Design optimization of periodic flows using a time-spectral discrete adjoint method [electronic resource]
Keywords: Aeronautics and Astronautics

Standard methods for unsteady optimization carry heavy computational costs and large storage requirements, mostly due to the lengthy time integration involved in the unsteady flow simulations. Such difficulties limit its practical application to cases where the time integration is performed over only a smaller segment of the entire period. The result is a loss of accuracy in the representation of the physical model. For certain unsteady flows with periodicity, a dramatic reduction in both compu- tational cost and required storage is realized through implementing the Time Spectral method. Furthermore, by introducing an adjoint-based method as an alternative way of obtaining gradient information, computational cost is further reduced. This combi- nation of Time-Spectral and adjoint-based methodology therefore allows for unsteady optimization within a reasonable time frame while maintaining accuracy. In this dissertation, the Discrete Adjoint method is implemented and applied to unsteady flows with periodicity, in the context of the Time Spectral Method. The acquired adjoint gradient information is fed into an optimizer and truly unsteady optimization work is carried out for the first time on a realistic test case. The devel- opment and implementation of necessary boundary conditions prove crucial for the successful implementation of the Discrete Adjoint method. As a simple test case, the NACA 0012 airfoil is selected for simulation in steady inviscid, unsteady inviscid, steady viscous, and unsteady viscous flows. In each case, the resulting gradient information obtained from both the adjoint and finite difference method is compared. Upon completion of the airfoil test case, the adjoint-based method is applied to a helicopter blades, UH60, for both steady and unstaedy inviscid flows. The gradient information obtained by the adjoint-based method shows good agreement with the conventional, Finite Difference gradient information. The design methodology was developed for a single processor, however, multi- processor capability is also implemented. In order to accommodate realistic meshes, multi-block capability is added as well. With all of the necessary components im- plemented, optimization is carried out on the UH60 helicopter blade. The objective function is time-averaged torque over all time instances and the optimized result shows an improvement of 5 % over the current configuration. Stanford University Multi-block (SUmb), while implementing the unsteady Reynolds-Averaged Navier Stokes equations with multi-block and multi-processor algorithms, is the chosen flow solver. PETSc is employed as the adjoint solver. Successful implementation of the Discrete Adjoint method to unsteady fluids with periodicity provides the gradient information more easilty than the traditional finite difference method which is hindered by its heavy computational cost and large stor- age requirements. This research establishes a new optimization methodology which utilizes Discrete Adjoint gradient information derived from flow solutions, obtained using the Time Spectral method.