Energy interactions in homogeneously sheared magnetohydrodynamic flows

REU Student: Diane Collard, Kansas State University, Manhattan, KS

Faculty Mentor: Dr. Sharath Girimaji

Grad Student Mentor: D. Praturi

We investigate the behavior of homogeneously sheared magnetohydrodynamic (MHD) flows subject to perturbations in various directions. We perform direct numerical simulations (DNS) to examine the interplay between magnetic, kinetic, and internal energies. For perturbation wavevectors oriented along the spanwise direction, computations exhibit behavior that is impervious to the magnetic field. We observe that the magnetic and velocity fields are tightly coupled and harmonic in nature in the case of streamwise oriented perturbations. The oscillatory behavior intensifies as the magnetic field strength increases, indicating a strong harmonic exchange. Oblique perturbations at ?? = 30° and 60° display similar characteristics depending on the dominant component. The oscillatory streamwise behavior is dominant at ?? = 30°, but the spanwise component keeps the kinetic energy from decaying to zero.  Likewise, when ?? = 60° the spanwise component is dominant and the behavior is predominantly a monotonic increase in kinetic energy. Slight initial oscillations occur at high magnetic field strengths due to the influence of the streamwise component.

Bandwidth effects on mack-mode instability

REU Student: Jeremy A. Pohly, University of Alabama in Huntsville

Faculty Mentor: Dr. Helen Reed

Grad Student Mentors: Alexander J. Moyes, Travis S. Kocian and Daniel Mullen

Prediction of transition onset is vital to the design of future hypersonic vehicles. The ability to control laminar-to-turbulent transition can allow for cheaper, lighter thermal protection systems, as well as more efficient combustion in scramjet engines. Transition and stability analysis can be performed through test flights, experimentally in wind tunnels, and computationally. One computational method of stability analysis is the implementation of nonlinear parabolized stability equations (NPSE). In this case, the NPSE code EPIC is used to analyze the hypersonic Mack-mode instability on the Purdue Compression Cone. Currently, only discrete mode disturbances are considered in nonlinear stability analysis computations. However, experiments show that a finite band of frequencies contributes to the disturbance. Kuehl et al. previously analyzed the effects of bandwidth using the NPSE code JoKHeR. These results are extended using a more comprehensive NPSE code EPIC. The experimental bands are computationally replicated in order to quantify the effects of additional frequencies on the disturbance. Increasing the width of the band and the number of modes and harmonics included in the band suppresses the most amplified disturbance amplitude relative to analyzing only a discrete mode. As a result, these parameters directly reduce the Mack-mode growth and should be included in the analysis to more accurately model the instability.