Session BP: Supersonic and Hypersonic Flows

Effects of upstream boundary layer on the unsteadiness of shock induced separation

The relationship between the upstream boundary layer and the unsteadiness of the separated flow in a Mach 2 compression ramp interaction is investigated by performing wide-field PIV and PLS measurements in streamwise-spanwise planes. Measurements in the upstream boundary layer indicate the presence of spanwise strips of elongated regions of uniform momentum with lengths greater than $40\delta$. These long coherent structures have been observed in a Mach 2 supersonic boundary layer and they exhibit strong similarities to those that have been found in incompressible boundary layers. At a wall-normal location of $y/\delta = 0.2$, the upstream envelope of the separation region is found to oscillate between $x/\delta =$ -3 and -1 (where $x/\delta = 0$ is the ramp corner). The instantaneous spanwise separation line is found to respond to the elongated regions of uniform momentum. It is shown that high- and low-momentum regions are correlated with smaller and larger scale for the separation region, respectively. Furthermore, the instantaneous separation line exhibits large-scale undulations that conform to the low- and high-speed regions in the upstream boundary layer. The low frequency unsteadiness of the separation region/shock foot observed in numerous previous studies can be explained by a turbulent mechanism that includes elongated regions of uniform momentum.   

Effects of Boundary Layer Transition on Shock Wave Boundary Layer Interactions

Shock wave boundary layer interactions generated with a cylinder on a flat plate were visualized in a Mach 5 flow.~ High-speed (10-20 kHz) planar laser scattering (PLS) was used to obtain images of the interactions.~ An emphasis was placed on how the interactions varied with respect to where the interaction occurred within the streamwise length of the transition process. These variations were looked at in terms of overall shape, unsteadiness, and frequency and range of motion.~ When the interactions occurred towards the laminar side of transition they were found to be more unsteady and to have a broader range of motion in the streamwise direction than the interactions occurring at the aft end of transition.~ These differences are explained in terms of the evolution of flow structures through the transition process, in particular, the finger-like structures that protrude through the upstream edge of the interaction and turbulent spots.   

Hypersonic Shock Wave Computations Using the Generalized Boltzmann Equation

Hypersonic shock structure in diatomic gases is computed by solving the Generalized Boltzmann Equation (GBE), where the internal and translational degrees of freedom are considered in the framework of quantum and classical mechanics respectively [1]. The computational framework available for the standard Boltzmann equation [2] is extended by including both the rotational and vibrational degrees of freedom in the GBE. There are two main difficulties encountered in computation of high Mach number flows of diatomic gases with internal degrees of freedom: (1) a large velocity domain is needed for accurate numerical description of the distribution function resulting in enormous computational effort in calculation of the collision integral, and (2) about 50 energy levels are needed for accurate representation of the rotational spectrum of the gas. Our methodology addresses these problems, and as a result the efficiency of calculations has increased by several orders of magnitude. The code has been validated by computing the shock structure in Nitrogen for Mach numbers up to 25 including the translational and rotational degrees of freedom. [1] Beylich, A., ``An Interlaced System for Nitrogen Gas,'' Proc. of CECAM Workshop, ENS de Lyon, France, 2000. [2] Cheremisin, F., ``Solution of the Boltzmann Kinetic Equation for High Speed Flows of a Rarefied Gas,'' Proc. of the 24th Int. Symp. on Rarefied Gas Dynamics, Bari, Italy, 2004.   

Characterization of supersonic flow boundary layer in the presence of a DC Glow Plasma Discharge Actuator

An experimental investigation is performed to study the effect of DC surface glow discharge on a Mach 3 supersonic boundary layer. A flat plate with pin-like electrodes ($\sim $0.1'' dia) flush mounted on the surface is used. Boundary layers ranging from laminar to turbulent are studied. The DC surface glow discharge provides a high bandwidth flow actuation with characteristic actuation time scale smaller than 0.1 milliseconds and with actuator power of just a few 10's of Watts. Laser schlieren imaging reveals immediate formation of a weak shock in the presence of the discharge. Previous work indicates the bulk heating and also perhaps electrostatic forcing as the primary sources of flow actuation. The average gas temperature at the set point current, estimated using optical emission spectroscopy is around 500 K, which is about 5 times the free stream temperature. The discharge is found to be about 3 mm high, which is approximately the boundary layer thickness. Planar laser scattering from a condensed fog is used to visualize the effect of the discharge on the flow.   

Viscous Effects in Supersonic Micro-Nozzle Flow

In this study we investigate viscous flow behavior in supersonic micro-nozzles. The supersonic flow field is characterized by $Re < 1000$ so that subsonic boundary layers can occupy a significant portion of the expander section. Numerical simulations are performed for realistic monopropellant flows in both linear and bell- shaped expanders. Emphasis has been on 2-D, adiabatic nozzles under steady and transient flow conditions. Steady simulations have revealed that viscous forces degrade micro-nozzle performance on multiple fronts. First, there is the reduction in flow linked to sizeable viscous subsonic layers near the nozzle walls. Compensating for this by increasing the expander angle, however, incurs performance reduction due to large transverse velocity components at the nozzle exit. Lastly, the under-expanded exit flow in a space environment results in premature flow turning near the nozzle exit due to the upstream propagation of backpressure information via the subsonic layer. For 2-D linear nozzles an expander half-angle of approximately 30$^\circ$ maximizes thrust production-- a value roughly $2\times$ that used in macro-scale expanders. Transient simulations reveal a lag in flow response during start-up as flow inertia must initially overcome viscous forces; in contrast, no lag is observed during shut-down as viscous forces aid in the flow reduction. Additional impacts associated with 3-D geometry and heat transfer through the nozzle walls will also be discussed.   

Small-scale materials blast testing using gram-range explosives and air-shock loading

Many material properties are unknown under the high strain rates of shock wave impulse from an explosion in air. Actual blast testing is required for this, but full-scale explosive tests are expensive and dangerous, and yield limited data. Here we explore the possibility that gram-range explosive charges can be used for such testing in an ordinary laboratory setting. The explosion is characterized by high-speed digital shadowgraphy and piezoelectric pressure records of shock speed and overpressure duration. These data yield an explosive impulse describing the strength of shock loading at various standoff distances from a material sample (typically 25cm diameter). Simultaneously, twin high-speed digital cameras and surface tracking software provide material displacement and strain rate data during the test. In principle, these data and the measured shock loading provide a means to find dynamic material properties by an inverse computational approach. A scaling analysis also relates the gram-range blast test to a large-scale blast from the same or a different explosive.