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Adjoint-based shape optimization constraint by turbulent two-phase Navier-Stokes systems
Citation Link: https://doi.org/10.15480/882.3794
Publikationstyp
Doctoral Thesis
Date Issued
2021-10
Sprache
English
Author(s)
Advisor
Title Granting Institution
Technische Universität Hamburg
Place of Title Granting Institution
Hamburg
Examination Date
2021-09-21
Institut
TORE-DOI
Citation
Technische Universität Hamburg (2021)
The thesis aims to advance gradient-based optimization methods for non-parametrized shapes exposed to immiscible two-phase flows using an adjoint Reynolds-Averaged Navier-Stokes (RANS) approach. Attention is given to the trade-off between adjoint consistency and industrial process capability. The efforts can be structured into four building blocks (I-IV): Compatible fully turbulent (I) primal (physical) and (II) dual (mathematical, adjoint) relationships together with appropriate objective functional formulations (III) are analysed with curiosity and scepticism at the same time, in order to attain the required accuracy, robustness and efficiency. The geometry engine (IV), which translates the computed sensitivities into shape deformations and grid adjustments, is crucial for the efficiency of the process, the technical usability of the result, and the HPC capability. Different aspects of the simulation-driven shape optimization process are addressed. This research’s common ground is to analyse potential issues in greater depth rather than to formulate ad-hoc measures. The guiding principle frequently follows the concept of ”Learning from the Adjoints”. It is seen that potential weaknesses displayed by an adjoint approach –e.g. when developing (continuous) analytical solutions, in conjunction with (discrete) convergence problems– are often attributable to weaknesses of the primal formulation and a twist of the research question can lead to fruitful insights.
Contributions to (I) refer to the development of an efficient engineering Cahn-Hilliard (CH) Volume-of-Fluid (VoF) branch. In line with analytical considerations for a model problem, a nonlinear Equation of State (EoS) is derived to relate an indicator function with the fluid properties. Building block (II) covers the derivation of discrete adjoint VoF formulations and the implementation of an adjoint VoF sub-cycling strategy. The suggestion of a discretely differentiable EoS, together with a novel combination of an inconsistent adjoint VoF method and the CH-VoF approach, allows for a robust and (flexible-) consistent adjoint two-phase formulation. Another major part is concerned with a continuous adjoint complement to 2D, incompressible, first-order boundary-layer equations. The findings support the heuristic neglect of the adjoint transposed convection term and offer analytical expressions for adjoint laminar boundary-layer parameters. The thesis is also concerned with improving adjoint investigations of turbulent flows using mixing-length arguments for the frozen turbulence strategy and a Law of the Wall consistent approach. An algebraic expression provides a consistent closure of the adjoint momentum equation in the logarithmic layer. Spatial decoupling of the control from the objective (III) affects the formulation of boundary conditions and reduces iterative efforts when the design surface does not cover the entire wetted surface. Additionally, an implicit surface metric approach is presented to extract the inherently smooth gradient (IV) out of the possible rough sensitivity derivative. Attention is devoted to compliance with geometrical constraints, e.g. constant volume or maximum outer dimensions. Finally, an adaptive floatation module is added to the gradient-based optimization procedure, which is not differentiated and considered frozen during the adjoint simulation. Examples included underline the capability of the frozen floatation approach and provide partially drastically improved ship hull shapes. It is demonstrated that fixed floatation can lead to optimization losses when the final shape is released.
Almost without exception, applications relate to maritime two-phase flows at the industrial level. Some of them are conducted even in full-scale. They refer to a Kriso container ship, a generic submarine, a double-ended ferry, and an offshore-supply vessel.
Contributions to (I) refer to the development of an efficient engineering Cahn-Hilliard (CH) Volume-of-Fluid (VoF) branch. In line with analytical considerations for a model problem, a nonlinear Equation of State (EoS) is derived to relate an indicator function with the fluid properties. Building block (II) covers the derivation of discrete adjoint VoF formulations and the implementation of an adjoint VoF sub-cycling strategy. The suggestion of a discretely differentiable EoS, together with a novel combination of an inconsistent adjoint VoF method and the CH-VoF approach, allows for a robust and (flexible-) consistent adjoint two-phase formulation. Another major part is concerned with a continuous adjoint complement to 2D, incompressible, first-order boundary-layer equations. The findings support the heuristic neglect of the adjoint transposed convection term and offer analytical expressions for adjoint laminar boundary-layer parameters. The thesis is also concerned with improving adjoint investigations of turbulent flows using mixing-length arguments for the frozen turbulence strategy and a Law of the Wall consistent approach. An algebraic expression provides a consistent closure of the adjoint momentum equation in the logarithmic layer. Spatial decoupling of the control from the objective (III) affects the formulation of boundary conditions and reduces iterative efforts when the design surface does not cover the entire wetted surface. Additionally, an implicit surface metric approach is presented to extract the inherently smooth gradient (IV) out of the possible rough sensitivity derivative. Attention is devoted to compliance with geometrical constraints, e.g. constant volume or maximum outer dimensions. Finally, an adaptive floatation module is added to the gradient-based optimization procedure, which is not differentiated and considered frozen during the adjoint simulation. Examples included underline the capability of the frozen floatation approach and provide partially drastically improved ship hull shapes. It is demonstrated that fixed floatation can lead to optimization losses when the final shape is released.
Almost without exception, applications relate to maritime two-phase flows at the industrial level. Some of them are conducted even in full-scale. They refer to a Kriso container ship, a generic submarine, a double-ended ferry, and an offshore-supply vessel.
Subjects
Shape Optimization
Turbulent Two-Phase Flow
Maritime Applications
Computational Fluid Dynamics
Adjoint-Based Sensitivity Analysis
DDC Class
620: Ingenieurwissenschaften
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