Wall Pressure Due to Turbulent Flow Through Orifice Plate

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:15 No:02 36 Wall Pressure Due to Turbulent Flow Through Orifice Plate Mohamed A. Siba 1, Wan Mohd Faizal Wan Mahmood 2, a, Mohd Z. Nuawi 2, b, Rasidi Rasani 2, c, and Mohamed H. 3, d* Nassir 1 Institute of Technology-Baghdad, Foundation of Technical Education, Baghdad, Iraq. moh_siba@yahoo.com 2 Department Mechanical and Material, Faculty of Engineering and Built Environment, National University of Malaysia, Selangor, 43600 Bangi, Malaysia; a wmfaizal@eng.ukm.my; b zakinuawi@eng.ukm.my; c rasidi@eng.ukm.my; d* mohamedh.nassir@taylors.edu.my Abstract-- Flow velocity and pressure are two related phenomena in the flowing fluid in a pipe containing an orifice. In this study, the focus will be on the pressure which is known to researchers under variety of names such as pressure distribution, pressure fluctuation, static pressure, pressure loss, or line pressure. This pressure (not the dynamic pressure) is triggered by the disturbance of the flow passed the orifice as the flow contract spinning, rotation, and circulation through which the flow transiently causes pressure on the wall which increasingly becomes a real concern to the designers of piping circuit of nuclear plant, turbines, or, more importantly, the flow measurement. Navier-Stocks equations have been employed to describe the velocity, pressure, stress, vorticity, strain, and total deformation using commercial CFD code ANSYS for incompressible fluid. The pressure fluctuation in conjunction with flow velocity was studied at three aspect ratios of 0.2, 0.4, and 0.6 at Reynolds number of 10000, 20000, and 30000. The study shows a strong correlation between the flow velocity (directly related to Reynolds number) and both the pressure and the stress acting on the wall. The axial maximum magnitude of the velocity and pressure appear around the orifice plate and both diminish beyond that. Vorticity and flow velocity are well correlated and are in good agreement with previous studies. The maximum stress, strain, and total deformation have powerful effect on wall at aspect ratio of 0.2 while this effect is almost nullified when the aspect ratio is higher. The study adds to the body of knowledge better understanding to the effect of higher Reynolds numbers and higher aspect ratios. Index Term-- Orifice, CFD-ANSYS, Mechanical Properties, Navier-Stokes Equation. I. INTRODUCTION The orifice plate could be treated as an extra fitting controlling and measuring the flow. Currently, there are many devices measuring the flow rate; however the accuracy needed for special equipment is not always satisfied. In addition to this critical point, the pipes that contain orifice plate suffer from high differential pressure and subsequent vibration. The geometry of a typical orifice plate is illustrated in Figure 1(a). There are three parameters governing fabrication and adaptation of an orifice plate. The first parameter is that the total length ( ) is nearly equal to 40 times the pipe radius. The other parameter is known as the aspect ratio ( ) which allows us to control the velocity and the pressure variation across the orifice plate. The last parameter of the orifice geometry is the thickness of the plate which is approximated to 0.0625. The orifice plate has many types, however shown in Figure 1b the most famous three types which are flat, backward, and forward [1, 2]. (a) (b) Fig. 1. The Geometry (a) and (b) types of an orifice meter [1] The velocity of the flow within and passed the orifice is significantly disturbed due to developing back stream, vorticities, and swirling eddies. These developments results in partial pressure in axial and radial direction [3]. Figure 2 shows the mechanism of the flow through a typical orifice plate. The pressure (static) is applied by an external pump and it is constant during the operation. The differential pressure is measured by manometer containing mercury. This differential pressure represents pressure loss which experiences highest value at vena contracta and decreases as the flow back to its normal conditions. The region of interest is located between the orifice plate and at the axial location when the pressure loss has a minimum value. The pressure loss is called the static wall pressure which is closely related to the flow velocity. The location of vena contracta where minimum pressure loss occurs at axial location ranges between 0.75 and 1.50, where is the radius of the pipe [1]. The orifice plate, as a measurement device, is subject to industrial code of ISO 5167 (2003) [4].

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:15 No:02 37 Fig. 2. Pressure distribution along the pipe containing an orifice plate Investigating the flow behavior has been studied extensively at various aspect ratios ranges between 0.2 and 0.7 [5, 6].Moreover, the flow was also investigated using several type of orifice [6, 7]. The main two purposes of these studies are to show the velocity and pressure profile of the flow within a region of maximum of 1.5 downstream after the orifice plate, where is the radius of the pipe. The laminar or turbulent flow suffers from adding extra fittings or modifying an existence geometrical shape of the piping circuit including the orifice itself. As such, the flow behavior, namely velocity and pressure distribution, passed an orifice plate should be monitored. Monitoring the flow characteristics is normally performed by three techniques: experimental [8, 9], theoretical [10], numerical [11], and simulation technique [12, 13]. Theoretically, Navier-Stokes theorem provides a complete mathematical description of the flow of incompressible Newtonian fluids in which there are four unknowns which include the velocity along the -, - and -axis (,, and ) and the static pressure. The main purpose of all these investigations is to obtain very accurate flow measurements and minimizing the risk caused by any accuracy. Almost all industrial applications such as food industry, petrochemical, and oil/gas processing require certain accuracy, however when it comes to very high accuracy such as in pharmaceutical field, the experimental, theoretical, and simulation techniques are to be carefully conducted. Errors in flow measurement can result in significant cost losses and inefficiency repercussions or damaging the system itself. Consequently, attempts are now being made to improve the accuracy of existing orifice metering facilities. Most prior efforts toward this goal have concentrated on determination of discharge coefficients [6]. The main disadvantage of pipe fittings, in this sense, is the generation of distorted velocity profiles associated with arying degrees of swirl at the inlet of the flow meter. Satisfactory stipulations to avoid flow meter calibration and measurement errors entail a flow with 2º swirl angle and a ratio of axial velocity at any point on a given pipe cross section to the maximum axial velocity at the same cross section is within 5% of the corresponding ratio of fully developed flow as measured in the same pipe after 100 pipe diameter length (ISO, 2003) [4]. The accuracy of the flow measurements depends, to a certain extent, on the effects of velocity and pressure variation which is caused by the construction of the orifice plate. Previous studies in this regard have investigated the velocity and pressure variation at considerable range of Reynolds number (both laminar and turbulent) at several values of aspect ratio. Recent studies performed by Smith et al. [6], Naveenji [14], and Olivera et al. [15] have focused on numerical analysis and simulation technique. Discharge coefficient and calibration of orifice meter were the theme of these studies in which the velocity and pressure distribution were extensively investigated. In his Ph. D. thesis, Nail [16] has focused on dependency of the flow measurements on axial velocity and wall pressure profiles. A pressure drop is generated across a fixed restriction in the flow. Orifice meters have high pressure losses and correspondingly high pumping costs, but because they are mechanically simple, they are cheap and easy to install [17,18]. Regarding improving the functioning of orifice, several attempts are being currently made to get better accuracy of the existing orifice metering instrument. These improvements result in saving millions of dollars annually in the natural gas industry alone [16]. In addition to low cost and low maintenance, piping vibrations are problematic in causing fire and explosion in industrial plants. During the past 30 years, for instance, an explosion caused by the effect of vibration in a petrochemical plant in 1974 resulted in over $114,000,000 in property damage [19]. In this study, axial velocity, differential pressure across the orifice, the vorticity of the flow passed the orifice are studied. In addition, the effect of the flow on the mechanical properties of the pipe such as stress, strain, and total deformation were examined. All measurements were tested at aspect ratio of 0.2, 0.4, and 0.6 for Reynolds number of 10000, 20000, and 30000. 2. MODELING AND THEORETICAL APPROACH The numerical solution sought in this study relies on the mean approach since most engineering applications for turbulent flow do not take all details but, instead, consider solutions that depend on models without considering full time-dependent flow. In principles, investigating how turbulence affects the mean flow is the primary goal. The classical models are based on Reynolds Average Navier- Stokes (RANS) equations. The following models could be classified according to the number of equations taken into consideration to investigate the behavior of the flow. Thus, currently available the zero equation model, one equation model, two equation models k- and k- model, and seven equation model (Reynolds Stress) model As another approach for seeking solutions for flow behavior is based on models using the Boussinesq hypothesis where the turbulence decays unless there is shear in isothermal incompressible flow. One of findings of Boussinesq hypothesis is that turbulence increases as the mean rate of deformation increases. In this study, numerical

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:15 No:02 38 solution of the time dependent three dimensions Navier- Stokes equations will be presented in order to show the structure of flow and the numerical observation of unsteady three dimensional flows through a wall pipe conveying fluid. Three dimensional calculations are performed using equation determined by the following assumptions that the flow is turbulent and the fluid is Newtonian (with variable viscosity) and incompressible. The commercial CFD code ANSYS, version 14.0 is customized by building in some relatively Low Reynolds number (LRN) ( ε) turbulence models. Solutions were sought for unsteady flow through an orifice plate with a diameter ratio of one half of the pipe diameter. The flow field was represented by mesh of 2,350,000 elements and global iteration required in the presented work is 1000; however, if solution is not converged, extra 1000 iteration is to be taken into account. It was shown that solutions converged after 1220 iterations and all residuals fell below error of 10-4. The parameters that were considered in this study are: velocity, differential pressure, vorticity, strain, stress, and total deformation. Simulation was taken for three Reynolds numbers: 10000, 20000, and 30000 and three aspect ratios ( of 0.2, 0.4, and 0.6. The fundamental equations of continuity and the momentum equations are to be considered and modified according to certain parameters that play an import role in solving Navier- Stokes equations using commercial version of CFD. study, three Bossinesq hypotheses and one Reynolds stress approaches are employed. The standard k-ε model is a two equation eddy viscosity turbulence model. In this model, the eddy viscosity is computed based on the turbulence kinetic energy k, and the turbulence dissipation rate ε using: ( ( ) [( ) ] (4) ( ( ) [( ) ] ( (5) where are empirical constants. For details, the k-ε model turbulence has five empirical constants,,, and with values of 0.09, 1.0, 1.3, 1.44 and 1.92, respectively. (7) The turbulence viscosity of the k-ε model is linked to the turbulence kinetic energy and dissipation via the relation: where is a constant., = 0.09, and is the k-ε turbulence model constant due to viscous forces, which is modeled using: (6) (8) ( ) ( ) (9) Continuity equation: ( (1) Momentum equation: ( ( ) [ ( )] ( ) ( The Reynolds stress term, in (2) represents the nonlinear convective term in the un-averaged equation and reflects the fact that convective transport due to turbulent velocity fluctuations will act to enhance mixing over and above that caused by fluctuations at the molecular level. It needs to be modeled to close the system of equations. A common method employs the Boussinesq hypothesis to relate the Reynolds stresses to the mean velocity as shown in the following stress in (3): Boussinesq hypothesis: ( ) ( ) (3) where is the turbulent viscosity. This approach has the advantage of the relatively low computational cost associated with the computation of though it assumes as an isotropic scalar quantity, which is not strictly true. The alternative approach, embodied in the Reynolds Stress Models through which transport equations are to be solved for each of the terms in the Reynolds stress tensor. In this 3. METHODOLOGY 3.1 The orifice Orifice plate is described in Figure 3 (a and b). The pipe is 1.00 m-length, 0.01 m-internal diameter, and 0.02 m-outer diameter, and 0.005 m-thickness is adopted for the orifice plate in the present study. (a) (b) Fig. 3. The Orifice (a) Mesh construction, and (b) Cross-sectional 3.2 Setting the Experiment Solution for Navier-Stoks equations using commercial CFD code ANSYS, version 14.0 is performed for unsteady, low turbulent flow and ( ε) turbulence models. The mesh was taken at 2,350,000 elements and convergent solutions were sought such that the residuals fell below error of 10-4. The parameters that were considered in this study are: velocity, differential pressure, vorticity, strain, stress, and total deformation. Simulation was taken for three Reynolds numbers: 10000, 20000, and 30000 at aspect ratios ( of 0.2, 0.4, and 0.6.

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:15 No:02 39 4. RESULTS AND DISCUSSION The velocity profile pattern predicted by turbulence k-ε model at, 0.4, and 0.6 and Reynolds number of 10000, 20000, and 30000 for each aspect ratio does not significantly change. For this reason, a typical velocity profile pattern taken at 0.4 and three relevant Reynolds number of 10000, 20000, and 30000 is taken and shown in Figure 4. As Re number increases from 10000 to 30000, the relevant velocity magnitude increases from 17 to 45 m/s. Increasing velocity is expected since the run is carried out for incompressible fluid (density is constant), at no temperature change (viscosity is constant), and the pipe characteristics stay intact. Under these conditions, the velocity in Reynolds formula is the only parameter that keeps changing with the value of Reynolds number. To study the effect of the aspect ratio, Figure 5 shows the velocity profile at Reynolds number of 10000 while the aspect ratio was set at 0.2, 0.4, and 0.6. The relevant flow velocity decreases from 17 m/s for to 1.9 m/s for The velocity profile in Figures 5 and 6 shows that the flow spins counterclockwise at the upper half and spins clockwise at the lower half. These results are in good agreement with findings of [5 and 6]. Regarding the shape of the velocity contour of the streamline flow at a given seemingly the shape suffers significant change at different values of aspect ratio or Reynolds number as shown in Figures 4 and 5. When the aspect ratio is fixed during the run and Reynolds number increases, the contour lines become denser which suggests that the wall pressure increases. In another case, when Reynolds number is fixed (for example 10000 as shown in Figure 5) and the aspect ratio increases from 0.2, 0.4, to 0.6, the contour lines become more relaxed and move closer to the wall suggesting that the wall pressure decreases. Fig. 4. Velocity at and (a) Re = 10000, (b) 20000, and (c) 30000 Fig. 5. The effect of the aspect ratio on the flow velocity distribution taken at Re = 10000 The same sequence of parameters considered in previous case are taken again to show the vorticity images at of 0.2 and Reynolds number of 10000, 20000, and 30000 as shown in Figure 6. As Reynolds number increases, the size of the tail of the spinning flow increases suggesting increasing velocity and more pressure on the wall. This result agrees with the previous analysis of the velocity and in full agreement with the results presented in [5, 6, and 7]. The influence of the aspect ratio on the vorticity at a specified Reynolds number is shown in Figure 7. The vorticity images clearly show that the vorticity loops are diminishing as the aspect ratio increases from 0.2 to 0.6. The diminishing of the vorticity loop suggests that the flow velocity decreases with decreasing pressure fluctuation at the pipe wall surface. Both results agree with the previous assessment of the velocity-aspect ratio-reynolds number relations. All vorticity magnitude images shown in Figure 6 and 7 are positive which means that the vorticity circulates or spin in counterclockwise direction. This particular result is in agreement with the assessment of [20] and the findings shown in Figures 5 and 6. (a) (b) (c) Fig. 6. Vorticity at and (a) Re = 10000, (b) 20000, and (c) 30000

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:15 No:02 40 The predicted velocity profile with the axial distance along the pipe at a single aspect ratio of 0.2 and Reynolds number of 10000, 20000, and 30000 is shown in Figure 8a. The magnitude of the velocity has its peak maximum at nearly 0.5 m where the orifice plate is located. The peak velocity diminishes significantly as Reynolds number decreases from 30000 to 10000. The axial static pressure variation is shown in Figure 8. A sudden increase in the static pressure at the location of the orifice is shown at nearly the location of the orifice. The maximum pressure variation takes place at Reynolds number of 30000 as predicted and earlier shown. The results of the velocity and the pressure as well are in good agreement with the findings presented in [5, 6, and 21]. It is noticed that as Re increases, the maximum velocity slightly shifted backwards. One possible reason for this shifting is due to strong counterclockwise vorticity which causes strong reverse swirling pushing the velocity in back direction. This result is clearly shown in Figure 8b as the differential pressure across the orifice is significantly increased as Reynolds number increases. The pressure gradient, shows it s maximum value at Re = 30000 when the velocity is at its highest value. (a) Fig. 8. The maximum axial velocity (a) and the differential pressure (b) at and Reynolds number of 10000, 20000, and 30000 The mechanical properties such as stress and strain of the pipe caused by the flow are shown in Figure 9. At, the maximum stress, strain, or the total deformation follows same trend as shown in Figure 9(a, b, or c). As the Reynolds number increases accompanied with increasing velocity, the (a) (b) 0.4 (c) 0.6 Fig. 7. Vorticity at Reynolds number of 10000 and and 0.6 (b) mechanical factors show significant increase by approximately three time for Re 10000 and about six times for Reynolds number of 30000. This dramatic increase is expected as the pressure increases across the orifice plate. This result agrees with the finding suggested by [14]. For and 0.6, the mechanical properties significantly deviate as compared to of 0.2 as all mechanical properties are faded away suggesting that the stress/strain becomes insignificant. (a) (b) (c) Fig. 9. Maximum Stress (a), Maximum Strain (b), and Maximum Deformation (c) at aspect Ratios of 0.2, 0.4, and 0.6 for Reynolds Number of 10000, 20000, and 30000 CONCLUSIONS In this study, a solution of unsteady and incompressible fluid was sought using a circular orifice as a function of three aspect ratios of 0.2, 0.4, and 0.6 taken at Reynolds number of 10000, 20000, and 30000. The solution was carried out using commercial CFD code ANSYS, version 14.0 and mesh of 2,350,000 elements and convergent solutions were sought such that the residuals fell below error of 10-4. The study includes the velocity profile, the differential pressure, and the mechanical properties. The velocity and the differential pressure are correlated and are in agreement with the other reported similar studies. The shape and the location of velocity contours play an important role in determining the pressure and the mechanical properties acting on the wall of the pipe. The maximum magnitude of the axial velocity shifts slightly back as indicative to increasing pressure due to increasing Reynolds numbers. The vorticity which shows the flow swirling behavior before and after the orifice suggests that the flow is turbulent. The pressure across the orifice shows very steep gradient as the Reynolds number increases.

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