Showing papers on "Shock tube published in 1996"

Shock waves in a liquid containing small gas bubbles

Abstract: Numerical and experimental studies of the transient shock wave phenomena in a liquid containing non‐condensable gas bubbles are presented. In the numerical analysis, individual bubbles are tracked to estimate the effect of volume oscillations on the wave phenomena. Thermal processes inside each bubble, which have significant influence on the volume oscillation, are calculated directly using full equations for mass, momentum and energy conservation, and those results are combined with the averaged conservation equations of the bubbly mixture to simulate the propagation of the shock wave. A silicone oil/nitrogen bubble mixture, in which the initial bubble radius is about 0.6 mm and the gas volume fraction is 0.15% – 0.4%, is used in the shock tube experiments. The inner diameter of the shock tube is chosen to be 18 mm and 52 mm in order to investigate the multidimensional effects on the wave phenomena. In a fairly uniform bubbly mixture, the experimental results agree well with the numerical ones computed using a uniform spatial distribution of bubbles. On the other hand, in all the other experiments, the bubbles in the shock tubes are not distributed uniformly, being relatively concentrated along the axis of the tube. This non‐uniformity substantially alters the profile of the shock waves. The numerical predictions where such a distribution is taken into account agree well with those experimental data.

Shock tube and modeling study of 1,3‐butadiene pyrolysis

Abstract: 1,3-Butadiene (1,3-C4H6) was heated behind reflected shock waves over the temperature range of 1200–1700 K and the total density range of 1.3 × 10−5 −2.9 × 10−5 mol/cm3. Reaction products were analyzed by gas-chromatography. The concentration change of 1,3-butadiene was followed by UV kinetic absorption spectroscopy at 230 nm and by quadrupole mass spectrometry. The major products were C2H2, C2H4, C4H4, and CH4. The yield of CH4 for a 0.5% 1,3-C4H6 in Ar mixture was more than 10% of the initial 1.3-C4H6 concentration above 1500 K. In order to interpret the formation of CH4 successfully, it was necessary to include the isomerization of 1,3-C4H6 to 1,2-butadiene (1,2-C4H6) and to include subsequent decomposition of the 1,2-C4H6 to C3H3 and CH3. The present data and other shock tube data reported over a wide pressure range were qualitatively modeled with a 89 reaction mechanism, which included the isomerizations of 1,3-C4H6 to 1,2-C4H6 and 2-butyne (2-C4H6). © 1996 John Wiley & Sons, Inc.

Soot formation in a shock tube under elevated pressure conditions

Abstract: High pressure soot formation from methane, ethylene, acetylene, propane and n-heptane was studied at rich burning conditions applying the shock tube technique. Pressure behind reflected shock was varied between 15 and 100 bar. Time resolved measurements of soot particle diameter and number density were carried out using an extinction-scattering technique at 488 nm. It could be shown that soot formation at high pressures is characterized by particle diameters below 30 nm that decrease with pressure. The corresponding high particle number densities in the range of N≈1012 — 10131/cm3 turned out to be considerably higher than at atmospheric conditions. This behavior has to be attributed to reduced coagulation coefficients in the transition regime between free molecular and continuum flow. It was found that an increase in carbon concentration has a strong promoting influence on soot volume fraction. Total pressure, however, does significantly enhance soot yield at pressures up to 30 bar and loses its ...

Experimental Characterization of Combustion Behaviour of New Diesel Fuels for Low Emission Engines

Abstract: Some oxygenated hydrocarbons were tested as pure fuels in two different DI diesel engines, and their emission potential was compared to n-tetradecane combustion. Two colours pyrometry method was used to infer in-cylinder sooting tendency of tested fuels. Pure pyrolysis of the same fuels was also investigated in a conventional shock lube at high temperature (1700–2500 K) and pressure (9–13 bar), using light scattering/extinction methods. All oxygenated compounds tested in the engines exhibited a strong decrease of soot loading compared with tetradecane combustion. The long soot induction times, as measured in shock tube experiments, and the oxygen content of the fuel molecules seem to provide a plausible explanation of soot lacking in oxygenated fuels combustion. Emission measurements at the exhaust of a four cylinder engine fully confirm the trends obtained by two colours pyrometry and shock tube experiments. As a matter of fact, the oxygenated synthetic fuels strongly reduce both gaseous and total partic...

Computational analysis of dense gas shock tube flow

Abstract: Nonclassical phenomena associated with the classical dynamics of real gases in a conventional shock tube are studied. A TVD predictor-corrector (TVD-MacCormack) scheme with reflective endwall boundary conditions is used for the one-dimensional Euler equations to simulate the evolution of the wave field of a van der Waals gas. Depending upon the initial conditions of the gas, wave fields are produced that contain nonclassical phenomena such as expansion shocks, composite waves, splitting shocks, etc. In addition, the interactions of waves reflected from the endwalls produce both classical and nonclassical phenomena. Wave field evolution is depicted using plots of the flow variables at specific times and withx-t diagrams.

Dynamics of explosive degassing of magma: Observations of fragmenting two-phase flows

Abstract: Liquid explosions, generated by rapid degassing of strongly supersaturated liquids, have been investigated in the laboratory with a view to understanding the basic physical processes operating during bubble nucleation and growth and the subsequent behavior of the expanding two-phase flow. Experiments are carried out in a shock tube and are monitored by high-speed photography and pressure transducers. Theoretical CO_2 supersaturations up to 455 times the ambient saturation concentration are generated by a chemical reaction; K_2CO_3 solution is suddenly injected into an excess of HCl solution in such a way as to mix the two solutions rapidly. Immediately after the injection event, a bubble nucleation delay of a few milliseconds is followed by rapid nucleation and explosive expansion of CO_2 bubbles forming a highly heterogeneous foam. Enhanced diffusion due to advection in the flow coupled with continuous mixing of the reactants, and hence on-going bubble nucleation after injection, generates an increasingly accelerating flow until the reactants become depleted at peak accelerations of around 150 g and velocities of about 15 m s^(−1). Stretching of the accelerating two-phase mixture enhances the mixing. Liberation of CO_2 vapor is spatially inhomogeneous leading to ductile fragmentation occurring throughout the flow in regions of greatest gas release as the consequence of the collision and stretching of fluid streams. The violence of the eruptions is controlled by using different concentrations of the HCl and K_2CO_3 solutions, which alters the CO_2 supersaturation and yield and also the efficiency of the mixing process. Peak acceleration is proportional to theoretical supersaturation. Pressure measurements at the base of the shock tube show an initial nucleation delay and a pressure pulse related to the onset of explosive bubble formation. These chemically induced explosions differ from liquid explosions created in other experiments. In explosions caused by sudden depressurization of CO_2-saturated water, the bubbles nucleate uniformly throughout the liquid in a single nucleation event. Subsequent bubble growth causes the two-phase mixture to be accelerated upward at nearly constant accelerations. Explosively boiling liquids, in which heterogeneous nucleation is suppressed, experience an evaporation wave which propagates down into the liquid column at constant average velocity. Fragmentation occurs at the sharply defined leading edge of the wavefront. The chemical flows effectively simulate highly explosive volcanic eruptions as they are comparable in terms of flow densities, velocities, accelerations, and in the large range of scales present. The large accelerations cause strong extensional strain and longitudinal deformation. Comparable deformation rates in volcanic systems could be sufficient to approach conditions for brittle fragmentation. Tube pumice is a major component of plinian deposits and ignimbrites and preserves evidence of accelerating flow conditions.

Experimental investigation of Richtmyer–Meshkov instability in shock tube

Abstract: An experimental investigation of the Richtmyer–Meshkov instability is carried out in a shock tube. The purpose of this study is to obtain information on the growth in the thickness of the turbulent mixing zone, which is induced by the impulsive acceleration of the interface between two gases of different densities. The turbulent phase of the evolution of this instability is of interest here. The thickness of the turbulent mixing zone is inferred from two different diagnostic techniques: measurements of infrared emission of CO2 and black‐and‐white or color schlieren photographs. Following an assessment of the diagnostic techniques, discussions of the main experimental difficulties as the presence of membrane fragments and the disturbances induced by the wall boundary layers, are given. Comparisons of the thickness and the thickness growth rate of the turbulent mixing zones obtained in the present experiments, with both experimental and theoretical results, are made. A tentative picture of the evolution in ...

Shock initiation of crystalline boron in oxygen and fluorine compounds

Abstract: : The ignition delay and combustion of amorphous and crystalline boron particles is investigated at elevated temperatures and pressures for wet, dry, and fluorine-containing atmospheres. Particles ranging from submicron to 32 microns in diameter are ignited in the ambient conditions produced by a reflected shock wave in a shock tube. The ignition delay and combustion times are examined as a function of temperature for pressures of 8.5, 17, and 34 atm and for oxidizer mixtures of 100% oxygen, 30% water vapor, 1-3% sulfur hexafluoride, and 6-12% hydrogen fluoride. Results indicate that pressure in the range studied does not affect the ignition delay or burn time. The additives, water vapor and sulfur hexafluoride, reduce the ignition delay time for amorphous and sub-micron crystalline boron when compared to oxygen. For 20 microns particles, H2O and SF6 reduce the ignition temperature limit from 2500 deg K in pure oxygen to 2200 deg K and 1900 deg K, respectively. Burn time is unaffected by the additives. Hydrogen fluoride did not show any change in ignition delay or burn time compared to pure oxygen. At the range of temperatures tested, very little (less than 2%) of HF is dissociated into H and F atoms. The report also presents reviews of previous chemical and physical models that have attempted to explain why boron powder is relatively difficult to ignite. Ignition of metal powder, Shock tube initiation.

X‐ray measurements of growth rates at a gas interface accelerated by shock waves

Abstract: A new experimental technique to measure the density of a high atomic number gas at a shock-accelerated interface has been developed and demonstrated. It is based on the absorption of x rays by the high atomic number gas, and it was implemented in a vertical square shock tube. The object of the study was the turbulent entrainment and mixing of shock-accelerated air/xenon interfaces prepared by retracting a metal plate, initially separating the two gases, prior to the release of the shock wave. Interfaces of two types, quasi-sinusoidal and nominally flat, were examined. The amplitude of large wavelength (25–100 mm) perturbations on the interface, and the thickness of the interface were measured. An integral definition for the interface mean line was adopted, making it possible to study and time evolution of the individual Fourier modes of the perturbations. A new integral definition for the interface thickness was proposed, making it feasible to study for the first time the time evolution of the thickness of quasi-sinusoidal interfaces. Images of interfaces after interacting with a series of weak waves reverberating between the interface and the shock tube end wall were obtained. The perturbations are studied at the late stages of their evolution, when their amplitude is no longer small compared to their wavelength. Consequently, the measured growth rates of the modal amplitudes are smaller than those predicted by the impulsive model based on the small amplitude approximation. In the case of nominally flat interfaces, the thickness is observed to grow linearly at rates comparable to values previously reported.

Hybrid shock tube/LEDC system for initiating explosives

Abstract: In a non-electric system for initiating explosives, a shock tube is initiated by the detonation of a low-energy detonating cord (LEDC) whose wall has been placed adjacent to an initiation-sensitive region of a thin membrane in the shock tube, or in a capping member to an open end of a shock tube or in a capping member to the detonator itself, wherein the inner surface of the bore of the shock tube or the end-capping member is coated with a reactive composition of an explosive or a deflagrating compound The end capping member fits over and seals the open end of the shock tube or fits in and seals a detonator with or without a shock tube in it, acting as a shock tube itself The thin membrane accepts the detonation from the LEDC, whereby the shock tube or capping member is initiated and relays a pressure pulse to the shock tube or the detonator affixed thereto Novel shock tubes, shock tube/detonator units, and a detonator for use in the hybrid shock tube/LEDC system are disclosed

Thermal stability of fullerenes: a shock tube study on the pyrolysis of and

Abstract: The thermal stability of fullerenes and dispersed in Ar was studied behind shock waves by following the time-dependent absorption and emission of the proposed decomposition product . The gas - particle mixtures filled into the shock tube were heated to temperatures at pressures of . Because of the relatively high vapour pressure of the fullerenes, they evaporate in a few microseconds so that both and are in the gas phase during most of the observation time. concentration profiles were measured by a ring dye laser spectrometer at . Simultaneously, the time behaviour of spectrally resolved light emitted from the shock-heated aerosol was recorded by an intensified CCD camera. A simplified reaction mechanism with both formation and consumption reactions was proposed and the experimental results were discussed in terms of kinetic parameters. Rate coefficients and of the initial pyrolysis reactions (R1) and (R2) were determined. Two different models for the further decomposition of fullerene fragments were discussed and compared with computer simulations.

Quasi-Steady Structures in the Two-Dimensional Initiation of Detonations

Abstract: Two regimes of reflected-shock-induced ignition of explosive gases are known to exist, referred to as strong and weak (or mild) ignition. Experimental studies have shown that the former is manifested by the early appearance of a plane shock wave of chemical activity near the back wall of the shock tube and the whole strong-ignition process is a nominally one-dimensional phenomenon. When small distinct regions of increased chemical activity exist near the wall from which the incident wave reflects, localized thermal runaway leads directly to detonations that are multidimensional in character; this is the situation in what is called mild ignition. Although both strong and weak modes have been studied experimentally (in the 1960s and 1970s) and visualized by means of streak-camera and stroboscopic-laser-schlieren techniques, up to now most studies which use the methods of computational fluid dynamics have concentrated on the one-dimensional case. Previous analytical/numerical studies have shown how the three-dimensional structure of detonations can appear as a consequence of the instability of an initially ideal planar Zeldovich-von Neumann-Doring detonation. The latter is subject to some small-amplitude disturbances, and subsequent events lead to the eventual appearance of triple points along the front. In this paper some of the transient phenomena that take place in the first few microseconds after incident shock reflection from the closed end of a shock-tube are examined by means of a number of numerical simulations. A small hot-spot is assumed to exist in one of the corners between the reflective end plate and the walls of the shock tube. Evolution of the flow is followed, from the time of incident shock reflection, through the genesis of curved reaction waves, on to the appearance of an `explosion within the explosion' ending with the creation of a nearly plane detonation wave and its gradual contamination by triple-shock-wave features. The events portrayed in this way are recognizable stages in the story that the experimental studies revealed 25 years ago. The all-important region between reflective wall and reflected shock, within which intense chemical activity begins and which, because of its small geometric extent, is not well resolved in the schlieren photographs, is here replaced by high resolution images of the primitive variables of the flow. The wealth of data provided by these simulations is subsequently correlated to reveal the existence of quasi-steady structures in the form of reaction waves (specifically, weak detonations and fast flames or deflagrations), which previously have been shown to be part of the evolutionary processes only in strictly one-dimensional phenomena.

Real gas corrections in shock tube studies at high pressures

Abstract: Reaction kinetics studies at high pressure in shock tubes can be significantly affected by the influence of real gas effects on state variables. The effect on the temperature, pressure, and density can be calculated by solving the shock wave equations using real gas equations of state (EOS). We present a method to solve the shock wave equations in a straightforward way by taking advantage of the recently-developed real gas properties package by Schmitt et al. (U. of Iowa Rep. UIME PPB 93–006, 1994). The solutions of these equations for shock waves in pure argon are presented. We find that the reflected shock temperatures and densities can be significantly different from those predicted by using an ideal gas EOS. Using the Peng-Robinson EOS, for example, the calculated real gas reflected shock temperature is less than the ideal gas temperature by 83 K per 1000 atm. An illustrative example of the effect of real gas corrections on a rate coefficient determination is also presented.

Shock Wave Interaction in Hypervelocity Flow. Appendix C.

Abstract: : The interaction of a weak oblique shock with the strong bow shock ahead of a blunt body in supersonic flow produces extreme heat transfer rates and surface pressures. Although the problem has been studied extensively in low enthalpy flows, the influences of high enthalpy real gas effects are poorly understood. Existing perfect gas models predict greatly increased heating with increasing Mach number and decreasing ratio of specific heats. Experiments are conducted in a free piston shock tunnel to determine the effects of thermochemistry on the problem at high enthalpy. The flow topology is simplified by studying the nominally two dimensional flow about a cylinder with a coplanar impinging shock wave. High resolution holographic interferometry is used to investigate changes in the flow structure as the location of the impinging shock wave is varied. Fast response heat transfer gauges provide time resolved measurements of the model surface temperature. The data that are obtained do not support the existing predictions of greatly increased heat transfer at high enthalpy. A model is developed to study the thermochemical processes occurring in the interaction region. The phenomenon arises because the stagnation streamline is forced to pass through a system of oblique shock waves that produce less entropy than the undisturbed bow shock. Peak heating is shown to result from a balancing of the strengths of the oblique shock waves. This condition is demonstrated to simultaneously minimize the influence of thermochemistry on the flow. Real gas effects are shown to become important at lower Mach numbers (< 7.5) and for shock angles weaker or stronger than that which produces maximum heating. The model accurately reproduces the experimental observations.

Shock waves from an open-ended shock tube with different shapes

Abstract: A new method for decreasing the attenuation of a shock wave emerging from an open-ended shock tube exit into a large free space has been developed to improve the shock wave technique for cleaning deposits on the surfaces in industrial equipments by changing the tube exit geometry. Three tube exits (the simple tube exit, a tube exit with ring and a coaxial tube exit) were used to study the propagation processes of the shock waves. The detailed flow features were experimentally investigated by use of a two-dimensional color schlieren method and by pressure measurements. By comparing the results for different tube exits, it is shown that the expansion of the shock waves near the mouth can be restricted by using the tube exit with ring or the coaxial tube exit. Thus, the attenuation of the shock waves is reduced. The time histories of overpressure have illustrated that the best results are obtained for the coaxial tube exit. But the pressure signals for the tube exit with ring showed comparable results with the advantage of a relatively simple geometry. The flow structures of diffracting shock waves have also been simulated by using an upwind finite volume scheme based on a high order extension of Godunov's method as well as an adaptive unstructured triangular mesh refinement/unrefinement algorithm. The numberical results agree remarkably with the experimental ones.

A Free-Lagrange method for unsteady compressible flow: simulation of a confined cylindrical blast wave

Abstract: A Free-Lagrange numerical procedure for the simulation of two-dimensional inviscid compressible flow is described in detail. The unsteady Euler equations are solved on an unstructured Lagrangian grid based on a density-weighted Voronoi mesh. The flow solver is of the Godunov type, utilising either the HLLE (2 wave) approximate Riemann solver or the more recent HLLC (3 wave) variant, each adapted to the Lagrangian frame. Within each mesh cell, conserved properties are treated as piece-wise linear, and a slope limiter of the MUSCL type is used to give non-oscillatory behaviour with nominal second order accuracy in space. The solver is first order accurate in time. Modifications to the slope limiter to minimise grid and coordinate dependent effects are described. The performances of the HLLE and HLLC solvers are compared for two test problems; a one-dimensional shock tube and a two-dimensional blast wave confined within a rigid cylinder. The blast wave is initiated by impulsive heating of a gas column whose centreline is parallel to, and one half of the cylinder radius from, the axis of the cylinder. For the shock tube problem, both solvers predict shock and expansion waves in good agreement with theory. For the HLLE solver, contact resolution is poor, especially in the blast wave problem. The HLLC solver achieves near-exact contact capture in both problems.

Experimental study and kinetic modeling of the thermal decomposition of gaseous monomethylhydrazine. Application to detonation sensitivity

Abstract: The thermal decomposition of gaseous monomethylhydrazine has been studied in a 384 mm id shock tube behind a reflected shock wave at 1040–1370 K, 140–455 kPa and in mixtures containing 97 to 99 mol% argon, by using MMH absorption at 220 nm A chemical kinetic model based on MMH decomposition profiles has been developed This model has been used, with some assumptions, to evaluate the detonation sensitivity of pure gaseous MMH This compound is found to be much less sensitive to detonation than hydrazine

A holographic interferometric study of shock wave focusing in a circular reflector

Abstract: A holographic interferometric study was made of the focusing of reflected shock waves from a circular reflector. A diaphragmless shock tube was used for incident shock Mach numbers ranging from 1.03 to 1.74. Hence, the process of reflected shock wave focusing was quantitatively observed. It is found that a converging shock wave along the curved wall undergoes an unsteady evolution of mach reflection and its focusing is, therefore, subject to the evolution of the process of shock wave reflections. The collision of triple points terminates the focusing process at the geometrical focus. In order to interprete quantitatively these interferograms, a numerical simulation using an Eulerian solver combined with adaptive unstructured grids was carried out. It is found numerically that the highest density appears immediately after the triple point collision. This implies that the final stage of focusing is mainly determined by the interaction between shock waves and vortices. The interaction of finite strength shock waves, hence, prevents a curved shock wave from creating the infinite increase of density or pressure at a focal point which is otherwise predicted by the linear acoustic theory.

A numerical investigation of transient detonation in granulated material

Abstract: A two-phase model based upon principles of continuum mixture theory is numerically solved to predict the evolution of detonation in a granulated reactive material. Shock to detonation transition (SDT) is considered whereby combustion is initiated due to compression of the material by a moving piston. In particular, this study demonstrates the existence of a SDT event which gives rise to a steady two-phase Chapman-Jouguet (CJ) detonation structure consisting of a single lead shock in the gas and an unshocked solid; this structure has previously been independently predicted by a steadystate theory. The unsteady model equations, which constitute a non-strictly hyperbolic system, are numerically solved using a modern high-resolution method. The numerical method is based on Godunov's method, and utilizes an approximate solution for the two-phase Riemann problem. Comparisions are made between numerical predictions and known theoretical results for 1) an inert two-phase shock tube problem, 2) an inert compaction wave structure, and 3) a reactive two-phase detonation structure; in all cases, good agreement exists.

Flow through a perforated surface due to shock-wave impact

Abstract: The factor which is of prime importance in influencing the shock reflection geometry, and resulting pressures, following impingement of a shock wave on a porous surface is the velocity of the flow into the surface. A set of experiments has been conducted, using holographic inferometry in a shock tube, on the impingement of a shock wave on a surface covered with slits, over the full range of shock incidence angles from 0 to 90°. Inverse shock pressure ratios of 0.4, 0.5 and 0.7 were used, and detailed characterization of the flow fields determined. A number of methods are used to infer the inflow into the surface, and measurements are also conducted on the downstream side of the slit plate in order to establish the pressure ratio across the plate. The tests include choking of the flow through the slits. Shock reflection angles are found to be depressed compared to reflection from an impervious wall for cases of regular reflection, but are similar in the case of Mach reflection with the incident wave near glancing incidence. Contrary to assumptions made in previous work it is shown that for wall angles from zero up to approximately 60° the inflow to the plate is inclined to the surface at about 17° and then tends to straighten out until, for normal shock reflection, the flow is also normal to the plate. It appears that this behaviour is linked to the separation of the flow at the inlet to the pores of the model, due to shock wave diffraction. The maximum value of the absolute inflow velocity occurs in the region of transition from regular to Mach reflection. A series of starting vortices is shed on the underside of the slit and is found to follow a path nearly normal to the plate. These vortices lie along a contact surface whose motion is compatible with the strength of the shock wave transmitted through the plate.

Modeling mass entrainment in a quasi-one-dimensional shock tube code

Abstract: A quasisteady mass-entrainment model for shock tube boundary layers, specifically for use in quasi-one-dimensional codes, is described. Using this model, we calculate shock tube test times for the turbulent regime.

Kinetics of Hexane Combustion in a Shock Tube

Abstract: Faculty of Aerospace Engineering, Technion - Israel Institute of Technology, Haifa 32000, Israel(Received 2 May 1996 and in revised form 25 July 1996)Abstract. A detailed shock tube investigation on the ignition delay times inmixtures containing n-hexane and oxygen diluted in argon is reported. The productdistribution ofthepre-ignited mixtures was also investigated and a computer model­ing of the combustion kinetics was performed. The experiments covered the tem­perature range 1020-1725 K at pressures of 1-7 atm. A computer simulation wasperformed with a large number of elementary reactions (386), which was thenreduced to a scheme containing only

Model identification of a kulite pressure transducer

Abstract: A simple model of a Kulite pressure transducer is identified. A parametric linear time invariant system whose response matches the experimental data is constructed. Our results show that the transducer may be modeled as a third order system with one real pole, a pair of complex conjugate poles with small damping, and a real zero. The transfer function of the identified model may be used to compute the frequency response (magnitude and phase) of the transducer for frequencies up to about 300 kHz. The identified model may also be used to reconstruct the input to the transducer given a record of its output. The accuracy of the identified model is limited by the fact that the experimental inputs used for identification are step inputs (shock waves). KULITE RESPONSE TO WEAK SHOCKS The four-inch shock tube, in the Aerospace Sciences Laboratory at Purdue University, was used to provide a known input for a hemisphere-cylinder model with a Kulite pressure transducer mounted in the nose. [1] Weak shocks were produced which were impinged upon this system to excite the Kulite resonance frequency. 'Supported in part by the National Science foundation under VIA award no. ECS-93-58288. f Associate Professor ' Research Assistant 1 Copyright ©1996 by the American Institute of Aeronautics and Astronautics, Inc. AE Rights Reserved. Apparatus fc Procedure The tip of the hemisphere-cylinder model (2.5 inches in length) was placed at the end of the driven section of the shock tube as shown in Figure 1. A Kulite Pressure transducer, model XCQ-062-25A, was mounted inside the model and flush with the nose. This Kulite was constructed without screens so that the diaphragm was as nearly flush with the front face as possible. The remaining space was factory filled with RTV. The silicon-based strain-gauge transducers were supplied with 5.00 V from a REF02 integrated circuit. [2] The Kulite output was amplified by Burr-Brown INA103 instrumentation amplifiers; the DC-output voltage was multiplied by 100, and then AC-coupled and further amplified by 100 using a second INA103. The AC-coupled signal was high-pass filtered at 840 Hz. The amplifiers have a small-signal bandwidth of 800 kHz at a gain of 100. The distance between the tip of the model and Kulite system and the second Kistler pressure transducer (K -2) was 6.2 inches. K -2 was then 24.1 inches away from the first Kistler transducer (K-l) (i.e. 30.3 inches from the Kulite system). The model 603A Kistler pressure transducers were connected to a model 504A amplifier. The Kistler amplifier was set so that the pressure-gauge conversion factor was 28.4 psi/V [3]. The Validyne pressure transducer, model DP15-22, with a 20 psi gauge diaphragm was hooked up to the driver section of the tube and connected to a Validyne carrier demodulator, model CD223. The zero and the span on the Validyne amplifier were adjusted to provide maximum resolution. A Seegers pressure gauge (model no. SS-2170-30), with 0.05 psi gauge subdivisions and a 0 to 30 psig range, was also connected to the driver section and provided a means of calibrating the Validyne and Kulite pressure transducers. Diaphragms, made out of aluminum foil, wax paper, and 0.001 inch mylar, were used to obtain a driving pressure range between 1.0 psig and 12.0 psig. The driven section was operated at atmospheric pressure. A LeCroy 9304AM digital oscilloscope was used to record the data, which was sampled at 50 MHz with 250,000 pts/channel. The LeCroy oscilloscope has four channels, and resolves eight bits to a bandwidth of 100 MHz and includes analog amplifiers that resolve to 2 mV/division for a maximum of ten divisions. The LeCroy oscilloscope was set up to acquire data on four channels which were hooked up to the Kulite, Validyne, and the Kistler's, Kl and K-2, respectively. After each run, the output from the Validyne was recorded and the other channels were saved to disk. The trigger was set in order to capture the driving pressure, measured using the Validyne, before the diaphragm broke and the run began. The shock tube was operated by placing a diaphragm between the driven and driver sections. For each run, the pressure of the flow ahead of the shock wave (pj) was at atmospheric in the driven section. The pressure in the driver section (p4) was then increased until the diaphragm broke. This caused a shock wave to travel downstream towards the end of the driven section. The Kistler pressure transducers (K-l and K -2) and the Kulite were used to detect the shock wave as it passed by. The static pressure behind the shock was measured by the Kistlers and the total pressure by the Kulite. The pressure behind the shock wave (pg) was also computed in two different ways. One way involved the measured time and distance between the Kistlers and the Kulite pressure transducers, from which the shock speed was computed. The speed of sound (a) in the driven section was determined from the initial temperature (T), the ratio of specific heats (7) assumed constant at 1.4, and the gas constant (R) at 286.8 J/kg-K where a = T/*/RT. The shock Mach number was then known, along with the initial conditions pi and P4. Using standard compressible flow relations [4], pressure behind the shock was calculated from the initial conditions alone and then from the shock Mach number (Ms), and plotted in Figure 5. The equations used to compute the flow properties in the shock tube are El Pi (7i -1) 71

The reflection of a shock wave over a cone

Abstract: An investigation was made of the reflection of planar shock waves from cones 86 cones, the half apex angle of which varied from 10° to 52° at every 05°, were installed in a 60 mm×150 mm diaphragmless shock tube equipped with holographic interferometry The diaphragmless shock tube had a high degree of reproducibility with which the scatter of shock wave Mach number was within ±025% for shock wave Mach number ranging from 116 to approximately 20 The reflection of shock waves over cones was visualized using double exposure holographic interferometry Whitham's geometrical shock wave dynamics was used to analyse the motion of Mach stems over cones It is found that for relatively smaller apex angles of cones trajectory angles of resulting irregular reflections coincide with the so-called glancing incidence angles and their Mach stems appear to be continuously curved from its intersection point with the incident shock wave, which shows the chractericstic of von Neumann reflection The domain of the existence of the von Neumann reflection was analytically obtained and was found to be broadened much more widely than that of two-dimensional reflections of shock waves over wedges