Documents

Flow Through Pipe Bend

Description
Pipe bend effects the flow and create jet drag
Categories
Published
of 7
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Related Documents
Share
Transcript
   Flow in a Pipe Bend Rahul kumar, Pawan kumar, Sagar Babu, Harish Verma, R.S.S. Sri Ram, Vinodth Palithya B. Tech Aerospace Engineering, Indian Institute of Space Science and Technology  Abstract   —  this experiment is conducted in aerodynamics lab study the flow around bend pipes and observe the effect of streamline curvature on the pressure distribution in the constant area circular bend by measuring the static pressure distribution along the wall in the flow direction at different regular positions as well as perpendicular to it. . In this experiment the pressure at different points was measured using the manometer along the streamline (along the curvature of the bend in the duct), as well as the pressure across the curvature (perpendicular to the streamline). Using this pressure distribution the velocity at different points was calculated across and along the curvature of the duct, and the results were compared with the theoretical values calculated using Bernoulli’s equation.   Keywords-component; inviscid, wind tunnel, streamline, pitot tube, calibration curve, vortex I.   I  NTRODUCTION  If a fluid is moving along a straight pipe that after some point  becomes curved, the bend will cause the fluid particles to change their main direction of motion. There will be an adverse  pressure gradient generated from the curvature with an increase in pressure, therefore a decrease in velocity close to the convex wall, and the contrary will occur towards the outer side of the  pipe. in a curved pipe the water is continually changing its  position with respect to the sides of the pipe, and the water which is flowing near the Centre at one part approaches the sides as it moves through the pipe and flowing near the sides it exerts a ‘scouring’ action on the pipe walls  . The change of direction forced on a fluid when it negotiates a  bend produces turbulence in the fluid and a consequent loss of energy. The net loss in pressure is greater than that for the same length of straight pipes. Abrupt changes of direction produce greater turbulence and larger energy losses than do smoothly contoured changes. Flows through the bend in a duct may be classified as internal flows to distinguish them from flows over bodies such as airfoils, called external flows. It is sometimes necessary to shape a duct in such a way that particular requirements are met. For example, it may be necessary to change the shape of cross-section from square to rectangular with a small loss of total  pressure, or it may be required to form a bend in such a way that the distribution of velocity at the exit is as nearly uniform as it can be made. Due to the presence of boundary layers along the duct walls, the fluid mechanics of such flows are sometimes extremely complicated. Separation may be produced where the pressure rises in the direction of flow. The curvature of the flow is accompanied by a pressure gradient which rises across the section from the inner to the outer wall. The pressure gradient extends over the whole section, so that the boundary layers on the upper and lower walls are subjected to the same pressure gradient as the main flow. But because the streaming velocity in the boundary layer is less than in the main part of the flow, the curvature of the streamlines in the boundary layer is more severe. This gives rise to a net inward-directed flow adjacent to the upper and lower walls, which sets up a secondary flow in the form of a double rotation, superimposed on the main stream. The motion emerging from the curve in the duct is therefore a pair of contra-rotating spirals, the strength of which depends on the amount of curvature and on the thickness of the boundary layer. II.   T HEORY  A streamline is a line drawn at a given instant in time so that its tangent is at every point in the direction of the local fluid velocity . Streamlines indicate local flow direction, not speed, which usually varies along a streamline. General equations of motion for inviscid in compressible flows can be written in streamline co-ordinates as Where r is the streamline radius of curvature and s, n are directions along and normal to the streamline respectively. From these equations, it could be seen that, if the streamlines are curved a pressure gradient is set up normal to flow direction also.    Figure 1. Air flow through the bend Within the bend we shall assume a free vortex distribution of velocity, given by Where u is the streaming velocity at radius r from the centre of curvature of the bend. Separation and secondary flow will be neglected. The constant C may be found by applying the equation of continuity as follows: Q = Ub(r  2 -r  1 ) = b  ʃ  udr Where b is the width of the section of the duct. Substituting for u from Equations and performing the integration leads to the result The corresponding pressure distribution may be found by assuming that Bernoulli’s equation may be applied bet ween the upstream section and a section within the bend as follows: where p o  is the static pressure upstream and p is the pressure at radius r in the bend. III.   E XPERIMENT  The experimental set up consists of the blower connected to a diverging channel, which in turn, attached to a settling chamber followed by a converging channel. Finally, the converging channel is linked to the constant area 90 0  bend duct through which the air flows. There are three reference atmospheric pressure tapping, and three sets of tappings on the  bend duct; one set of 10 along the outer curved wall, one set of 10 along the inner curved wall and a set of 5 along a radius of the bend. Besides, other two pressure tappings are located on the inlet and exit of converging channel. Figure 2. Experimental setup Figure 3. Motor control set IV.   PROCEDURE   During the experiment “Flow around a bend in a duct” the following steps were taken. The pressure tapings along the outer wall, the reference tapping 0 and the pressure tapping in the air box are all connected to the manometer. The air speed is adjusted to a value slightly below the maximum, as indicated  by the air box pressure, and the pressures are recorded. (The setting of air speed slightly below the maximum is to ensure that the same setting may be repeated in later tests). The tapings on the inner wall are then connected in place of the ones on the outer wall. The air box pressure is adjusted to the  previous value and a further set of readings are recorded. Finally the procedure is repeated with the third set of pressure tapings V.   OBSERVATION   TABLE I. R  EADING TABLE 1 Identify applicable sponsor/s here. (sponsors)    Pressure Readings on Inner Wall RPM P1 P2 P3 P4 P5 P6 P7 P8 P9 600 12 12.1 12.3 12.3 12.2 12.3 12.3 12.2 12.1 800 12 12.2 12.5 12.6 12.4 12.6 12.6 12.3 12.1 1000 11.8 12.2 12.7 12.8 12.4 12.9 12.9 12.3 12.1 TABLE II. R  EADING TABLE 2 R  pm Pressure Readings on Outer Wall  P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 600 12 12 11.9 11.9 11.9 11.9 11.9 12 12 12.1 12.2 800 12 12 11.9 11.8 11.8 11.8 11.8 11.9 12 12.2 12.2 1000 11.8 11.8 11.6 11.8 11.8 11.7 11.8 11.7 11.8 12 12 TABLE III. R  EADING TABLE 1 Rpm Pressure Readings in Radial Direction Wind Tunnel P21 P22 P23 P24 P25 P29 P30 600 12 12 12 12.2 12.3 12 11.4 800 11.9 11.9 12.1 12.3 12.5 11.9 10.8 1000 11.6 11.8 12 12.5 12.6 11.7 10 Series 1   rpm 600 Series 2   rpm 800 Series 3   rpm 1000  VI.   RESULT  The main feature of flow through a bend is the presence of a radial pressure gradient created by the centrifugal force acting on the fluid. Because of this, the fluid at the center of the pipe moves towards the outer side and comes back along the wall towards the inner side. This creates a double spiral flow field.   If the bend curvature is strong enough, the adverse pressure gradient near the outer wall in the bend and near the inner wall  just after the bend may lead to flow separation at these points, giving rise to a large increase in pressure losses. Pressure drop in the inner radius is due to the flow separation taking place during entry of air from test section to bent tube. Fluid particles in this region, because of their close proximity to the wall, have low velocities and cannot overcome the adverse pressure gradient and this leads to a separation of flow from the boundary and consequent losses of energy in generating local eddies. The distribution of Cp over the radial section is comparable to the calculated one to a great extent, indicating that the assumption of a free vortex velocity distribution made in Equation (4), together with Bernoulli’s equation is fairly reasonable Since the plane of curvature of the pipe is reasonably  perpendicular to the gravity so neglecting the body forces due to gravity seems to be a good approximation as the component of this body force will be negligibly small while the force equilibrium is considered in the normal direction. Pressure loss in the tunnel circuit is also due to the following factors: ã   Friction loss due to flow through the tunnel circuit ã   Pressure loss due to flow separation and turbulence in the different sections ã   Pressure loss due to spiral flow due to secondary flow Since the friction effects cannot be completely eliminated in the tunnel hence there are pressure drop for every section considered in wind tunnel and bent pipe A CKNOWLEDGMENT We would like to acknowledge with appreciation the numerous and valuable persons whose contribution has been important in this project. We would like to thank our instructor Dr. Satheesh K for his valuable help. We also thank our lab assistants for clearing our doubts. R  EFERENCES   [1]   Equation of Motion in Streamline Coordinates Ain A. Sonin, MIT [2]   http://www.tafsm.org/PROJ/FSI/mesh.html [3]   http://rspa.royalsocietypublishing.org/content/234/1198/335.abstract [4]   http://www.diva-portal.org/smash/get/diva2:515647/FULLTEXT02 [5]   http://www.thermopedia.com/content/577/?tid=104&sn=1422 
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks