William R. Wolf
School of Mechanical Engineering and Center for Computing in Engineering & Sciences – University of Campinas
Turbulence is present in our everyday life either in the flow past aircraft, automotive vehicles and ducts, as well as in the ocean currents, weather predictions and dispersion of gases in the atmosphere. For all these cases, turbulence has a direct impact on several physical processes such as friction, heat and mass transfer, besides noise generation. For example, reducing the drag of air flow along road vehicles and airplanes imply on fuel economy and, hence, the reduction of both transportation costs and greenhouse gas emissions.
Turbulent flow past airfoil. High-fidelity simulation (left) and reduced order model (right).
Over the previous years, with advance in the power of supercomputers, scientists have been able to perform more accurate numerical simulations of turbulent flows. Such large-scale simulations are important to increase our capability to design more efficient engineering devices which are energy efficient. Moreover, numerical simulations also reduce the overall design cost by reducing the number of experimental and prototype tests.
Currently, high-fidelity, large-scale simulations can be used to solve complex industrial problems. However, despite their overall cost reduction, the high computational power required for the numerical analysis of turbulent flows still makes these simulations expensive and time consuming. Aiming to design even more efficient devices, lower cost numerical techniques for fluid flows are still required. These methods are called reduced order models and have gained considerable attention of scientists and engineers in the past years. Reduced order models (ROMs) find application in preliminary stages of design where several aerodynamic configurations need to be analyzed. Furthermore, ROMs can also be used for shape optimization and flow control. In order to be used for the previous applications, such models should be robust and recover the main features of the turbulent flows.
In general, ROMs developed for fluid flow analysis are based on the approximation of physical laws such as mass and energy conservation and Newton’s second law. Although these methodologies are still based on first principles, they lack in robustness and, in general, present numerical instabilities due to numerical approximations which are required to reduce computational costs.
Several techniques have been proposed in literature to solve the issue of robustness in ROMs. However, they usually work in simplified non-turbulent flows. Thus, researchers of the School of Mechanical Engineering and CCES developed novel reduced order models with increased robustness. Our group has a long-term experience on numerical simulations and analysis of turbulent flows of industrial scale and, therefore, we decided to combine recent techniques from machine learning with our previous numerical methods. This new class of ROMs is able to learn from high-fidelity simulation data and the methodology developed on CCES at Unicamp has been successfully applied for the modeling of turbulent flows involving dynamic stall. Dynamic stall is a complex physical process that occurs on helicopter and wind turbine blades, maneuvering aircraft and even on drones and birds.
To obtain the high-fidelity simulation data, 100.000 hours were required in a supercomputer. On the other hand, the ROM requires only a few seconds to run in a single graphic card of a desktop computer, once a deep neural network is trained. Our novel methodology will be used to simulate turbulent flows over commercial aircraft in collaboration with The Boeing Company.
Associated scientific papers:
Lui, H. F. S. and Wolf, W. R., Construction of Reduced Order Models for Fluid Flows Using Deep Feedforward Neural Networks, Journal of Fluid Mechanics, to appear, 2019.