scholarly journals On a stabilization mechanism for low-velocity detonations

2017 ◽  
Vol 816 ◽  
pp. 539-553 ◽  
Author(s):  
Aliou Sow ◽  
Roman E. Semenko ◽  
Aslan R. Kasimov
Keyword(s):  
Steady State ◽  
Shock Waves ◽  
Euler Equations ◽  
Nonlinear Stability ◽  
Heat Losses ◽  
Stabilization Mechanism ◽  
Low Velocity ◽  
One Dimensional ◽  
Gaseous Detonations ◽  
Reactive Euler Equations

We use numerical simulations of the reactive Euler equations to analyse the nonlinear stability of steady-state one-dimensional solutions for gaseous detonations in the presence of both momentum and heat losses. Our results point to a possible stabilization mechanism for the low-velocity detonations in such systems. The mechanism stems from the existence of a one-parameter family of solutions found in Semenko et al. (Shock Waves, vol. 26 (2), 2016, pp. 141–160).

scholarly journals Modern infinitesimals and the entropy jump across an inviscid shock wave

2018 ◽  
Vol 17 (4-5) ◽  
pp. 502-520
Author(s):  
Roy S Baty ◽  
Len G Margolin
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Euler Equations ◽  
Nonstandard Analysis ◽  
Generalized Solutions ◽  
Perfect Gas ◽  
One Dimensional ◽  
Number Systems ◽  
Shock Thickness ◽  
Modern Mathematics

This article applies nonstandard analysis to study the generalized solutions of entropy and energy across one-dimensional shock waves in a compressible, inviscid, perfect gas. Nonstandard analysis is an area of modern mathematics that studies number systems that contain both infinitely large and infinitely small numbers. For an inviscid shock wave, it is assumed that the shock thickness occurs on an infinitesimal interval and that the jump functions for the field variables are smoothly defined on this interval. A weak converse to the existence of the entropy peak is derived and discussed. Generalized solutions of the Euler equations for entropy and energy are then derived for both theoretical and realistic normalized velocity profiles.

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