DEVELOPMENT AN EQUATIONS FOR FLOW OVER WEIRS USING MNLR AND CFD SIMULATION APPROACHES

International Journal of Civil Engineering and Technology (IJCIET) Volume 9, Issue 3, March 2018, pp. 70 79, Article ID: IJCIET_09_03_008 Available online at http://www.iaeme.com/ijciet/issues.asp?jtype=ijciet&vtype=9&itype=3 ISSN Print: 0976-6308 and ISSN Online: 0976-6316 IAEME Publication Scopus Indexed DEVELOPMENT AN EQUATIONS FOR FLOW OVER WEIRS USING MNLR AND CFD SIMULATION APPROACHES Hasan Ibrahim Al Shaikhli Assistant lecturer, College of Engineering, Civil Engineering Department, Warith Alanbiyaa University, Karbala, Iraq Kadhim Naief Kadhim College of Engineering, Civil Engineering/ University of Babylon ABSTRACT The objective of this paper is to predict the coefficient of discharge for various types of weirs, for this purpose, an equation has developed using multiple non liner regression (MNLR) and the code of computational fluid dynamic (CFD) approaches. A two weirs shape investigate experimentally and numerically, knows as rectangular notch with crest width (0.03m) and triangular V-notch with right angle (90 o ), the crest height for both rectangular and V-notch weirs is remain constant in experimental and numerical study. The results of experimental study and numerical code are used with deferent crest head to developing the hydraulic properties of flow over crest weir. Experimental results stats that the increase of crest head cause an increase in coefficient of discharge for both rectangular and triangular notch weirs. In CFD, results show that FLOW 3D software has the ability to simulate the hydraulic properties of open channel flow of flow over weir in both rectangular and triangular notch. MNLR approach used to predict the coefficient of discharge according to the equations that proposed based on dimensional analyses, results show that MNLR gives a reasonable acceptance to estimate the coefficient of discharge with efferent regression equal to (R 2 =0.99) for both rectangular and triangular V-notch weirs. Keywords: CFD, Weir, FLOW 3D, V-notch, MNLR Cite this Article: Hasan Ibrahim Al Shaikhli and Kadhim Naief Kadhim, Development an Equation for Flow over Weirs using MNLR and CFD Simulation Approaches, International Journal of Civil Engineering and Technology, 9(3), 2018, pp. 70 79. http://www.iaeme.com/ijciet/issues.asp?jtype=ijciet&vtype=9&itype=3 http://www.iaeme.com/ijciet/index.asp 70 editor@iaeme.com

Development an Equation for Flow over Weirs using MNLR and CFD Simulation Approaches 1. INTRODUCTION Weir structures are commonly used in irrigation systems near turnouts from the water delivery network to measure flows. A disadvantage of using weirs for flow measurements is that to ensure a free flow operation, the water upstream must be 'backed up' or its level increased substantially. This so-called 'head' is greater for weirs than for flumes. In addition, sediment and debris are often trapped by the weir. However, weir structures tend to provide more accurate discharge ratings than most other devices. Weir is a hydraulic structure set perpendicular to the flow direction with the objective to measure the flow discharge. The weir gives precise measurement for a different spread of flows. The lower triangular part of the weir manages the normal range of discharges at the measurement structure, the weir upper part living up to expectations for the unpredictable higher top flows. Weirs are usually used to observe rivers flow keeping in mind the end goal to shield from flooding and bolster navigation in rivers. The V-notch weir is one of the sharp crested weirs with a triangular section, used to measure small discharge values subsequent to the water head over the weir peak that is generally touchy to changes in flow. Consequently Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and algorithms to solve and analyze problems that involves fluid flow. FLOW 3D used to simulate the experimental models for evaluating the hydraulic properties of weirs. Most of the literature on FLOW 3D modeling discussed how the program uses a finite difference solution scheme and the volume of fluid (VOF) method, developed by (Hirt and Nichols, 1981), which allowed the model to include only the water portion of the flow. (Teklemariam et al., 2001)[Quoted from Rajab and Elgizawy, 2012] prepared a report outlining the use of FLOW 3D by engineers at Manitoba Hydro and Acres Manitoba Ltd to model various hydroelectric facility components. The document discussed how FLOW 3D is successful in matching the physical model test results for discharge as well as flow patterns and velocities in modeling of a Conawapa diversion port. The multiple nonlinear regression analysis (MNLR) studies the relationship between several independent or predictor variables and a dependent or criterion variable. MNLR can estimate a model using user defined model of nonlinear relationships between dependent and independent variables. The fitted model can be used later to forecast the values of any variable corresponding to new observations (Alfatlawi and Alshaikhli, 2015). Unfortunately, few studies were completed on the simulation of weirs by FLOW 3D software, along these lines this study was done to elucidate more fine points of interest concentrating on the flow regime of flow over notch and coefficient of discharge, for both rectangular and V-notch weirs model. 2. DIMENSIONAL ANALYSIS AND EXPERIMENT RESULTS Dimensional analysis can be defined as tool used to produce a hydraulic relationship or to minimizing the number of variables that has highly influence on the hydraulic phenomenon by using a mathematical formulation. Length L, mass M and time T are three fixed dimensions which has important affect to fluid mechanics. This technique gives relationships with dimensionless groups of variables. (White, 1999; Chadwick and Morfett, 1998). The variables which affect the coefficient of discharge Cd can be seen in equation (1) and (2) for both rectangular and V-notch weir, respectively. (1) (2) http://www.iaeme.com/ijciet/index.asp 71 editor@iaeme.com

Hasan Ibrahim Al Shaikhli and Kadhim Naief Kadhim Where: Cd is the Coefficient of discharge; dimensionless, ρ is the Mass density; (ML -3 ), μ is the Dynamic viscosity; (ML -1 T -1 ),V is the upstream velocity; (LT -1 ),H is the Head above weir crest; (L), g is the Gravitational acceleration; (LT -2 ), B is the channel width; (L), P is the weir opening height; (L), is the angle of V-notch opening; (dimensionless). The resulted dimensionless parameters were: Where:, Froude's number. The effect of dimensionless parameter can be neglected because it remains constant in all experiments. As the effect of viscosity is negligible in open channel flow, Refer to (3) and (4) can be written as: (3) (4) dimensionless parameter can be neglected; therefore, (6) The experimental work done by determining the discharge of notch, the volume of flow obtained using a volumetric tank, the time that required to collecting a known volume measured using stop watch. Each single run repeated two times to check the accuracy of an experiment. After that, controlling valve was used for increasing the head over notch. Finally, replace the rectangular notch plate with the V-notch plate and repeat the above steps with different heads. Based on experimental results, two weir shapes are studied, rectangular and V-notch shape as shown in Figure 1. (5) a. Rectangular weir b. V-notch weir Figure 1 Various types for shape of weirs These weirs are installed in the lab device and the results observed and calculated as shown Figure 2-a and 2-b, respectively. http://www.iaeme.com/ijciet/index.asp 72 editor@iaeme.com

Development an Equation for Flow over Weirs using MNLR and CFD Simulation Approaches a. Installation device b. Operating device Figure 2 Lab device; installation and operation Bernoulli s equation can be applied to determine the results of flow over weir, so the coefficient of discharge can obtain experimentally by equations (7) and (8), respectively. (7) (8) The experimental results can be summarized in table (1) and (2) for both rectangular and V-notch weir. (Fuller, 2010) Table 1 Experimental results of rectangular weir Shape B(m) H (m) Q (lit/sec) R 0.03 0.0100 0. 05070 R 0.03 0.0192 0.135906 R 0.03 0.0300 0.271214 R 0.03 0.0392 0.402240 R 0.03 0.0505 0.603319 R 0.03 0.0585 0.756292 R 0.03 0.0642 0.870364 Table 2 Experimental results of V-notch weir Shape Ө H (m) Q (lit/sec) V 90 0.0200 0. 071300 V 90 0.0255 0. 138663 V 90 0.0310 0. 232886 V 90 0.0345 0. 301750 V 90 0.0395 0. 455402 Figures 3 and 4 shows the head-discharge relationship for both rectangular and V-notch weirs, respectively. Figures 5 and 6 shows the head- coefficient of discharge relationship for both rectangular and V-notch weirs, respectively. It can be seen that the increasing of head cause an increasing in coefficient of discharge for both shapes. http://www.iaeme.com/ijciet/index.asp 73 editor@iaeme.com

Cd Cd Q (m 3 /sec) Q (m 3 /sec) Hasan Ibrahim Al Shaikhli and Kadhim Naief Kadhim 0.0010 0.0008 0.0006 0.0004 0.0002 0.0000 0 0.005 0.01 0.015 0.02 H (m) Figures 3 Show head-discharge relationship for rectangular weir 0.0005 0.0004 0.0003 0.0002 0.0001 0.0000 0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 H (m) Figures 4 Show head-discharge relationship V-notch weir 0.6100 0.6020 0.5940 0.5860 0.5780 0.5700 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 H Figures 5 Show head- coefficient of discharge relationship for rectangular weir 0.6400 0.6200 0.6000 0.5800 0.5600 0.5400 0.5200 0.018 0.022 0.026 0.03 0.034 0.038 H Figures 6 Show head- coefficient of discharge relationship for V-notch weir http://www.iaeme.com/ijciet/index.asp 74 editor@iaeme.com

Development an Equation for Flow over Weirs using MNLR and CFD Simulation Approaches 3. FLOW 3D APPLICATIONS AND CFD RESULTS Numerical modelling techniques have been rapidly developing as computational power enhanced to the point where numerical solutions are now possible for many applications, so, it s nominated as a computational fluid dynamics. FLOW 3D is one of the powerful numerical modelling software that capable of solving a wide range of fluid flow problems. A good selection of different options across the entire FLOW 3D, graphical user interface allows the software to be applicable to such a wide variety of situations. FLOW 3D allows either one or two fluid flow, with or without a free surface, and a multitude of available physics options to suit the specific application. Various meshing and geometry options are available including multi-block grids and the ability to draw simple objects in the software or import different forms of more complex geometry or topographic files. A large selection of boundary conditions is also available to properly model for each specific application (Chanel, 2008). FLOW 3D version 11.0.4 was used to solve the governing equations of Navier-Stokes equations in Cartesian coordinates staggered grid. Mesh and cell size can affect both the accuracy of the results and the simulation time, so it was important to minimize the amount of cells while including enough resolution to capture the important features of the geometry as well as sufficient flow details. FLOW 3D mesh generator uses the FAVOR method to handle the complicated geometries in an orthogonal mesh defined in Cartesian or cylindrical coordinates. Only the orthogonal mesh was allowed to simplify the process of meshing domain in FLOW 3D and the boundary conditions of this simulation can be shown in Figures 7 and 8, respectively. (Alfatlawi and Alshaikhli, 2015). Figure 7 Shows the process of meshing domain in FLOW 3D According to figure 8 the boundary conditions that used in this simulation can be summarized, where S represents the symmetrical surface, W represents the wall surface; P and O are the input and output surfaces, respectively. The wear body is defined as the solid component of this system. (Dargahi, 2006) Figures 9 and 10 plots the pressure and velocity magnitude with distributions of fluid flow along the body of wear in 2D. http://www.iaeme.com/ijciet/index.asp 75 editor@iaeme.com

Hasan Ibrahim Al Shaikhli and Kadhim Naief Kadhim Figure 8 Shows the boundary conditions of Flow 3D simulation Figures 9 Shows the pressure distributions of fluid flow along the body of wear Figures 10 Shows the velocity magnitude distributions of fluid flow along the body of wear http://www.iaeme.com/ijciet/index.asp 76 editor@iaeme.com

Development an Equation for Flow over Weirs using MNLR and CFD Simulation Approaches Figures 11 and 12 shows the results of pressure and velocity magnitude in FLOW 3D simulation, this results shows that the FLOW 3D has the ability to simulate the flow over weir with mach agreeability. Results has taken out for CFD process to extrapolating the hydraulic properties of both rectangular and V-notch weir. Figures 11 Shows the magnitude pressure distributions in 3D simulation Figures 12 Shows the magnitude of velocity distributions in 3D simulation 4. MULTIPLE NON LINER REGRESSION RESULTS Based on experimental results and by benefits of dimensional analyses, an equation to predict the coefficient of discharge has developed. The equation that resulted from dimensional analyses state that coefficient of discharge is a function of Froude number as shown in equation 9: (9) Form equation 9 it can be seen that the height of crest is constant and has no effect to the behavior of coefficient of discharge. By using the SPSS statistics software this equation has putted in mathematical form as shown in equation 10 to estimate the parameters for both rectangular and V-notch weir: (10) The parameters (a, b) has estimated statically in IBM SPSS statistics software, the resulted equation 11 and 12 for both rectangular and V-notch weirs, respectively: (11) http://www.iaeme.com/ijciet/index.asp 77 editor@iaeme.com

Hasan Ibrahim Al Shaikhli and Kadhim Naief Kadhim (12) Coefficient of discharge prediction model using the multiple nonlinear regression (MNLR) approach is presented refer to (11) that has (R 2 equal to 0.99) and Refer to (12) that has (R 2 equal to 0.99) for rectangular and triangular shapes, respectively. Table 3 and 4 shows coefficient of discharge that has calculated from experimental, numerical and MNLR study in addition to the theoretical observations for both rectangular and V-notch weirs, respectively. Table 3 shows coefficient of discharge for rectangular weirs No. Head (m) Theoretical Cd Experimental Cd Numerical Cd MNLR Cd 1 0.0100 0.6084 0.5723 0.5202 0.5204 2 0.0192 0.6084 0.5766 0.5211 0.5213 3 0.0300 0.6084 0.5892 0.6745 0.6747 4 0.0392 0.6084 0.5850 0.6164 0.6167 5 0.0505 0.6084 0.6001 0.5772 0.5774 6 0.0585 0.6084 0.6034 0.5739 0.5741 7 0.0642 0.6084 0.6040 0.5892 0.5895 8 0.0700 0.6084-0.6016 0.6018 9 0.0800 0.6084-0.6106 0.6108 10 0.0900 0.6084-0.6152 0.6154 Table 4 shows coefficient of discharge for triangular V-notch weirs No. Head (m) Theoretical Cd Experimental Cd Numerical Cd MNLR Cd 1 0.0200 0.6349 0.5332 0.4407 0.4409 2 0.0255 0.6349 0.5649 0.4857 0.4858 3 0.0310 0.6349 0.5823 0.5639 0.5641 4 0.0345 0.6349 0.5774 0.6124 0.6124 5 0.0395 0.6349 0.6213 0.6173 0.6175 6 0.0500 0.6349-0.6243 0.6244 7 0.0600 0.6349-0.6269 0.6270 8 0.0700 0.6349-0.6341 0.6342 9 0.0800 0.6349-0.6431 0.6432 10 0.0900 0.6349-0.6487 0.6487 5. CONCLUSION Many points can be stats according to results of this paper. The coefficient of discharge in triangular shape (V-notch) weir is higher than coefficient of discharge for rectangular weir. The crest head increases cause an increasing in coefficient of discharge for both rectangular and V-notch weir. FLOW 3D has the ability to predicate and simulate the flow over weir with reasonable acceptance for both rectangular and V-notch weirs. MNLR approach efficiently represents the measured data to predicate the coefficient of discharge with agreeable regression coefficient for both rectangular and triangular notch weirs. http://www.iaeme.com/ijciet/index.asp 78 editor@iaeme.com

Development an Equation for Flow over Weirs using MNLR and CFD Simulation Approaches Based on the predicated results, the percentage of error in MNLR approach is decrease when the crest head is increase for both rectangular and triangular notch weirs. According to the predicate equations, the Freud number is less than 1, that means the flow over crest is sub-critical in minimum and maximum crest head for both rectangular and V-notch weirs. REFERENCES [1] Alfatlawi T. J. and Alshaikhli H. I., Prediction the Coefficient of Discharge for Stepped Morning Glory Spillway Using ANN and MNLR Approaches, International Journal of Civil and Environmental Engineering, 2015, ISSN: pp. 1701-8285, Vol.37, Issue.2. [2] Dargahi, B., Experimental Study and 3D Numerical Simulations for a Free- Overflow Spillway, Journal of Hydraulic Engineering, 2006, ASCE, Vol. 132, pp. 899-907. [3] Hirt, C.W. and Nichols, B.D., Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries, Journal of Computational Physics, 1981, Vol. 39, pp. 201-225. [4] Kadhim Naief Kadhim and ahmed A.( The Geotechnical Maps for bearing capacity by using GIS and quality of groundwater for AL_Imam District(Babil-IRAQ).IJCIET, vol.6, issue 10, Oct. 2015, pp 176-184. [5] Teklemariam, E., Korbaylo, B, Groeneveld, J., Sydor, K., Fuchs, D., Optimization of Hydraulic Design Using Computational Fluid Dynamics, Presented at Waterpower, 2001, XII, 9-11 July 2001, Salt Lake City, Utah. [6] Rajab, H. and Elgizawy, A. Design of Spill Tube with Features for Controlling Air Bubble Generated for Aircraft Application s, ASME Early Career Technical Conference, ASME ECTC November 2-3, 2012, Atlanta, Georgia USA. [7] Chanel, P.G., An Evaluation of Computational Fluid Dynamics for Spillway Modeling, M.Sc. Thesis, University of Manitoba, Winnipeg, 2008, Manitoba, Canada. [8] Flow since, FLOW 3D version 10.0.1 user manual, 2010. [9] Armfield Limited, Instruction Manual F1-13, Ringwood, Hampshire. BH24 1DY England, 2001. [10] Fuller, J., Flow over Weirs, Fluid Mechanics Lab, 2010. [11] Chadwick, A. J. and Morfett, J. C., Hydraulics in Civil and Environmental Engineering, Fourth Edition, Volume 1, Jul 9, Technology & Engineering, 1998, pp. 342. [12] White, F. M., Fluid Mechanics, Fourth Edition, University of Rhode, Island, 1999, pp. 278. [13] Peddi Dilleswara Rao and B. Nageswara Rao. CFD Simulations and Validation Through Test Data of a Double Pipe Counter Flow Heat Exchanger. International Journal of Mechanical Engineering and Technology, 8(5), 2017, pp. 818 831 [14] Abhishek Kr. Singh and Durg Vijay Rai, The Variation In Physical Properties Affects The Vertical Compressive Strength of The Rudraksha-Bead (Elaeocarpus Ganitrus Roxb). International Journal of Mechanical Engineering and Technology, 7(3), 2016, pp. 276 284. http://www.iaeme.com/ijciet/index.asp 79 editor@iaeme.com