STEADY STATE SOLUTIONS OF THE EQUATION OF BURNING
Abstract
When a substance such as a low-order explosive or a propellant is ignited, the burning proceeds with a speed and temperature which are described by a certain partial differential equation. The general solution of this equation is not known. The present report deals with a special case of this equation, namely, the case of steady state, in which the burning progresses with uniform speed. We assume moreover that the burning substance has the shape of a thin rod of infinite length. The limitation to the steady-state case not only has the advantage of simplifying the problem mathematically, but it is interesting because in many practical cases the phenomenon of burning approaches the steady-state rapidly. Thus, the steady-state solutions presented in this report may also be thought of as limiting cases of more general solutions. Similarly the limitation to a thin infinite rod is made mostly because it simplifies the problem; but the solutions for many other shapes do not differ much from the ones obtained here. The present report considers both the case of a perfectly heat-insulated rod and that of a rod which loses heat to its surroundings. For the first case, all possible solutions are obtained; for the second case, the report is limited to the commonly observed ranges of values of flame speed, heat loss and room temperature. Within these limits, the various possible types of solutions are discussed and a small number of solutions are presented numerically so that other solutions may be obtained by interpolation.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 24, 1948
- Accession Number
- AD0818545
Entities
People
- Franz L. Alt
Organizations
- Ballistic Research Laboratory