Encyclopaedia Index

## Simultaneous Solid-stress, Fluid-flow and Thermal analysis

[Chapter 3 of the lecture CAD to SFT.

### 3.1. The current practice and its disadvantages

Engineers often need to make both flow and solid-stress calculations for the same system. However, because of the differing methodologies of the CFD and CASA codes, they find it necessary to use one code for the fluid calculations and another for the stress ones.

• they must possess both codes, and staff who are able to use them;
• the output from the CFD code must be converted into a format acceptable to the CASA code, which often entails loss of accuracy;
• when stresses cause deformations, which may be large enough to influence flows, the output from CASA becomes the input to CFD;
• the two-way information transfers then have to be made iteratively, until convergence is achieved.

### 3.2 A single algorithm for SFT problems

(a) The basic idea

Fortunately, it is possible to devise an algorithm which will solve the solid-stress equations in one part of the field and the fluid- flow ones in another (see, for example, Spalding, 1997); and this can be (and has been) incorporated in a single computer code.

The basic idea is very simple: it rests on the fact that, when the solid-stress equations are formulated with displacements as the dependent variables, their form is almost identical with those governing the velocities in the fluid-flow regions.

Therefore, provided that the detailed programming work is carefully conducted, displacements can be computed for one part of the field while velocities are being computed for the other; and temperatures (which of course influence displacements in the solid regions and the material properties throughout) are computed simultaneously.

(b) Current status and future prospects

The SFT technique is rather new, and publications making use of it are only now beginning to appear. The work of the present author and his colleagues has indeed been confined to demonstrating the practicability and accuracy of the technique, before applying it to serious practical problems.

It is however now ready for such applications, of which the following spring to mind:-

• thermal-stress problems arising in unevenly-heated and -cooled piping systems;
• thermal-stress problems arising in electronics equipment;
• thermal- and mechanical-stress problems in the blades, disks and combustors of gas turbines;
• residual-stress problems in casting and other forming processes.

So far, only elastic strains have been considered; but there appears to be no obstacle to extending the technique to plastic deformations.

### 3.3 Examples of SFT analysis

(a) The thick-walled pipe

The first example shows what happens when a thick-walled horizontal pipe carries a hot fluid inside it, while being immersed in a larger-diameter duct carrying a cooler fluid.

Because of gravity, convection occurs within both fluids; this leads to departures of the temperature field from axial symmetry and so to to non-uniform thermally-induced stresses.

Adding the stress calculation increased computer time very little.

Click to return here after viewing Figures The next four pictures show:-

Further calculations have concerned the situation sketched below, which might represent one of many such elements in an electronics- equipment assembly.

Fig 3.3-5 The system considered.

```

cooling air ----- :-           duct                    -----:-  exit
H-------------                 -------------H
Horizontal H// steel ///|____ cavity _____|/// steel //H Horizontal
Constraint H////////////|_________________|////////////H Constraint
H////////////// aluminium //////////////////H
H///////////////////////////////////////////H
IIIIIIIIIIIIIIIIIIII insulated wall IIIIIIIIIIIIIIIIIIII
```
The radiating wall and the cooling air combine to produce temperature gradients in the metal blocks, which have different thermal-expansion coefficients. The task is to compute the resulting stresses.

This task has been performed in the manner described above.

The following pictures display:-

• the velocity and displacement vectors;
• the horizontal strains (derived from the displacements);
• the vertical strains (similarly derived);
• the horizontal stresses;
• the vertical stresses.

In the present case, the assembly is prevented from expanding downward, and to the left or the right.

Once again, it is scarcely more time-consuming to compute the stresses and strains than not to do so.

All that is necessary is to activate a "solve-for-stresses" switch, and then to supply the necessary boundary conditions. The latter supply information concerning mechanical constraints.

### 3.4 Concluding remarks about SFT

The foregoing arguments and examples, while not being conclusive, lend plausibility to the following suggestions:

(a) It would have been difficult to conduct SFT analyses of either the horizontal-tube or the two-metal-block problems by the currently-common two-program approach, even though the deformations did not influence the flow of fluid.

(b) If the latter influence had to be taken into account, it would have been almost impossible to do so; the single-program method would however encounter no difficulty.

(c) The fact that the same algorithm (SIMPLEST) works for both velocities and displacements is what allows the unification of the CASA and CFD fields; and, since this unification is so advantageous to engineering designers, its widespread use appears to be limited only by the (understandable) conservatism of the profession.