Development of Adjoint Solvers for Engineering Gradient-Based Turbomachinery Design Applications

High-fidelity computational fluid dynamics (CFD) are common practice in turbomachinery design. Typically, several cases are run with manually modified parameters based on designer expertise to fine-tune a machine. Although successful, a more efficient process is desired. Choosing a gradient-based optimization approach, the gradients of the functions of interest need to be estimated. When the number of variables greatly exceeds the number of functions, the adjoint method is the best-suited approach to efficiently estimate gradients. Until recently, the development of CFD adjoint solvers was regarded as complex and difficult, which limited their use mostly to academia. This paper focuses on the problem of developing adjoint solvers for legacy industrial CFD solvers. A discrete adjoint solver is derived with the aid of an automatic differentiation tool that is selectively applied to the CFD code that handles the residual and function evaluations. The adjoint-based gradients are validated against finite-difference and complex-step derivative approximations.Copyright © 2009 by ASME