Experimental and Numerical Investigations of Hydraulics in Water Intake with Stop-Log Gate

: A stop-log gate, installed in water intake of hydropower project, has become an e ﬀ ective facility in achieving selective withdrawal and temperature control for the sake of beneﬁting downstream ecosystems. Hence, it is of great importance to comprehensively explore the water intake hydraulics with the gate, not limited to some speciﬁc case studies. This study deals, through laboratory experiments and numerical simulations, with ﬂow features of such a gate-functioned intake. The physical model test is used to validate the numerical simulation. Subsequently, a series of numerical cases considering di ﬀ erent hydraulic and geometric conditions are performed to help look into the behaviors. Particular attention is paid to the ﬂow regimes, head loss and ﬂow velocity distributions. The results showcase the e ﬀ ect of the gate on the intake ﬂow regime, and in terms of head loss and ﬂow velocity distribution, the inﬂuences of the upstream water head, intake chamber width and withdrawal depth are revealed in detail. An empirical expression, with regard to the coe ﬃ cient of head loss, is derived and validated by data from the available literature. Moreover, it is found that the maximum velocity at trash rack section is dependent exclusively on the relative withdrawal depth and always occurs at a certain height range above the gate. These results may provide a meaningful reference for the research of water intake with similar situations. effects in our study subjected to 1:40, are negligibly small. The model consists of a model reservoir, a selective withdrawal intake with a stop-log gate and a connecting tunnel.


Introduction
In the past decades, large quantities of hydropower stations and man-made reservoirs have been constructed to achieve efficient utilization of water resources. However, these infrastructures are inevitably destroying the balance of reservoir ecology and surface runoff [1]. Most reservoirs with a large depth are typically temperature stratified. As a result, temperature variance of reservoirs significantly affects the downstream ecosystem, ecological diversity and agricultural irrigation [2][3][4][5]. Therefore, the temperature management has been a great concern for designers and operators [6,7]. To this end, selective water withdrawal from different depths of a reservoir is widely adopted, and different facilities are developed to achieve the selective withdrawal, e.g., the stop-log gate and the temperature-control curtain [8,9].
Stop-log gates are originally designed as typical closure systems for dewater spillway gates in many dams [10]. At present, they are employed for water intake to achieve selective withdrawal and mitigate the outflow temperature problem in many hydropower projects, e.g., Jingping-I, Guangzhao, Baihetan, Nuozhadu, etc. [11]. In the vicinity of the water intake, a stop-log gate forces all released

Theoretical Considerations
To achieve the water withdrawal from different layers, a stop-log gate with adjustable height is designed. Figure 1 shows the sketch of the intake geometry. Three sections are selected to help illustrate the flow features: Section 1 is placed upstream of the water intake in the reservoir, where the water level is not disturbed; Section 2 is in the place of trash rack, 2 m upstream of the stop-log gate, and Section 3 is downstream of tunnel transaction, where the flow reaches a stable state. The geometric parameters contain h s (m) as the height of the stop-log gate, l (m) as the width of intake chamber and d (m) as the diameter of the withdrawal tunnel. The hydraulic parameters are total water head H (m) in reservoir, withdrawal depth above the stop-log gate h i = H − h s (m), withdrawal discharge Q (m 3 /s) and averaged flow velocity v 3 (m/s) in Section 3. The water head loss ΔH (m), between Sections 1 and 3, is an essential parameter for evaluation of the water intake. The main factors that affect the ΔH include: where g (m/s 2 ) is the gravitational acceleration. Selecting Q, g and d as the independent basic quantities and using Buckingham Π theorem, Equation (1) is simplified into: where ξ is defined as the dimensionless coefficient of head loss. It indicates that the ξ is a function of H/d, hi/d and l/d and reads as The Equation (3) is consistent with the earlier work [20,[24][25][26], and it is widely acknowledged, thus a reasonable comparison can be made in the present work.

Numerical Simulation
Based on the Fluent package in ANSYS (ANSYS Inc., Canonsburg, PA, USA) [27], a numerical model is set up to help understand the complex flow features of the water intake.

Governing Equations
The flow field is governed by the incompressible viscous Navier-Stokes equations [27]. The turbulence effects are modelled by a URANS method, which is based on the Boussinesq's assumption. The finite-volume method is used to discrete the flow domain and governing equations with secondorder accuracy [27]. The governing equations are given as: Continuity equation: Momentum equation: The water head loss ∆H (m), between Sections 1 and 3, is an essential parameter for evaluation of the water intake. The main factors that affect the ∆H include: where g (m/s 2 ) is the gravitational acceleration. Selecting Q, g and d as the independent basic quantities and using Buckingham Π theorem, Equation (1) is simplified into: where ξ is defined as the dimensionless coefficient of head loss. It indicates that the ξ is a function of H/d, h i /d and l/d and reads as The Equation (3) is consistent with the earlier work [20,[24][25][26], and it is widely acknowledged, thus a reasonable comparison can be made in the present work.

Numerical Simulation
Based on the Fluent package in ANSYS (ANSYS Inc., Canonsburg, PA, USA) [27], a numerical model is set up to help understand the complex flow features of the water intake.

Governing Equations
The flow field is governed by the incompressible viscous Navier-Stokes equations [27]. The turbulence effectsre modelled by a URANS method, which is based on the Boussinesq's assumption. The finite-volume method is used to discrete the flow domain and governing equations with second-order accuracy [27]. The governing equations are given as: Continuity equation: where t is time; U i and U j are velocity components in the X i and X j directions; P is pressure; ρ is water density; v is kinematic viscosity coefficient; τ ij is the specific Reynolds stress tensor; F i is the body force in the X i direction. X i , X j and X k stand for the X, Y and Z directions, respectively. The Volume of Fluid method (VOF) is used to simulate the free surface. The method is proposed by Hirt and Nichols [28], which is a free-surface technique. Based on the Eulerian method, a fixed mesh is applied to track the shape and position of the interface between air and water. The VOF for each fluid is calculated throughout the domain. The water is usually defined as a primary phase, and the air is a secondary phase.
According to previous studies (e.g., Jothiprakash et al. [29], Teng et al. [30], Zhang et al. [31]), the RNG κ-ε turbulence model is capable of achieving a good balance between prediction accuracy and computational cost, compared to those computationally expensive Large Eddy Simulations (LES). This model is more suitable for representing free-surface flows. The standard wall functions are used to avoid resolving the turbulent boundary layers, which do not play an important role in this hydraulic simulation. Kinetic energy κ and turbulent dissipation rate ε are obtained by: where ν t is kinematic eddy viscosity ν t = C µ κ 2 ε , C µ = 0.09, σ k = 1.0, σ ε = 1.3, C ε1 = 1.44 and C ε2 = 1.92.

Model Setup
The computational domain and numerical grid are illustrated in Figure 2, in which a 3D coordinate system (X, Y, Z) is defined. The X-coordinate is along the water intake bottom (positive downwards); the Y-coordinate is placed perpendicular to the X (positive leftside), and the Z-coordinate is positioned perpendicular to the X and Y plane (positive upwards). The grid is generated using the ICEM. The domain length is 200 m. In the vicinity of the gate and close to the water intake, the grid density level is higher. A quality grid is the prerequisite for reliable simulations. To guarantee the numerical quality, a check of grid independence is necessary. Grid independence is checked through steady-state flow calculations. Three quadrilateral grids are examined, with the number of cells being about 150,000 (coarse), 260,000 (medium), and 400,000 (fine), respectively, and corresponding to the average cell size of approximately 0.70, 0.40 and 0.25 m. For the grid independence check, the velocity v 2 and turbulent intensity I are compared. I = U /U mean , where U and U mean denote the root-mean-square of the velocity fluctuations and mean flow velocity, respectively. The comparison is shown in Figure 3. The dotted lines represent the position of cross-beams. The results indicate that the medium size grid is sufficient to model the water intake flow. For the whole domain, it is finally divided into 260,000 hexahedral cells.
corresponding to the average cell size of approximately 0.70, 0.40 and 0.25 m. For the grid independence check, the velocity v2 and turbulent intensity I are compared. I = U'/Umean, where U' and Umean denote the root-mean-square of the velocity fluctuations and mean flow velocity, respectively. The comparison is shown in Figure 3. The dotted lines represent the position of cross-beams. The results indicate that the medium size grid is sufficient to model the water intake flow. For the whole domain, it is finally divided into 260,000 hexahedral cells.   Regarding the definition of boundary conditions, the upstream boundary is specified with a pressure inlet corresponding to the water depth and air pressure with the atmospheric pressure. The downstream boundary is defined as a velocity inlet, corresponding to the average outflow at the Section 3. Negative value denotes that the flow runs out of the domain. The upper boundary is set as pressure inlets. The turbulence conditions at the inlets are expressed in terms of turbulence intensity level and turbulence viscosity ratio; their embedded values in the program are 3% and 5, respectively, which are typical for inlet conditions [32,33]. The solid (concrete) boundaries, including the reservoir bottom and all the surrounded walls are treated as walls, with no-slip condition irrespective of phase. The free surface is assumed to be a smooth surface without any water level fluctuations. There is intermittent air engulfment observed at the free surface when the water withdrawal depth is small, i.e., ≤15 m. To eliminate the effect of air engulfment, the study is performed with the withdrawal depth in the range of 18-30 m. The values of some parameters adopted in the model are listed in Table 1. In the simulations, 18 cases are taken into account with respect to the H, l and hi, as listed in Table  2   Regarding the definition of boundary conditions, the upstream boundary is specified with a pressure inlet corresponding to the water depth and air pressure with the atmospheric pressure. The downstream boundary is defined as a velocity inlet, corresponding to the average outflow at the Section 3. Negative value denotes that the flow runs out of the domain. The upper boundary is set as pressure inlets. The turbulence conditions at the inlets are expressed in terms of turbulence intensity level and turbulence viscosity ratio; their embedded values in the program are 3% and 5, respectively, which are typical for inlet conditions [32,33]. The solid (concrete) boundaries, including the reservoir bottom and all the surrounded walls are treated as walls, with no-slip condition irrespective of phase. The free surface is assumed to be a smooth surface without any water level fluctuations. There is intermittent air engulfment observed at the free surface when the water withdrawal depth is small, i.e., ≤15 m. To eliminate the effect of air engulfment, the study is performed with the withdrawal depth in the range of 18-30 m. The values of some parameters adopted in the model are listed in Table 1. Table 1. Parameter values adopted in the model. In the simulations, 18 cases are taken into account with respect to the H, l and h i , as listed in Table 2

Experimental Tests
The experiments are performed in the Hydraulic Laboratory of Zhongnan Engineering Corporation Limited in Changsha, China. The experimental layout is shown in Figure 4. It consists of a pump, an approach conduit, a large feeding basin, a physical model and a flow return system. Based on the Froude similarity criterion, the physical model is designed at a scale of 1/40, which is also in consideration of previous research and the laboratory site conditions [34]. In terms of the intake hydraulic model, the scale ratio of 1:50 to 1:100 is acceptable. Therefore, the induced scale effects in our study subjected to 1:40, are negligibly small. The model consists of a model reservoir, a selective withdrawal intake with a stop-log gate and a connecting tunnel. The crossbeams in two layers are placed in the water intake, with the stop-log gate in between, also marked in Figure 1. There are 10 crossbeams in total, and the centerline distance two beams in vertical direction is 8 m. Water is supplied by pumping it from an underground reservoir. A discharge measured weir is equipped at the end of the flow return system.
Water 2020, 12, x FOR PEER REVIEW 6 of 17 effects in our study subjected to 1:40, are negligibly small. The model consists of a model reservoir, a selective withdrawal intake with a stop-log gate and a connecting tunnel. The crossbeams in two layers are placed in the water intake, with the stop-log gate in between, also marked in Figure 1.
There are 10 crossbeams in total, and the centerline distance two beams in vertical direction is 8 m.
Water is supplied by pumping it from an underground reservoir. A discharge measured weir is equipped at the end of the flow return system. The water level in the reservoir (Section 1) is measured by stylus, with an error of ±0.1 cm. The velocity v2 (m/s) at Section 2 is measured through LGY-Ⅱ flowmeter, with an error of ≤1.5%. At the connecting tunnel (Section 3), four points in a circumference are arranged with manometers to measure the pressure head p (m) and velocity head pv (m). Preliminary trials prove that the physical model shows acceptable reproducibility. To minimize the error, for each case investigated, five parallel measurements are carried out to eliminate the measurement uncertainty.

Comparisons Between Measurements and Simulations
To estimate the model accuracy, the calculated values of v2 and ΔH are compared with the measured data. Figure 5 shows the comparison of velocity profiles at Section 2 for Cases 3, 8 and 17. Table 3 presents the comparison of ΔH. For v2, the computed results match well with the measured ones, although there is a certain discrepancy for some points. For ΔH, the calculated results are in compliance with the measured data. The results indicate satisfied model performance for both v and ΔH calculations. The water level in the reservoir (Section 1) is measured by stylus, with an error of ±0.1 cm. The velocity v 2 (m/s) at Section 2 is measured through LGY-II flowmeter, with an error of ≤1.5%. At the connecting tunnel (Section 3), four points in a circumference are arranged with manometers to measure the pressure head p (m) and velocity head p v (m). Preliminary trials prove that the physical model shows acceptable reproducibility. To minimize the error, for each case investigated, five parallel measurements are carried out to eliminate the measurement uncertainty.

Comparisons Between Measurements and Simulations
To estimate the model accuracy, the calculated values of v 2 and ∆H are compared with the measured data. Figure 5 shows the comparison of velocity profiles at Section 2 for Cases 3, 8 and 17. Table 3 presents the comparison of ∆H. For v 2 , the computed results match well with the measured ones, although there is a certain discrepancy for some points. For ∆H, the calculated results are in compliance with the measured data. The results indicate satisfied model performance for both v and ∆H calculations.

Flow Regime
The flow behaviors from reservoir running into the water intake are distinct with and without a stop-log gate and exhibit complex features. The flow runs relatively smoothly into the water intake in the absence of the gate (see Figure 6a). From the inlet to its downstream, the velocity shows an augment and reaches the maximum approximately at the Section 3, with the peak value of ~5 m/s. However, it is disadvantaged to withdrawal water at a selective layer. In the presence of a stop-log gate, as shown in Figure 6b-e, the bottom water in the reservoir is blocked to some extent, and the relative up-layer water runs into the intake. This realizes the water withdrawal at a given layer with expected temperature by adjustment of the gate height. To examine the flow features under the variations of H, l and hs, the longitudinal flow regimes on the X-Z coordinate plane are displayed for selected cases.

Flow Regime
The flow behaviors from reservoir running into the water intake are distinct with and without a stop-log gate and exhibit complex features. The flow runs relatively smoothly into the water intake in the absence of the gate (see Figure 6a). From the inlet to its downstream, the velocity shows an augment and reaches the maximum approximately at the Section 3, with the peak value of~5 m/s. However, it is disadvantaged to withdrawal water at a selective layer. In the presence of a stop-log gate, as shown in Figure 6b-e, the bottom water in the reservoir is blocked to some extent, and the relative up-layer water runs into the intake. This realizes the water withdrawal at a given layer with expected temperature by adjustment of the gate height. To examine the flow features under the variations of H, l and h s , the longitudinal flow regimes on the X-Z coordinate plane are displayed for selected cases.

Flow Regime
The flow behaviors from reservoir running into the water intake are distinct with and without a stop-log gate and exhibit complex features. The flow runs relatively smoothly into the water intake in the absence of the gate (see Figure 6a). From the inlet to its downstream, the velocity shows an augment and reaches the maximum approximately at the Section 3, with the peak value of ~5 m/s. However, it is disadvantaged to withdrawal water at a selective layer. In the presence of a stop-log gate, as shown in Figure 6b-e, the bottom water in the reservoir is blocked to some extent, and the relative up-layer water runs into the intake. This realizes the water withdrawal at a given layer with expected temperature by adjustment of the gate height. To examine the flow features under the variations of H, l and hs, the longitudinal flow regimes on the X-Z coordinate plane are displayed for selected cases. In comparison of Case 3 and 5, the effect of H is illustrated in Figure 6b,c; comparing Case 3 and 13 in Figure 6b,d, the effect of l is obtained; to compare the Figure 6b,e, the impact of h i is demonstrated. The gate acts as a submerged sharp-crested weir, and the inflow bypassing the gate experiences great changes in flow direction. Local head losses occur as the streamlines are directed away from the axial direction of flow due to the changes of the wall geometry, which complies with the study of Hager [35]. Additionally, the flow mixing in the intake chamber also induces some head losses. Looking downwards and behind the gate, a large recirculation zone occurs at the bottom of the intake chamber and a small one is also observed for case 5. The occurrences are attributable to the variations of chamber wall geometry. The recirculation zones reduce the effective inflow area at the location, and thus cause an additional acceleration of the flow. It is believed that recirculation zones are associated with high turbulence phenomena, leading to considerable energy loss [35].

Head Loss
Head loss is an essential parameter when evaluating the flow running into the intake. As aforementioned, the ξis a function of H/d, h i /d and l/d. Figure 7a shows the relationship between ξ and H/d. It is noticed that the ξaugments with the increase of H/d following an approximately linear relationship, which suggests that the increase of the water head in the reservoir leads to a larger head loss at the intake. The result is consistent with previous prototype studies [21]. For a given withdrawal depth h i , the increase of the water head H means a larger h s . It contributes to the observations in Figure 7c, where vortices are observed between two crossbeams and the generating turbulent vortices shedding could further develop in the chamber, causing some energy loss. In comparison of Case 3 and 5, the effect of H is illustrated in Figure 6b,c; comparing Case 3 and 13 in Figure 6b,d, the effect of l is obtained; to compare the Figure 6b,e, the impact of hi is demonstrated. The gate acts as a submerged sharp-crested weir, and the inflow bypassing the gate experiences great changes in flow direction. Local head losses occur as the streamlines are directed away from the axial direction of flow due to the changes of the wall geometry, which complies with the study of Hager [35]. Additionally, the flow mixing in the intake chamber also induces some head losses. Looking downwards and behind the gate, a large recirculation zone occurs at the bottom of the intake chamber and a small one is also observed for case 5. The occurrences are attributable to the variations of chamber wall geometry. The recirculation zones reduce the effective inflow area at the location, and thus cause an additional acceleration of the flow. It is believed that recirculation zones are associated with high turbulence phenomena, leading to considerable energy loss [35].

Head Loss
Head loss is an essential parameter when evaluating the flow running into the intake. As aforementioned, the ξ is a function of H/d, hi/d and l/d. Figure 7a shows the relationship between ξ and H/d. It is noticed that the ξ augments with the increase of H/d following an approximately linear relationship, which suggests that the increase of the water head in the reservoir leads to a larger head loss at the intake. The result is consistent with previous prototype studies [21]. For a given withdrawal depth hi, the increase of the water head H means a larger hs. It contributes to the observations in Figure 7c, where vortices are observed between two crossbeams and the generating turbulent vortices shedding could further develop in the chamber, causing some energy loss.  Figure 7b depicts the relationship between ξ and l/d. It shows that the ξ exhibits a nonlinear decrease trend with the increase of l/d, which is coincident to that obtained by Lei et al. [22]. They report that the relatively large l is recommended in the design of the intake geometry so as to get good flow regime and small head loss. There would be a large flow velocity gradient in the chamber in the situation of small l, contributing to the extensive flow momentum exchange and consequently generating energy dissipation. Moreover, the head loss due to the presence of recirculation zone is greatly affected by the intake geometry. However, the former plays a dominant role. Figure 7c presents the results between ξ and hi/d. The ξ decreases with the increases of hi/d, implying that for a given H, a larger hi corresponds to a smaller hs, leading to less head loss. To achieve a balance between the least head loss and selective water withdrawal, it is suggested to consider the three parameters simultaneously but not in a separate way.
Based on the measured data, the relationship between ξ and H/d, l/d, hi/d is derived by means of the multiple regression analysis and reads as  To verify the derived Equation (8), systematic data from previous studies inclusive of experimental and numerical results are collected for comparison, as listed in Table 4. Moreover, Figure 9 gives the comparisons between previous (subscript pre) and calculated (subscript cal) results with respect to the ξ. The dotted lines indicate a relative error (Err) of 15% based on the following equation.  Figure 7b depicts the relationship between ξ and l/d. It shows that the ξ exhibits a nonlinear decrease trend with the increase of l/d, which is coincident to that obtained by Lei et al. [22]. They report that the relatively large l is recommended in the design of the intake geometry so as to get good flow regime and small head loss. There would be a large flow velocity gradient in the chamber in the situation of small l, contributing to the extensive flow momentum exchange and consequently generating energy dissipation. Moreover, the head loss due to the presence of recirculation zone is greatly affected by the intake geometry. However, the former plays a dominant role. Figure 7c presents the results between ξ and h i /d. The ξ decreases with the increases of h i /d, implying that for a given H, a larger h i corresponds to a smaller h s , leading to less head loss. To achieve a balance between the least head loss and selective water withdrawal, it is suggested to consider the three parameters simultaneously but not in a separate way.
Based on the measured data, the relationship between ξ and H/d, l/d, h i /d is derived by means of the multiple regression analysis and reads as  Figure 7b depicts the relationship between ξ and l/d. It shows that the ξ exhibits a nonlinear decrease trend with the increase of l/d, which is coincident to that obtained by Lei et al. [22]. They report that the relatively large l is recommended in the design of the intake geometry so as to get good flow regime and small head loss. There would be a large flow velocity gradient in the chamber in the situation of small l, contributing to the extensive flow momentum exchange and consequently generating energy dissipation. Moreover, the head loss due to the presence of recirculation zone is greatly affected by the intake geometry. However, the former plays a dominant role. Figure 7c presents the results between ξ and hi/d. The ξ decreases with the increases of hi/d, implying that for a given H, a larger hi corresponds to a smaller hs, leading to less head loss. To achieve a balance between the least head loss and selective water withdrawal, it is suggested to consider the three parameters simultaneously but not in a separate way.
Based on the measured data, the relationship between ξ and H/d, l/d, hi/d is derived by means of the multiple regression analysis and reads as  To verify the derived Equation (8), systematic data from previous studies inclusive of experimental and numerical results are collected for comparison, as listed in Table 4. Moreover, Figure 9 gives the comparisons between previous (subscript pre) and calculated (subscript cal) results with respect to the ξ. The dotted lines indicate a relative error (Err) of 15% based on the following equation. To verify the derived Equation (8), systematic data from previous studies inclusive of experimental and numerical results are collected for comparison, as listed in Table 4. Moreover, Figure 9 gives the comparisons between previous (subscript pre) and calculated (subscript cal) results with respect to the ξ. The dotted lines indicate a relative error (Err) of 15% based on the following equation.   [20] 89 The multiple correlation coefficients between the previous results ξpre and the calculated results ξcal are 0.98, and no data scatter >15% on basis of Equation (9), indicating the obtained results agree reasonably well with the previous data. These errors might be ascribed to some different inlet geometries in certain projects.

Flow Velocity Distribution
Flow velocity distribution at the trash rack, i.e., Section 2 in Figure 1, is an essential indicator for the structural design, and it is usually characterized by the maximum flow velocity v2m (m/s) and its position Zm. To examine the two parameters, Case 4 as an example is chosen for illustration. Figure  10 presents its cross-sectional flow velocity distributions at Section 2. The multiple correlation coefficients between the previous results ξ pre and the calculated results ξ cal are 0.98, and no data scatter >15% on basis of Equation (9), indicating the obtained results agree reasonably well with the previous data. These errors might be ascribed to some different inlet geometries in certain projects.

Flow Velocity Distribution
Flow velocity distribution at the trash rack, i.e., Section 2 in Figure 1, is an essential indicator for the structural design, and it is usually characterized by the maximum flow velocity v 2m (m/s) and its position Z m . To examine the two parameters, Case 4 as an example is chosen for illustration. Figure 10 presents its cross-sectional flow velocity distributions at Section 2.
The flow velocity exhibits a general downward trend from the top of the gate to the water surface. In Figure 10a, it shows that the flow cross-section is divided by the vertical beams into three independent parts, and the velocity distributions in each part are almost identical. The flow velocity is also affected significantly by the presence of horizontal crossbeams. Several different flow regions, as a result, are noticed the cross-section. Figure 10b shows the corresponding flow velocity profile in the vertical direction. The flow velocity is relatively small in the region below the top of stop-log gate, as the flow is blocked by the gate. When the Z increases from Z = 0, flow velocity augments gradually.
Once it exceeds the top of the gate, flow velocity surges to the maximum (v 2m = 1.5-1.8 m/s), and then, it decreases. Such flow deceleration is also caused by the horizontal crossbeam. Then similar rebounds in flow velocity exist between two crossbeams till the surface. Considering the structure safety and the racks accessible for cleaning, the v 2m is of great concern in practical and previous experience suggests that v 2m should not be a large value, preferable v 2m ≤ 1.5 m/s, which is also evidenced by Johnson [36]. The flow velocity exhibits a general downward trend from the top of the gate to the water surface. In Figure 10a, it shows that the flow cross-section is divided by the vertical beams into three independent parts, and the velocity distributions in each part are almost identical. The flow velocity is also affected significantly by the presence of horizontal crossbeams. Several different flow regions, as a result, are noticed the cross-section. Figure 10b shows the corresponding flow velocity profile in the vertical direction. The flow velocity is relatively small in the region below the top of stop-log gate, as the flow is blocked by the gate. When the Z increases from Z = 0, flow velocity augments gradually. Once it exceeds the top of the gate, flow velocity surges to the maximum (v2m = 1.5 − 1.8 m/s), and then, it decreases. Such flow deceleration is also caused by the horizontal crossbeam. Then similar rebounds in flow velocity exist between two crossbeams till the surface. Considering the structure safety and the racks accessible for cleaning, the v2m is of great concern in practical and previous experience suggests that v2m should not be a large value, preferable v2m ≤ 1.5 m/s, which is also evidenced by Johnson [36].

Maximum Velocity
In light of the flow velocity at the trash rack, it has some relationship with H/d, l/d and hi/d. To examine the maximum velocity at the trash rack, a dimensionless velocity distribution coefficient K is defined by the v2m and (m/s), where = the average velocity at Section 2, and A2e = the corresponding active inflow area. The relationship between K and H/d is presented in Figure 11a. It is noticed that K fluctuates slightly with the variations of H/d; the data points are scattered in the range of K = 1.6 − 1.9, with an average value of K = 1.7. Such scattering behavior is the effect of crossbeams on the velocity distribution. As mentioned above in Figure 10, the presence of the crossbeams has a bear on the flow field. Under the different H, the relative vertical position of the crossbeams differs in the section, leading to the difference of flow velocity distributions in Section 2.

Maximum Velocity
In light of the flow velocity at the trash rack, it has some relationship with H/d, l/d and h i /d. To examine the maximum velocity at the trash rack, a dimensionless velocity distribution coefficient K is defined by the v 2m and v 2 (m/s), where v 2 = the average velocity at Section 2, and A 2e = the corresponding active inflow area. The relationship between K and H/d is presented in Figure 11a. It is noticed that K fluctuates slightly with the variations of H/d; the data points are scattered in the range of K = 1.6-1.9, with an average value of K = 1.7. Such scattering behavior is the effect of crossbeams on the velocity distribution. As mentioned above in Figure 10, the presence of the crossbeams has a bear on the flow field. Under the different H, the relative vertical position of the crossbeams differs in the section, leading to the difference of flow velocity distributions in Section 2 Similarly, the relationship between K and h i /d is plotted in Figure 11b. It shows that the K keeps a constant value of 1.7 with different l/d values, implying that the change of width of the intake chamber has little effect on the flow velocity at the trash rack. It is shown in Figure 11c that the K increases from 1.4 to 2.2 with the increase of h i /d, indicating that the smaller h i is accompanied with the larger disparity between the v 2m and the v 2 . For a given Q, it is noted that a larger A 2e is exposed to a larger h i and consequently leading to a smaller v 2 (v 2 = Q/A 2e ). This could contribute to the augments of K with h i /d. Scattered point is also observed in Figure 11c, which holds the same reason with that of Figure 10a, i.e., the effect of the relative crossbeams positions subjected to different H.
To summarize, in terms of the flow velocity at the trash rack, three parameters, i.e., H/d, l/d and h i /d, are taken into consideration. The results show that the K is roughly proportional to the h i /d, exhibiting an increasing trend. It implies that the velocity is affected noticeably by the h i , also a result of the h s adjustment. Similarly, the relationship between K and hi/d is plotted in Figure 11b. It shows that the K keeps a constant value of 1.7 with different l/d values, implying that the change of width of the intake chamber has little effect on the flow velocity at the trash rack. It is shown in Figure 11c that the K increases from 1.4 to 2.2 with the increase of hi/d, indicating that the smaller hi is accompanied with the larger disparity between the v2m and the . For a given Q, it is noted that a larger A2e is exposed to a larger hi and consequently leading to a smaller (v2 = Q/A2e). This could contribute to the augments of K with hi/d. Scattered point is also observed in Figure 11c, which holds the same reason with that of Figure 10a, i.e., the effect of the relative crossbeams positions subjected to different H.
To summarize, in terms of the flow velocity at the trash rack, three parameters, i.e., H/d, l/d and hi/d, are taken into consideration. The results show that the K is roughly proportional to the hi/d, exhibiting an increasing trend. It implies that the velocity is affected noticeably by the hi, also a result of the hs adjustment.

Position of the Maximum Velocity
The position of the maximum flow velocity Z m is described by the relative position Z m /h s in the present work. The relationship between Z m /h s and H/d, l/d, h i /d is presented in Figure 12. The change of Z m /h s with these three parameters is not significant, in spite of some slight fluctuations in Figure 12a,c. Such fluctuations are also ascribed to the changes in flow velocity distribution, induced by the different relative positions of crossbeams in different cases.
It displays that all data points scatter in the range of Z m /h s = 1.05-1.30, suggesting that the maximum flow velocity always occurs at a small height above the stop-log gate. Therefore, more attention should be paid to the flow velocity in this range for the design of trash rack structures.
The result is consistent with that of the previous study [37], in which a range of Z m /h s = 1.05-1.15 is reported. The present work indicates a more extensive range of Z m /h s , because more cases with different geometries are taken into account.
of Zm/hs with these three parameters is not significant, in spite of some slight fluctuations in Figure  12a,c. Such fluctuations are also ascribed to the changes in flow velocity distribution, induced by the different relative positions of crossbeams in different cases.
It displays that all data points scatter in the range of Zm/hs = 1.05 − 1.30, suggesting that the maximum flow velocity always occurs at a small height above the stop-log gate. Therefore, more attention should be paid to the flow velocity in this range for the design of trash rack structures. The result is consistent with that of the previous study [37], in which a range of Zm/hs = 1.05 − 1.15 is reported. The present work indicates a more extensive range of Zm/hs, because more cases with different geometries are taken into account.

Conclusions
The research presents an investigation on the hydraulic features of a water intake functioned with a stop-log gate. Considering different flow conditions and geometries, both laboratory experiments and numerical simulations are performed to help understand the intake flow behaviors, including the flow regime, head loss and maximum flow velocity. Simulation results are verified against the experiment data in the present work. The main conclusions are summarized as follows: (1) At the water intake, flow regime changes dramatically after the employment of stop-log gate; the occurrence of flow recirculation and vortices in the intake chamber is affected considerably by the water head and the intake geometry. (2) Head loss at the intake depends significantly on the upstream water head, width of intake chamber and withdrawal depth. Based on the regression analysis of systematical data, an empirical equation for the coefficient of head loss is derived; the calculated results from the equation show a good agreement with both experimental and numerical data from previous studies. (3) Flow velocity at the trash rack section varies vertically in a great manner. The velocity distribution coefficient is dependent exclusively on the relative intake depth, showing a range of 1.4-2.2 with different depths. Regardless of the different water head and the geometry of stop-log gate, the maximum flow velocity always occurs at roughly 1.05-1.30 times of the gate height.
The combination of the experimental and numerical results reveals the flow behaviors of water intake with stop-log intake, providing general insights into similar hydraulic situations in practice.

Author Contributions:
The manuscript is written by W.R. and Q.X., with comments from J.W. J.W. is responsible for the experimental measurements and numerical simulations, with participants from W.R., Q.X. and B.M. The project is administered by B.M. and L.W. All authors have read and agreed to the published version of the manuscript.