Jan 27 2020
Water flowing from a regular faucet has more to say about how it traveled through a pipe. The gushing stream from the faucet is turbulent—disorderly and chaotic, similar to the crash of ocean waves—at high velocities.
Left: da Vinci’s sketch of eddies in a turbulent pool. Right: schematic of the energy spectrum corresponding to the flow inside the marked region in da Vinci’s sketch. Image Credit: Okinawa Institute of Science and Technology Graduate University.
Researchers understand not much about turbulence, compared to orderly laminar flows, such as the steady stream from the faucet at low velocities. Knowledge about how laminar flows turn turbulent is even less. Transitional flows, which are a blend of disorderly and orderly flows, occur if fluids travel at intermediate velocities.
At present, researchers Dr Rory Cerbus, Dr Chien-chia Liu, Dr Gustavo Gioia, and Dr Pinaki Chakraborty, from the Fluid Mechanics Unit and the Continuum Physics Unit of the Okinawa Institute of Science and Technology Graduate University (OIST), have used a very old turbulence theory to devise a new method to investigate transitional flows.
The study outcomes have been reported in the Science Advances journal, and could help gain a more comprehensive, conceptual insight into turbulent and transitional flows, with practical implications in the field of engineering.
Turbulence is often touted as the last unsolved problem in classical physics—it has a certain mystique about it. And yet, under idealized conditions, we have a conceptual theory that helps explain turbulent flows. In our research, we’re striving to understand if this conceptual theory might also shed light on transitional flows.
Dr Rory Cerbus, Researcher, Fluid Mechanics Unit, Institute of Science and Technology Graduate University
Finding Order in Disorder
For a long time, researchers have been fascinated by turbulent flows. In the 15th century, Leonardo da Vinci elucidated turbulent flows as groups of swirling eddies, or circular currents, of different sizes.
Later, in 1941, mathematician Andrey Kolmogorov formulated a conceptual theory that uncovered the order that underlies the energetics of apparently disordered eddies.
As illustrated in DaVinci’s drawing, a stream that plunges into a pool of water first forms a huge, swirling eddy. This instantly turns unstable and disintegrates into progressively smaller eddies. Transfer of energy from the large to ever-smaller eddies takes place until the smallest eddies dissipate the energy through the viscosity of the water.
Kolmogorov’s theory captures this representation in terms of mathematics, thus predicting the energy spectrum—a function that describes how the kinetic energy (the energy from motion) is distributed over eddies of varying sizes.
Most notably, according to the theory, the small eddies possess universal energetics, implying that even if turbulent flows appear to be different, the energy spectrum of the smallest eddies in all turbulent flows is the same.
That such simple concepts can elegantly elucidate a seemingly intractable problem, I find it truly extraordinary.
Dr Pinaki Chakraborty, Fluid Mechanics Unit, Okinawa Institute of Science and Technology Graduate University
However, there is an obstacle. The theory proposed by Kolmogorov is widely considered to be applicable only to a small set of idealized flows, but not the flows of day-to-day life, such as the transitional flows.
Cerbus and his colleagues investigated these transitional flows by performing experiments on water that flows through a glass cylindrical pipe with a length of 20 m and a diameter of 2.5 cm. Small, hollow particles with roughly the same density as water were added by the researchers, thus enabling the flow to be visualized.
A method known as laser doppler velocimetry was used to quantify the velocities of the eddies in the transitional pipe flows. They calculated the energy spectrum using these measured velocities.
Fascinatingly, it was discovered that, in spite of being apparently different from turbulent flows, in transitional flows, the energy spectrum corresponding to the small eddies was in accordance with the universal energy spectrum as per Kolmogorov’s theory.
This finding not just offers new conceptual insight into transitional flows, but could also find applications in engineering. In the last 20 years, the study by Gioia and Chakraborty has demonstrated that energy spectra can be useful in estimating the friction between the flow and the pipe, which is the main cause of concern for engineers. The amount of friction in a pipe is directly proportional to the difficulty in pumping and transporting fluids such as oil.
Our study combines esoteric mathematical ideas with factors that engineers care about. And, we’ve found that Kolmogorov’s theories have wider applicability that anyone thought. This is an exciting new insight into turbulence as well as into the transition to turbulence.
Dr Pinaki Chakraborty, Fluid Mechanics Unit, Okinawa Institute of Science and Technology Graduate University