Unsteady effects in a thin viscous shock layer near a three-dimensional stagnation point of a body moving with given acceleration and deceleration

Abstract

An unsteady viscous shock layer near a stagnation point is studied. The Navier-Stokes equations are analyzed in the limit γ → 1, Re0 → ∞, df/dt = αn-mF(t/αm). The Reynolds number Re0 is defined in the paper by Eq. (1.3) (df/dt is the velocity of the body with respect to an inertial frame of reference moving with the original steady velocity −V't8, α2 = (γ − 1)/(γ + 1)). Various flow regimes in the case α ≪ 1, ɛ ≪ l, n ≥ max(2m, m + 1), m ≥ 0, where ɛ2 = 1/Re0 are analyzed. Equations are derived that generalize the asymptotic analysis to the case of a viscous unsteady flow of gas in a thin three-dimensional shock layer. The problem of a thin unsteady viscous shock layer near the stagnation point of a body with two curvatures is formulated. Examples of numerical solution are given for different ratios of the principal curvatures of the body, the wall temperature, the parameters of the original steady flow, and the acceleration and deceleration regimes.