detonation wave in the primary detonation driver can be eliminated completely.     

Detonation driver for enhancing shock tube performance

The development of a shock-induced detonation driver for enhancing the performance of a shock tube is described. The detonation wave is induced by the expansion of helium or air. Various gaseous fuel-oxidizer combinations are examined. This method produces a detonation wave which propagates downstream that transitions into a shock wave in the driven section. High-enthalpy flows with a maximum total temperature of 4200 K and a maximum total pressure of 34 atm in the driven tube are achieved. The problems of achieving the so-called perfectly-driven mode as well as those of inadequate fuel-oxidizer mixing are discussed.Received: 26 April 2002, Accepted: 23 December 2002, Published online: 28 April 2003     

Interaction of a shock wave with a loose dusty bulk layer

The interaction of a planar shock wave with a loose dusty bulk layer has been investigated both experimentally and numerically. Experiments were conducted in a shock tube. The incident shock wave velocity and particle diameters were measured with the use of pressure transducers and a Malvern particle sizer, respectively. The flow fields, induced by shock waves, of both gas and granular phase were visualized by means of shadowgraphs and pulsed X-ray radiography with trace particles added. In addition, a two-phase model for granular flow presented by Gidaspow is introduced and is extended to describe such a complex phenomenon. Based on the kinetic theory, such a two-phase model has the advantage of being able to clarify many physical concepts, like particulate viscosity, granular conductivity and solid pressure, and deduce the correlative constitutive equations of the solid phase. The AUSM scheme was employed for the numerical calculation. The flow field behind the shock wave was displayed numerically and agrees well with our corresponding experimental results.      

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     

Evaluation of glued-diaphragm fibre optic pressure sensors in a shock tube

Glued-diaphragm fibre optic pressure sensors that utilize standard telecommunications components which are based on Fabry–Perot interferometry are appealing in a number of respects. Principally, they have high spatial and temporal resolution and are low in cost. These features potentially make them well suited to operation in extreme environments produced in short-duration high-enthalpy wind tunnel facilities where spatial and temporal resolution are essential, but attrition rates for sensors are typically very high. The sensors we consider utilize a zirconia ferrule substrate and a thin copper foil which are bonded together using an adhesive. The sensors show a fast response and can measure fluctuations with a frequency up to 250 kHz. The sensors also have a high spatial resolution on the order of 0.1 mm. However, with the interrogation and calibration processes adopted in this work, apparent errors of up to 30% of the maximum pressure have been observed. Such errors are primarily caused by mechanical hysteresis and adhesive viscoelasticity. If a dynamic calibration is adopted, the maximum measurement error can be limited to about 10% of the maximum pressure. However, a better approach is to eliminate the adhesive from the construction process or design the diaphragm and substrate in a way that does not require the adhesive to carry a significant fraction of the mechanical loading.      

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.      

Computational study of reacting flow establishment in expansion tube facilities

We study the temporal evolution of the combustion flowfield established by the interaction of ram accelerator-type projectiles with an explosive gas mixture accelerated to hypersonic speeds in an expansion tube. The Navier-Stokes equations for a chemically reacting gas mixture are solved in a fully coupled manner using an implicit, time accurate algorithm. The solution procedure is based on a spatially second order, total variation diminishing scheme and a temporally second order, variable-step, backward differentiation formula method. The hydrogen-oxygen-argon chemistry is modeled with a 9-species, 19-step mechanism. The accuracy of the solution method is first demonstrated by several benchmark calculations. Numerical simulations of expansion tube flowfields are then presented for two different geometries: an axisymmetric projectile and a ram accelerator configuration. The development of the shock-induced combustion process is followed. The temporal variations of the calculated thrust and drag forces on the ram accelerator projectile are also presented. In the axisymmetric projectile case, which was designed to ensure combustion only in the boundary layer, the radial extent of the flame front during the initial transient phase was surprisingly large. In the ram accelerator configuration the flame propagated upstream along both the projectile and tube wall boundary layers, resulting in unstart. Received 25 September 1996 / Accepted 15 January 1997     

Weighted average flux method and flux limiters for the numerical simulation of shock waves in rigid porous media

The one‐dimensional flow field generated by the passage of a shock wave in a rigid, thermoelastic porous foam has been simulated using a two‐phase mathematical model. The work presented here makes use of the weighted average flux method to solve the system of six equations that govern the problem. Spurious oscillations are eliminated through the application of total variation diminishing limiting methods. Four different limiters were tested: van Leer, SuperA, MinA and van Albada. Numerical tests were carried out to verify the performance of each flux limiter in terms of accuracy. The results were compared to analytical and previously obtained data to assess the performance of the mathematical model. Excellent agreement was obtained. Copyright © 2002 John Wiley & Sons, Ltd.     

One-dimensional model for microscale shock tube flow

A one-dimensional model for the numerical simulation of transport effects in small-scale, i.e., low Reynolds number, shock tubes is presented. The conservation equations have been integrated in the lateral directions and three-dimensional effects have been introduced as carefully controlled sources of mass, momentum and energy, into the axial conservation equations. The unsteady flow of gas behind the shock wave is reduced to a quasi-steady flow by choosing a coordinate system attached to the shock. The boundary layer problem is thereby reduced to a laminar solution, similar to the Blasius solution, with the exception that the wall velocity can be nonzero. The resulting one-dimensional equations are then solved numerically using a two-step Lax-Wendroff/ MacCormack scheme with flux correction transport. For validation purposes, comparisons are performed against previously published shock structure and low Reynolds number shock tube experiments; good agreement is observed. The model has been used to predict the performance of a 10μm shock tube and the result of this simulation shows the possibility of shock wave disappearance at lower pressure ratios for a micro-scale shock tube.      

Numerical simulation of flow in Hartmann resonance tube and flow in ultrasonic gas atomizer

The gas flow in the Hartmann resonance tube is numerically investigated by the finite volume method based on the Roe solver.The oscillation of the flow is studied with the presence of a needle actuator set along the nozzle axis.Numerical results agree well with the theoretical and experimental results available.Numerical results indicate that the resonance mode of the resonance tube will switch by means of removing or adding the actuator.The gas flow in the ultrasonic gas atomization (USGA) nozzle is also studied by the same numerical methods.Oscillation caused by the Hartmann resonance tube structure,coupled with a secondary resonator,in the USGA nozzle is investigated.Effects of the variation of parameters on the oscillation are studied.The mechanism of the transition of subsonic flow to supersonic flow in the USGA nozzle is also discussed based on numerical results.     

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     

Simulation of the starting flow in a wedge–like nozzle

The starting process of the flow in a wedge-like expansion nozzle of a shock tunnel is simulated by an unsplit 2-D GRP scheme on an unstructured grid. The scheme is briefly outlined and results are presented and discussed in comparison to the experimental (shadowgraph) findings obtained by Amann. The simulated pattern of reflected and transmitted shock waves in the nozzle inlet region and inside the nozzle is found to agree well with the experimental data. Received 5 April 1996 / Accepted 16 June 1997     

A driver gas detection device for shock tunnels

A device has been produced which can detect the contamination of the test gas by the driver gas in a reflected shock tunnel. This device monitors the static pressure in a converging duct. The duct is designed to choke at a predetermined contamination level due to the change in the specific heat ratio produced by the contaminants. Experimental results are given for a freestream enthalpy of nominally 6 MJ/kg.