The complex flow and wave pattern following an initially planar shock wave transmitted through a double-bend duct is studied experimentally and theoretically/numerically. Several different double-bend duct geometries are investigated in order to assess their effects on the accompanying flow and shock wave attenuation while passing through these ducts. The effect of the duct wall roughness on the shock wave attenuation is also studied. The main flow diagnostic used in the experimental part is either an interferometric study or alternating shadow–schlieren diagnostics. The photos obtained provide a detailed description of the flow evolution inside the ducts investigated. Pressure measurements were also taken in some of the experiments. In the theoretical/numerical part the conservation equations for an inviscid, perfect gas were solved numerically. It is shown that the proposed physical model (Euler equations), which is solved by using the second-order-accurate, high-resolution GRP (generalized Riemann problem) scheme, can simulate such a complex, time-dependent process very accurately. Specifically, all wave patterns are numerically simulated throughout the entire interaction process. Excellent agreement is found between the numerical simulation and the experimental results. The efficiency of a double-bend duct in providing a shock wave attenuation is clearly demonstrated.

Experimental and theoretical study of shock wave propagation through double-bend ducts

Shock wave reflection from a wedge in a dusty gas

The flow developed behind shock wave transmitted through a screen or a perforated plat is initially highly unsteady and nonuniform. It contains multiple shock reflections and interactions with vortices shed from the open spaces of the barrier The present paper studies experimentally and theoretically/numerically the flow and wave pattern resulted from the interaction of an incident shock wave with a few different types of barriers, all having the same porosity but different geometries

Experimental and Numerical Study of Shock Wave Interaction with Perforated Plates

One-dimensional self-similar unsteady isothermal and adiabatic flows behind a strong exponential shock wave driven out by a cylindrical piston moving with time according to an exponential law in a rotational axisymmetric non-ideal gas is investigated. The medium is assumed to be non-ideal gas rotating about the axis of symmetry. The fluid velocities in the ambient medium are assumed to be varying with time according to an exponential law. Similarity solutions exist only when the surrounding medium is of constant density. Solutions are obtained, in both the cases, when the flow between the shock and the piston is isothermal or adiabatic by taking into account components of vorticity vector. It is found that the assumption of zero temperature gradient brings a profound change in the density and compressibility distributions as compared to that of the adiabatic case. The effect of an increase in the value of the parameter of the non-idealness of the gas is investigated. Also, a comparison between the solutions in the cases of isothermal and adiabatic flows is made. Further, it is shown that the consideration of zero temperature gradient and the effect of variation of the parameter of non-idealness of the gas decrease the shock strength and widens the disturbed region between the shock and piston. The shock waves in non-ideal gas can be important for description of shocks in supernova explosions, in the study of a flare produced shock in solar wind, central part of star burst galaxies, nuclear explosion, rupture of pressurized vessel, in the analysis of data from exploding wire experiments, and cylindrically symmetric hypersonic flow problems associated with meteors or reentry vehicles, etc. The findings of the present work provided a clear picture of whether and how the non-idealness of the gas and consideration of zero temperature gradient affect the propagation of shock and the flow behind it.

Similarity solutions for unsteady flow behind an exponential shock in an axisymmetric rotating non-ideal gas

Similarity solutions are obtained for one-dimensional unsteady isothermal and adiabatic flows behind a strong exponential cylindrical shock wave propagating in a rotational axisymmetric dusty gas, which has variable azimuthal and axial fluid velocities. The shock wave is driven by a piston moving with time according to an exponential law. Similarity solutions exist only when the surrounding medium is of constant density. The azimuthal and axial components of the fluid velocity in the ambient medium are assumed to obey exponential laws. The dusty gas is assumed to be a mixture of small solid particles and a perfect gas. To obtain some essential features of the shock propagation, small solid particles are considered as a pseudo-fluid; it is assumed that the equilibrium flow conditions are maintained in the flow field, and that the viscous stresses and heat conduction in the mixture are negligible. Solutions are obtained for the cases when the flow between the shock and the piston is either isothermal or adiabatic, by taking into account the components of the vorticity vector. It is found that the assumption of zero temperature gradient results in a profound change in the density distribution as compared to that for the adiabatic case. The effects of the variation of the mass concentration of solid particles in the mixture \(K_p\), and the ratio of the density of solid particles to the initial density of the gas \(G_a\) are investigated. A comparison between the solutions for the isothermal and adiabatic cases is also made.

Self-similar solutions for unsteady flow behind an exponential shock in an axisymmetric rotating dusty gas

The interaction of a planar shock wave with a square cavity is studied experimentally and numerically It is shown that such a complex, time-dependent, process can be modelled in a relatively simple manner The proposed physical model is the Euler equations which are solved numerically, using the second-order-accurate high-resolution GRP scheme, resulting in very good agreement with experimentally obtained findings Specifically, the wave pattern is numerically simulated throughout the entire interaction process Excellent agreement is found between the experimentally obtained shadowgraphs and numerical simulations of the various flow discontinuities inside and around the cavity at all times As could be expected, it is confirmed that the highest pressure acts on the cavity wall which experiences a head-on collision with the incident shock wave while the lowest pressures are encountered on the wall along which the incident shock wave diffracts The proposed physical model and the numerical simulation used in the present work can be employed in solving shock wave interactions with other complex boundaries

Experimental and numerical study of the interaction between a planar shock wave and a square cavity

Whitham's approximation for handling shock wave propagation in area changes (reductions) in a duct was checked in comparison with a numerical solution. Also the Whitham approximation for shock wave propagation from a constant cross-sectional duct to a duct of a smaller cross-sectional area was studied and compared with a numerical solution. It was found that for modest incident shock Mach numbers and modest area reductions the Whitham approximation provided a fair solution for the shock Mach number and for the post-shock pressure. For higher shock Mach numbers and/or area reductions, large discrepancies exit between the approximate and exact solutions. A wider range of applicability of the Whitham approximation is found for the monotonical area reduction case; it is quite narrow for the passage of a shock wave from a wider to a narrower duct case. In addition, the effect of the extent of the area change region on the time required for reaching a quasi-steady flow was studied. It was shown that the longer the area change segment is, the longer it takes to reach a quasi-steady flow.

Shock wave interaction with area changes in ducts

A simple entrainment model is used to estimate droplet streamlines, velocity and mass flux in rocket exhaust plumes. Since droplet mass flux constitutes only about 1% of the exhaust mass flux, the effect of droplet entrainment on the gas flow is neglected. The novelty of the present model is in obtaining the droplet distribution within the nozzle by assuming a small radial random velocity component for droplets at the throat. Gas flow in the nozzle is approximated as isentropic plus a correction for the boundary layer. The computed distribution of droplet mass flux is found to be in good agreement with experimental data.

A random simulation of droplet distribution in nozzle and plume flows

The wave pattern that arises from the interaction of a planar shock wave with a square cavity was studied experimentally and numerically. It was shown that the resulting configuration depended on whether or not the post-incident-shock-wave flow was subsonic or supersonic. In both cases the numerical solution reconstructed the position and shape of the waves, inside and outside the cavity, very accurately.

J. Falcovitz

Papers

Experimental and numerical study of the interaction between a planar shock wave and a square cavity

Shock wave reflection from a wedge in a dusty gas

Shock wave interaction with area changes in ducts

A random simulation of droplet distribution in nozzle and plume flows

The Interaction of a Normal Shock Wave with a Square Trench