Theoretical Modeling of Two-Body Interaction in Supersonic Flow

Abstract

Atmospheric and space launch stage separation depends on the aerodynamic interference between separating bodies. Quick means of estimating and controlling repulsion or attraction lift associated with this interaction are an important enabling technology to achieve the best compromise between launch separation rocket motor weight and safe staging. Asymptotic methods, scattering, and slender-body theories are used to obtain systematic approximation schemes that advantageously couple with computational methods. Theoretical solutions for the lift interference between two bodies in supersonic flow agree well with numerical solutions. The theory sheds light on important scattering phenomena not previously recognized as relevant to this problem. The analysis helps to identify lumped dimensionless parameters and provides scaling laws as well as closed-form expressions for the interference not accessible solely from computations. These results can be used for interpolation and extrapolation of computational fluid dynamics solutions as well as efficient testing and design of flight vehicles. Nomenclature A = cross-sectional body area a = body radius C L = integral lift coefficient c L = local lift coefficient h = vertical distance between bodies' axes L = lift force l = body length l n = body nose length M = Mach number p = pressure T = temperature u, v, w = velocity components x, y, z = Cartesian coordinates x 0 = streamwise distance from the nose tip to the point where shock crosses the body axis = induced angle of attack "= characteristic flow deflection = density = perturbation potential

Aerodynamic Interference on Finned Slender Body

“…In addition to the research which discusses the overall interference loads, it is important to understand the detailed underlying flow physics. Of particular interest are the shock-body interactions which have been studied previously for a number of configurations 9,10,13,15 . Brosh 16 and Hung 2 investigated a wedge-generated shock impinging on a cylinder at M ∞ =3 and showed that the shock footprint, in terms of local pressure rise, decreased as the shock diffracted around the body.…”

“…More recently, Volkov 9 investigated the effect of lateral separation between two axially aligned slender bodies and found reasonably good agreement between the measured and calculated loads. Finally, both Malmuth 10 and Fedorov 15 have reported theoretical approaches to the calculation of overall loads on two slender bodies in close proximity.…”

Computational and experimental investigation into aerodynamic interference between slender bodies in supersonic flow

“…In addition to studies which report the overall interference loads, it is important to understand the detailed underlying flow physics. Of particular interest are the shock-body interactions which have been studied previously for a number of configurations [7,8,[11][12][13][14][15]. Brosh et al [14] and Hung [2] investigated a wedge-generated shock impinging on a cylinder at M ∞ =3 which showed that the shock footprint, in terms of local pressure rise, decreased as the shock diffracted around the body.…”

“…More recently, Volkov and Derunov [7] investigated the effect of lateral separation between two axially aligned slender bodies and found reasonably good agreement between the measured and predicted loads. Finally, both Malmuth and Shalaev [8] and Fedarov et al [13] have reported theoretical approaches to the prediction of overall loads on two slender bodies in close proximity.…”