# Immersed Boundary Method

### Key Takeaways

• The immersed boundary method is a numerical technique used for the simulation and analysis of fluid movement and deformation around the structure without the need for elaborate meshing.

• The immersed boundary method uses a set of points or markers that can be used to analyze the fluid-structure interaction and the associated deformations.

• In aircraft design, CFD tools allow the implementation of the immersed boundary method and the associated fluid-structure interaction algorithm to simulate flow and the associated structural response.

The immersed boundary method eliminates the need for meshing

What is the common process for simulating flow around an object? Let us consider that a spherical ball is placed as an obstacle in the flowing stream of fluid. Normally, a mesh is explicitly created around the ball and the flow behavior is simulated to analyze its movement and effect around the object. However, there is another way of doing this.

The immersed boundary method allows representation of the object and the flow movement around it without creating a structured mesh. Instead, the object and its boundaries are represented using a set of points. The movement of these points or markers can be used to analyze the fluid-structure interaction and the associated deformations.

In aircraft design, the arbitrary shapes and sizes of components increase the complexity of the simulation process. The use of the immersed boundary method removes the need for creating a  conformal mesh and significantly reduces the time and cost of computation.

## Aerodynamic Design Challenges

The problem with fluid-structure interaction in aerodynamic design arises when the flowing air comes in contact with the airplane structure and induces phenomena like lift, drag, and turbulence. These forces significantly affect the structural response of the aircraft. For example, when the aircraft wings or engine nacelles are subjected to complex flow behavior, the result may be structural deformation and vibration. The deformation can lead to changes in aerodynamic forces such as lift and drag as well as affect the structural integrity of the engine and other aircraft components.

The simulation of the fluid-structure interaction is thus important so as to analyze the impact of different flow conditions on aircraft performance. The accurate prediction of the interaction allows the engineers to make optimization decisions to reduce effects like flutter, noise, and deformations and ensure the safety and efficiency of the aerodynamic operation. This can be done efficiently with the help of effective simulation techniques.

Simulation using the immersed boundary method provides several advantages over the traditional mesh-based simulation method. For example:

• Accurately captures the complex geometry of the aerodynamic components such as wings, fuselages, engine nacelles, etc.
• Eliminates the need for meshing and refinement near the structure.
• Models the interaction between airflow and structure under extreme conditions, i.e., high speed or high angle of attack.
• Simulate unsteady flow for analysis of turbulence, vortex shedding, or flow separation.

## Implementing the Immersed Boundary Method

The immersed boundary method is the computational technique used for the simulation and analysis of fluid movement and deformation around the structure. In aircraft design, the immersed boundary method can be implemented to analyze the fluid-structure interaction using the following steps.

 Simulation With the Immersed Boundary Method Define the geometry Define the geometry of the fluid and structural components.Define the fluid properties such as density, viscosity, etc.Define the density, stress, and strain of the solid component. Discretization Discretize the solid geometry into a set of points or markers and transfer them to the fluid domain.Discretize the fluid domain into a fine grid of cells.Use the markers to define the boundary conditions for the fluid domain. Define how the fluid and structural components interact. Fluid-structure interaction (FSI) algorithm Calculate the deformation on the solid component.Using the interpolation method, transfer the forces from the solid to the fluid domain.Calculate the force acting on each marker. Simulation Run the simulation using the FSI algorithm.Simulate the fluid flow, structural deformation, and their interaction to understand the behavior of the fluid and structural components. Optimization Based on the simulation results, optimize the design of the structural component, including changes to geometry, FSI algorithm, or material properties.

## Effective Fluid-Structure Interaction Simulation for Improved Aerodynamic Performance

Computational fluid dynamics (CFD) is an effective way of simulating and predicting fluid-structure interaction problems in aerodynamic analysis. CFD allows the simulation of airflow motion around the aircraft and the corresponding structural response. Using techniques such as the immersed boundary method, the deformation of the components can be easily analyzed for complex geometries. The valuable insight obtained from the immersed boundary method can be used to improve the fluid-structure interaction and improve the aerodynamic performance through optimization of the aircraft design.

Subscribe to our newsletter for the latest CFD updates or browse Cadence’s suite of CFD software, including Fidelity and Fidelity Pointwise, to learn more about how Cadence has the solution for you.

# About the Author

With an industry-leading meshing approach and a robust host of solver and post-processing capabilities, Cadence Fidelity provides a comprehensive Computational Fluid Dynamics (CFD) workflow for applications including propulsion, aerodynamics, hydrodynamics, and combustion.

Untitled Document