مجله هیدرولیک
سال پانزدهم شماره 2 (تابستان 1399)

Culverts are common structures for runoff drainage system in the design and construction of roads and railways, in both urban and rural areas. Due to the nature of runoff flow, large amount of sediments, foliage, urban waste and debris materials may accumulate in the entrance of culverts, particularly in flood events. Blockage in the culvert’s entrance can result in a significant increase in flood risk, through elevated flood levels and diverted flow paths through the urban or rural areas (Rigby et al., 2002). Sudden blockage in a runoff system is also one of the common problems. The study of culvert’s blockage would be useful in the prediction and prevention of flood hazard in the vicinity of drainage systems. Current study deals with this problem in box culverts. Blockage effects on the upstream water level were investigated using both experimental and numerical modeling. The FLOW-3D model was chosen, because the sufficiency of this model for such flow conditions was already reported by several studies such as Abad et al. (2008), Ayaseh (2010), Brethour and Brunham (2009) and Gunal et al. (2019).

Experimental tests were conducted in Hydraulic Laboratory of Water Engineering Department in Bu Ali Sina University, Hamedan, Iran. The box culvert models made of glass and smooth water pipes used as circular culvert models. The experimental setup includes a glass wall flume with 10m length, 0.5m width and 0.6m deep. Rectangular plates in different sizes were used in order to make sudden blockage into the culverts. An extensive experiment tests was conducted under different flow condition and blockage scenarios, and 21 experimental data sets were provided. The FLOW-3D model, Version 11.3, was performed on the main server of Water Institute at the University of Tehran, and adapted to the experimental data sets from this study. The stability and sensitivity of this model have been tested according to: mesh cell size, simulation time step, turbulent model, and culvert hydraulic characteristics such as wall roughness. The simulation convergence was achived with an efficient simulation time step of 80 seconds. Three different mesh blocks were used for pre-simulation cases, and a block in block with 1.0 cm and 0.5 cm mesh cell sizes were chosen as the best meshing senario. The RNG was found to be an apropriate turbulence model. The slope of culvert barrel was changed from horizontal to 0.005 in the flow direction, and the roughness coefficient modified from 0.00085 m to 0.001 m in the culvert barrel. The relative error of simulated water levels and discharge for calibrated model were to be in the order of acceptance ranges, and the simulation FLOW-3D model was adjusted as an efficient and reliable tool. The FLOW-3D model was then calibrated and verified using the experimental data sets, and was used to simulate different flow conditions into the culverts, under different entrance-blockage scenarios.

Effect of the inlet blockage on upstream water level was tested for three flow rates (the design discharge of 27.5 lit/s, and two lower discharges of 10.5 lit/s and 16.5 lit/s), in four different sizes of inlet blockage (B). Simulation results showed a good agreement in upstream backwater level in all cases. In the case of flow with 16.5 lit/s, upstream water level raised from 28.5 cm in non-blocked inlet to 31.4, 34.2 and 38.5 cm in presence of 20% ,40% and 60% blocked inlet area, respectively. The rate of the upstream water level increase (DHu) against the reduced inlet area (1-B) represents a higher rate for discharges smaller than the culvert-design discharge. The evaluated equations for upstream water level enhancement were : DH_u=-0.48(1-B)+45.089 (1) DH_u=-0.82(1-B)+75.663 (2) in which, Eq. (1) is for design discharge and Eq. (2) for the smaller discharges. Blokage has been affected flow in the barrel and in the downstream of the culvert. Investigation of turbulent characteristics and shear velocity values in both the barrel and downstrem indicated the impact of blocked inlet. Turbulent enrgy of flow in the 60% blocked-inlet area was 5 times greater than that of non-blocked inlet for the design discharge. Also shear velocity in the same blockage situation increased by 2 times in downstream which results in a greater scouring power of the flow downstream. Sorourian et al. (2015) rep[orted this phenomenon with even higher scour downstream of bocked cualverts. Maximum value of shear velocity increased with the increase level of blockage in the all flow condition, however in the design discharge it seems to be constant for blockages greather than 40%.

The FLOW-3D model was calibrated and validated to simulate the flow into the culverts. Influence of inlet obstruction on the upstream water level and flow characteristics into the barrel and downstream of the culvert was investigated. The results show a linear increase in the upstream water level by decreasing the percentage of culvert inlet. The upstream water level for the design discharge was lower than the other tested discharges. Changes in turbulent flow properties and shear velocity inside the barrel and downstream were also investigated in the presence of obstruction. Shear velocity increased 3 times in the presence of 80% blockage for 10.5 lit/s. and for the design discharge (27.5 lit/s) with 60% inlet blockage increased 2 times. The turbulence energy for the design discharge has also increased by about 5 times. The present results confirm the previous studies on the effect of the culvert inlet obstruction on the geometry of the scour hole downstream of culverts.

Vortex induced vibration is a well-known phenomenon in the engineering applications involving the fluid/structure interaction. Especially, it has been observed in various ocean engineering applications such as offshore risers, deep water bridge piers and oil pipelines. In the flow around bluff bodies such as marine risers, in a specific range of Reynolds numbers, the asymmetric vortex shedding at the bluff body wake results in periodic hydrodynamic forces on the riser and consequently the vortex-induced- vibration. When the vortex shedding frequency is close to the natural frequency of the structure, the cylinder tends to dramatically vibrates in transverse direction which is commonly termed as the "lock-in" phenomenon. Since vortex induced vibration is one of the most important causes of fatigue damage and structural instability in marine risers, exploring efficient ways to reduce or suppress vortex induced vibrations, has attracted the attention of many ocean engineering researchers. In the present study, two-way fluid/structure interaction simulation of vortex induced vibration of the circular and truncated cylinders are conducted. For this purpose, laminar flow around an elastically supported two degree of freedom cylinder (circular or truncated), which can freely vibrate in stream-wise and transverse directions, is considered.

To solve the governing equations of two-dimensional, unsteady and incompressible flow over circular and truncated cylinders, a finite volume technique is employed. Moreover, the rigid body motion equations in stream-wise and transverse directions are incorporated into the computational fluid dynamics solver to treat the coupling which exists between the fluid flow and cylinder movement. To calculate the rigid body motion of cylinder and treat the fluid-cylinder interaction, a User-Defined Function is used. In every time step, the temporal variation of hydrodynamic forces (lift and drag) determined by solving the mass and momentum equations are employed as the source terms in rigid body motion equations to compute the velocity and displacement of cylinders. Fluid-structure interaction is handled using the Fluent's moving deforming mesh feature which deforms and remeshes cells during transverse and streamwise motions of the cylinders. The pressure-based solver with first-order implicit unsteady formulation is employed to solve the discretized continuity and momentum equations. The coupling between pressure and velocity fields are handled by using computationally efficient fractional step method along with the non-iterative time-advancement algorithm for time matching strategy in computational fluid dynamics solver. To solve the governing equation for the velocity fields, one needs suitable boundary conditions at the inlet, outlet, lower and upper boundaries, and on the surface of cylinders. A uniform profile of free-stream velocity is used at the inlet. At the outlet, the downstream boundary is located far from the cylinders such that the streamwise gradients for the velocity vectors could safely be set equal to zero. Along the upper and lower boundaries, the y-component velocity is considered to be zero while for the x-component velocity, the gradient in the y-direction is set equal to zero. At the cylinder’ walls, the no-slip condition is imposed on both velocity components.

In order to validate the numerical method used in the study of fluid-structure interaction, the results for the transverse oscillations of the circular cylinder and truncated one (with truncation angle of 45 degrees) at different Reynolds numbers are compared with the results of Kumar et al. (2018). It is noteworthy that the obtained results in the present study are in good agreement with those of Kumar et al. (2018) and the numerical model accurately predicts the maximum amplitude of transverse vibration and the width of the lock-in region. Moreover, the influence of the truncation angle (behind the cylinder) on the vibration suppression of truncated cylinders is evaluated. The results show that as the Reynolds number increases from 80 to 85, the vibration of the truncated cylinders enters the lock-in region and experiences a sharp jump in their transverse displacement. Also, in this region, the truncation angle does not have a significant effect on the transverse vibrations of the cylinders and merely reduces their in-line vibration. However, changing the structural design of the cylinder (making a truncation at the back of the cylinder) has a substantial effect on the vibration reduction in the right half of the synchronization region. At Re = 100 (Reynolds number corresponding to the lock-out region), when the truncation angle increases from zero to 60 degrees, the transverse vibration of the cylinder is reduced by about 66%.

In summary, it is concluded that the significant difference in the oscillation amplitude of the circular and truncated cylinders is in the right half of the lock-in region. When the truncation angle increases, the width of the lock-in region decreases.

The newest Type of nonlinear weir is piano key weir. Initial studies on this weir have shown that this weir significantly increases the discharge, has a relatively simple structure, and is an economic structure. Various studies have been to investigate the factors affecting the discharge and optimization of this Type of weir. The purpose of this study was to modify the Type A piano key weir to better perform this Type of weir in discharge and Ventilation at the outlet. In this research, by applying changes such as a triangular nose at the entrance and a semicircular crest in the outlet of the A-type piano key weir, its performance has been investigated numerically by Flow-3D software. In the numerical simulation, the RNG turbulence model used. Validate the numerical model by the results of an experimental study on a Type A piano key weir in a laboratory flume with a length of 10 meters, a width of 0.75 meters, and a height of 0.8 meters used. The laboratory channel wall made of glass and its floor is metal. In the numerical simulation of the four piano key weir models, the first type PKW A has the same physical model characteristics and the modified model concurrently with changes such as upstream nose and semicircular cross-section (PKW B +). The third Type was added by removing the input overhang and using a semicircular cross-section at the modeled outlet (PKW C), and the fourth Type was added by the nose only upstream of the Type A piano key weir (PKW D). In the numerical model, of the three meshes, one in the upstream weir with dimensions of 2×0/4×0/6, the second in the weir site with dimensions of 0/5×0/4×0/6 and the third in the downstream weir dimension 1×0/4×0/6 was used. At the inlet boundary of block 1, the volume flowrate boundary condition, in the outlet boundary of block 3, outflow boundary condition, at the upper boundaries of the field, left and right of the inlet flow, and between the blocks, the symmetry boundary condition, and at the bottom boundary, the wall boundary condition. The simulation time is set to 15 seconds, according to the software, which states that the current is stable after about 13.5 seconds. The performance of PKW C and PKW D weir in the discharge coefficient is better than PKW A weir. One of the most important causes of PKW C weir coefficient is the low total length compared to PKW A as well as no downstream Overhang. Decreasing the weir length due to the general equation of weirs and the constant of all its parameters increases the discharge coefficient. Also, the lack of Downstream overhang of the weir reduces downstream turbulence and better directs the outflow. As a result, we see an increase in the discharge coefficient in PKW C weir over PKW A weir. Also, the dewatering coefficient by creating a nose upstream of the weir (PKW D) has increased, mainly due to better conduction of the current to the weir input key. However, with the increase of the head, due to more interference of the flow layers, the effect of this separation is reduced and results in a decrease in the discharge coefficient compared to the lower heads. Each of the changes in Type A piano key weir on the discharge coefficient individually compared to the simple piano key weir mode improved the discharge coefficient on average by 5 to 10%. Also, the simultaneous effect of these two changes, based on the results of the piano key weir, improved the discharge by about 12%. By tec-plot software, the flow lines in PKW A and PKW B + weirs are plotted and compared. Flow lines are drawn in the PKW A weir indicate a 90-degree deviation of the flow lines after collision weir and scrolling further to pass through the weir input keys. Also, the focusing of the flow lines at a part of the lateral length (Bb) interferes with the flow layers, thereby reducing the flow velocity within that range. But by creating a nose upstream of the weir, the flow lines are redirected to the weir inlet prior to the weir by the nose. Also, no overhang in the PKW B + weir reduced the formation of vortices downstream of the weir, which eventually reduced the turbulence. Another benefit of non-evacuation is the reduction of the volume of air trapped in the weir outlet key, which increases the weir discharge. 

Shaft spillways are one of the major hydraulic structures in dam engineering, influencing the flow field inside the dam reservoir, by inducing swirling flow and air-core vortices. Formation of vortex at vertical shaft is one of the critical problems encountered in these kinds of shafts. Intake vortices are the result of angular momentum conservation at the flow constriction, where angular velocity increases with a decrease in the cross sectional area. This phenomenon usually happens when a free-water surface enters a closed area such as a shaft pipeline or morning-glory spillway. Swirling flows at vertical shaft spillways have the potential to engender flow fluctuations, reduce efficiency, and cause structural damages. In order to make the vortex weakness or totally omitted, the strength of the vortex must be limited by some obstacles in its formation point and caused uniform flow toward the spillway. To this end, using the anti-vortex plates will increase both discharge coefficient and spillway efficiency, while decrease the water flow oscillation. Due to numerous design variables, the optimal hydraulic design of such structures is not deeply understood. In the present study, a comprehensive investigation by simulated model is conducted to examine the effects geometrical parameters of anti-vortex plates on reduction of swirling flow over the intake.

The aim of this study is to make the model of anti-vortex plates at vertical shaft in Flow-3D software. Flow-3D software is Computational Fluid Dynamic (CFD) software with the ability of assimilation of fluid flow on free surface. The effects of different anti-vortex plate geometries, including numbers, dimensions, positioning angles and also the shape of anti-vortex plates on the weir flow discharge coefficient are taken into account. Three different configurations, (D×D, 2D×2D, 3D×3D), of square and circular anti-vortex plates in four angles, 0‎‏◦‏‎ ‎‎(single), 90‎‏◦‏‎ (pair), 120‎‏◦‏‎ (triad) and 180‎‏◦‏‎ (four anti-vortex plates), were investigated. Previous experimental study suggested that optimal size for square anti-vortex plate is 2D×D if R=D/2 (R is the horizontal distance between the shaft center and plate edge) and Z=0, i. e. the vertical distance between shaft edge and palate center (Kabiri-Samani and Borghei, 2013). In present study, the same position R=D/2 and Z=0 for anti-vortex plate is considered.

In order to model-validation of the no-plate model, one D×D anti-vortex plate (p1) and two 2D×2D anti-vortex plates (P2) were considered in 10 cm, and 7.5 cm diameters of the shaft, respectively. In no-plate numerical simulation, six different discharges (0.00604 – 0.0019 m3/s) was considered for each diameter individually, and in P1 and P2 simulation the variation of discharge is 0.0125 to 0.0019 (m3/s). The results of verification showed that flow-3D software has good performance in numerical simulation with error less than 8%. In the present study, square anti-vortex plates with D×D, 2D×2D, 3D×3D dimensions and circular ‎with diameter D, were modeled at the angles 0‎‏◦‏‎ ‎‎(single), 90‎‏◦‏‎ (pair), 120‎‏◦‏‎ (triad) and 180‎‏◦‏‎ (four anti-vortex plates) for square and 180‎‏◦‏‎ for circular. ‎The results showed that in four square anti-vortex plates (n=4) and size D×D negative pressure on vertical intake and high pressure around the tank shells was not observed. Thus, the four square anti-vortex plates (n=4) with D×D dimensions is the best configuration in terms of negative pressure and air core. Water free surface elevations have been investigated for the best number of square anti-vortex plates (n=4) for D×D, 2D×2D and 3D×3D. The results shows that the square anti-vortex plate with D×D dimension has a lower water level which indicate passing more water through the shaft. Circular anti-vortex plates in comparison with square type, in the same condition, shows the higher water level. That is proof weak performance of the circular model versus the square. Investigation of velocity components over the intake indicate that the fluctuation of vertical component is more than the radial and tangential velocity components. The maximum velocity value is obtained for radial velocity component of square anti-vortex plates.

Vertical shaft is one of the most important and the most practical one among the spillways. In the present study, different configuration of anti-vortex plates has been considered to reduce or minimize swirling flow strength and air entrainment at the vertical shaft spillways. A parametric study was carried out on the main geometric variables of the anti-vortex plates based on model simulation. Based on results obtained from numerical modeling, application of four D×D square anti-vortex plates is more effective compared to one, two, or three square plates and also four circular anti-vortex plates. Head-discharge diagrams indicate that four D×D square anti-vortex plates in similar discharges, has the minimal water height above the spillway. So the four D×D square anti-vortex plates are introduced as the optimal case and circular anti-vortex plate can be applied as the second choice. Keywords: Shaft Spillway, Anti-Vortex Plates, Vortex flow, Velocity component.

The discharge coefficient (Cd) of irrigation gates is one of the important parameters for predicting the flow discharge through these structures. This parameter depends on the geometrical conditions of the gate as well as the upstream and downstream flow conditions. During the past decades attempts have been done to develop relations for different types of gates. Most of such studeis have been carrie out by researchers in the laboratory and therefore various types of relationships have been proposed. In the present study, the Cd value of the elliptical lopac gate with a gradual transition upstream was investigated. Rectangular lopac gate were invented in the 1980s by Peter Langman et al. to measure and manage water level fluctuations in irrigation canals and their successful applications have been reported in several projects [3]. This structure acts as a lopac lid that can adjust the flow of water upstream of the surface by adjusting the flow direction [8]. This structure acts like a gate that can also be adjusted the flow through the upstream surface by installing it in the flow direction [8]. Different equations for the coefficient of discharge of rectangular lopac gate with and without upstream transition have been extracted by different researchers. For the elliptical lopac gate without upstream conversion, Pilbala et al. (2018), Pilbala(2018) and Nesi et al (2018) have reported ectensive laboratory investigation to presented the required expressions for determination of Cd. In a wide channel, for beter performance and saving the cost of operation, it is advise to install narrower gate. Therefore a gradually transition at the upstream of the gate is usually designed and installed to help passing of the flow smoothly. By the knowledge of the authors, the effect of such structures on Cd have not been studied yet and thus the main goal of this paper is to conducted experimental tests to provide required data.

In this study first, using the Buckingham theory the effective non-dimensional parameters were extracted (Eq. 4) and the experimental program was carried out accordingly. Experiments were conducted on a flume with a length of 800 cm, a height of 80 cm and width of 60 cm. At the beginning of the flume, a rock filled basket was installed to calm the flow which enters the flume. Four meters away from the basket, The Elliptical lopac gate models made of galvanized iron with a thickness of 2 mm and a width and height of 40 cm and a radius of 5 cm were installed. The gate was connected to the flume wall at a distance of 15 cm from the wall of the flume by a sudden conversion of the PVC sheet. Then, using this type of sheet, gradual transition was made and installed.

In this study total of 108 experiments including 27 experiments with no presence of gradual transition and 81 experiments with three different models of gradual upstream transition were performed at three different angles (Table 1). For each experiment, the discharge coefficient was calculated from Eq.5 and the trend of discharge coefficient variation was studied by changing the dimensionless parameters obtained in dimensional analysis including upstream gradient angle, relative gate opening rate as well as the submergence. At the end data were analysed and presented in form of graphically or expression. The most finding of the present stduy can be outline as follows:

In general, the results show that the coefficient of discharge increases with the increase in the gate’s opening ratio. From the data analysis it was found that with the relative increase of the gate opening from 0.41 to 0.49, the discharge coefficient increased from 39.4% up to 77.7%. It was also found that increasing the rate of submergence decreases the discharge coefficient. This trend was investigated by decreasing the percentage of submergence from the maximum increase of discharge coefficient and it was observed that with decrease of submergence from 0.9 to 0.7, the discharge coefficient increased between 89.6 to 58.7%. Another parameter that was investigated was the gradual upward angle of the gate upstream. The lowest coefficient of discharge obtained for the case of no transition upstream or sudden transition with angle of 90 degree. The elliptic lopac gate discharge coefficient with the gradual transition of 22.5 degree was 37% higher than that of the sudden transition. SPSS version 25 software was appleid to developed expression for predicting Cd (Eq. 9). This relation was extracted using 80% of obtained expremental data and the remaining 20% of the data was applied to validated the relation. Comparing the predicted values of Cd and the experimental data show high accuracy of this relationship.

The diversion dams are used to increase the water level and diversion flow from the river to intakes. Increasing the water level in the river will increase the potential flow energy upstream of the dam, as a result, the flow velocity on the overflow increases. Flow at the toe of a spillway is supercritical. If the high energy of water does not dissipated, causing scouring of the river's materials. Therefore, stilling basins are usually used to dissipate the energy of water exiting the spillway of a dam. If the flow energy is high in the toe, the stilling basins will have a larger dimension and the cost of the design will increase. Information about how to change the speed and depth of the flow during the spillway and calculating the flow characteristics in the in the toe of a dam is the most important factor in determining the type and dimensions of the stilling basins. Few studies have been conducted on the amount of energy loss and the flow characteristics in the toe of the dam. One of the objectives of this study is to provide an appropriate Formula for determining the amount of energy depreciation on the spillway that can be used to calculate the amount of depth and flow velocity in the toe of the dam. Investigation of the effect of surface roughness on discharge coefficient, flow velocity profile and the energy dissipation rate are other goals of this research.

In this paper, Savage and Johnson’s (2001) experimental data were used for evaluating the accuracy of the FLUENT model results. A physical model of a typical ogee spillway, with a design head Hd of 301 mm was fabricated and tested at the UWRL. The model was constructed of Plexiglas and was fabricated to conform to the distinctive shape of an ogee crest. The model also included a tangent section and a typical flip bucket. Plexiglas was chosen because it could be fabricated with smooth curves and easily instrumented with pressure taps. The model was 1.83 m wide and approximately 0.80 m high. The P/Hd ratio (height of crest/design head) was 2.7. Wall boundary condition was applied to the spillway body and vertical walls and floor of reservoir. Zero pressure boundary condition is applied in output and upper flow field. Zero pressure is applied in air inlet and velocity inlet in upstream boundary. VOF (volume of fluid) was used to determine free surface for solving flow field and to determine boundary condition of two-phase flow. The value of volume fraction is considered equal to zero on all boundaries, except that the water inlet flow value is applied equal to one. Using available experimental data, the depth of water on the weir crest and the pressure on the overflow body were calculated and compared with the observed results. In order to study the effect of bed roughness on velocity profile, flow coefficient and energy loss, the values of 0.01, 1 and 3 mm were considered for roughness and the FLUENT model was again applied for these values. By performing some simulations, relation to energy loss over ogee spillway was presented.

Based on the simulations carried out by the FLUENT model, the k-ε RNG turbulence model and the PISO algorithm are suitable for separating the governing equations. The water depth and pressure on spillway calculated by the FLUENT model is very close to the observed data. The average relative errors of the numerical model in estimating the water depth is 3.35% and average errors in estimating pressure on spillway are 0.88, 1.22 and 1.51cm for Q/Qd=1.33,1,0.625 respectively, which are suitable for predicting the characteristics of flow passing through a ogee spillway. Comparison of the results of the numerical model and observational values shows that the correlation coefficient of the pressure data is about 97.5%, which indicates the proper accuracy for simulating the flow through the overflow. One of the factors influencing the characteristics of the flow through the overflow is the body roughness. The discharge flow rate decreases slightly as surface roughness height and maximum velocity at any section is slightly decreasing as the surface roughness.

The results show that with increasing roughness of the weir crest at low discharge, about 6% of the discharge coefficient decreases compared to the smooth state. Also, with an increase in roughness at low discharge, about 50 percent of the energy in the toe of a spillway is reduced. In this study, a relationship was also proposed for the amount of energy loss over ogee spillway, which provides an accurate precision for calculating the amount of energy at the beginning of the stilling basins.

Weirs are hydraulic structure commonly used for controlling flow characteristics and water level (Vischer, 1998). Also, in dams, weirs are responsible for the controlled release of flood flows from the dam reservoir to the downstream channels. One of the types of weir is piano key weir (PKW). Piano key weirs are also very cost-effective and cheap to maintain, increase reservoir storage capacity, and offer better flood control (Ortel, 2018). The main problem at the downstream of hydraulic structures, such as weir, is the scour and movement of bed materials. Scouring in the downstream of weirs is an important issue for weir stability and has been extensively researched. In this study, the geometry of scour holes in the downstream of piano key weirs was investigated by the use of experimental models. According to previous researches, trapezoidal piano key weirs (TPKW) are more efficient than rectangular piano key weir (RPKW) (Mehboudi, 2016). While there are limited studies on scour downstream of RPKWs, the scouring downstream of the trapezoidal piano key have not yet been researched according to the authors' knowledge(Jüstrich, 2016). So it is important to study their scour, and it is necessary to compare the performance of these two types of PKWs in terms of scouring issues. Due to the fact that the geometric shape of the weir affects the downstream scour condition, in this study the downstream scour of the piano key weir with trapezoidal geometric shape has been considered and the characteristics of the scour and its rate of was compared to a rectangular geometric shape. Accordingly, the impact of discharge and the tail water depth on the characteristics of the scour hole at the downstream of the rectangular and trapezoidal piano key weirs and the comparison of these changes in the two models have been considered. Measurements were made to predict the scour specifications of the rectangular and trapezoidal piano key weirs, including the maximum depth of the scour hole, the distance between maximum scour depth and weir foundation, and the length of the scour hole (Figure 2).

In this study, two experimental models of PKWs with rectangular and trapezoidal geometry were made and tested in a flume with a length of 6.0 m, a width of 1.0 m and a height of 0.6 m. 2.0 m length with an average thickness of 25 cm was formed from sandy material with median grain size d_50=7.8 m (Figure 3). Three hydraulic conditions in upstream and three different tail water depth considered in downstream and totally 18 experimental runs were conducted. A summary of the initial conditions, numbers, and codes of the experiments is given in Table 2. The range of changes in discharge in this research is between 19 to 33 liters per second. The reason for choosing this range for discharge is to examine the conditions of the scour profile in a wide range of flow rate changes. In addition, the dimensions of the channel and the pump used do not allow the discharge to exceed 33 liters per second.

Effect of discharge on the scour hole profile downstream of the rectangular and trapezoidal PKW models are shown in Figure (8). It can be seen that in all models, as discharge and upstream head increase, so do the hole depth and hole length and the distance of maximum scour depth from the weir toe. Previous studies have reported similar findings for linear and nonlinear weirs (Jüstrich, 2016). As shown in Figure (4),In this study, the arrangement of inlet and outlet keys of weirs was considered different from previous researches, so it was observed that the maximum depth of downstream scour occurs below the output keys, the reason for this is the external spill jets from the output keys, which cause the scour hole to fall into the downstream through vertex. Also, comparison the scour hole characteristics of downstream rectangular and trapezoidal piano key weirs in Figure (9) shows that the maximum scour hole depth downstream of the rectangular model is higher than the trapezoidal model. The higher score hole depth in the downstream of the rectangular model than the trapezoidal model in similar hydraulic conditions can be attributed to the fact that, for any given flow rate, upstream-downstream total head difference is greater in the rectangular weir comparison to the trapezoidal weir . As shown in Figure (11), For both rectangular and trapezoidal models, at a constant flow rate, the depth and length of the scour hole have decreased with the increase of tail water depth. It is due to a decrease in the height of the drop jet and increase in jet speed during impact to downstream flow. To determine the effect of the geometric shape of PKW and the tailwater depth, the scour characteristics in rectangular and trapezoidal models in the range of conducted experiments were examined and compared based on the configuration of Equation ∅_s/H=a〖F_rd〗^b (H/h)^c. Then, the nonlinear regression method was used to determine the coefficients a, b, and c and formulate a number of equations for predicting the maximum scour depth, its location, and the scour hole length for rectangular and trapezoidal PKWs. These equations are presented in Table (3) .

The measurement results of the cascade characteristics showed that with increasing the flow rate and decreasing the tail water depth, the geometric characteristics of the score hole increase in both models. Also, the depth of scour in the rectangular model is more than the trapezoidal model. in all discharges, on averagely, get decreases %7 the ratio of dimentionless maximum scour depth of trapezoidal piano key to the rectangular model. but this difference decreases with increasing flow and total head on the weir, so that when in F_rd>3.9 this difference becomes insignificant and there is not a significant difference in the shape of the hole for both models. Using the regression method, several equations with appropriate accuracy were formulated for predicting the maximum scour hole depth, its location, and the scour hole length downstream of the models.

Accurate flood routing through the river reaches is one of the essential issues in the river training activities and flood warning systems. Especially when the river passes near residential areas of cities, it is vital to have enough information about the maximum flow that can flow through the river without damaging its surroundings. Due to the complexity of the complete solution process of Saint-Venant equations, over the years, many researchers have tried to provide alternative models that, in addition to simplicity, have the necessary accuracy. Previous models usually have two significant drawbacks. First, the process of solving most of them is step-by-step, and to calculate the outflow discharge at each time step, the estimated flow in the previous step is required. Second, sometimes the model coefficients change during the resolution process. Therefore, in the present study, an attempt was made to provide a clear and direct relationship. Also, if the coefficients are known for determining the flow rate in each time step, there is no need for the values of the previous steps.

In order to prove the prevailing analytical relationship, in this research, first, the two processes of flood transfer and flood dispersion in the river reaches were conceptually separated. For this purpose, the river reach was divided into three interconnected reservoirs. The first reservoir is an index of the flood convection, and the next two reservoirs were the index of flood propagation process. The runoff volume, obtained from the upper basin, was calculated using multiplying the runoff coefficient to the rainfall height. Then, it was suddenly applied to upstream of the river reach by using the Dirac delta function. By adding the spatial flow variation coefficient to the reservoirs of the propagation operation as well as applying the mass equilibrium and inclining the dimensions of the reservoirs to zero, the differential equations governing each reservoir were obtained. The outflow of each reservoir was used as the boundary condition of the next one, and the final equation, obtained from the interconnected reservoir system, was used as the output hydrograph relationship. In order to evaluate the performance of the introduced model, the data of four flood events that were recorded on (19 - 3 – 2017), (15 - 4 – 2017), (29 - 1 – 2019), and (31 - 3 - 2019) in Simineh River were used. Simineh River is located south of Lake Urmia and provides 11% of the lake's water. The flood data was recorded at three stations of BUCKAN Bridge, DASHBAND BUCKAN, and MIANDOAB Bridge with two-hours interval.

The proposed model is a four-parameter model that works directly by operation of its parameters. Therefore, firstly the model parameters were estimated and then the output hydrograph was simulated at the end of the river reach. The simulated hydrographs by the proposed model were very consistent with the measured data at the end of the interval, indicating its efficiency. Statistical indicators of coefficient of determination (R2), root mean square error (RMSE), and Nash-Sutcliff (DC) were used to quantify the desirability of the model. The above-mentioned statistical parameters for all flood events were calculated as triple sets of (0.86, 0.07, 0.95), (0.82, 0.11, 0.8), (0.97, 0.07, 0.94), and (0.93, 0.1, 0.9), respectively which also proves its quantitative suitability. By creating linear relationships between the residence times of the flood in each of the interconnected reservoirs, the relevant volumes were calculated. It was also found that the length of each reservoir can be calculated separately by applying a mean cross sectional area in the river reach. The flood volume was calculated to be 30, 50, 63 and 37 million cubic meters for events of 1 to 4, respectively. This value is equal to the total volume of the assumed reservoirs in the river reach. Ratio (V/T) was calculated for all reach lengths and flood events, and it was found that its value decreases with the increasing of reach length, but its value for larger floods is higher than for smaller ones. Besides, it was found that the position of the dispersion reservoirs in the river reach can be exchanged with each other, and the total volume of them is the diffusion index.

Finally, it was observed that the proposed model has good compatibility with observational hydrographs, except in the initial points of raising limb. Optimization or numerical methods can also be used to obtain model parameters. Moreover, the explicitness and directness of the discharge calculation by this method is the most crucial advantage of this model. This model also has the capability of reconstructing hydrographs affected by the spatially varied flow.

Rivers can be classified as straight, meandering and braiding, Meandering is the most common plan-form acquired by natural rivers. The meandering channel flow is considerably more complex than the straight channel. Compound meandering channels are abundant in nature that including the main channel for the flow in normal times and one or two floodplain (usually covered with plants) at the sides during floods. Vegetation is an important property of many rivers, enhancing amenity values for people and providing habitat for other organisms. Vegetation stabilizes stream banks, provides shade that performs an essential role in nutrient cycling and water quality and supports wildlife. Therefore, it is necessary to study this issue in order to better understand the flow during floods. This study is focused on the influence of vegetation on overbank flow characteristics. In this research, the effect of non-submerged rigid artificial vegetation in the floodplain on two relative depths of 0.35 and 0.55 has been studied in the laboratory.

The experimental research was carried out in a non-mobile bed meandering channel constructed in a 10 m long and 0.78 m wide flume which included the main channel and two floodplains on its sides. The channel wavelength and meander belt width were one meter and 0.58 m, respectively with the sinuosity of 1.3. The geometrical parameters for the main channel were: width, Bmc=0.2 m and depth, Hmc= 0.1 m. Plastic cylinders of 9mm diameter are used to simulate the emergent floodplain vegetation. A movable weir located at downstream of flume controlled water level. Velocity data were extracted and analyzed using Acoustic Doppler Velocimetry. The minimum recording time for each point velocity was 60s. ADV measures the 3D velocities of water particles located 5 cm below its probe. The measurement sections located 6 m downstream of channel inlet, with the names of S1 to S5.

The results showed that the presence of vegetation in the plain flood for a constant relative depth has reduced the flow capacity. The decrease in discharge for depths of 0.35 and 0.55 is equal to 23 and 12 percent, respectively, for a density of 0.77 percent per unit area of one square meter. The pattern of contour lines of the longitudinal velocity in the main channel in the presence of vegetation changes at both relative flow depths relative to the uncovered state. The absolute values of velocity in the main channel in the uncovered state are greater than in the covered state. Also, the values in the transverse and vertical velocity components in plain floods with vegetation are much higher than in uncovered conditions. The directional secondary vectors of the flow in section S1 indicate a counter-clockwise flow in the main channel. The presence of vegetation at a relative depth of 0.55 has reduced the size and values of these vectors in both the main channel and the floodplain. It seems that the presence of coverage, as observed during the experiments, has changed the patterns and directions of vectors on the floodplain. These changes are also observed at the relative depth of 0.35, but specifically the presence of vegetation at this relative depth has caused the flow transfer from the right floodplain to the left floodplain. For all sections, the average values of longitudinal velocity on both sides of the floodplain are greater than the uncovered state and increase by moving away from the main channel to the glass wall of the channel. Although the capacity of covered flow is less than the uncovered one, flow velocities in and around the main channel seem to be close to those measured in uncovered channel. This indicates the high impact of floodplain vegetation on the hydraulics of the flow in the compound meandering channels. Also, the presence of cylinders has increased turbulence and consequently increased shear stress. The values of shear stress at the bottom of the main channel and the convex coast of the floodplain are higher than other areas. In addition, the cover has increased shear stress in the floodplain and reduced the kinetic energy of turbulence (TKE) in the floodplain.

In this study, using a laboratory model, the effect of non-submerged rigid artificial vegetation on the floodplain of a compound meandering channel was investigated. The following is a summary of the results of this study. The presence of vegetation reduced the water transfer capacity, due to the increased resistance to flow. The average longitudinal velocity of the flow in the cross section of the channel in the uncovered state is higher than in the case with the cover. Due to the non-submerged rigid artificial vegetation used, the shear stress in the floodplain has increased. Keywords: Flood, Flow Pattern, Meander Channel, Relative Depth, Vegetation

Weirs are hydraulic structures with a various application as flow measurement, flow diverting, and/or flow control. Weirs are designed under free-flow conditions meaning tailwater is lower than weir crest, in this state, flow passing the weir is governed by the weir geometry and the approach flow condition. When the tail-water exceeds the crest elevation, the weir is submerged. Under submerged conditions for a certain discharge, a higher upstream head is required to pass the flow relative to the free flow state. Therefore, the submerged head-discharge relationship is different from free condition one. According to the literature, there are three main methods to extract the relationship between dependent and independent variables: experimental methods, classic regression equations, and intelligent algorithms. The previous researches showed that more studies have been performed experimentally to predict the head-discharge relationship for linear and labyrinth weirs while using artificial intelligence has been proved to include more accuracy to adapt complex hidden relationships among dependent and independent variables. In this paper, two intelligent algorithms namely SVM and GEP have been applied to extract the relationship between a submerged head-discharge function for linear and labyrinth weirs. The results of these two mentioned algorithms were compared with experimental and regression modeling.

To simulate H^*/H_o using SVM and GEP, two scenarios were defined. At the first scenario, the amount of H^*/H_o for labyrinth submerged weir was modeled using five dimensionless parameters as Fr1, Cd, H_d/H_o , H_o/P, and α. For the SVM algorithm, the Nu-class classification method with Redial Basis Function as kernel function were selected using setting parameters as γ and Nu. GEP was applied as another algorithm to model H^*/H_o for the labyrinth weir. In the second scenario, SVM and GEP were applied to predict H^*/H_o for the linear submerged weir. To compare the performance assessment of an intelligent algorithm, two types of equations were obtained using classic regression models. The first one was the extracted relationship of Tullis et al. (2007) and the second one was the SPSS regression equation. All simulations were compared with four assessment criteria as root mean square error (RMSE), determination coefficient (R2), relative error (RE), and standardized developed discrepancy ratio (ZDDR). Sensitivity analysis was the last step of the H^*/H_o prediction.

Training and testing phases of SVM and GEP were assessed using the above four mentioned assessment criteria. The included dimensionless parameter for the submerged labyrinth weir to predict H^*/H_o were Fr1, Cd, H_d/H_o , H_o/P, and α whereas for the second scenario only Fr1 and H_d/H_o were opted as the effective parameters. The amount of RMSE, R2, RE and ZDDR for SVM at the first scenario during training and testing phases were calculated as (0.0081, 0.9999, 3.34, 66.496) and (0.0104, 0.9996, 1.741, 45.267) respectively. Those of GEP were obtained as (0.2225, 0.9986, 4.42, 23.48) and (0.0157, 0.9992, 0.533, 19.73) respectively. According to these values, SVM was selected as the superior model than to GEP. A comparison was done between SVM and other regression simulations. The values of mentioned assessment criteria for Tullis et al.’s relationship and SPSS extracted equation were computed as (0.02855, 0.9990, 1.756, 19.115) and (0.0307, 0.9990, 8.503, 20.875) respectively. Therefore, among all the used predicting the head-discharge relationship of labyrinth submerged weir, the SVM model was selected as the best model. Sensitivity analysis was performed to determine which parameter has the most effect on the head-discharge relationship. This procedure was done with dropping each of five included parameters and computing four mentioned assessment criteria. According to the calculation, the most significant parameter based on the most decrease of SVM accuracy was Fr1. In the second scenario, a similar calculation was done on the linear submerged weir. The best performance was accrued for the SVM algorithm for training and testing phases. The corresponding accuracy indices values during testing phase for SVM and GEP were (0.0066, 0.9996, 0.320, 67.91) and (0.0088, 0.9998, 0.5432, 63.73) respectively. The priority of SVM performance than to the classic regression equations namely Tullis et al.’s (2007) relationship and SPSS equation were proved with the accuracy indices. The amount of assessment criteria values for two above mentioned models were (0.0118, 0.9997, 0.653, 60.69) and (0.0507, 0.9965, 3.444, 8.76) respectively. According to the sensitivity analysis, the most effective parameters with the most impact was H_d/H_o for the linear submerged weir.

The results showed that intelligent algorithms have the most performance than to the other classic and experimental relationships to extract the head-discharge relationship for the submerged labyrinth and linear weirs. Of two SVM and GEP models, the first one was the top model for the labyrinth and linear weirs head-discharge relationship prediction. It’s recommended to use an intelligent algorithm to predict and extract the complicated and hidden relationship among dependent and independents variables.