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.

Analysis of Transient Two-Phase Flow in Pressure Safety Valve Outlet Headers

2018 ◽  
Author(s):  
Maral Taghva ◽  
Lars Damkilde
Keyword(s):  
Steady State ◽  
Shock Waves ◽  
High Speed ◽  
Two Phase Flow ◽  
Safety Valve ◽  
Strong Shock ◽  
Flow Property ◽  
Phase Flow ◽  
Transient Pressure ◽  
Two Phase

To protect a pressurized system from overpressure, one of the most established strategies is to install a Pressure Safety Valve (PSV). Therefore, the excess pressure of the system is relieved through a vent pipe when PSV opens. The vent pipe is also called “PSV Outlet Header”. After the process starts, a transient two-phase flow is formed inside the outlet header consisting of high speed pressurized gas interacting with existing static air. The high-speed jet compresses the static air towards the end tail of the pipe until it is discharged to the ambiance and eventually, the steady state is achieved. Here, this transient process is investigated both analytically and numerically using the method of characteristics. Riemann’s solvers and Godunov’s method are utilized to establish the solution. Propagation of shock waves and flow property alterations are clearly demonstrated throughout the simulations. The results show strong shock waves as well as high transient pressure take place inside the outlet header. This is particularly important since it indicates the significance of accounting for shock waves and transient pressure, in contrast to commonly accepted steady state calculations. More precisely, shock waves and transient pressure could lead to failure, if the pipe thickness is chosen only based on conventional steady state calculations.

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).

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.

Paper 14: Numerical Solutions of Flows behind Shock Waves in Non-Uniform Regions

1969 ◽  
Vol 184 (7) ◽  
pp. 36-44
Author(s):  
J. Gururaja ◽  
B. E. L. Deckker
Keyword(s):  
Shock Waves ◽  
High Speed ◽  
Numerical Solutions ◽  
Computing Time ◽  
Sudden Change ◽  
Two Dimensional ◽  
Cell Method ◽  
Flow Problems ◽  
Pressure Time ◽  
Machine Calculation

Different computational schemes for the calculation of multi-dimensional non-stationary problems of gas dynamics with shock waves present are reviewed. A differencing scheme developed in the last few years at the Los Alamos Scientific Laboratory, known as the ‘fluid-in-cell’ method, has been employed to obtain numerical solutions for the time-dependent two-dimensional flows initiated by the passage of a shock wave in a duct with either a gradual or sudden change in cross-section and in a branched duct. The numerical results have been displayed in the form of contours of density, pressure, and internal energy. The main features of the computed solutions have been compared with the experimental flow patterns obtained by the authors. Comparison of pressure–time records shows good agreement. The fluid-in-cell method is well suited for machine calculation on a high-speed electronic computer and can treat unsteady two-dimensional compressible flow problems involving a single material within closed boundaries, without excessive demands on storage and computing time.

Two-Dimensional Heat Transfer Considerations for Thermoreflectance Measurements

2018 ◽  
Author(s):  
Dipta Sarkar ◽  
Partha Pratim Chakraborty ◽  
B. Terry Beck ◽  
Zayd C. Leseman
Keyword(s):  
Steady State ◽  
Heat Equation ◽  
Continuous Wave ◽  
Dirichlet Boundary Conditions ◽  
Transient Condition ◽  
Neumann Condition ◽  
Two Dimensional ◽  
Laser Beam Intensity ◽  
Steady State Condition ◽  
Dimensional Approximation

In the Suspended ThermoReflectance (STR) technique a microcantilever is heated with a laser power at the free end of the microcantilever and as heat propagates through it, another laser is used to measure the temperature along the beam.[1] In this paper, the heat equation is solved for two-dimensional heat flow in the microcantilever to determine the material’s thermal conductivity and heat capacity. Two of the dimensions of the microcantilever, width and length, are significantly greater than the third dimension, the thickness, leading to the two-dimensional approximation. Two boundaries along the length of the structure and one boundary along the width are assumed to be under Dirichlet boundary conditions, while the other boundary has Neumann condition. The Neumann or flux condition has a Gaussian profile due to the nature of laser beam intensity. The heat equation is solved using under 3 different flux conditions: (1) Steady-state, (2) Transient, and (3) Periodic. A steady-state condition mimics the experimental condition when a continuous wave laser is used to heat the microcantilever’s tip. A transient condition is possible when quickly removing or adding the continuous wave laser’s flux from the microcantilever’s tip using a chopper. Finally, a periodic condition can be achieved when an electro-optic modulator is utilized experimentally. Closed form analytical expressions are evaluated against the finite element model and experimental results for microcantilever beams and micro-structures of Si that have lengths on the order of a mm, width on the order of 100 microns, and thicknesses of 1 micron or less.

Steady Mach reflection with two incident shock waves

2018 ◽  
Vol 855 ◽  
pp. 882-909 ◽  
Author(s):  
Xiao-Ke Guan ◽  
Chen-Yuan Bai ◽  
Zi-Niu Wu
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Mach Reflection ◽  
Lower Surface ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Neumann Condition ◽  
Mach Stem ◽  
Stem Height ◽  
Reflecting Surface

Mach reflection in steady supersonic flow with two incident shock waves is studied. The second incident shock wave is produced by an additional deflection of the wedge lower surface, at some point ensuring that the two incident shock waves would intersect at the reflecting surface in case of normal reflection. Both theory and computational fluid dynamics (CFD) are used to study the flow structure and the influence of the second incident shock wave. The overall flow configuration, in case of Mach reflection, is shown to be composed of a triple shock structure, a shock/shock interaction structure and a shock/slipline reflection structure. Similar phenomenon, triggered by a high downstream pressure, has been observed before numerically, but not studied theoretically. The second incident shock wave reflects over the slipline to deflect the slipline more towards the reflecting surface, increasing thus the Mach stem height, advancing the transition of regular reflection to Mach reflection of the first incident shock wave, and causing an inverted Mach reflection below the usual von Neumann condition. A Mach stem height model built for a weak second incident shock wave is used to study the influence of the second incident shock wave on the Mach stem height. Both theory and CFD predict a maximum of the Mach stem height at some additional wedge deflection angle.

Characteristics of Two-Dimensional Radiation behind Strong Shock Waves in Air(1st Report) Total Radiation Emission.

1997 ◽  
Vol 45 (523) ◽  
pp. 453-457
Author(s):  
Toshihiro MORIOKA ◽  
Yoshiki MATSUURA ◽  
Nariaki SAKURAI ◽  
Jorge KOREEDA ◽  
Kazuo MAENO ◽  
...  
Keyword(s):  
Shock Waves ◽  
Strong Shock ◽  
Two Dimensional ◽  
Total Radiation ◽  
Radiation Emission ◽  
Strong Shock Waves
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