Simple models of optical phase distortion for shock waves and turbulent boundary and shear layers

Abstract

Simple analytical models are presented for assessment of the phase distortions on circular optical beams caused by shock waves, turbulent boundary layers, and turbulent shear layers. The shock wave formulas are applicable for wedge- shaped vehicles traveling at supersonic or hypersonic speeds. The boundary layers analysis is formulated for turbulent flow along on optical window surface. The shear layer solution is developed mainly for aerowindows; but it is also useful for wake flow behind obstructions, for jet flow from plumes, etc., that interfere with an optical beam. For the optical phase distortion associated with shocks, the flow conditions are evaluated using oblique shock relations and the beam deflection is based on Snell's law. On turbulent flow, both ordered and random phase variations are treated. The density fluctuations is considered to be driven by the temperature gradient. For turbulent flow over a surface, the turbulent eddy size distribution and the mean flow property profiles are based on empirical correlations. The numerical results obtained for turbulent boundary layer at various Mach numbers and altitudes are found to be in fair agreement with reported measurements from a subsonic aircraft. For the shear layer formed between two fluid streams, the method formulated is similar to those commonly employed. In the present work, however, a simple approach is applied to account for the fluid composition difference, and hence the Gladstone-Dale coefficient variation, between the two streams. Expansion waves and laminar flow conditions are also indicated.