Mach 10 Bow-Shock Unsteadiness Modeled by Linear Combination of Two Mechanisms

This paper presents mechanisms to explain, as well as mathematics to model, time-averaged spatially resolved amplitude observations of number density and number density unsteadiness in a Mach 10 flow as it transitions from the freestream, through a bow-shock wave, and into the gas cap created by a blunt-body model. The primary driver for bow-shock unsteadiness is freestream unsteadiness or "tunnel noise." Primary unsteadiness is bow-shock oscillation. It scales spatially with the number density first derivative and is modeled using a sech2(z) term. Secondary weaker unsteadiness begins as freestream unsteadiness and increases linearly in direct proportion to the gas number density across the bow shock and into the gas cap. This is the well-known amplification of the freestream turbulent kinetic energy mechanism and is modeled using a tanh(z) term. Total unsteadiness [fit using tanh(z) term + sech2(z) term] is expressed as the number density standard deviation and modeled as a linear combination of these two independent, simultaneous, and nonlinear unsteadiness mechanisms. Relationships between mechanism coefficients and various flowfield and wind-tunnel parameters are discussed. For example, bow-shock and gas cap oscillation amplitudes are linearly correlated with stagnation pressure and, by deduction, freestream unsteadiness.