Computationally Efficient Reduced Order Model for Complex Flows

Abstract

Reduced-order models (ROM) based on Proper orthogonal decomposition (POD) hold importance in uid dynamics due to their utilization in ow control, optimization, and design applications. POD-ROMs have shown promising results for laminar ows, however, they lack accuracy for complex and turbulent ows. Higher POD modes of turbulent ows are discarded in ROM in order to get more computational advantage over the full order simulation. Although higher modes contain low amount of energy, but they are responsible for viscous dissipation in ROM. These viscous e ects in ROM are modeled by using di erent linear and nonlinear closure modeling techniques. Nonlinear closure models have shown promising results for turbulent ow, however, they are computationally expensive. This study presents a computationally e cient nonlinear closure model, which is based on a dynamical system approach for complex ows. We assess the proposed model by simulating the ow past a circular cylinder. Although the ow problem is relatively simple, but plays a vital role in investigation, modeling, and control of complicated ows. The performance of ROM is judged by four assessment criteria which are the temporal coe cients, the mean velocity, the root mean square (rms) of velocity uctuations, and Reynolds stresses. The results con rm that the proposed model improves the accuracy of ROM. Moreover, this model is computationally less expensive as compared to other nonlinear closure models. We investigate three aspects of ROM: closure modeling, ROM for control applications, and ROM for aerodynamic forces. For control applications it becomes a chalii lenging task to develop a closure model in the presence of nonhomogeneous boundary conditions. We investigate the closure model for nonhomogeneous boundary conditions and demonstrate the closure modeling e ects in control applications. Generally, the ROM considers the velocity eld in the ow. On the other hand, the surface pressure is also important for analyzing the fatigue and failure of structure. However, the ROM for pressure forces is a relatively less explored research area. Therefore, we develop a computationally e cient ROM for aerodynamic forces using pressure mode decomposition (PMD). We consider the localized pressure POD modes on the cylinder surface, integrate each mode on the surface, and decompose them into normal and streamwise components, namely lift and drag decomposition coe cients, respectively. These coe cients are scalar quantities and are independent of spatial coordinates. The lift and drag coe cients are expanded in a Galerkin fashion using the decomposition coe cients. The temporal coe cients are computed through a mapping function based on a quadratic stochastic estimator. The rst odd pair of lift decomposition coe cients and the rst even pair of drag decomposition coe cients are more signi cant than any other pair in modeling the aerodynamic forces. These ndings help us in the development of computationally e cient ROM for aerodynamic forces based on a speci c pair of decomposition coe cients.