Adjoint methods for car aerodynamics

Abstract

The adjoint method has long been considered as the tool of choice for gradient-based optimisation in computational fluid dynamics (CFD). It is the independence of the computational cost from the number of design variables that makes it particularly attractive for problems with large design spaces. Originally developed by Lions and Pironneau in the 70's, the adjoint method has evolved towards a standard tool within the development processes of the aeronautical industries. Its uptake in the automotive industry, however, lags behind. The first systematic applications of adjoint methods in automotive CFD have interestingly not taken place in the classical shape design arena, but in a relatively young discipline of sensitivity-based optimisation: fluid dynamic topology optimisation. While being an established concept in structure mechanics for decades already, its transfer to fluid dynamics took place just ten years ago. We demonstrate that specifically for ducted flow applications, like airducts for cabin ventilation or engine intake ports, it constitutes a very powerful tool and has matured over the last years to a level that allows its systematic usage for various automotive applications. To drive adjoint-based shape optimisation to the same degree of maturity and robustness for car applications is the subject of ongoing research collaborations between academia and the car industry. Achievements and challenges encountered during these efforts are presented. BackgroundComputational Fluid Dynamics (CFD) is a central element of the automotive development process. Besides the classical external aerodynamics for the prediction of drag and lift coefficients, there is a whole plethora of applications for ducted flows: airducts for cabin ventilation, engine intake ports, exhaust systems including catalytic converters, air intakes, water jackets of cylinder heads, cooling plates for electric vehicle battery packs and many more ( Figure ). The standard procedure of developing these parts still consists of manual iteration loops between designer and computational engineer, and automatic optimisation methods are being used systematically only for some selected CFD applications (e.g. for airducts, Figure ). Via an automatic process chain consisting of a CAD (Computer-Aided Design) system, meshing software, CFD solver and post-processor a black-box optimisation algorithm, typically of the evolutionary strategy type, is employed to drive a parameterised CAD-model into an optimal state.Due to the high computational effort associated with black-box optimisation, where the number of CFD evaluations scales roughly linearly with the number of design variables, the explorable design space is very limited: In our current practice, these methods cannot afford more than ten design parameters. An additional obstacle that inhibits the further

An adjoint method for gradient-based optimization of stellarator coil shapes

“…Adjoint methods were developed in the 1970s for sensitivity analysis of drag and flow dynamics [21] and have been widely used for shape optimization in the field of aerodynamics and computational fluid dynamics (CFD) [19,20,[22][23][24]. Only recently have these methods been used for tokamak physics in the context of fitting model parameters with experimental edge data on ASDEX-Upgrade [25] and advanced divertor design with plasma edge simulations [26].…”

Computing local sensitivity and tolerances for stellarator physics properties using shape gradients

“…Hence, second derivative information (which we will not consider here) is needed to understand variation in f total about an optimum [40], but second derivative information is not necessary to understand the sensitivity of any individual criterion f j at the optimum. Figure reproduced from [14], licensed under CC BY 2.0; the original has been cropped.…”

Fixed point discrete adjoint of SIMPLE-like solvers

“…One of the most widely used adjoint codes is the continuous adjoint of OpenFOAM 8 which has entered routine industrial application with topology optimisation. 9 Discrete adjoints for the SIMPLE method 10 have been presented, 11-13 but use 'brute-force' methods, which here means black-box application of AD.…”