Study on Fiber Motion in Turbulent Flow

Abstract

Turbulence means agitation, commotion and disturbance. This definition is, however too general and does not suffice to characterize turbulent fluid motion in the modern sense. Osborn Reynolds in the study of turbulent flows, named this type of motion "sinuous motion". The use of the word "turbulent" is to characterize a certain type of flow, namely the counterpart of streamline motion. In fluid dynamics, turbulence or turbulent flow is a fluid regime characterized by chaotic, stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time. Turbulence occurs nearly everywhere in nature. It is characterized by the efficient dispersion and mixing of vorticity, heat, and contaminants. In flows over solid bodies such as airplane wings or turbine blades, or in confined flows through ducts and pipelines, turbulence is responsible for increased drag and heat transfer. Turbulence is therefore a subject of great engineering interest. On the other hand, as an example of collective interaction of many coupled degrees of freedom, it is also a subject at the forefront of classical physics. Origin of turbulence is a central role in determining the state of fluid motion played by the Reynolds number. In general, a given flow undergoes a succession of instabilities with increasing Reynolds number and, at some point, turbulence appears more or less abruptly. It has long been thought that the origin of turbulence can be understood by sequentially examining the instabilities. In 1937, Taylor and Von Karman [29] gave the definition, "Turbulence is an irregular motion which in general makes its appearance in fluids, gaseous or liquid, when they flow past solid surfaces or even when neighboring streams of the same fluid flow past or over one another." According to this definition, the flow has to satisfy the condition of irregularity. This irregularity is a very important feature. Because of irregularity, it is impossible to describe the motion in all details as a function of time and space coordinates. But turbulent motion is irregular in the sense that it is possible to describe it by the laws of probability. It appears possible to indicate distinct average values of various quantities, such as velocity, pressure, temperature etc. If turbulent motion were entirely irregular, it would be inaccessible to any mathematical treatment. Therefore, it is not sufficient to say that turbulence is an irregular motion. According to J.O. Hinze [11], the turbulent flow is "Turbulent fluid motion is an irregular condition of flow in which the various quantities show a random variation with space and time coordinates, so that statistically only distinct average values can be discerned." The addition "with space and time coordinates" is necessary; it 1s not sufficient to define turbulent motion as irregular in time alone. For instance, the case in which a given quantity of a fluid is moved bodily in an irregular way; the motion of each part of the fluid is then irregular with respect to time to a stationary observer, but not to an observer moving with the fluid. Again, turbulent motion is not irregular in space alone, because a steady flow with an irregular flow pattern might then come under the definition of turbulence. According to the definition of Taylor and Von Karman [29] there are two distinct types of turbulence, wall turbulence and free turbulence. Wall Turbulence: Turbulence generated by a viscous effect due to presence of a solid wall is designated by wall turbulence. Free Turbulence: Turbulence in the absence of wall generated by the flow of layers of fluids at different velocities is called free turbulence. Turbulent flow occurs in our daily life. If we observe the smoke rising out of a chimney of a factory or a cigarette, we find that upto a certain length from the chimney or the cigarette, the smoke has a regular shape and after that its shape becomes irregular and if we see still farther then the smoke becomes completely irregular. Again, if a drop of ink is dropped in a glass of water, we find a similar phenomenon, i.e, a regular ink thread falling for a short distance after which it spreads and a vortex type motion can be observed. Ultimately the thread splits into several vortices and motion becomes irregular. The flows with such irregular motions are usually called turbulent flows. Turbulent flow also occurs in large arteries at branch points, m diseased and narrowed (stenotic) arteries and across stenotic heart valves………………………………………..