### Tech Briefs Benchmarking Thermal FSI Capabilities

In an earlier News we focused on the benchmarking of fluid-structure interaction finite element procedures assuming that there are no temperature effects, see also the reference given below.

Of course, there are many problems where changing temperature conditions must be included in the analysis. The temperature may vary spatially over the problem domain and may change as a function of time. The problem domain considered here is the solid/structure fully coupled with the fluid. The temperature changes may then significantly affect the analysis results, including the deformations and stresses in the structure.

ADINA is a particularly powerful tool for the analysis of such problems (see e.g. News). A simulation may include

• The solid and structure modeled assuming small or large deformations, including temperature effects and contact

• The fluid modeled as a Navier-Stokes fluid including temperature effects (Newtonian or non-Newtonian flow)

• Steady-state or transient conditions

• Fully coupled conditions between the fluid and the solid or structure (of course, one-way coupling can also be assumed)

• Conduction, convection, temperature dependent material properties, heat generation due to plasticity or friction

We illustrate some of these features in two simple but insightful problem solutions, where fully coupled conditions are modeled.

Problem 1

The problem in the figure below shows a rubber ring (Ogden material model) subjected to a temperature gradient and internal fluid pressure. The ring expands from an outer radius of 2 to a radius of 8.72, clearly undergoing very large deformations. In this simulation, the fluid mesh moves with the rubber ring expansion, in order to span over the increasingly larger fluid domain. The above movie shows the response of the ring and the fluid. Schematic of Problem 1 Meshes Used in Problem 1

Problem 2

In the second problem, we consider a plate subjected to tangential fluid flow. The plate is fixed at its ends, and the temperature of the fluid increases leading to thermal induced buckling. The plate is modeled using a thermoplastic material with temperature dependent yield stress and coefficient of thermal expansion. The figures below show the problem, the finite element mesh used, and some solution results. Schematic of Problem 2 Meshes Used in Problem 2 Results of Problem 2: Temperature and Velocity Plots

The results assuming an isotropic elastic material, uniform temperature rise, and very small fluid pressure can be compared with an analytical solution based on beam theory. This comparison is given in the last figure showing the vertical displacement at the middle of the plate (normalized by the length of the plate) versus the applied temperature. The buckling load and the post buckling displacement, both, agree with the analytical solution. Comparison of Results of Simplified Problem 2 with an Analytical Solution

It is clear that the ADINA FSI capabilities including temperature effects can be very useful in the simulation of many problems arising in various industries.

For more information on ADINA FSI, please refer to our page on fluid-structure interaction.

Reference

 K. J. Bathe and G.A. Ledezma, Benchmark problems for incompressible fluid flows with structural interactions, Computers & Structures, 85, 628-644, 2007.