Structural analysis

To investigate whether this design could withstand the pressure and thermal stress to which it would be subjected in service, a finite element analysis was performed in SolidWorks Simulation. The component was restrained by a soft spring (elastic support) attached to the face that would generate 1 MPa of stress per mm of movement in any direction.

Figure 6.11. Face to which the soft spring restraint was applied in the FEA model.

As section 4.8 noted, thermal stresses are mitigated when a part is long in the direction of the thermal gradient compared to its other two dimensions. In this design, each recuperator wedge would be long in the axial as well as radial direction if it were built as a complete 64-wafer unit. To solve this problem, it must be split up axially into “short stacks” comprising perhaps 4-16 wafers.

The first case considered was a model of a single wafer. This was done to develop an understanding of the “basic” stresses that are unavoidable – those due to pressure and thermal stress in a single wafer. Although CFD results can be imported to create thermal and pressure loads in FEA, there is not much visibility into this process; for example, the loads cannot be plotted or visualized. To make sure all loads were even and symmetrical, for this simple case the loads were applied manually. The study was done in two phases. First, fixed temperatures of 382K and 1416K were applied at the outer and inner manifold surfaces, respectively, and a thermal study was performed. This resulted in the temperature distribution shown in part (a) of Figure 6.12. This was imported into a structural FEA simulation, which also included a pressure load of 101,325 Pa in the direction that would collapse the exhaust channels.

The results are shown in part (b) of the figure. This plots first principal stresses (for brittle materials, this is the appropriate failure criterion) and indicates a maximum stress value just under 30 MPa. The model was also run without the pressure loads, and the results were nearly the same, indicating that thermal stresses are much larger than pressure stresses for this design. Both of these findings fit with the author’s previous experience with a wide range of recuperator wafer shapes.

Figure 6.12. FEA results for a single wafer after applying loads manually (not from CFD).

Next, a larger stack was modeled, using CFD results to create the boundary conditions. This should model the thermal gradients and thermal stresses more realistically than the fixed loads used for the single wafer. In cases (a) and (b), a symmetry boundary condition was used to reduce the number of nodes in the model, so that a finer grid could be used. In the third case, there was no symmetry boundary condition, so all eight wafers were modeled with a coarser grid. Figure 6.13 shows the results.

Peak stresses were around 120 MPa in all cases, giving a safety factor of 2.8 relative to CeSZ’s measured room temperature strength of 340 MPa. The strength at high temperature will not necessarily be the same, and if the real part is not constrained in the same way as the FEA model, this could generate different stresses. However, the safety factor is high enough to allow some margin for this. Also, most of the model is shown in blue/green, indicating stresses of 60 MPa and below; the peak stresses are only at sharp corners in the model. This could indicate an analysis error due to sharp element angles in the mesh, or it could be due to actual stress concentrations in the design due to the sharp corners. Either way, rounding off all sharp

(a) Thermal FEA results for a single wafer in which fixed temperatures were applied at the inner and outer manifolds. The thermal gradient is

severe.

(b) Structural FEA results for a single wafer with combined pressure and thermal loads. Thermal load was the temperature distribution

in (a); pressure load was 101,325 Pa inward pressure on the exhaust channel walls.

corners would be a good idea, and could give in-service peak stresses of perhaps 70 MPa throughout the part. After doing this, it would also be worthwhile to perform a CARES/Life analysis to evaluate probability of failure over time due to low cycle fatigue and crack growth.

First, however, it would be sensible to build and test some prototype wedges made from short 8-16 wafer subsections that are axially stacked and bonded, using flexible adhesive to bond and seal the cool exhaust outlet manifolds, and rigid glue to bond the hot manifolds. The geometry could be modified to include enlarged-area bonding flanges on the end wafer of each short stack. If each is at least eight wafers tall, the flow blockage would be minimal.

Figure 6.13. First principal stress in 8-wafer and 16-wafer stacks, with pressure and thermal loads imported from CFD.

(a) 8-wafer stack. Four wafers were modeled, and a symmetry boundary condition was applied (green arrows). Blue cones represent

the soft spring restraint.

(b) 16-wafer stack with loads from CFD. Eight wafers modeled with symmetry condition (green arrows).

(c) 8-wafer stack without the symmetry boundary condition. All eight wafers were modeled. Results were similar to the other two studies.