Interfacial Mixing in Pipe Flows

An Interim Report is available.

### Objective

To measure mixing rates between fluids of different viscosities in laminar pipe flow and to determine how mixing is affected by roughness of pipe.

To reduce energy costs to pump oil through pipes while minimising contamination of batches due to interfacial mixing between oil of different grades.

### Background

A series of laboratory experiments have been run and analyzed to examine mixing between two fluids (glycerol and salt water solutions) driven from rest by a constant pressure gradient along a straight horizontal acrylic pipe. Viscosity differences between the fluids are established by increasing the glycerol concentration, and the salt water concentration is set to ensure the density between the two fluids is equal. (See interim report for a detailed description of the experimental set-up.)

### Results to date

In control experiments, in which both fluids are fresh water, the flow in a smooth pipe is found to be laminar at Reynolds numbers below 2000, turbulent at Reynolds numbers above 3000 and transitional in between. These results are consistent with {\it in situ} observations of oil pumped through pipe lines. The critical Reynolds number is approximately $2100$. In flow through a uniformly roughened pipe, the laminar to turbulent transition occurs at a larger Reynolds number of 4100 in control experiments. If the two fluids have different viscosities, it is found that interfacial mixing is inhibited if the average of the Reynolds numbers of the less viscous and more viscous fluids is less than the critical Reynolds number. Thus increased viscosity of one fluid inhibits turbulent interfacial mixing.

### Ongoing research

To reduce the energy costs required to drive turbulent flow but to inhibit mixing between two fluids, it is found that the pipe line should be operated at transitional Reynolds numbers. Numerical simulations are being developed at present to examine interfacial mixing for a broader class of circumstances, while using the experiments as a test of the validity of the code. The simulations will be employed to determine an accurate measure of the transitional Reynolds number.

This research has been funded by the following sponsors:
 Imperial Oil Charitable Foundation the Pacific Institute for the Mathematical Sciences (PIMS) the Alberta Science and Research Authority (ASRA)

Last updated by:
Bruce R. Sutherland, Dec. 99,