From:leishman@hellcat.eng.umd.edu (leishman)Organization:University of Maryland, College ParkDate:12 May 94 13:19:37References:1 2Followups:1

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In article <airliners.1994.1180@ohare.Chicago.COM> ngupta@nano.mit.edu (Nitin Gupta) writes: > I looked into this, and i'm not so sure that the faint "reflections" are > due to changes in refractive index... > ...I do not see n changing enough to manifest > enough contrast to actually be visible on a sunny day. I'm not into > airfoil dynamics, so I have no idea what the nature of schockwaves are in > terms of their temporal pressure. Careful here!! The observation of flowfields containing shocks and other density variations are routinely examined by means of a class of density gradient flow visualization methods known, in general, as schlieren methods. A simple schlieren system is direct shadowgraphy - which is essentially what is being described by the various observers of shockwave images on transport aircraft wings. Note that the refractive index varies if the density in the flow changes. For practical purposes, the refractive index, n, is related to the density, rho, by the equation n-1 = k * rho where k is a constant for a particular gas and wavelength of light. This equation can be written as n-1 =(n_0-1)(rho/rho_0) where _0 indicates the quantities at a reference temperature and pressure. For air, n_0=1.000292 at 0 deg C and 760 mm Hg and for 5893A. Consider a beam of light (could be from the sun) passing through a flow with a density variation (a shockwave being a good example), and this beam of light eventually falls on a viewing screen (the wing of an airplane, say). If the density changes (at the shock, for example) then the time of arrival of a particular point on the screen on a light wave will change because the velocity of light, c, is related to the refractive index, n, by the equation c=(1/n) c* where c* is the velocity of light in a vacuum. If there is a gradient in refractive index normal to the light rays, then the rays will be deflected because the light travels more slowly where the refractive index is larger according to the above equation. The deflection of these light rays is a measure of the first derivative of the density with respect to distance, that is the density gradient, and can be observed using various schlieren techniques (which require lenses or mirrors and a knife edge or graduated filter for a cut-off). If the refractive index gradient normal to the light rays varies, then deflection of adjacent rays will differ, so they will converge or diverge giving regions of increased or decreased illumination on a viewing screen (dark or bright bands). This is the basis of the direct shadowgraph method. It requires no lenses or mirrors and is essentially a measure of the second derivative of the density field. These schlieren methods are routinely used in the laboratory when examining high speed flows containing shockwaves. Turbulence and vortices can also be observed, such as those behind propellers and helicopter rotors. In the field, obviously it is much more difficult to visualize such flows, but the example of the "natural" shadowgraph of the shockwave on a transport wing has been cited in the literature for many years. It is indeed interesting to me that so many of our friends on the internet have also observed such phenomena. J. Gordon Leishman Associate Professor of Aerospace Engineering, University of Maryland at College Park