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- 1. Numerical study of flow through Linear Weir Abstract The use of Computational Fluid Dynamics for simulating flow around weirs and hydraulic structures is gaining popularity as constructing physical models every time for analysis takes up lots of time and energy and also not economical. CFD is increasingly used for study of flow around old as well as new structures and for studying their behavior to flow dynamics. The study of flow around a linear weir has been undertaken in this paper. The simulation result has been compared to the experimental result from literature. The head-discharge relationship of the weir has also been compared to standard equations available in literatures. The paper confirms the use of CFD as a tool for accurately predicting flow patterns around hydraulic structures. Keywords: Linear weir, Computational Fluid dynamics, PISO Algorithm, Discharge-Head relationship. 1. Introduction Precipitation is one of the major sources of water resources and fresh water constitutes only 2.5 % of all water on earth and is very fundamental for all forms of life (Sathe, Khir et al. 2012, Jedhe, Srivastava et al. 2014).The substantial Population growth has initiated a water stress scenario (Shukla, Khire et al. 2013, Gleick 2014).The recent Political Tension between India and Pakistan regarding Indus Treaty, the increasing dispute over Nile Basin, Afghanistan and Iran Water Dispute, Long time Tensions in the Euphrates-Tigris, Cauvery Water Dispute in India within states and the Israel and its Arab Neighbors over control of water sources in the Jordan River drainage basin in 1967 stand testimony to the increasing Water conflicts as the rivers are the main contributors of fresh water among the surface sources along with providing groundwater water requirements. This use of a finite Resource has led Researchers around the world to move towards a sustainable and optimum use of Water.Hydraulic structures are frequently used for water resources development and management (Hirshleifer, De Haven et al. 1969, Griffin 2016). Dams, barrages, weirs, head and cross regulators are some significant
- 2. structures and they are applied to store and regulate the surface water of river. The flow domain in the vicinity of these hydraulic structures consists of spatial as well as temporal variation of velocity. India is a monsoon country with rainfall not falling throughout the year but concentrated in 3-4 months. Thisimplies India gets all of its fresh water resource in around 3-4 months. This leads a greater responsibility on the water resource professionals to better manage this finite water source so that its sustainable use can be availed all around the year. Dams are the most former and elemental type of civil engineering hydraulic structures. All great cultures have been discovered with the construction of dams and reservoir appropriate to their demands, to meet drinking and irrigation demands originating through the evolution and elaboration of engineered farming. Transverse hydraulic structures are structure placed across the open channel river and is used for flow modifications in the open channel flow(Naik, Panda et al. 2008).A Linear weir is the simplest type of transverse hydraulic structure which is basically an obstruction constructed perpendicular to the flow of open channel covering entire width of the channel. The water flows over the linear weir and thus allows the measurement of discharge by measuring the upstream head. A Linear weir is abundantly used in irrigation systems along with industries and laboratories. Weirs have different shapes like rectangular, triangular, trapezoidal, labyrinth, morning glory types etc. (Arvanaghi and Oskuei 2013). Weirs are generally used for following purposes: (a) Flow discharge control and measurement (b) Channel stabilization (c) Water level moderation (d) Environmental improvement etc. Flow system is complex over a weir, however taking the energy principles into account, the discharge flowing through over a linear weir can be related to the head over the weir crest. √ (1) Where, Q= flow rate (m3 /s) h= head on the weir (m) l= crest length of the weir (m) g= acceleration due to gravity (9.81 m/s2 ) Cd = discharge constant of the weir.
- 3. 2. Experimental results and Numerical Models The numerical model is constructed based on experimental model of (Tiwari and Sharma (2017)). A linear weir of height 160 mm was placed perpendicular in open channel flow over the entire width of 84 mm taken for 3D numerical simulation. Meshing and Boundary Condition The top and outlet of the numerical model was designated as pressure outlet while the two side lengths were taken as symmetry. The primary phase was taken as air while the secondary phase as water. The model was run as transient simulation in presence of gravity. The phase interaction between air and water was provided in the form of surface tension force. The upstream distance from inlet to weir was taken as 3.0 meters while the total length of channel was 4.16 meters. Height of inlet was taken as 125mm. Around 650,000 elements were created for linear weir meshing. Computational fluid dynamics (CFD) simulation using FLUENT solver is selected for our numerical study for flow over. Free surface as determined with CFD study has been compared with experimental results. PISO algorithm for Pressure-Velocity Coupling Method was used. Also, the Realizable (k-ε) model is used in the present study as the viscous model to simulate the effect of turbulence. “Realizable” model implies that the model is consistent with the physics of Turbulent flow and satisfies certain mathematical constraints on the Reynolds stresses. Verification of the Numerical Model CFD analysis shows the discharge capacity of linear rectangular weir to be in close agreement with the experimental results from literature. Probe tool was used to ascertain the height over the weir across the direction of flow over the weir and their average is as shown in the Table 3 below. Time step of the analysis for linear weir was taken up as 0.01 s. The solution converged and the continuity error was well within the limit. 3. Results and Discussion The scaled residuals in continuity dropped well below the third order of magnitude (10-3 ) for discharges and remained steady while other residuals in X-velocity, Y-velocity, Z-velocity, k, ε and volume fraction (air) dropped to fifth order of magnitude (Fig.1) and thereafter the residuals attained a constant value. The probe tool used for ascertaining height of water over the weir for a
- 4. constant discharge is shown in Fig. 2. The Iso-surface plot for a discharge is shown in Fig. 3. Iterations was kept constant at 10 for all the different discharges in the numerical model. Fig. 1: Residuals of CFD Analysis for linear weir The result from the CFD analysis is in very close agreement with the experimental finding as presented in the Fig.4 below where series 1 is the data from literature and series 2 is the data from numerical model. The maximum error obtained was well within 3 percent for all discharges. Fig. 2: Probe at the center of the linear weir for volume fraction
- 5. Fig. 3: Iso-surface plot for the linear weir. Fig. 4: Discharge vs head for linear weir 4. Conclusion The study focused here on a simple geometry across the flow path and showed that the numerical findings were in close agreement with the experiment data from literature. It can hence be concluded from our study of numerical model that CFD can effectively be
- 6. applied to solve natural flow patterns in open channel flow. It also paves a way to utilize CFD to analyses flows in complex hydraulic structures like labyrinth weirs and morning glory spillways or the recently founded Piano Key Weirs. This area needs further study as numerical models save lot of time and resources and thus are gaining popularity.