Axisymmetric cavities in hypersonic flow

Abstract

A detailed experimental campaign is conducted to investigate the shear layer characteristics of an axisymmetric open cavity exposed to a Mach $6$ freestream. Experiments are performed in a Ludwieg tunnel for varying Reynolds numbers ($23000\leq Re_D \leq 74000$) based on cavity depth ($D$). The effects of geometry are examined through length-to-depth ratios ($[L/D]=[2,4,6]$) and non-dimensional rear-face height differences ($[Δh/D]=[-0.5,-0.25,0,0.25,0.5]$). Shear layer evolution is interpreted using qualitative schlieren and Planar Laser Rayleigh Scattering (PLRS) along with quantitative unsteady pressure measurements. For all $[L/D]$, the shear layer remains laminar at low $Re_D$ and develops Kelvin-Helmholtz (K-H) vortices as $Re_D$ increases. For the longest cavity ($[L/D]=6$), transition to turbulence occurs at the highest $Re_D$ due to a longer K-H growth length. Spectral analysis of pressure signals and PLRS intensity shows a shift in dominant frequency from the first Rossiter mode to higher modes for $[L/D]=6$. Except for $[L/D]=6, [Δh/D]=0$, dominant frequencies agree with Rossiter predictions and remain largely Reynolds-number independent. Variation of $[Δh/D]$ leads to mode switching identified using POD of PLRS snapshots. Negative $[Δh/D]$ favors K-H modes (5th-6th Rossiter), whereas positive values promote a strong flapping mode (1st Rossiter) due to pressure build-up inside the cavity. At $[Δh/D]=0$, both modes may coexist depending on $Re_D$. Azimuthal measurements indicate dominant axisymmetric behavior in flapping cases and weaker correlation for K-H dominated shear layers.

Figures (18)

• Figure 1: (a) A typical schematic showing the short-duration hypersonic Ludwieg tunnel at Technion. Key components: 1. driver tube, 2. converging-diverging (C-D) nozzle, 3. view/optical ports, 4. dump/vacuum tank, 5. model mounting station, 6. vacuum pump, 7. fast-acting valve, 8. dry-air cylinder, and 9. CO$_2$ cylinder; (b) A schematic showing the high-speed schlieren imaging setup. Key components: 1. high-speed camera, 2. knife edge, 3. plane mirror, 4. parabolic mirror, 5. slit, 6. light source, and 7. computer; (c) A schematic showing the high-speed planar laser Rayleigh scattering setup. Key components: 1. continuous wave laser (532 nm), 2. sheet optics + collimator, 3. thin laser sheet, 4. plane mirror, 5. high-speed camera, and 6. computer.
• Figure 2: (I) Typical pressure plot depicting the repeatability of the signal obtained from a location just upstream of the C-D nozzle. The fluctuation intensity ($\sigma$) across the runs for $p/p_{01}$ is found to be $\approx 0.66\%$. (II) The local pressure depicting the fluctuation levels at the indicated locations marked in the snippet for the plain cone (a,b), and the cavity-mounted cone (c,d). $p_2$ corresponds to the static pressure post the conical leading edge shock, as can be referred from Table \ref{['tab:freestream_cond']}. $t_r$ refers to the run time for which the incoming pressure is found to be approximately constant.
• Figure 3: Schematic of the cone-mounted cavity configuration, highlighting the key dimensions and cavity nomenclatures used in the present study. $L_F$ will be different based on the $[L/D]$. $S_1$, and $S_2$, correspond to locations of the unsteady pressure probes.
• Figure 4: I-(a,c) High-resolution schlieren image obtained for plain cone flow, and cavity mounted cone, respectively with vertical lines marking the profiles along which the space-time plots are construed; I-(b,d) Typical space-time ($y-t$) diagrams, representation of the temporal fluctuations for the respective cases of plain cone and cone-cavity configuration. II-(a) Sectional and (b) 3D side view of the hypersonic cone-cavity to highlight the shadowing of the cavity near the trailing edge while rotating the model about the cone-axis. Cavity configuration corresponds to $[L/D] = 4,\ [\Delta h/D]=0$, and incoming flow $Re_D$ is $74000$. Flow features: 1 - leading-edge shock, 2 - separated shear layer.
• Figure 5: Instantaneous (a) PLRS snapshot obtained during high-repetition rate imaging for (I) plain cone flow, and (II) cavity-mounted cone flow. (b, c) represent respective space time ($y-t$), and space-frequency ($y-f$) plots. Cavity configuration corresponds to $[L/D] = 4,\ [\Delta h/D]=0$, and incoming flow $Re_D$ is $74000$.