Effects of Mach Number on Non-Rankine–Hugoniot Shock Zone of Mach Reflection

Haochen Liu; Hao Chen; Bin Zhang; Hong Liu

doi:10.2514/1.a34251

Turbulent jet in crossflow analysis with LES approach

Aircraft Engineering and Aerospace Technology ◽

10.1108/aeat-10-2014-0167 ◽

2016 ◽

Vol 88 (6) ◽

pp. 717-728 ◽

Cited By ~ 1

Author(s):

Mojtaba Tahani ◽

Mohammad Hojaji ◽

Seyed Vahid Mahmoodi Jezeh

Keyword(s):

Mach Number ◽

Free Stream ◽

Dynamic Pressure ◽

Pressure Ratio ◽

Content Type ◽

Order Polynomial ◽

Pressure Area ◽

Barrel Shock ◽

Free Stream Mach Number ◽

Shock Zone

Purpose This study aims to investigate effects of sonic jet injection into supersonic cross-flow (JISC) numerically in different dynamic pressure ratio values and free stream Mach numbers. Design/methodology/approach Large Eddy simulation (LES) with dynamic Smagorinsky model is used as the turbulence approach. The numerical results are compared with the experimental data, and the comparison shows acceptable validation. Findings According to the results, the dynamic pressure ratio has critical effects on the zone related to barrel shock. Despite free stream Mach number, increasing dynamic pressure ratio leads to expansion of barrel shock zone. Consequently, expanded barrel shock zone would bring about more obstruction effect. In addition, the height of counter-rotating vortex pair increases, and the high-pressure area before jet and low-pressure area after jet will rise. The results show that the position of barrel shock is deviated by increasing free stream Mach number, and the Bow shock zone becomes stronger and close to barrel shock. Moreover, high pressure zone, which is located before the jet, decreases by high free stream Mach number. Practical implications In this study, LES with a dynamic Smagorinsky model is used as the turbulence approach. Effects of sonic JISC are investigated numerically in different dynamic pressure ratio values and free stream Mach numbers. Originality/value As summary, the following are the contribution of this paper in the field of JISC subjects: several case studies of jet condition have been performed. In all the cases, the flow at the nozzle exit is sonic, and the free stream static pressure is constant. To generate proper grid, a cut cell method is used for domain modelling. Boundary condition effect on the wall pressure distribution around the jet and velocity profiles, especially S shape profiles, is investigated. The results show that the relation between representing the location of Mach disk centre and at transonic regime is a function of second-order polynomial, whereas at supersonic regime, the relationship is modelled as a first-order polynomial. In addition, the numerical results are compared with the experimental data demonstrating acceptable validation.

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Non-Rankine–Hugoniot Shock Zone of Mach Reflection in Hypersonic Rarefied Flows

Journal of Spacecraft and Rockets ◽

10.2514/1.a33411 ◽

2016 ◽

Vol 53 (4) ◽

pp. 619-628 ◽

Cited By ~ 10

Author(s):

Hao Chen ◽

Bin Zhang ◽

Hong Liu

Keyword(s):

Mach Reflection ◽

Rarefied Flows ◽

Shock Zone

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A new approach to problems of shock dynamics Part I Two-dimensional problems

Journal of Fluid Mechanics ◽

10.1017/s002211205700004x ◽

1957 ◽

Vol 2 (2) ◽

pp. 145-171 ◽

Cited By ~ 270

Author(s):

G. B. Whitham

Keyword(s):

Wave Propagation ◽

Mach Number ◽

Mach Reflection ◽

Linear Equations ◽

Plane Waves ◽

Propagation Speed ◽

Approximate Theory ◽

Two Dimensional ◽

Sound Waves ◽

Mathematical Techniques

In this paper, two-dimensional problems of the diffraction and stability of shock waves are investigated using an approximate theory in which disturbances to the flow are treated as a wave propagation on the shocks. These waves carry changes in the slope and the Mach number of the shock. The equations governing the wave propagation are analogous in every way to the non-linear equations for plane waves in gas dynamics, and their solutions can be deduced by the same mathematical techniques. Since the propagation speed of the waves is found to be an increasing function of Mach number, waves carrying an increase in Mach number will eventually break and form what we may call a ‘shock’, corresponding to the breaking of a compression wave into a shock in the ordinary plane wave case. Such a ‘shock’ moving on the shock is called ashock-shock.The shock-shock is a discontinuity in Mach number and shock slope, and it must be fitted in to satisfy the appropriate relations between these are interpreted as the trace of cylindrical sound waves in the flow behind the shock. In particular a shock-shock is the trace of a genuine shock in the flow behind, and thus corresponds to Mach reflection.The general theory of the wave propagation is set out in § 2. The subsequent sections contain applications of the theory to specific problems, including the motion of a shock along a curved wall, diffraction by a wedge, stability of plane shocks and the instability of a converging cylindrical shock.

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Shock transformation and hysteresis in underexpanded confined jets

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.231 ◽

2017 ◽

Vol 823 ◽

pp. 538-561 ◽

Cited By ~ 3

Author(s):

R. Arun Kumar ◽

G. Rajesh

Keyword(s):

Experimental Study ◽

Mach Number ◽

Total Pressure ◽

Mach Reflection ◽

Internal Flow ◽

Incident Shock ◽

Pressure Variation ◽

Regular Reflection ◽

Confined Jets ◽

Underexpanded Jet

This study investigates the shock transformation in an underexpanded jet in a confined duct when the jet total pressure is increased. Experimental study reveals that the Mach reflection (MR) in the fully underexpanded jet transforms to a regular reflection (RR) at a certain jet total pressure. It is observed that neither the incident shock angle nor the upstream Mach number varies during the MR–RR shock transformation. This is in contradiction to the classical MR–RR transformations in internal flow over wedges and in underexpanded open jets. This transformation is found to be a total pressure variation induced transformation, which is a new kind of shock transformation. The present study also reveals that the critical jet total pressures for MR–RR and RR–MR transformations are not the same when the primary pressure is increasing and decreasing, suggesting a hysteresis in the shock transformations.

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Osher Flux with Entropy Fix for Two-Dimensional Euler Equations

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.2014.m469 ◽

2016 ◽

Vol 8 (4) ◽

pp. 670-692 ◽

Cited By ~ 1

Author(s):

Huajun Zhu ◽

Xiaogang Deng ◽

Meiliang Mao ◽

Huayong Liu ◽

Guohua Tu

Keyword(s):

Mach Number ◽

Euler Equations ◽

Mach Reflection ◽

Finite Volume Methods ◽

Second Order ◽

Two Dimensional ◽

First Order ◽

Shock Stability ◽

Double Mach Reflection ◽

High Mach

AbstractWe compare in this paper the properties of Osher flux with O-variant and P-variant (Osher-O flux and Osher-P flux) in finite volume methods for the two-dimensional Euler equations and propose an entropy fix technique to improve their robustness. We consider both first-order and second-order reconstructions. For inviscid hypersonic flow past a circular cylinder, we observe different problems for different schemes: A first-order Osher-O scheme on quadrangular grids yields a carbuncle shock, while a first-order Osher-P scheme results in a dislocation shock for high Mach number cases. In addition, a second-order Osher scheme can also yield a carbuncle shock or be unstable. To improve the robustness of these schemes we propose an entropy fix technique, and then present numerical results to show the effectiveness of the proposed method. In addition, the influence of grid aspects ratio, relative shock position to the grid and Mach number on shock stability are tested. Viscous heating problem and double Mach reflection problem are simulated to test the influence of the entropy fix on contact resolution and boundary layer resolution.

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