Supersonic flow past a bluff body with a detached shock Part I Two-dimensional body

Abstract

The flow at high Mach number past a body with a rounded nose is considered. Viscosity and heat conduction are neglected, and the body is assumed to be two-dimensional and symmetrical about an axis parallel to the incident stream.

An exact solution is first obtained in the case λ → 1, M → ∞, where λ is the adiabatic index and M is the Mach number. This solution is then used as the basis of a double expansion in δ = (λ - 1)/(λ + 1) and M⁻², after the exact solution has been modified to make the series expansion converge near the body. The expansion is carried out as far as the terms of order (δ + M⁻²)².

The results are displayed for various values of δ and M⁻²; typical results are as follows. With M⁻² = 0, δ = 1/6 (λ = 1.4), and for a parabolic body having unit radius of curvature at the nose, the shock is approximately a parabola with radius of curvature 1.822 at the nose. The distance between the body and the shock along the axis of symmetry is 0.323, and the height of the sonic point from this axis is 0.744 both on the shock and on the body. The actual pressure distribution on the body is shown in figure 4, and agrees well with experiment. The pressure falls to zero at a distance 0.86 downstream from the nose of the body, measured along the axis of symmetry. On the assumption that the pressure remains negligible beyond this point, the total drag is 1.39 _ρV², where ρ₀ is the density andV is the velocity of the incident stream.