Session QR: Supersonic and Hypersonic Flows II

Fluid-thermal validation of a high-fidelity multi-physics computational tool

In order to efficiently design any vehicle, a detailed knowledge of the potential conditions it will see during operation is essential, especially for sustained hypersonic flight. Traditionally, experimental research supplemented with semi-analytical modeling provided the necessary, reliable information to create effective designs. Recently, designs are being pushed outside the existing experimental datasets available for model calibration and there exists debate whether new experiments are possible. There is thus more emphasis being placed on computation-based investigations of the performance of various subsystems. Without sufficient experimental evidence to validate the numerical models, it is difficult to place the necessary confidence in the computational results needed to produce feasible designs. Research is underway to produce a high-fidelity, multi-physics validated computational tool to make predictions of structural-thermal response in the hypersonic regime. To validate the accuracy of the new code, a coupled fluid-thermal simulation is being conducted to reproduce results from an experiment in the NASA Langley 8-foot high-temperature tunnel.   

Porous coatings for hypersonic laminar flow control

We present the results of linear and nonlinear simulations of hypersonic boundary layers over ultrasonic absorptive coatings consisting of uniform arrays of rectangular pores. Through direct numerical simulation of the two-dimensional Navier-Stokes equations, we explore the effects of coatings of various porosities and pore aspect ratios on the growth rate of the second mode instability. The performance of deep pores operating in the attenuative regime, in which acoustic waves are attenuated by viscous effects within the pores, is contrasted with more shallow pores operating in the cancellation/reinforcement regime. The results of linear simulations in many cases match the results of linear stability theory and confirm the ability of such coatings to stabilize the second mode. At certain conditions such as high porosity and large acoustic Reynolds numbers, the porous layer leads to instability of slow waves, introducing a new instability due to coupled resonant forcing of the cavity array. We confirm the observed instability arises in the linear stability theory, and suggest constraints on cavity size and spacing. Finally, nonlinear simulations of the same geometries confirm the results of our linear analysis; in particular, we did not observe and ``tripping'' of the boundary layer due to small scale disturbances associated with individual pores.   

A numerical study of compressible turbulent boundary layers

Compressible turbulent boundary layers with free-stream Mach number ranging from 2.5 up to 20 are analyzed by means of direct numerical simulation of the Navier--Stokes equations. The simulation generates its inflow condition using the rescaling-recycling method. The main objective is to study the effect of Mach number on turbulence statistics and near-wall turbulence structures. The present study shows that the main turbulence statistics can be correctly described as variable-density extensions of incompressible results. We show that the apparent increase in the magnitude of the fluctuating Mach number with increasing free-stream Mach number is a variable-property effect. Using the mean density to scale the fluctuating Mach number collapses results for different freestream Mach number. The increase in the pdf tails of the dilatation is also shown to be a variable-property effect. Compressible boundary layers are shown to be similar to incompressible boundary layers in that, without the linear coupling term, the turbulence cannot be sustained. The linear coupling term is necessary to generate the wall-layer streaks. For an adiabatic wall, the near-wall structure exhibits the same characteristics as in incompressible turbulent flow in terms of the spanwise spacing of the streaks ($\approx 100^+$). For isothermal walls, near-wall turbulence structures show their dependence on the surface heat flux.   

Estimation of Measurement Errors in Supersonic Wall-Bounded Flows using CFD-Based Simulated PIV

Particle-lag and resolution effects of PIV are being investigated by applying PIV processing techniques to synthetic CFD-based particle fields. Used previously by several investigators, this method aids in identifying sources of error in the flow and in the comparison of experimental and computational data. The technique utilizes time-resolved DNS or LES data and a modified Stokes flow model of particle motion to evolve a particle field and generate pairs of synthetic PIV images. A simulated Mach 5 inlet-isolator flow exhibiting multiple shock reflections and significant separation is used as a test application; simulated TiO$_{2}$ particles ranging in size from 0.1 $\mu $m to 2.0 $\mu $m are distributed uniformly within the model geometry and evolved in time. In agreement with previous experimental results, particle fields rapidly become inhomogeneous in high-gradient regions, with increased inhomogeneity occurring with greater particle size. A preliminary comparison of synthetic PIV-derived velocity fields with those from the LES data indicate significant errors in regions of high gradients, in particular shocks and regions of separated flow, with higher particle inertia yielding increasing errors.   

Transition of high-speed flow induced by roughness elements

Transition induced by isolated and distributed roughness elements at supersonic speeds is studied using DNS on unstructured grids. Flow past a hemispherical bump placed on a flat plate is simulated for three Mach numbers [3.37, 5.26, 8.23] with simulation parameters chosen to match the experiments carried out by Danehy et al. (AIAA-2009-394). Unsteady flow structures were observed for Ma=3.37, 5.26 while Ma=8.23 remained laminar downstream of the trip. Qualitative comparison between the computation and experiment show good agreement. Based on the computed skin friction coefficient values, Ma=3.37 appeared to become turbulent in nature, Ma=5.26 was transitional and Ma=8.23 was laminar. The effect of distributed roughness on transition was studied at Ma=2.9. A laminar boundary layer at Ma=2.9 was observed to transition to a turbulent boundary layer that shows good quantitative agreement with experimental data. The free-stream Mach number and roughness amplitude were seen to strongly influence whether or not the flow transitions. A local Reynolds number based on bump/roughness amplitude is seen to correlate the tendency to transition for both single bump and distributed roughness cases.   

Transition delay in hypervelocity boundary layers via CO2 injection

A novel method to delay transition in hypervelocity flows in air over slender bodies by injecting CO2 into the boundary layer is demonstrated and investigated. Experimental data were obtained in Caltech's T5 reflected shock tunnel. The experimental model was a 5 degree half-angle sharp cone instrumented with thermocouples, providing heat transfer measurements from which transition locations were determined by comparison with laminar and turbulent heat flux correlations. An appropriate injector was designed, and the efficacy of injecting CO2 in delaying transition was gauged at various mass flow rates, and compared with both no injection and Ar injection cases. At an enthalpy of approximately 6 MJ/kg, no transition delay due to CO2 was observed, but for an enthalpy of approximately 10 MJ/kg, transition delays of up to 100\% in terms of Reynolds number were repeatedly documented.   

Laser-Induced Fluorescence Imaging of Droplet Vaporization and Fuel Dispersion in Supersonic Flow

The disruption of simulated fuel droplets in supersonic flow is examined experimentally in a draw-down wind tunnel. Monodisperse 100 $\mu $m diameter fluid droplets of 2-propanol and a 50/50 by volume hexanol/pentane (Hex-Pen) mixture are generated upstream of the tunnel entrance. The Hex-Pen droplets potentially become superheated as the local static pressure drops below the vapor pressure. The droplets achieve supersonic velocities relative to the surrounding air, a relative Mach number as high as 1.8 and Weber numbers as high as 300. Laser-Induced Fluorescence imaging of the disrupting droplets and the expelled vapor was performed with a pulsed 266 nm Nd:YAG laser. Droplets containing 5{\%} acetone were illuminated by a laser light volume sufficient to capture the entire disrupting droplet. The dispersion of the expelled vapor indicates that Hex-Pen droplets evaporate more rapidly with downstream distance than the non-volatile 2-propanol droplets. The degree to which the vaporization rate for the Hex-Pen droplets exceeds that of the 2-propanol droplets increases at the point downstream of throat where superheating appears to commence.   

Experimental investigation of compressibility effects in a separated boundary layer in supersonic flow

The structure of the mixing layer formed at the edge of a separation bubble, in a supersonic boundary layer subjected to an impinging oblique shock wave is explored experimentally. An estimation of the spreading rate, based on PIV measurements of velocity variance is proposed. It is shown that, in spite of the rather high convective Mach number produced in the separated zone, the rate of spread of the mixing layer is quite large. It is checked this is only the result of the orientation of the layer with respect to the surrounding flow: this increases significantly the mass entrainment. Moreover, it is shown that the resulting level of turbulent friction is just adapted to this spatial growth rate. It is concluded that, as a first approximation, the behavior of this shear layer follows the physics of the canonical compressible mixing layer.   

A study of entropy rise across supersonic pressure exchange enhancing rotors

Pressure exchange can be envisioned as a process where work is done by a fluid with high kinetic energy on another fluid with relatively low kinetic energy by utilizing the non-steady pressure forces at the fluid-fluid interface in the laboratory frame of reference. A novel supersonic ejector based on this process was conceptualized and offers non-dissipative flow induction, improved efficiency and environmental benefits. Entropy production in such devices holds the key to any efficiency improvements and therefore, entropy generation from flow structures such as oblique shocks under supersonic flow conditions was studied using schlieren photography. Oblique shocks emanating from the apexes of three cone-vane type of rotors (Truncated Ramp Vane, Ramp Vane and Double cone type) of different semi-cone vertex angles (20 deg., 10 deg., 25 deg. respectively), designed to produce pressure exchange were captured for upstream mach numbers (M=1.5, 1.75, 2) in air. Entropy rise across the oblique shocks was estimated from shock angle measurements and compared to a theoretical entropy rise. Analysis revealed that Double Cone Rotor produced three orders of magnitude higher entropy rise than the Ramp Vane Rotor. Furthermore, an increase in entropy rise (approximately 0.5 orders of magnitude) due a small angle of attack (2.5 deg.) was observed in the Ramp Vane Rotor.   

High-Energy Molecular Beam Source Using a Non-Diaphragm Type Small Shock Tube

The molecular beam technique is one of the powerful tools to analyze gas-surface interactions. In order to generate high-energy molecular beam in a range of 1 - 5 eV, which corresponds to the typical activation energy of surface reactions, we are developing a beam source using a non-diaphragm type shock tube, which can operate at a repetition rate high enough for efficient data acquisition. We made the volume of a tube much smaller than that of conventional ones so that the evacuation time between each shot becomes as short as possible. Our measurement of shock Mach numbers showed that even small diameter (2 or 4 mm) tubes, in which the wall boundary layer has a large influence on the propagation of shock waves, could generate molecular beam with the translational energy of more than 1 eV. This is because the reduction of shock formation distance by rapid opening of the valve, which separates a high pressure room from a low pressure room, weakened the effect of viscous damping on the accelerating shock wave. In addition, the convergent shock tubes of which diameters linearly decrease from 4 to 2 mm exhibited higher Mach numbers than straight ones. This indicates that the application of the convergent tube with the optimized geometry would be promising for generating high-energy molecular beam.