ReviewDrag reduction in flow: Review of applications, mechanism and prediction
Section snippets
Basic definitions
To begin, there are two main types of flow: laminar and turbulent. In a cylindrical conduit one can visualize the laminar flow as a series of co-axial cylinders oriented along the flow direction; such a flow structure is known as telescopic shear. The central part of the fluid which includes the axis has the highest velocity u0. The velocity at the wall is necessarily zero, with intermediate velocities in-between. A schematic representation is shown in Fig. 1. Another way to create laminar flow
Applications
DR as defined above has numerous applications in a variety of fields. To give the first example, large urban agglomerations in India – and in other countries as well – find their sewer systems inadequate in the face of doubled or tripled populations. An alternative to digging out the entire municipal sewer system and replacing it by conduits with larger diameters is the use of DR agents. First of all, this is a much faster and cheaper solution. More importantly, however, it is not a temporary
Manifestations and characteristic features of DR
The reason the present author started working in the area of DR was in response to a challenge. In the Spring of 1980 Jacques Zakin, Ohio State University, Columbus, told this author that the DR phenomenon is unexplained – in spite of its numerous applications. Actually, a number of explanations have been provided but each of them was able to explain only a part of the experimental findings. Clearly a model which would explain all facts was needed – and therein was the challenge.
The original
Mechanism of drag reduction
Given the practical importance of DR, various explanations how it occurs have been advanced. Models based on fluid mechanics were of the continuum type, did not take into account discrete polymer + solvent interactions and were not successful. The starting point for a successful model of DR was the puzzling observation (c) named above. Clearly ‘closer cooperation’ between the macromolecular chains and the solvent molecules provided more and more stable DR.
A model was created in 1983 [16] and is
Mechanical degradation in flow
We need to describe quantitatively the drag reduction and its changes with time t caused by MDF. Let us call the initial DR at the beginning of the flow λ0 and the fluid viscosity at the same time η0 . Scission of chains caused by MDF results in a lower drag reduction λ and can also lower viscosity η. Then
Quite generally, the key property we seek to evaluate MDF is the change of the ratio λ/λ0 with time.
An equation for that ratio λ/λ0 was derived in [16], used with good results in [19]
Experimental determination of DR
Having discussed in detail the mechanism of DR, we now turn to the question how is DR measured. A turbulent flow rheometer based on the classical design of Hoyt [47] works well. There is a motor-driven syringe; the delivery rate of the syringe is controlled by speed of a small motor. A linear actuator drives the syringe plunger and is coupled to the motor. In the beginning, a full dissolution of a given DR agent is achieved by slow stirring for 6–24 h; the time depends on nature of the fluid,
The flocculation connection
As emphasized by Rustum Roy [51] and also by Roald Hoffmann [52], various groups try to compartmentalize disciplines of Science and Engineering and cut them into pieces for their own convenience or benefit. By contrast, our discussion above of DR shows integration of several ostensibly ‘unconnected’ disciplines.
However, there is still more. It is difficult to get solid constituents out of a liquid solution or suspension. Fine particles with diameters on the order of 10 μm will not settle out of
Acknowledgements
Discussions with: the late Prof. Paul J. Flory at Stanford University on the nature of polymer solutions; the late Prof. Jürgen Springer at the Technical University of Berlin on solutions structure; with Prof. Abdel Azim A. Abdel Azim, Egyptian Petroleum Research Institute, Cairo; Prof. Michael Bratychak, Lvivska Politechnika National University; Prof. Hyoung Jin Choi, Inha University, Incheon; Dr. Tea Datashvili, LAPOM, University of North Texas; Prof. Ulf W. Gedde, Royal Institute of
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