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Cavitation poses a formidable challenge to modern boat design, especially for high-speed sailing vessels participating in events like America's Cup, Vendee Globe, and Route du Rhum. Hydrofoils, in particular, are susceptible to cavitation, which can cause surface damage and even catastrophic failure, putting the crew at risk and incurring significant expenses. Propellers, too, suffer from cavitation, leading to reduced efficiency, durability, and costly replacements. In this blog post, we'll explore how the advanced features in adaptive grid refinement (AGR) in Fidelity Fine Marine help model and simulate cavitation in hydrofoils to achieve fast and accurate results. Don't let cavitation hold back your boat's performance any longer. With Fine Marine, you'll be able to tackle this challenge head-on and stay ahead of the race!
DTC Propeller - Golf (2018)
Modeling cavitation requires a new phase, which is vapor. So, there are three phases in cavitation simulation, i.e., the water, free surface, and vapor. To top it all, the flows can be quite unsteady and complicated, as you can observe in the pictures below, where the vapor pockets detach themselves from the surface. Moreover, the technical constraints while simulating cavitations make the simulations highly dependent on the mesh. To properly capture even the smallest details of cavity pockets, mesh refinement zones must be defined. This process is demanding in terms of engineering time and requires a significant amount of skill and knowledge.
Images from LEGI cavitation tunnel, Grenoble.
AGR is widely used in various applications such as resistance and seakeeping, for self-propulsion with actuator disk and meshed propeller, and ventilation around hydrofoils and propellers. This technique has proven reliable and useful in gaining accuracy and reducing computation time. AGR in Fine Marine simplifies the setup for such applications.
The technology behind AGR in Fine Marine is simple. Based on the assessment criteria, isotropic and anisotropic subdivisions of the initial mesh cells are performed. AGR refines the free face to obtain the desired level of precision. The left-side image shows no specific level of refinement at the free surface, while the image towards the right shows many divisions that achieve the right cell size level.
Free surface refinement using AGR in Fidelity Fine Marine
Steps behind an AGR call.
The benefit of using AGR is its relatively low CPU cost. You can call it often and potentially adapt it to highly unsteady flows, such as cavitation.
Regarding cavitation, we focus on two criteria: multi-surface and flex components.
The Multi-surface (MS) criterion helps capture the free surface or cavitation interface between two fleets: water and air or water and vapor. The interface can be easily controlled by setting the target cell size, thereby imposing the desired resolution to capture the free interface.
The Flux-component Hessian (FCH) criterion captures all the flow features and works by refining the matrix of second derivatives of both the pressure and velocity fields. By capturing pressure and velocity well, it provides a superior flow resolution. To control this criterion, there are two parameters - a threshold that controls its sensitivity to flow features and a limiter that sets a minimum cell size to avoid creating excessively fine cells.
Refinement using the combined criteria using the software MS-FCH.
The multi-surface and flux-component Hessian criteria are combined and available in the software as MS-FCH. The simulation process is a combination of various factors, including the Hessian threshold that controls sensitivity. You can adjust a slider to choose between accuracy, high sensitivity, and a relatively local simulation. By selecting the appropriate value, you can determine the type of simulation you want. Mesh is dynamically adapted to the flow, guaranteeing optimal grid size at any time and space. As a CFD engineer, you won't have to worry about refining your simulation to capture the physics because the combined criteria and threshold will cover everything. It will capture the free surface, interface of fluids and other important flow features. This, in turn, changes the way you create meshes.
Hessian threshold is varied to switch between the coarse and fine mesh.
AGR parameters directly influence the fineness of the grid. For example, in the above 2D hydrofoil, you can vary the Hessian threshold to switch between a relatively coarse and a very fine mesh. You can choose the precision you need from the start. The best part is that changing the Hessian threshold is like performing a grid convergence study. In a traditional grid convergence study, you create several meshes from coarse to fine, and then compare the results. But with AGR, you can create different computations by changing only one value; you don't have to re-mesh. Instead, variations can be used to mimic a grid convergence study.
One interesting thing to note is that the ideal mesh for your simulation is no longer something you had prepared in advance. Instead, it is the output of the simulation.
Creating a coarse mesh has many advantages when generating the ideal mesh. One of them is that it allows for easier insertion of values in Fidelity Hexpress, and the inflation technique can be used for fine-tuning to ensure a smooth transition with the far-field mesh. This technique also preserves the possibility of having a full-hex mesh.
However, there is one downside to using a coarse mesh. Very dense surface refinement can compress viscous layers, leading to small thicknesses of the boundary layer, as seen in the image on the left. On the other hand, the image on the right shows a much coarser mesh generated for AGR, where the thickness of the boundary layer is much greater. The coarse mesh also creates a big region with cells aligned along the geometry in the viscous layer. By looking at the mesh on the right, the divisions that will be performed to obtain a mesh with good accuracy can already be imagined.
Very dense surface refinement can compress viscous layers.
To better understand how AGR changes the way the mesh is generated, let's look at a 3D example. We never apply volumetric refinement in this case since AGR always takes care of it. This eliminates the need for refinement boxes and allows AGR to delegate the process, resulting in a cost-effective mesh. The image on the left shows a classic mesh while the same mesh has been coarsened for AGR on the right, illustrating the significant difference in the level of robustness and confidence that AGR provides.
Classic mesh to coarse mesh using AGR.
In conclusion, AGR offers a paradigm shift that simplifies the meshing task for CFD engineers while ensuring a good compromise between cell count and accuracy. By enabling the creation of a coarse mesh and producing the ideal mesh as an output of the simulation, it allows for easy performance of grid convergence studies on unsteady cases. AGR paves the way toward more automation, offering robustness and confidence that can be enabled with limited skill sets and knowledge.
To learn more about AGR for unsteady cases using Fidelity Fine Marine, watch the recorded webinar High Accuracy Cavitation Simulation of Hydrofoils –