Energy dissipation characteristics of sharp-edged orifice plate

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1 Research Article Energy dissipation characteristics of sharp-edged orifice plate Advances in Mechanical Engineering 2015, Vol. 7(8) 1 6 Ó The Author(s) 2015 DOI: / aime.sagepub.com Ai Wanzheng Abstract The energy loss coefficient, relating directly to the energy dissipation ratio, is an important index of this energy dissipater. In this article, this coefficient and its affecting parameters were analyzed by theoretical considerations, and their relationships were obtained by numerical simulations. It could be concluded that the energy loss coefficient of sharp-edged orifice plate and its backflow region length were mainly dominated by the contraction ratio of the orifice plate. Sharpedged orifice plate s energy loss coefficient and its backflow region length all increase slightly with the increase in its thickness. When Reynolds number is in the range of , Reynolds number has little impacts on energy loss coefficient and backflow region length. Two empirical expressions, relating to backflow region length and energy loss coefficient, respectively, were presented. Keywords Backflow region, contraction ratio, energy dissipater, energy loss coefficient, orifice plate, dimensionless thickness Date received: 5 January 2015; accepted: 1 June 2015 Academic Editor: Chun-Liang Yeh Introduction The orifice plate, as a kind of energy dissipaters with sudden reduction and sudden enlargement forms, has been used in large-scale hydropower projects successfully. 1 3 As early as 1960s, a plug dissipater, similar to orifice plate in energy dissipation mechanism, was used in the flood discharge tunnel of the Mica dam in Canada; the flow velocity of the flood discharge tunnel was decreased from 52 to 35 m/s at the head of 175 m. 4,5 In the Xiaolangdi hydropower project in China, three orifice plates in the flood discharge tunnel obtained the energy dissipation ratio of 44% and controlled effectively the flow velocity through the gate less than 35 m/s under the condition of the head of 145 m. 6 8 Orifice plate has a wide application prospect in practical engineering The flow through sharp-edged orifice plate is shown in Figure 1. There exist the vortex regions of ring form before and after the sharp-edged orifice plate due to the sudden reduction and sudden enlargement of the orifice plate, and those vortices are the original regions of the energy dissipation, especially the backflow region after sharp-edged orifice plate is the main key source of energy dissipation Many researches were conducted on the energy dissipaters with sudden reduction and sudden enlargement forms The interesting areas have been focused on orifice plate s incipient cavitation number, embodying its cavitation risk, and its energy loss coefficient, relating to its energy loss ratio Previous researches show that the energy loss coefficient and incipient cavitation number were closely related to orifice plate s contraction ratio (b), defined as the ratio of the orifice diameter (d) of the energy dissipater to the diameter (D) of flood discharge Marine College of Zhejiang Ocean University, Zhoushan, P.R. China Corresponding author: Ai Wanzheng, Marine College of Zhejiang Ocean University, Zhoushan , P.R. China. aiwanzheng@126.com Creative Commons CC-BY: This article is distributed under the terms of the Creative Commons Attribution 3.0 License ( which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages ( open-access-at-sage).

2 2 Advances in Mechanical Engineering Figure 1. Flow through sharp-edged orifice plate. tunnel. Qu et al. 21,22 regarded that energy loss coefficient and incipient cavitation number increase with the decrease in contraction ratio. The orifice plate s other geometric parameters also have slight impact on its incipient cavitation number. 24 Cai and Zhang 24 deemed that sloping-approach orifice plate is effective in improving the orifice plate cavitation performance, compared with the sharp-edged and square-edged orifice plates. However, sloping-approach orifice plate is inferior to the other two in energy dissipation ratio. As stated above, the researches conducted in the past focused mainly on the trend relationship between contraction ratio and energy loss coefficient or incipient cavitation number As a matter of fact, the length of backflow region L b (as shown in Figure 1) after orifice plate is an important parameter; not only it is closely related to orifice plate s energy dissipation efficiency but also it is a valuable reference parameter when designing the distance between two orifice plates in multi-stage orifice plates The purposes of this work, therefore, are to investigate the effects of the geometric parameters, that is, the contraction ratio and the sharp-edged orifice plate thickness, and the hydraulic parameters, that is, Reynolds number on the energy loss coefficient and backflow region length when the top angle u is 60, and to present empirical expression of the energy loss coefficient and the backflow region length to relating parameters, by means of numerical simulations. Numerical simulations Numerical simulation model The commercial package FLUENT RNG k e model was selected to calculate the hydraulic parameters of the flow through the orifice plate, due to its suitability for simulating the flow inside large change boundary forms as well as its high precision and calculation stability. For the steady and incompressible flows, the governing model equations include continuity, momentum, and the k e closure The control volume method and staggered grid are employed. The basic equations are integrated over each control volume to obtain the discrimination equations. The pressure implicit with splitting of operator (PISO) method is used to solve the velocity and pressure field. The main difference between PISO and the well-known SMPLE method is the second adjustment used in PISO. The block-off method is adopted to treat the control volumes occupied by the orifice plate so that the variables in these control volumes keep equal to 0 throughout the whole computation. The calculation boundary conditions are treated as follows: in the inflow boundary, the turbulent kinetic energy k in and the turbulent dissipation rate e in can be defined, respectively, as k in = 0:0144u 2 in, e in = k1:5 in (0:25D) ð1þ where u in is the average velocity in the inflow boundary. In the outflow boundary, the flow is considered as developed fully. The wall boundary is controlled by the wall functions. The symmetric boundary condition is adopted, that is, the radial velocity on symmetry axis is 0. Given an orifice plate discharge tunnel has axial symmetry characteristics, three-dimensional numerical simulations of the orifice plate discharge tunnel flow can be simplified as two-dimensional ones. Numerical simulation methods and phases The energy loss coefficient of sharp-edged orifice plate can be defined as follows 15 j = Dp (0:5ru 2 ) ð2þ where Dp is the pressure difference between the section before 0.5D orifice plate, in which flows are undisturbed, and the section after 7.0D orifice plate, where flows already recover; 15 r is the flow s density; u is the flow s average velocity in discharge tunnel. There are many parameters that affect the energy loss coefficient j and the backflow region length L b (shown as in Figure 1) of sharp-edged orifice plate, and the relevant parameters of dimensional analysis may include the following: the density of water r (kg/m 3 ), the dynamic viscosity of water m (N s/m 2 ), the tunnel diameter D (m), the orifice plate diameter d, the orifice plate thickness T (m) (as shown in Figure 1), the average flow velocity in tunnel u (m/s), and the pressure difference Dp (Pa). The top angle u also has effects on energy loss coefficient j and the backflow region length L b, but in order to consider structure safety, 60 top angle is adopted in general in practical engineering, so the case of 60 top angle is only investigated in this article. Because each of the above parameters is a function of

3 Wanzheng 3 Table 1. Variations in l b and j with Re (b = 0.50, a= 0.25). Re (310 5 ) l b j Table 2. Variations in j and l b with b and a (Re = ). b a j l b j l b j l b j l b j l b the initial independent parameters, the expression of the above parameters can be obtained L p, Dp = f (D, d, T, r, m, u) ð3þ This relationship could be rewritten in terms of dimensionless parameters Dp d, l b = f 0:5ru 2 D, T D, ud ð4þ m=r That is j, l b = f (b, a, Re) ð5þ where Re is the Reynolds number Re = ud/(m/r); a is the orifice plate dimensionless thickness, a = T/D; b is the orifice plate contraction ratio, b = d/d; l b is the dimensionless backflow region length, l b = L b /D. Equation (9) implies that the energy loss coefficient j and the dimensionless backflow region length l b are the function of b, a, and Re. The study procedure was outlined considering variable parameters in the energy loss coefficient and dimensionless backflow length variations in equation (5) in order to find out the effects of each parameter independently on them (i.e. j and l b ). According to the above analysis, two kinds of calculation phases were simulated and their phases are as follows: Phase No. 1, to calculate the energy loss coefficient j and the dimensionless backflow region length l b at the range of Reynolds number Re = when b = 0.50 and a = 0.25, in order to analyze the effects of Re on j and l b ; Phase No. 2, to calculate the energy loss coefficient j and the dimensionless backflow region length l b at the different b and a when Re = , to discuss the variations in the energy loss coefficient j and the dimensionless backflow region length l b with b and a and to establish the relationship expression of them. The calculation diameter (D) of the tunnel is 0.21 m. The range of the numerical simulations was selected at 6.0D before the sharp-edged orifice plate at the beginning and at 6.0D after the sharp-edged orifice plate at the end. The energy loss coefficient j is calculated by equation (9). The method to determine backflow region length is as follows: taking a section along tunnel direction, which is very close to the tunnel s wall; viewing the flow s horizontal velocity at this section; regarding the distance between orifice plate front and the point, where flow s horizontal velocity is 0, as the backflow region length. Numerical simulation results The results of Phase No. 1 and Phase No. 2 are shown in Tables 1 and 2, respectively. Discussions Effects of Reynolds number Table 1 presents the numerical simulation results of the dimensionless backflow region length after the sharpedged orifice plate l b and Reynolds number Re and of the energy loss coefficient of the sharp-edged orifice

4 4 Advances in Mechanical Engineering plate j and Re when the contraction ratio b = 0.50 and the ratio of the dimensionless thickness a = It could be seen that the energy loss coefficient j and the dimensionless backflow region length l b increase with the increase in Reynolds number Re when Reynolds number Re is less than 10 5 and are constants approximately when Reynolds number Re is in the range of And they changed from 3.18 to 3.20 and from to 32.06, respectively, with regard to the changes in Reynolds number Re from to Therefore, it could be concluded that the effects of Reynolds number Re could be neglected on either the energy loss coefficient j or the dimensionless backflow region length l b when Re is from to , that is to say, l b and j are only the functions of the geometric parameters of the sharp-edged orifice plate, that is, b and a, when Re is in the range of This conclusion agrees with the experiment. 15 Effects of thickness and contraction ratio Table 2 presents the numerical simulation results of the dimensionless backflow region length after the sharpedged orifice plate l b and of the energy loss coefficient of the sharp-edged orifice plate j when the contraction ratio b varies from 0.40 to 0.80 and dimensionless thickness a varies from 0.05 to It can be learned that the energy loss coefficient j and the dimensionless backflow region length l b increase with the decrease in the contraction ratio b, but dimensionless thickness a has little impact on both the energy loss coefficient j and the dimensionless backflow region length l b, that is, when a is 0.10, the energy loss coefficient j increases from 1.68 to 90.18, and the dimensionless backflow region length l b increases from 1.41 to 3.56 with regard to the changes in the contraction ratio b from 0.80 to 0.40; when b is 0.50, although the dimensionless thickness a changes from 0.05 to 0.25, the energy loss coefficient j, which is approximately 32.51, and the dimensionless backflow region length l b, which is approximately 3.23, are almost constant. From the above analysis, Reynolds number Re and the dimensionless thickness a hardly affect both the dimensionless backflow region length l b and the energy loss coefficient j in the simulation scope; their impacts on them could be neglected, and then equation (5) can be expressed as l b, j = f (b) ð6þ Figure 2 is drawn using the data in Table 2 when dimensionless thickness a (a = T/D) is 0.10 and Reynolds number Re is , which embodies the relationship between the contraction ratio b and the dimensionless backflow region length l b. If neglecting Figure 2. Relationship between b and l b. Figure 3. Relationship between b and j. the impacts of Reynolds number Re and the dimensionless thickness a on the dimensionless backflow region length l b, the empirical expression of the dimensionless backflow region length l b, by means of fitting the curve in Figure 2, could be obtained l b = 10:29b 2 + 6:96b + 2:41 ð7þ This expression is valid for b = , a = , u =60 and Re = Similarly, Figure 3 is drawn using the data in Table 2 when dimensionless thickness a (a = T/D) is 0.10 and Reynolds number Re is , which embodies the relationship between the contraction ratio b and the energy loss coefficient j. The empirical expression of the energy loss coefficient j if neglecting the impacts of Reynolds number Re and the dimensionless thickness a on it, by means of fitting the curve in Figure 3, could be obtained j = 0:58b 5:67 ð8þ The above expression is valid for b = , a = , u =60 and Re = Figure 4 introduces the turbulence dissipation rate when Reynolds number Re is , dimensionless thickness a (a = T/D) is 0.10, and contraction ratio b is Figure 4 demonstrates that the backflow region after sharp-edged orifice plate due to the sudden reduction and sudden enlargement of the orifice plate is the main original region of the energy dissipation. Figure 5 shows the effects of the dimensionless backflow region length l b on the energy loss coefficient j, which was drawn by means of the data of Table 2. The energy loss coefficient j is, obviously, not bigger than 1.69 when

Wanzheng 5 Figure 4. Turbulence dissipation rate (Re = 1.8310 5, a = 0.10, b = 0.70). Figure 6. Comparison between experiment data and calculated data. Figure 5. Relationship between l b and j.

5 Wanzheng 5 Figure 4. Turbulence dissipation rate (Re = , a = 0.10, b = 0.70). Figure 6. Comparison between experiment data and calculated data. Figure 5. Relationship between l b and j. the dimensionless backflow region length l b is less then 1.42 for dimensionless thickness a (a = T/D) being 0.10, while it increases rapidly when the dimensionless backflow region length l b is bigger than 1.69 for this dimensionless thickness a (a = T/D). It should be noted that the appearance of those results is also related to the dimensionless backflow region height h b. The height increases with the decrease in the contraction ratio b on the basis of h b =(12 b)/2. Since the water volume of the backflow region after the orifice plate has cubic relation of characteristic parameter D, the combination of the backflow region length and height makes this water volume change greatly. Verification In order to verify the rationality of equation (8), the comparison results between model experiment data measured by Zhang and Cai 33 and the data calculated using equation (8) are shown in Figure 6. From Figure 6, it can be seen that the results calculated using equation (8) are approximately equal to those obtained by the experiment, and the relative errors of equation (8) are all less than 10%. Conclusion For a sharp-edged orifice plate energy dissipater, its energy loss coefficient j and its dimensionless backflow region length l b after it are all the function of the contraction ratio b, the dimensionless thickness a, and the Reynolds number Re of the flow on the basis of equation (5). And the effects of Re and a are weak and could be neglected on the j and l b when Re is in the range of The contraction ratio b, which brings about the effects on the energy loss coefficient j through the magnitude and the length of the backflow region, is the key factor that dominates the energy loss coefficient j. The smaller is the contraction ratio b, the bigger is the energy loss coefficient j. The relationship between j and b could be expressed as equation (8). Compared with the numerical simulation results and the model experimental results, the relative errors of equation (8) are all less than 10%. Declaration of conflicting interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Funding This article was funded by CRSRI Open Research Program (Program SN:CKWV /KY) References 1. Xiang T and Cai J-m. Study and practice of interior energy dissipater for flood discharge tunnels. J Water Conserv Hydropower Technol 1999; 30: (in 2. Zhou J, Yang Z and Chen G. Status and challenges of high dam in China. J Hydraul Eng: ASCE 2006; 37: (in 3. Zhang Y, Mao Q, Xiang W, et al. Step-orifice applied in nuclear piping system. Nucl Power Eng 2009; 30: 1 9 (in 4. Piao L, Zhang T, Wang J, et al. Optimization of doublecone orifice rotameter based on CFD. J Tianjin Univ 2012; 45: (in 5. Russell SO and Ball JW. Sudden-enlargement energy dissipater for Mica dam. J Hydr Eng Div: ASCE 1967; 93: Yi C and Zhang L. CFD simulation and experiment research of pipe downstream with orifice and jet impingement. Atom Energ Sci Technol 2012; 46: (in 7. Zhang Y and Li W. Experimental on multiple bubble motion in a wedged orifice flow meter. J Liaoning Tech Univ(Nat Sci) 2012; 31: (in

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