Löhner, Rainald

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.

Coupling of unstructured, overlapping 3D grids in finite-volume methods (FVM) is usually based on a local interpolation of field values, which (a) is insufficient to guarantee mass conservation and (b) requires a sufficient overlap of the wetted domain. Effects of the non-conservative coupling are analysed and the mass-dependent pressure in incompressible FVM is stabilised by global mass conservation practices. Areas with an insufficient overlap are numerically manipulated to allow the simulation of dynamic body contact. This enhanced approach is validated and applied, e.g. within the simulation of a gear pump and for contact simulations of a cylinder/sphere with a wall. The latter reveal a significant increase and a coupling of additional resistance and inertia forces.

To efficiently calculate the sensitivity derivative of hydrodynamic objective functionals with respect to the shape, the adjoint Navier-Stokes equations were derived analytically. Consistent adjoint discretisation schemes were developed term-wise from the primal finite-volume discretisation. The adjoint method, implemented in the framework of a general-purpose pressure-correction based RANS code for unstructured grids, was validated against analytical solutions and verified by means of the direct-differentiation method. The adjoint-based sensitivity derivative was computed to guide a manual re-design of a ship hull to improve the wake field. Moreover, automatic shape-optimisation runs were carried out to reduce the power loss for ducted flows.

Filters

Settings

Sort By

Results per page