Adjoint-based geometry optimisation with applications to automotive fuel injector nozzles

Methods of Computational Fluid Dynamics (CFD) have matured, over the last 30 years, to a stage where it is possible to gain substantial insight into fluid flow processes of engineering relevance. However, the motives of fluid dynamic engineers typically go well beyond the level of improved understanding, to the pragmatic aim of improving the performance of the engineering systems in consideration. It is in recognition of these circumstances that the present thesis investigates the use of automated design optimisation methodologies in order to extend the power of CFD as an engineering design tool. Optimum design problems require the merit or performance of designs to be measured explicitly in terms of an objective function. At the same time, it may be required that one or more constraints should be satisfied. To describe allowable variations in design, shape parameterisation using basic geometric entities such as straight lines and arcs is employed. Taking advantage of previous experience in the research group concerning cavitating flows, a fully automated method for nozzle design/optimisation was developed. The optimisation is performed by means of discharge coefficient (Cd) maximisation. The objective is to design nozzle hole shapes that maximise the nozzle Cd for a given basic nozzle geometry (i.e. needle and sac profile) and reduce or even eliminate the negative pressure region formed at the entry of the injection hole. The deterministic optimisation model was developed and implemented in the in-house RANS CFD code to provide nozzle shapes with pre-defined flow/performance characteristics. The required gradients are calculated using the continuous adjoint technique. A parameterisation scheme, suitable for nozzle design, was developed. The localised region around the hole inlet, where cavitation inception appears, is parameterised and modified during the optimisation procedure, while the rest of the nozzle remains unaffected. The parameters modifying the geometry are the radius of curvature and the diameter of the hole inlet or exit as well as the relative needle seat angle. The steepest descent method has been used to drive the calculated gradients to zero and update the design parameters. For the validation of the model two representative inverse design cases have been selected. Studies showing the behaviour of the model according to different numerical and optimisation parameters are also presented. For the purpose of optimising the geometries, a cost function intended to maximise the discharge coefficient was defined. At the same time it serves the purpose of restructuring geometries which have controlled or eliminated cavitation inception in the hole entrance. This is identified in the steady-state mode by reduction of the volume of negative relative pressure appearing in the hole entrance. Results of cavitation control on some representative nozzle geometries show significant benefits gained by the use of the developed method. This is mainly because the developed model performs optimisation on numerous parametric combinations automatically. Results showed that, by using the proposed method, geometries with larger Cd values can be achieved and the cavitation inception can, in some cases, be completely eliminated. Cases where all the parameters were combined for redesign the geometry required less modification to predict larger Cd values than cases where each parameter was modified individually. This is an important result since manufacturers are seeking improvement in the performance of products resulting from the least geometry modifications.