Journal of Applied Mechanical Engineering

Flow in curved pipes

3^rd International Conference on Fluid Dynamics & Aerodynamics

October 25-26, 2018 | Berlin, Germany

R S Srivastava

Defence Science Centre, India

Scientific Tracks Abstracts: J Appl Mech Eng

Abstract:

Dean (1927, 1928) considered the steady motion of an incompressible fluid through a pipe of circular cross section which is coiled in a circle which amounts to flow in curved pipes. He found that to a first approximation (Dean 1927) the relation between the pressure gradient and rate of flow is not dependent on the curvature. He modified the analysis and was able to show (Dean 1928) that reduction in flow due to curvature depends on a single variable K equal to , R being the Reynolds number based on the maximum axial velocity, a being the radius of the tube and L is the radius of curvature of the curved tube. K is known as Dean???s number in literature. McConaloque and Srivastava (1968) extended Dean???s work numerically and introduced a new non- dimensional parameter D based on the mean pressure gradient. The parameter D is related to Dean???s K and R by the relation: and the numerical solution was obtained from D=96 (upper limit of Dean???s work) to D=605.72. The iterative Fourier series solution of Dean???s (1927) equations provided the results. For several values in this range, secondary flow has been obtained. It has been observed that higher the D, stronger is the secondary motion. Also, the non-dimensional velocity perpendicular to the plane of cross section of the pipe has been obtained. In engineering situations laminar flow rarely occurs because Reynolds numbers are usually too high and for this reason research on laminar secondary flow have been neglected. But in the cardiovascular systems, the flow is usually laminar. Study of this system (in only parts of which curved tubes occur) makes it desirable, therefore, to investigate laminar secondary flows. Understanding of this streamline problem can assist for example in understanding the distribution of injected substances and this portion of work has been completed by McConaloque (1970). The contribution of McConaloque (1970) compares favorably well with experimental results of Dr. Caro (1966). The work of McConaloque and Srivastava (1968) on the prediction of axial maximum velocity in curved pipes for different D???s has tallied extremely well with ultrasound measurements. Recently (2016) some results on flow through curved pipes of elliptical cross sections has been obtained which would be helpful for the cardiovascular system. There is enormous application of this subject in science, engineering and other important fields. Recent Publications 1. McConaloque D J and Srivastava R S (1968) Motion of fluid in curved tube. Proc. Roy. Soc A DOI: 10.1098/rspa.1968.0173. 2. McConaloque D J (1970) The effects of secondary flow on the laminar dispersion of an injected substance in a curved tube, Proc. Roy. Soc. A DOI: 10.1098/rspa.1970.0031 3. Caro C G J (1966) The dispersion of indicator flowing through simplified models on the circulation and its relevance to velocity profile in blood vessels. Physical 185(3):501-19.

Biography :

R S Srivastava has been working in the field of Fluid Mechanics for a considerable period of time. He has by now published more than 70 research papers on flow through curved tubes, shock wave diffraction, heat transfer, flow through rotating pipes and non-Newtonian fluids. His work has received international recognition and has been referred widely and profusely in international journals and books by very eminent persons in the area. His work on flow through curved pipes has found application in most of the disciplines in Science, Engineering and Medicine. His prediction of position of maximum axial velocity in curved pipes for different parameters of Mc Conalogue has tallied extremely well with ultrasound measurements. He has written two books: “Turbulence (Pipe Flows)” and “Interaction of Shock Waves”. He has worked with Prof. Sir James Lighthill, F R S, Prof. I I Glass and Prof. Akira Sakurai at Imperial College, London, Institute for Aerospace Studies, Toronto, Tokyo Denki University, Tokyo, respectively. He has delivered several lectures at many international symposia.

E-mail: rssuncle@yahoo.co.uk