Hull form hydrodynamic design using a discrete adjoint optimization method

Computational fluid dynamics based optimization is becoming increasing popular in hull form hydrodynamic designs; however, existing optimization studies commonly utilize gradient-free methods which can only handle a handful of design variables. Ship hull geometry is necessarily described by a large number of design variables since the hydrodynamic drag is strongly influenced by small changes in the hull shape. To break this limit, in this paper we utilize a gradient-based optimization approach along with the adjoint method for efficient gradient computation. To demonstrate its power, we optimize the stern region of the KVLCC2 tanker using more than 100 design variables subject to proper geometric constraints (volume and thickness) for practical shape. We also evaluate the impact of propellers on the optimization results. We neglect the freesurface since the Froude number is low and the design changes are in the stern region. Overall, we obtain 2.9% and 1.3% hydrodynamic drag reduction for the cases with and without the propeller, respectively. 1999, Mader & Martins 2013, Kenway et al. 2014, Othmer 2014, Lyu et al. 2015, Xu et al. 2015). The adjoint method has also been used in the marine context (Martinelli & Jameson 2007), although their method has not seen wide spread adoption. This is likely due to the challenges of dealing with the naturally unsteady nonlinear interaction of ship waves, and the computational challenges associated with wave breaking. There is another important reason why the adjoint method lags behind in terms of adoption by the hull form design community. We believe it is because the implementation of adjoint derivative computation requires the access to the CFD source code and a dedicated effort for code development; however, current hull form optimization studies commonly rely on commercial CFD solvers whose source codes are not publically available. Fortunately, we developed an efficient adjoint optimization framework based on an open-source CFD solver (OpenFOAM). Our optimization framework has been successfully applied to constrained aerodynamic optimizations for aircraft and automobiles (He et al. 2017). In this paper, we extend this framework for ship hull form optimization. To demonstrate its power, we conduct hydrodynamic shape optimization for the stern region of the KVLCC2 tanker. We parameterize the hull shape using more than 100 design variables and impose proper geometric constraints (volume and thickness) for practical shape. Moreover, we evaluate the impact of propellers on the optimization results. The free-surface is neglected and a double-body boundary condition is imposed on the calm-water plane. It is import to note that there are two different methods for formulating the adjoint of a flow solver: continuous and discrete. The continuous approach derives the adjoint formulation from the NavierStokes (N-S) equations and then discretizes for numerical solution. In contrast, the discrete approach starts from the discretized N-S equations and differentiates the discretized equations to get the adjoint terms. Although these two approaches handle adjoint formulation in different ways, they both converge to same answer for a sufficiently refined mesh (Nadarajah & Jameson 2000). We opt to use the discrete approach since the adjoint derivative is consistent with the flow solutions. Moreover, it is easier to derive formulation for new boundary condition and objective functions. The rest of the paper is organized as follows: In Section 2, we introduce the optimization framework and its components. The hull shape optimization results for KVLCC2 is shown in Section 3. Last, the conclusion remarks are summarized in Section 4.