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Component Coupling within the Fluid-Structure Interaction and Thermal Stress Evolution Models

This development note, written by Senior Developer James Brethour, Ph.D., describes new capabilities of the fluid structure interaction and thermal stress evolution models in FLOW-3D v11.

A new feature in FLOW-3D v11 is an upgrade to the existing finite-element solid mechanics solver that allows the elastic stresses between neighboring Fluid-Structure Interaction (FSI) components and/or the Thermal Stress Evolution (TSE) solidified fluid region to be coupled. This new capability opens the door to a wealth of modeling possibilities, including simulating thermal stresses and deformations in complex, deforming, multi-material parts (e.g., a metal casting solidifying in a mold, or bimetallic gauges), and simulating forces on connected hydraulic structures, like radial gates and pipeline support systems.

There are several different options in the model that allow for efficient computation of complex processes:

Two simulations are presented to demonstrate the new features of the model in more detail. The first situation uses the full coupling option to model a bimetallic strip bending in response to a time varying temperature, while the second example shows the use of the partial coupling model to look at thermal stresses during the solidification of a V6 engine block in a die.

Full Coupling Example: Bimetallic Strip

One of the simplest examples of the full coupling option is the motion of a bimetallic strip in response to temperature gradients. Such strips are commonly used in thermal switches and bend because the two metals do not expand at the same rate in response to changes in temperature.  The bimetallic strip modeled in the simulation is a cantilever beam consisting of a 15cm long, 0.5cm thick steel strip bonded to a copper strip of same dimensions, as shown in Figure 1.

Figure 1: Schematic of a bimetallic strip used in example simulation; the black arrow indicates where the deflection is probed; positive deflections are upward.

The strip was then placed in an environment where the temperature was uniformly varied over 70 seconds. Figure 2 shows the deflection of the tip of the strip for the simulation and an analytical solution at various temperatures over time. The results show some interesting features, including a slight delay between when the temperature changed and the response of the strip due to the thermal inertia of the strip. This delay also influences the difference in timing between the computed and analytical deflections because the analytical solution assumed instantaneous changes in temperature. The differences in amplitude of the displacement can be attributed to the assumption of an infinitely thin strip in the analytical result. The thickness in the computational model adds additional stresses at the mounting point which leads to an increased deflection.

Deflection plot of bimetallic strip simulation
Figure 2: Deflection at the tip of the strip over the simulation time. Shown on the plot are the analytical (light blue) and computed (red) deflections, as well as the mean temperature of the strip (dark blue).

Partial Coupling Example: Metal Casting within a Deformable Die

The second example simulation uses the partial coupling model to show the stress development in a metal casting within a deformable steel die. The two halves of the die and the solidified fluid are partially coupled to one another, meaning that they interact through normal stresses and friction. The simulation shows the thermal stress evolution in the die and the cast part as they cool from just below the solidus temperature at 770K to the surrounding temperature of 293K. The cast part is composed of A380 aluminum alloy while the die halves are composed of H-13 steel.

The finite element mesh of the cast part and of the surrounding die is composed of 3,665,533 elements and 3,862,378 nodes, as shown in Figure 3.

Figure 3: Cutaway view of temperature profile of a V6 engine block, 7 seconds from start of the simulation. Also shown are the meshes, which are separate for each die half and the TSE solidified fluid region. The red circles on the front face are due to the support pistons, which are not shown.
Cutaway view of engine block showing temperature, normal displacement and von Mises stress magnitude 90s after initial solidification.
Figure 4: Cutaway view of engine block showing temperature (K), normal displacement (cm) and von Mises stress magnitude (dyne/cm2) 90 seconds after initial solidification; displacements are magnified 100 times. The stresses at the interface between the mold and solidified fluid surfaces are partially coupled, and the constrained shrinkage can be seen.

Figure 4 shows the resulting deformation in the cast part and one half of the die partway through the simulation. The die halves and the casting shrink at different rates as the temperature decreases, resulting in large stresses in the interfering regions and indicating potential problem areas. Computing the coupled stresses in the die and in the part will allow users to better predict the stresses developing within each component and give insight into how to improve part quality and extend tool life.


The interaction of different solid objects is an important part of modern design and engineering. The addition of the new coupling options between FSI components and TSE solidified fluid regions to FLOW-3D provides a useful tool for evaluating the complex geometries regularly encountered by today's engineers.

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