CAREER: The restricted nonlinear framework: A new paradigm for modeling, analysis and control of wall-bounded turbulent flows

Johns Hopkins University, Baltimore MD

Investigators

Abstract

A restricted nonlinear framework for modeling, analysis and control of wall-bounded turbulent flows project will develop a suite of models and tools for studying the characteristics of flow over surfaces. These flow properties have important implications in transport applications, where the interaction between the vehicle surface and the air flowing over it leads to increased friction drag and associated reductions in fuel efficiency. Wind farms are another related application, in which the air flowing over the farm interacts with both the ground and the wind turbines leading to flow patterns that directly impact the efficiency of the farm. The state-of-the-art mathematical models of the flow physics tend to be extremely complex and of high-dimension, which makes them hard to analyze and computationally expensive to simulate. The resulting models will be used to both study the flow phenomena, and to improve the accuracy of certain state-of-the-art computational tools that employ models of certain aspects of the flow to reduce the computational burden of numerical studies. Outreach activities at local Baltimore elementary schools and through a JHU summer program for high school students will therefore emphasize the connections between fundamental fluid mechanics and sustainable energy in order to put the mathematics and science they are learning in the context of pressing societal concerns. This project will develop a novel reduced order modeling framework that seeks to help overcome the challenges of characterizing wall-bounded turbulent flows, which is complicated by both the analytical intractability of the governing equations, and the associated large computational costs of fully resolved simulations. In particular, the proposed research will develop the core theory and simulation tools to extend restricted nonlinear (RNL) modeling principles to wall models for large eddy simulations (LES), high Reynolds number boundary layer flows and wind farm flow fields. The RNL model is a reduced-order model for wall-turbulence that is obtained through a dynamical restriction of the Navier-Stokes (NS) equations that leads to both simplified dynamics and an intrinsic order reduction, resulting in vastly reduced analytical and computational complexity. The expected outcomes of this work include a suite of tools for (i) analyzing and isolating key flow phenomena, (ii) developing mechanistic models of key flow processes, (iii) improving the accuracy of LES (through a RNL wall model), and (iv) designing model-based wind farm control strategies. The research is tightly coupled with an education and outreach plan that includes training of two graduate students as well as activities for elementary and high school students illustrating the application of mathematics and science to improve the efficiency of wind energy.