Analysis of the hydrodynamic torque effects on large size butterfly valves and comparing results with AWWA C504 standard recommendations

Journal of Mechanical Science and Technology 26 (9) (2012) 2799~2806 www.springerlink.com/content/1738-494x DOI 10.1007/s12206-012-0733-8 Analysis of the hydrodynamic torque effects on large size butterfly valves and comparing results with AWWA C504 standard recommendations Farid Vakili-Tahami 1, Mohammad Zehsaz 1,*, Mahdi Mohammadpour 2 and Ali Vakili-Tahami 3 1 Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran 2 Department of Mechanical Engineering, Loughborough University, UK 3 Mechanic AB Co., Shahid Rajaie Industrial Centre, Tabriz, Iran (Manuscript Received June 18, 2011; Revised March 13, 2012; Accepted April 4, 2012) ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Abstract Butterfly valves are widely used in various industries such as water distribution, sewage, oil and gas plants. The hydrodynamic torque applied on the butterfly valve disk is one of the most important factors which should be considered in their design and application. Although several methods have been used to calculate the total torque on these valves, most of them are based on hydrostatic analysis and ignore the hydrodynamic effect which has a major role to determine the torque of the large-size valves. For finding the dynamic-valvetorque, some empirical formulas and methods have been proposed; for example in AWWA C504 standard, a relationship for calculating the dynamic torque has been given and its variation versus disk angle has been stated. However, the use of these empirical relationships is restricted due to the conditions defined in the standards. In this paper, the dynamic-valve-torque has been calculated for a large butterfly valve under different conditions and also at the different opening angles of the valve disk. For this purpose a computational fluid dynamics (CFD) method has been used. The results have been compared with those given in the AWWA C504 standard recommendations. Moreover, the effects of the disk shape and its deformation, surface roughness, upstream/downstream pressure variation and disk-offset value have been studied. Keywords: Butterfly valve; Hydrodynamic torque; Computational analysis; CFD ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction Large butterfly valves are widely used in water distribution systems, fuel transferring lines, power plants etc. Different scientific and industrial researches have been carried out to study the hydro-mechanical behavior of these valves. Pressure loss, cavitations and the required torque to operate these valves are the most important subjects which are discussed in these works. Kimura et al. [1] and Grieco and Marmo [2] obtained the pressure loss in butterfly valves using numerical methods and compared their results with experimental data. Igarashi and Inagaki have shown that general equations concerning the vortex shedder used for the Karman vortex flowmeter can also be applied to obtain the hydraulic losses of the flow control devices which are asymmetrical to the crosssection of the pipe such as butterfly valves [3]. Also, Kimura et al. investigated the flow-mechanic performance of a butterfly valve [1]. They formulated a theoretical loss coefficient from a contraction factor obtained by applying the generalized Borda mouthpiece theory. Song et al. [4] used a numerical * Corresponding author. Tel.: +984113393060, Fax.: +984113354351 E-mail address: zehsaz@tabrizu.ac.ir Recommended by Associate Editor Sung Hoon Ahn KSME & Springer 2012 simulation using commercial package-cfx and ANSYS to study the fluid and structural behavior of large butterfly valves. To perform fluid analysis and structural analysis perfectly, large valve models are generated in three dimensions without much simplification. The result of fluid analysis is imported to structure analysis as a boundary condition. In addition, to describe the flow patterns and to measure the performance when valves are opened for various angles, a verification of the performance whether the valve could work safely at these different conditions or not was conducted. The result shows that the valve is safe in a given inlet velocity of 3 m/s, and it's not necessary to be strengthened anywhere. Huang and Kim [5] investigated the incompressible flow characteristics of butterfly valve flows in three dimensions (3-D). Eom [6] investigated the performance of two different configurations of butterfly valves: perforated blades and different diameter of solid blades that allow partial opening of the valve at closed position. The experimental results obtained from this research support the suitability of a butterfly valve for good flow control. Hassis has studied the experimental cavitation effects on the acoustic variables [7]. Morris and Dutton have used an experimental method to study the performance of the butterfly valves place d after an elbow [8] and performance of two

2800 F. Vakili-Tahami et al. / Journal of Mechanical Science and Technology 26 (9) (2012) 2799~2806 butterfly valves mounted in series [9]. Yang et al. tried to predict the cavitation in butterfly valves using fluid transfer instruments [10]. Sarpkaya investigated the torque and cavitation characteristics of idealized two-dimensional and axially symmetrical butterfly valves [11]. He obtained theoretical results for the two-dimensional case and compared them with the ones obtained experimentally and by a relaxation technique. Based on the results of the two-dimensional case, an approximate solution has been presented for the more general and practical case of three-dimensional butterfly valves. His results were in good agreement with the actual flow tests. Kimura and Ogawa developed a numerical method to calculate the required torque to operate butterfly valves [12]. Leutwyler and Dalton studied the torque characteristics of the butterfly valves with compressible fluid flow [13]. Danbon and Solliec investigated the effect of an elbow on the aerodynamic torque for a butterfly valve [14]. Also, Solliec and Danbon defined a new torque coefficient in which the dynamic pressure of the flow is the normalization factor instead of the pressure drop. Advantages and drawbacks of each normalization method are described in their work [15]. Park and Chung used a method to study the hydrodynamic torque in a butterfly valve [16]. Kalsi et al. studied the effects of the different parameters on the torque which is required for opening and closing the valves [17]. Merati et al. obtained different valve efficiencies using CFD methods [18]. Rammohan et al. studied the cavitations in a butterfly valve using CFD methods in three dimensions and compared CFD-based results with the experimental data [19]. Guillermo et al. also used CFD methods to study the hydro-mechanical behavior of the valves and compared their results with the experimental data [20]. Recent research works on butterfly valves show that the CFD method is a strong tool to study the hydro-mechanical behavior of the valves and enables one to study the effect of different parameters on their performance. 1.1 Computational analysis The manufacturing and testing of large butterfly valves is expensive; therefore, there is a general trend to use numerical methods to study the hydro-mechanical behavior of these valves. In this way, any malfunction or short-coming in their design would be identified and solved before starting the actual manufacturing process. In this research work, computational analysis has been carried out using the computational fluid dynamics (CFD) based software COSMOS FloWorks to study the hydro-mechanical behavior of a D = 1000 mm butterfly valve. In this model, the Reynolds-averaged Navier- Stokes and continuity equations have been solved numerically for an incompressible fluid flow: 1 C K P+ ν C= + ( C. ) C ρ t C = 0.0, t (1) in which C is velocity, P is pressure, ν is kinematic viscosity, ρ is density, t is time and K are body forces. Since the size and diameter of the valve is large (1000 mm), the body forces including gravitational forces also play a major role in this solution, and therefore they have been taken into account. For example, the mass of water within the valve and the mass of the valve-disk is 550 kg and 300 kg, respectively. In solving Navier-Stokes equations near the walls, fluid flow pattern has been considered to be layer-turbulent. To deal with the turbulence model, the Reynolds-averaged Navier-Stokes equations (RANS) have been utilized [21]. With RANS, a turbulence model is needed to close the momentum equations. Two-equation turbulence models such as the k ε model, k ω model and Reynolds Shear Stress model are usually used in industry because of their robustness. The k ε model is chosen in this solution model because it does not involve the complex non-linear damping functions required for the other models and is therefore more accurate and more robust [22]. In finding boundary layer conditions, the turbulence distance has been assumed to be 20 mm with a turbulence factor of 2 percent. Three-dimensional cubic elements with the maximum dimensions equal to 23.592 mm have been used to carry out the CFD analysis. The equations have been solved for steady state condition with constant fluid flow. The CFD mesh includes fluid field within the upstream and downstream connecting pipes, valve-solid-body and valve disk. To study the mesh sensitivity, the analysis has been repeated for different mesh-sizes until the results have converged with an acceptable error limit of 0.1 percent. 1.2 Solution methodology and boundary conditions Generally, large butterfly valves are manufactured in casting or they may be produced using metal forming processes. Because of the application and manufacturing conditions, large butterfly valves are usually designed with single offset, and rarely, symmetric or double offset types are produced. Nominal operating pressure is usually 10, 16 or 25 bar. According to the manufacturing method and its quality, surface smoothness can be different; however, the inner and outer surface of the valve are painted to increase the corrosion resistance, so the valve body can be considered as a smooth surface. In this research work, the valve has 1000 mm nominal diameter with working pressure of 10 bar. It is a single offset valve with the offset value of 50 mm and its shaft is located in the downstream side. The results have been obtained with constant upstream pressure of 11 bar-absolute and the downstream pressure is assumed to be 1 bar-absolute (atmospheric discharge pressure). Upstream and downstream pressures have been defined according to the AWWA C504 recommendations [23]. Based on these recommendations, upstream and downstream connecting pipes have been used with the length of two and six times of the nominal diameter. However, in calculating the pressure drop of the valve, the pressure drop of

F. Vakili-Tahami et al. / Journal of Mechanical Science and Technology 26 (9) (2012) 2799~2806 2801 Table 1. Numbering different disk types used in the paper (all considered with 1000 mm nominal diameter, 50 mm offset and 176 mm maximum disk thickness). Disk type No. 6 5 4 3 2 1 Disk front face Disk back face these pipes has been excluded. Water temperature was assumed to be 25 C. In some operating conditions, cavitation may occur in these valves, which can damage the valve body, disk or pipes. It can also cause severe pressure loss, which reduces the valve discharge and increases the required torque. Cavitation has been taken into account in the computational analysis and the minimum fluid pressure for cavitation (boundary pressure for cavitation) has been considered to be the saturated vapor pressure of water at 25 C. There are numerous forms of the dimensionless number or parameter which have been used to mathematically describe cavitation. The cavitation parameter or index is a dimensionless ratio used to relate the conditions which inhibit cavitation (P 2 P V ) to the condition which causes cavitation ( P). Hence, the fundamental form of this parameter is σ 2 = (P 2 -P v )/ P which uses the downstream valve pressure (P 2 ), the vapor pressure of the liquid (P V ), and the pressure drop of the valve ( P). It is necessary to use this parameter for determining specific cavitation effects such as size and scale effects. If the value of σ 2 calculated for the actual operating pressures of a valve is less than the value of σ 2 for a cavitation limit, the valve will experience a level of cavitation more severe than that associated with the limit. The results have shown that in all types of disk shapes, cavitation occurs in disk opening angles below 25 degrees, and above this angle there is no cavitation. The shape of the valve disk has a major role in the hydrodynamic behavior of the valves and on the operating dynamic torque. Therefore, six different shapes for the valve disk (see Table 1) have been considered, and the results have been obtained and compared for all these disks. These disk shapes are defined according to the manufacturing requirements to increase the strength of the disks and to reduce their deformation. Numbers 1 to 6 are used to refer to these disk types in this Fig. 1. Static pressure contours for different opening angles for disk no. 1. Flow direction is from right to left, upstream pressure: 11 barabsolute, and downstream pressure: 1 bar-absolute. paper. Fig. 1 shows the potential pressure contours for different opening angles for disk type no. 1. As it can be seen, due to

2802 F. Vakili-Tahami et al. / Journal of Mechanical Science and Technology 26 (9) (2012) 2799~2806 the disturbances (flow separation and recirculation zones) caused by the disk at given angle, the distribution of fluid pressure along the disk surface both in the front and back side change significantly. The results show that the average pressure on the front surface of the disk is maximum (about 9.5 bar) for the opening angle of 40 degrees. However, when the average pressure on both surfaces has been calculated, the results show that the total average pressure is maximum when the opening angle is 10 degrees. Also the total force on disk is maximum (about 950 kn) when the opening angle is 40 degrees. 2. AWWA C504 standard recommendations for calculating the hydro-dynamic torque in butterfly valves The AWWA C504 standard is one of the most reliable references for designing and manufacturing of the butterfly valves. According to this standard, the hydrodynamic torque can be calculated using [23]: T = C D P (2) d 3 ( t ) where T d is hydrodynamic torque; C t is dynamic torque factor; P is the pressure loss in two sides of the valve; and, D is the disk diameter. Dynamic torque factor can be calculated using Eq. (3) in which P is replaced by ρv 2 in Eq. (2). Td Ct = (3) 2 3 ρv D In this equation ρ is fluid density and V is average fluid velocity. According to this code, the maximum torque may occur at the opening disk angle of between 9 and 50 degrees. Because of high pressure loss in small opening angles, the maximum dynamic torque factor is expected at the opening angles of 65 to 80 degrees. Based on Eq. (2), the dynamic torque is directly proportional to the pressure loss caused by the valve. Although this equation has a simple form, at the absence of experimental data concerning factor C t, it is very difficult to use it for practical purposes. Also, to use this equation, the upstream and downstream pressures should be obtained at two sections far from the valve (with the distance two pipe diameters at the upstream and at least six pipe diameters at the downstream). This is for reducing the disturbance effects at these sections. It should be highlighted that at these sections, the pressure changes at different points, and therefore, average pressure should be used. Both the C t (dynamic torque factor) and P (pressure drop at the valve) strongly depend on the disk shape. Calculating the C t (dynamic torque factor) for different valves and at different disk opening angles is a very difficult task, and therefore, for using the above equations, experimental data is necessary. However, by the implementation of the numerical methods, the hydrodynamic torque can be calculated before the valve has been actually manufactured. In this work, using the CFD model and numerical solutions, the distribution of the up and downstream pressures have been obtained and their average values have been calculated at the specified sections for different disk shapes and opening angles. Upstream and down stream pressures are assumed to remain constant in all solutions at 11 and 1.0 bar-absolute, respectively. Upstream and downstream pressures have been defined according to the AWWA C504 recommendations [23]. To avoid any disturbances caused by stream flow through the valve, a distance of two pipe diameters at the upstream and six pipe diameters at the downstream has been assumed in the model. With these conditions, the average inlet velocity for full opening condition of the valve is 46.5 m/s and it reduces to 10.64 m/s at disk opening angle of 10 degrees. Also, the distribution of the pressure on both sides of the valve disk has been obtained (see Fig. 1). These results have been used to calculate the dynamic torques, and these values have been compared with those obtained using Eq. (2). Also, the effect of different parameters on the dynamic torque has been studied. 3. Effect of the outlet pressure on the hydrodynamic torque Fig. 2(a) shows the variation of the hydrodynamic torque for disk no. 1 with different downstream pressures. For various pressure drops, the hydrodynamic toque is almost the same. It also shows that the maximum torque is about 30000 N-m and occurs at the opening angle from 65 to degrees. The dynamic torque variations with the opening angle for all downstream pressures are almost the same (with 5 percent difference), but for the outlet pressure of above 4 bar, the dynamic torque reduces significantly. Therefore, it can be concluded that unlike the AWWA recommendations, the relationship between the inlet-outlet pressure difference and the dynamic torque is nonlinear. This is due to the variation of the pressure distribution on the disk surface, variation of the fluid velocity and local cavitations. Fig. 2(a) also shows that direction of the torque changes when the opening angle is larger than 83 to 85 degrees. The variation of the hydrodynamic torque with the disk opening angle for different disk types is presented in Fig. 2(b). The torque values have been obtained for upstream and downstream pressures of 11 and 3 bar-absolute, respectively. The maximum torque for all types occurs at about degrees of disk angle; for example, disk 5 provides a lower maximum torque of about 29300 Nm, and disk 3 shows the maximum torque of about 3635 Nm. The dynamic torque rises significantly above 30 degrees and rapidly drops about degrees of the opening angle. This is due to the disturbances generated by the disk. For the disk types of 2, 3 and 4, the torque is negative at the opening of the valve (below 25 degrees),

F. Vakili-Tahami et al. / Journal of Mechanical Science and Technology 26 (9) (2012) 2799~2806 2803 Torque(N.m) Torque (N.m) 40000 30000 20000 10000-10000 -20000-30000 -40000 0 10 20 30 40 50 60 80 90 40000 30000 20000 10000-20000 -30000-40000 Disk-1 Disk-2 Disk-3 Disk-4 Disk-5 Disk-6 Disk Angle (a) Outlet Pressure 1bar Outlet Pressure 2bar Outlet Pressure 3bar Outlet Pressure 4bar Outlet Pressure 5bar Outlet Pressure 6bar Outlet Pressure 7bar 0 0 10 20 30 40 50 60 80 90 100-10000 Disk Angle (Degrees) (b) flow is constant 3 m/s. As it can be seen, the variation of the dynamic torque coefficient obtained in this research for the valve with 1000 mm diameter and disk shape 1 shows the same trend as given by Song et al [21] and reaches its maximum value of about 0.32 at the disk opening angle of 75 degrees. The results provided in Fig. 2(a) and (b) give the maximum hydraulic torque at disk opening angle of degrees, and considering the differences in valve size and disk shape, the results compare well with the experimental data. It has to be highlighted that most of the data given in the standards including AWWA C504 for dynamic torque are obtained in constant velocity condition. Therefore, when the valve is closing, the pressure drop increases, which leads to high dynamic torques. For example, AWWA C504 mentions that the dynamic torque is high at disk angles of 9 to 50 degrees [23]. However, in this research work, the upstream and down stream pressure is assumed to be constant, so the pressure drop of the valve remains almost constant and the velocity of the flowing water decreases as the valve closes. This type of boundary condition is more practical. In calculating the valve pressure drop, the amounts of the pressure losses along the inlet and outlet pipes are excluded. Hence, in calculating the dynamic torque, the pressure drop across the valve remains constant and the effect of its change is eliminated, so the dynamic torque is maximum in the disk opening angle of degrees as it can be seen in Fig. 2(a) and (b). Also, in Fig. 2 (b) and (c), the trend of change of dynamic torque and dynamic torque coefficient is similar because the pressure drop in the valve is kept constant during the numerical solution. All these reveal the shortcomings of using dynamic torque to study the behavior of butterfly valves, and therefore, it is recommended to use C t or dynamic torque factor, which can be calculated using Eq. (2) or (3) in which interaction between dynamic torque and P or ρv 2 is included. 4. The effect of other parameters on the hydrodynamic torque (c) Fig. 2. (a) The variation of the hydrodynamic torque for different downstream pressures. Upstream pressure is constant 11 bar abs; (b) The variation of the hydrodynamic torque for different disk types with upstream pressure of 11 bar-absolute and down stream pressure of 3 bar-absolute; (c) Experimental and simulation results of the Hydraulic Torque Coefficient Ct for 1800 Butterfly valve at various disk opening angles obtained by Song et al. [21]. showing that the downstream pressure actually keeps the disk closed. Also, Fig. 2(c) shows the experimental data and results obtained using CFD simulation by Song et al. [21] for a prototype 1800 mm diameter butterfly valve manufactured from cast steel with machined inside surface. The speed of water Based on the AWWA C504 standard, the value of the C t used in Eq. (2), is a function of the parameters such as disk shape, disk opening angle, location of the shaft with respect to the disk and fluid flow rate, valve type and its offset [23]; however, these effects have not been discussed qualitatively in this standard. In this research work, the effects of the valve wall roughness, disk shape and offset value on the dynamic torque have been studied using CFD based numerical analysis. 4.1 Surface roughness The surface roughness has a major effect on the boundary layer thickness and fluid motion. To study the roughness effect, the 30 degrees disk opening angle has been selected with 5 bar downstream pressure. Three different surface rough-

2804 F. Vakili-Tahami et al. / Journal of Mechanical Science and Technology 26 (9) (2012) 2799~2806 Table 2. Variation of hydrodynamic torque with disk shape. Disk number Disk 1 Zero torque angle θ = ) ( T 0 83 Maximum torque angle ( θ ) T max Maximum torque T (N.m) max 34100 Disk 2 Disk 3 Disk 4 84& 23 86& 24 84&23 340 36500 34500 Disk 5 Disk 6 83,22 82 29300 31500 5135 4.0 Torque (Nm) 5105 5075 5045 5015 4985 4955 4925 4895 0.0 0 100 200 300 400 500 600 nesses, 100, 250 and 500 micro meter, on walls are assumed. For each roughness, the disk opening torque has been calculated as 4960, 5080 and 5130 N.m, respectively. Fig. 3 shows the variation of the disk opening-torque with surface roughness. The calculation results show that at low disk opening angles, the effect of surface roughness is more significant and this is due to the higher water velocity; however, overall, surface roughness has insignificant effect on the disk-opening torque. 4.2 Disk shape variation Roughness (micron) Torque for disk Angle 30 degree Difference in Torque (%) Fig. 3. Variation of disk-opening-torque (N.m) with surface roughness (µm). Table 2 shows the maximum hydrodynamic torque values acting on the valve disk for six different disk shapes (Table 1) at downstream pressure equal 1 bar (free discharge) and maximum allowable upstream pressure of 11 bar-absolute. Results in this table show that the disk shape can change the maximum hydrodynamic torque up to 15%. Although the disk angle for the zero torque (θ T=0 ) and also the angle for the maximum torque (θ Tmax ) do not change significantly with the disk shape, by changing the disk shape (no. 2-5) two different zero torque angles can be seen, which means that the valve will be self operating in these angles. By changing the disk shape, the flow pattern, velocity and pressure drop across the valve change, and therefore, it is expected to have different values for the dynamic torque. Also, the dynamic torque of the valve 3.5 3.0 2.5 2.0 1.5 1.0 0.5 Difference in Torque (%) Fig. 4. The effect of disk-offset on the disk-torque. strongly depends on distribution of the total fluid-pressure on both sides of the disk as it can be seen in Fig. 1. The gravitational forces have been taken into account in this solution. Different disks have different weights and different center of gravity. For example disk no. 3 with weight of 3000 N, provides gravitational torque of 150 Nm, which is negligible when compared with the hydro-dynamic torque. Also, according to the definition of the dynamic torque, given by AWWA C504, in calculating this torque, the effect of different torques such as disk weight, friction of bearings should be excluded. 4.3 Offset from symmetric axis Large butterfly valves are usually designed and manufactured with single offset. Fig. 4 shows the variation of the opening torque with the disk-offset starting from symmetric disk, 50, 100 and 150 mm offset. As the offset increases, torque values decrease with almost constant rate. If the offset of 100 mm, which is 0.1 of nominal diameter, has been considered as a base value, by decreasing the offset value to 50 mm, maximum torque decreases by 8%. This is because of the tangential forces applied on the disk surface due to the offset. Calculations show that the moment of the perpendicular forces on the disk surface is 5 times bigger than the moment of the tangential forces. Moreover, Fig. 4 shows that increasing the offset value provides initial zero torque angle and reduces the second zero torque angle. For example, a symmetric disk has only second zero torque angle of 85 degrees, but a disk with 100 mm offset has two zero torque angles of 23 and 83 degrees. This will cause different self-opening and self-closing valve conditions. 5. Conclusions The dynamic-valve-torque has been calculated for a largebutterfly valve under different conditions and disk opening angles using computational fluid dynamics (CFD) methods.

F. Vakili-Tahami et al. / Journal of Mechanical Science and Technology 26 (9) (2012) 2799~2806 2805 Moreover, the effects of disk shape and its deformation, surface roughness, upstream/downstream pressure variation and disk-offset value have been studied. The results show that: The total average pressure is maximum when the opening angle is 10 degrees. Also, the total force on disk is maximum (about 950 kn) when the opening angle is 40 degrees. Unlike the AWWA recommendations, the relationship between the inlet-outlet pressure difference and the dynamic torque is nonlinear. The maximum torque occurs at the opening disk angle of 60 to degrees, and the direction of the torque changes when the opening angle is larger than 82 to 85 degrees, which mostly depends on the outlet pressure and disk shape. The maximum torque for all disk types occurs at the same disk angle; however, disk type 5 provides minimum torque value (29293 N.m) and disk type 3 requires the maximum torque of 36350 N.m. Surface roughness has an insignificant effect on the diskopening torque. By changing the disk shape (no. 2-5) two different zero torque angles can be seen, which means that the valve will be self operating at these angles. As the disk-offset increases, torque values decrease with almost constant rate. Also, increasing the offset value provides initial zero torque angle and reduces the second zero torque angle. Acknowledgment The authors would like to acknowledge and appreciate the cooperation, help and support of Mechanic AB Company, for providing technical information based on their long manufacturing experience and field observations. Nomenclature------------------------------------------------------------------------ C C t D K P T d t V P θ ρ σ 2 ν : Velocity : Dynamic torque factor : Nominal diameter of the valve or pipe : Body force : Pressure : Hydraulic dynamic torque : Time : Average fluid velocity : Pressure loss : Disk angle : Density : Cavitation parameter : Kinematic viscosity References [1] T. Kimura, T. Tanaka, K. Fujimoto and K. Ogawa, Hydraulic characteristics of butterfly valve- prediction of pressure loss characteristics, Elsevier Science B.V., ISA Transactions, 34 (4) (1995) 319-326. [2] E. Grieco and L. Marmo, Predicting the pressure drop across the solids flow rate control device of a circulating fluidized bed, Powder Technology, Elsevier B. V., 161 (2) ( 2006) 89-97. [3] T. Igarashi and T., S. Inagaki, Hydraulic losses of flow control devices in pipes, JSME,Series B, 38 (3) (1995) 398-404. [4] X. G. Song, L. Wang and Y. C. Park, Fluid and structural analysis of a large diameter butterfly valve, Journal of Advanced Manufacturing Systems, 8 (1) (2009) 81-88. [5] C. Huang and R. H. KIM, Three-dimensional analysis of partly open butterfly valve flows, Journal of Fluids Engineering, Trans. ASME, 118 (1996) 562-568. [6] K. Eom, Performance of butterfly valves as a flow controller, Journal of Fluids Engineering, Trans. ASME, Journal of Fluids Engineering, 110 (1988) 16-19. [7] H. Hassis, Noise caused by cavitating butterfly and monovar, Journal of Sound and Vibration, 225 (3) (1999) 515-526. [8] M. J. Morris and J. C. Dutton, An experimental investigation of butterfly valve performance downstream of an elbow, Journal of Fluids Engineering, 113 (1) (1991) 81-85. [9] M. J. Morris and J. C. Dutton, The performance of two butterfly valves mounted in series, Journal of Fluids Engineering, 113 (3) (1991) 419-423. [10] B. S. Yang, W. W. Hwang, M. H. Ko and S. J. Lee, Cavitation detection of butterfly valve using support vector, Journal of Sound and Vibration, 287 (1) (2005) 25-43. [11] T. Sarpkaya, Torque and cavitation characteristics of butterfly valves. Journal of Applied Mechanics, Trans. ASME (1961) 511-518. [12] T. Kimura and K. Ogawa, Hydrodynamic characteristics of a butterfly valve-prediction of torque, Elsevier Science B.V., 34 (4) (1995) 327-333. [13] Z. Leutwyler and C. Dalton, Computational study of torque and forces due to compressible flow on a butterfly valve disk in mid-stroke position, Journal of Fluids Engineering, 128 (5) (2006) 1074-1083. [14] F. Danbon and C. Solliec, Aerodynamic torque of a butterfly valve influence of an elbow on the time-mean and instantaneous aerodynamic torque, Journal of Fluids Engineering, 122 920 (2000) 337-345. [15] C. Solliec and F. Danbon, Aerodynamic torque acting on a butterfly valve, Comparison and choice of a torque coefficient, Journal of Fluids Engineering, Trans. ASME, 121 (1999) 914-917. [16] J. Y. Park and M. K. Chung, Study on hydrodynamic torque of a butterfly valve, Journal of Fluids Engineering, 128 (1) (2006) 190-196. [17] M. S. Kalsi, B. Eldiwany, V. Sharma and A. Richie, Effect of butterfly valve shape variations on torque requirements

2806 F. Vakili-Tahami et al. / Journal of Mechanical Science and Technology 26 (9) (2012) 2799~2806 for power plant, Eighth NRC/ASME Symposium on Valve and Pump Testing, Washington, D.C. (2004). [18] P. M. J. Merati, M. J. Macelt and R. B. Erickson, Flow investigation around a V-sector ball valve, Journal of Fluids Engineering, 123 (2001) 662-671. [19] S. Rammohan, S. Saseendran and S. Kumaraswamy, CFD based prediction in butterfly, The 6th International Conference on Cavitations, The Netherlands (2006). [20] P. S. Guillermo, A. V. Jaime and H. F. Steven, Three- dimensional control valve with complex geometry: CFD modeling and experimental validation, 34th Fluid Dynamics Conference and Exhibit, Portland, Oregon (2004). [21] X. G. Song and Y. C. Park, Numerical analysis of butterfly valve-prediction of flow coefficient and hydrodynamic torque coefficient, Proceedings of the World Congress on Engineering and Computer Science, 2007, 24-26 October, San Francisco, USA. [22] B. Mohammadi and O. Pironneau, Analysis of the K- epsilon turbulence model (Research in Applied Mathematics), Wiley (Import), Masson, Paris, August (1994). [23] AWWA Standard for rubber-seated butterfly valves, American Water Work Association, ANSI/AWWA C504-00, Revision of ANSI/AWWA C504-94, American Water Works Association (2000). Farid Vakili-Tahami is currently an Associate Professor of Mechanical Engineering at the University of Tabriz, Iran. He received B.Sc.and M.Sc. degrees in Mechanical Engineering from the University of Tabriz, and Ph.D from the University of Manchester, UMIST in U.K. in 1988, 1991 and 2002, respectively. His current research interests include CDM analysis of mechanical engineering parts, creep damage of weldments, design of machine elements, numerical analysis of engineering components and FE based software coding for structural analysis. Mohammad Zehsaz is currently an Associate Professor of Mechanical Engineering at Tabriz University in Iran. He received the B.Sc. and M.Sc. degrees in Mechanical Engineering from the Amirkabir University of Tehran, Iran, and the Ph.D from Liverpool University in U.K. 1978, 1983 and 1997, respectively. His current research interests are in vibration and fatigue.