http://rulrepository.ru.ac.bd/handle/123456789/114 2026-04-07T23:17:05Z 2026-04-07T23:17:05Z Ahmed, Shams Forruque http://rulrepository.ru.ac.bd/handle/123456789/503 2022-05-29T09:42:22Z 2010-01-01T00:00:00Z

Study on Fiber Motion in Turbulent Flow Ahmed, Shams Forruque 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……………………………………….. This thesis is Submitted to the Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh for The Degree of master of Philosophy (Mphil)

2010-01-01T00:00:00Z Mumtahinah, Mst. http://rulrepository.ru.ac.bd/handle/123456789/208 2022-04-24T07:38:41Z 2014-01-01T00:00:00Z

A Study on Turbulent and Magneto-hydrodynamic turbulent Flow in Incompressible Fluid Mumtahinah, Mst. The first chapter is a general introductory chapter and gives the general idea of turbulence, distribution functions and their principal concepts. Some results and theories which are needed in the subsequent chapters have been included in this chapter. Types and examples of turbulence, different stages of Reynolds number, Reynolds equation, averaging rules, Coriolis effect etc have been briefly discussed. Distribution functions, Joint distribution functions, equation of motion of dust particles, spectral representation of turbulence and Fourier Transformation of the Navier-Stockes equation have also been discussed. Lastly, a brief review of the past researchers related to this thesis have also been studied in this chapter. Throughout the work we have considered the flow of fluids to be isotropic and homogeneous. The notions generally adopted are those used by Taylor, Vonkarman, Hinze, Reynolds, Deissler, Sarker, Kisore, Batchelor, Coriolis and Lundgren. The Second chapter consist of two parts. In part A, we have studied the decay of temperature fluctuations in dusty fluid homogeneous turbulence prior to the final period considering correlations between fluctuating quantities at two- and three- point. In this part we have tried to solve the correlation equations by converting it to spectral form by taking their Fourier transform. Lastly, by integrating the energy spectrum over all wave numbers, the energy decay law of temperature fluctuations in homogeneous turbulence before the final period in presence of dust particle is obtained. In part B, we have studied the decay of temperature fluctuations in dusty fluid homogeneous turbulence before the final period in presence of Coriolis force and have considered correlations between fluctuating quantities at two- and three- points by neglecting the fourth order correlation in comparison to the second and third order correlations. The correlation equations for two- and three- point in a rotating system in presence of dust particles are obtained and these equations are converted to spectral form by taking their Fourier transforms. Finally by integrating the energy spectrum over all wave numbers, the energy decay law of temperature fluctuations in homogeneous dusty fluid turbulence before the final period in presence of Coriolis force is obtained. The Third chapter consists of two parts. In part A, we have studied the joint distribution functions for simultaneous velocity, temperature, concentration fields in turbulent flow undergoing a first order reaction in presence of Coriolis force. The various properties of the constructed joint distribution functions have been discussed. In this chapter we have tried to derive the transport equations for one and two point joint distribution functions of velocity, temperature, concentration in convective turbulent flow due to first order reaction in presence of coriolis force. In part B, we have an attempt to derive the transport equation for the joint distribution function of certain variables in convective turbulent flow undergoing a first order reaction in a rotating system in presence of dust particles. Equations for the evolution of one- point and two- point joint distribution function for velocity, temperature and concentration in convective turbulent flow field undergoing first- order reaction in a rotating system in presence of dust particles have been derived. Finally we have made a result with comparison of the equation for one- point distribution function in the case of zero coriolis force in the absence of the dust particles and negligible diffusivity. In Chapter four, we have studied the statistical theory of certain variables for three- point distribution functions in MHD turbulent flow in a rotating system in presence of dust particles. In this chapter we have made an attempt to derive the transport equations for evolution of distribution functions for simultaneous velocity, magnetic, temperature and concentration fields in MHD turbulent flow due to Coriolis force in presence of dust particles and various properties of the distribution function have been discussed. In Chapter five, we have made an attempt to discuss the summary about the whole thesis. This thesis is submitted to the Department of Applied Mathematics, University of Rajshahi, Rajshahi Bangladesh for the Degree of Master of Philosophy (MPhil)

2014-01-01T00:00:00Z