High temperature effects in moving shock reflection with protruding Mach stem

The influence of high temperature effects on the protrusion of Mach stem in strong shock reflection over a wedge was numerically investigated. A two-dimensional inviscid solver applies finite volume method and unstructured quadrilateral grids were employed to simulate the flow. Theoretical analysis was also conducted to understand the phenomenon. Both numerical and theoretical results indicate a wall-jet penetrating forward is responsible for the occurrence of Mach stem protrusion. The protrusion degree seems to depend on the thermal energy buffer capacity of the testing gas. Approaches to increase the energy buffer capacity, such as vibrational relaxation, molecular dissociation, and increase of frozen heat caoacitv, all tend to escalate the orotrusion effect.

Configurations of Shock Regular Reflection by Straight Wedges

We are concerned with the shock regular reflection configurations of unsteady global solutions for a plane shock hitting a symmetric straight wedge.It has been known that patterns of the shock reflection are various and complicated,including the regular and the Mach reflection.Most of the fundamental issues for the shock reflection have not been understood.Recently,there are great progress on the mathematical theory of the shock regular reflection problem,especially for the global existence,uniqueness,and structural stability of solutions.In this paper,we show that there are two more possible configurations of the shock regular reflection besides known four configurations.We also give a brief proof of the global existence of solutions.

Experimental and numerical studies on interactions of a spherical flame with incident and reflected shocks

Observations are presented from experiments and calculations where a laminar spherical CH4/air flame is perturbed successively by incident and reflected shock waves. The experiments are performed in a standard shock tube arrangement, in which a high-speed shadowgraph imaging system is used to record evolutions of the flame. Numerical simulations are conducted by using second-order wave propagation algorithms, based on two-dimensional axisymmetric Navier-Stokes equations with detailed chemical reactions. Qualitative agreements are obtained between the experimental and numerical results. Under actions of incident shock waves, Richtmyer-Meshkov instability responsible for the flame deformation is induced in the flame, and the distoned flame takes a barrel shape. Then, under subsequent actions of the shock wave reflected from a planar wall, the flame takes an inclined non-symmetrical kidney shape in a symmetric cross section, which means a mushroom-like shape of the flame comes finally into being. The vorticity direction in the ring cap has been altered by the reflected shock＇s action, which makes the head of the mushroom-like flame extend quickly to the side wall.

Achieving an optimal shock-wave mitigation inside open channels with cavities for weak shock waves:A computational study

This paper deals with a numerical study of weak shock-waves propagation and their attenuation in channel flow having different heights and exhibiting a hollow circular cavities with different depths and diffraction angles inside.The effect of initial diffraction angle and cavity depth on the shock mitigation is investigated.A better shock attenuation is achieved with diffraction angle by a factor of approximately 17%in terms of shock-Mach number and 38%in terms of total energy.The obtained results show also,in addition to the initial diffraction angle and cavity depth,the importance of reducing the channel heights as well as the position of the reduced section in achieving an optimal shock-wave attenuation.The presence of a cavity inside the channel helps to attenuate faster the shock wave.The underlying physics relies on the shock diffraction phenomenon that generates large amount of vortical structures capable of dissipating part of the shock energy by inducing a pressure loss behind it.A subtle arrangement of channel position/height and a cavity location leads to an efficient pressure attenuation by approximately a factor of 57%forMs=1.6 and 16%for Ms=1.1..

Shock wave mitigation using zig-zag structures and cylindrical obstructions

The present study focuses on the mitigation of shock wave using novel geometric passages in the flow field.The strategy is to produce multiple shock reflections and diffractions in the passage with minimum flow obstruction,which in turn is expected to reduce the shock wave strength at the target location.In the present study the interaction of a plane shock front(generated from a shock tube)with various geometric designs such as,1)zig-zag geometric passage,2)staggered cylindrical obstructions and 3)zigzag passage with cylindrical obstructions have been investigated using computational technique.It is seen from the numerical simulation that,among the various designs,the maximum shock attenuation is produced by the zig-zag passage with cylindrical obstructions which is then followed by zig-zag passage and staggered cylindrical obstructions.A comprehensive investigation on the shock wave reflection and diffraction phenomena happening in the proposed complex passages have also been carried out.In the new zig-zag design,the initial shock wave undergoes shock wave reflection and diffraction process which swaps alternatively as the shock front moves from one turn to the other turn.This cyclic shock reflection and diffraction process helps in diffusing the shock wave energy with practically no obstruction to the flow field.It is found that by combining the shock attenuation ability of zig-zag passage(using shock reflection and diffraction)with the shock attenuation ability of cylindrical blocks(by flow obstruction),a drastic attenuation in shock strength can be achieved with moderate level of flow blocking.

A study on characteristics of shock train inside a shock tube

Shock tubes are devices which are used in the investigation of high speed and high temperature flow of compressible gas. lnside a shock tube, the interaction between the reflected shock wave and boundary layer leads to a complex flow phenomenon. Initially a normal shock wave is formed in the shock tube which migrates toward the closed end of the tube and that in turn leads to the reflection of shock. Due to the boundary layer interaction with the reflected shock, the bifurcation of shock wave takes place. The bifurcated shock wave then approaches the contact surface and shock train is generated. Till date only a few studies have been conducted to investigate this shock train phenomenon inside the shock tube. For the present study a computational fluid dynamics （CFD） analysis has been performed on a two dimensional axi-symmetric model of a shock tube using unsteady, compressible Navier-Stokes equations. In order to investigate the detailed characteristics of shock train, parametric studies have been performed by varying different parameters such as the shock tube length, diameter, pressure ratio used inside the shock tube.

A COMPARISON OF FOUR RECENT NUMERICAL SCHEMES GIViNG HIGH RESOLUTION OF SHOCK WAVE AND CONCENTRATED VORTEX

In recent ten years high resolution difference schenies for the computation of thefull unsteady Eulerian system of equations for invisid compressible gas finds celebratedprogress. This paper tests furtherly, by a complex two-dimensional unsteady problem,four recent schemes. to them attentions are paid. The test problem is the initial stageof a two-dimensional diffraction and reflection of a plane shock wave, impinging on arectangular obstacle. At whose top side there are two sharp corners, near which flow.parameters finds severe variation. There is occurrence of expansion fan with a centerand also concentrated vortices. To simulate them well, the schemes should have goodadaptivity. The special shock Mach number M,=2.068 is so chosen, that at this M,the partical velocity behind impinging shock in fixed coordinate system is just equal tothe speed of sound there, this condition also occurs along a curve in the region ofexpansion fan with a center at the corner. This can clarify the computational featureof different schemes in case,when one of the eigenvalues is just zero. Zero eigenvaluemay spoil some schemes locally. Graphical visualization of the computational resultsmay, show features of the tested schemes about the shock wave resolution, schemeviscosity, expansion wave and the ability. to simulate the process of the generation ofunsteadv concentrated vortex.

THE INTERACTION OF A SHOCK WAVE WITH THE BOUNDARY LAYER IN A REFLECTED SHOCK TUNNEL

The influence of a nontotal reflection on the interaction of a reflected shock wave with the boundary layer in a reflected shock tunnel has been investigated. The calculating method of the velocity, the temperature and the Mach number profiles in the boundary layer in reflected shock fixed coordinates has been obtained. To account for equilibrium real gas effects of nitrogen, the numerical results show that the minimum Mach number in the boundary layer has been moved from the wall into the boundary layer with the increasing of the incident shock Mach number. The minimum Mach number, the shock angle in the bifurcated foot and the jet velocity along the wall to the end plate are reduced owing to the Increasing of the area of nozzle throat. The numerical results are in good agreement with measurements.

The shape of incident shock wave in steady axisymmetric conical Mach reflection

For internal flow with supersonic inflow boundary conditions,a complicated oblique shock reflection may occur.Different from the planar shock reflection problem,where the shape of the incident shock can be a straight line,the shape of the incident shock wave in the inward-facing axisymmetric shock reflection in steady flow is an unknown curve.In this paper,a simple theoretical approach is proposed to determine the shape of this incident shock wave.The present theory is based on the steady Euler equations.When the assumption that the streamlines are straight lines at locations just behind the incident shock is adopted,an ordinary differential equation can be derived,and the shape of the incident shock wave is given by the solution of this ordinary differential equation.The predicted curves of the incident shock wave at several inlet conditions agree very well with the results of the numerical simulations.

Improving Solution of Euler Equations by a Gas-Kinetic BGK Method

Aim.The well known JST(Jameson-Schmidt-Turkel) scheme requires the use of a dissipation term.We propose using gas-kinetic BGK(Bhatnagar-Gross-Krook) method,which is based on the more fundamental Boltzmann equation,in order to obviate the use of dissipation term and obtain,we believe,an improved solution.Section 1 deals essentially with three things:(1) as analytical solution of molecular probability density function at the cell interface has been obtained by the Boltzmann equation with BGK model,we can compute the flux term by integrating the density function in the phase space;eqs.(8) and(11) require careful attention;(2) the integrations can be expressed as the moments of Maxwellian distribution with different limits according to the analytical solution;eqs.(9) and(10) require careful attention;(3) the discrete equation by finite volume method can be solved using the time marching method.Computations are performed by the BGK method for the Sod′s shock tube problem and a two-dimensional shock reflection problem.The results are compared with those of the conventional JST scheme in Figs.1 and 2.The BGK method provides better resolution of shock waves and other features of the flow fields.

Trajectory predictions of new lift separation sabots

This paper presents a modified analytical model to evaluate the trajectories of various lift separation sabot configurations.The aerodynamic forces acting on the sabot surfaces during a supersonic flight are modeled in the present analytical model by incorporating the pressures on the windward side of the sabot due to the detached/attached shock and its reflections and then integrated using the 3-DoF dynamical equations.The trajectory and the aerodynamic coefficients were obtained for these configurations at a projectile Mach number of 3.The sabot configurations,which include two new designs,are compared with each other and with the conventional free flight trajectory data of the conventional sabots.The mechanical interaction between the sabot and projectile is also addressed in the present work.The comparison shows that the new designs with the aerodynamic surfaces close to the center of gravity,lift-off from the projectile with minimal mechanical interaction compared to a conventional sabot.

Reflection of a moving shock wave over an oblique shock wave

The reflection of a moving shock wave over a wedge immersed in a still gas and the reflection of a wed ge induced steady shock wave over symmetrical and asymmetrical reflecting surfaces have received intensive considerations since more than 70 years ago.Here we consider a different shock reflection problem—reflection of a moving shock wave over an initially steady oblique shock wave induced by a wedge immersed in supersonic flow.For the flow condition we considered,five moving triple points,with each connecting an incident shock wave,a reflected shock wave and a Mach stem,are identified.By using the reference frame co-moving with each triple point,the type of each shock wave of this triple point is clarified.The present study is significant in that it treats a new shock reflection problem leading to a new shock reflection configuration and showing potential applications in supersonic flow with unsteady shock interaction.

Symmetric Mach reflection configuration with asymmetric unsteady solution

Symmetric Mach reflection in steady supersonic flow has been usually studied by solving a half-plane problem with the symmetric line treated as reflecting surface,thus losing the opportunity to discover antisymmetric flow structures.Here in this paper we treat this problem as an entire-plane problem.Using an unsteady numerical approach,we find that the two sliplines exhibit antisymmetric unsteadiness if the Mach stem height is small while the flow remains symmetric if the Mach stem height is large.The mechanism by which disturbance,generated in the downstream of the flow duct between the two sliplines,propagates upstream is identified and it is also shown that the interaction between the transmitted expansion waves and the sliplines increases the amplitude of the unstable modes.The present study suggests a new type of compressible jet that deserves further studies.

TWO-DIMENSIONAL RIEMANN PROBLEMS:FROM SCALAR CONSERVATION LAWS TO COMPRESSIBLE EULER EQUATIONS

In this paper we survey the authors＇ and related work on two-dimensional Riemann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four sections： 1. Historical review. 2. Scalar conservation laws. 3. Euler equations. 4. Simplified models.

Analysis of shock wave reflection from fixed and moving boundaries using a stabilized particle method

In the present paper, the efficiency of an enhanced formulation of the stabilized corrective smoothed particle method （CSPM） for simulation of shock wave propagation and reflection from fixed and moving solid boundaries in compressible fluids is investigated. The Lagrangian nature and its accuracy for imposing the boundary conditions are the two main reasons for adoption of CSPM. The governing equations are further modified for imposition of moving solid boundary conditions. In addition to the traditional artificial viscosity, which can remove numerically induced abnormal jumps in the field values, a velocity field smoothing technique is introduced as an efficient method for stabilizing the solution. The method has been implemented for one- and two-dimensional shock wave propagation and reflection from fixed and moving boundaries and the results have been compared with other available solutions. The method has also been adopted for simulation of shock wave propagation and reflection from infinite and finite solid boundaries.

Accuracy of the Adaptive GRP Scheme and the Simulation of 2-D Riemann Problems for Compressible Euler Equations

The adaptive generalized Riemann problem(GRP)scheme for 2-D compressible fluid flows has been proposed in[J.Comput.Phys.,229(2010),1448–1466]and it displays the capability in overcoming difficulties such as the start-up error for a single shock,and the numerical instability of the almost stationary shock.In this paper,we will provide the accuracy study and particularly show the performance in simulating 2-D complex wave configurations formulated with the 2-D Riemann problems for compressible Euler equations.For this purpose,we will first review the GRP scheme briefly when combined with the adaptive moving mesh technique and consider the accuracy of the adaptive GRP scheme via the comparison with the explicit formulae of analytic solutions of planar rarefaction waves,planar shock waves,the collapse problem of a wedge-shaped dam and the spiral formation problem.Then we simulate the full set of wave configurations in the 2-D four-wave Riemann problems for compressible Euler equations[SIAM J.Math.Anal.,21(1990),593–630],including the interactions of strong shocks(shock reflections),vortex-vortex and shock-vortex etc.This study combines the theoretical results with the numerical simulations,and thus demonstrates what Ami Harten observed"for computational scientists there are two kinds of truth:the truth that you prove,and the truth you see when you compute"[J.Sci.Comput.,31(2007),185–193].

Modified Form of Space-time Conservation Scheme

The space time conservation scheme is derived on the basis of Cartesian coordinates and rectang ular conservation cells. It is shown that the basic ideas of the scheme are consistent with the finite volume concept when the volume is considered in space time coordinates. This modified space time conservation scheme produces good results for shock reflection.