Transition from regular to Mach reflection of shock waves Part 2. The steady-flow criterion

1982 ◽  
Vol 123 ◽  
pp. 155-164 ◽  
Author(s):  
H. G. Hornung ◽  
M. L. Robinson
Keyword(s):  
Shock Waves ◽  
Steady Flow ◽  
Mach Reflection ◽  
Strong Shock ◽  
Hysteresis Effect ◽  
Neumann Condition ◽  
Flow Transition ◽  
Von Neumann ◽  
Mach Numbers ◽  
Flow Criterion

It is shown experimentally that, in steady flow, transition to Mach reflection occurs at the von Neumann condition in the strong shock range (Mach numbers from 2.8 to 5). This criterion applies with both increasing and decreasing shock angle, so that the hysteresis effect predicted by Hornung, Oertel & Sandeman (1979) could not be observed. However, evidence of the effect is shown to be displayed in an unsteady experiment of Henderson & Lozzi (1979).

Derivation of the critical angle for Mach reflection for strong shock waves

1992 ◽  
Vol 45 (8) ◽  
pp. 6130-6132 ◽  
Author(s):  
M. De Rosa ◽  
F. Famà ◽  
V. Palleschi ◽  
D. P. Singh ◽  
M. Vaselli
Keyword(s):  
Shock Waves ◽  
Critical Angle ◽  
Mach Reflection ◽  
Strong Shock ◽  
Strong Shock Waves

The persistence of regular reflection during strong shock diffraction over rigid ramps

2001 ◽  
Vol 431 ◽  
pp. 273-296 ◽  
Author(s):  
L. F. HENDERSON ◽  
K. TAKAYAMA ◽  
W. Y. CRUTCHFIELD ◽  
S. ITABASHI
Keyword(s):  
Stokes Equations ◽  
Mach Reflection ◽  
Strong Shock ◽  
Navier Stokes ◽  
Regular Reflection ◽  
Navier Stokes Equations ◽  
Von Neumann ◽  
Initial Appearance ◽  
Self Similar ◽  
Initial Shock

We report on calculations and experiments with strong shocks diffracting over rigid ramps in argon. The numerical results were obtained by integrating the conservation equations that included the Navier–Stokes equations. The results predict that if the ramp angle θ is less than the angle θe that corresponds to the detachment of a shock, θ < θe, then the onset of Mach reflection (MR) will be delayed by the initial appearance of a precursor regular reflection (PRR). The PRR is subsequently swept away by an overtaking corner signal (cs) that forces the eruption of the MR which then rapidly evolves into a self-similar state. An objective was to make an experimental test of the predictions. These were confirmed by twice photographing the diffracting shock as it travelled along the ramp. We could get a PRR with the first exposure and an MR with the second. According to the von Neumann perfect gas theory, a PRR does not exist when θ < θe. A viscous length scale xint is a measure of the position on the ramp where the dynamic transition PRR → MR takes place. It is significantly larger in the experiments than in the calculations. This is attributed to the fact that fluctuations from turbulence and surface roughness were not modelled in the calculations. It was found that xint → ∞ as θ → θe. Experiments were done to find out how xint depended on the initial shock tube pressure p0. The dependence was strong but could be greatly reduced by forming a Reynolds number based on xint. Finally by definition, regular reflection (RR) never interacts with a boundary layer, while PRR always interacts; so they are different phenomena.

Transition study for asymmetric reflection between moving incident shock waves

2021 ◽  
Vol 929 ◽  
Author(s):  
Miao-Miao Wang ◽  
Zi-Niu Wu
Keyword(s):  
Shock Waves ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Neumann Condition ◽  
Plane Shock ◽  
Von Neumann ◽  
Transition Criteria ◽  
Shock Motion ◽  
Reduced Problem

The transition criteria seen from the ground frame are studied in this paper for asymmetrical reflection between shock waves moving at constant linear speed. To limit the size of the parameter space, these criteria are considered in detail for the reduced problem where the upper incident shock wave is moving and the lower one is steady, and a method is provided for extension to the general problem where both the upper and lower ones are unsteady. For the reduced problem, we observe that, in the shock angle plane, shock motion lowers or elevates the von Neumann condition in a global way depending on the direction of shock motion, and this change becomes less important for large shock angle. The effect of shock motion on the detachment condition, though small, displays non-monotonicity. The shock motion changes the transition criteria through altering the effective Mach number and shock angle, and these effects add for small shock angle and mutually cancel for large shock angle, so that shock motion has a less important effect for large shock angle. The role of the effective shock angle is not monotonic on the detachment condition, explaining the observed non-monotonicity for the role of shock motion on the detachment condition. Furthermore, it is found that the detachment condition has a wavefunction form that can be approximated as a hybrid of a sinusoidal function and a linear function of the shock angle.

A Switch Function-Based Gas-Kinetic Scheme for Simulation of Inviscid and Viscous Compressible Flows

2016 ◽  
Vol 8 (5) ◽  
pp. 703-721 ◽  
Author(s):  
Yu Sun ◽  
Chang Shu ◽  
Liming Yang ◽  
C. J. Teo
Keyword(s):  
Shock Waves ◽  
Compressible Flows ◽  
Stokes Equations ◽  
Mach Reflection ◽  
Strong Shock ◽  
Kinetic Scheme ◽  
Numerical Dissipation ◽  
Flow Problems ◽  
Viscous Compressible Flows ◽  
Strong Shock Waves

AbstractIn this paper, a switch function-based gas-kinetic scheme (SF-GKS) is presented for the simulation of inviscid and viscous compressible flows. With the finite volume discretization, Euler and Navier-Stokes equations are solved and the SF-GKS is applied to evaluate the inviscid flux at cell interface. The viscous flux is obtained by the conventional smooth function approximation. Unlike the traditional gas-kinetic scheme in the calculation of inviscid flux such as Kinetic Flux Vector Splitting (KFVS), the numerical dissipation is controlled with a switch function in the present scheme. That is, the numerical dissipation is only introduced in the region around strong shock waves. As a consequence, the present SF-GKS can well capture strong shock waves and thin boundary layers simultaneously. The present SF-GKS is firstly validated by its application to the inviscid flow problems, including 1-D Euler shock tube, regular shock reflection and double Mach reflection. Then, SF-GKS is extended to solve viscous transonic and hypersonic flow problems. Good agreement between the present results and those in the literature verifies the accuracy and robustness of SF-GKS.

scholarly journals Transition to Mach reflexion of shock waves in steady and pseudosteady flow with and without relaxation

1979 ◽  
Vol 90 (3) ◽  
pp. 541-560 ◽  
Author(s):  
H. G. Hornung ◽  
H. Oertel ◽  
R. J. Sandeman
Keyword(s):  
Steady Flow ◽  
Dynamic Equilibrium ◽  
Neumann Condition ◽  
Relaxation Length ◽  
Displacement Effect ◽  
Von Neumann ◽  
Transition Condition ◽  
Reflected Shock ◽  
Relaxation Effects ◽  
Mach Reflexion

Experiments were conducted in the free-piston shock tube and shock tunnel with dissociating nitrogen and carbon dioxide, ionizing argon and frozen argon to measure the transition condition in pseudosteady and steady flow. The transition condition in the steady flow, in which the wall was eliminated by symmetry, agrees with the calculated von Neumann condition. In the real gases this calculation assumed thermo-dynamic equilibrium after the reflected shock. In the pseudosteady flow of reflexion from a wedge the measured transition angle lies on the Mach-reflexion side of the calculated detachment condition by an amount which may be explained in terms of the displacement effect of the boundary layer on the wedge surface. A single criterion based on the availability of a length scale at the reflexion point explains the difference between the pseudosteady and steady flow transition condition and predicts a hysteresis effect in the transition angle when the shock angle is varied during steady flow. No significant effects on the transition condition due to finite relaxation length could be detected. However, new experiments in which interesting relaxation effects should be evident are suggested.

Dynamic effects on the transition between two-dimensional regular and Mach reflection of shock waves in an ideal, steady supersonic free stream

2011 ◽  
Vol 676 ◽  
pp. 432-460 ◽  
Author(s):  
K. NAIDOO ◽  
B. W. SKEWS
Keyword(s):  
Steady State ◽  
Shock Waves ◽  
Experimental Evidence ◽  
High Speed ◽  
Mach Reflection ◽  
Neumann Condition ◽  
Two Dimensional ◽  
Reflection Transition ◽  
Strong Reflection ◽  
Transition Criteria

There have been numerous studies on the steady-state transition criteria between regular and Mach reflection of shock waves generated by a stationary, two-dimensional wedge in a steady supersonic flow, since the original shock-wave reflection research by Ernst Mach in 1878. The steady, two-dimensional transition criteria between regular and Mach reflection are well established. There has been little done to consider the dynamic effect of a rapidly rotating wedge on the transition between regular and Mach reflection. This paper presents the results of an investigation on the effect of rapid wedge rotation on regular to Mach reflection transition in the weak- and strong-reflection ranges with the aid of experiment and computational fluid dynamics. The experimental set-up includes a novel facility to rotate a pair of large aspect ratio wedges in a 450 mm × 450 mm supersonic wind tunnel at wedge rotation speeds up to 11000 deg s−1. High-speed images and measurements are presented. A numerical solution of the inviscid governing flow equations was used to mimic the experimental motion and to extend the investigation beyond the limits of the current facility to explore the influence of variables in the parameter space. There is good agreement between experimental measurements and numerical simulation. This paper includes the first experimental evidence of the regular to Mach reflection transition beyond the steady-state detachment condition in the weak- and strong-reflection ranges. It also presents results of simulations for the dynamic regular to the Mach reflection transition which show a difference between the sonic, length-scale and detachment conditions. This paper includes experimental evidence of the Mach to regular reflection transition below the steady-state von Neumann condition.

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