Non-Linear Frequency Domain Based Optimum Shape Design for Unsteady Three-Dimensional Flow

Abstract

This paper presents an adjoint method for the optimum shape design of unsteady flows. The goal is to develop a set of discrete unsteady adjoint equations and the corresponding boundary condition for the non-linear frequency domain method. First, this paper presents the complete formulation of the time dependent optimal design problem. Second, we present the non-linear frequency domain adjoint equations for three-dimensional flows. Third, we present results that demonstrate the application of the theory to a three-dimensional wing.

Optimum Shape Design for Unsteady Three-Dimensional Viscous Flows Using a Nonlinear Frequency-Domain Method

“…The pressure distribution is compared to experimental data and prior inviscid results. 16 In the second section, a redesign of the LANN wing is demonstrated. Lastly, a gradient comparison between various number of temporal modes is presented and the convergence of the objective function.…”

Three-Dimensional Aeroelastic Solutions via the Nonlinear Frequency-Domain Method

“…The two-dimensional flow solver employed in section 6.1 is the single-block single-processor code used in the work of Kachra and Nadarajah [43]. The three-dimensional implementation is based on the work of Nadarajah et al [65] and Nadarajah and Jameson [64], and consists in a parallel multiblock finite-volume NLFD flow solver.…”

Local-in-time adjoint-based topology optimization of unsteady fluid flows using the lattice Boltzmann method

“…Techniques such as receding horizon control (Hou et al, 1997) and non-linear frequency domain methods (Choi et al, 2008;Nadarajah et al, 2006) have been proposed. Receding horizon control techniques replace the original time-dependent optimization problem dealing with the entire time interval with a sequence of local optimal control problems defined for a number of equal subintervals.…”

“…These methods compute only the local sensitivity, leaving the required global sensitivity unsolved, so solutions to optimal design problems are unavailable. Nadarajah et al (2006) proposed a gradientbased method for the discrete adjoint sensitivity analysis, and Choi et al (2008) developed an adjoint-based optimization procedure based on the time-spectral formulation, but both of these methods provide suboptimal results and are only applicable to time-periodic problems. Yamaleev et al (2010) proposed a LT discrete adjoint-based optimization methodology that combines the best features of both groups of methods described above.…”