Measurements of shock wave thickness in perfluoro-n-hexane (PP1)

Shock Waves @ Marseille III

“…The profile of the index of reflection n is approximately determined from the Gladstone-Dale relation, the total jump Lln over the shock, which enters the resulting equation, from the more accurate Lorentz-Lorenz equation. Measurements with a similar set-up using argon and nitrogen and reported earlier (Chaves et al 1989) lead to satisfactory results, whereas shock thicknesses for perfluoro-n-hexane shown there exhibit large scatter. (2) The hyperbolic tangent is the exact solution of the Mott-Smith theory and also results from the Navier-Stokes equations in the limit M --+l.…”

“…10-5 ) caused by the density gradient of the shock, integration of the Fresnel formulas for infinitesimal layers over the shock leads to RI = 1 + tan 4 13 JF(y)J2 F(y) = 1 00 dn e-2 >riyx dx (1) 4 -co dx with y = 2 cos 13 j AI, where AI is the light wave length. This could be shown by Walenta (Chaves et al 1989) using electron beam attenuation and laser differential interferometry. Assuming a hyperbolic tangent profile of density yields 7r 2 yLj2 F(y) = Lln sinh(7r2yLj2) From Eqs.1 and 2 the shock thickness is determined via a bisection method.…”

“…Fig.2a shows measured shock thicknesses scaled with the mean free path A ahead of the shock as a function of Mach number M. Also included are results obtained by Walenta using electron beam densitometry for initial conditions PI = 5.33 J.lbar and at room temperature. The resulting value of total viscosity -2.036 times the shear viscosity -was taken from Chaves et al (1989). The resulting value of total viscosity -2.036 times the shear viscosity -was taken from Chaves et al (1989).…”