Investigating focusing of Mach waves by Prandtl-Meyer expansion fan as an explanation for some spatiospectral lobe phenomena

2019 ◽  
Vol 146 (4) ◽  
pp. 3000-3000
Author(s):  
S. Hales Swift ◽  
Kent L. Gee
Keyword(s):  
Expansion Fan ◽  
Mach Waves

Size and shape of shock waves and slipline for Mach reflection in steady flow

2017 ◽  
Vol 818 ◽  
pp. 116-140 ◽  
Author(s):  
Chen-Yuan Bai ◽  
Zi-Niu Wu
Keyword(s):  
Shock Wave ◽  
Turning Point ◽  
Mach Reflection ◽  
Weak Shock ◽  
Weak Shock Wave ◽  
Reflected Shock Wave ◽  
Reflected Shock ◽  
Expansion Fan ◽  
Slope Discontinuity ◽  
Mach Waves

For Mach reflection in steady supersonic flow, the slipline and reflected shock wave from the triple point are disturbed by secondary Mach waves generated over the slipline and by the expansion fan from the rear wedge corner. Analytical expressions for the shape of the curved slipline and reflected shock wave are derived in this paper. It is found that, due to transmitted expansion waves from the expansion fan, the slipline has a slope discontinuity at the turning point, i.e., the intersection point of the slipline and the leading characteristics of the transmitted expansion wave. The hypothetical shock wave calculated by considering this slope discontinuity as flow deflection angle matches a similar wave observed in numerical results by computational fluid dynamics, suggesting the existence of a weak shock wave from this turning point. The effects of the secondary Mach waves upstream of the turning point and of the turning point weak shock wave mutually cancel out approximately so that the transmitted Mach waves can be approximated as straight characteristic lines. This simplification leads to a fast analytical model which can predict the Mach stem height and shape of the slipline and reflected shock wave with increasing accuracy for the decreasing deflection angle of the slipline at the triple point. The slipline slope discontinuity at the turning point and the hypothetical turning point weak shock wave are new phenomena found in this work.

On expansion waves generated by the refraction of a plane shock at a gas interface

1967 ◽  
Vol 30 (2) ◽  
pp. 385-402 ◽  
Author(s):  
L. F. Henderson
Keyword(s):  
Expansion Wave ◽  
Plane Shock ◽  
Wave System ◽  
Expansion Waves ◽  
Reflected Wave ◽  
Expansion Fan ◽  
New Type ◽  
Self Similar ◽  
Fixed Boundaries ◽  
Mapping Theory

The paper deals with the regular refraction of a plane shock at a gas interface for the particular case where the reflected wave is an expansion fan. Numerical results are presented for the air–CH4 and air–CO2 gas combinations which are respectively examples of ‘slow–fast’ and ‘fast–slow’ refractions. It is found that a previously unreported condition exists in which the reflected wave solutions may be multi-valued. The hodograph mapping theory predicts a new type of regular–irregular transition for a refraction in this condition. The continuous expansion wave type of irregular refraction is also examined. The existence of this wave system is found to depend on the flow being self-similar. By contrast the expansion wave becomes centred when the flow becomes steady. Transitions within the ordered set of regular solutions are examined and it is shown that they may be either continuous or discontinuous. The continuous types appear to be associated with fixed boundaries and the discontinuous types with movable boundaries. Finally, a number of almost linear relations between the wave strengths are noted.

scholarly journals Fluid Dynamics Android Application: An Efficient Semi-Implicit Solver for Compressible Flows

2019 ◽  
Author(s):  
Shivam Singhal ◽  
Yayati Gupta ◽  
Ashish Garg
Keyword(s):  
Fluid Dynamics ◽  
Numerical Methods ◽  
Language Learning ◽  
Compressible Flows ◽  
General Purpose ◽  
Android Application ◽  
Standard Atmosphere ◽  
Expansion Fan ◽  
Implicit Solver ◽  
Isentropic Flows

The computing power of smartphones has not received considerable attention in the mainstream education system. Most of the education-oriented smartphone applications (apps) are limited to general purpose services like Massive Open Online Courses (MOOCs), language learning, and calculators (performing basic mathematical calculations). Greater potential of smartphones lies in educators and researchers developing their customized apps for learners in highly specific domains. In line with this, we present Fluid Dynamics, a highly accurate Android application for measuring flow properties in compressible flows. This app can determine properties across the stationary normal and oblique shock, moving normal shock and across Prandtl $-$ Meyer expansion fan. This app can also measure isentropic flows, Fanno flows, and Rayleigh flows. The functionality of this app is also extended to calculate properties in the atmosphere by assuming the International Standard Atmosphere (ISA) relations and also flows across the Pitot tube. Such measurements are complicated and time-consuming since the relations are implicit and hence require the use of numerical methods, which give rise to repetitive calculations. The app is an efficient semi-implicit solver for gas dynamics formulations and uses underlying numerical methods for the computations in a graphical user interface (GUI), thereby easing and quickening the learning of concerned users. The app is designed for the Android operating system, the most ubiquitous and capable surveillance platform, and its calculations are based on JAVA based code methodology. In order to check its accuracy, the app's results are validated against the existing data given in the literature.

scholarly journals Experimental and finite difference modelling of borehole mach waves

1992 ◽  
Author(s):  
N. Cheng ◽  
Z. Chu ◽  
C. H. Cheng ◽  
M. N. Toksoz
Keyword(s):  
Finite Difference ◽  
Mach Waves

scholarly journals Visualization of interaction of Mach waves with a bow shock

2017 ◽  
Author(s):  
Al. Pavlov ◽  
M. Golubev ◽  
A. Kosinov ◽  
A. Pavlov
Keyword(s):  
Bow Shock ◽  
Mach Waves

The boundary layer interaction with shock wave and expansion fan

2000 ◽  
Vol 9 (2) ◽  
pp. 109-114 ◽  
Author(s):  
Marat A. Goldfeld ◽  
Roman V. Nestoulia ◽  
Alexei V. Starov
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Layer Interaction ◽  
Boundary Layer Interaction ◽  
Expansion Fan

scholarly journals Steepened Mach waves near supersonic jets: study of azimuthal structure and generation process using conditional averages

2019 ◽  
Vol 880 ◽  
pp. 594-619 ◽  
Author(s):  
Pierre Pineau ◽  
Christophe Bogey
Keyword(s):  
Acoustic Waves ◽  
Large Scale ◽  
Flow Direction ◽  
Temporal Analysis ◽  
Wave Radiation ◽  
Flow Structures ◽  
Positive Pressure ◽  
Generation Process ◽  
Azimuthal Mode ◽  
Mach Waves

The azimuthal structure and the generation process of steepened acoustic waves are investigated in the near field of temporal round jets at Mach numbers of 2 and 3. Initially, the shear layers of the jets are in a laminar state and display instability waves whose main properties are close to those predicted from linear temporal analysis. Then, they transition to a turbulent state and generate high-intensity Mach waves displaying sharp compressions typical of those recorded for jets producing crackle noise. These waves are first shown to be poorly reproduced when only the axisymmetric mode is considered, but to be well captured with the first five azimuthal modes. Their generation process is investigated by performing conditional averages of the flow and acoustic fields triggered by the detection of intense positive pressure peak close to the jets. No steepened waves are visible in the conditionally averaged pressure profiles when the procedure involves only one azimuthal mode at a time. However, sharp compressions are obtained based on the first five modes taken together. In that case, the steep compressions are correlated over a limited portion of the jet circumference and are steeper as more azimuthal modes are considered. Moreover, a direct link is established between the steepened waves and the supersonic convection of large-scale coherent flow structures located in the supersonic core of the jets. This indicates that these waves constitute an extreme, nonlinear case of Mach wave radiation by these structures. In addition, the capacity of flow structures to generate sharp, steepened waves is related to their shapes. More particularly, flow structures with a large extent in the radial direction are shown to produce stronger and steeper Mach waves than those that are elongated in the flow direction.

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