Bengaluru Oct 9, 2018, (Research Matters):
We have all been in an aircraft when all of a sudden the captain asks you to fasten your seatbelts because of 'turbulence'. Although you might experience a few bumps because of this turbulence, which is a technical term for unsteady and chaotic airflow, you may think nothing of it. But, guess what? Turbulent flows are ubiquitous -- from stars and supernovae to mixing of air and fuel in an automobile engine to the flow of water in domestic pipelines.
Turbulence enormously increases mixing rates be it in industrial reactors, or in the atmosphere and oceans, although, all of this comes at the expense of an increased energy consumption. A fundamental understanding of turbulence has, however, remained one of the last major challenges in classical physics. Such an understanding would, for instance, allow one to design better aeroplane wings and not only save you a bumpy ride but save enormous amounts of fuel too.
In a recent study, published in the journal Physical Review Letters, a team of researchers , led jointly by Prof. V. Shankar from the Indian Institute of Technology (IIT) Kanpur and Prof. Ganesh Subramanian from the Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR), Bengaluru, have been able to theoretically explain experimental results showing unexpected turbulence in polymer solutions. They have discovered a hitherto unexplored mechanism by which turbulence can arise in such solutions—a feat that could have far-reaching implications in stimulating future studies on turbulence.
The flow of fluids, like water or air, is described by their stickiness or viscosity. An understanding of this stickiness goes back to Isaac Newton who first characterized it in terms of the resistance to the sliding of adjacent fluid layers in a laminar flow. Water and air are thus examples of 'Newtonian fluids'. Adding polymers to such fluids imparts a certain `springiness’ in addition to the stickiness already present. Such fluids which exhibit both viscous and elastic effects are one of the prominent examples of 'non-Newtonian fluids', and are appropriately referred to as 'viscoelastic fluids'.
In the said study, the researchers have the examined the onset of turbulence in polymer solutions, an important class of viscoelastic fluids. It turns out that such fluids are not only of fundamental interest but also have critical industrial applications. “Addition of polymers to crude oil is well-known to reduce pumping costs in the turbulent regime drastically, and this is exploited in the trans-Alaskan oil pipeline,” explains Prof. V. Shankar from IIT Kanpur.
The flow of Newtonian fluids turns turbulent only at very high flow speeds. Experiments in the past have shown that the flow of viscoelastic fluids, on the other hand, turns turbulent at much lower flow speeds. However, the reasons for this so-called `early turbulence’ had never been understood until now.
Many studies carried out over the last century have shown that Newtonian pipe flow stays laminar or smooth when it is subjected to disturbances that are sufficiently small. These flows are said to be ‘linearly stable’ for minor disturbances. The current belief in the fluid dynamics community is based on the extrapolation of this Newtonian scenario to viscoelastic pipe flows as well. “The belief was so ingrained that not even a single attempt was made in the literature to analyse the stability of viscoelastic pipe flow. When we realised this lacuna, Prof. Subramanian and I felt that it is worth exploring this further”, says Prof. Shankar, explaining the motivation behind the study.
The researchers of this study were able to theoretically calculate the motion of the viscoelastic fluid and confirm, for the first time, that the addition of polymers strongly destabilised the laminar flow rendering it susceptible to the tiniest of disturbances.
“To our surprise, we found a linear instability for viscoelastic flows in both circular pipes and channels, and the icing on the cake was the qualitative agreement with experimental observations of transition in viscoelastic flows. We would be able to make reasonable predictions of the flow speeds at which turbulence begins in polymer solutions”, exclaims Prof. Shankar.
The results of the study have significant ramifications for our understanding of the behaviour of these non-Newtonian fluids and their broader applications. They will also serve as a ‘template' for future theoretical calculations under less idealised conditions and may well end up as a critical ingredient in any future model of turbulent flows of polymeric liquids.