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Effects of varying orifice diameter and Reynolds number on discharge coefficient and wall pressure
Flow Measurement and Instrumentation 65 (2019) 219–226
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Flow Measurement and Instrumentation journal homepage: www.elsevier.com/locate/flowmeasinst
Effects of varying orifice diameter and Reynolds number on discharge coefficient and wall pressure
T
⁎
Hareth Maher Abd, Omar Rafae Alomar , Ibrahim Atiya Mohamed Northern Technical University, Engineering Technical College of Mosul, Cultural Group Street, Mosul, Iraq
A R T I C LE I N FO
A B S T R A C T
Keywords: Orifice meter Coefficient of discharge Beta ratio Static wall pressure Laminar and turbulent flow Recirculation flow
In this paper, an experimental study has been performed to investigate the performance of varying diameter of orifice that made from acrylic plastic on the flow characteristics. A colour water has been used as a working fluid to flow through a PVC pipe system. The orifice has a sharp-edged with 30° angle and the pipe system has thirty tapping points across the orifice for the pressure measurement. The experiments have been carried out for different beta ratio and Reynolds number. The results clearly demonstrated that the beta ratio has a positive effects on the discharge coefficient particularly at the laminar flow regime whereas it has inversely effects on pressure head losses. Therefore, geometric parameters are required to be properly designed in order to achieve the desired objective. It has been also found that the orifice discharge coefficient reduces with increasing in Reynolds number for all values of beta ratio especially at the turbulent flow regime and hence adequate must be taken while designing such orifice. The results obtained in the present study have been compared with that predicted from an empirical correlations and they show a good agreement between them. Finally, a statistical analysis has been carried out in order to determine a fitting correlation for the discharge coefficient based on the present experimental data.
1. Introduction The orifice meter device is one of the ancient differential pressure flow meters that has widely used due to relatively inexpensive, ease of installation and maintenance as compared to another flow meter available [1]. The orifice meter performance depends on various parameters such as contraction ratio, amount of discharge, properties of fluid and differential pressure for installation location upstream and downstream of the orifice meter [2]. An extensive studies related to this topic have been conducted in the last five decades in order to evaluate the effectiveness of orifice meter and installation requirement of the orifice meter [3–10]. Eiamsa-ard et al. [3] numerically studied the flow field characteristics through circular orifice plate using various turbulence modelling with different orifice beta ratio (β) and Reynolds number. In their results, it has been found that the static wall pressure profiles and centreline fluid velocity slightly better as compared with other schemes. Later, Singh et al. [4] numerically performed the effect of plate thickness on the discharge coefficient (Cd) under the nonstandard condition using four different beta ratio (β) and Reynolds number (Re). The results show that the Cd has proportional effects with respect to the plate thickness for a higher β and has inversely effects with respect to the plate thickness for a lower value of β. ⁎
Jianhuaa et al. [5] theoretically analysed the effective parameters such as head loss coefficient, contraction ratio and the ratio of orifice plate diameter and the discharge tunnel diameter, the ratio of the orifice plate thickness to the tunnel diameter, the dimensionless recirculation length region and the Reynolds number on the energy dissipation ratio. The relationships have been obtained by numerical simulations and physical model experiments. In their results, it has been observed that the head loss coefficient mainly dominated by the contraction ratio and the ratio of the orifice plate thickness by the effects of the recirculation length. Ntamba [6] conducted an experimental study of the flow in orifice plates by measuring the pressure loss coefficients and discharge coefficients using both Newtonian fluids and non-Newtonian fluids in both laminar and turbulent flow regimes. The results show that the discharge coefficient is increased with increasing in Re in laminar flow regime. On the other hand, this coefficient remains constant in turbulent flow regime. In their results, it has been also obtained a correlation equation which can predict the pressure loss coefficient from laminar to turbulent flow regime. Later, Shah et al. [7] numerically simulated the orifice flow pattern, pressure recovery, pressure profiles and velocity profiles using Open FOAM-1.6 solver. In their results, it has been obtained a relationship between maximum pressure drop through an orifice and flow rate for
Corresponding author. E-mail address: [email protected] (O.R. Alomar).
https://doi.org/10.1016/j.flowmeasinst.2019.01.004 Received 14 September 2018; Received in revised form 22 November 2018; Accepted 4 January 2019 Available online 08 January 2019 0955-5986/ © 2019 Elsevier Ltd. All rights reserved.
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Nomenclature
A a ac CC Cd Cv D d g h hf L
Recirculation length = x / D Pressure, Pa Fluid discharge, m3/sec Actual fluid discharge, m3/sec Reynolds number = ρvD / μ Fluid velocity, m/sec Distance from orifice plate, m Gradient Difference Beta ratio, which represents the ratio between orifice diameter and pipe diameter = d/ D μ Dynamic viscosity, Kg/m.s 1/ 1 − β 4 Called the velocity of approach factor
Lr p Q Qact Re v x Δ β
Pipe area, m2 Orifice area, m2 contraction area, m2 Contraction coefficient = ac / a Discharge coefficient Velocity coefficient Pipe diameter, m Orifice meter diameter, m Acceleration of gravity, m/s2 Manometer head, m Head loss, m Pipe length, m
stresses, the pressure loss and the discharge coefficient at a Reynolds number of 25,000. The LES results has been compared with the available experimental data and ISO 5167-2. The LES results indicated that pressure loss and discharge coefficients are shown to be in very good agreement with the predictions of ISO 5167-2. A thoroughly literature review reveals that considerable attention have been given only to the discharge coefficient and the energy dissipation ratio with a wide range of orifice diameter. On the other hand, the wall pressure profiles have been investigated only with numerical simulations. Therefore, in the present study, the effect of beta ratio (β) for a sharp-edged orifice with 30° angle on the flow characteristics and static wall pressure across the orifice has been experimentally investigated. In addition, the discharge coefficient, the pressure head loss and the minimum pressure location near the orifice wall for different Reynolds number (Re) have been evaluated. Moreover, the results obtained from the present study have been compared with that predicted by using an empirical correlation that presented by Swamee [17].
Re between 4489 and 9012. Ai and Wang [8] theoretically analysed the effect of orifice contraction ratio and relative orifice plate thickness to the flood-discharging tunnel diameter for various Re. Their relationships have been obtained using physical model experiments, where the lower wall pressure coefficient is mainly dominated by contraction ratio. Parshad and Kumar [9] studied the effect of varying orifice diameter on the discharge coefficient. The results show that Cd is increased with increasing in orifice diameter. Wanzheng [10] numerically simulated the energy loss coefficient of sharply edged orifice plate for different Re and β. In their results, it has been found that the energy loss coefficient and downstream region length have mainly affected by the contraction ratio of orifice plate. The energy loss coefficient and downstream region length have been increased with increasing in the orifice plate thickness. Hernandez-Alvarado et al. [11] experimentally studied the void fraction and bubble size in the down flow bubble column rector. The axial and radial distributions of void fraction has been determined by using Gamma-ray densitometry, whereas the bubble size has been measured by using a high speed camera along with borescope. The results show that the new bubble generation technique provides high interfacial concentration and high overall void fraction in comparison with alter bubble column reactor design. Later, Mutharasu et al. [12] performed an experimental and numerical study on multiphase flow conditions encountered in novel down-flow bubble column. For experiments, a novel mechanism of gas-liquid injection has been employed in order to generate a high concentration of micro bubbles. For numerical simulation, on the other hand, a 3D Euler-Euler CFD model has been employed to investigate the flow behaviour inside the column under different operating conditions. In their study, the experimental and numerical results indicate that the novel mechanism of gas-liquid injection can be produced a high concentration of microbubbles without liquid recirculation in a column of larger cross-section area. Hernandez-Alvarado et al. [13] also performed an experimental and numerical study on 2D particle image velocimetry to analyse the interaction of multiphase vertical liquid jets single-phase flow. The results show that a good agreement between the experiments and CFD simulations. Shan et al. [14] studied the effects of beta ratio on the flow field behind a thin circular square-edged orifice plate by adopting a particle image velocimetry (PIV) system. The results show that the local peak Reynolds stresses have been found to be independent of beat ratio in the shear-layer region close to the orifice plate. Shan [15] conducted an experimental study on the planar particle image velocimetry system to measure the flow field in the downstream of a circular square-edged orifice plate in the range of Reynolds number of 25,000–55,000. They assessed the reliability of the Reynolds stress model to perform orifice flows by comparing numerical results with experimental results. Benhamadouche [16] performed a numerical study on flow inside a squareedged orifice in a around pipe to predict the velocity, the Reynolds
2. Experimental setup and procedure 2.1. Experimental model In the present study, the experiments have been carried out on a test-rig model as shown in Fig. 1. Two calibrated Rotameters have been used in order to measure the actual volume flowrate through the loop system. A colour water has been used in the experiments, where the volume flow rate of water has been varied from 3 l/min to 30 l/min.
Fig. 1. Test-rig experimental model. 220
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convergence (Section 1) and the greatest contraction (section C) as shown in Fig. 6 [20,21]. By considering incompressible flow and neglecting the pipe friction, the discharge equation can be derived by applying both Bernoulli's and continuity equations between two sections. Therefore, the contraction (Cc) and velocity (Cv) coefficients have been used to compensate the jet area at section C by orifice area at point 2 in order to evaluate the actual volume flowrate (Qact) as follow [18]:
Water is circulated from the source tank in a continuous loop using two centrifugal pumps. The Rotameters have been set in a parallel line way and then combined together in order to increase the amount of flowrate as shown schematically in Fig. 2. An on/off valve has been situated for both ends of tested pipe in order to restrict the amount of water flowing through the selected orifice diameter. The orifice has been inserted in PVC pipe with internal diameter equal to 2.4 cm. On the other hand, the upstream and downstream pipe lengths have been designed to be 20D and 30D, respectively, in order to avoid the fluid recirculation at the inlet and the outlet tested section that resulting due to the valves. The PVC pipe has been provided with thirty tapping points, where nine tapping points have been set in the upstream region and the remaining points have been set in the downstream region. The distance between each tapping points has been selected to be 12 mm in order to demonstrate the fluid recirculation around the orifice, where the jet has a maximum effects at 2D and 8D in the upstream and downstream regions, respectively [18]. Two tapping points have been set near the orifice wall (4 mm) from both sides to study the pressure drop at a lower distance from the orifice wall. The tapping points have been coupled with a long piezometers. The length of piezometers are equal 75 cm. Then piezometers have been connected together from the upper in order to measure the differential static pressure between each different points along the pipeline as shown in Fig. 2. At the outlet of the tested pipe, the water has been transferred to a scale tank, where it could be used for Rotameters calibration. Due to a large number of piezometers and in order to avoid the oscillation during the reading data, a Canon EOS M 18.0MP digital camera 22 mm f2 has been employed to better reading the static pressure as shown in Fig. 3. The optical zoom of the camera is 3.1x with auto focus and the sensor resolution is 18MP and hence, the maximum video resolution approximately equal to 1920 × 1080. The range of light sensitivity are varied between 100 and 12,800 and 1920 × 1080, respectively. The maximum shutter speed is 4000 s and the focal length range between 18 mm and 55 mm. Regarding to the orifice geometry, a circular orifice with five different inside diameters (d = 1.2, 1.4, 1.6, 1.8 and 2 cm) has been chosen. The beta ratio (β = d/D) has been selected to be (0.5, 0.6, 0.65, 0.75 and 0.85). The orifice has been made from the acrylic plastic with 2.5 mm thickness. Medeiros et al. [19] pointed out that the angle of bevel can be varied in the range between 30° and 45°. Therefore, the angle of bevel has been selected to be 30° towards the downstream direction in the present study as shown in Fig. 4.
2g∆h 1−Cc2 × (d/ D) 4
Q act = Cc aC v ×
(1)
Eq. (1) can be rearranged by using a single coefficient (Cd) instead of Cc and Cv that obtained experimentally as follow:
Q act = aCd
1 1−β4
2g∆h (2)
where a is the orifice area, h is the manometer head, and Cd represents the discharge coefficient and is defined as follow:
Cd =
Q act 1−β4 a 2g∆h
(3)
2.3. Uncertainties analysis The accuracies of the measured parameters and the maximum uncertainties in the evaluated of the pressure head (h) have been obtained by multiple tests of piezometer reading data at the same test conditions. This error has been limited to (Δh = 6.48%). On the other hand, the Rotameters uncertainties have been found by using the scale tank in the device and stop watch. By using the estimation method of Coleman and Steele [22], the maximum uncertainties of the investigated non-dimensional parameters are ΔCd = 4.98% and ΔRe = 4.47%. The uncertainties equations of Cd and Re are given in Eqs. (4) and (5), respectively: 1
2
∆Cd ∆Qact ⎞ ∆h ⎞2⎫ 2 = ⎧⎛ +⎛ ⎨ ⎝ Qact ⎠ Cd ⎝ h ⎠⎬ ⎩ ⎭ ⎜
⎟
2
2
(4) 2
1
∆ρ ⎞ ∆μ ⎞ ⎫ 2 ∆Re ⎧ ∆Qact ⎞ = ⎛ ⎟ ⎟ + ⎜⎛ + ⎜⎛ ⎨ Re Q ⎝ ρ ⎠ ⎝ μ ⎠⎬ ⎩ ⎝ act ⎠ ⎭ ⎜
2.2. Mathematical analysis In particular, the orifice meter consists of two components. The major component includes a circular thin plate containing a varying edges and diameters inserted in a section of straight running pipe which causes a change in the energy due to the losses in the kinetic energy. The minor component, on the other hand, includes a differential gauge (differential pressure) that used to measure the change in the energy or indicates the fluid velocity. In order to have reliable and accurate measurements while using different types of orifice, several basic factors shall be taken into consideration such as differential piezometer pressure locations since the pressure has different values along the wall of the pipe at any given value of flowrate. In the present study, the orifice diameter ratio (d/D) shall be referred as beta ratio (β). For a smaller diameter ratio, the head loss and the discharge coefficient errors (accidental errors) would be too large due to the edge sharpness of the orifice plate, particularly for higher value of Re [9]. The plate thickness and edges can be designed in different shapes such as square, sharp and quadrant-edged, as shown in Fig. 5, depending on the type of flow, the discharge flow and the orifice coefficient [18]. The discharge equation can be achieved by computation the crosssectional area of pipeline, orifice plate bore and the pressure difference. It is measured between the two sections at the beginning of
⎟
Fig. 2. Schematic representation of the test setup. 221
(5)
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(a) Re=6200
(b) Re=12400
(C) Re=6200 Fig. 3. Piezometers pressure in pipe-wall for β = 0.65 and various Re.
Fig. 4. Orifice meter diameter.
Fig. 6. Schematic representation of orifice device.
2.4. Experimental procedure
Fig. 5. Types of orifice edges.
As far as the performance of orifice meter is concerned, a certain bore diameter (d) has been firstly fixed in the test-rig model. An external pressure gradient (pumps) drives the water at the inlet to flow 222
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show the effects of beta ratio (β) on the discharge coefficient and the wall pressure profiles across the orifice. The pressure head loss and the minimum pressure location near the orifice wall for different Re have been evaluated. Moreover, the results obtained from this study have been compared with that predicted by using an empirical correlation. 3.1. Comparison of experiments and empirical correlation In order to demonstrate the validation of this study, the results obtained from the current study has been compared with that predicted by using an empirical correlation. The comparison is presented in terms of Cd as a function of Re. The correlation equation of Swamee [17] has been used for comparison when β = 0.65. Swamee correlation, as presented in Eq. (6), has been obtained by using a method of curve fitting to practical curves of Streeter and Wylie that explicit for a wide range of Re from 4 × 103 to 106 and β from 0.05 to 0.7. Fig. 7 shows the variations of Cd as a function of Re for β = 0.65. Comparison of Cd reveals that the present experimental data are nearly similar to the ones with empirical equation of Swamee. The average absolute error in the predicted values of Cd has been found to be 8.5%. The reason behind the difference between the present and Swamee results can be attributed to that correlation equation presented by Swamee [17] has been obtained for a wide range of Re and β as compared to the present study.
Fig. 7. Comparison of Cd between experiments and correlation of Swamee model [17] for β = 0.65.
Cd = { [0.675 + 0.6β 2 − 0.02lnRe] 10 + [0.5 + 0.43β 2] 10 } 0.1
(6)
3.2. Discharge coefficient (Cd) In order to demonstrate the performance of orifice meter, the variations of Cd as function of Re has been presented in Fig. 8 for different values of β. It can be noted here that Cd has been calculated based on Eq. (3), where Δh has been measured according to the maximum pressure difference that occurs between the tapping points [20]. It is clear from Fig. 8 that with the increase in Re until (Re≤9000) for all values of β, Cd is increased, and reaches its largest value, and then slightly decreases with further increasing in Re in the fully turbulent flow regime for Re > 9000. It has been also reported that the flow would be moderately turbulent flow when Re≈ 10,000 [21]. For higher Re, Cd is nearly constant. This behaviour can be attributed to an orifice plate's effect on the velocity profile inside the pipe. Since the highest velocities are located in the centre of the pipe, the low value of Re (laminar flow) have large Cd due to the orifice plate has no effect on the velocity that associated with the flow passes the flow meter as compared with large value of Re. The velocity profile strongly affected with further increasing in Re that has inversely effect on Cd until it becomes constant [23]. Furthermore, it can be observed from the figure that Cd increases with increasing in β until (Re≤ 9000) and then starts gradually decreases with further increasing in Re. Such behaviour can be attributed to the effects of flow types (i.e., laminar and turbulent flow) and this is consistent with previous studies (e.g., Colter [23]). It has been also concluded from the most previous studies that the Cd has a proportional effects with orifice diameter when β ≥ 0.5 and inversely effects when β < 0.5. The maximum value of Cd has been observed at Re = 9300 for all different β. In addition, the maximum value of Cd has been found for β = 0.85. A small values of Cd is obtained for a lower value of β owing to the smaller contraction area near the orifice plate. In the present study, the obtained results have been correlated to produce a useful tool for calculation of Cd. This coefficient has been correlated with respect to Re and β. The correlation equation has been obtained for the ranges of Re (3100–18,600) and β (0.5, 0.6, 0.65, 0.75 and 0.85). The evaluation of the correlation constants has been carried out on the basis of the minimum sum of the square error (SSE), and the maximum correlation coefficient (R2), which is equal to proportion of variance and accounted. The statistical analysis has been carried out by using STATISTCA software, version 5.5, in which a non-linear estimation for the regression function using Quasi-Newton method. The error
Fig. 8. Variations of Cd with respect Re for various β.
Fig. 9. Variations of hf with respect Re for various β.
through the pipe. The amount of flow has been adjusted by an on/off valve that situated at both ends of the tested pipe. The amount of water flow (actual volume flow rate) has been recorded by Rotameters device. The piezometers head within reading range has been adjusted by the valve above of them. The difference in reading head (Δh) for thirty piezometers have been recorded by a digital camera as shown in Fig. 3. This process has been repeated with different water flowrate for a certain value of β where the Qact and Δh have been recorded. 3. Results and discussion As mentioned before, the main purpose of the present study is to 223
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Fig. 10. Variations of static wall pressure head as a function of recirculation length for various β and Re.
3.3. Orifice head loss
of this method represents the difference between the observed and predicted values. The correlation equation has been obtained as follow:
Cd = 0.49364 Re 0.04617 β 0.1586
Fig. 9 shows the variations of the orifice head loss (hf) in cm of H2O as function of Re for various β. The hf occurs due to change in the pressure head between the section at beginning of contraction in the orifice plate and the section behind the orifice plate when the normal uniform flow is occurred. It can be observed from the figure that hf increases with increasing in Re. It is also clear from the figure that hf sharply decreases with increasing in β due to decrease in recirculation flow in the downstream region resulting from the shear stresses and friction.
(7)
where SEE and R are equal to 0.01% and 84%, respectively. The standard error for Eq. (7) has been found to be within ± 2% with the percentage of observations equal to 83%. It can be noted here that the format of Eq. (7) has been chosen to be simple and more general as well as to obtain a higher value of correlation coefficient (R). The Cd in Eq. (7) is a function of Re and β and hence, this expression is valid only between the ranges of Re and β that used in the present study.
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obtained by previous studies in [8,11–13].
3.4. Static wall pressure
As a final remark, different researchers [14–16] addressed the pressure gradients and velocity inside orifice meter experimentally and numerically. Therefore, in order to improve the present experimental work, the pressure gradient should be measured with differential pressure transducers with a more populated tap pressure points near the orifice plate as the practice frequently used in aerodynamic test. This issue shall be taken up later in the future.
Fig. 10 shows the variations of the static wall pressure head (in cm of H2O) as a function of recirculation length (Lr = x/D) across the orifice plate for various β and Re. The static wall pressure has been evaluated by subtracting the head pressure at each tapping point from both head pressure at the outlet and head loss (hf) caused by orifice due to both contraction and sudden expansions [7,8]. For a fixed value of Re, it is evident from the figure that the static wall pressure in the downstream region decreases with decreasing in β. This can be attributed to a narrow area of the orifice that leads to increase the velocity in the downstream region. According to the Bernoulli's equation, the static wall pressure has inversely effects with respect to the square velocity of the fluid [20]. It can be also observed from the figure that the static wall pressure decreases by increasing in Re due to increase the velocity in the downstream region. When β is decreased from 0.85 to 0.5, the pressure drop is increased from 0.1 to 1.1 cm of H2O for Re = 3100 and from 3.7 to 31.6 cm of H2O for Re = 18,600. It is also clear from Fig. 10 that the distance of fluid recirculation in the downstream region is slightly extended with an increase in Re and decrease in β. This can be explained by increasing the shear stress at the pipe boundary layer due to increase the fluid velocity. Therefore, the working fluid requires a further distance in order to return in a uniform distribution flow behaviour. On the other hand, the fluid recirculation in the upstream region has only a minor influence for all values of Re and β and hence it remains nearly constant around (x/D = 1.5). Most importantly, the location of greatest fluid contraction which occurs at point (c) shifts towards the downstream direction with either increasing in Re or decreasing in β (i.e., from (x/D = 0.2) for β = 0.75 and 0.85 to (x/ D = 0.5) for β = 0.5, 0.6 and 0.65) due to increase in the inertia for the fluid resulting from the velocity increasing for a small value of β.
Acknowledgment The authors gratefully acknowledge the Northern Technical University, Engineering Technical College of Mosul,Iraq for their laboratory support for this work. Conflict of interest None Appendix A. Supporting information Supplementary data associated with this article can be found in the online version at doi:10.1016/j.flowmeasinst.2019.01.004. References [1] M.M. Tukiman, M.N.M. Ghazali, A. Sadikin, N.F. Nasir, N. Nordin, A. Sapit, M.A. Razali, CFD simulation of flow through an orifice plate, IOP Conf. Ser. Mater. Sci. Eng. 243 (2017) 012036. [2] P. Yang, Numerical Study of Cavitation within Orifice Flow (M.Sc. thesis of Mechanical Engineering), Texas A&M University, 2015. [3] S. Eiamsa-ard, A. Ridluan, P. Somravysin, P. Promvonge, Numerical investigation of turbulent flow through a circular orifice, J. Kmitl Sci. J. 8 (1) (2008) 43–50. [4] R.K. Singh, S.N. Singh, Seshadri, performance evaluation of orifice plate assemblies under non-standard conditions using CFD, Indian J. Eng. Mater. Sci. 17 (2010) 397–406. [5] W. Jianhuaa, A. Wanzhengb, Z. Qib, Head loss coefficient of orifice plate energy dissipator, J. Hydraul. Res. 48 (4) (2010) 526–530. [6] B.M. Ntamba, Non-Newtonian Pressure Loss and Discharge Coefficients for Short Square-Edged Orifice Plates (M.Sc. thesis of Mechanical Engineering), Cape Peninsula University of Technology, 2011. [7] M.S. Shah, J.B. Joshi, A.S. Kalsi, C.S.R. Prasad, D.S. Shukla, Analysis of flow through an orifice meter: CFD simulation, J. Chem. Eng. Sci. 71 (2011) 300–309. [8] W. Ai, J. Wang, Minimum wall pressure coefficient of orifice plate energy dissipater, Sci. Water Sci. Eng. 8 (1) (2015) 85–88. [9] H. Parshad, R. Kumar, Effect of varying diameter of orifice on coefficient of discharge, Int. J. Eng. Sci. Paradig. Res. (2015) 19–22. [10] A. Wanzheng, Energy dissipation characteristics of sharp-edged orifice plate, Adv. Mech. Eng. 7 (8) (2015) 1–6. [11] F. Hernandez-Alvarado, D.V. Kalaga, D.E. Turney, S. Banerjee, J.B. Joshi, M. Kawaji, Void fraction, bubble size and interfacial area measurements in cocurrent down-flow bubble column reactor with microbubble dispersion, Chem. Eng. Sci. 168 (31) (2017) 403–413. [12] L.C. Mutharasu, D.V. Kalaga, M. Sathe, D.E. Turney, D. Griffin, X. Li, M. Kawaji, K. Nandakumar, J.B. Joshi, Experimental study and CFD simulation of the multiphase flow conditions encountered in a novel Down-flow bubble Column, Chem. Eng. J. (2018), https://doi.org/10.1016/j.cej.2018.04.211. [13] F. Hernandez-Alvarado, R. Samaroo, D.V. Kalaga, T. Lee, S. Banerjee, M. Kawaji, Numerical and experimental analysis of single-phase jet interactions, in: Proceedings of the Conference on Fluids Engineering Division Summer Meeting FEDSM 2016, July 10–14, Washington DC, USA, ASME, 2016, pp. V01BT33A007V01BT33A007. [14] F. Shan, Z. Liu, W. Liu, Y. Tsuji, Effects of the orifice to pipe diameter ratio on orifice flows, Chem. Eng. Sci. 152 (2016) 497–506, https://doi.org/10.1016/j.ces. 2016.06.050. [15] F. Shan, A. Fujishiro, T. Tsuneyoshi, Y. Tsuji, Particle image velocimetry measurements of flow field behind a circular square-edged orifice in a round pipe, Exp. Fluids 54 (2013) 1553, https://doi.org/10.1007/s00348-013-1553-z. [16] S. Benhamadouche, M. Arenas, W.J. Malouf, Wall-resolved Large Eddy Simulation of a flow through a square-edged orifice in a round pipe at Re = 25,000, Nucl. Eng. Des. 312 (2017) 128–136, https://doi.org/10.1016/j.nucengdes.2016.09.010. [17] P.K. Swamee, Discharge equations for venturi meter and orifice meter, J. Hydraul. Res. 43 (4) (2005) 417–420. [18] H.S. Sondh, S.N. Singh, V. Seshadri, B.K. Gandhi, Design and development of variable area orifice meter, Flow. Meas. Instrum. 13 (2002) 69–73. [19] A.K.A. Medeiros, J.F. Lima, G.G. Medeiros, N.F.S. Junior, R.N.B. Felipe,
4. Conclusions and final remarks In the present study the performance of orifice meter diameter on the discharge coefficient and pressure head losses has been experimentally investigated. The orifice meter has made from the acrylic plastic and it has been bevelled in 30°. PVC pipe system has been used, where the pipe has a thirty tapping points across the orifice meter for the pressure measurement. The experiments have been carried out for various β and Re. The main conclusions of the present study are: 1. The results show that the Cd increases with increasing in β when Re≤ 9000 whereas this coefficient decreases with increasing in β when Re > 9000. 2. The results clearly demonstrated that the β has a positive effects on the Cd whereas it has inversely effects on pressure head losses. 3. The maximum fluid recirculation length in the downstream region occurs at x/D = 6. The results also show that the fluid recirculation length moves towards the downstream region with increasing in Re and reduces with increasing in β. 4. The comparison between the results obtained from the present study and with that predicted by using the empirical correlation show a good agreement, where the average absolute error is approximately 8.5%. 5. Based on the present experimental data, the best statistical analysis correlation has been obtained for Cd that cover a wide range of Re and β. This correlation provides a useful tools for calculation of Cd in the future. 6. The head loss (hf) increases with increasing in Re and decreases with increasing in β owing to decrease in the recirculation flow in the downstream region. 7. For a fixed value of Re, the static wall pressure in the downstream region decreases with decreasing in β. The static wall pressure decreases by increasing in Re owing to increase the velocity in the downstream region. This observations are quite similar with that 225
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02, 2002. [22] H.W. Coleman, W.G. Steele, Experimentation, Validation, and Uncertainty Analysis for Engineers, 3rd ed., John Wiley & Sons, Inc., Hoboken, New Jersey, 2009. [23] C.L. Hollingshead, Discharge Coefficient Performance of Venturi, Standard Concentric Orifice Plate, V-cone, and Wedge Flow Meters at Small Reynolds Numbers (M.Sc. thesis of Science in Civil and Environmental Engineering), Utah State University, 2011.
R.C.T.S. Felipe, Parameters for dimensional inspection of orifice plates and roughness of the straight stretches of the tubing, Int. J. Braz. Arch. Biol. Technol. 49 (2006) 1–8. [20] M.P. Boyce, Perrys Chemical Engineering Hand Book, 8th ed., McGraw-Hill Companies, 2008. [21] D.R. Durgaiah, Fluid Mechanics and Machinery, Published by K.K. Gupta for New Age International (P) Limited, 4835/24, Ansari Road, Daryaganj, New Delhi-110
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Flow Measurement and Instrumentation journal homepage: www.elsevier.com/locate/flowmeasinst
Effects of varying orifice diameter and Reynolds number on discharge coefficient and wall pressure
T
⁎
Hareth Maher Abd, Omar Rafae Alomar , Ibrahim Atiya Mohamed Northern Technical University, Engineering Technical College of Mosul, Cultural Group Street, Mosul, Iraq
A R T I C LE I N FO
A B S T R A C T
Keywords: Orifice meter Coefficient of discharge Beta ratio Static wall pressure Laminar and turbulent flow Recirculation flow
In this paper, an experimental study has been performed to investigate the performance of varying diameter of orifice that made from acrylic plastic on the flow characteristics. A colour water has been used as a working fluid to flow through a PVC pipe system. The orifice has a sharp-edged with 30° angle and the pipe system has thirty tapping points across the orifice for the pressure measurement. The experiments have been carried out for different beta ratio and Reynolds number. The results clearly demonstrated that the beta ratio has a positive effects on the discharge coefficient particularly at the laminar flow regime whereas it has inversely effects on pressure head losses. Therefore, geometric parameters are required to be properly designed in order to achieve the desired objective. It has been also found that the orifice discharge coefficient reduces with increasing in Reynolds number for all values of beta ratio especially at the turbulent flow regime and hence adequate must be taken while designing such orifice. The results obtained in the present study have been compared with that predicted from an empirical correlations and they show a good agreement between them. Finally, a statistical analysis has been carried out in order to determine a fitting correlation for the discharge coefficient based on the present experimental data.
1. Introduction The orifice meter device is one of the ancient differential pressure flow meters that has widely used due to relatively inexpensive, ease of installation and maintenance as compared to another flow meter available [1]. The orifice meter performance depends on various parameters such as contraction ratio, amount of discharge, properties of fluid and differential pressure for installation location upstream and downstream of the orifice meter [2]. An extensive studies related to this topic have been conducted in the last five decades in order to evaluate the effectiveness of orifice meter and installation requirement of the orifice meter [3–10]. Eiamsa-ard et al. [3] numerically studied the flow field characteristics through circular orifice plate using various turbulence modelling with different orifice beta ratio (β) and Reynolds number. In their results, it has been found that the static wall pressure profiles and centreline fluid velocity slightly better as compared with other schemes. Later, Singh et al. [4] numerically performed the effect of plate thickness on the discharge coefficient (Cd) under the nonstandard condition using four different beta ratio (β) and Reynolds number (Re). The results show that the Cd has proportional effects with respect to the plate thickness for a higher β and has inversely effects with respect to the plate thickness for a lower value of β. ⁎
Jianhuaa et al. [5] theoretically analysed the effective parameters such as head loss coefficient, contraction ratio and the ratio of orifice plate diameter and the discharge tunnel diameter, the ratio of the orifice plate thickness to the tunnel diameter, the dimensionless recirculation length region and the Reynolds number on the energy dissipation ratio. The relationships have been obtained by numerical simulations and physical model experiments. In their results, it has been observed that the head loss coefficient mainly dominated by the contraction ratio and the ratio of the orifice plate thickness by the effects of the recirculation length. Ntamba [6] conducted an experimental study of the flow in orifice plates by measuring the pressure loss coefficients and discharge coefficients using both Newtonian fluids and non-Newtonian fluids in both laminar and turbulent flow regimes. The results show that the discharge coefficient is increased with increasing in Re in laminar flow regime. On the other hand, this coefficient remains constant in turbulent flow regime. In their results, it has been also obtained a correlation equation which can predict the pressure loss coefficient from laminar to turbulent flow regime. Later, Shah et al. [7] numerically simulated the orifice flow pattern, pressure recovery, pressure profiles and velocity profiles using Open FOAM-1.6 solver. In their results, it has been obtained a relationship between maximum pressure drop through an orifice and flow rate for
Corresponding author. E-mail address: [email protected] (O.R. Alomar).
https://doi.org/10.1016/j.flowmeasinst.2019.01.004 Received 14 September 2018; Received in revised form 22 November 2018; Accepted 4 January 2019 Available online 08 January 2019 0955-5986/ © 2019 Elsevier Ltd. All rights reserved.
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Nomenclature
A a ac CC Cd Cv D d g h hf L
Recirculation length = x / D Pressure, Pa Fluid discharge, m3/sec Actual fluid discharge, m3/sec Reynolds number = ρvD / μ Fluid velocity, m/sec Distance from orifice plate, m Gradient Difference Beta ratio, which represents the ratio between orifice diameter and pipe diameter = d/ D μ Dynamic viscosity, Kg/m.s 1/ 1 − β 4 Called the velocity of approach factor
Lr p Q Qact Re v x Δ β
Pipe area, m2 Orifice area, m2 contraction area, m2 Contraction coefficient = ac / a Discharge coefficient Velocity coefficient Pipe diameter, m Orifice meter diameter, m Acceleration of gravity, m/s2 Manometer head, m Head loss, m Pipe length, m
stresses, the pressure loss and the discharge coefficient at a Reynolds number of 25,000. The LES results has been compared with the available experimental data and ISO 5167-2. The LES results indicated that pressure loss and discharge coefficients are shown to be in very good agreement with the predictions of ISO 5167-2. A thoroughly literature review reveals that considerable attention have been given only to the discharge coefficient and the energy dissipation ratio with a wide range of orifice diameter. On the other hand, the wall pressure profiles have been investigated only with numerical simulations. Therefore, in the present study, the effect of beta ratio (β) for a sharp-edged orifice with 30° angle on the flow characteristics and static wall pressure across the orifice has been experimentally investigated. In addition, the discharge coefficient, the pressure head loss and the minimum pressure location near the orifice wall for different Reynolds number (Re) have been evaluated. Moreover, the results obtained from the present study have been compared with that predicted by using an empirical correlation that presented by Swamee [17].
Re between 4489 and 9012. Ai and Wang [8] theoretically analysed the effect of orifice contraction ratio and relative orifice plate thickness to the flood-discharging tunnel diameter for various Re. Their relationships have been obtained using physical model experiments, where the lower wall pressure coefficient is mainly dominated by contraction ratio. Parshad and Kumar [9] studied the effect of varying orifice diameter on the discharge coefficient. The results show that Cd is increased with increasing in orifice diameter. Wanzheng [10] numerically simulated the energy loss coefficient of sharply edged orifice plate for different Re and β. In their results, it has been found that the energy loss coefficient and downstream region length have mainly affected by the contraction ratio of orifice plate. The energy loss coefficient and downstream region length have been increased with increasing in the orifice plate thickness. Hernandez-Alvarado et al. [11] experimentally studied the void fraction and bubble size in the down flow bubble column rector. The axial and radial distributions of void fraction has been determined by using Gamma-ray densitometry, whereas the bubble size has been measured by using a high speed camera along with borescope. The results show that the new bubble generation technique provides high interfacial concentration and high overall void fraction in comparison with alter bubble column reactor design. Later, Mutharasu et al. [12] performed an experimental and numerical study on multiphase flow conditions encountered in novel down-flow bubble column. For experiments, a novel mechanism of gas-liquid injection has been employed in order to generate a high concentration of micro bubbles. For numerical simulation, on the other hand, a 3D Euler-Euler CFD model has been employed to investigate the flow behaviour inside the column under different operating conditions. In their study, the experimental and numerical results indicate that the novel mechanism of gas-liquid injection can be produced a high concentration of microbubbles without liquid recirculation in a column of larger cross-section area. Hernandez-Alvarado et al. [13] also performed an experimental and numerical study on 2D particle image velocimetry to analyse the interaction of multiphase vertical liquid jets single-phase flow. The results show that a good agreement between the experiments and CFD simulations. Shan et al. [14] studied the effects of beta ratio on the flow field behind a thin circular square-edged orifice plate by adopting a particle image velocimetry (PIV) system. The results show that the local peak Reynolds stresses have been found to be independent of beat ratio in the shear-layer region close to the orifice plate. Shan [15] conducted an experimental study on the planar particle image velocimetry system to measure the flow field in the downstream of a circular square-edged orifice plate in the range of Reynolds number of 25,000–55,000. They assessed the reliability of the Reynolds stress model to perform orifice flows by comparing numerical results with experimental results. Benhamadouche [16] performed a numerical study on flow inside a squareedged orifice in a around pipe to predict the velocity, the Reynolds
2. Experimental setup and procedure 2.1. Experimental model In the present study, the experiments have been carried out on a test-rig model as shown in Fig. 1. Two calibrated Rotameters have been used in order to measure the actual volume flowrate through the loop system. A colour water has been used in the experiments, where the volume flow rate of water has been varied from 3 l/min to 30 l/min.
Fig. 1. Test-rig experimental model. 220
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convergence (Section 1) and the greatest contraction (section C) as shown in Fig. 6 [20,21]. By considering incompressible flow and neglecting the pipe friction, the discharge equation can be derived by applying both Bernoulli's and continuity equations between two sections. Therefore, the contraction (Cc) and velocity (Cv) coefficients have been used to compensate the jet area at section C by orifice area at point 2 in order to evaluate the actual volume flowrate (Qact) as follow [18]:
Water is circulated from the source tank in a continuous loop using two centrifugal pumps. The Rotameters have been set in a parallel line way and then combined together in order to increase the amount of flowrate as shown schematically in Fig. 2. An on/off valve has been situated for both ends of tested pipe in order to restrict the amount of water flowing through the selected orifice diameter. The orifice has been inserted in PVC pipe with internal diameter equal to 2.4 cm. On the other hand, the upstream and downstream pipe lengths have been designed to be 20D and 30D, respectively, in order to avoid the fluid recirculation at the inlet and the outlet tested section that resulting due to the valves. The PVC pipe has been provided with thirty tapping points, where nine tapping points have been set in the upstream region and the remaining points have been set in the downstream region. The distance between each tapping points has been selected to be 12 mm in order to demonstrate the fluid recirculation around the orifice, where the jet has a maximum effects at 2D and 8D in the upstream and downstream regions, respectively [18]. Two tapping points have been set near the orifice wall (4 mm) from both sides to study the pressure drop at a lower distance from the orifice wall. The tapping points have been coupled with a long piezometers. The length of piezometers are equal 75 cm. Then piezometers have been connected together from the upper in order to measure the differential static pressure between each different points along the pipeline as shown in Fig. 2. At the outlet of the tested pipe, the water has been transferred to a scale tank, where it could be used for Rotameters calibration. Due to a large number of piezometers and in order to avoid the oscillation during the reading data, a Canon EOS M 18.0MP digital camera 22 mm f2 has been employed to better reading the static pressure as shown in Fig. 3. The optical zoom of the camera is 3.1x with auto focus and the sensor resolution is 18MP and hence, the maximum video resolution approximately equal to 1920 × 1080. The range of light sensitivity are varied between 100 and 12,800 and 1920 × 1080, respectively. The maximum shutter speed is 4000 s and the focal length range between 18 mm and 55 mm. Regarding to the orifice geometry, a circular orifice with five different inside diameters (d = 1.2, 1.4, 1.6, 1.8 and 2 cm) has been chosen. The beta ratio (β = d/D) has been selected to be (0.5, 0.6, 0.65, 0.75 and 0.85). The orifice has been made from the acrylic plastic with 2.5 mm thickness. Medeiros et al. [19] pointed out that the angle of bevel can be varied in the range between 30° and 45°. Therefore, the angle of bevel has been selected to be 30° towards the downstream direction in the present study as shown in Fig. 4.
2g∆h 1−Cc2 × (d/ D) 4
Q act = Cc aC v ×
(1)
Eq. (1) can be rearranged by using a single coefficient (Cd) instead of Cc and Cv that obtained experimentally as follow:
Q act = aCd
1 1−β4
2g∆h (2)
where a is the orifice area, h is the manometer head, and Cd represents the discharge coefficient and is defined as follow:
Cd =
Q act 1−β4 a 2g∆h
(3)
2.3. Uncertainties analysis The accuracies of the measured parameters and the maximum uncertainties in the evaluated of the pressure head (h) have been obtained by multiple tests of piezometer reading data at the same test conditions. This error has been limited to (Δh = 6.48%). On the other hand, the Rotameters uncertainties have been found by using the scale tank in the device and stop watch. By using the estimation method of Coleman and Steele [22], the maximum uncertainties of the investigated non-dimensional parameters are ΔCd = 4.98% and ΔRe = 4.47%. The uncertainties equations of Cd and Re are given in Eqs. (4) and (5), respectively: 1
2
∆Cd ∆Qact ⎞ ∆h ⎞2⎫ 2 = ⎧⎛ +⎛ ⎨ ⎝ Qact ⎠ Cd ⎝ h ⎠⎬ ⎩ ⎭ ⎜
⎟
2
2
(4) 2
1
∆ρ ⎞ ∆μ ⎞ ⎫ 2 ∆Re ⎧ ∆Qact ⎞ = ⎛ ⎟ ⎟ + ⎜⎛ + ⎜⎛ ⎨ Re Q ⎝ ρ ⎠ ⎝ μ ⎠⎬ ⎩ ⎝ act ⎠ ⎭ ⎜
2.2. Mathematical analysis In particular, the orifice meter consists of two components. The major component includes a circular thin plate containing a varying edges and diameters inserted in a section of straight running pipe which causes a change in the energy due to the losses in the kinetic energy. The minor component, on the other hand, includes a differential gauge (differential pressure) that used to measure the change in the energy or indicates the fluid velocity. In order to have reliable and accurate measurements while using different types of orifice, several basic factors shall be taken into consideration such as differential piezometer pressure locations since the pressure has different values along the wall of the pipe at any given value of flowrate. In the present study, the orifice diameter ratio (d/D) shall be referred as beta ratio (β). For a smaller diameter ratio, the head loss and the discharge coefficient errors (accidental errors) would be too large due to the edge sharpness of the orifice plate, particularly for higher value of Re [9]. The plate thickness and edges can be designed in different shapes such as square, sharp and quadrant-edged, as shown in Fig. 5, depending on the type of flow, the discharge flow and the orifice coefficient [18]. The discharge equation can be achieved by computation the crosssectional area of pipeline, orifice plate bore and the pressure difference. It is measured between the two sections at the beginning of
⎟
Fig. 2. Schematic representation of the test setup. 221
(5)
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(a) Re=6200
(b) Re=12400
(C) Re=6200 Fig. 3. Piezometers pressure in pipe-wall for β = 0.65 and various Re.
Fig. 4. Orifice meter diameter.
Fig. 6. Schematic representation of orifice device.
2.4. Experimental procedure
Fig. 5. Types of orifice edges.
As far as the performance of orifice meter is concerned, a certain bore diameter (d) has been firstly fixed in the test-rig model. An external pressure gradient (pumps) drives the water at the inlet to flow 222
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show the effects of beta ratio (β) on the discharge coefficient and the wall pressure profiles across the orifice. The pressure head loss and the minimum pressure location near the orifice wall for different Re have been evaluated. Moreover, the results obtained from this study have been compared with that predicted by using an empirical correlation. 3.1. Comparison of experiments and empirical correlation In order to demonstrate the validation of this study, the results obtained from the current study has been compared with that predicted by using an empirical correlation. The comparison is presented in terms of Cd as a function of Re. The correlation equation of Swamee [17] has been used for comparison when β = 0.65. Swamee correlation, as presented in Eq. (6), has been obtained by using a method of curve fitting to practical curves of Streeter and Wylie that explicit for a wide range of Re from 4 × 103 to 106 and β from 0.05 to 0.7. Fig. 7 shows the variations of Cd as a function of Re for β = 0.65. Comparison of Cd reveals that the present experimental data are nearly similar to the ones with empirical equation of Swamee. The average absolute error in the predicted values of Cd has been found to be 8.5%. The reason behind the difference between the present and Swamee results can be attributed to that correlation equation presented by Swamee [17] has been obtained for a wide range of Re and β as compared to the present study.
Fig. 7. Comparison of Cd between experiments and correlation of Swamee model [17] for β = 0.65.
Cd = { [0.675 + 0.6β 2 − 0.02lnRe] 10 + [0.5 + 0.43β 2] 10 } 0.1
(6)
3.2. Discharge coefficient (Cd) In order to demonstrate the performance of orifice meter, the variations of Cd as function of Re has been presented in Fig. 8 for different values of β. It can be noted here that Cd has been calculated based on Eq. (3), where Δh has been measured according to the maximum pressure difference that occurs between the tapping points [20]. It is clear from Fig. 8 that with the increase in Re until (Re≤9000) for all values of β, Cd is increased, and reaches its largest value, and then slightly decreases with further increasing in Re in the fully turbulent flow regime for Re > 9000. It has been also reported that the flow would be moderately turbulent flow when Re≈ 10,000 [21]. For higher Re, Cd is nearly constant. This behaviour can be attributed to an orifice plate's effect on the velocity profile inside the pipe. Since the highest velocities are located in the centre of the pipe, the low value of Re (laminar flow) have large Cd due to the orifice plate has no effect on the velocity that associated with the flow passes the flow meter as compared with large value of Re. The velocity profile strongly affected with further increasing in Re that has inversely effect on Cd until it becomes constant [23]. Furthermore, it can be observed from the figure that Cd increases with increasing in β until (Re≤ 9000) and then starts gradually decreases with further increasing in Re. Such behaviour can be attributed to the effects of flow types (i.e., laminar and turbulent flow) and this is consistent with previous studies (e.g., Colter [23]). It has been also concluded from the most previous studies that the Cd has a proportional effects with orifice diameter when β ≥ 0.5 and inversely effects when β < 0.5. The maximum value of Cd has been observed at Re = 9300 for all different β. In addition, the maximum value of Cd has been found for β = 0.85. A small values of Cd is obtained for a lower value of β owing to the smaller contraction area near the orifice plate. In the present study, the obtained results have been correlated to produce a useful tool for calculation of Cd. This coefficient has been correlated with respect to Re and β. The correlation equation has been obtained for the ranges of Re (3100–18,600) and β (0.5, 0.6, 0.65, 0.75 and 0.85). The evaluation of the correlation constants has been carried out on the basis of the minimum sum of the square error (SSE), and the maximum correlation coefficient (R2), which is equal to proportion of variance and accounted. The statistical analysis has been carried out by using STATISTCA software, version 5.5, in which a non-linear estimation for the regression function using Quasi-Newton method. The error
Fig. 8. Variations of Cd with respect Re for various β.
Fig. 9. Variations of hf with respect Re for various β.
through the pipe. The amount of flow has been adjusted by an on/off valve that situated at both ends of the tested pipe. The amount of water flow (actual volume flow rate) has been recorded by Rotameters device. The piezometers head within reading range has been adjusted by the valve above of them. The difference in reading head (Δh) for thirty piezometers have been recorded by a digital camera as shown in Fig. 3. This process has been repeated with different water flowrate for a certain value of β where the Qact and Δh have been recorded. 3. Results and discussion As mentioned before, the main purpose of the present study is to 223
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Fig. 10. Variations of static wall pressure head as a function of recirculation length for various β and Re.
3.3. Orifice head loss
of this method represents the difference between the observed and predicted values. The correlation equation has been obtained as follow:
Cd = 0.49364 Re 0.04617 β 0.1586
Fig. 9 shows the variations of the orifice head loss (hf) in cm of H2O as function of Re for various β. The hf occurs due to change in the pressure head between the section at beginning of contraction in the orifice plate and the section behind the orifice plate when the normal uniform flow is occurred. It can be observed from the figure that hf increases with increasing in Re. It is also clear from the figure that hf sharply decreases with increasing in β due to decrease in recirculation flow in the downstream region resulting from the shear stresses and friction.
(7)
where SEE and R are equal to 0.01% and 84%, respectively. The standard error for Eq. (7) has been found to be within ± 2% with the percentage of observations equal to 83%. It can be noted here that the format of Eq. (7) has been chosen to be simple and more general as well as to obtain a higher value of correlation coefficient (R). The Cd in Eq. (7) is a function of Re and β and hence, this expression is valid only between the ranges of Re and β that used in the present study.
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obtained by previous studies in [8,11–13].
3.4. Static wall pressure
As a final remark, different researchers [14–16] addressed the pressure gradients and velocity inside orifice meter experimentally and numerically. Therefore, in order to improve the present experimental work, the pressure gradient should be measured with differential pressure transducers with a more populated tap pressure points near the orifice plate as the practice frequently used in aerodynamic test. This issue shall be taken up later in the future.
Fig. 10 shows the variations of the static wall pressure head (in cm of H2O) as a function of recirculation length (Lr = x/D) across the orifice plate for various β and Re. The static wall pressure has been evaluated by subtracting the head pressure at each tapping point from both head pressure at the outlet and head loss (hf) caused by orifice due to both contraction and sudden expansions [7,8]. For a fixed value of Re, it is evident from the figure that the static wall pressure in the downstream region decreases with decreasing in β. This can be attributed to a narrow area of the orifice that leads to increase the velocity in the downstream region. According to the Bernoulli's equation, the static wall pressure has inversely effects with respect to the square velocity of the fluid [20]. It can be also observed from the figure that the static wall pressure decreases by increasing in Re due to increase the velocity in the downstream region. When β is decreased from 0.85 to 0.5, the pressure drop is increased from 0.1 to 1.1 cm of H2O for Re = 3100 and from 3.7 to 31.6 cm of H2O for Re = 18,600. It is also clear from Fig. 10 that the distance of fluid recirculation in the downstream region is slightly extended with an increase in Re and decrease in β. This can be explained by increasing the shear stress at the pipe boundary layer due to increase the fluid velocity. Therefore, the working fluid requires a further distance in order to return in a uniform distribution flow behaviour. On the other hand, the fluid recirculation in the upstream region has only a minor influence for all values of Re and β and hence it remains nearly constant around (x/D = 1.5). Most importantly, the location of greatest fluid contraction which occurs at point (c) shifts towards the downstream direction with either increasing in Re or decreasing in β (i.e., from (x/D = 0.2) for β = 0.75 and 0.85 to (x/ D = 0.5) for β = 0.5, 0.6 and 0.65) due to increase in the inertia for the fluid resulting from the velocity increasing for a small value of β.
Acknowledgment The authors gratefully acknowledge the Northern Technical University, Engineering Technical College of Mosul,Iraq for their laboratory support for this work. Conflict of interest None Appendix A. Supporting information Supplementary data associated with this article can be found in the online version at doi:10.1016/j.flowmeasinst.2019.01.004. References [1] M.M. Tukiman, M.N.M. Ghazali, A. Sadikin, N.F. Nasir, N. Nordin, A. Sapit, M.A. Razali, CFD simulation of flow through an orifice plate, IOP Conf. Ser. Mater. Sci. Eng. 243 (2017) 012036. [2] P. Yang, Numerical Study of Cavitation within Orifice Flow (M.Sc. thesis of Mechanical Engineering), Texas A&M University, 2015. [3] S. Eiamsa-ard, A. Ridluan, P. Somravysin, P. Promvonge, Numerical investigation of turbulent flow through a circular orifice, J. Kmitl Sci. J. 8 (1) (2008) 43–50. [4] R.K. Singh, S.N. Singh, Seshadri, performance evaluation of orifice plate assemblies under non-standard conditions using CFD, Indian J. Eng. Mater. Sci. 17 (2010) 397–406. [5] W. Jianhuaa, A. Wanzhengb, Z. Qib, Head loss coefficient of orifice plate energy dissipator, J. Hydraul. Res. 48 (4) (2010) 526–530. [6] B.M. Ntamba, Non-Newtonian Pressure Loss and Discharge Coefficients for Short Square-Edged Orifice Plates (M.Sc. thesis of Mechanical Engineering), Cape Peninsula University of Technology, 2011. [7] M.S. Shah, J.B. Joshi, A.S. Kalsi, C.S.R. Prasad, D.S. Shukla, Analysis of flow through an orifice meter: CFD simulation, J. Chem. Eng. Sci. 71 (2011) 300–309. [8] W. Ai, J. Wang, Minimum wall pressure coefficient of orifice plate energy dissipater, Sci. Water Sci. Eng. 8 (1) (2015) 85–88. [9] H. Parshad, R. Kumar, Effect of varying diameter of orifice on coefficient of discharge, Int. J. Eng. Sci. Paradig. Res. (2015) 19–22. [10] A. Wanzheng, Energy dissipation characteristics of sharp-edged orifice plate, Adv. Mech. Eng. 7 (8) (2015) 1–6. [11] F. Hernandez-Alvarado, D.V. Kalaga, D.E. Turney, S. Banerjee, J.B. Joshi, M. Kawaji, Void fraction, bubble size and interfacial area measurements in cocurrent down-flow bubble column reactor with microbubble dispersion, Chem. Eng. Sci. 168 (31) (2017) 403–413. [12] L.C. Mutharasu, D.V. Kalaga, M. Sathe, D.E. Turney, D. Griffin, X. Li, M. Kawaji, K. Nandakumar, J.B. Joshi, Experimental study and CFD simulation of the multiphase flow conditions encountered in a novel Down-flow bubble Column, Chem. Eng. J. (2018), https://doi.org/10.1016/j.cej.2018.04.211. [13] F. Hernandez-Alvarado, R. Samaroo, D.V. Kalaga, T. Lee, S. Banerjee, M. Kawaji, Numerical and experimental analysis of single-phase jet interactions, in: Proceedings of the Conference on Fluids Engineering Division Summer Meeting FEDSM 2016, July 10–14, Washington DC, USA, ASME, 2016, pp. V01BT33A007V01BT33A007. [14] F. Shan, Z. Liu, W. Liu, Y. Tsuji, Effects of the orifice to pipe diameter ratio on orifice flows, Chem. Eng. Sci. 152 (2016) 497–506, https://doi.org/10.1016/j.ces. 2016.06.050. [15] F. Shan, A. Fujishiro, T. Tsuneyoshi, Y. Tsuji, Particle image velocimetry measurements of flow field behind a circular square-edged orifice in a round pipe, Exp. Fluids 54 (2013) 1553, https://doi.org/10.1007/s00348-013-1553-z. [16] S. Benhamadouche, M. Arenas, W.J. Malouf, Wall-resolved Large Eddy Simulation of a flow through a square-edged orifice in a round pipe at Re = 25,000, Nucl. Eng. Des. 312 (2017) 128–136, https://doi.org/10.1016/j.nucengdes.2016.09.010. [17] P.K. Swamee, Discharge equations for venturi meter and orifice meter, J. Hydraul. Res. 43 (4) (2005) 417–420. [18] H.S. Sondh, S.N. Singh, V. Seshadri, B.K. Gandhi, Design and development of variable area orifice meter, Flow. Meas. Instrum. 13 (2002) 69–73. [19] A.K.A. Medeiros, J.F. Lima, G.G. Medeiros, N.F.S. Junior, R.N.B. Felipe,
4. Conclusions and final remarks In the present study the performance of orifice meter diameter on the discharge coefficient and pressure head losses has been experimentally investigated. The orifice meter has made from the acrylic plastic and it has been bevelled in 30°. PVC pipe system has been used, where the pipe has a thirty tapping points across the orifice meter for the pressure measurement. The experiments have been carried out for various β and Re. The main conclusions of the present study are: 1. The results show that the Cd increases with increasing in β when Re≤ 9000 whereas this coefficient decreases with increasing in β when Re > 9000. 2. The results clearly demonstrated that the β has a positive effects on the Cd whereas it has inversely effects on pressure head losses. 3. The maximum fluid recirculation length in the downstream region occurs at x/D = 6. The results also show that the fluid recirculation length moves towards the downstream region with increasing in Re and reduces with increasing in β. 4. The comparison between the results obtained from the present study and with that predicted by using the empirical correlation show a good agreement, where the average absolute error is approximately 8.5%. 5. Based on the present experimental data, the best statistical analysis correlation has been obtained for Cd that cover a wide range of Re and β. This correlation provides a useful tools for calculation of Cd in the future. 6. The head loss (hf) increases with increasing in Re and decreases with increasing in β owing to decrease in the recirculation flow in the downstream region. 7. For a fixed value of Re, the static wall pressure in the downstream region decreases with decreasing in β. The static wall pressure decreases by increasing in Re owing to increase the velocity in the downstream region. This observations are quite similar with that 225
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02, 2002. [22] H.W. Coleman, W.G. Steele, Experimentation, Validation, and Uncertainty Analysis for Engineers, 3rd ed., John Wiley & Sons, Inc., Hoboken, New Jersey, 2009. [23] C.L. Hollingshead, Discharge Coefficient Performance of Venturi, Standard Concentric Orifice Plate, V-cone, and Wedge Flow Meters at Small Reynolds Numbers (M.Sc. thesis of Science in Civil and Environmental Engineering), Utah State University, 2011.
R.C.T.S. Felipe, Parameters for dimensional inspection of orifice plates and roughness of the straight stretches of the tubing, Int. J. Braz. Arch. Biol. Technol. 49 (2006) 1–8. [20] M.P. Boyce, Perrys Chemical Engineering Hand Book, 8th ed., McGraw-Hill Companies, 2008. [21] D.R. Durgaiah, Fluid Mechanics and Machinery, Published by K.K. Gupta for New Age International (P) Limited, 4835/24, Ansari Road, Daryaganj, New Delhi-110
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