Experimental investigation of the interaction of a weak planar shock with grid turbulence in a counter-driver shock tube

The impacts of the interaction with grid turbulence of a turbulent Mach number in the range $0.6\times {10}^{-2}$ to $2.4\times {10}^{-2}$ (representative value) on a planar shock wave with a shock Mach number of about 1.04 were experimentally investigated. Using the counter-driver shock tube with a 120 mm × 120 mm square cross section, the turbulent Mach number level and the interaction length at the observation section were varied independently. Within resolvable experimental data, the shock Mach number became a decreasing function of the interaction length. The thickness of the shock front side-view profile increased as the turbulent Mach number and the interaction length increased. With a turbulent Mach number of $2.4\times {10}^{-2}$ (representative value) and an interaction length longer than 200 mm, the shock front profile became fragmented. The condition for the fragmentation is consistent with the “broken shock” criterion proposed by numerical studies.

Figure 1

Schematic illustration of the CD-ST. The active diaphragm rupture system for R-Driver is set symmetrically to that for L-Driver shown in the figure.

Figure 2

Example of the space-time ($x-t$) diagram of shock tube operation: SW, shock wave; EF, expansion fan; CS, contact surface; L-, left; R-, right; i, incident; t, transmitted (except for the region [GT]); r, reflected; $p_{4\mathrm{L}}=55.0$ kPa, $p_1=43.0$ kPa, $p_{4\mathrm{R}}=99.9$ kPa, ${\tilde{M}}_{\mathrm{s},\mathrm{L}-\mathrm{tSW}}=1.04, {\tilde{M}}_{\mathrm{t},\mathrm{GT}}=1.1\times {10}^{-2}$, and $L=981$ mm.

Figure 3

Characteristics of grid turbulence measured by single driver operations, $z=60$ mm, $p_1=43.0$ kPa: (a) $y$ variation of total temperature of region [GT] measured using a cold wire, ${\overline{T}}_{\mathrm{total},\mathrm{GT}}$, normalized by $T_1$; (b) example of hot-wire signal, $E$, and $u_x$ that was obtained based on the calibration with $T=T_{\mathrm{total},2{\mathrm{R}}^{\prime }}$ at $y=60$ mm, $\mathrm{\Delta }x=0.45$ m, $y=60$ mm, and ${\overline{u}}_x=102.7\mathrm{m}/\mathrm{s}$; (c) $y$ variation of ${\overline{u}}_{x,\mathrm{GT}}$; (d) $y$ variation of ${u_{x,\mathrm{GT}}}^{\prime }$; and (e) $\mathrm{\Delta }x$ variations of $M_{\mathrm{t},\mathrm{GT}}^2$ on the center axis ($y=60$ mm). The diagram in (a) was obtained using a cold wire; diagrams (b)–(e) were obtained using a hot wire. A small error bar is hidden behind a symbol, (a)–(d) $p_{4\mathrm{R}}=99.9$ kPa, (e) open symbol, $p_{4\mathrm{R}}=99.9$ kPa; solid symbol, $p_{4\mathrm{R}}=68.0\mathrm{kPa}$.

Figure 4

$M_{\mathrm{s},\mathrm{L}-\mathrm{tSW}}$ vs $L$.

Figure 5

Shadowgraph images of a shock wave propagating through turbulence with various values of $L$ indicated as a white number in each frame. A negative value corresponds to the image before interaction. (a) ${\tilde{M}}_{\mathrm{t},\mathrm{GT}}=0.6\times {10}^{-2}$, (b) ${\tilde{M}}_{\mathrm{t},\mathrm{GT}}=1.1\times {10}^{-2}$, and (c) ${\tilde{M}}_{\mathrm{t},\mathrm{GT}}=2.4\times {10}^{-2}$.

Figure 6

Broken shock criteria and the shock front condition in the experiment on $\widetilde{M_{\mathrm{s}}}-\widetilde{M_{\mathrm{t}}}$ coordinates; solid symbols, broken shock front profile with the largest $L$; open symbols, continuous shock front profile; LLM93, Ref. [17]; LL09, Ref. [18]; D12, Ref. [20]; and LBL13, Ref. [24].