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Experimental and numerical research on portable short-throat flume in the field
Flow Measurement and Instrumentation 47 (2016) 54–61
Contents lists available at ScienceDirect
Flow Measurement and Instrumentation journal homepage: www.elsevier.com/locate/flowmeasinst
Experimental and numerical research on portable short-throat flume in the field Yizhou Xiao a, Wene Wang a,n, Xiaotao Hu a, Yan Zhou b a b
College of Water Resources and Architectural Engineering, Northwest A&F University, Yangling, Shaanxi, PR China Department of Biosystems and Agricultural Engineering, Oklahoma State University, Stillwater, OK 74078-6016, USA
art ic l e i nf o
a b s t r a c t
Article history: Received 9 June 2015 Received in revised form 22 October 2015 Accepted 27 November 2015 Available online 8 December 2015
The use of portable short-throat flume in the field is an emerging technique developed for water discharges measurement of inlet in the field. Based on the principle of critical flow and RNG k–ε threedimensional turbulence model along with the TruVOF technique, experiments and corresponding simulations were performed for 16 working conditions on the 76 mm width flume with discharges up to 40.01 L/s to determine its hydraulic performance. Hydraulic performance of the flume obtained from simulation analyses were later compared with observed results based on time-averaged flow field, flow pattern, Froude number and velocity distribution. Comparison yielded a solid agreement between results from two methods with relative error below 710%. Regression models developed for upstream depth versus discharge under different working conditions were satisfying with the relative error of 9.16%, which met the common requirements of flow measurement in irrigation areas. Compared to the longthroat flume, head loss of portable short-throat flume in the field was significantly less. Further, head loss under the free flow condition was less than that under the submerged flow condition of portable shortthroat flume with a flat base in the field. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Portable short-throat flume in the field Numerical simulation Froude number Velocity Equations of upstream depth versus discharge Head loss
1. Introduction Accurate flow measurement is a fundamental component in the collection, distribution, delivery, and application of water resources [1], especially in irrigation systems. Flow-measuring structures are used for continuous measurement of discharges in open channels [2]. As mentioned by Wang [3], flumes, compared to other existing flow-measuring devices, are more suitable for flow measurement in open channels and easier to be widely applied. Previous researches indicated that the Parshall flume has been investigated extensively based on the experimental data obtained from former researchers. In 1917, Cone [4] first reported the Venturi flume, which consisted of a converging section, a diverging section and a short throat between them. The floor was level and placed at the elevation of the bottom of the channel in which it was set. Parshall [5] developed the Improved Venturi flume, a simpler, less expensive and more accurate flume later known as the Parshall flume. Skogerboe et al. [6,7] conducted experiments on the Parshall flume under free and submerged flow conditions. Wright et al. [8] developed a numerical model to predict the effect n
Corresponding author. E-mail address: [email protected] (W. Wang).
http://dx.doi.org/10.1016/j.flowmeasinst.2015.11.003 0955-5986/& 2015 Elsevier Ltd. All rights reserved.
of fluid viscosity on the depth-discharge relationship. Numerical model successfully validated through experimental data for the flume sizes studied. Cox et al. [1] determined a rating equation applicable to the large Parshall flumes with a supercritical flow. A 1.5 m Parshall flume was tested with discharges up to 0.854 m3/s and Froude number varying from 0.67 to 1.31. Singh et al. [9] fabricated four different sizes of the small Parshall flumes in the laboratory under free flow condition. An accurate equation between discharge and upstream head valid for the different Parshall flume sizes was obtained. On the basis of a brief review of previous studies, it would be say that there is not much work attempt for small size flume or flume set at water inlet in the field, so that water users could not get or control the discharge into the field accurately. The flume, measuring the discharge of flow into the field, needs to meet the requirements of simple structures, cheap prices, a reasonable accuracy and a low head loss [3]. The Parshall flume has lots of advantages, such as a high accuracy and low head loss. However, owing to its high price and complex structure, the Parshall flume is difficult to apply widely on water discharge measurement of water inlet in the field. Thus the Parshall flume is not the optimum choice for water discharge measurement of water inlet in the field. Originated from the Parshall flume developed by Cone [4] and Parshall [5], portable short-throat flume, consisted of a flat-bottom flume with converging, throat and diverging sections, was
Y. Xiao et al. / Flow Measurement and Instrumentation 47 (2016) 54–61
u u, v, w
Nomenclature The following terms are used in this paper Fx, Fy, Fz Fr H h hu hw i, j L Q S
t
body forces, Fx ¼0, Fy ¼0, Fz ¼ ρg (N) Froude number head over the triangular weir (m) depth in cross-section 3 (m) head in upstream cross-section 1 (m) head loss (m) i ¼1, 2, 3; j¼1, 2, 3 distance between section 1 and the control section (mm) discharge through the flume (L/s) dimensionless submergence ratio, S is downstream depth in cross-section 11 divided by upstream depth in cross-Section 3 time (s)
ρ μ k
ε μeff α k, α ε
Gk
flow velocity vectors (m/s) averaged flow velocity components in Cartesian coordinates x, y, and z, respectively (m/s) density of fluid (kg/m3) dynamic viscosity of fluid (N s/m2) turbulence kinetic energy (m2/s2) turbulence dissipation rate (kg m2/s3) effective hydrodynamic viscous coefficient, μeff ¼ μ þ μt , μt ¼ ρCμk2/ε, Cμ ¼ 0.0845 (N s/m2) αk ¼ αε ¼1.39 generation item of turbulence kinetic energy k due to gradient of the averaged flow velocity, ∂u
Gk = μt ( ∂xi + j
C1*ε
C1*ε = C1ε − Eij =
C2ε
55
1 ∂ui ( 2 ∂xj
+
∂uj ∂ui ) ∂xi ∂xj η (1 − η / η0 )
∂uj
1 + βη3
) ∂xi ,
,
C1ε ¼ 1.42,
η0 ¼4.377, β ¼0.012
k
η = (2Eij⋅Eij )1/2 ε ,
C2ε ¼1.68
evaluated by laboratory experiments and FLOW-3D software. Portable short-throat flume was a device for flow-measurement of inlet in the field to control the discharge into the field accurately, which was not affected by type, size and bottom slope of channels.
2. Physical model and experimental setup 2.1. Physical model Portable short-throat flume made from galvanized sheet iron, which consisted of a converging section, a throat section and a diverging section with a flat bottom, was placed at the water inlet of the field in practical application and divided into 11 measuring cross-sections (Table 1) in laboratory experiments to measure hydraulic parameters of flow. Plan-view and profile-view sketches of the flume are illustrated in Fig. 1. The flume had a length of 914 mm and a vertical height of 500 mm, while the width of the throat section was 76 mm, and the side wall was perpendicular to the bottom of the flume. 2.2. Experimental setup and methods The experimental setup contained a pumping station, an electromagnetic flowmeter, water supply pipes, a water valve, a stabilization pond, portable short-throat flume, a backwater drainage channel and a 90° V-notch weir (Fig. 2). The flume was placed at the stabilization pond in this experimental setup similar to the actual working condition, and there was a flow condition like a water storage pit in front of the water inlet in the field. Owing that cross-section area of water inlet in the field was much larger than the entrance of the flume, water in front of the flume entrance flowed smoothly. Therefore, the cross-section area in front of the Table 1 Distance from first section to each measuring cross-section. Section number
Distance from first section (mm)
Section number
Length from first section (mm)
1 2 3 4 5 6
0.00 114.25 228.50 342.75 457.00 495.00
7 8 9 10 11
533.00 571.00 609.00 761.50 914.00
Fig. 1. Plan-view and profile-view sketches and cross sections of portable shortthroat flume (Unit: mm).
flume was much larger than the entrance area of the flume in the experimental setup, being consistent with actual flow conditions. Experience showed that flow capacity of the ditch in the irrigated areas ranged from approximately 10 L/s to 50 L/s [3]. The actual discharge in experiments was measured by the 90° V-notch weir using empirical Eq. (1) [10,11]. Depths of cross-sections were recorded by point gauge with resolution of 0.1 mm. 16 laboratory experiments under free flow and submerged flow conditions were conducted for the purpose of evaluating hydraulic performance of portable short-throat flume. Water was pumped into the flume, flowed through the flume and then entered the backwater drainage channel. Once flow stabilized, discharges were measured by the 90° V-notch weir [10,11], and the depths of each flume crosssection were recorded.
56
Y. Xiao et al. / Flow Measurement and Instrumentation 47 (2016) 54–61
Fig. 2. Sketch of experimental setup.
Q = 1.343H 2.47 × 1000
(1)
3. Numerical approaches 3.1. Governing equations and turbulence model Numerical simulations were performed with the CFD (Computational Fluid Dynamics) software FLOW-3D. The continuity and Navier–Stokes equations for incompressible, viscous flow are given by Eqs. (2) and (3) [12,13].
∂ρ ∂(ρu) ∂(ρv) ∂(ρw ) + + + =0 ∂t ∂x ∂y ∂z
k–ε three-dimensional turbulence model was employed, where k is the turbulence kinetic energy (Eq. (4)), ε is the turbulence dissipation rate (Eq. (5)).
∂ ( ρkui ) ∂(ρk ) ∂ ⎡ ∂k ⎤ ⎢ αk μeff ⎥ + Gk + ρε + = ∂t ∂xi ∂xj ⎣ ∂xj ⎦
(4)
∂( ρεui ) ∂(ρε) ε2 ∂ ⎡ ∂ε ⎤ C1*ε ε ⎢ αε μeff ⎥+ Gk − C2ε ρ + = k k ∂t ∂xi ∂xj ⎣ ∂xj ⎦
(5)
3.2. Description of the model
(2)
∂(ρu) ∂p + div (ρuu) = − + div (μ grad u) + Fx ∂t ∂x
(3a)
∂(ρv) ∂p + div (ρvu) = − + div (μ gradv) + Fy ∂t ∂y
(3b)
According to the actual size of the flume and experimental setup, three-dimensional geometrical models were developed with the software AutoCAD. To steady and smooth the upstream flow, a pool of 2.0 m long and 0.5 m deep was connected to the flume entrance, which was consistent with the actual working condition. A backwater drainage channel of 1.0 m wide was connected to the outlet of the flume. 3.3. Mesh generation
∂(ρw ) ∂p + div (ρw u) = − + div (μ gradw ) + Fz ∂t ∂z
(3c)
Here, the concepts of divergence and gradient are introduced as: div(a)¼ ∂ ax/∂ x þ ∂ ay/∂ yþ ∂ az/∂ z, grad(b) ¼ ∂ (b)/∂ x þ ∂ (b)/∂ yþ ∂ (b)/ ∂ z. The finite difference method was adopted to solve the governing equations with the second-order up-wind scheme. TruVOF method used in FLOW-3D was chosen, which only computed the unit of the fluid, not the unit of the air, to reduce time of convergence and describe the shape of the free surface graphically. In order to allow the closure of the Navier–Stokes equations, the RNG
Meshes were established for flow domain by FAVOR (Fractional Area Volume Obstacle Representation) method that generated grids. The size of a grid was set at 0.02 m long, 0.02 m wide, 0.02 m high, and the number of all the grids is 543,000. FAVOR method was employed by FLOW-3D to generate grids on the model, which used the finite difference method to simulate complicated models. Further, FAVOR method used fewer hexahedron grid units, in terms of the proportion of flow domain, to smooth and eliminate the rough regions, which builds a mesh model without any distortion.
Y. Xiao et al. / Flow Measurement and Instrumentation 47 (2016) 54–61
57
Fig. 3. Entire model geometry and boundary conditions.
3.4. Boundary conditions
4.1. Analysis of the simulated value compared with the experimental results
through the supply pipes into the stabilization pond, and went through portable short-throat flume and finally was drained to the backwater drainage channel. As water kept on flowing in the system, water surface in the stabilization pond and portable shortthroat flume rose slowly to a steady level, and now the flow field was approximately steady flow. For flow pattern in portable shortthroat flume, parameters comparison between observations and simulations, especially the depths of flow, indicated a solid agreement between numerical predictions and experimental results. The average relative error between experimental and numerical results was 1.72%, and the maximum relative error was 9.21%, which met the common requirement of accuracy in the most irrigated areas [3]. Flow pattern in portable short-throat flume with the open channel flow discharge of 10.67 L/s under free flow condition is illustrated in Fig. 4. FLOW-3D and TruVOF method were employed to simulate truthfully the characteristics of flow through portable short-throat flume.
4.1.1. Analysis of flow pattern Flow pattern was observed through experiments and simulations. When the upstream valve was opened, water flowed
4.1.2. Water surface profiles Water surface profile is an important parameter to describe the flow pattern. Fig. 5 displays the water surface profiles along the
Fig. 3 shows the boundary conditions of the mathematic model. The inlet boundary was a specified volumetric flow rate from the whole open area of the channel inlet at the upstream side, with auto-adjusted fluid height. An outflow-outlet condition was positioned at the downstream backwater drainage channel exit. The bottom of the model and the side walls were set as a wall boundary condition. What's more, the air inlet at the top of the model was set as a symmetry boundary condition, which was default that no fluid flows through the boundary.
4. Results and analyses
Fig. 4. Comparison of measured and simulated flow patterns (from the downstream view). (a) Measured flow pattern, (b) simulated flow pattern, (c) profile of simulated flow pattern.
58
Y. Xiao et al. / Flow Measurement and Instrumentation 47 (2016) 54–61
Fig. 5. Variation of the water surface profiles along the centerline of the flume. (a) Free flow condition, (b) submerged flow condition.
centerline of the flume measured under free flow condition and submerged flow condition. Water flowed smoothly through converging section of portable short-throat flume, and began to descend slowly near throat section. As a result of lateral contraction of throat section, there was a sudden drop of water surface profile, causing a change of flow state from subcritical to supercritical. Then water discharged through diverging section to the backwater drainage channel. There were hydraulic jumps at the end of diverging section under the submerged flow condition, which caused that water level at the converging section and diverging section under submerged flow condition was higher than that under free flow condition in the same discharge. The depth values predicted by FLOW-3D software agreed well with the experimental results with an error smaller than 7 10%.
the experiments. Both experimental and predicted Froude numbers along the center line of the flume at 21.44 L/s are shown in Fig. 6. It is clearly illustrated in Fig. 6 that Froude numbers went up as flow rate increase under free flow condition. Comparatively under submerged flow condition, Froude number increased at first, peaked at the throat section, and decreased to less than 1. Froude numbers at the converging section was less than 0.5, which met the requirement of Froude number in flow measurement [14]. At the throat section, the state of flow changed from subcritical to supercritical, and the location of critical flow with submerged flow located more towards the downstream direction than that of free flow. 4.3. Distribution of velocity
4.2. Froude number Froude number Fr is a dimensionless parameter used to discriminate flow regime, flow is considered subcritical when Froude number is less than 1, supercritical when Froude number is greater than 1, and critical when Froude number is 1 [10]. Froude numbers observed from experiments on 16 discharges coincided closely with estimations from FLOW-3D model. Froude number is the value calculated by the depth of each measuring cross-section in
The development of cross-sectional velocity distributions is presented in Fig. 7. The accuracy between experimental and simulated values with free-flow and submerged-flow were gained as 7.09% and 8.65% to the maximum respectively. These values presented a satisfactory agreement between experimental and simulated results. At the converging section, velocity increased at the converging section, and kept increasing at the throat section. Then, velocity peaked in the latter part of the throat section.
Fig. 6. Fr variation along the flow of portable short-throat flume. (a) Free flow condition, (b) submerged flow condition.
Y. Xiao et al. / Flow Measurement and Instrumentation 47 (2016) 54–61
59
Fig. 7. Development of cross-sectional velocity distributions (Unit: m/s).
Finally, velocity kept increasing under free flow condition, and decreased rapidly under submerged flow condition. As seen in Fig. 7, velocity near the bottom and center of the cross section was much higher.
4.4. Equations of upstream depth versus discharge By the contraction of throat section, the occurrence of critical flow plays an important role in flow measurement. According to
60
Y. Xiao et al. / Flow Measurement and Instrumentation 47 (2016) 54–61
Table 2 Head loss. Outflow condition
Measured discharge (L/s)
hu (m)
hw (m)
hw/hu (%)
Free flow
6.77 10.67 14.41 21.44 25.17 31.83 35.91 40.01
0.1387 0.1888 0.2276 0.2898 0.3251 0.3748 0.3964 0.4189
0.0057 0.0127 0.0195 0.0253 0.0297 0.0397 0.0429 0.0436
4.11 6.73 8.57 8.73 9.14 10.59 10.82 10.41
Submerged flow
6.77 10.67 14.41 21.44 25.17 31.83 35.91 40.01
0.1480 0.1929 0.2265 0.2960 0.3148 0.4003 0.4358 0.4567
0.0165 0.0226 0.0292 0.0347 0.0362 0.0398 0.0443 0.0570
11.15 11.71 12.89 11.72 11.50 9.94 10.17 12.48
energy consumed by hydraulic jumps downstream of the flume exit. Therefore, the head loss of portable short-throat flume under free flow condition, due to excluding the energy consumed by hydraulic jumps downstream of the flume exit, was less than the head loss under submerged flow condition.
Fig. 8. Comparison of discharges values.
the correlations between discharges and depths at each upstream cross-section in converging section, depth in cross-Section 3 showed the most solid correlation with the discharge with a correlation coefficient of 0.9859. Thus depth in cross-Section 3 was chosen to calculate discharge. An equation of upstream depth versus discharge with free flow is given by Eq. (6), and an equation of upstream depth and submergence ratio versus discharge with submerged flow is given by Eq. (7).
Q = 168.2h1.6182
(6)
Q = 405.8S 1 − S h1.5445
(7)
As shown in Fig. 8, the measured and calculated discharge values were in reasonable agreement with 710% errors. Additionally, the maximum error of calculated discharge using depth-discharge equation with free flow and submerged flow were 3.97% and 9.16% respectively, which met the common requirement of the accuracy in the irrigated areas [3]. 4.5. Analysis of the head loss The head loss of this flume was defined as head difference between upstream cross-Section 1 and downstream cross-section 11. The head included water level head, pressure head and velocity head. The head losses under different working conditions were calculated in Table 2. As shown in Table 2, the maximum head loss accounts for 12.89% of the total head upstream, considerably less than that of the long-throat flume [15]. Thus portable short-throat flume was more suitable for flow measurement in the field than the long-throat flume. According to Table 2, it was concluded that head loss in freeflow condition was less than that of submerged flow condition. However, the conclusion was different from the conclusion concluded by Li [16]. The reason for the difference is that the head loss of the Parshall flume studied by Li, which was set in the open channel, was the difference between the head at a section 1.10 m upstream of the flume entrance and the head at a section 2.10 m downstream of the flume exit. The location of hydraulic jumps was in the channel downstream with free flow condition, not in the flume, which means that the head loss studied by Li included the
5. Conclusions In the present study, the FLOW-3D analyses of portable shortthroat flume have been performed to investigate the parameters, such as Froude number, velocity and the head loss. The three-dimensional turbulence model RNG k–ε along with the TruVOF method enabled one to reproduce the characteristics of flow through portable short-throat flume. And the results of the numerical model agreed well with the experimental results related to the flow pattern, water surface profiles and velocity distributions along the flume centerline. Equations of upstream depth versus discharge under free flow and submerged flow working conditions were fitted out by regression analyses with a deviation of 710%, which met the requirement of flow measurement with discharges up to 40 L/s in the irrigated areas. Additionally, compared to the long-throat flume, the head loss of portable shortthroat flume in the field was less. All in all, it is concluded that portable short-throat flume has the advantages of simple structure, low prices and high accuracy, plus its application is less dependent on type, size and bottom slope of channels. The present results in this study can encourage further the researchers in making new different types or sizes of flumes located in the field.
Acknowledgment The authors would like to acknowledge the financial supports given by the Special Fund for Agro-scientific Research in the Public Interest of China (201503125) and the National Nature Science Foundation of China (51179163).
References [1] A.L. Cox, C.I. Thornton, S.R. Abt, Supercritical flow measurement using a large Parshall flume, J. Irrig. Drain. Eng. ASCE 139 (8) (2013) 655–662. [2] W. Boiten, Flow-measuring structures, Flow Meas. Instrum. 4 (1) (1993) 17–24. [3] C.D. Wang, Water Measurement Technique and Measure, Water & Power Press, Beijing, China, 2005.
Y. Xiao et al. / Flow Measurement and Instrumentation 47 (2016) 54–61
[4] V.M. Cone, The Venturi Flume, J. Agric. Res. 9 (4) (1917) 115–129. [5] R.L. Parshall, The Improved Venturi Flume, Bulletin 336, Colorado Experiment Station, Colorado Agricultural College, Fort Collins, CO, 1928. [6] G.V. Skogerboe, M.L. Hyatt, J.D. England, J.R. Johnson, Measuring Water with Parshall Flumes, Reports, 1966. [7] G.V. Skogerboe, M.L. Hyatt, K.O. Eggleston, Design and Calibration of Submerged Open Channel Flow Measurement Structures: Part 1 – Submerged Flow, Reports, 1967, Paper 93. [8] S.J. Wright, B.P. Tullis, T.M. Long, Recalibration of Parshall flumes at low discharges, J. Irrig. Drain. Eng. ASCE 120 (2) (1994) 348–362. [9] J. Singh, S.K. Mittal, H.L. Tiwari, Discharge relation for small Parshall flume in free flow condition, Int. J. Res. Eng. Technol. 3 (4) (2014) 317–321. [10] H.X. Lv, G.X. Pei, L.X. Yang, Hydraulics, Agriculture Press, Beijing, China, 2011. [11] U.S Department of the Interior Bureau of Reclamation, Water Measurement Manual, U.S. Government Printing Office, Washington, D.C., 2001.
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[12] A.S. Ramamurthy, R. Tadayon, Numerical simulation of flows in cut-throat flumes, J. Irrig. Drain. Eng. ASCE 134 (6) (2008) 857–860. [13] M.C. Aydin, M.E. Emiroglu, Determination of capacity of labyrinth side weir by CFD, Flow Meas. Instrum. 29 (2013) 1–8. [14] J.M. Liu, W.E. Wang, X.T. Hu, Numerical simulation of water-measuring pillar with round head in the U-shaped channel, J. China Agric. Univ. 19 (1) (2014) 168–174. [15] G.J. Li, X.Y. Mou, J.S. Li, L. Wang, X. Dai, Research on the hydraulic characteristics of U-shaped channel of straight wall tanks, China Rural Water Hydropower 5 (2010) 124–127. [16] J. Li, H.X. Lv, W.X. Xu, Experimental study on hydraulic characteristics of Parshall flume, Water Sav. Irrig. 12 (2009) 45–47.
Contents lists available at ScienceDirect
Flow Measurement and Instrumentation journal homepage: www.elsevier.com/locate/flowmeasinst
Experimental and numerical research on portable short-throat flume in the field Yizhou Xiao a, Wene Wang a,n, Xiaotao Hu a, Yan Zhou b a b
College of Water Resources and Architectural Engineering, Northwest A&F University, Yangling, Shaanxi, PR China Department of Biosystems and Agricultural Engineering, Oklahoma State University, Stillwater, OK 74078-6016, USA
art ic l e i nf o
a b s t r a c t
Article history: Received 9 June 2015 Received in revised form 22 October 2015 Accepted 27 November 2015 Available online 8 December 2015
The use of portable short-throat flume in the field is an emerging technique developed for water discharges measurement of inlet in the field. Based on the principle of critical flow and RNG k–ε threedimensional turbulence model along with the TruVOF technique, experiments and corresponding simulations were performed for 16 working conditions on the 76 mm width flume with discharges up to 40.01 L/s to determine its hydraulic performance. Hydraulic performance of the flume obtained from simulation analyses were later compared with observed results based on time-averaged flow field, flow pattern, Froude number and velocity distribution. Comparison yielded a solid agreement between results from two methods with relative error below 710%. Regression models developed for upstream depth versus discharge under different working conditions were satisfying with the relative error of 9.16%, which met the common requirements of flow measurement in irrigation areas. Compared to the longthroat flume, head loss of portable short-throat flume in the field was significantly less. Further, head loss under the free flow condition was less than that under the submerged flow condition of portable shortthroat flume with a flat base in the field. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Portable short-throat flume in the field Numerical simulation Froude number Velocity Equations of upstream depth versus discharge Head loss
1. Introduction Accurate flow measurement is a fundamental component in the collection, distribution, delivery, and application of water resources [1], especially in irrigation systems. Flow-measuring structures are used for continuous measurement of discharges in open channels [2]. As mentioned by Wang [3], flumes, compared to other existing flow-measuring devices, are more suitable for flow measurement in open channels and easier to be widely applied. Previous researches indicated that the Parshall flume has been investigated extensively based on the experimental data obtained from former researchers. In 1917, Cone [4] first reported the Venturi flume, which consisted of a converging section, a diverging section and a short throat between them. The floor was level and placed at the elevation of the bottom of the channel in which it was set. Parshall [5] developed the Improved Venturi flume, a simpler, less expensive and more accurate flume later known as the Parshall flume. Skogerboe et al. [6,7] conducted experiments on the Parshall flume under free and submerged flow conditions. Wright et al. [8] developed a numerical model to predict the effect n
Corresponding author. E-mail address: [email protected] (W. Wang).
http://dx.doi.org/10.1016/j.flowmeasinst.2015.11.003 0955-5986/& 2015 Elsevier Ltd. All rights reserved.
of fluid viscosity on the depth-discharge relationship. Numerical model successfully validated through experimental data for the flume sizes studied. Cox et al. [1] determined a rating equation applicable to the large Parshall flumes with a supercritical flow. A 1.5 m Parshall flume was tested with discharges up to 0.854 m3/s and Froude number varying from 0.67 to 1.31. Singh et al. [9] fabricated four different sizes of the small Parshall flumes in the laboratory under free flow condition. An accurate equation between discharge and upstream head valid for the different Parshall flume sizes was obtained. On the basis of a brief review of previous studies, it would be say that there is not much work attempt for small size flume or flume set at water inlet in the field, so that water users could not get or control the discharge into the field accurately. The flume, measuring the discharge of flow into the field, needs to meet the requirements of simple structures, cheap prices, a reasonable accuracy and a low head loss [3]. The Parshall flume has lots of advantages, such as a high accuracy and low head loss. However, owing to its high price and complex structure, the Parshall flume is difficult to apply widely on water discharge measurement of water inlet in the field. Thus the Parshall flume is not the optimum choice for water discharge measurement of water inlet in the field. Originated from the Parshall flume developed by Cone [4] and Parshall [5], portable short-throat flume, consisted of a flat-bottom flume with converging, throat and diverging sections, was
Y. Xiao et al. / Flow Measurement and Instrumentation 47 (2016) 54–61
u u, v, w
Nomenclature The following terms are used in this paper Fx, Fy, Fz Fr H h hu hw i, j L Q S
t
body forces, Fx ¼0, Fy ¼0, Fz ¼ ρg (N) Froude number head over the triangular weir (m) depth in cross-section 3 (m) head in upstream cross-section 1 (m) head loss (m) i ¼1, 2, 3; j¼1, 2, 3 distance between section 1 and the control section (mm) discharge through the flume (L/s) dimensionless submergence ratio, S is downstream depth in cross-section 11 divided by upstream depth in cross-Section 3 time (s)
ρ μ k
ε μeff α k, α ε
Gk
flow velocity vectors (m/s) averaged flow velocity components in Cartesian coordinates x, y, and z, respectively (m/s) density of fluid (kg/m3) dynamic viscosity of fluid (N s/m2) turbulence kinetic energy (m2/s2) turbulence dissipation rate (kg m2/s3) effective hydrodynamic viscous coefficient, μeff ¼ μ þ μt , μt ¼ ρCμk2/ε, Cμ ¼ 0.0845 (N s/m2) αk ¼ αε ¼1.39 generation item of turbulence kinetic energy k due to gradient of the averaged flow velocity, ∂u
Gk = μt ( ∂xi + j
C1*ε
C1*ε = C1ε − Eij =
C2ε
55
1 ∂ui ( 2 ∂xj
+
∂uj ∂ui ) ∂xi ∂xj η (1 − η / η0 )
∂uj
1 + βη3
) ∂xi ,
,
C1ε ¼ 1.42,
η0 ¼4.377, β ¼0.012
k
η = (2Eij⋅Eij )1/2 ε ,
C2ε ¼1.68
evaluated by laboratory experiments and FLOW-3D software. Portable short-throat flume was a device for flow-measurement of inlet in the field to control the discharge into the field accurately, which was not affected by type, size and bottom slope of channels.
2. Physical model and experimental setup 2.1. Physical model Portable short-throat flume made from galvanized sheet iron, which consisted of a converging section, a throat section and a diverging section with a flat bottom, was placed at the water inlet of the field in practical application and divided into 11 measuring cross-sections (Table 1) in laboratory experiments to measure hydraulic parameters of flow. Plan-view and profile-view sketches of the flume are illustrated in Fig. 1. The flume had a length of 914 mm and a vertical height of 500 mm, while the width of the throat section was 76 mm, and the side wall was perpendicular to the bottom of the flume. 2.2. Experimental setup and methods The experimental setup contained a pumping station, an electromagnetic flowmeter, water supply pipes, a water valve, a stabilization pond, portable short-throat flume, a backwater drainage channel and a 90° V-notch weir (Fig. 2). The flume was placed at the stabilization pond in this experimental setup similar to the actual working condition, and there was a flow condition like a water storage pit in front of the water inlet in the field. Owing that cross-section area of water inlet in the field was much larger than the entrance of the flume, water in front of the flume entrance flowed smoothly. Therefore, the cross-section area in front of the Table 1 Distance from first section to each measuring cross-section. Section number
Distance from first section (mm)
Section number
Length from first section (mm)
1 2 3 4 5 6
0.00 114.25 228.50 342.75 457.00 495.00
7 8 9 10 11
533.00 571.00 609.00 761.50 914.00
Fig. 1. Plan-view and profile-view sketches and cross sections of portable shortthroat flume (Unit: mm).
flume was much larger than the entrance area of the flume in the experimental setup, being consistent with actual flow conditions. Experience showed that flow capacity of the ditch in the irrigated areas ranged from approximately 10 L/s to 50 L/s [3]. The actual discharge in experiments was measured by the 90° V-notch weir using empirical Eq. (1) [10,11]. Depths of cross-sections were recorded by point gauge with resolution of 0.1 mm. 16 laboratory experiments under free flow and submerged flow conditions were conducted for the purpose of evaluating hydraulic performance of portable short-throat flume. Water was pumped into the flume, flowed through the flume and then entered the backwater drainage channel. Once flow stabilized, discharges were measured by the 90° V-notch weir [10,11], and the depths of each flume crosssection were recorded.
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Fig. 2. Sketch of experimental setup.
Q = 1.343H 2.47 × 1000
(1)
3. Numerical approaches 3.1. Governing equations and turbulence model Numerical simulations were performed with the CFD (Computational Fluid Dynamics) software FLOW-3D. The continuity and Navier–Stokes equations for incompressible, viscous flow are given by Eqs. (2) and (3) [12,13].
∂ρ ∂(ρu) ∂(ρv) ∂(ρw ) + + + =0 ∂t ∂x ∂y ∂z
k–ε three-dimensional turbulence model was employed, where k is the turbulence kinetic energy (Eq. (4)), ε is the turbulence dissipation rate (Eq. (5)).
∂ ( ρkui ) ∂(ρk ) ∂ ⎡ ∂k ⎤ ⎢ αk μeff ⎥ + Gk + ρε + = ∂t ∂xi ∂xj ⎣ ∂xj ⎦
(4)
∂( ρεui ) ∂(ρε) ε2 ∂ ⎡ ∂ε ⎤ C1*ε ε ⎢ αε μeff ⎥+ Gk − C2ε ρ + = k k ∂t ∂xi ∂xj ⎣ ∂xj ⎦
(5)
3.2. Description of the model
(2)
∂(ρu) ∂p + div (ρuu) = − + div (μ grad u) + Fx ∂t ∂x
(3a)
∂(ρv) ∂p + div (ρvu) = − + div (μ gradv) + Fy ∂t ∂y
(3b)
According to the actual size of the flume and experimental setup, three-dimensional geometrical models were developed with the software AutoCAD. To steady and smooth the upstream flow, a pool of 2.0 m long and 0.5 m deep was connected to the flume entrance, which was consistent with the actual working condition. A backwater drainage channel of 1.0 m wide was connected to the outlet of the flume. 3.3. Mesh generation
∂(ρw ) ∂p + div (ρw u) = − + div (μ gradw ) + Fz ∂t ∂z
(3c)
Here, the concepts of divergence and gradient are introduced as: div(a)¼ ∂ ax/∂ x þ ∂ ay/∂ yþ ∂ az/∂ z, grad(b) ¼ ∂ (b)/∂ x þ ∂ (b)/∂ yþ ∂ (b)/ ∂ z. The finite difference method was adopted to solve the governing equations with the second-order up-wind scheme. TruVOF method used in FLOW-3D was chosen, which only computed the unit of the fluid, not the unit of the air, to reduce time of convergence and describe the shape of the free surface graphically. In order to allow the closure of the Navier–Stokes equations, the RNG
Meshes were established for flow domain by FAVOR (Fractional Area Volume Obstacle Representation) method that generated grids. The size of a grid was set at 0.02 m long, 0.02 m wide, 0.02 m high, and the number of all the grids is 543,000. FAVOR method was employed by FLOW-3D to generate grids on the model, which used the finite difference method to simulate complicated models. Further, FAVOR method used fewer hexahedron grid units, in terms of the proportion of flow domain, to smooth and eliminate the rough regions, which builds a mesh model without any distortion.
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Fig. 3. Entire model geometry and boundary conditions.
3.4. Boundary conditions
4.1. Analysis of the simulated value compared with the experimental results
through the supply pipes into the stabilization pond, and went through portable short-throat flume and finally was drained to the backwater drainage channel. As water kept on flowing in the system, water surface in the stabilization pond and portable shortthroat flume rose slowly to a steady level, and now the flow field was approximately steady flow. For flow pattern in portable shortthroat flume, parameters comparison between observations and simulations, especially the depths of flow, indicated a solid agreement between numerical predictions and experimental results. The average relative error between experimental and numerical results was 1.72%, and the maximum relative error was 9.21%, which met the common requirement of accuracy in the most irrigated areas [3]. Flow pattern in portable short-throat flume with the open channel flow discharge of 10.67 L/s under free flow condition is illustrated in Fig. 4. FLOW-3D and TruVOF method were employed to simulate truthfully the characteristics of flow through portable short-throat flume.
4.1.1. Analysis of flow pattern Flow pattern was observed through experiments and simulations. When the upstream valve was opened, water flowed
4.1.2. Water surface profiles Water surface profile is an important parameter to describe the flow pattern. Fig. 5 displays the water surface profiles along the
Fig. 3 shows the boundary conditions of the mathematic model. The inlet boundary was a specified volumetric flow rate from the whole open area of the channel inlet at the upstream side, with auto-adjusted fluid height. An outflow-outlet condition was positioned at the downstream backwater drainage channel exit. The bottom of the model and the side walls were set as a wall boundary condition. What's more, the air inlet at the top of the model was set as a symmetry boundary condition, which was default that no fluid flows through the boundary.
4. Results and analyses
Fig. 4. Comparison of measured and simulated flow patterns (from the downstream view). (a) Measured flow pattern, (b) simulated flow pattern, (c) profile of simulated flow pattern.
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Fig. 5. Variation of the water surface profiles along the centerline of the flume. (a) Free flow condition, (b) submerged flow condition.
centerline of the flume measured under free flow condition and submerged flow condition. Water flowed smoothly through converging section of portable short-throat flume, and began to descend slowly near throat section. As a result of lateral contraction of throat section, there was a sudden drop of water surface profile, causing a change of flow state from subcritical to supercritical. Then water discharged through diverging section to the backwater drainage channel. There were hydraulic jumps at the end of diverging section under the submerged flow condition, which caused that water level at the converging section and diverging section under submerged flow condition was higher than that under free flow condition in the same discharge. The depth values predicted by FLOW-3D software agreed well with the experimental results with an error smaller than 7 10%.
the experiments. Both experimental and predicted Froude numbers along the center line of the flume at 21.44 L/s are shown in Fig. 6. It is clearly illustrated in Fig. 6 that Froude numbers went up as flow rate increase under free flow condition. Comparatively under submerged flow condition, Froude number increased at first, peaked at the throat section, and decreased to less than 1. Froude numbers at the converging section was less than 0.5, which met the requirement of Froude number in flow measurement [14]. At the throat section, the state of flow changed from subcritical to supercritical, and the location of critical flow with submerged flow located more towards the downstream direction than that of free flow. 4.3. Distribution of velocity
4.2. Froude number Froude number Fr is a dimensionless parameter used to discriminate flow regime, flow is considered subcritical when Froude number is less than 1, supercritical when Froude number is greater than 1, and critical when Froude number is 1 [10]. Froude numbers observed from experiments on 16 discharges coincided closely with estimations from FLOW-3D model. Froude number is the value calculated by the depth of each measuring cross-section in
The development of cross-sectional velocity distributions is presented in Fig. 7. The accuracy between experimental and simulated values with free-flow and submerged-flow were gained as 7.09% and 8.65% to the maximum respectively. These values presented a satisfactory agreement between experimental and simulated results. At the converging section, velocity increased at the converging section, and kept increasing at the throat section. Then, velocity peaked in the latter part of the throat section.
Fig. 6. Fr variation along the flow of portable short-throat flume. (a) Free flow condition, (b) submerged flow condition.
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Fig. 7. Development of cross-sectional velocity distributions (Unit: m/s).
Finally, velocity kept increasing under free flow condition, and decreased rapidly under submerged flow condition. As seen in Fig. 7, velocity near the bottom and center of the cross section was much higher.
4.4. Equations of upstream depth versus discharge By the contraction of throat section, the occurrence of critical flow plays an important role in flow measurement. According to
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Table 2 Head loss. Outflow condition
Measured discharge (L/s)
hu (m)
hw (m)
hw/hu (%)
Free flow
6.77 10.67 14.41 21.44 25.17 31.83 35.91 40.01
0.1387 0.1888 0.2276 0.2898 0.3251 0.3748 0.3964 0.4189
0.0057 0.0127 0.0195 0.0253 0.0297 0.0397 0.0429 0.0436
4.11 6.73 8.57 8.73 9.14 10.59 10.82 10.41
Submerged flow
6.77 10.67 14.41 21.44 25.17 31.83 35.91 40.01
0.1480 0.1929 0.2265 0.2960 0.3148 0.4003 0.4358 0.4567
0.0165 0.0226 0.0292 0.0347 0.0362 0.0398 0.0443 0.0570
11.15 11.71 12.89 11.72 11.50 9.94 10.17 12.48
energy consumed by hydraulic jumps downstream of the flume exit. Therefore, the head loss of portable short-throat flume under free flow condition, due to excluding the energy consumed by hydraulic jumps downstream of the flume exit, was less than the head loss under submerged flow condition.
Fig. 8. Comparison of discharges values.
the correlations between discharges and depths at each upstream cross-section in converging section, depth in cross-Section 3 showed the most solid correlation with the discharge with a correlation coefficient of 0.9859. Thus depth in cross-Section 3 was chosen to calculate discharge. An equation of upstream depth versus discharge with free flow is given by Eq. (6), and an equation of upstream depth and submergence ratio versus discharge with submerged flow is given by Eq. (7).
Q = 168.2h1.6182
(6)
Q = 405.8S 1 − S h1.5445
(7)
As shown in Fig. 8, the measured and calculated discharge values were in reasonable agreement with 710% errors. Additionally, the maximum error of calculated discharge using depth-discharge equation with free flow and submerged flow were 3.97% and 9.16% respectively, which met the common requirement of the accuracy in the irrigated areas [3]. 4.5. Analysis of the head loss The head loss of this flume was defined as head difference between upstream cross-Section 1 and downstream cross-section 11. The head included water level head, pressure head and velocity head. The head losses under different working conditions were calculated in Table 2. As shown in Table 2, the maximum head loss accounts for 12.89% of the total head upstream, considerably less than that of the long-throat flume [15]. Thus portable short-throat flume was more suitable for flow measurement in the field than the long-throat flume. According to Table 2, it was concluded that head loss in freeflow condition was less than that of submerged flow condition. However, the conclusion was different from the conclusion concluded by Li [16]. The reason for the difference is that the head loss of the Parshall flume studied by Li, which was set in the open channel, was the difference between the head at a section 1.10 m upstream of the flume entrance and the head at a section 2.10 m downstream of the flume exit. The location of hydraulic jumps was in the channel downstream with free flow condition, not in the flume, which means that the head loss studied by Li included the
5. Conclusions In the present study, the FLOW-3D analyses of portable shortthroat flume have been performed to investigate the parameters, such as Froude number, velocity and the head loss. The three-dimensional turbulence model RNG k–ε along with the TruVOF method enabled one to reproduce the characteristics of flow through portable short-throat flume. And the results of the numerical model agreed well with the experimental results related to the flow pattern, water surface profiles and velocity distributions along the flume centerline. Equations of upstream depth versus discharge under free flow and submerged flow working conditions were fitted out by regression analyses with a deviation of 710%, which met the requirement of flow measurement with discharges up to 40 L/s in the irrigated areas. Additionally, compared to the long-throat flume, the head loss of portable shortthroat flume in the field was less. All in all, it is concluded that portable short-throat flume has the advantages of simple structure, low prices and high accuracy, plus its application is less dependent on type, size and bottom slope of channels. The present results in this study can encourage further the researchers in making new different types or sizes of flumes located in the field.
Acknowledgment The authors would like to acknowledge the financial supports given by the Special Fund for Agro-scientific Research in the Public Interest of China (201503125) and the National Nature Science Foundation of China (51179163).
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