Evaluation of optimal control flow control in computational fluid dynamics
Chia, Jackson Han Wei
Date of Issue2017-05-18
School of Mechanical and Aerospace Engineering
Traditional forms of optimization have been used over the years in making the most effective use of available resources. However, as greater improvements are demanded, traditional methods have proven to be too costly and time-consuming. Thus, the development of new methods with the use of optimal control have gained momentum and interest. In this report, the adjoint based optimization method will be explained and evaluated using computational fluid dynamic problems. The adjoint method is a gradient based method that makes use of control theory for optimization. Through the derivation of the sensitivity, and manipulation of the flow equation, the adjoint equation can be derived and solved subsequently. In addition, the two approaches of using the adjoint method, namely the discrete and continuous approach, will also be discussed and evaluated. Implementation of the adjoint method will be examined and discussed using the hanging rope problem, and the simulation of a two-dimensional laminar flow over a cylinder. The hanging rope problem is used for explaining the derivation of the adjoint equation, while the simulation is done using ANSYS Fluent to illustrate the solution through computational means. The adjoint method have gained such interest due to its benefits of cost savings and reduced computational time. It generally requires only two iterative solutions for the determination of an optimum point, regardless of the number of flow variables. This is a vast difference as compared to traditional methods, which require a solution of the flow equation for every flow variable. Although it has limitations, there are ways around them, and the use of the adjoint method will still be advantageous for complicated problems.
Final Year Project (FYP)
Nanyang Technological University