Real-Time Simulation of Fluid Flow Based on Sensor Data Using ODE Constrained Optimization



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A growing idea in the field of wind energy research is the concept of wake steering. Wake steering is the idea that by controlling the placement of the wake away from subsequent rows of turbines, an overall net increase in power production can be achieved by a wind farm. However, in order steer the wake, one must first know where it is, or short of that, have a reliable numerical method for determining its location. At the time of this publication, full Computation Fluid Dynamics (CFD) simulations for fluid flows are too expensive in order to achieve an approximation that could be used in relevant decision making; i.e. using the fluid flow approximation as part of a steering strategy. The purpose of this work is to aid this field of research by developing a method for simulating a fluid flow approximation based off of sensor data in real-time. Once the approximation to the flow is achieved, numerous techniques can be applied to determine the location of the wake. In order to achieve this approximation, we will utilize the theory of Reduced-Order Modeling (ROM). To achieve a ROM, we will need to derive appropriate basis and coefficient functions. The basis functions our ROM will rely on will be calculated using a Proper Orthogonal Decomposition (POD). This methodology requires a library of fluid data collected from the span of desired parameters that the ROM will be considered reliable for. This data will be supplied via Viento, a CFD simulator we developed during the course of our research. The generation of these basis functions will occur outside of the time-sensitive context of creating the approximation. To determine the time-dependent coefficient functions two methods will be considered: solving the reduced-order forward problem as a type of benchmark and solving the Karush-Kuhn-Tucker (KKT) system generated from an Ordinary Different Equation (ODE) constrained-optimization problem. It is the second-type, in which we minimize the difference between the values produced by the approximation and the available sensor data, that we are proposing be used to generate fluid flow approximations in real-time.



fluid flow approximation, Karush-Kuhn-Tucker conditions, Proper Orthogonal Decomposition, Ordinary Different Equation ODE constrained optimization