FEA Simulation - Detailed Observations

The figure below (left side) provides a detailed picture of the location of these high stresses, which were shown to localise around the vertices of the leg support/lattice structure interface. The high stress concentration at these locations is as expected since the faces that made up this interface consisted of many sharp right angles. The figure below (right side) shows the contour of equivalent (von Mises) stress, regions at the base chamber of the tank with stress magnitudes almost approaching the yield stress of stainless steel occurred within 6s after the injection of the coolant. The continual subjection of such thermal induced stress may eventually compromise the structural integrity of this part of the tank.

Fluid Structure Interaction (FSI) analysis is a complex process that requires the use of numerical methods and computational tools to simulate the interaction between fluids and deformable solid structures. The steps involved in conducting an FSI analysis are:

**Problem Definition**: The first step is to define the problem and set up the geometry of the fluid domain and the solid structure. This includes specifying boundary conditions, material properties and initial conditions for both the fluid and the solid.

**Discretisation**: The continuous governing equations (Navier-Stokes for fluids and equations of motion for solids) need to be discretised to convert them into a set of algebraic equations that can be solved numerically. Common techniques for discretisation include finite element analysis (FEA) for solids and finite volume method (FVM) for fluids.

**Mesh Generation**: Separate meshes are created for the fluid domain and the solid structure. The fluid mesh is designed to capture the flow behaviour accurately, whilst the solid mesh must be refined to capture the deformations and stresses in the structure.

**Solver Selection**: Choosing an appropriate numerical solver for the FSI analysis is crucial. Advanced computational fluid dynamics (CFD) solvers and structural mechanics solvers are commonly used and they need to be compatible and able to exchange information during the simulation.

**Coupling Approach**: FSI simulations involve the interaction between two separate domains (fluid and solid), which requires a coupling strategy. There are two main approaches:__One-Way FSI Coupling:__

In one-way FSI coupling, the interaction is unidirectional, meaning that the fluid affects the structure, but the structure's response does not influence the fluid. The simulation is typically performed in two steps:

Step 1 > Fluid Analysis: The fluid dynamics simulation is carried out using a fluid solver (e.g. ANSYS Fluent). The fluid forces acting on the structural domain are computed.

Step 2 > Structural Analysis: The computed fluid forces are then used as boundary conditions for the structural analysis, which is performed independently using a structural solver (e.g. ANSYS Mechanical).

One-way FSI is suitable when the influence of the structure on the fluid flow is negligible, such as when studying the effect of fluid loading on a rigid structure.__Two-Way FSI Coupling:__

Two-way FSI coupling involves bidirectional interaction between the fluid and structure, where both domains influence each other. The simulation is performed in a fully coupled manner, where the fluid and structural equations are solved simultaneously.

Fluid-Structure Interaction: The fluid solver (e.g. ANSYS Fluent) calculates the fluid forces acting on the structure and the structural solver (e.g. ANSYS Mechanical) computes the deformation of the structure.

Data Exchange: At each time step, information (such as fluid pressures and deformations) is exchanged between the fluid and structural solvers to update the system's behaviour.

Two-way FSI is more computationally intensive than one-way coupling but is necessary when studying problems with significant interactions between the fluid and structure.**Time Integration**: As FSI analysis is often time-dependent, time integration schemes are used to advance the solution in time. Implicit time integration methods are preferred as they offer stability and accuracy but they may require more computational resources.

**Post-Processing**: After completing the simulation, post-processing is performed to analyse and visualise the results. This includes extracting relevant quantities such as forces, pressures, and structural deformations for further analysis and interpretation.

FSI simulations are computationally demanding and often require access to high-performance computing resources. The complexity of FSI analysis necessitates the use of high-fidelity software packages that can handle both fluid and structural simulations and provide robust coupling capabilities.

We were engaged to perform a fluid structure interaction (FSI) study on a mixing tank using computational fluid dynamics (CFD) and finite element analysis (FEA). The client's previous mixing tank buckled under the thermal stresses induced by its cooling jacket. The client has since redesigned the mixing tank, but would like to simulate the thermal-induced stresses on the new design using FSI analysis to ascertain whether the improved tank will buckle before commencing fabrication.

Computational fluid dynamics (CFD) is the science of predicting fluid flow, heat transfer, mass transfer, chemical reactions and related phenomena by solving the mathematical equations which govern these processes using a numerical process. Fluent solvers are based on the finite volume method where a domain is discretised into a finite set of control volumes or cells. The shape of each individual cell is dependent upon the domain geometry. For 2-D modelling, the available shapes are triangle or quadrilateral. For 3-D modelling, the shapes available are tetrahedron, hexahedron, pyramid and prism/wedge. Finite element analysis (FEA) is a numerical based method in predicting how a system or a component reacts to structural and thermal load. In FEA, the physical system is discretised into elements and nodes containing material properties and information. These nodes are then solved simultaneously across all elements based on a set of governing equations. As one of the leading FSI simulation consulting firms within the Asia Pacific Region, our FSI analysis specialists employ FEA to perform structural analysis or together with CFD to perform fluid structure interaction analysis.

The main objectives of this study are as follows:

- Perform a CFD study on the fluid phase of the system (flow inside the cooling jacket) to obtain the transient temperatures induced by the fluid phase on the solid phase. To achieve this, a transient simulation will be performed to model the feeding of coolant into the tank jacket using ANSYS Fluent. As it starts from the bottom, this part of the tank will be subjected to -15⁰C first whereas the top part remains at room temperature. Hence, this simulation will provide the data to be used as the boundary conditions for the FEA simulation component. This will take into consideration the flow rate of coolant and room initial tank temperature.

- Perform a stress and displacement analysis on the solid phase (the tank) using the FEA method and the transient temperature results from the CFD study as inputs. To achieve this, a one-way coupling structural analysis using ANSYS Mechanical will be conducted by importing the transient temperature distributions impacting on various part of the tank, obtained from CFD post-processing. This part of the simulation will take into consideration all the structural physical properties of the tank.

As shown in the figure below (left side) the tank geometry was created using ANSYS Design Modeller. To render the geometry suitable for simulation, selected elements of the original geometry were defeatured to avoid low quality mesh elements for both the fluid and solid domains. These features were deemed to have minimal impact on the CFD and FEA relevant results. After the geometry was created, it was meshed using ANSYS Mesh as shown in the figure below (right side). Mesh generation is one of the most important steps to ensure a highly accurate and reliable result. To ensure the results are accurate and mesh independent, a mesh independence test was conducted on the geometrical model. Two meshes of differing cell densities were generated for each of the CFD and FEA simulations. Then simulations were ran on each of this mesh and the results compared to each other.

CFD Results - Temperature Distribution

The figure below (left side) shows our CFD simulations provided the transient temperature distribution inside the mixing tank fluid domain within the first 20s as propylene glycol at -15⁰C is injected into the mixing tank cooling jacket. At approximately around 20s post injection, propylene glycol in lower half of the tank reached subzero temperatures.

FEA Simulation- Deformation Visualisation

The figure below (right side) illustrates the displacement magnitudes and the deformation mode of the tank due to the thermal stresses induced upon it at various points in the simulation within 20s of coolant injection. As illustrated in the contours of total displacement, the displacement magnitudes were not significant, with a maximum displacement magnitude of approximately 0.9 mm located at the outlet pipe of the mixing tank cooling jacket. The orientation of the pipe displacement also infers that there was a relative (but small) displacement between the inner tank and outer shell since the temperatures of the inner tank dropped rapidly whilst the temperatures at outer shell remained at room temperature. This could potentially affect components that were attached to both the inner tank and outer shell such as the inlet and outlet pipes, leg supports and lattice structure. Despite such a phenomenon, as will be demonstrated, the stresses caused by the relative displacement of the inner tank and outer shell were within the yield stress of the material.

FEA Simulation - Stress Visualisation (von Mises)

The figure below shows the equivalent (von Mises) stress magnitudes of the tank due to thermal stresses induced upon it at various points within the first 20s of coolant injection. Shown for each point in time are: Temperature distribution of Propylene Glycol in the mixing tank cooling jacket (top left) and equivalent stress magnitudes at the Outer Shell (top right), Inner Tank (bottom left) and Inner Tank Cross Section (bottom right) of the mixing tank.

FSI Study - Conclusion

A fluid structure interaction (FSI) study was performed to ascertain whether the injection of propylene glycol coolant at -15⁰C into the Washed Oil Chiller tank cooling jacket will cause the tank to buckle under the severe thermal loads induced. From the simulation results, it was observed that whilst the tank would not buckle significantly under these extreme thermal loads, as evidenced by a maximum deformation of less than 1 mm, several areas such as the leg support/lattice structure interface and cooling jacket base chamber were identified to experience stress levels that exceeded the yield stress of the stainless steel tank construction material. Based on the results analysed and observed, the fabrication of this tank was not recommended. It was further recommended that a design review supported by the results of this study be conducted and have the highlighted problem areas addressed.

**AUSTRALIA SINGAPORE**