Encyclopaedia Index

### (f) Examples of two-fluid-model simulations; mixing and unmixing

The two-fluid turbulence model is of use for other phenomena than combustion, and especially for those in which density differences interact with body forces.

Many examples arise in the atmosphere, lakes, rivers and oceans.

The two-fluid model, for example, can satisfactorily simulate the mixing-followed-by-unmixing behaviour when a salt-water layer, lying below fresh water, is heated for a short time.

```
_________      _________      _________
|         |    | * ** *  |    |         |
|  fresh  |    |* *  * **|    |         |
|         |    | * ** *  |    |         |
|*********|    |* *  * **|    |*********|
|* salty *|    | * ** *  |    |*********|
|*********|    |* *  * **|    |*********|
---------      ---------      ---------
start         later           later
still
```

Mixing appears to take place soon after heating equalises the densities. But it is macro- not micro-mixing; so "unmixing" follows.

Experiments by Spalding and Stafford at Imperial College during 1979, in which the heating was effected by passing an electric current through the fluids, brought the mixing/unmixing phenomenon to light.

It was consideration of these experiments which prompted the development of the two-fluid model of turbulence, which has here been used to simulate it.

In this and the following pictures, which show contours computed by way of the two-fluid turbulence model:

• the vertical scale represents height from the bottom of the fluid layers; while
• the horizontal scale represents time.

The first picture shows the volume fraction of lower (saline) fluid. Note the initial delay; then mixing; then unmixing.

This picture shows how the temperature of the saline fluid first rises; it falls later, as heat is transferred to the fresh-water fluid.

This picture shows how the fresh-water temperature rises, gaining its heat from the saline fluid.