Re: Stalls

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