Shock tube schematic. Diaphragm is placed between Driver and Driven sections. Shock wave travels from right to left, with pressure transducers (PT) labeled 1–4. Shock speed is calculated between PT2 and PT3, and diagnostics are triggered off of PT3, while PT4 is coincident with IC location to measure time of shock interaction.
Initial condition vertical velocity. (a) Spatial map of vertical velocity, w, for initial conditions. z = 0 represents the top wall of the shock tube at the nozzle exit. (b) Comparison of streamwise profiles for initial condition vertical velocity, w, at different vertical positions. The red dashed line represents the x-y imaging plane 2 cm below the nozzle exit, with a maximum velocity of 1.38 m/s occurring at the center.
Theoretical x(m)-t(ms) wave diagram for (a) Mach 1.21, (b) Mach 1.36, and (c) Mach 1.50 with experimental pressure trace rises overlaid (red squares). x = 0 is the location of the diaphragm. IS, incident shock; RS, reflected shock; EF, expansion fan; REF, reflected expansion fan; CS, contact surface; Interface, location of the gas curtain.
(a) Photograph of test cell used for spanwise laser variation and volume fraction calibrations, and PLIF imaging of the laser sheet using the calibration test cell, with background subtracted for (b) IC and (c) DYN cameras.
PLIF images of Left: (a) ICs before laser sheet correction, and (b) a Mach 1.50 experiment at 1200 μs before laser sheet correction. Right: (c, d) The same images after correction.
Sample density maps from Mach 1.50 experiments indicating flow field nomenclature used in the body of the text. Images were acquired at (a) 125, (b) 300, and (c) 475 μs.
Full time evolution of SF6 volume fraction maps for Mach 1.21 experiments. Each image is labeled with time t and distance traveled (x). Contrast for all images is set at 1% to 30% SF6 by volume fraction.
Full time evolution of SF6 volume fraction maps for Mach 1.36 experiments. Each image is labeled with time t and distance traveled (x). Contrast for all images is set at 1% to 30% SF6 by volume fraction.
Full time evolution of SF6 volume fraction maps for Mach 1.50 experiments. Each image is labeled with time t and distance traveled (x). Contrast for all images is set at 1% to 30% SF6 by volume fraction.
Illustration of repeatability for the Mach 1.50 experiments: PLIF images from separate runs of the experiment at (a) 150 μs, (b) 275 μs, and (c) 600 μs after shock impact.
A selection of SF6 volume fraction maps from each Mach number experiment, with contrast customized for each image. Images in each row were acquired at roughly the same location as indicated in the figure, with time t and distance traveled (x).
Mach number comparison of vorticity map evolution shows the breaking down of the primary vortices over time.
(a) Up to five wavelengths were used to calculate an average circulation of positive vortices for each time. The top image shows the raw PIV data at 300 μs in a Mach 1.36 experiment, for an example. The bottom image shows the velocity field with arrows, and vorticity with the color map. The magenta boxes indicate the path along which the line integral was calculated. (b) Mean circulation as a function of distance traveled, x.
Definition of mixing layer width, δ, using Mach 1.35 experiments at (a) 230 μs, and (b) 425 μs. The width is the distance between the farthest upstream and downstream extents at which at least 5% SF6 volume fraction is present.
(a) Mixing layer width vs time. (b) Mixing layer width vs distance traveled shows the same growth rate for each M, but with a vertical offset separating the experiments until x ≈ 15.
(a) vs t * * collapses the data up to t * * = 40. (b) δ* vs distance traveled collapses the data to x ≈ 25. (c) δ* vs τ collapses the data to τ ≈ 475.
Measures of mixedness: (a) area of PLIF signal as a function of distance traveled, and (b) as a function of distance traveled.
Streamwise profiles of mean volume fraction of SF6, . Plots compare for each Mach number for 3 different scaled time regimes.
PDFs for volume fraction of SF6 for each Mach number at 3 different scaled time regimes.
(a) ⟨b⟩ as a function of time. (b) ⟨b⟩ as a function of distance traveled.
Evolution of Ξ with distance traveled.
Evolution of Θ with distance traveled.
Maps of χ(x, y) corresponding to the volume fraction maps in Figure 13 , giving time, t, and distance traveled, x. Images are displayed on a log scale with intensity corresponding to I = log(χ + 1), and contrast set to I = [0 : 0.3].
χ total as a function of time.
χ total as a function of distance traveled.
Interface length at the 5% SF6 volume fraction level as a function of distance traveled.
List of parameters governing the flow, with ′ denoting post-shock conditions when ambiguous.
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