Session F15: Flow Control: Coherent Structures and Reduced Order Modeling

Energy amplification and coherent structure evolution due localized forcing in flat plate boundary layer flow

Input-output analysis of the linearized Navier Stokes equations is used to evaluate the effect of localized forcing for laminar and turbulent flat plate boundary layer base flows. First, a stochastic forcing is applied at different heights above the plate to determine the wall-normal location that leads to the largest steady-state variance (output energy). Next, the time evolution of streamwise coherent structures due to impulse forcing at two wall-normal locations is studied. Forcing at the location associated with maximum energy amplification is compared with forcing at the wall, where inputs are typically applied in experiments. The inclination angles of the coherent structures as well as the wall-normal positions associated with maximum energy are compared for the laminar and turbulent base flows. The results show that the wall-normal location of the forcing matters more for turbulent base flows than for laminar ones. This study may provide insights for determining actuator placement in flow control applications.
  

Modulation of large-scale motions due to blowing and suction

Our previous studies revealed that large-scale energy containing structures in turbulent channel flows can be modulated by using blowing perturbations to yield improved heat and mass transfer. In the present study, we investigate the impact of suction perturbations on large-scale motions in a turbulent channel flow at a moderate Reynolds number. The flow is decomposed into its constituent scales by using proper orthogonal decomposition. Anisotropic factor for each mode is computed and used to separate the flow into two groups: large-scale motions and small-scale motions. The effects of both blowing and suction on Reynolds stresses and turbulent heat fluxes are demonstrated.      

Koopman mode representations of vortex interactions and instabilities

Coherent vortices play an important role in many systems like turbomachinery and aircraft. The dynamics of vortices affect the performance and safety of the system and neighboring ones. While stability and control of these vortices has been the subject of a great deal of work, there are still several unsolved issues. Here we propose to address these challenges using dynamical systems theory, including recent advances on Koopman mode analysis. First, a meaningful and practical definition of stability is needed. In many cases, where the overall flow is robust, linear stability analysis yields unstable eigenvalues associated with an extremely small amount of vorticity. Second, the presence of real-world imperfections may be sufficient to drive drastically different behavior from canonical predictions. Note that decompositions based on energy-containing modes (such as POD) may also fail in this case, as low-energy vortices can drive drastic changes in the dynamics. By contrast, a Koopman mode approach will be better suited to represent these flows. In this talk, we apply KMD to vortical flows, starting with vortex merger and proceeding to more complex examples. In all cases, KMD robustly recovers unstable eigenvalues.   

On the Robustness of POD-Galerkin ROMs with Symmetrizable Governing Equations

Evolution of Reduced-Order Models (ROMs) to successfully respond to a variety of flow conditions is crucial to their adjustment to flow control demands. This study is focused on the influence of inner product definition on the robustness of POD-Galerkin models. The quality of Symmetry inner product in improving stability of compressible flow ROMs has been demonstrated in previous studies. The current work shows that, when unsteady discontinuities in supersonic flows resolved by original high-fidelity simulation are not resolved in a lower-order space over a limited number of leading POD modes through Galerkin ROMs, using the Symmetry inner product notably restricts the amount by which the ROM deviates from its ideal stable and accurate state. The L2 ROM on the other hand, easily leaps toward extremely unstable conditions in a low-order space. Meanwhile, when the originally unstable linear and nonlinear ROMs based on L2 and Symmetry inner products are stabilized by an Eigenvalue Reassignment method empowered by Particle Swarm Intelligence, the Symmetry ROMs have shown to be more robust against suboptimal control laws.    

Robust reconstruction of flow fields from limited measurements

In many applications it is important to estimate the structure of a flow field from limited and possibly corrupt measurements. Many current methods in flow estimation use least squares regression to reconstruct the flow field, which searches for the minimum-energy solution that is consistent with the measured data. However, this approach is known to be prone to overfitting and is sensitive to noise. To address these challenges we instead seek a sparse representation of the data in a library of examples rather than a minimum-energy solution. Sparse representation has been widely used in image recognition and reconstruction examples, and is well-suited to structured data with limited measurements, corruption, and outliers. We demonstrate sparse representation for flow reconstruction using various fluid data sets, including vortex shedding past a cylinder at low Reynolds number, a mixing layer, and two geophysical flows. In particular we find considerable improvements in overall estimation accuracy and robustness compared with least squares methods such as gappy POD. Sparse representation is a promising framework for extracting useful information from complex flow fields with realistic measurements.   

Influence of orifice aspect ratio on synthetic jet trajectory in crossflow

The periodic ingestion and ejection of fluid through an orifice yield vortex rings forming an unsteady jet. The ability to impart momentum with a zero net mass flux makes synthetic jet actuators coveted components in flow control applications, most of which include interaction of the jet with an incoming boundary layer. Knowledge of the trajectory of the jet becomes important under such circumstances as it allows targeted use of the actuator. Trajectory of the synthetic jet relies on critical parameters such as the Strouhal number, the velocity ratio and the orifice geometry. In this investigation, a synthetic jet is issued from rectangular orifices with aspect ratio 3, 6 and 12, for different operating frequencies and blowing ratios. We will attempt to establish the scaling characteristics of the jet trajectory that accounts for aspect ratio, momentum ratio and Strouhal number of the jet.