PA5: Contributed Session

Room: Old Main Academic Center 3110

Webex Link

Chair:  Adrian Sescu, Mississippi State University

Omar Es-Sahli, Mississippi State University

Time: 4:00 pm - 4:20 pm (CST)

Title: High-Speed Boundary Layer Optimal Control


High-amplitude free-stream turbulence and large surface roughness elements can excite a laminar boundary layer sufficiently enough to cause streamwise oriented vortices to form. The latter is accompanied by streaks of varying amplitudes that `wobble' through inviscid secondary instabilities and, ultimately, transition to turbulence. We formulate a mathematical framework for the optimal control of compressible boundary layers to suppress the growth rate of the streamwise vortex system before breakdown occurs. This has a commensurate impact on the wall shear stress and kinetic energy at the wall. Flow instabilities are introduced via free-stream disturbances. The compressible Navier-Stokes equations are reduced to the nonlinear boundary region equations (NBRE) in a high Reynolds number asymptotic framework wherein the streamwise wavelengths of the disturbances are assumed to be much larger than the spanwise and wall-normal counterparts. The method of Lagrange multipliers is used to derive the adjoint compressible boundary region equations (ABRE) via an appropriate transformation of the original constrained optimization problem into an unconstrained form. The wall transpiration velocity represents the control variable while the wall shear stress represents the cost functional. Our study shows that this kind of control approach induces a significant reduction in the kinetic energy and wall shear stress of the boundary layer flow. Contour plots visually demonstrate how the primary instabilities gradually flatten out as more control iterations are applied.

(joint work with Adrian Sescu, Mohammed Afsar, Yuji Hattori, and Makoto Hirota)

Zheng Qiao,  Mississippi State University

Time: 4:20 pm - 4:40 pm (CST)

Title: Reduced-order modeling of flame dynamics functions with inlet acoustic modulation


The study presents a G-equation based cost-efficient reduced-order model for predicting the flame dynamics function (FDF) with inlet acoustic modulation. A novel two-step approach is employed in this model: first, a steady-flame profile, which is obtained via detailed simulation, is employed to predict the linear mode-shape of the flow field; and then the simulation based on the G-equation is carried out to capture the dynamic behavior of the flame accurately. The main advantage of this method is that the flame profile in the nontrivial aerodynamic environment can be precisely replicated, and the flame dynamic is predicted under the physically-consistent flow modulation mode. In the present work, we demonstrate the efficacy of our model with the consideration of the premixed Bunsen flame and M-shaped flame, and the comparison of our predictions with the DNS simulation results will be discussed in detail.

Matthew W. Brockhaus, Mississippi State University

Time: 4:40 pm - 5:00 pm (CST)

Title: Model Reduction for Advection Dominated PDEs Using Modal Decomposition


Dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD) comprise two singular-value decomposition (SVD) tools often used in the construction of reduced-order models (ROM). We conduct preliminary investigations of the accuracy of these tools for advection-dominated partial differential equations in one- and two- dimensions and explore their sensitivity to initial conditions. To construct the full order models (FOM), a first-order forward time backward space scheme is applied to the 1 dimensional linear advection equation with spatial and temporal intervals [-2,4] and [0,5], respectively. Likewise, a first-order forward time hybrid space (backward space for advection, central space for diffusion) scheme is applied to the nonlinear advection diffusion equation with spatial and temporal intervals [(0,2);(0,2)] and [0,0.5], respectively. Several cases with differing initial conditions (Gaussian, sinusoid, and step functions) are presented for comparison between reduced order and full order models. Dynamic mode decomposition and proper orthogonal decomposition are shown to provide adequate performance in both current state reconstruction and future state prediction for the cases considered if trained on a sufficiently rich data set and provided with an energy-specified number of modes.

 (joint work with Edward Luke and Adrian Sescu).