Impact of Free Surfaces on Turbulent Kinetic Energy in Ships

Turbulent Kinetic Energy (TKE) is a fancy term for measuring the unsteady loads that ships face when moving through water. This measurement is important for designing things like propellers and devices that help save energy. Most of the time, Simulations are done using a simplified model that assumes symmetry to save time and effort. However, real-life ships do not have this luxury. They deal with a free surface of water, which can change the game entirely.

In a case study involving a large vessel known as the Japan Bulk Carrier, simulations were performed with and without considering the free surface. These simulations looked into TKE in the Vortex Cores behind the ship. The focus was also on pinpointing the center of these vortices, as getting this right is crucial for understanding the flow patterns.

Interestingly, when finer mesh simulations were run, they revealed an unexpected trend in TKE, prompting a deeper investigation to rule out any method-related issues from using a hybrid model. Basically, we found that moving the positions of the vortex cores around altered the results significantly, which raises questions about how reliable the experimental center positions are.

To improve the comparison of results, a fixed position for the vortex cores was used for all cases. This modification revealed a different story. The medium meshes were then adjusted, and one refinement box was extended further forward, leading to results that better matched the fine meshes. It turned out that when looking at TKE as a whole, there wasn’t much of a difference between simulations that included the free surface and those that didn’t. However, the structure of the ship was still influenced by the water’s surface, which changed local characteristics.

As everyone became more concerned about energy efficiency due to ecological reasons, there was a strong push for developing optimizations and devices to reduce energy demands for large vessels. Many studies showed that improvements are often marginal, sparking debates about whether simulation results can truly lead to improvements in the real world. Many simpler models ignored the free surface altogether, using a flat mirror instead. But as even slow ships still create ripples behind them, it's clear that a free surface impacts the flow around them.

Newer software tools can handle Free Surfaces through different methods. Research on underwater bodies near the surface has shown changes in the flow pattern and drag, even at lower speeds. For larger vessels, differences in flow velocities were noted, but they generally did not impact key factors like resistance. In more extreme situations, such as in waves, the impact on energy-saving devices (ESDs) was significant enough that the loss in thrust was greater with ESDs than without.

Turbulent kinetic energy remains an important measurement, as it not only affects thrust but also structural integrity. The main goal of this study was to see how the free surface influenced TKE around the wake of the Japan Bulk Carrier. They hoped to collect insights to understand how much the interface matters when analyzing results that could be affected by changing loads.

The paper began with explanations about motivation and existing knowledge before diving into the theoretical background, mesh setups, and case specifications. The results section presented some basic verification data, followed by a discussion of grid convergence and preliminary results. Further simulations and analyses were conducted due to some inconsistencies that arose, and these were explored in depth in the discussion.

Unsteady loads acting on propellers in a ship's wake are generally caused by three things: changes in velocity due to variations in the ship's speed or the surrounding waves, non-uniformity in the wake, and strong turbulence, particularly in larger vessels like tankers and bulk carriers. While the first point wasn't examined, the second could be covered using commonly accepted techniques, while analyzing the third required looking into turbulence structures using more advanced methods.

A previous workshop highlighted that TKE levels in various sections behind the Japan Bulk Carrier differed significantly when calculated with different techniques. Earlier studies pointed out that propeller thrust fluctuations identified in URANS (a more traditional simulation method) tend to be regular and low. In comparison, thrust fluctuations identified through hybrid methods were irregular with higher peaks. This highlighted the need to use hybrid methods to accurately capture turbulence in the wake.

Interestingly, while one study found that the free surface had some effect, another study found no significant relationship. However, it is crucial to analyze these findings closely. Experiments previously conducted on the Japan Bulk Carrier were performed at a low Froude number, allowing the assumption of symmetry in the modeling. However, just a handful of simulations looked at how the free surface influenced flow. None of these were done using advanced turbulence-resolving methods.

In earlier research, attempts were made to measure the influence of free surfaces on TKE, mainly through experiments. A basic takeaway is that there are differences in pressure distribution that occur due to the moving ship creating waves and altering the surface. This essential change affects the pressure patterns and is particularly evident when considering small movements.

One researcher conducted experiments with flat plates and undisturbed surfaces to analyze the wake with particle image velocimetry. He showed that secondary flows emerged from the mixed boundary conditions due to the free surface. Others demonstrated that turbulence caused by free surfaces was linked to wave-breaking, and then further studies showed that even short and steep laboratory waves can result in turbulence due to the motion of the water.

Further studies have shown that free surfaces can alter velocity fields, as found in CFD simulations. The results from simulations using the volume-of-fluid method were more in line with actual experiment findings. TKE was found to be higher due to the free surface, causing a slowdown in flow, even at lower speeds. Yet, these simulations relied mainly on traditional methods, leading to limited insights into detailed flow features.

One recent study previously attempted to tackle the issue but only used a single mesh size. It was acknowledged that smaller Courant numbers and a longer average time were preferred when using scale-resolving methods, as initial choices may have led to ambiguous identification of vortex cores. The necessity of different grid sizes was not recognized back then, and differences in results stemmed from later adjustments.

For vessels, fully turbulent flow is assumed above a certain speed. However, the usual design speed for ships typically corresponds to a range where turbulence is not fully developed. A hybrid model is optimal when there are significant separations in the boundary layer. Given that turbulence is a rapidly fluctuating behavior, transient CFD codes become crucial in describing the flow accurately.

The simulations utilized a specific turbulence model to ensure that resolved TKE aligns with the expected outcomes. It was essential to implement a blending function for the hybrid model, allowing a smoother transition between modeling methods. The meshes created were validated through previous benchmarks, and simulations were run using different methods to analyze the free surface.

Different methods exist to model the free surface in computational fluid dynamics. The study mainly used two approaches from the OpenFOAM framework. One was algebraic VOF, while the other was geometric VOF, allowing for more precise interactions at the water's surface. These simulations were compared with earlier research outputs to ensure consistency and reliability.

A significant part of the study involved manually extracting a sector around the vortex core to analyze TKE, looking for maximum axial vorticity. The outputs gathered were then processed to visualize the TKE and identify the position of vortex cores accurately. These analyses aimed to gauge the intensity of turbulence related to the vortices and evaluate the flow features captured in the simulations.

Different meshes were created to ensure proper grid spacing for accurate results, with a reference length based on the ship’s dimensions. Employing a hybrid approach allowed for using wall functions efficiently. The fine meshes needed to be adequately resolved, particularly around the waterline, to capture the interface effectively.

Boundary conditions were set to simulate realistic fluid behaviors, and performance evaluations were conducted using high-performance computing resources to run the simulations. The results were analyzed through various methods, looking at the TKE distributions and ensuring they aligned closely with experimental data.

A main observation was that the TKE values fluctuated significantly between different mesh sizes and methods used. While grid convergence studies are essential, they can become complicated with hybrid methods. Though some discrepancies were noted, it’s crucial to understand that these differences could arise from the method itself or from the mesh sizes used.

When results were presented following established guidelines, it became clear that variations in TKE were evident, indicating the complexity of the flow patterns. The methodology also established a fixed vortex center for future observations. This method helped standardize the comparisons and suggested improved alignment of results.

While examining the overall trends, it was noticed that integral TKE values did not highlight significant differences between the single-phase and two-phase simulations. However, the spatial distributions showed some variances, suggesting that factors like mesh size may play a crucial role under certain conditions.

After finalizing the analysis of vortex core positions and adjusting grid configurations accordingly, TKE distributions began to converge in a more reliable manner. Despite earlier concerns about the fine mesh, further refinements indicated that it could provide insights closer to experimental findings.

Ultimately, even though the free surface had little impact on TKE measurements, how it presented different spatial characteristics remained a focal point. When considering devices that depend on the effects of fluid flow, the free surface could substantially alter pressure distributions and needs careful consideration in simulations to ensure accurate designs.

In conclusion, investigating the influence of free surfaces when measuring turbulent kinetic energy remains a complex yet vital undertaking for ship design. While the findings indicate no significant differences in total TKE, the varying spatial distribution highlights the importance of detailed simulations. Moving forward, it’s essential to take these results into account and continue exploring how free surfaces affect different vessel designs, especially in more challenging environments like shallow waters or different speeds.

Further research will look at how these findings can apply to different ship types and conditions, leading to a better understanding of the relationship between TKE, free surfaces, and overall energy efficiency. In the quest for greener and more efficient shipping practices, every little bit helps.