In the first attached article: "Behavior of free and impinging supersonic micro-jets" in Figure 15 the radial measurement, of a PITOT tube after the Mach disk in a supersonic free gas expansion, is presented. Similar measurement is also presented in Figure 4 of the second attached article: "Flow and acoustic properties of... under-expanded supersonic jets". Regarding these distributions- the authors only state that the radial profile obtained is due to lower-velocity core and a higher velocity annulus downstream from the end of the first shock cell.
My main question is:
1) What is the physical explanation for having lower core velocity and higher velocity annulus after the Mach disk?
Two more related questions are:
2) The radial profiles presented in the mentioned figures are of the total pressure and the Mach number. Is it safe to assume that also the jet radial density has the same profile ? and why ?
3) The above mentioned measurements were obtained in conditions of NPR= 6 to 9 (Where NPR is the ratio between the nozzle exit pressure and the ambient pressure ). In our experiment we got similar profiles of density, but our NPR is of the order of 10^7. This is so since in our case the expansion of the jet is from several bars (through a converging nozzle) to a vacuum of 10^(-4) torr (it is a pulsed jet). Under these conditions the location of the Mach disk, according to the formula: X_mach=d*0.67*(P0/P_ambient)^0.5 (~2 meter), is well beyond the length of our test chamber. So the explanation of having a central dip after the Mach disk location does not seem to apply in our case.
My question is if someone encountered articles about free expanding jets into vacuum with similar NPR as ours (maybe pulsed jets) , which do have shocks/Mach disks in their test chamber ? - If so please attach those articles, and if not- Does someone have a reasonable explanation to having central dip in our case ?
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