Citation: Yang, Y.; Yan,Y.; Chen, C.; Wu, Q.; Kwembe, T.A.; Wu, R. Modal Analysis on MVG Controlled Supersonic Flow at Different Mach Numbers. Processes 2022, 10, 1456. https://doi.org/10.3390/pr10081456 Academic Editor: Alessandro D’ Adamo Received: 1 July 2022 Accepted: 22 July 2022 Published: 25 July 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). processes Article Modal Analysis on MVG Controlled Supersonic Flow at Different Mach Numbers Yong Yang 1 , Yonghua Yan 2, *, Caixia Chen 3 , Qingquan Wu 1 , Tor A. Kwembe 2 and Ryan Wu 2 1 Department of Mathematics, West Texas A&M University, Canyon, TX 79016, USA; yyang@wtamu.edu (Y.Y.); qwu@wtamu.edu (Q.W.) 2 Department of Mathematics & Statistical Sciences, Jackson State University, Jackson, MI 39217, USA; tor.a.kwembe@jsums.edu (T.A.K.); ryanboydwu@yahoo.com (R.W.) 3 Department of Mathematics and Computer Science, Tougaloo College, Tougaloo, MI 39174, USA; cchen1@tougaloo.edu * Correspondence: yonghua.yan@jsums.edu Abstract: Modal analysis on micro-vortex generator (MVG)-controlled supersonic flow at different Mach numbers is performed in this paper. The purpose of this investigation is to clarify the different properties of streamwise and ring-like vortical modes, and the effects of different Mach numbers on these modes, to further understand the vortical structures as they travel from MVG down to the shock wave/boundary-layer interaction (SWBLI) region. To this end, a high order and high resolution large eddy simulation (LES) was carried out, which identified the vortical structures behind the MVG and in the shock wave/boundary-layer interaction (SWBLI) region in the supersonic ramp flow with flow speeds of three different Mach numbers 1.5, 2.0, and 2.5. The proper orthogonal decomposition (POD) then was adopted to investigate the modes of the fluctuation flow field. It emerged that the streamwise and ring-like vortical modes were disparate in energy distribution, structural order, frequency and amplitude. Furthermore, it showed that as the Mach number increased, the energy of the streamwise modes increased while the opposite was true for ring-like modes; and the streamwise modal structures were altered more significantly than the ring-like modes, and the frequency of each mode scarcely varied. It was also found that the streamwise vortices absorbed energy from the ring-like vortices while they traveled from the MVG down to the SWBLI region, but the dominant frequency of each mode rarely changed during this process. Keywords: LES; MVG; SWBLI; POD 1. Introduction The shock wave/boundary-layer interaction (SWBLI) has remained an unsolved phenomenon in aerodynamics for many years, due to its complexity. It reduces flow quality by inducing large-scale flow separation, which can significantly decrease aircraft and engine performance. This often results in undesirable effects such as total pressure loss, unstable engine flow, increased engine drag and high wall heating. To reduce the adverse effects caused by SWBLI, the micro vortex generator (MVG) is a simple and reliable device that induces separation control. MVGs are passive control devices that are smaller (below the thickness of the supersonic boundary layer) than conventional vortex generators used for low-speed flow control. Due to this small size, MVGs can sustain much lower drag losses while mitigating flow separation [1–6]. In the last decade, experiments and computational investigations on MVGs have been carried out. Babinsky et al. [2] performed a series of experiments on different MVGs and created a detailed study on their control effects. Sun et al. [7] made a PIV investigation of the 3D instantaneous flow organization behind a micro-ramp in a supersonic boundary layer, and Wang et al. [8] performed an NPLS and PIV experimental study in a low-noise supersonic wind-tunnel. Numerical simulations have been made on MVGs for comparative Processes 2022, 10, 1456. https://doi.org/10.3390/pr10081456 https://www.mdpi.com/journal/processes