Semiempirical calculations of the interaction of a slightly underexpanded jet with a quiescent atmosphere

Abstract

Nomenclature a= speed of the sound; also (7 -l)/(y + 1), Eq. (10) c p = specific heat at constant pressure h = specific static enthalpy M* = Mach number based on the critical speed of the sound n,p = p e /po and pressure, respectively pt f = stagnation pressure behind a normal shock r b) r e = local jet boundary and nozzle exit radii, respectively T = temperature v = velocity in the x direction X,Y = axial and radial coordinates, respectively x,y,y = X/r e , Y/r e , and F/r&, respectively j8 = free mixing length coefficient y = specific heat ratio /*,p = molecular weight and density, respectively Subscripts b,c,e = jet boundary, centerline, and nozzle exit, respectively x = at specific location in x direction 0,£ = ambient condition and stagnation condition, respectively 1 = condition at start of isobaric region A SEMIEMPIRICAL approach developed by Abramovich 1 for determining the flowfield properties of a slightly offoptimum supersonic jet exhausting into a quiescent atmosphere is extended to rocket exhausts typical of Martian retro-conditions. If the soft landing of scientific instruments on Mars is to be accomplished by the use of terminal decelerating rockets, it will be necessary to estimate the extent of descent corridor significantly affected by the jet as well as the extent of the surface interaction. The former problem requires the estimate of the growth of the jet while the latter requires more detail as to the internal structure of the jet. The method described herein allows engineering estimates of both the size and structure of the jet but does not attempt to describe the jet-surface interaction.The analysis of a high-speed, compressible jet into a near quiescent ambient flow has been carried out by several investigators in the past. For highly underexpanded jets the size of the mixing region is considered negligible with respect to the radius of the inviscid core of the jet, and the rate of growth of the plume is considered to be much greater than the rate of growth of the mixing region. Consequently, the jet

The choked jet flowing into a stationary atmosphere

“…A previous discussion' 11 of the expanding flow of a choked axi-symmetric jet into a stationary atmosphere drew attention to the differences between various existing sets of observations and between observation and analysis. One reason advanced for these discrepancies was the influence of the mixing region at the edge of the jet while another was the degree of uniformity and steadiness of the flow at exit from the nozzle.…”