Plasma-based Control of Supersonic Nozzle Flow

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) and axisymmetric (m = 0). In this fluid dynamics video http://ecommons.library.cornell.edu/bitstream/1813/13723/2/Alljoinedtotalwithmodetextlong2-Datta%20MPEG-1.m1v, http://ecommons.library.cornell.edu/bitstream/1813/13723/3/Alljoinedtotalwithmodetextlong2-Datta%20MPEG-2.m2v}, unsteady and phase-averaged quantities are displayed to aid understanding of the vortex dynamics associated with the m = +/- 1 and m = 0 modes excited at the preferred column-mode frequency (Strouhal number 0.3). The unsteady flow in both contains a broad spectrum of coherent features. For m = +/- 1, the phase-averaged flow reveals the generation of successive distorted elliptic vortex rings with axes in the flapping plane, but alternating on either side of the jet axis. This generates a chain of structures where each interacts with its predecessor on one side and its successor on the other. Through self and mutual interaction, the leading segment of each loop is pinched and passes through the previous ring before rapidly breaking up, and the mean jet flow takes on an elliptic shape. The m = 0 mode exhibits relatively stable roll-up events, with vortex ribs in the braid regions connecting successive large coherent structures.Comment: 3 pages. Video submission to Gallery of Fluid Motion, American Physical Society, Division of Fluid Dynamics, 62nd Annual Meeting, November 22-24, 2009, Minneapolis, MN. Replacement deletes TeX commands to correct web link

Data-driven Control Method for Impinging Jets

A data-driven framework using snapshots of an uncontrolled flow is proposed to identify, and subsequently demonstrate, effective control strategies for different objectives in supersonic impinging jets. The approach, based on a dynamic mode decomposition reduced order model (DMD-ROM), determines forcing receptivity in an economical manner by projecting flow and actuator-specific forcing snapshots onto a reduced subspace and then evolving the results forward in time. Since it effectively determines a linear response around the unsteady flow in the time-domain, the method differs materially from typical techniques that use steady basic states, such as stability or input-output approaches that employ linearized Navier-Stokes operators in the frequency-domain. The method naturally accounts for factors inherent to the snapshot basis, including configuration complexity and flow parameters such as Reynolds number. Furthermore, gain metrics calculated in the reduced subspace facilitate rapid assessments of flow sensitivities to a wide range of forcing parameters, from which optimal actuator inputs may be selected and results confirmed in scale-resolved simulations or experiments. The DMD-ROM approach is demonstrated from two different perspectives. The first concerns asymptotic feedback resonance, where the effects of harmonic pressure forcing are estimated and verified with nonlinear simulations using a blowing-suction actuator. The second examines time-local behavior within critical feedback events, where the phase of actuation becomes important. For this, a conditional space-time mode is used to identify the optimal forcing phase that minimizes convective instability initiation within the resonance cycle.Comment: 10 pages, 7 figure

Full trajectory optimizing operator inference for reduced-order modeling using differentiable programming

Accurate and inexpensive Reduced Order Models (ROMs) for forecasting turbulent flows can facilitate rapid design iterations and thus prove critical for predictive control in engineering problems. Galerkin projection based Reduced Order Models (GP-ROMs), derived by projecting the Navier-Stokes equations on a truncated Proper Orthogonal Decomposition (POD) basis, are popular because of their low computational costs and theoretical foundations. However, the accuracy of traditional GP-ROMs degrades over long time prediction horizons. To address this issue, we extend the recently proposed Neural Galerkin Projection (NeuralGP) data driven framework to compressibility-dominated transonic flow, considering a prototypical problem of a buffeting NACA0012 airfoil governed by the full Navier-Stokes equations. The algorithm maintains the form of the ROM-ODE obtained from the Galerkin projection; however coefficients are learned directly from the data using gradient descent facilitated by differentiable programming. This blends the strengths of the physics driven GP-ROM and purely data driven neural network-based techniques, resulting in a computationally cheaper model that is easier to interpret. We show that the NeuralGP method minimizes a more rigorous full trajectory error norm compared to a linearized error definition optimized by the calibration procedure. We also find that while both procedures stabilize the ROM by displacing the eigenvalues of the linear dynamics matrix of the ROM-ODE to the complex left half-plane, the NeuralGP algorithm adds more dissipation to the trailing POD modes resulting in its better long-term performance. The results presented highlight the superior accuracy of the NeuralGP technique compared to the traditional calibrated GP-ROM method

Reynolds-Stress Budgets in an Impinging Shock Wave/Boundary-Layer Interaction

Implicit large-eddy simulation (ILES) of a shock wave/boundary-layer interaction (SBLI) was performed. Comparisons with experimental data showed a sensitivity of the current prediction to the modeling of the sidewalls. This was found to be common among various computational studies in the literature where periodic boundary conditions were used in the spanwise direction, as was the case in the present work. Thus, although the experiment was quasi-two-dimensional, the present simulation was determined to be two-dimensional. Quantities present in the exact equation of the Reynolds-stress transport, i.e., production, molecular diffusion, turbulent transport, pressure diffusion, pressure strain, dissipation, and turbulent mass flux were calculated. Reynolds-stress budgets were compared with past large-eddy simulation and direct numerical simulation datasets in the undisturbed portion of the turbulent boundary layer to validate the current approach. The budgets in SBLI showed the growth in the production term for the primary normal stress and energy transfer mechanism was led by the pressure strain term in the secondary normal stresses. The pressure diffusion term, commonly assumed as negligible by turbulence model developers, was shown to be small but non-zero in the normal stress budgets, however it played a key role in the primary shear stress budget