ISSN 9 86 Volume, Issue 9 Setember 07 Otimisation of Pressure Loss and Flow Distribution at Pie Bifurcation Dr. Nagaraj Sitaram Professor, Deartment of Civil Engineering,School of Engineering Technology, Jain University, Jakkasandara Post, Kanakaura Taluk, Karnataka, India Abhijeeth Nagaraj Post Graduate Student, Det. of Mechanical Engg., Bangalore Institute of Technology, KR Road, V.V Puram, Bengaluru, Karnataka, India Abstract Pie networks are very common in industries where liquids or gases to be transorted from one location to the other. Combining and dividing ie junctions are of interest to hydraulic engineers in ie network articularly in water distribution system. The dividing junction involves additional geometric arameters comared to comonents with a single flow ath. There is also a need to know the ressure loss at the junction and arameters which influences these losses. The aer focuses in determination of ressure losses and flow distribution of ie bifurcation using the exerimental technique at various flow rates and ressures. The exerimental data and analysis for 00mm main and 75 mm bifurcated ies show the correlation between ressure loss coefficient (K) with a slit flow ratio,,. The exeriments have been conducted for four different bifurcation angles- 0 o, 5 o, 0 o, 0 o. The bifurcation loss coefficient (K) also deends u on the line ressures, bifurcation angles, and ratio of main to branch ie diameters. The exerimental findings also suggest that the head loss at the bifurcation junction will be minimum when equal discharge flow in branched ies. The hydraulic behaviour of the right and left branches for equal angle of bifurcation is also studied. Keywords: Pie, Dividing junctions, ressure loss, bifurcation, slit flow ratio, equal discharge, loss coefficient.. Introduction The division of two streams at different velocity results in loss of energy at the junction and changes to velocity for a given ressure. A hydraulic engineer is interested to know the slit flow ratios and ressure loss for a given configuration of bifurcation which is mainly used in ie networks and house lumbing. The determination of ressure loss coefficient (K) at bifurcation deends uon the geometric arameters like ie area ratio, diameter of the ie and angle of bifurcation, fluid arameters like density of the fluid, viscosity and temerature of the fluid, and flow arameters like ressure and discharge. The loss of energy at the ie bifurcation is mainly due to searation and reattachment of the fluid flow atterns near the bifurcation. The exchange of the fluid momentum and energy transfer at bifurcation junction totally deends uon the angle of bifurcation, line ressure in the ies, diameter ratios of the main and branch ies. The aer aims at the determination of loss of co-efficient at the bifurcation for various ressures and flow rates for a given angle of bifurcation ( = 0, 5, 0, 0). Also to determine the flow ratio for which ressure loss co-efficient is minimum. The various configurations of bifurcation are shown in figure below: 99 Dr. Nagaraj Sitaram, Abhijeeth Nagaraj
ISSN 9 86 Volume, Issue 9 Setember 07 Figure Right bifurcation Figure Left bifurcation Figure Y bifurcation. Theory The discharge valves in branch ies are measured and added together to obtain the flow in main ie based on the conservation of mass called continuity equation. The total energy for each ie is determined based on line ressure. Energy at will always be more than energy at and resectively in figure. As er the different bifurcation conditions given in figures to, the equations are: Figure Right bifurcation = + () = + () = + () The loss of co-efficient at each ie is comuted by Blevins equation (98) K = () K = (5) K = (6) K = (7) The overall loss co-efficient (K) in bifurcation junction is defined based on the branch di scharge ratio and branch loss coefficients: 00 Dr. Nagaraj Sitaram, Abhijeeth Nagaraj
0 Dr. Nagaraj Sitaram, Abhijeeth Nagaraj International Journal of Engineering Technology Science and Research ISSN 9 86 Volume, Issue 9 Setember 07 K K K (8) The total energy (E) for all horizontal ies (Z =Z =Z =Z ) is comuted by, g V E w (9) g V E w (0) g V E w () g V E w () The outflow energy (O) of flow is comuted by, V O () V O () V O (5) V O (6). Losses at Pie Bifurcation: The bifurcations are rovided in ies to change the direction and division of flow through it. An additional loss of head, aart from that due to fluid friction, takes lace in course of flow through ie bend. The fluid takes a curved ath while flowing through a ie bifurcation as shown in Figure 5. The flow near the shar corners creates turbulence and searation. Figure 5 Losses in Right Bifurcation
ISSN 9 86 Volume, Issue 9 Setember 07 This results in an increase in ressure near the outer wall of the bend, starting at some oint A (Figure 6) and rising to a maximum at some oint B. There is also a reduction of ressure near the inner wall giving a minimum ressure at C and a subsequent rise from C to B. Figure 6 Right Bifurcation in Pie flow Therefore between A and B and between C and towards outflow the fluid exeriences an adverse ressure gradient (the ressure increases in the direction of flow). Whenever a fluid flows in a curved ath, force acting radially inwards on the fluid to rovide the inward acceleration, known as centrietal acceleration. Fluid articles in this region, because of their close roximity to the wall, have low velocities and cannot overcome the adverse ressure gradient and this leads to a searation of flow from the boundary and consequent losses of energy in generating local eddies. Losses also take lace due to a secondary flows in the radial lane of the ie because of a change in ressure in the radial deth of the ie. This flow, in conjunction with the main flow, roduces a tyical siral motion of the fluid which ersists even for a downstream distance of fifty times the ie diameter from the central lane of the bend. This siral motion of the fluid increases the local flow velocity and the velocity gradient at the ie wall, and therefore results in a greater frictional loss of head than that which occurs for the same rate of flow in a straight ie of the same length and diameter. The additional loss of head due to friction the loss of head will occur due to change in direction, change in diameter and ie bends. The bend loss and is usually exressed as a fraction of the velocity head as: KV H bend g Where V is the average velocity of flow through the ie. The value of K deends on the total length of the bend and the ratio of radius of curvature R of the bend and ie diameter D and is given as: K f R D The radius of curvature R is usually taken as the radius of curvature of the centre line of the bend. The factor K varies slightly with Reynolds number Re in the tyical range of Re encountered in ractice, but increases with surface roughness. (7) (8). Exerimental Setu The exerimental setu consists of half Horse Power um, 600 mm manifold to maintain the constant ressure in the ie line. A 00 mm ieline is used as main ie which bifurcates into 75 mm ielines of galvanized iron material. The ressure gauges and flow meter are installed to know the line ressure and the values of discharge in each ie varied from 0 to 0 (-variants in bifurcation angle). The flows 0 Dr. Nagaraj Sitaram, Abhijeeth Nagaraj
ISSN 9 86 Volume, Issue 9 Setember 07 through the ies are discharged to a recirculating collecting tank. The readings for ressure and discharge are taken for a given bifurcation angle at various flow rates. The temerature of water is noted at the beginning and end of the exeriment. Figure 7 Exerimental setu. Valve control combination: The check valves, ressure gauges and flow meter are rovided in each ie. The valves are controlled to achieve the desired flow rate and ressure in each ie. The conditions of valves are varied to obtain ressure loss coefficient (K) for each combination (Refer Figure to ). Valve, are fully oen Valve is controlled Valve is closed Temerature = O C -7 O C Results and Discussions Obtained data is analysed to obtain the hydraulic loss of co-efficient for individual ies (K and K ) and for the junction (K) based on equation 8. Figure 8 Energy Vs. Slit Flow As the slit flow ratio in branch ie- increases the flow energy in the branch ie- also increases as shown in the Figure 8. The non-dimensional arameters like energy ratio (E /E ), Flow ratio ( / ), ressure ratios (P /P ) are comuted. 0 Dr. Nagaraj Sitaram, Abhijeeth Nagaraj
ISSN 9 86 Volume, Issue 9 Setember 07 Figure 9 Pressure Loss Coefficient Vs Discharge Figure 0 shows the variation of loss coefficients of branch ies with their resective slit flow ratios. The loss coefficients for the straight ie (branch ) in relatively more as comared to the branched ies and whose 0& 0.The grah also shows as the flow in the bifurcated ies tend to equalize (i.e. = = 0. 5. The overall loss coefficients (K) at bifurcation tend to reduce to minimum. Right Branch Left Branch Figure 0 Pressure Loss Coefficient Vs Discharge Figure 0 gives a comrehensive value for a combined loss co-efficient at bifurcation (K) with the slit flow ratio and also clearly signifies that ressure loss behaviour is symmetrical for right and left bifurcation for a given. It also clearly indicates as the slit flow ratio are nearly equal, the ressure loss co-efficient is minimum and the value is near unity. 0 Dr. Nagaraj Sitaram, Abhijeeth Nagaraj
ISSN 9 86 Volume, Issue 9 Setember 07 The ressure distribution in a tyical bifurcation is shown through the results obtained from Comutational Fluid Dynamics in figure. Figure Pressure distribution from Comutational Fluid Dynamics Figure Branch Pressure Loss Coefficient Vs of Outflow Energy The nature of the figure is similar to figure. It indicates that the ressure loss coefficients also related to the out flow energy at the various branches and the value is otimized when the flow is slits into equal discharge. 05 Dr. Nagaraj Sitaram, Abhijeeth Nagaraj
ISSN 9 86 Volume, Issue 9 Setember 07 Figure Combined Loss Co-efficient Vs Slit Flow for extreme angles Table - Exerimental Data Discharge Pie (cm /s) Discharge Pie (cm/s) Net Discharge = + (cm/s) / / Energy at Inlet E /E Energy at Inlet E /E Energy at outlet O /O Energy at outlet O /O 7.69 6.9 790.85 0.79 0.5708 0.98 0.5 0.7 0.60 8.6879 505.869 789.508 0.59 0.6067 0.977 0.69 0.5 0.8 0.099 550.055 75.69 0.680 0.797 0.979 0.70 0.068.5 5.888 67.668 76.5567 0.577 0.88 0.987 0.70 0.07.87.06567 7.758 7.8 0.005 0.95695 0.98 0.788 0.00.66. Conclusions Detailed exeriments are conducted to understand the ressure loss at ie bifurcation with various arameters. The loss behaviour at the ieline bifurcation has been tested for right, left and central bifurcation. It is observed that for a given bifurcation angle, the loss coefficients for the right and left bifurcation are nearly same. The exerimental findings also suggest that the minimum loss at the ie line junction will occurs when the slit flow ratios are equal. Also the loss co-efficient increases as the branch angle increases. The head loss at the ie bifurcation junction is contributed by both the individual ies and angle of bifurcation. In case of straight ie bifurcation, the contribution of head loss is relatively more by the straight ie comared to branch ie. It is lanned to conduct more exeriments with angles of bifurcation.5, 5, 5 and 0. References Achantha Ramakrishna Rao, Bimlesh Kumar (009). Energy losses at ie trifurcation. Urban Water Journal, Vol.6 (). Albert Rurecht, Tomas Helmrich, Ivana Buntic (00). Very large eddy simulation for the rediction of unsteady vortex motion. th International Conference on Fluid Flow Technologies, -6. Blevins, R D. (98) Alied fluid dynamics handbook. Van Nostrand Reinhold Co., New York, USA. Bransilav Basara, Herwig A Grogger. (000) Exerimental and numerical study of the flow through trifurcation, Advanced Stimulation Technologies. RK Malik, Paras Paudel, (009) D Flow Modelling of the Trifurcation Made in Neal, Hydro Neal, 56-6 (9). Miller, D.S (990). Internal flow systems nd Edition. Gulf Publishing Comany, Houston, USA 06 Dr. Nagaraj Sitaram, Abhijeeth Nagaraj