ABSTRACT:

The multi-hole orifice plate is one of the effective devices for measuring flow rate accurately. In this study an experimental and numerical investigation of the flow characteristics behavior caused by a water flow through a multi-hole orifice configuration is reported. A circular centered single hole orifice and a multi-hole orifices are used for the test. Orifices of interest for present study have an area ratio of 0.36, the equivalent diameter ratio of 0.6 and number holes 9, 16 and 25. Discharge coefficients for flow through multi-hole orifices are evaluated. Parameters investigated were hole numbers, orifice pressure drop and Reynolds number. In the present work, k-? turbulence model has been used to predict velocity fields, pressure loss and discharge coefficient around this device. Advantages gained by using multiple holes in an orifice plate instead of single hole are discussed. It is shown that number of holes, hole diameter and aspect ratio influences the discharge coefficients. Tests were conducted under laboratory conditions. The experimental results were compared with numerical modeling and appropriate conclusions are discussed.

Key Words- Multi-hole orifice, Equivalent diameter ratio, Discharge coefficient, Reynold’s Number

1. Introduction

Flow measurement is one of the most complex and demanding tasks in industry. Even today there does not exist a universal measuring instrument for all applications. Orifice plates are mainly used as a device of flow measurement for fluid delivery systems is based on the measurement of the pressure difference created when forcing the fluid to flow through a restriction in the pipe. The multi-hole orifice plates or perforated plates are assumed to be composed of a number of individual orifices acting independently and parallel will have flow characteristics different compared to the flow characteristics of a single hole orifice plate having same flow area 1. This is basically because of the flow restriction due to the small flow area of each hole.

Tianyi Zhao et al.2 investigated the key factors affecting multi-hole orifices throttle or flow control characteristics. Shanfang Huang et al. 3 presented the discharge coefficient of a perforated orifice with t = 3 and t/D is 0.1, 0.21, 0.31, Stefano Malavasi et al 4 has conducted two experimental campaigns to investigate the dissipation characteristics of multi-hole orifices under cavitation-free conditions. B. Laribi and M. Mehdi 5 presents a numerical experimentation on the perforated plate flow conditioner with a 90° double bend and a valve 50% closed. The simulation is done with air as fluid in 100 mm pipe diameter with Reynolds numbers 104, 105 and 106. D. Maynes G. J. Holt J. Blotter 6 experimentally investigated the loss coefficient and cavitation caused by water flow through perforated plates. Plates with beta ratio = 0.11 to 0.6, and t/d = 0.25 to 0.33 were considered. Akshay Dandwate et al. 7 compared orifice plates with various geometry on the basis of their coefficient of discharge with the help using simulations done with k-? and SST model on CFX as a solver.

A literature review shows that a great deal of work has been done on the pressure drop characteristics of orifice plates in pipe flows. The performance characteristics of the multi hole orifice meter are limited in the open literature. whatever little information available shows that for an orifice plate whose axis is coincident with that of duct or for a multi-hole orifice plate with regularly spaced holes, the factors influencing flow characteristics of the multi hole plates are area ratio of the plate (m), the number of holes and its distribution on the plate. Past research has also shown that the value of Cd is primarily considered to be a function of aspect ratio (t/d), equivalent diameter ratio (? = d/D) and nature of flow defined using the pipe/hole Reynolds number (Re).

The paper therefore addresses the problem of relating flow rate to pressure drop and the discharge coefficient prediction by experiments and numerical simulations through single orifice over multi hole orifice geometries and operating conditions. The main objective is to validate the numerical simulations with experimental data to predict pressure loss, velocity fields and discharge coefficient Cd. The present paper is subdivided into three sections. The experimental setup is first presented. Numerical models are then detailed. Comparison of experimental results with numerical simulations is done in the last section

2. Experimental arrangement and measurements:

To measure pressure drop across multi hole orifice plates at known flow rates experiments were conducted. Experimental test section consists of 30 D upstream and 50 D downstream side of the orifice. At a location 50mm upstream and 25.4mm downstream from the orifice flange pressure taps were used to measure pressure differences across the orifice using water –mercury manometer. By means of the collecting tank the discharges were measured volumetrically. Systematic procedure was used in making the orifice plates and experiments were conducted at room temperature. Twenty square edged orifice plates were studied during this work. All holes were drilled on a vertical drill press with plates backed by wooden blocks to prevent excess burring. After drilling, the plates were drawn across No. 0 emery paper on a flat surface to knock off the burrs.

Data for each orifice plate were collected by strict set of test procedures to ensure the collection of repeatable and accurate data. Air was removed from the system by the help of knob providing for the purpose whenever the orifice plate was changed. Once the air was removed the system was run for approximately 15 minutes in the maintenance configuration. About seven to eight data points were taken for each orifice plate, corresponding to a pressure drop across the orifice meter using mercury manometer. To check the consistency of the data five to six runs were made independently on the same plate to get a good sample of the data. The coefficient of discharge Cd was obtained for all the orifice plates.

The physical data and other dimensions for all the orifices used for the computations and experiments are summarized in Table 1.

Table 1: The relevant parameters in these experiments/Computations

Number of holes

Diameter of the hole mm

Aspect Ratio t/d

Equivalent Diameter Ratio d/D

1.5 mm thickness of the Orifice plate

1

30

0.05

0.6

9

10

0.15

0.6

16

7.5

0.2

0.6

25

6

0.25

0.6

Overall Range: 0.05 < t/d < 0.25 and d/D = 0.6 3. Numerical approach: 3.1 Computational model: The Numerical investigation using the CFD code "Fluent" was implemented in the present work for multi-hole orifice plate. The main objective is to minimize the pressure loss and maximize the discharge coefficient of the multi-hole orifice plate. The computational domain was extended 5 D upstream and 10D downstream of the plate. The distance 5D upstream the plate was used to ensure a fully developed flow at inlet during the simulation. Numerical simulation was performed by solving the standard k-? model with enhanced wall treatment was used to model turbulence and simulate the near wall flow. Discretization was performed using the finite volume technique. The applied discretization schemes are second order scheme for pressure, SIMPLE scheme for pressure–velocity coupling and second order upwind scheme for momentum, kinetic energy (k) and turbulence dissipation rate (?). Convergence was considered to be achieved when the residuals of mass, momentum and turbulence are less than 1x10-6. Figure.1 Schematic layout of the computational domain 3.2 Governing equations: In the modeling, mass, momentum, energy conservation equations (if necessary) must be satisfied. The governing equations for present study are: Continuity :?.( ?V) =0. momentum: ?. (?uV) = - (?p/?x) + (??xx/?x) +(??yx/?y) + (??zx/?z) +? g ?.(?vV) = - (?p/?y) + (??xy/?x) +(??zy/?y) + (??zx/?z) +? g ?. (?wV) = - (?p/?z) + (??xz/?x) + (??yz/?y) + (??zz/?z) +? g 3.3 Boundary conditions: The present three-dimensional flow field is solved by considering water as incompressible fluid. There are three boundaries: inlet, outlet and the wall. The boundary conditions are summarized in Table 2. Table 2: Boundary conditions Sl.No Quantities Condition/value 1 Working fluid Water 2 Inlet velocity 0.5 to 1.5 m/sec 3 outlet Zero Pascals 4 Wall No slip 3.4 Grid independence study: A hexahedral block structured mesh is employed for the entire computational domain using mesh application from ANSYS Workbench. In order to test the adequacy of the discretization, the number of elements is varied in the range 4.5×105 to 1.6×106. The computational meshes employed for simulation with full domain and section plane detail of discretized fluid domain for nine orifice holes model with 3D hexahedral mesh is presented in Fig.2 and Fig.3. The mesh principal parameters are presented in Table 3. Table 3: The mesh principal parameters Element size (mm) Number of Elements Number of nodes Skewness Aspect ratio Orthogonal quality 1 1.6x106 166526 0.098 1.182 0.989 1.2 9.2x105 964627 0.108 1.207 0.989 1.3 7.5x105 792270 0.112 1.220 0.988 1.4 5.7x105 608990 0.117 1.215 0.987 1.5 4.5x105 484219 0.136 1.237 0.984 Figure 2 Discretized fluid domain for nine Figure 3. Section plane detail of discretized fluid orifice holes model with 3D hexahedral mesh domain for nine orifice holes model with 3D hexahedral mesh .3.5. Validation: The validation of the CFD analysis has been done by comparing the CFD results with the results Obtained by experiments for single hole orifice plate with mass flow rate of 2.091x10-3 m3/sec in terms of discharge coefficient and pressure drop. The validation results are presented in table 4. Table 4: Validation results Element size (mm) Number of Elements Pressure drop ?P (Pa) Coefficient of discharge C d Relative error % Exp Num Exp Num ?P C d 1 1.6x106 8528.81 9002.2 0.6682 0.6504 5.25 2.66 1.2 9.2x105 8862.85 0.6556 3.76 1.88 1.3 7.5x105 8602.7 0.6655 0.858 0.40 1.4 5.7x105 8829.35 0.6569 3.4 1.69 1.5 4.5x105 9181.2 0.6441 7.12 3.61 It is observed that for all the meshes studied the agreement between computed and experimental values C d and ?P is reasonably good. On the basis of this study a mesh size of 7.5×105 and element size of 1.3mm with finer mesh is adequate for ensuring accurate computation. 4. Results and discussion: a. Pressure drop with volume flow rate b. Variation of coefficient of discharge with Re Figure.4. Comparison between numerical and experimental results of (Fig. a) pressure drop with volume flow rate and (Fig. b) coefficient of discharge with Reynold's number for single and multi hole orifice c. Pressure recovery (For Q =2.091e-3 m3/s) d. Variation of Velocity Profiles Figure.5. Comparison of variation of pressure (Fig. c) and velocity (Fig. d) with number of holes for orifice with t=1.5mm, ?=0.6 Pressure drops in single and multi-hole orifice meter at various flow rates were calculated by experiments and simulation. Figure 4 (a) shows the graph of volumetric flow rate vs. pressure drop. It can be seen that the pressure drop increases with increase in flow rate, also as the number of hole increases pressure drop decreases. Figure 4 (b) shows coefficient discharge vs. Renold's number. As observed from figure 4 (b) that higher coefficient of discharge is obtained for multi-hole orifice plate over a wide range of Reynold's number. It can be seen that the Cd found out from the simulation is greater than that found from experimentation. This is because losses are not considered in CFD. The Cd obtained through simulations is 1% - 4% greater than experimental Cd. Static pressure recovery and axial velocity profiles are given in figure 5 (c) and (d) respectively. figure 5(c) shows that, energy has to be conserved at all the points in the domain, accordingly the pressure decreases when the flow approaches orifice meter, reaching the minimum at vena-contracta and starts recovering as the flow moves further downstream. The recovery of flow in multi-hole orifice flow meter is faster compared to the single-hole orifice flow meter. This leads to a better turbulent mixing resulting in a faster recovery of flow for the multi-hole orifice as compared to the single-hole orifice. As seen in figure 4(d) axial velocity increases as the flow approaches the throat of orifice meter. The further it travels downstream of orifice meter and reaches its maxima at 276.5 mm. Beyond this point the velocity decreases. This implies that discharge coefficient of single-hole orifice meter can be improved by distributing the flow area into multiple number of holes 5. Conclusions: In this analysis, multi-hole orifices have been experimentally and numerically studied in terms of discharge coefficient and pressure drop and compared with a single hole orifice plate which is generally used in orifice meters to measure flow. The following points are obtained as the results of this study. Multi hole orifice plate has better performance characteristics than a single hole orifice plate. Through simulation and experimentation, the 16 and 25 holes orifice plate are found to be having the highest value of the coefficient of discharge i.e. 0.83 with an actual discharge of 2.09x10-3 m3/s. Compared with single hole orifice plate, the coefficient of discharge of 16 and 25 holes orifice plate is 25 % greater. The Cd found out from CFD is greater than that found from experimentation because of the losses occurring in the physical model due to friction inside the pipe, leakage, impurities present in the fluid, etc. which are not considered in CFD. .