Session F07: Compressible Flow: Turbulence and Instability (3:55pm - 4:40pm CST)

Stability analysis of the compressible flow past a NACA0012 airfoil at low Reynolds numbers

Compressible flows at low Reynolds number are characterized by very low density and/or pressure and, nowadays, they are of very interest since these conditions can be found in many innovative applications such as the Hyperloop train, the stratospheric flight and the martian exploration. In the view of stratospheric flight, our work aims to investigate how compressibility affects the wake dynamics of a NACA0012 profile. We first characterize the unsteady flow past the airfoil at $Re=1000$ using DNS for various angles of attack $\alpha \in [0^\circ; 20^\circ]$ and Mach numbers up to $M=0.5$. Compressibility is found to attenuate the double harmonic oscillations of the wake, which is directly observable in the aerodynamic coefficients. Then, a steady flow is obtained using the filtering technique of \r{A}kervik \textit{et al.} (2006). These flow fields are used as base flows for a global stability analysis. At these angles of attack the neutral curves are determined in the $(M,Re)$ plane. For a given Reynolds number, we observe a stabilizing or a destabilizing effect of compressibility depending on the angle of attack, while the increase of the Mach number always results in a decrease of the critical Reynolds number for all $\alpha$.   

Stability Characteristics of Open Cavities at High Mach Numbers

Rectangular open cavity flows at supersonic freestream Mach numbers, and a length-to-depth ratio of 6 are studied using linear operator-based modal analysis techniques. The flow conditions are representative of those encountered during high-speed flight. Stability analyses indicate that increasing the Mach number stabilizes both two- and three-dimensional modes, however, their structures indicate increasing decoupling from the shear layer that bridges the cavity. The present observations thus support the hypothesis that at high enough Mach numbers, the behavior of the system resembles that of an acoustic box resonator. Subsequent resolvent analyses on this flow reveal that the amplification rates of individual modes are influenced by incoming forcing from the freestream, which is further confirmed by the method of characteristics. The influence of the inclination angle of the aft wall of the cavity on the shear-layer oscillations is also examined. It is observed that increasing the angle weakens the associated feedback loop and changes the nature of the instabilities. The results have important implications for safety in the operation of aircraft cavity bays at supersonic flight conditions, as well as in cavity flameholders in supersonic combustion applications.   

Kinetic energy transfer in compressible anisotropic homogeneous turbulence.

Kinetic energy transfer in compressible anisotropic homogeneous turbulence is studied using numerical simulations, including turbulence in periodic box with large-scale anisotropic forcing and homogeneous shear turbulence. First, inter-scale energy transfer and inter-component energy transfer are investigated using a filtering approach. At large scales, the subgrid-scale (SGS) flux of kinetic energy is anisotropic and dominated by streamwise component. As turbulent Mach number increases, the direct SGS flux of kinetic energy is suppressed by expansion motions and enhanced by compressible motions, while the reverse SGS flux is enhanced by expansion motions and suppressed by compressible motions. The pressure--strain components mainly transfer energy from the streamwise direction to transverse direction. Meanwhile, using Helmholtz decomposition, it is found that kinetic energy is transferred from solenoidal mode to compressible mode by the nonlinear advection term which increases with turbulent Mach number in anisotropic turbulence in periodic box, and decreases with turbulent Mach number in homogeneous shear turbulence. This indicates that the uniform mean shear suppressions the exchange of kinetic energy between solenoidal mode and compressible mode.   

Effects of Local Wall Cooling on Hypersonic Boundary-Layer Stability on a Blunt Cone

The transition location from a laminar to turbulent flow is a critically important parameter in the development of hypersonic aircraft. It has a significant impact on aerodynamic heating, drag force, engine performance, and vehicle operation. Earlier studies showed that cooling the surface of the body stabilizes the first mode; however, it destabilizes the second mode. This study aims to investigate the stabilization and excitation behaviors of local cooling strips embedded in the vehicle surface. The cooling process can be achieved actively or passively. Active cooling systems circulate coolant to transfer heat from a hot surface to somewhere cold. Passive cooling systems rely on changing material properties. In this study, we numerically investigated several cooling strategies that can be achieved in cooling applications. We developed a direct numerical simulation (DNS) solver and linear stability theory (LST) code to investigate the hypersonic flow stability over a 5-degree half-angle blunt cone with a 0.001-inch bluntness radius at Mach 6. Employing local cooling strips may balance the stabilization of the first mode and destabilization of the second mode. As a result of this, the transition may be delayed or controlled.