Domains and boundaries of non-stationary oblique shock-wave reflexions. 1. Diatomic gas

Abstract

Interferometric data were obtained in the UTIAS 10 × 18 cm hypervelocity shock tube of oblique shock-wave reflexions in nitrogen at initial temperatures and pressures of about 300 K and 15 torr. The shock-Mach-number range covered was 2 ≤Ms≤ 8 over a series of wedge angles 2° ≤ θw≤ 60°. Dual-wavelength laser interferograms were obtained by using a 23 cm diameter field of view Mach-Zehnder interferometer. In addition to our numerous results the available data for nitrogen, air and oxygen obtained over the last three decades were also utilized. It is shown analytically and experimentally that in non-stationary flows seven domains exist in the (Ms, θw) plane where regular reflexion (RR), single-Mach reflexion (SMR), complex-Mach reflexion (CMR) and double-Mach reflexion (DMR) can occur. In addition, the transition boundaries between these regions were established. The experimental results from many sources substantiate the present analysis, and areas of disagreement which existed in the literature are now clarified and resolved. It is shown that real-gas effects have a significant influence on the size of the regions and their boundaries. The comprehensive, accurate and sensitive isopycnic data will form a base for comparing existing and future numerical analyses of such complex flows.

ALEGRA Validation Studies for Regular, Mach, and Double Mach Shock Reflection in Gas Dynamics

“…The main thing we wish to emphasize in this discussion is that there is difficulty associated with fully analyzing the calculated values that is associated with lack of verification, in particular solution convergence, of the particular calculations under scrutiny. In conclusion, we stress that the nominal computed values of the pressure ratios (1) R , (2) R , and (3) R shown in Figures 3.3 and 3.4 are rational. They also show the best agreement with the experimental data when variability uncertainty in the plot data is analyzed as above.…”

“…These constraints, plus (2.3), (2.4), and (2.6), form fourteen equations for eighteen variables. Specification of the initial state plus the angle of incidence of the initial shock wave allows simplification of these equations to a tenth order polynomial for the pressure 2 p . All but three of the roots of this polynomial can be discarded on physical grounds.…”

“…Due to computational problems that we will discuss further, care must be applied in the selection of values of 1 p , 2 p and 3 p for use in equations (2.5), (2.7), and (2.8). The anomaly at 43.5 degree could well be an artifact of the choices we make for 2 p in reducing the computational data. Because the error bars for the experimental data in Figure 3.4 are smaller than in Figure 3.3, a smaller percentage of our computed data lie within the experimental error bars.…”

“…The pressure plots along the wedge for the Mach 1.37, 50-degree incident angle are plotted in Figure 3.7. The maximum pressure, as well as the pressure at locations three, six, and nine zones behind the peak pressure zone, was used to compute the pressure ration (2) R . These three points correspond to the semi-constant plateau region behind the peak pressure in the Mach stem.…”

“…The maximum pressure was chosen, along with the location eleven zones behind the peak pressure, for computing the pressure ratio (3) R . The pressures thirteen, fifteen, and twenty-two zones ahead of the peak pressure were used to compute the pressure ratio (2) R . These results are summarized in Figure 3.10 (a).…”