Theory for producing a single-phase rarefaction shock wave in a shock tube

2001 ◽  
Vol 445 ◽  
pp. 37-54 ◽  
Author(s):  
S. H. FERGASON ◽  
T. L. HO ◽  
B. M. ARGROW ◽  
G. EMANUEL
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Shock Tube ◽  
Single Phase ◽  
Van Der Waals ◽  
Small Region ◽  
Incident Flow ◽  
Global Theory ◽  
Rarefaction Shock ◽  
Shock Tube Experiment

Although predicted early in the 20th century, a single-phase vapour rarefaction shock wave has yet to be demonstrated experimentally. Results from a previous shock tube experiment appear to indicate a rarefaction shock wave. These results are discussed and their interpretation challenged. In preparation for a new shock tube experiment, a global theory is developed, utilizing a van der Waals fluid, for demonstrating a single-phase vapour rarefaction shock wave in the incident flow of the shock tube. The flow consists of four uniform regions separated by three constant-speed discontinuities: a rarefaction shock, a compression shock, and a contact surface. Entropy jumps and upstream supersonic Mach number conditions are verified for both shock waves. The conceptual van der Waals model is applied to the fluid perfluoro-tripentylamine (FC-70, C15F33N) analytically, and verified with computational simulations. The analysis predicts a small region of initial states that may be used to unequivocally demonstrate the existence of a single-phase vapour rarefaction shock wave. Simulation results in the form of representative sets of thermodynamic state data (pressure, density, Mach number, and fundamental derivative of gas dynamics) are presented.

Shock wave propagation in non-uniform gas mixtures

2011 ◽  
Vol 226 (2) ◽  
pp. 123-130
Author(s):  
J Falcovitz ◽  
O Igra ◽  
D Igra
Keyword(s):  
Shock Wave ◽  
Wave Propagation ◽  
Shock Tube ◽  
Mass Fraction ◽  
Molar Fraction ◽  
Gaseous Mixture ◽  
Linear Distribution ◽  
Wave Patterns ◽  
Driver Section ◽  
Shock Tube Experiment

We consider a classical shock tube with Helium-filled driver section, and a driven section filled with a He– Ar gaseous mixture of continuously varying composition. We simulate a shock tube experiment, where the driven section composition starts out with pure Ar and ends with pure He (denoted ‘ − ’), or vice versa (denoted ‘+’). The initial pressures are 2 and 0.01 MPa. Two alternate initial species compositions are assumed: ‘Molar fraction’ – a linear distribution of the molar fraction; ‘Mass Fraction’ – a linear distribution of the mass fraction. Wave patterns arising in every case are presented and discussed.

Experimental investigation of diaphragm material combinations in a small-scale shock tube

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Anugya Singh ◽  
Aravind Satheesh Kumar ◽  
Kannan B.T.
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Shock Tube ◽  
Production Capacity ◽  
Incident Shock ◽  
Small Scale ◽  
Content Type ◽  
Shock Mach Number ◽  
Reinforcing Material ◽  
Shock Wave Mach Number

Purpose The purpose of this study is to experimentally investigate the trends in shock wave Mach number that were observed when different diaphragm material combinations were used in the small-scale shock tube. Design/methodology/approach A small-scale shock tube was designed and fabricated having a maximum Mach number production capacity to be 1.5 (theoretically). Two microphones attached in the driven section were used to calculate the shock wave Mach number. Preliminary tests were conducted on several materials to obtain the respective bursting pressures to decide the final set of materials along with the layered combinations. Findings According to the results obtained, 95 GSM tracing paper was seen to be the strongest reinforcing material, followed by 75 GSM royal executive bond paper and regular 70 GSM paper for aluminium foil diaphragms. The quadrupled layered diaphragms revealed a variation in shock Mach number based on the position of the reinforcing material. In quintuple layered combinations, the accuracy of obtaining a specific Mach number was seen to be increasing. Optimization of the combinations based on the production of the shock wave Mach number was carried out. Research limitations/implications The shock tube was designed taking maximum incident shock Mach number as 1.5, the experiments conducted were found to achieve a maximum Mach number of 1.437. Thus, an extension to further experiments was avoided considering the factor of safety. Originality/value The paper presents a detailed study on the effect of change in the material and its position in the layered diaphragm combinations, which could lead to variation in Mach numbers that are produced. This could be used to obtain a specific Mach number for a required study accurately, with a low-cost setup.

Rarefaction shock wave near the critical liquid–vapour point

1983 ◽  
Vol 126 ◽  
pp. 59-73 ◽  
Author(s):  
A. A. Borisov ◽  
Al. A. Borisov ◽  
S. S. Kutateladze ◽  
V. E. Nakoryakov
Keyword(s):  
Shock Wave ◽  
Shock Tube ◽  
Critical Point ◽  
Wave Front ◽  
Propagation Velocity ◽  
Test Substance ◽  
Unperturbed State ◽  
Long Wave ◽  
Rarefaction Shock ◽  
Negative Shock

The existence of a rarefaction shock wave or negative shock wave in a substance whose unperturbed state is close to the thermodynamic critical liquid–vapour point has been demonstrated experimentally. Its evolution and propagation velocity in a shock tube with Freon-13 as the test substance are described. It is shown that the steepness of the wave front does not diminish as the wave evolves. An equation is derived that describes the evolution of long-wave perturbations near the critical point.

Three-dimensional shock tube flows for dense gases

2007 ◽  
Vol 583 ◽  
pp. 423-442 ◽  
Author(s):  
ALBERTO GUARDONE
Keyword(s):  
Shock Wave ◽  
Shock Tube ◽  
Shock Front ◽  
Numerical Simulations ◽  
Three Dimensional ◽  
Dense Gas ◽  
Complex Flow ◽  
The Many ◽  
The One ◽  
Rarefaction Shock

The formation process of a non-classical rarefaction shock wave in dense gas shock tubes is investigated by means of numerical simulations. To this purpose, a novel numerical scheme for the solution of the Euler equations under non-ideal thermodynamics is presented, and applied for the first time to the simulation of non-classical fully three-dimensional flows. Numerical simulations are carried out to study the complex flow field resulting from the partial burst of the shock tube diaphragm, a situation that has been observed in preliminary trials of a dense gas shock tube experiment. Beyond the many similarities with the corresponding classical flow, the non-classical wave field is characterized by the occurrence of anomalous compression isentropic waves and rarefaction shocks propagating past the leading rarefaction shock front. Negative mass flow through the rarefaction shock wave results in a limited interaction with the contact surface close to the diaphragm, a peculiarity of the non-classical regime. The geometrical asymmetry does not prevent the formation of a single rarefaction shock front, though the pressure difference across the rarefaction wave is predicted to be weaker than the one which would be obtained by the complete burst of the diaphragm.

A Simplified Presentation of Shock Wave Parameters in Dissociating Air Flow

1960 ◽  
Vol 64 (595) ◽  
pp. 438-439
Author(s):  
T. R. F. Nonweiler
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Shock Waves ◽  
Chemical Equilibrium ◽  
Incident Flow ◽  
Perfect Gas ◽  
Thermodynamic State ◽  
Independent Variables ◽  
Wave Parameters ◽  
Temperature And Pressure

As is well known, the analysis of shock waves is complicated when the gas becomes dissociated on passage through the wave. As well as showing a dependence on the Mach number of the incident flow and non-dimensional quantities characteristic of the nature of the gas, as does the analysis when applied to a perfect gas, it then also shows a dependence on the thermodynamic state of the upstream air, as described for instance by its temperature and pressure. A growing number of calculations is becoming available, especially for air in complete thermal and chemical equilibrium, but the interpolation to give results appropriate to the three independent variables (of upstream state and incident velocity) needed in any particular application can often be rather troublesome, and one has still less faith in extrapolation.

Velocity and vorticity in weakly compressible isotropic turbulence under longitudinal expansive straining

2007 ◽  
Vol 584 ◽  
pp. 301-335 ◽  
Author(s):  
SAVVAS XANTHOS ◽  
MINWEI GONG ◽  
YIANNIS ANDREOPOULOS
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Pressure Gradient ◽  
Shock Tube ◽  
Isotropic Turbulence ◽  
Strain Tensor ◽  
Velocity Fluctuations ◽  
Total Enthalpy ◽  
Expansion Waves ◽  
Custom Made

The response of homogeneous and isotropic turbulence to streamwise straining action provided by planar expansion waves has been studied experimentally in the CCNY shock tube research facility at several Reynolds numbers. The reflection of a propagating shock wave at the open endwall of the shock tube generated an expansion fan travelling upstream and interacting with the induced flow behind the incident shock wave which has gone through a turbulence generating grid.A custom-made hot-wire vorticity probe was designed and developed capable of measuring the time-dependent highly fluctuating three-dimensional velocity and vorticity vectors, and associated total temperature, in non-isothermal and inhomogeneous flows with reasonable spatial and temporal resolution. These measurements allowed the computations of the vorticity stretching/tilting terms, vorticity generation through dilatation terms, full dissipation rate of kinetic energy term and full rate-of-strain tensor. The longitudinal size of the straining zone was substantial so that measurements within it were possible. The flow accelerated from a Mach number of 0.23 to about 0.56, a value which is more than twice the initial one.Although the average value of the applied straining was only betweenS11= 130 s−1andS11= 240 s−1and the gradient Mach number was no more than 0.226, the amplitude of fluctuations of the strain rateS11were of the order of 4000 s−1before the application of straining and were reduced by about 2.5 times downstream of the interaction. This characteristic of high-amplitude bursts and the intermittent behaviour of the flow play a significant role in the dynamics of turbulence.One of the most remarkable features of the suppression of turbulence is that this process peaks shortly after the application of the straining where the pressure gradient is substantial. It was also found that the total enthalpy variation follows very closely the temporal gradient of pressure within the straining region and peaks at the same location as the pressure gradient.Attenuation of longitudinal velocity fluctuations has been observed in all experiments. It appears that this attenuation depends strongly on the characteristics of the incoming turbulence for a given straining strength and flow Mach number. The present results clearly show that in most of the cases, attenuation occurs at large times or distances from the turbulence generating grids where length scales of the incoming flow are high and turbulence intensities are low. Thus, large eddies with low-velocity fluctuations are affected the most by the interaction with the expansion waves. Spectral analysis has indicated that attenuation of fluctuations is not the same across all wavenumbers of the spectrum. The magnitude of attenuation appears to be higher in cases of finer mesh grids.

A study of the impulsive wave discharged from the inclined exit of a tube

2003 ◽  
Vol 217 (2) ◽  
pp. 271-279 ◽  
Author(s):  
H-D Kim ◽  
Y-H Kweon ◽  
T Setoguchi
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Shock Tube ◽  
Good Accuracy ◽  
Propagation Direction ◽  
Impulsive Wave ◽  
Compressible Euler ◽  
Computational Work ◽  
Initial Shock ◽  
Tube Exit

The propagation of the impulsive wave discharged from the inclined exit of a tube is investigated using a shock tube experiment and by numerical computations. The pressure histories and wavefront geometries of the impulsive wave propagating outside the exits of the tube with several different configurations are analysed for the range of an initial shock wave Mach number between 1.1 and 1.4. In the shock tube experiments, the impulsive waves are visualized by a Schlieren optical system for the purpose of validation of computational work. Computations using the two-dimensional, unsteady, compressible, Euler equations are carried out to represent the experimental impulsive waves. The results obtained show that the inclination angle of the tube exit reduces the magnitude of the impulsive wave and affects the wavefront geometry of the impulsive wave. It is also found that the propagation direction and magnitude of the impulsive wave depend on the Mach number of the initial shock wave, while the impulsive waveform does not significantly vary with the Mach number of the initial shock wave. The computed results obtained predict the experimental ones with quite good accuracy.

Estimation of Mach Number of Shock Wave Propagating in Pipe

2003 ◽  
Author(s):  
Takanori Yamazaki ◽  
Masaki Endo
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Mach Number ◽  
Shock Tube ◽  
Dynamic Characteristic ◽  
Pressure Transducer ◽  
Shock Strength ◽  
Pressure History ◽  
Boundary Layer Interaction ◽  
Shock Mach Number

A useful way to estimate the local Mach number of shock propagating in a pipe is proposed in this paper. The shock Mach number, or the shock strength gradually decreases or increases as the shock propagates downstream in pipe due to the shock-boundary layer interaction. In general, the shock Mach number is estimated through the measurement of the time, which it takes for the shock to propagate between any two points along the pipe. This technique is very useful if the decreasing rate of the shock strength is given and it, after all, yields the average Mach number between the two points. In this paper the measurement of the local Mach number of shock in the shock tube is examined using one pressure transducer. The pressure history after the shock reaches the pressure tap is analyzed. The method to estimate the local Mach number is discussed considering the dynamic characteristic of the pressure transducer.

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