Shock Waves In Flow Research Articles

Rarefied hypersonic flow in a plane channel with a surface glow discharge

The gasdynamic structure of a hypersonic molecular nitrogen flow in a plane channel whose opposite surfaces are segmented electrodes for generating a continuous surface glow discharge is investigated using a two-dimensional computational model. The electrodynamic structure of the surface glow discharge in the hypersonic rarefied gas flow (distributions of the charged particle concentrations, current density, and electric potential) is studied. A two-dimensional conjugate electrical-gasdynamic model consisting of the continuity, Navier-Stokes, and energy conservation equations and the chargedparticle continuity equations in the ambipolar approximation is proposed. The real thermophysical and transport properties of molecular nitrogen are taken into account. It is shown that using a surface glow discharge in a hypersonic rarefied gas flow makes it possible effectively to modify the shock-wave flow structure and hence to consider this type of discharge as additional tool for controlling rarefied gas flows.

Shock-wave flow of a gas driven by harmonic oscillations of a piston in a closed cylindrical tube

A shock-wave flow of a gas driven by harmonic oscillations of a piston in a closed cylindrical tube has been studied using numerical integration of the narrow-channel model equations in the flow regimes characterized by moderate Mach and Reynolds numbers. The structure of a stationary motion of the gas at various moments of the cycle is presented by radial profiles of the longitudinal velocity component and the temperature.

The Full Flowpath Analysis of a Hypersonic Vehicle

A numerical study has been carried out to investigate the full flow path and aerodynamic characteristics of a hypersonic vehicle at a 7.0 free stream Mach number. Results indicate that the inlet started and unstarted operations have remarkable effects on the flow pattern of the full flow path. When the inlet operates in a started mode, the transverse pressure gradient generated by the forebody alters the air captured characteristics and the entering flow quality of the inlet. Furthermore, the expansion process of the nozzle jet flow is obviously affected by the external flow field around the afterbody with the cross section shape transiting from a near rectangle at the exit of the nozzle to a near triangle at the tail of the vehicle. When the inlet operates in an unstarted mode, the aerodynamic instability can be observed in the full flow path of the vehicle. Due to the oscillation of the external compressed shock wave and nozzle jet flow, the aerodynamic characteristics of the vehicle vary periodically with the lift-drag ratio changing from 0.25 to 2.09. Finally, by comparing to the experimental data, the reliability of the CFD is verified.

Criterion for the onset of a shock-wave flow in a gas driven by harmonic oscillations of a piston in a closed cylindrical tube

A criterion for the onset of a shock wave motion of a gas column driven by resonance harmonic oscillations of a piston in a closed tube is formulated based on an analysis of the results of experiments and theoretical investigations. The validity of the proposed criterion in a broad range of parameters has been verified within the framework of numerical integration of a nonstationary system of narrow-channel gasdynamics equations written in a divergent form.

Shock-wave flow regimes at entry into the diffuser of a hypersonic ramjet engine: Influence of physical properties of the gas medium

The physical aspects of the effective-adiabatic-exponent model making it possible to decompose the total problem on modeling of high-velocity gas flows into individual subproblems (“physicochemical processes” and “ aeromechanics”), which ensures the creation of a universal and efficient computer complex divided into a number of independent units, have been analyzed. Shock-wave structures appearing at entry into the duct of a hypersonic aircraft have been investigated based on this methodology, and the influence of the physical properties of the gas medium in a wide range of variations of the effective adiabatic exponent has been studied.

Calculation of shock compression of porous media in conical solid-state targets with an outlet hole

The Godunov-type method that was earlier developed for the hydrodynamic equations of compressible media on regular grids is extended to the case of shock wave flows in elastoplastic porous media. The results of numerical simulations of a hypothetical experimental plant for checking the effect of an increased intensity of converging shock waves in porous media with increasing degree of porosity are presented. This effect was earlier discovered by numerical simulations.

Numerical investigation of the laminar shock-wave gas flow excited by harmonic vibrations of the piston in a closed cylindrical tube

The shock-wave gas flow in a closed cylindrical tube caused by harmonic vibrations of a flat piston has been considered. The solution has been obtained by means of numerical integration of the system of nonstationary equations of a narrow channel written in divergent form. A scheme of the 1st order of time accuracy and a scheme of the 2nd order of space accuracy have been used. The regularities in the behavior of the dynamic and temperature boundary layers for the unstable regime of gas flow in the tube at various moments of the cycle have been analyzed.

Collapse of Shock Waves upon Their Interaction with a Local Energy Source

Numerical analysis is performed of the interaction of a shock wave with a local energy source and the wake behind it. It is shown that for specified shock-wave intensity and flow parameters there is a threshold value of the energy release starting with which the shock wave collapses.

Comparison of modern numerical methods for shock wave simulation in gases

A comparative analysis of several numerical methods for hyperbolic equations is carried out aiming to select the most effective of them for purposes of simulation of shock-wave flows. The computational efficiency is determined using a relation of the computation time and the error of the result obtained. Schemes for temporal and spatial discretization are tested separately by solution of the Riemann problem. According to the test results, an optimal combination of discretizations was chosen. The algorithm obtained is superior to all others in the accuracy and performance within the entire ranges of the Courant number and space steps.

Abel inversion of axially-symmetric shock wave flows

Finite-fringe interferograms produced for axisymmetric shock wave flows are analyzed by Fourier transform fringe analysis and an Abel inversion method to produce density field data for the validation of numerical models. For the Abel inversion process, we use basis functions to model phase data from axially-symmetric shock wave structure. Steady and unsteady flow problems are studied, and compared with numerical simulations. Good agreement between theoretical and experimental results is obtained when one set of basis functions is used during the inversion process, but the shock front is smeared when another is used. This is because each function in the second set of basis functions is infinitely differentiable, making them poorly-suited to the modelling of a step function as is required in the representation of a shock wave.

Solidification analysis of micro-scale metallic particles in the laser supersonic heating technique

In this paper, the authors analysed the solidification phenomenon in the laser supersonic heating technique used for producing metallic particles. A mathematical model was established to predict the velocity, temperature and solidification situation of metallic particles leaving a spray nozzle. The numerical analysis method was used to simulate the flow field structure of shock waves and to proceed with related experiment. In the experiment, a pulsed Nd–YAG laser was used as the heat source on a carbon steel target within the nozzle, and carbon steel particles were ejected by high pressure air. The solidification problem of carbon steel particles with radii of 1–50 µm in the compressible flow field was calculated and compared with experimental results. The result shows that the shock wave flow fields are generated at different entrance pressures (3–7 bar), and there is no significant difference in the radii of carbon steel particles produced by a fixed laser energy; however, in the flow field without the shock wave effect, the cooling effect is less evident in the solidification process.

Converging shock waves in porous media

We have numerically solved several problems related to converging shock waves, including (i) one-dimensional spherical and cylindrical waves with cumulation limited to a ball or cylinder of small radius and (ii) shock-wave flow in a cone-shaped solid target. The passage from a continuous loaded substance to a porous medium in these problems leads to a significant increase in both temperature and pressure in the sample. This character of pressure variation depending on the porosity qualitatively differs from the case of plane waves of constant intensity, for which an increase in the sample porosity under otherwise equal conditions of loading always leads to a decrease in the pressure.

Self-induced oscillations in the shock wave flow pattern formed in a stationary supersonic flow over a double wedge

Numerical simulations of a two-dimensional supersonic flow of an inviscid perfect gas over a double wedge in the Mach numbers range 5⩽M⩽9, revealed the existence of self-induced oscillations in the shock wave flow pattern in a narrow range of geometrical parameters.

The direct simulation Monte Carlo of flows composed of asymmetric potential scatterers

Predicted fluid transport properties are dictated by the assumed interaction-potential model between molecules. The direct simulation Monte Carlo (DSMC) method has been developed principally for those potentials that may be included efficiently in computational terms. In this paper nonisotropic scattering models are investigated for the Couette flow, with both shear stress and heat flux being calculated; the results are then compared to those predicted by the variable hard sphere (VHS) and the variable soft sphere (VSS) models. The same procedure is then repeated for a shock wave flow case. It is concluded that, even when extreme post-collision directionality is modeled, statistically similar results to VHS and VSS models are obtained if the total collision cross section and its variation with temperature are appropriately normalized. This demonstrates the important result that to achieve convergence with the measured transport properties of heat flux and viscosity, as well as with shock flow structures then highly precise molecular models are not required for DSMC. Conversely, the adoption of different scattering models, attempting to simulate specific features of the underlying physics of a collision, may not always be achieved using the DSMC method. Variation of the total cross section with temperature is a well-recognized phenomenon included in all successful models for molecular processes. Of itself, however, this variation does not determine the post-collision partners, rather it influences the rate at which processes can occur. As a result it is contributive to, rather than the determinant of, the physical outcome from a collision.

Numerical and experimental investigations on a shock wave related cavitational flow

Shock waves often occur in hydraulic systems, including pipes, valves and pumps due to quickly closing valves. As a result, cavitation and air-release-related bubbles are created due to local pressures in the liquid dropping below the liquid saturation pressure. The developed model, combining fluid dynamics of the flow and a numerical model of cavitation and air release, computes all flow characteristics, including the behaviour of pressure, mass flow and volumetric void fractions of vapour and air in liquid. The occurrence of the shock waves and their relation to cavitation are explained and discussed in detail. To avoid numerical oscillations and to maintain a high numerical accuracy in shock wave flows, the total variation diminishing method is applied to discretize the equation system. Furthermore, various limiters are used to prevent the numerical solutions from overshooting or undershooting. Finally, the computational results are compared with the experimental data measured on a simple pipeline terminated with a valve. This comparison shows very good agreement with the experiment.

Modifications of Gasdynamic Equations of Higher Approximations of the Chapman-Enskog Method

The non-Navier-Stokes continuum models proposed earlier on the basis of a modification of the gasdynamic equations of the higher (starting from the Burnett) approximations of the Chapman-Enskog method for shock wave flow are generalized to include the case of three-dimensional flows of a simple (monatomic) gas. The models are tested on the problems of shock wave structure and cylindrical Couette rarefied gas flow.

Numerical Analysis of Fluid Motions by Three-Dimensional Thermal Lattice Boltzmann Model.

This paper is concerned with the three-dimensional thermal lattice Boltzmann BGK model which can be applied to the numerical analysis of fluid motions. In the model proposed here, the local equilibrium distribution of microscopic particles is represented more simply than some previous lattice BGK models. In the numerical simulations of three-dimensional fluid flows to examine the feature of this model, the viscosity and the one-dimensional propagation of shock wave appear appropriately, compared with the other numerical results. In the unsteady shock wave flow around the cubic body, the reflection can be observed. These results show that it is possible to apply the lattice Boltzmann method to practical analysis of fluid motions with the compressibility.

Calculation of the stress-strain state of a solid exposed to local explosive loading

We consider a method for calculating the residual stress-strain state of an explosion-loaded metal in the case of nonuniform geometry of shock-wave flows with the use of a rather realistic viscoelastic-plastic model of the medium. We have derived relations that allow one to describe the configuration of the “stress-strain band” created by explosive loading in a metal and to determine the parameters of this band. Calculation results for plates made of low-carbon steel have been compared with experimental data. Satisfactory agreement has been attained. Ways for improving the calculational procedure proposed, in particular, ways for taking into account the metal viscosity versus the deformation velocity, have been proposed.

Transient shock wave flows in tubes with a sudden change in cross section

This paper describes propagation of shock waves within circular cross-section shock tubes with a sudden area change in cross section. A dispersion-controlled scheme was used to solve the Euler equations assuming axisymmetric flows. For experimental visualizations an aspheric cylindrical test section was designed to keep collimated incident light rays parallel once they were reflected or refracted on the inner and outer surfaces of the test section. For effective comparisons with experimental results, equivalent numerical interferograms were constructed to demonstrate effectiveness of the numerical method and verify the observed shock-wave phenomena. The numerical method was used to calculate three further cases with variations of the initial shock-wave Mach number and the flow geometry to clarify the role of these parameters. Complex transient shock-wave phenomena, such as shock-wave reflection, shock/vortex interaction and shock-wave focusing were observed in these cases, and interpreted with shock wave theory. In addition, the research clearly shows that combination of CFD with experiments is effective to highlight physical phenomena in axisymmetric flows.

Numerical simulation of a porous cooling effect observed when a hypersonic stream of viscous gas with a decaying shock wave flows round a wall

The concept of porous cooling observed when a hypersonic stream of viscous gas with a decaying shock wave flows round a wall is substantiated by means of a finite-difference solution of the Reynolds equations, closed by using a two-parameter dissipative turbulence model.