Fluid Structure Interaction
A Coupled Finite-Element/Finite-Difference Model in FLOW-3D
This article highlights developments to be released in FLOW-3D version 10.0 in 2011.
FLOW-3D version 10.0 will debut an integrated solid mechanics modeling capability, called the fluid structure interaction model. This new model makes use of the finite element method (FEM) to simulate and analyze the stresses within solid components and solidified fluid regions and the resulting deformations. Stresses develop in the solid due to the forces exerted by the surrounding fluid, thermal gradients within the solid, and/or constraints imposed by walls or other components. The new model in FLOW-3D lets the user seamlessly solve coupled fluid-solid problems.
This simulation capability is particularly useful for casting and hydraulics processes. Examples of this are:
- Casting defects form from unwanted deformations (shrinkage or expansion) during cooling;
- Size imperfections occur when the mold expands due to large temperature gradients or high pressures;
- A steel plate, acting as a hatch at the bottom of a pool behind a concrete dam, bends under the hydrostatic pressure from the column of water above.
This fluid structure interaction model also includes something never before seen in FLOW-3D: finite element modeling with a body-fitted mesh. The goal is to use the computational method most suited to solving each part of the problem to obtain the most accurate and time efficient solution. In other words, the fluid domain is solved using finite difference techniques and then the forces surrounding the solid are passed to the finite element solver as boundary conditions. In the past, FLOW-3D users had to use elaborate customizations to couple FLOW-3D with third-party solid analysis software to compute stresses and deformations of solids.
Capabilities of the Fluid Structure Interaction Model
- Mesh any complex shape, whether produced from CAD geometry stereolithography (STL) files or via FLOW-3D’s geometry input. These meshes use the standard FLOW-3D Cartesian mesh as the starting point. The shape of the elements that contain the surface are then adjusted to fit the surface shape of the solid. This meshing is done automatically.
- Simulate fully transient and three-dimensional stress analyses within all solid regions. Data output includes all stress & strain components, displacement, mean stresses, and volume change.
- Full interaction between fluid and solid regions – the fluid exerts pressure on the surface of solid regions, and the motion of the solid interface induces fluid motion.
- Thermal effects due to non-uniform heating and cooling of solid regions.
- The ability to provide temperature-dependent material properties such as bulk, shear, or elastic moduli, Poisson ratio and thermal expansion coefficient.
Stress Analysis of Sample Casting Simulation
Below are sample results from the fluid structure interaction model. Figure 1 shows an alternator housing part, which has a diameter of around 6 cm. The part is cast from aluminum alloy A380 and is cooled from an initial temperature of 450°C to an ambient environment of 20°C. Figure 2 shows the mesh that was created by the new solid mesh generator in FLOW-3D, and contains 82,460 elements, and 92,635 nodes. Depending on the mesh size some details of the part might not be picked up by the finite element mesh. This is easily resolved using nested blocks or fixed points to generate high resolution regions where needed (Fig. 3).
Figure 4 shows the temperature change after 60 seconds of cooling. The temperature change is computed using existing models in FLOW-3D. The temperature change is not uniform; i.e., the more massive region of the part takes the longest to cool. Such non-uniform cooling leads to thermal stress development. The mean isotropic stress is shown in Fig. 5. The mean isotropic stress is a stress invariant and is insensitive to the coordinate system used.
Figure 1: Alternator housing from a
CAD-generated stereolithography (STL) file.
Figure 2: Mesh created automatically with the new solid mesh generator in
FLOW-3D. Only the surface elements can be seen here; all internal
elements are regular hexahedra. Plot created using Tecplot 360.
|Figure 3: Local refinement of the FLOW-3D mesh improves the level of details that appear in the finite element mesh. Plot (a) shows the part as produced by FLOW-3D's stereolithography (STL) file viewer. Plot (b) shows a sample result of the new finite-element meshing, while plot (c) shows how fine details can be resolved with the new finite-element mesh generator by increasing the resolution of the FLOW-3D mesh. Plot (a) created in FLOW-3D; plots (b) and (c) created using Tecplot 360.|
Figure 4: Temperature difference (°C) due to cooling
after 60 s of simulation. Plot created using Tecplot 360.
Figure 5: Mean isotropic stress (dynes/cm2) after 60 s of simulation. This is
a measure of stress magnitude and akin to pressure. Negative values indicate
regions under isotropic compression, while positive values are under isotropic
tension. Thus, red regions are where cracking is most likely to occur.
Plot created using Tecplot 360.
The variations in stress shown in Fig. 5 are due to the unequal shrinkage of the part due to different cooling rates and geometry. The largest stress is where the most massive region of the part joins the thinner region. The greatest gradient in cooling rates occurs here, as seen in Fig. 4.
Figure 6: Von Mises stress (dynes/cm2) after 60 s of simulation.
This is a measure of tearing stresses. Values of von Mises stress
are always positive, and larger values indicate regions where
shearing forces are largest. Thus, red regions in the figure are where
tearing is most likely to occur. Plot created by Tecplot 360.
Figure 7: Fractional volume expansion (dimensionless); negative values
indicate shrinkage. The colors indicate the local amount of volume change,
where blue indicates the greatest amount of shrinkage and red the least.
Regions that have shrunk the least (red) are most likely to contain residual
stresses due to frustrated shrinkage. Plot created by Tecplot 360.
Figure 6 shows the magnitude of the von Mises stress. This is another measure of the magnitude of the stress, and like the mean isotropic stress, it is insensitive to the coordinates chosen. In systems under uniform compression or tension, the von Mises stress is zero. The von Mises stress is a measure of the magnitude of shearing stresses. The von Mises stress is greatest at the junction of the more massive and the thinner section of the part. Differences in shrinkage cause larger shearing, and thus tearing is most likely to occur in the vicinity of the junction.
Finally, Fig. 7 shows the net volume expansion after 60 s of simulation. Negative values of volume expansion indicate shrinkage. Since the total amount of cooling does not vary much beyond 60 s (the temperature range in Fig. 4 is less than 5°C), in a part without internal stresses, one would expect to see nearly uniform shrinkage. As can be seen in Fig.7, some regions of the part shrink more than twice as much as other regions. This indicates that there remain significant amounts of stresses that frustrate further shrinkage—the regions in red are where this is greatest. Figures 5 and 6 agree with this analysis.
FLOW-3D’s New Capabilities Take the Stress out of Stress Modeling
FLOW-3D version 10.0’s new modeling capabilities will allow engineers to simulate fluid and solid systems in a completely coupled way. The work presented here is just a small window into the potential real-life problems that can be tackled. Using the new finite-element/finite difference model in FLOW-3D, many examples not discussed in this note can be simulated, including:
- Simulating the stresses within a casting mold during high pressure die casting and subsequent solidification and cooling.
- Simulating the interaction between fluid and solids in micro-electro-mechanical devices to more accurately include the effects of solid deformations in such systems.
- Any simulation where the interaction between fluids and solids are key to understanding solutions to problems.