This thesis explores fast simulation of time-periodic flows, characterized by behavior that repeats at regular intervals. These flows are present in both natural and engineered systems. Examples include flows past wind turbines, in the heart and arteries, and around propellers. Due to their long time domains, time-periodic flows pose challenges in both experimental and numerical studies.
Many engineering tasks, like optimization, require numerous model evaluations across a wide range of inputs. We need a fast and accurate model to directly interact with the model in the design process. To contribute to this goal, we first develop a high-fidelity method specifically designed for time-periodic flows. Using this model, we then create a time-periodic reduced-order model to enhance simulation efficiency.

In the high-fidelity model, we employ the isogeometric analysis framework to achieve higher-order smoothness in both space and time. The discretization is performed using residual-based variational multiscale modelling and weak boundary conditions are adopted to enhance the accuracy near the moving boundaries of the computational domain. We enforce the time-periodic boundary condition within the isogeometric discretization spaces, which converts the two-dimensional time-dependent problem into a three-dimensional boundary value problem. The motion is known a priori and we restrict ourselves to two spatial dimensions. Application of the computational setup to heaving and pitching hydrofoils displays very accurate and exactly periodic results for lift and drag.

We use the high-fidelity model to develop a POD-Galerkin reduced-order model, which retains inherits the features of the high-fidelity model while reducing the number of variables in both space and time. We evaluate the reduced-order model with numerical experiments on moving hydrofoils. Reduced-order model solutions agree well with those of the high-fidelity model. The errors over the entire time period of the computed forces are less than 0.2%. Our time-periodic reduced-order model offers speed-ups ranging from O(10^2) - O(10^3) compared to the full-order model.

The non-linear nature of the Navier-Stokes equations creates a computational bottleneck in the reduced-order model. We explore hyper-reduction techniques to mitigate these challenges. We focus on empirical interpolation methods, which have shown promise in reducing the complexity of non-linear operators. The model performed well for the experiment with steady flow, with force and solution errors ranging from O(0.01% − 10%), depending on the sampling method. The hyper-reduced model achieves a speed-up of O(10^5) compared to the full-order model, and O(10^3) compared to the reduced-order model. This enables real-time computations with direct interation of the user. However, the hyper-reduced model could not provide a solution for the time-periodic flow experiment.

To show the applicability of the reduced-order model to an industrial problem, we apply the the model to a vertical axis wind turbine. Vertical-axis wind turbines offer significant advantages for urban applications over conventional wind turbines due to their lower noise levels. However, their performance is highly sensitive to various factors requiring high-fidelity simulations to optimize its performance. The model was used to determine the optimal operating point of the turbine, maximizing energy production per cycle under the given conditions. It was observed that the turbine's energy output was negative, likely due to the low Reynolds number (Re = 1000) used in this study.

Future research can expand on this thesis in several ways. Extending the model to three spatial dimensions would require solving four-dimensional boundary value problems, potentially benefiting from mesh adaptivity techniques. Further exploration of hyper-reduction methods, such as empirical quadrature procedures or neural network-based models, could enhance the model's efficiency. Applying hyper-reduction directly within isogeometric discretizations may also offer significant advantages. Additionally, further verification for higher Reynolds numbers and adaptation to other industrial applications, like wind farm and ship propeller optimization, could bridge the current theoretical advances with practical use. Finally, using time-periodic data from standard models to develop time-periodic reduced-order models could expand their applicability.@en

Extreme wave impacts can damage ships and pose a risk to those on board. An extreme wave impact can be green water: a wave impact on a ship's deck or superstructure, or slamming: a ship's underside slamming on a wave. To prevent serious accidents these green water and slamming impacts need to be minimized. Predicting the probability and impact pressures can make minimizing impacts possible. Extreme wave impacts are challenging to predict as they are multiphase, nonlinear, turbulent and rare. The rarity, complexity and variety of impacts have resulted in limited studies into the statistics of extreme wave impacts, causing questions about the probability, distributions and ranges in which impacts occur. To predict extreme wave impacts answers to these questions would be helpful.

The goal of this thesis is to study the statistics of extreme wave impacts. To fulfill this goal a large data set of extreme wave impacts is collected. A new testing facility is created to collect data by adding a wave maker to an existing recirculating tank. In the test facility water and waves flow past the model, allowing for long testing times. Three large experimental data sets with a ship with forward velocity in head waves are collected. The collected data is in total 246 hours of experimental data over 23 test cases, representing over 2766 hours of continuous sailing at full scale.

From the first experimental data set the probability of occurrence of green water and the expected maximum pressures during green water events are identified. The data set contains green water events in different sea states, forward speeds and drafts. Two proposed methods to estimate the probability of green water occurrence are compared. One method is based on the probability of water exceeding the deck and one on a ship’s freeboard and the significant wave height, the former being in better agreement with the data, the latter being more practical for designers. The maximum pressures caused by green water are distributed according to the Fréchet distribution, also called extreme value distribution II. With the newly identified distribution, an equation to calculate the probability of a pressure limit being exceeded for a ship in operation is formulated. This first data set shows that the distribution of the time between green water occurrences is exponential, indicating that when green water occurs is independent of the time since the last occurrence.

The second set of experiments is aimed at identifying the influence of surge on green water and slamming. Long-running experiments with forward velocity and irregular waves are repeated with and without surge. Surge is found to increase the probability of green water events, but the impact pressures on deck and the probability of a green water event reaching the deck box decreases when the ship is free to surge. In this second data set green water and slamming events turn out to not occur independently as both event types cluster. The clusters occur for large probabilities of occurrence, which is why the first data set did not show these dependent clusters. Clusters are caused by large pitch motions. Larger pressures on deck are found for clustered events.

The conditions under which green water occurs and the relation between water exceeding the deck and green water are investigated. The relation is not direct and a difference between green water and exceedance that does not develop into a flow on deck is identified. A proposed prediction method follows from the difference between green water and exceedance. Pitch is identified as an important indicator for green water as green water events consistently occurred with large forward pitch motion, while exceedance also occurred with neutral pitch.
A prediction method of probability is proposed that implements separate limits for the motions and wave elevation that occur simultaneously, thus including the phase difference between the motions and wave elevation.

Design variations with different drafts and freeboards at the bow are tested in the third set of tests. A large set of 3263 green water events in irregular waves with forward velocity is experimentally obtained for six different bow designs. The data demonstrates that both freeboard and draft at the bow affect the probability of green water. Increasing the draft at the bow increases the swell-up, reducing the effective freeboard and in turn, increasing the probability of green water.

Increasing the freeboard results in a decrease in the probability of green water, as expected. However, the probability is not reduced equally for different green water impact pressures. The joint probability of green water occurrence and pressures shows that increasing the freeboard only decreases the probability of low-pressure events. Increasing the freeboard increases the probability of high-pressure events. These results highlight the importance of statistics when designing for green water.

The large experimental data sets have been combined with a machine learning method: SINDy. The models are trained to predict the acceleration of heave and pitch with the parameters heave, pitch, velocity of heave and pitch and the wave elevations along the hull. As a first step, a model is trained on fictitious data. The data is based on empirical response amplitude operators. The resulting model represents a damped mass-spring system with external forcing. The identification of the damped mass-spring system with external forcing is sensitive to random noise in the input data. Models have also been trained on the experimental data available. The models trained on experimental data did not result in the expected damped mass-spring system with external forcing model. The likely cause is noise in the experimental data.@en

The interaction of a turbulent flow with the leading edge of a foil is one of the dominant noise sources for many engineering applications, including aircraft wings, (wind) turbine blades, and non-cavitating marine propellers such as those found on tidal turbines, naval vessels and submarines. Incorporating a better understanding of the turbulence intensity on the far-field radiated noise in the early design phases can help reduce low-frequency broadband noise that is harmful to humans and (marine) wildlife. A simple framework, such as that proposed by Amiet, can provide fast predictions once validated for more complex problems. The current work assesses numerical predictions on far-field radiated noise by the leading edge of a NACA0008 airfoil for varying turbulence intensities. The flow is simulated within ReFRESCO, a partially averaged Navier-Stokes solver in which turbulence is generated using a synthetic inflow turbulence generator. Inflow turbulence and predicted far-field noise by the Ffowcs Williams-Hawkings formulations are experimentally and numerically validated, showing that the proposed method can generate realistic turbulence, pressure data on the foil surface and associated far-field noise. Variation in the turbulence intensity shows an unwanted change in the integral length scale, which did not seem to affect the far-field radiated noise. In agreement with Amiet, a linear increase in turbulence intensity leads to a near quadratic increase of the radiated noise for a receiver directly above the foil. A rapid change in scaling is seen for receivers more closely aligned with the flow direction both up- and downstream of the foil, for which the far-field noise scales with the turbulence intensity to the sixth power. Variations in the turbulence intensity between 4 % and 16 % dominate over a change in the integral length scale from 30 mm to 65 mm.

Facing the critical challenge of reducing greenhouse gas (GHG) emissions in the maritime industry, this thesis explores the potential of smart control systems using Reinforcement Learning (RL) for autonomous sailing. Traditional controls for sailing fall short in navigating the complex, dynamic conditions of maritime environments. RL has shown to be effective for continuous control applications in these types of conditions, however, primarily in simulated environments. Therefore, this study aims to show the potential of RL for autonomous sailing control (ASC) by means of a small scale project. A fast-time simulation of an Optimist is used to train the sailing controls required to reach an upwind target. The controls are then transferred to a robotized Optimist in a real-world environment to test the transferability of the simulation trained controls. First, the reality gap, or modelling error, between the simulation and real-world environment is quantified to be able to assess the performance of the used techniques to bridge the existing gap. The sim-to-real techniques of Domain Randomization (DR) and the addition of observation noise (ON) are applied during the training process. To test the effectiveness of the trained RL controls, the best performing ones in the simulation are selected and tested in the real-world environment. The performance of the RL controlled Optimist is compared to state-of-the-art controls in robotic sailing. Their performances are measured and compared by means of success rate and a physics-based metric that calculates the efficiency of the sailboat to use the power of the wind to propel itself, called the energy ratio. The results show that the RL controls are highly successful in the sailing simulation, however, the transfer to the real-world remains a major challenge. DR does improve the sim-to-real transfer, resulting in an agent that is able to reach a 100% success rate throughout 12 runs in the real-world environment.