Drag Optimisation of Ship Shapes (DROPSS)
Final Report Abstract
The project was concerned with gradient-based optimization methods for CAD-free and thus non-parametrized shapes exposed to immiscible two-phase flows using an adjoint Cahn-Hilliard Volume-of-Fluid Reynolds-Averaged Navier-Stokes (CH-VoF-RANS) approach. Attention was given to the trade-off between adjoint consistency and industrial process capability. The efforts have been structured into four building blocks (I-IV): Accurate and robust (I) adjoint two-phase flow models have been employed that included (II) dynamic floatation aspects, (III) an improved CAD-free shape parameterization for partially wetted shapes subjected to manufacturing constraints and (IV) a novel reduced adjoint turbulence treatment. Different aspects of the simulation-driven shape optimization process have been addressed. Contributions to (I) refer to the derivation, implementation, verification and validation of an efficient engineering CH-VoF branch. In line with analytical considerations for a model problem, a nonlinear equation of state has been derived to relate an indicator function (a.k.a. concentration) with the fluid properties. The work package also covered the derivation of discrete adjoint VoF formulations and the implementation of an adjoint VoF sub-cycling strategy. The suggestion of a discretely differentiable equation of state, together with a novel combination of an inconsistent adjoint VoF method and the CH-VoF approach, allowed for a robust and flexible consistent adjoint two-phase formulation. Building block (II) covered aspects of an adaptive floatation module that has been added to the gradient-based optimization procedure. The floating model was not differentiated and considered frozen during the adjoint simulation. Examples included underlined the capability of the frozen floatation approach and provide partially drastically improved ship hull shapes. It was also demonstrated that fixed floatation can lead to optimization losses when the final shape is released. An implicit surface metric (III) approach was presented to extract the inherently smooth gradient out of the possible rough sensitivity derivative. Attention was devoted to compliance with geometrical constraints, e.g. constant volume, maximum outer dimensions or a plane transom. Finally, the project has been also concerned with improving adjoint investigations of (IV) turbulent flows. A unified algebraic adjoint momentum equation has been derived using mixing-length arguments for the frozen turbulence strategy and a Law of the Wall consistent (differentiated) approach. A simple algebraic expression provided a consistent closure of the adjoint momentum equation in the logarithmic layer. Two additional contributions (V) have been identified: The first (V.1) was concerned with a continuous adjoint complement to 2D, incompressible, first-order boundary-layer (b.-l.) equations. The findings support the heuristic neglect of the adjoint transposed convection term used by many authors of continuous adjoint optimization studies in complex engineering shear flows and offer analytical expressions for adjoint laminar b.-l. parameters. Besides, spatial decoupling (V.2) of the control from the objective affected the formulation of boundary conditions and reduced the iterative efforts when the design surface does not cover the entire wetted surface. Practical applications referred to maritime two-phase flows at the industrial level, namely a Kriso container ship (KCS) and an offshore-supply vessel (OSV). Selected studies have been conducted even in full-scale.
Publications
- Decoupling of Control and Force Objective in Adjoint-Based Fluid Dynamic Shape Optimization. AIAA Journal, 57(9):4110–4114, 2019
N. Kühl, P. M. Müller, A. Stück, M. Hinze, and T. Rung
(See online at https://doi.org/10.2514/1.J058376) - Cahn-Hilliard Navier-Stokes Simulations for Marine Free-Surface Flows. Experimental and Computational Multiphase Flow, 2020
N. Kühl, M. Hinze, and T. Rung
(See online at https://doi.org/10.1007/s42757-020-0101-3) - A Novel p-Harmonic Descent Approach Applied to Fluid Dynamic Shape Optimization. Accepted for publication in: Structural and Multidisciplinary Optimization, 2021
P. M. Müller, N. Kühl, M. Siebenborn, K. Deckelnick, M. Hinze, and T. Rung
(See online at https://doi.org/10.1007/s00158-021-03030-x) - Adjoint Complement to the Universal Momentum Law of the Wall. Flow, Turbulence and Combustion, 2021
N. Kühl, P. M. Müller, and T. Rung
(See online at https://doi.org/10.1007/s10494-021-00286-7) - Adjoint Complement to the Volume-of-Fluid Method for Immiscible Flows. Journal of Computational Physics, 440: 110411, 2021
N. Kühl, J. Kröger, M. Siebenborn, M. Hinze, and T. Rung
(See online at https://doi.org/10.1016/j.jcp.2021.110411) - Continuous Adjoint Complement to the Blasius Equation. Physics of Fluids, 33(3):033608, 2021
N. Kühl, P.M. Müller, and T. Rung
(See online at https://doi.org/10.1063/5.0037779)
