A goal-oriented adjoint-based optimization approach to model vortex generator flows using smooth source term distributions

Abstract

Vortex generators (VGs) are typically about two orders of magnitude smaller than their host component (such as an airplane wing). For this reason, conducting a fully-resolved RANS simulation to isolate their impact on the flow field is computationally expensive. This work presents a goal-oriented adjoint-based approach to model vortex generators using smooth source term distributions to make their simulations tractable.

Several approaches to modelling VGs have been proposed in the past. Phenomenological models such as BAY and jBAY form source term descriptions, while others directly model the vortex or its effects. Recently, a goal-oriented approach to model VGs was introduced. Florentie et al. optimized a set of discrete source terms in a cuboidal domain at the location of the VG, using a fully-resolved solution as a reference. The superior accuracy of the model motivated Dierickx et al. to develop a surrogate model of the optimized source term in order to extend its applicability to any mesh and account for the variability in boundary conditions (Inflow angle and Reynolds number). However, the reduced-order source term produced discretization errors due to the presence of steep gradients.

To overcome the shortcomings associated with the goal-oriented approach and its reduced-order modelling, in this work, a smooth-basis representation of a co-rotating VG array was constructed using a trust-region-based optimization algorithm. The descent direction was obtained from an adjoint system of equations formulated based on an unconstrained optimization problem involving an objective/goal functional and the RANS equations.

The developed framework produced source term distributions that were smooth enough to be resolved on a coarse mesh and accurate enough to generate a good representation of the VG’s effect on the flow field. Specifically, flow parameters such as the Reynolds stress, shape factor and boundary layer profiles corresponding to the fully-resolved simulation were accurately recreated on the coarse mesh. To account for the evolving inflow angle at the VG-surface junction during the flow field calculation, a surrogate model was constructed to vary the source term accordingly.

The developed smooth source term framework brings a new capability to aerodynamic design as, unlike the previous approaches, it can also be used to accurately model arbitrary flow control devices on relatively coarse meshes.