Analytical solution of double-Mach reflection

G. Ben-Dor

doi:10.2514/3.7708

Analytical solution of double-Mach reflection

G. Ben-Dor

Department of Mechanical Engineering

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

The double-Mach reflection (DMR) of oblique shock waves in pseudo-stationary flows has been investigated. The equations of motion of the first and second triple point were formulated, as well as the relative motion between these two triple points. The equation of motion for each triple point consists of 14 nonlinear algebraic equations. An analytical method of solution is presented. Consequently, for the first time a complete analytical solution of a DMR is given. Utilizing this analytical solution a method for predicting the second triple-point trajectory angle is developed. The analytical results are compared with experiments that were performed on the 10 × 18 cm Hypervelocity Shock Tube at the University of Toronto Institute for Aeronautical Studies. Good agreement was obtained.

Original language	English
Pages (from-to)	1036-1043
Number of pages	8
Journal	AIAA Journal
Volume	18
Issue number	9
DOIs	https://doi.org/10.2514/3.7708
State	Published - 1 Jan 1980

ASJC Scopus subject areas

Aerospace Engineering

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10.2514/3.7708

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title = "Analytical solution of double-Mach reflection",

abstract = "The double-Mach reflection (DMR) of oblique shock waves in pseudo-stationary flows has been investigated. The equations of motion of the first and second triple point were formulated, as well as the relative motion between these two triple points. The equation of motion for each triple point consists of 14 nonlinear algebraic equations. An analytical method of solution is presented. Consequently, for the first time a complete analytical solution of a DMR is given. Utilizing this analytical solution a method for predicting the second triple-point trajectory angle is developed. The analytical results are compared with experiments that were performed on the 10 × 18 cm Hypervelocity Shock Tube at the University of Toronto Institute for Aeronautical Studies. Good agreement was obtained.",

author = "G. Ben-Dor",

note = "Funding Information: The experimental work reported in this paper was performed at the University of Toronto Institute for Aerospace Studies. I wish to thank I. I. Glass of UTIAS for his invaluable help during the course of this project. His advice and suggestions are gratefully acknowledged. The financial assistance from the National Research Council of Canada and the U.S. Air Force under Contract AF-AFOSR 77-3303 is gratefully acknowledged. I also wish to thank M. Kline for her assistance.",

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N2 - The double-Mach reflection (DMR) of oblique shock waves in pseudo-stationary flows has been investigated. The equations of motion of the first and second triple point were formulated, as well as the relative motion between these two triple points. The equation of motion for each triple point consists of 14 nonlinear algebraic equations. An analytical method of solution is presented. Consequently, for the first time a complete analytical solution of a DMR is given. Utilizing this analytical solution a method for predicting the second triple-point trajectory angle is developed. The analytical results are compared with experiments that were performed on the 10 × 18 cm Hypervelocity Shock Tube at the University of Toronto Institute for Aeronautical Studies. Good agreement was obtained.

AB - The double-Mach reflection (DMR) of oblique shock waves in pseudo-stationary flows has been investigated. The equations of motion of the first and second triple point were formulated, as well as the relative motion between these two triple points. The equation of motion for each triple point consists of 14 nonlinear algebraic equations. An analytical method of solution is presented. Consequently, for the first time a complete analytical solution of a DMR is given. Utilizing this analytical solution a method for predicting the second triple-point trajectory angle is developed. The analytical results are compared with experiments that were performed on the 10 × 18 cm Hypervelocity Shock Tube at the University of Toronto Institute for Aeronautical Studies. Good agreement was obtained.

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Analytical solution of double-Mach reflection

Abstract

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