Arvind T. Mohan

Model Reduction and Analysis of Deep Dynamic Stall on a Plunging Airfoil using Dynamic Mode Decomposition

Recent years have seen increased emphasis on mathematical model reduction using modal decomposition techniques of high dimensional flow field data from experiments as well as numerical simulations. These tools decode the complex unsteady flow-field into several modes. Different tools highlight different flow dynamics. In the experimental community, Proper Orthogonal Decomposition (POD) has been the most commonly used technique, ranking modes by their relative energy content, thereby losing temporal information. However, many dynamics are not highlighted by the most energetic structures. In transitional flows for example, growth of flow structures is a more important indicator. The Dynamic Mode Decomposition (DMD) technique highlighted by Schmid1 achieves this by ranking modes by the most dynamically varying flow features. In this work, we use DMD and POD to analyze flow past a SD7003 airfoil undergoing periodic plunging motion, which is representative of a wide variety of phenomena present in MAVs and UAVs.The DMD modes highlight the dynamically varying nature of highly transient low Reynolds number flows and identify the specific flow structures associated with the plunging motion.A stability analysis of the computed DMD modes is performed and unstable flow structures are identified. Flow structures which are common to the dominant modes in both POD and DMD are identified using the two techniques in conjunction with each other. Further, the original flow field is reconstructed from the DMD modes and their individual modal behavior is analyzed to understand the net contribution of the mode to the total flow field.Finally, DMD modes in local regions are used to decide optimum probe placement locations, which capture majority of the flow dynamics based on sparse available time signals.

Analysis of Airfoil Stall Control Using Dynamic Mode Decomposition

Airfoil stall is a major inhibitor of aircraft performance. Many methods have been successfully shown to inhibit or eliminate stall. However, the underlying dynamics of control remains relatively o...

Model Reduction and Analysis of NS-DBD Based Control of Stalled NACA0015 Airfoil

Recent years have seen increased emphasis on mathematical model reduction using modal decomposition techniques of high dimensional flow field data from experiments as well as numerical simulations. These tools decode the complex unsteady flow-field into several modes. Different tools highlight different flow dynamics. In the experimental community, Proper Orthogonal Decomposition (POD) has been the most commonly used technique, ranking modes by their relative energy content, without concern for temporal aspects. However, many dynamics are not highlighted by the most energetic structures. In transitional flows for example, structure growth is a more a more important indicator of the turbulent effects. The Dynamic Mode Decomposition (DMD) technique highlighted by Schmid [1] achieves this by ranking modes by the most dynamically varying flow features. In this work, we use DMD and POD to analyze flow past a NACA0015 airfoil at Reynolds number of 100,000 and AoA=15 degree, without and with control. The specific control technique employed is based on the Nano-second Pulsed Dielectric Barrier Discharge (NS-DBD) actuator. Experimentally validated high fidelity 3-D numerical simulations are employed to generate the required snapshots. From the DMD modes, the dominant time-varying flow structures associated with the two cases are identified, and their stability characteristics are compared. DMD and POD modes are compared to each other. The DMD modes highlight the dynamically varying nature of the flow-field. A Floquet stability analysis of the eigenvalues from DMD for both the no-control and control cases is presented. Further, the original flow field is reconstructed from the DMD modes and their individual modal behavior has been analyzed to show the effect of control authority on the flow.Copyright

A Preliminary Spectral Decomposition and Scale Separation Analysis of a High-Fidelity Dynamic Stall Dataset

Dynamic stall results in major excursions from the desired aerodynamic performance. Among the key events are flow separation and the formation of a leading edge vortex (LEV). In this work, we use data obtained from anextensively validated Large Eddy Simulation of a plunging SD 7003 airfoil to explore the spectral content and predominant length scales in the LEV, as well as the dynamically significant trailing edge vortex (TEV). The vortex detection is accomplished with an established approach which is shown to perform quite accurately for this highly turbulent flow. Two types of decomposition, Dynamic Mode Decomposition (DMD) and Empirical Mode Decomposition (EMD), are employed to analyze the spatio-temporal scales. Reconstruction is used as a measure of accuracy to identify scales with the highest contributions. A new approach combining EMD with FFT is examined to perform scale separation and spectral decomposition of the flow.

Contrasting Modal Decompositions of Flow Fields with & without Control

The unique attributes of Proper orthogonal (POD) and dynamic mode (DMD) decompositions are examined by considering Large-Eddy Simulations (LES) of two different turbulent flow fields comprised of a supersonic, perfectly-expanded jet (without and with control) and a subsonic NACA0015 airfoil in static stall. The objectives are not only to consider the physics of the interactions, but also to accelerate the derivation of statistical data, such as the time-mean, from the LES. The stationary (time-mean) from the LES corresponds to the dominant POD mode as anticipated, while a similar result was obtained with the neutrally-stable DMD mode. However, an amplitude-based ranking of DMD modes demonstrates that if the LES snapshots are not representative of the statistically stationary state, the mean is not represented by the dominant (primary) DMD mode. A detailed comparison is performed of the key features of these stationary modes with the ‘true’ mean-flow obtained from LES. The use of these decompositions as a means of accelerating the acquisition of a suitable mean flow is also examined. The results suggest that these techniques can accelerate the acquisition of a time-mean solution and success was also obtained on reconstruction of Reynolds shear stresses using limited data samples. A sensitivity study on the effects of data sampling parameters on the two decompositions is also described.