Aero-Optical Measurements in a Heated, Subsonic, Turbulent Boundary Layer

Abstract

A scaling relationship for OPD rms that accounts for the fluctuating total temperature profile within a turbulent boundary is derived from the modified Crocco relation. Experimental data from heated, compressible boundary layers at six subsonic Mach numbers in two wind tunnel facilities are shown to be consistent with the theory. The results show that a temperature mismatch between the freestream and underlying wall has a significant impact on the overall optical aberration.

Experimental studies of aero-optical properties of subsonic turbulent boundary layers

“…Substituting this expression into (4.8), gives OPD rms = (1.86 ± 0.16) × 10 −5 (ρ ∞ /ρ SL )δ * M 2 G(M). Comparing it with the presented model, given by (4.8), it follows that the subsonic model (4.10) is valid only for a limited, although wide, range of Re Θ and when G(M) = 0.91 ± 0.08, that corresponds to low subsonic Mach numbers below one, consistent with the Mach number range stated by Cress et al (2010).…”

“…As a result, the constant, C w , obtained experimentally in (4.11) was found to be between 0.7 and 1.0 for a range of Mach numbers between 0.8 and 7.8, which is much larger than the value of B = 0.19, measured in these studies. In addition, from their model (equation (4.11)), it follows that optical aberrations are inversely related to the wall temperature, predicting that the value of OPD rms will decrease as the wall temperature is increased; equation (4.10) and the experimental data presented by Cress et al (2010) pointedly contradict this result. Close inspection shows that the model by Wyckham & Smits (2009) is based upon the SRA rather than the ESRA, and assumes that total enthalpy is constant throughout the boundary layer, and therefore does not allow the total temperature to vary across the boundary layer.…”

“…Wavefronts can be useful in studying hypersonic boundary layers when other fluid-intrusive measurements are either limited or very difficult to perform. The potential of using wavefront sensing can also be extended to incompressible flows; as Cress (2010) and Cress et al (2010) have shown, moderate wall heating does not change the topology or dynamics of the large-scale structure, but simply amplifies optical distortions. Thus, moderate wall heating allows extending the use of sensitive non-intrusive optical diagnostic tools to study large-scale structures in boundary layers at low subsonic speeds, where density fluctuations are ordinarily very small.…”

“…Wittich et al (2007) presented experimental measurements of the optical distortions in a subsonic, M < 0.5, boundary layer for adiabatic walls, using simple scaling arguments, which can be described as OPD rms = (1.7 ± 0.2) × 10 −5 (ρ ∞ /ρ SL )δ * M 2 , where δ * is the displacement thickness and ρ SL is the sea-level density (= 1.225 kg m −3 ). Cress, Gordeyev & Jumper (2010) developed a more rigourous model, based on the use of the linking equation and the outer-variable velocity scaling, for adiabatic and heated walls, and verified the model experimentally for M < 0.6 over a range of different wall temperatures,…”

Computational Investigation of Wall Cooling and Suction on the Aberrating Structures in a Transonic Boundary Layer

“…and more recently by Cress, et al 14 The first study looked at Mach numbers between 0.6 and 0.9 while the latter investigated Mach numbers between 0.12 and 0.6. In both cases, the heating element was placed upstream of the aero-optical window, which means that the boundary layer is in recovery at the location of the optical measurements.…”