We use resolvent analysis to determine an unsteady active control setup to attenuate pressure fluctuations in turbulent supersonic flow over a rectangular cavity with a length-to-depth ratio of 6 at a Mach number of 1.4 and a Reynolds number based on cavity depth of 10,000. Large-eddy simulations (LES) and dynamic modal decomposition (DMD) of the supersonic cavity flow reveal the dominance of two-dimensional Rossiter modes II and IV. These predominantly two-dimensional vortical structures generate high-amplitude unsteadiness over the cavity through trailing-edge impingement and create oblique shock waves by obstructing the freestream. To disrupt the undesired formation of vortical structures, we introduce three-dimensional unsteady forcing along the cavity leading edge to generate streamwise vortical structures. Resolvent analysis with respect to the time-averaged base flow is leveraged to determine the optimal combination of forcing frequency and spanwise wavenumber. Instead of selecting the most amplified resolvent forcing modes, we seek the combination of control parameters that yields sustained amplification of the primary resolvent-based kinetic energy distribution over the entire length of the cavity. The sustained amplification is critical to ensure that the selected forcing input remains effective to prevent the formation of the large spanwise vortices. This resolvent-analysis-based flow control guideline is validated with a number of companion LES of the controlled cavity flows. The optimal control setup is verified to be the most effective in reducing the pressure root-mean-square level up to 52% along the aft and bottom cavity walls compared to the baseline cavity flow. The present flow control guideline derived from resolvent analysis should be applicable to flows that require the actuation input to remain effective over an extended region of interest.
A novel reduced-order model for nonlinear flows is presented. The model arises from a resolvent decomposition in which the nonlinear advection terms of the Navier-Stokes equation are considered as the input to a linear system in Fourier space. Results show that Taylor-Görtler-like vortices can be represented from a low-order resolvent decomposition of a nonlinear lid-driven cavity flow. The present approach provides an approximation of the fluctuating velocity given the time-mean and the time history of a single velocity probe.
The resolvent formulation of McKeon & Sharma (2010) is applied to supersonic turbulent boundary layers to study the validity of Morkovin's hypothesis, which postulates that high-speed turbulence structures in zero pressure-gradient turbulent boundary layers remain largely the same as its incompressible counterpart. Supersonic zero-pressure-gradient turbulent boundary layers with adiabatic wall boundary conditions at Mach numbers ranging from 2 to 4 are considered. Resolvent analysis highlights two distinct regions of the supersonic turbulent boundary layer in the wave parameter space: the rela…
This investigation aims to assess the effect of different types of actuator forcing on the feedback loop of an under-expanded Mach 1.27 planar impinging jet using a resolvent framework. To this end, we employ a Large Eddy Simulation database as a truth model. The time and spanwise-averaged mean flow is taken as an input to global stability and resolvent analyses with the purpose of examining both the intrinsic instability and input-output characteristics. The results show that the inherent instability and primary energy amplification are attributed to the Kelvin-Helmholtz (K-H) instability. Mo…
A novel method to estimate unsteady aerodynamic force coefficients from pointwise velocity measurements is presented. The methodology is based on a resolvent-based reduced-order model which requires the mean flow to obtain physical flow structures and pointwise measurement to calibrate their amplitudes. A computationally-affordable time-stepping methodology to obtain resolvent modes in non-trivial flow domains is introduced and compared to previous existing matrix-free and matrix-forming strategies. The technique is applied to the unsteady flow around an inclined square cylinder at low Reynold…
In this article, we propose a methodology to reconstruct, in a single step, the mean- and unsteady properties of a flow from very few time-resolved measurements. The procedure is based on the {\it a priori} alignement of Fourier- and Resolvent-modes over energetic frequencies, which is a common feature in shear-dominated transitional flows. Hence, the Reynolds-stresses, which determine the mean-flow, may be approximated from a series of Resolvent modes, which discretize the fluctuation field in the frequency space and whose amplitudes can be tuned thanks to few measurements. In practice, we so…
The aerodynamics of a projectile launched from barrels of various devices is quite complicated due to its interactions with the unsteady flow field around it. A computational study using moving grid method is performed here to analyze the effect of the projectile-shock wave interaction. Cylindrical and conical projectiles have been employed to study such interactions and the fluid dynamics of such flow fields. It is found that the overall effect of projectile overtaking a blast wave on the unsteady aerodynamic characteristics of the projectile is hardly affected by the projectile configuration…
Self-sustained oscillation in Mach 3 supersonic cavity with a length-to-depth ratio of 3 is investigated using wall modeled Large Eddy Simulation (LES) methodology for ReD = 3.39*10^5. The unsteady data obtained through computation is utilized to investigate the spatial and temporal evolution of the flow field, especially second invariant of velocity tensor; while the phase averaged data is analyzed over a feedback cycle to study the spatial structures. This analysis is accompanied by the Proper Orthogonal Decomposition (POD) data, which reveals the presence of discrete vortices along the shea…
Resolvent analysis is a powerful tool for modeling and analyzing turbulent flows and in particular provides an approximation of coherent flow structures. Despite recent algorithmic advances, computing resolvent modes for flows with more than one inhomogeneous spatial coordinate remains computationally expensive. In this two-part paper, we show how efficient and accurate approximations of resolvent modes can be obtained using a well-posed spatial marching method for flows that contain a slowly varying direction. In this first part of the paper, we derive a well-posed and convergent one-way equa…
Shock related unsteadiness over axisymmetric spiked body configurations is experimentally investigated at a freestream supersonic Mach number of 2.0 at 0$^\circ$ angle of attack. Three different forebody configurations mounted with a sharp spike-tip ranging from blunt to streamlined (flat-face, hemispherical, and elliptical) are considered. Steady and unsteady pressure measurements, short-exposure high-speed shadowgraphy, shock footprint analysis from $x-t$ plots, and identification of dominant spatiotemporal modes through modal analysis are carried out to explain the unsteady flow physics. Th…
We combine three-dimensional (3D) large-eddy simulations (LES) and resolvent analysis to design active separation control techniques on a NACA 0012 airfoil. Spanwise-periodic flows over the airfoil at a chord-based Reynolds number of $23,000$ and a free-stream Mach number of $0.3$ are considered at two post-stall angles of attack of $6^\circ$ and $9^\circ$. Near the leading edge, localized unsteady thermal actuation is introduced in an open-loop manner with two tunable parameters of actuation frequency and spanwise wavelength. For the most successful control case that achieves full reattachmen…
Phase-based analysis and control of supersonic turbulent cavity flows
University of California, Los Angeles（加州大学洛杉矶分校）；Japan Agency for Marine-Earth Science and Technology（日本海洋地球科学技术机构）；University of Florida（佛罗里达大学）；Illinois Institute of Technology（伊利诺伊理工学院）
The flow structure obtained when Localized Arc Filament Plasma Actuators (LAFPA) are employed to control the flow issuing from a perfectly expanded Mach 1.3 nozzle is elucidated by visualizing coherent structures obtained from Implicit Large-Eddy Simulations. The computations reproduce recent experimental observations at the Ohio State University to influence the acoustic and mixing properties of the jet. Eight actuators were placed on a collar around the periphery of the nozzle exit and selectively excited to generate various modes, including first and second mixed (m = +/- 1 and m = +/- 2) a…
An analysis of calibration for reduced-order models (ROMs) is presented in this work. The Galerkin and least-squares Petrov-Galerkin (LSPG) methods are tested on compressible flows involving a disparity of temporal scales. A novel calibration strategy is proposed for the LSPG method and two test cases are analyzed. The first consists of a subsonic airfoil flow where boundary layer instabilities are responsible for trailing-edge noise generation and the second comprises a supersonic airfoil flow with a transient period where a detached shock wave propagates upstream at the same time that shock-…
Response modes computed via linear resolvent analysis of a turbulent mean-flow field have been shown to qualitatively capture characteristics of the observed turbulent coherent structures in both wall-bounded and free shear flows. To make such resolvent models predictive, the nonlinear forcing term must be closed. Strategies to do so include imposing self-consistent sets of triadic interactions, proposing various source models, or through turbulence modelling. For the latter, several investigators have proposed using the mean-field eddy viscosity acting linearly on the fluctuation field. In th…
Through triglobal resolvent analysis, we reveal the effects of wing tip and sweep angle on laminar separated wakes over swept wings. For the present study, we consider wings with semi-aspect ratios from $1$ to $4$, sweep angles from $0^\circ$ to $45^\circ$, and angles of attack of $20^\circ$ and $30^\circ$ at a chord-based Reynolds number of $400$ and a Mach number of $0.1$. Using direct numerical simulations, we observe that unswept wings develop vortex shedding near the wing root with a quasi-steady tip vortex. For swept wings, vortex shedding is seen near the wing tip for low sweep angles, …
Current design constraints have encouraged the studies of aeroacoustic fields around compressible jet flows. The present work addresses the numerical study of unsteady turbulent jet flows as a preparation for future aeroacoustic analyses of main engine rocket plumes. An in-house large eddy simulation tool is used in order to reproduce high fidelity results of compressible jet flows. The large eddy simulation formulation is written using a second order numerical scheme for a finite difference spatial discretization. Numerical simulations of perfectly expanded jets are performed and the results …
The design of supersonic and hypersonic air-breathing vehicles is influenced by the transition between the Mach Reflection (MR) and Regular Reflection (RR) phenomena. The purpose of this study is to investigate the dynamic transition of unsteady supersonic flow from MR to RR over a two-dimensional wedge numerically. The trailing edge of the wedge moves downstream along the $x$-direction with a velocity, $V(t)$ at a free-stream Mach number of $3$. An unsteady compressible inviscid flow solver is used to simulate the phenomenon. Further, the Arbitrary Lagrangian-Eulerian (ALE) technique is appli…
The present work is concerned with a study of large eddy simulations (LES) of unsteady turbulent jet flows. In particular, the present analysis is focused on the effects of the subgrid-scale modeling used when a second-order spatial discretization methodology is employed for the numerical simulations. The present effort addresses perfectly expanded supersonic jets, because the authors want to emphasize the effects of the jet mixing phenomena. The LES formulation is discretized using the finite difference approach, after the equations are rewritten in a generalized coordinate system. Both space…
The decomposition of hydrodynamic and acoustic components of cavity flows can aid the understanding of the flow-acoustic interaction, which produces a variety of adverse effects in applications. We apply the approach of combining the resolvent analysis and Doak's momentum potential theory to examine the input-output flow-acoustic characteristics of compressible flow over an open cavity at Re=10,000. The methodology can decompose hydrodynamic and acoustic components from an input-output framework. We further localize the forcing at the leading-edge and front wall of the cavity and filter with a…
We consider closed-loop control of a two-dimensional supersonic boundary layer at M = 4.5 that aims at reducing the linear growth of second Mack mode instabilities. These instabilities are first characterized with local spatial and global resolvent analyses, which allow to refine the control strategy and to select appropriate actuators and sensors. After linear input-output reduced order models have been identified, multi-criteria structured mixed $H_{2}/H_{\infty}$ synthesis allows to fix beforehand the controller structure and to minimize appropriate norms of various transfer functions: the …
The impinging shock of varying strengths on the free shear layer in a confined supersonic cavity flow is studied numerically using the detached-eddy simulation. The resulting spatiotemporal variations are analyzed between the different cases using unsteady statistics, $x-t$ diagrams, spectral analysis, and modal decomposition. A cavity of length to depth ratio $[L/D]=2$ at a freestream Mach number of $M_\infty = 1.71$ is considered to be in a confined passage. Impinging shock strength is controlled by changing the ramp angle ($θ$) on the top-wall. The static pressure ratio across the impinging…
The transition between the Regular Reflection (RR) and Mach Reflection (MR) phenomenon impacts the design of the supersonic and hypersonic air-breathing vehicles. The aim of this paper is to numerically investigate the dynamic transition from RR to MR of unsteady supersonic flow over a two-dimensional wedge, whose trailing edge moves along the $x$-direction upstream with a velocity, $V(t)$ at a free-stream Mach number of $M_{\infty}=3$. The simulation is conducted using the unsteady compressible inviscid flow solver, which is implemented in OpenFOAM\textsuperscript{\textregistered}, the open-s…
Current design constraints have encouraged the studies of aeroacoustics fields around compressible jet flows. The present work addresses the numerical study of subgrid scale modeling for unsteady turbulent jet flows as a preliminary step for future aeroacoustic analyses of main engine rocket plumes. An in-house large eddy simulation (LES) tool is developed in order to reproduce high fidelity results of compressible jet flows. In the present study, perfectly expanded jets are considered because the authors want to emphasize the effects of the jet mixing phenomena. The large eddy simulation form…
The study of cavity flow is one of the most important research topics of unsteady aerodynamics. Supersonic turbulent flows over a cavity are mostly encountered in missiles, turbomachinery, and high-speed aircraft. The turbulence inside the cavity gives rise to excess drag, acoustic waves, pressure fluctuations, and vibrations which may lead to numerous problems like excess fuel consumption, failure of missile trajectory or mechanical parts, and aerodynamic heating. We conduct numerical simulations to investigate the flow and compare our results to existing experimental data to show quantitativ…
Current design constraints have encouraged the studies of aeroacoustics fields around compressible jet flows. The present work addresses the numerical study of unsteady turbulent jet flows for aeroacoustic analyses of main engine rocket plumes. A novel large eddy simulation (LES) tool is developed in order to reproduce high fidelity results of compressible jet flows which could be used for aeroacoustic studies with the Ffowcs Williams and Hawkings approach. The numerical solver is an upgrade of an existing Reynolds-averaged Navier-Stokes solver previously developed in the group. The original f…
Accurate high-speed flow simulations of practical interest require numerical methods with high-resolution properties. In this paper, we present an extension and demonstration of the high-accuracy Gradient-based reconstruction and $α$-damping schemes introduced by Chamarthi (2022) [1] for simulating high-speed flows in generalized curvilinear and dynamic mesh domains with the freestream preservation property. In the first part of this paper, the algorithms are detailed within the generalized curvilinear coordinate framework, with a focus on demonstration through stationary and dynamic mesh test…
We utilize resolvent and weakly nonlinear analyses in combination with direct numerical simulations (DNS) to identify mechanisms for oblique transition in a Mach 5 hypersonic flow over an adiabatic slender double-wedge. Even though the laminar separated flow is globally stable, resolvent analysis demonstrates significant amplification of unsteady external disturbances to the linearized flow equations. These disturbances are introduced upstream of the separation zone and they lead to the appearance of oblique waves further downstream. We demonstrate that large amplification of oblique waves ari…
In this paper, the shock dynamics due to the movement of a bump over a flat plate flying at supersonic speed are numerically investigated. The bump is located at the impingement position of the shock wave and is moved at different speeds. This study determines the suitable speed that achieves the minimum entropy change, which is the representation parameter of the transition period. The two-dimensional unsteady Navier-Stokes equations are solved using OpenFOAM to simulate the flow field variables, while the motion of the bump is tracked using the Arbitrary Lagrangian-Eulerian (ALE) technique. …
High-speed turbulent flows are encountered in most space-related applications (including exploration, tourism and defense fields) and represent a subject of growing interest in the last decades. A major challenge in performing high-fidelity simulations of such flows resides in the stringent requirements for the numerical schemes to be used. These must be robust enough to handle strong, unsteady discontinuities, while ensuring low amounts of intrinsic dissipation in smooth flow regions. Furthermore, the wide range of temporal and spatial active scales leads to concurrent needs for numerical sta…
