  The shape of the trailing edge of a gas turbine nozzle guide vane has a
significant effect on the downstream stagnation pressure loss and heat transfer
over the surface of the vane. Traditionally, adjoint-based design optimization
methods for turbomachinery components have used low-fidelity simulations like
Reynolds averaged Navier-Stokes. To reliably capture the complex flow phenomena
involved in turbulent flow over a turbine vane, high-fidelity simulations like
large eddy simulation (LES) are required. In this paper, an adjoint-based
trailing edge shape optimization using LES is performed to reduce pressure loss
and heat transfer over the surface of the vane. The chaotic dynamics of
turbulence limits the effectiveness of the adjoint method for long-time
averaged objective functions computed from LES. A viscosity stabilized unsteady
adjoint method is used to obtain gradients of the design objective function
with reasonable accuracy. A gradient utilizing Bayesian optimization is used to
robustly handle noise in the objective function and gradient evaluations. The
trailing edge shape is parameterized using a linear combination of $5$ convex
designs. Results from the optimization, performed on the supercomputer Mira,
are compared with optimal designs generated using derivative-free design
optimization of the same problem.
