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Energy concentration by spherical converging shocks generated in a shock tube
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Image of FIG. 1.
FIG. 1.

Circular shock tube used in the experiments. Legend, tube parts: (A) high pressure section; (B) inlet tube; (C) transformation section; (D) end cone. Connections: (1) driver gas inlet and pump; (2) pressure transducer; (3) membrane rupture indicator; (4) pressure transducer; (5) test gas valve; (6) vacuum pump. (S 1) − (S 3): shock sensors. Measures in centimeters.

Image of FIG. 2.
FIG. 2.

Schematic diagram of the spectrometric setup. The photomultiplier (PM) tube detects the first light from the shock wave, triggers a delay unit which in turn triggers the spectrometer. An oscilloscope stores the signals from the PM-tube and the shock sensors S 1S 3.

Image of FIG. 3.
FIG. 3.

Relative sensitivity of the Aryelle system.

Image of FIG. 4.
FIG. 4.

Computational domain and initial conditions for the test section simulations. The x-axis is a symmetric boundary.

Image of FIG. 5.
FIG. 5.

Numerical schlieren of the shock at different times. Calculations were made in the half-plane but the image was mirrored for clearer view.

Image of FIG. 6.
FIG. 6.

Relative maximum deviation from a spherical shock shape in the end cone for three initial Mach numbers, M S = 1.5, 3.9, and 5.5. The deviation Δr is the maximum deviation from the average . Dashed vertical lines mark the positions of the cone base and the end wall, measured along the axis.

Image of FIG. 7.
FIG. 7.

Variation of radius as a function of angle θ (see the sketch in Fig. 6) for different time instants. The times are relative to the instant of focus. Density contours at the same instants are shown in Fig. 8.

Image of FIG. 8.
FIG. 8.

Isopycnics for shock wave with initial M S = 3.9 as it converges (a-c) and reflects (d). The times are relative to the focus event. The plots have been mirrored over the x-axis.

Image of FIG. 9.
FIG. 9.

Shock front acceleration in the convergent section for three initial Mach numbers, M S = 1.5, 3.9, and 5.5. The Mach number along central axis is plotted; the major part of the shock strengthening takes place in the end cone, where the shock shape is nearly circular. Comparison with the spherical self-similar solution (full lines).

Image of FIG. 10.
FIG. 10.

Numerical wave diagrams of the cases in Table I, calculated along the central axis of the tube: (a) M S = 1.8; (b) M S = 3.9; and (c) M S = 6. Circles indicate the detection of shock waves passing the shock sensors and the squares the instant of focusing as recorded by the photomultiplier tube. The diaphragm is positioned at x = 0 and bursts at t = 0. For the readers' convenience, some details of the interactions are not shown, e.g., between the head of reflected expansion and the contact surface.

Image of FIG. 11.
FIG. 11.

Shock sensor and photomultiplier signals from three experiments in argon, (a) M S = 1.8; (b) M S = 3.9; and (c) M S = 6. The three shock sensors (black –, red – –, blue –·–) detect sharp temperature gradients whereas the photomultiplier (uppermost line) records the light emission at focus. In (c), a small intensity peak is detected—marked with an arrow—which probably is created by the focusing of a reflected part of the returning shock wave.

Image of FIG. 12.
FIG. 12.

Photomultiplier records from shock in argon at M S = 3.9 at p 1 = 10.0 kPa. Two photomultipliers were used: one was fed with light from a fiber viewing along the central axis of the tube (dashed) and the other from a fiber viewing only the opening (full line). Especially noticeable is the second large dip.

Image of FIG. 13.
FIG. 13.

Photomultiplier records of runs in argon (axial fiber), (a) M S = 3.4 at initial pressure p 1 = 20.0 kPa; (b) M S = 3.9, p 1 = 10.0 kPa; (c) M S = 4.3, p 1 = 5.0 kPa; and (d) M S = 5.7, p 1 = 1.0 kPa. The first dip corresponds to the convergence of the shock at the cone end.

Image of FIG. 14.
FIG. 14.

Photomultiplier records comparing the appearance of the second peak. Same initial pressures p 1 = 10.0 kPa with varying Mach numbers (a) and same initial Mach numbers M S = 3.9 for different pressures (b).

Image of FIG. 15.
FIG. 15.

Spectra from converging shock in argon. Initial M S = 3.9, p 1 = 10.0 kPa. The spectra are taken during separate runs at different times relative to the shock implosion, t trig , and with varying exposure times t exp . For (a)-(e), blackbody curve fits (dashed, red) are also plotted in the spectra. Note that (g) is taken during the second intensity peak.

Image of FIG. 16.
FIG. 16.

Photomultiplier signals of shock in argon at M S = 3.9; (a) signal from the oblique fiber, showing the averaged signal of ten runs, with standard deviation limits (dashed lines) and (b); signal from the axial fiber, a generic signal showing the start time of spectrometer exposure (arrows) for the spectra in Fig. 15.

Image of FIG. 17.
FIG. 17.

Spectrum of shock in nitrogen, M S = 5.3, p 1 = 1.7 kPa. Inset image shows a typical photomultiplier signal (axial fiber) of the light pulse. The spectrometer exposure time was set to cover the whole pulse.

Image of FIG. 18.
FIG. 18.

Spectrum taken from run in argon during convergence of the reflection of the diverging shock, 300 μs after initial implosion of the primary shock wave, M S = 6 and p 1 = 0.88 kPa. A continuum spectrum with apparent blackbody temperature of T = 7, 400 ± 200 K is superimposed on lines from transitions between the 4s − 4p shells.

Image of FIG. 19.
FIG. 19.

Glass damage caused by the focused shock.


Generic image for table
Table I.

Tests on shock propagation: measured experimental data of high and low pressures p 4 and p 1 and Mach number M S with maximal variation between runs. This experimental data were used as initial data for the calculations. For all cases, T 1=T 4 = 293 K.

Generic image for table
Table II.

Time between first and second peak in photomultiplier signals.


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Scitation: Energy concentration by spherical converging shocks generated in a shock tube