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# Accession Number:

## ADA090776

# Title:

## Fast Deflagration Waves.

# Descriptive Note:

## Interim technical rept.,

# Corporate Author:

## CORNELL UNIV ITHACA NY DEPT OF THEORETICAL AND APPLIED MECHANICS

# Report Date:

## 1980-07-01

# Pagination or Media Count:

##
45.0

# Abstract:

## The analysis of steady plane deflagration waves invariably starts with the combustion approximation where it is assumed that the Mach number, i.e. the flame speed divided by a characteristic sound speed, is vanishingly small. The momentum equation then implies that the pressure is nearly constant while the thermal and mechanical descriptions of the wave decouple, so that the task of solving for the structure is greatly simplified. Even then explicit formulas can only be obtained in the limit of large activation energy. We are currently interested in describing, by means of activation-energy asymptotics as far as possible, the transition from deflagration to detonation in gases. One of the first steps in such a theory is to analyze deflagration waves whose Mach numbers are not vanishingly small. Pressure variations cannot be neglected and hence the momentum equation must be retained in the description of the structure. We will show, in the present paper, that the method of activation-energy asymptotics gives an analytic description of these fast deflagrations, i.e. deflagrations travelling at speeds greater than those justifying the use of the combustion approximation. In addition we examine the limit of vanishingly small Mach number to shed light on the nature of the combustion approximation.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#