A POINT EXPLOSION IN A COLD EXPONENTIAL ATMOSPHERE,
Abstract
The problem considered is that of a strong shock propagating from a point energy source into a cold atmosphere whose density varies exponentially with altitude. An explicit analytic solution is obtained by taking the flow field as 'locally radial' and using an integral method with an energy constraint. A scaling law is given which eliminates the parametric dependence of the solution on the explosion energy, scale height, and atmospheric density at the point of the explosion. The scaling law also transforms the infinity of solutions for various polar angles into two distinct solutions which show that all motions of the ascending portion of the shock may be scaled from the vertically upward behavior and all motions of the descending portion of the shock may be scaled from the vertically downward behavior. The limit in the lateral direction of both of the fundamental solutions corresponds to the case of the uniform density atmosphere. Comparison with finite difference calculations shows excellent agreement. The empirical concept of 'modified Sachs scaling' for calculating the overpressure is considered and shown within this model to have a justification in the downward direction but a limited range of applicability in the upward direction. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1968
- Accession Number
- AD0671931
Entities
People
- Dallas D. Laumbach
- Ronald F. Probstein
Organizations
- Massachusetts Institute of Technology