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MUSES, the MUltiply-SharEd-Space method

1. The Problem

PHOENICS is equipped with means of simulating both one-phase and two-phase flow phenomena; but problems often arise in which it is necessary to consider the presence and interaction of more than two phases within the smallest volumes that are considered.

A shell-and-tube heat exchanger provides an example; for the smallest computational cell will usually contain:

each of which will have distinct pressure, temperature, composition and components of velocity.

If both the shell- and tube-side fluids are mixtures of both liquid and vapour, as may often occur, five phases have to be considered.

It would of course be possible, in principle, to generalise the two-phase coding in PHOENICS so as to enable it to handle as many phases as may be present. However, this would be a large undertaking, which would significantly increase the size of the executable, with attendant problems regarding economy, mantenance, etc. This route has therefore not been followed.

The MUSES technique has proved to be a simple and economical alternative.

2. The Solution

The essential idea is, having once provided a grid which covers the volume of space in question, to provide one or more extra grids covering the same volume, and on each of these to solve for different variable.

For a heat exchanger, for example, the first grid might be devoted to shell-side fluid, a second grid to the tube-side fluid, and a third to the metal.

Of course, the values of the variables on any one grid must be allowed to depend on the values of different variables on any other grid. For example, the metal temperature in a heat exchanger is influenced by, and in turn influences, the temperatures of the two fluids.

These mutual influences usually take the form of sources and sinks, of which PHOENICS is well able to compute the magnitude and evaluate the effects.

This is particularly easy when the PLANT method is employed; for the user has then only to insert the formulae expressing those sources, allowing the coding to be created automatically.

3. Examples of use

One of the first examples of the use of MUSES is to be described in the section of the PLANT library to be found by clicking here

MUSES is also extensively exploited in the SAFIR special-purpose version of PHOENICS which is used for blast-furnace simulation.

4. Future developments

The MUSES technique can be used for many difficult flow-simulation tasks, including those in which the volumes occupied by the various grids do not coincide.

Consider, for example, the task of simulating the launching of a boat on water.

One grid might be fixed relative to the water, while the other could be fixed relative to the boat.

Obviously, cells in the "water-grid" would have to have the same values of "grid-independent" values, such as pressure, as the instantaneously coincident cells in the "boat grid".

It would be the task of the PIL-generated sources and sinks to bring about the equality.