Deceleration and mass change of an ablating body during high-velocity motion in the atmosphere

Abstract

This paper examines the factors affecting the dynamics and mass loss of ablating bodies during high-velocity motion. The dynamics and ablation of the body are interdependent since the rate of mass loss depends on the velocity and since the deceleration is dependent on the ratio of mass to drag area (m C DA) which may change due to loss of mass and change of shape. The initial kinetic energy of the body decreases due to both a loss of mass and a loss of velocity. The relative rates of mass loss and velocity loss depend on the “efficiency” with which the energy lost due to fluidynamic drag is returned to the body and absorbed in the ablation process. The classic meteor case, where the flow is assumed to be of the free-molecule type with constant heat-transfer and drag coefficients, is reviewed and presented in terms of general dimensionless parameters which allow application to cases other than that of meteor atmospheric entry. This solution indicates a finite mass remaining after the deceleration, the magnitude of the mass relative to the initial mass depending on the “efficiency” described above. In general, cases with variable heat-transfer and drag coefficients require numerical machine solutions (now in progress). However, analytic solutions for certain cases are possible and are presented in this paper. An analytic solution is obtained for the specific variation of the heat-transfer coefficient corresponding to a sphere with laminar convective heating in hypersonic flight at a constant altitude. In this case, the increase of dimensionless heat-transfer coefficient due to decreasing body size (thus effectively increasing the ‘efficiency”) can result in a complete loss of mass during the deceleration process. For both this case and the meteor case, the velocity variation during the major part of the mass loss differs only slightly from that for a body with an unchanging ballistic coefficient (m C DA) . This approximation is used to formulate the analytic solution of a case which corresponds to the laminar convective heating of a sphere in hypersonic re-entry—i.e. a large slow meteor or fireball. Due to the dominant effect of the decrease in heat-transfer coefficient with increasing fluid density (thus effectively decreasing the “efficiency”), the rate of mass loss is reduced and the final mass is appreciable compared to the initial mass. The analytic results are compared with two well-observed fireballs.