مجله هیدرولیک
سال چهاردهم شماره 3 (پاییز 1398)

One of the main characteristics of stepped spillways is energy dissipation along the spillway during the flow transmission. This research is to propose a new form of spillways’ steps in order to achieve the maximum level of energy dissipation. In this paper flow hydraulics affected by geometric reform of steps to labyrinths with trapezoidal, triangular and rectangular shapes is investigated numerically using FLOW-3D model. The results show that production of flow interferences during flow passing over the labyrinth shapes is the main achievement of labyrinth stepped spillway. Also, trapezoidal labyrinth shape shows a better performance in accessing the maximum energy dissipation. In the same flow condition the rectangular, triangular and trapezoidal labyrinth shaped stepped spillways are effective in flow velocity reduction by 4.62%, 12.21% and 23.76% and also in more energy dissipation by 5.6%, 13.1% and 17% respectively compared to the usual flat stepped spillway. This is because of streamline interference and increasing the resistance against the flow and also the extension of recirculating region and production of more rotational flow. These types of spillways have fewer amounts of the residual head than that for flat stepped spillways. The residual head ratio (Hres/yc) in this type of spillway is ~2.57 while it is ~4.32 in the flat stepped spillway. Finally one can find these types of spillways as next generation of stepped spillways which increases the efficiency and hydraulic performance.

Introduction The occurrence of flood in the human’s history has always been one of mankind’s concerns. The methods of confronting this destructive phenomenon are of utter importance between researchers. One of the categories against this issue is flood routing. The financial losses of flood to human societies have made it very important to predict the occurrence of floods, so that it is necessary to accurately predict flood. In order to predict the outflows, in fact, the extraction of flood hydrographs is required in the downstream. The routing methods are divided into two hydraulic and hydrological groups. Hydraulic methods require the historical data and the solution of equations mainly through complex hydraulic methods is time consuming, however hydrological methods are preferred because of simplicity of their relative concepts. They are easy to implement and economize time. It is believed to be popular with researchers and has always tried to improve the accuracy of the results of the hydrological methods, which has become a good alternative to hydraulic methods. The Muskingum method is the most widely used hydrological routing technique which is divided into two groups of linear Muskingum and nonlinear Muskingum, depending on the relationship between the amount of storage and the inflows and outflows. Methodology Various methods for estimating the hydrological parameters of Muskingum model have been presented. Techniques for estimating the parameters of the Muskingum model can be classified into three categories: mathematical techniques, phenomenon-mimicking techniques and hybrid algorithms. Among various methods of routing, three parameters nonlinear Muskingum method are hugely popular. Evolutionary algorithms are used to estimate the optimal parameters of the nonlinear Muskingum method because of their convergence rate, no need to make very accurate initial estimate of the hydrological parameters and their randomness nature. In this paper, a gravitational search algorithm which is based on the Kepler algorithm was first used to routing three different hydrographs. In fact, Kepler algorithm is inspired by the elliptical motion of planets around the sun. At different times, the planets are very close to the sun, which represent the stage of the exploration of the algorithm, and at other times the planets are far away from the sun and express the stage of exploitation of the algorithm. Results and discussion Using the combination of gravitational search algorithm and Kepler algorithm (GSA-Kepler), the parameters of the Muskingum model are calculated for routing three different hydrographs: Wilson (1974), Wye River and Veissman and Lewis (2003). The first example is a benchmark problem that was first considered by Wilson (1974) to estimate the parameters of the Muskingum model. This river has no branch to the Belmont and has very little flow. The results of the GSA-Kepler and the Segmented Least Squares Method, BFGS, HJ + DFP, HJ + CG, Genetic Algorithm, Immune Clonal Selection Algorithm, Harmony Search Algorithm and Free Parameter Setting Harmony Search Algorithm are compared with each other. The second example is the flood hydrograph in the Wye River. It has no tributaries from Erwood to Belmont and has very little lateral flow. The third model is a multi-peak flow hygrograph that was first studied by Veissman and Lewis (2003). For the second example, the results of the GSA-Kepler algorithm, COBSA, PSO, DE, GA, BFGS and WOA are showed and for the third example, the results of the GSA-Kepler are compared with the results of the WOA and MHBMO algorithms. After determining the optimal hydrologic parameters, their uncertainty is estimated using the possibility theory. Selecting an analysis of uncertainty depends on many factors, such as knowledge of uncertainty sources and model complexities. There is no definite guideline for choosing the specific uncertainty analysis method that works best. The principles of analyzing the possibility theory are based on fuzzy theory, which was first pronounced by Zadeh in 1965. To investigate the uncertainty of the nonlinear Muskingum model parameters based on the possibility theory, the aforementioned algorithm and other algorithms include Least Squares Method, Gravitational Search Algorithm, BFGS algorithm, HJ + DFP, HJ + CG, Genetic Algorithm, Immune Clonal Selection Algorithm, Harmony Search Algorithm and Free Parameter Setting Harmony Search Algorithm were used. Then three triangular membership functions were assigned to the hydrological variables and the uncertainty of these parameters was calculated using the fuzzy alpha cut method. Conclusion Comparing the results of the GSA-Kepler with the results of the previous studies shows that the combined algorithm used in this study has an acceptable accuracy and high convergence rate. Based on the fuzzy alpha cut method, it is determined that for Wilson (1974) the uncertainty of parameter k is greater than the uncertainty of parameters x and m. Keywords: Membership function, GSA-Kepler, Possiblity theory.

Human activities everyday release a huge amount of domestic, industrial and agricultural waste into water bodies and continuously change the ecosystem conditions in the world. Considering the harmful effects of these pollutants entering water resources, study about pollution transfer in streams and predicting the pollutant concentration at downstream points seem to be important. For this purpose, the well-known classical advection-dispersion equation (ADE) was presented as the first attempt for describing mass transfer and energy transfer in physical systems. This equation is useful for channels with relatively prismatic and uniform cross-sections. Experimental studies carried out in rivers show that ADE is no longer applicable for natural streams, especially mountain pool and riffle streams because of their irregular cross-sections. Afterward, some more accurate models, referred dead zone models or transient storage models, were suggested by several researchers for predicting solute concentration in natural rivers and calibrated using tracer approach. Such models cause more realistic concentration-time distributions which have lower picks and longer residence time. Solving such models, for which in most cases the analytical solution doesn’t exist, needs numerical methods –methods which usually deal with complexity and is time-consuming. In this study, we have applied Network Simulation Method (NSM) –a powerful and efficient computational method for simulating systems governed by differential equations based on the electric circuit concepts and the analogy between the governing differential equations of hydrodynamic and electrical phenomena– which according to the previous studies simulates desirably the transport of mass in natural streams, to solve two transient storage models. The method consists of two phases of designing and simulating. In designing phase, the system of differential equations corresponding to the prototype must be discretized spatially over the studied domain and then, for each term of the discretized equations the equivalent electrical devices are chosen. These electrical elements are connected based on the algebraic sign of the terms to satisfy Kirchhoff’s current low. Regarding the mathematical models, in most studies, electric potential and electric current are equivalent to the value of the unknown variable and its flux, respectively. The last step of designing the electro-analogical model is the implementation of initial conditions and boundary conditions of unknown variables using appropriate dependent and/or independent, voltage and/or current sources. Simulating this equivalent electrical network is performed through an appropriate electrical-computational circuit code, such as PSpice code. PSpice, which is a powerful circuit analysis software, uses the Newton-Raphson iterative algorithm to solve this set of nonlinear equations and performing the transient analysis. In this paper, NSM is firstly verified by simulating a transient storage transport model developed by Bencala and Walters (1983) for unsteady conservative solute transfer in pool and riffle streams. This model includes two equations for solute concentration in the main channel and in the storage zone and involves one storage zone. The analytical solution for this model has been presented in Laplace domain by Kazezyılmaz-Alhan (2008) considering a hypothetical channel with a constant cross-sectional area, flow velocity, and dispersion coefficient and for two types of upstream boundary conditions including a continuous injection and a pulsating solute injection. The results of this verification were desirable. Then, the accuracy and efficiency of NSM were compared with Finite Volume Method (FVM) –a widely used numerical method in computational fluid dynamics- through simulating an unsteady reactive solute transport using a nested two-storage zone transport model developed by Kerr et al. (2013). This model consists of three equations and involves two storage zones including the surface and hyporheic storage zones interacting together. The results of simulating a hypothetical solute transport problem with this nested model indicate a good match between these two methods with near-zero error indices. The computational time needed for NSM and FVM were 117 seconds and 505 seconds, respectively. So, NSM is much faster. Furthermore, the implementation of boundary conditions in NSM is direct, easier and more flexible. Therefore, NSM is proposed as a precise and efficient alternative for numerical methods in solving one-dimensional coupled differential equations of unsteady transport, simultaneously and providing benchmarks without complex mathematical calculations. Because of its analogical based concept, it can be used as a predicting and monitoring tool for transport phenomena instead of using troublesome physical hydraulic models to perform the water quality studies with less time, low expense and higher accuracy. Hence, in critical conditions, including a sudden spill of a high-hazardous contaminant in a specified point of the river or increasing the concentration of a chemical element to its maximum level, the monitoring and controlling measures at different parts of the river can be carried out with an acceptable accuracy and speed to improve the water quality.

In the present research, it was tried to evaluate the pollution transport in the interconnected reservoirs by deriving a theoretical solution based on the TS model partial differential equations and by conducting an experimental model. The theoretical model has been solved by operation of the Laplace transform to the PDE equations, and a complete evaluation of the model applicability and the parameters’ magnitudes have been fulfilled using experimental data series of two interconnected reservoirs. The created rockfill dams in the laboratory flume have been produced using three different median diameters of the 1.1, 2.3, and 3.6 cm. The other experiment variables were the entrance discharges as 7, 9, 11, and 13.5 l/s and linear source concentration of the 100, 140, and 200 gr/l. The mean values of the velocities, dispersion coefficients, and the logarithm of the mass transfer coefficients between the storage area and the main flow have been determined as 4 cm/s, 2.4 cm2/s, and -10.5 respectively. The corresponding of the experimental breakthrough curves with theoretical ones have been assessed and confirmed using statistical parameters of the RMSE and Nash-Sutcliff, having the values of 0.21 and 0.7, respectively. In the present research, it was tried to evaluate the pollution transport in the interconnected reservoirs by deriving a theoretical solution based on the TS model partial differential equations and by conducting an experimental model. The theoretical model has been solved by operation of the Laplace transform to the PDE equations, and a complete evaluation of the model applicability and the parameters’ magnitudes have been fulfilled using experimental data series of two interconnected reservoirs. The created rockfill dams in the laboratory flume have been produced using three different median diameters of the 1.1, 2.3, and 3.6 cm. The other experiment variables were the entrance discharges as 7, 9, 11, and 13.5 l/s and linear source concentration of the 100, 140, and 200 gr/l. The mean values of the velocities, dispersion coefficients, and the logarithm of the mass transfer coefficients between the storage area and the main flow have been determined as 4 cm/s, 2.4 cm2/s, and -10.5 respectively. The corresponding of the experimental breakthrough curves with theoretical ones have been assessed and confirmed using statistical parameters of the RMSE and Nash-Sutcliff, having the values of 0.21 and 0.7, respectively. In the present research, it was tried to evaluate the pollution transport in the interconnected reservoirs by deriving a theoretical solution based on the TS model partial differential equations and by conducting an experimental model. The theoretical model has been solved by operation of the Laplace transform to the PDE equations, and a complete evaluation of the model applicability and the parameters’ magnitudes have been fulfilled using experimental data series of two interconnected reservoirs. The created rockfill dams in the laboratory flume have been produced using three different median diameters of the 1.1, 2.3, and 3.6 cm. The other experiment variables were the entrance discharges as 7, 9, 11, and 13.5 l/s and linear source concentration of the 100, 140, and 200 gr/l. The mean values of the velocities, dispersion coefficients, and the logarithm of the mass transfer coefficients between the storage area and the main flow have been determined as 4 cm/s, 2.4 cm2/s, and -10.5 respectively. The corresponding of the experimental breakthrough curves with theoretical ones have been assessed and confirmed using statistical parameters of the RMSE and Nash-Sutcliff, having the values of 0.21 and 0.7, respectively. In the present research, it was tried to evaluate the pollution transport in the interconnected reservoirs by deriving a theoretical solution based on the TS model partial differential equations and by conducting an experimental model. The theoretical model has been solved by operation of the Laplace transform to the PDE equations, and a complete evaluation of the model applicability and the parameters’ magnitudes have been fulfilled using experimental data series of two interconnected reservoirs. The created rockfill dams in the laboratory flume have been produced using three different median diameters of the 1.1, 2.3, and 3.6 cm. The other experiment variables were the entrance discharges as 7, 9, 11, and 13.5 l/s and linear source concentration of the 100, 140, and 200 gr/l. The mean values of the velocities, dispersion coefficients, and the logarithm of the mass transfer coefficients between the storage area and the main flow have been determined as 4 cm/s, 2.4 cm2/s, and -10.5 respectively. The corresponding of the experimental breakthrough curves with theoretical ones have been assessed and confirmed using statistical parameters of the RMSE and Nash-Sutcliff, having the values of 0.21 and 0.7, respectively.

Introduction Flow contact with the spillway piers causes rooster tail waves which could continue along the flood evacuation system. Therefore, the information about the height and location of these waves would be useful for the design of the spillway chute walls. On the other hand, the engineers try to design the converging chutes to reduce the excavation costs, and this convergence in many cases would increase the transverse flow depth. According to the literature, three kinds of waves could be formed in the spillway and chute system. The first wave is formed just after the spillway piers and called as rooster tail waves. The Flow passing through the two sides of a pier collide each other at a near distance after the pier and forming the first wave. The second wave is formed at the middle axis of the chute and could be considered as the result of the interaction of the first waves and the channel convergence. The third wave is formed due to the collision of the mentioned waves with the channel walls. Investigating the effect of the chute convergence on the depth and location of transverse waves is critical and necessary and could present suitable information about the three waves. In this paper, the numerical simulation of the Khair Abad dam flood evacuation system is performed for investigating the effects of chute convergence on the formation of the transverse waves along the chute. Methodology In this Research, the FLOW-3D is used for simulation of the effects chute convergence on transverse wave formation. The Khair Abad dam flood evacuation system laboratory tests results were used for verification of the numerical simulation. The present simulations considered four convergence angles of the chute, including 0, 3, 5 and 7 °. Also, the simulation was performed using three discharge rates consist of 3000, 7000 and 9000 m3 / s. The convergence angle of the Khairabad Dam spillway is approximately 5 degrees and the convergence angles were changed during the chute until the chute width reached from 66 m to 40 m. The chute width is kept constant after the convergence. Results and discussion The model validation was performed using the laboratory data of the Kheirabad Dam spillway Model developed by the Iran Water Research Institute. Since the size and number of the cells in the model affect the accuracy of the results and computational cost, this study concentrates in finding the optimum value of dimensions and number of cells for the simulation domain. This procedure could result in acceptable accuracy and suitable computational cost. The results of the verification showed that the smaller grid size and the greater number of cells, result in the higher correlation of the numerical results and the laboratory data. Hence, based on the above-mentioned method and available computational device, the best size and number of the cells were selected for simulating the effect of chute convergence on the three waves height. Simulation results show that the height of the first wave increases with increases in the flow discharge, and the spillway convergence has not a significant effect on the first wave height. Also, the second wave height is increased by the increase in flow discharge. It should be mentioned, the second wave doesn't appear when there is no convergence in the chute, but with increasing the convergence angle the wave height increases and the maximum wave height will move to upstream stations of the chute. In other words, with the increase of the angle of convergence of the chute, the location of the second wave formation will be closer to the spillway crest and its height will increase. The simulation results demonstrated that the increase in the flow discharge could lead to an increase of third waves heights. Also, the results show that the third waves could not be formed when the channel convergence angle is equal to zero, and increase of convergence angle could result in an increase of the third wave height. Also, the increase in the angle of convergence of the chute results in transport of the location of the third wave formation into upstream stations. In other words, the third waves will form closer to the spillway axis by an increase in convergence angle. Numerical simulation results show that the height of the third wave which formed beside the wall can be more than twice the average flow depth at the same point. This fact should be considerate in the design of the chute with convergence. The results also showed that increasing the flow discharge will cause to increase of the wave height, but it led to the decrease of the ratio of the third wave height to the average flow depth. This means that increasing the discharge has less effect on increasing the transverse wave height. Conclusion Simulation results show that the height of transverse waves increases by increasing the discharge. But the ratio of the maximum height of the waves to the average depth of the same station will reduce by the increase of the discharge. Also, Results show that, by increasing the chute’s convergence angle, the height of the transverse waves will increase and the location of the primary transverse waves will transmit to upstream locations of the chute.

Increasing frequency and intensity of flooding in urban areas have led to serious damage in urban areas. One of the major challenges in urban flood analysis is the two dimensional simulation of surface runoff caused by surcharged flows from urban drainage systems. Thus, development of an urban flood simulation model, which can rout the water flow on complex topography of urban catchments and determine flooded areas with acceptable computational time and accuracy is very important. In this study, a flood simulation model based on cellular automata approach is developed to reduce time and computational effort in compare with other 2D conventional hydraulic models. The developed model performance is compared with HEC-RAS, shallow water equation and TUFLOW models which simulate the water movement using conventional numerical schemes. Also the model’s stability is assessed by considering different time step and mesh size. The obtained results show that the proposed model, using topographic and surface roughness data as inputs, can simulate water movement with acceptable accuracy one- and two-dimensionally. In addition, the computational time is reduced up to roughly 60 times compared to the model which is based on shallow water equations. Increasing frequency and intensity of flooding in urban areas have led to serious damage in urban areas. One of the major challenges in urban flood analysis is the two dimensional simulation of surface runoff caused by surcharged flows from urban drainage systems. Thus, development of an urban flood simulation model, which can rout the water flow on complex topography of urban catchments and determine flooded areas with acceptable computational time and accuracy is very important. In this study, a flood simulation model based on cellular automata approach is developed to reduce time and computational effort in compare with other 2D conventional hydraulic models. The developed model performance is compared with HEC-RAS, shallow water equation and TUFLOW models which simulate the water movement using conventional numerical schemes. Also the model’s stability is assessed by considering different time step and mesh size. The obtained results show that the proposed model, using topographic and surface roughness data as inputs, can simulate water movement with acceptable accuracy one- and two-dimensionally. In addition, the computational time is reduced up to roughly 60 times compared to the model which is based on shallow water equations. Increasing frequency and intensity of flooding in urban areas have led to serious damage in urban areas. One of the major challenges in urban flood analysis is the two dimensional simulation of surface runoff caused by surcharged flows from urban drainage systems. Thus, development of an urban flood simulation model, which can rout the water flow on complex topography of urban catchments and determine flooded areas with acceptable computational time and accuracy is very important. In this study, a flood simulation model based on cellular automata approach is developed to reduce time and computational effort in compare with other 2D conventional hydraulic models. The developed model performance is compared with HEC-RAS, shallow water equation and TUFLOW models which simulate the water movement using conventional numerical schemes. Also the model’s stability is assessed by considering different time step and mesh size. The obtained results show that the proposed model, using topographic and surface roughness data as inputs, can simulate water movement with acceptable accuracy one- and two-dimensionally. In addition, the computational time is reduced up to roughly 60 times compared to the model which is based on shallow water equations. Increasing frequency and intensity of flooding in urban areas have led to serious damage in urban areas. One of the major challenges in urban flood analysis is the two dimensional simulation of surface runoff caused by surcharged flows from urban drainage systems. Thus, development of an urban flood simulation model, which can rout the water flow on complex topography of urban catchments and determine flooded areas with acceptable computational time and accuracy is very important. In this study, a flood simulation model based on cellular automata approach is developed to reduce time and computational effort in compare with other 2D conventional hydraulic models. The developed model performance is compared with HEC-RAS, shallow water equation and TUFLOW models which simulate the water movement using conventional numerical schemes. Also the model’s stability is assessed by considering different time step and mesh size. The obtained results show that the proposed model, using topographic and surface roughness data as inputs, can simulate water movement with acceptable accuracy one- and two-dimensionally. In addition, the computational time is reduced up to roughly 60 times compared to the model which is based on shallow water equations.

Evaluation of Hydraulic Performance of Ilam Gas Refinery fire-fighting water network (middle ring) Abstracts Hydraulic simulation of conveyance lines and fire-fighting distribution networks are considered appropriate tools for their assessment. In this research, Ilam gas refinery network (middle ring) was evaluated using field studies and hydraulic simulation software. The fire-fighting water network is divided into upper, middle and bottom rings. Each rings of the network are responsible for the one part of the refinery area. Hydraulic simulation of the water conveyance pipeline from the main reservoir to the middle ring reservoir were carried out in four modes of gate valve operation. Different fire scenarios were carried out to investigate the operation of fire-fighting network. The most critical scenario was the fires in floating roof tanks; with a flow rate of 1375 m3/h. Sensitivity analysis was performed on changes in the roughness coefficient of pipes and the required flow rate in the network. With an increase of roughness by 20%, the average pressure in the middle ring decreased by as much as 3.5%. In the case of increasing the required flow, the pumping pressure and deluge valve pressure drop by 3.2 and 12.2%, respectively. Field investigation showed that 20 percent of hydrants have problems and leaks. Field inspection of the cooling system operation of floating roof tanks was carried out with the activation of one and two electric pumps. The measured pressure gauge at the pumping station with one and two pumps is 11 and 12 bars, and these pressures are higher than 10 bar allowable pressure. The field inspection of tanks foam system was performed with the one of a diesel pump. The pressure gauge showed 12 bars at the middle-pumping station, which could cause a failure of the ring equipment. Keywords: Fire-fighting, hydraulic simulation, WaterGEMS, Ilam gas refinery Introduction Fire water distribution networks consist of interconnected sets of reservoirs, pipes, pumps, hydrants, hose reels and valves that are responsible for the transfer and distribution of water with suitable pressure and quality for firefighting demands. Hydraulic simulation of conveyance lines and fire-fighting distribution networks are considered appropriate tools for their assessment. In this research, Ilam gas refinery fire water network (middle ring) was evaluated using field studies and hydraulic simulation software. Methodology Ilam gas refinery fire water network is divided into upper, middle and bottom rings. Each rings of the network are responsible for the one part of the refinery area. The maximum and minimum diameter of the distribution pipes is 14 inches and 6 inches, respectively. Polyethylene pipes have a working pressure of 16 bars. The maximum allowable velocity in the pipes is 3.5 m /s. At the refinery site, several centrifugal pumps have been used to supply pressure during firefighting, maintaining a pressure of 10 bar in the main ring. The total number of hydrants, shut-off valves and hose reels are 170, 147 and 76, respectively. WaterGEMS hydraulic software was used to simulate Ilam gas refinery fire water network. Results and discussion Different fire scenarios were carried out to investigate the operation of fire-fighting network. The most critical scenario was the fires in floating roof tanks; with a flow rate of 1375 m3/h. Hydraulic simulation of the water conveyance pipeline from the main reservoir to the middle ring reservoir were carried out in four modes of gate valve operation. Field investigation showed that 20 percent of hydrants have problems and leaks. Field inspection of the cooling system operation of floating roof tanks was carried out with the activation of one and two electric pumps. The measured pressure gauge at the pumping station with one and two pumps is 11 and 12 bars, and these pressures are higher than 10 bar allowable pressure. The field inspection of tanks foam system was performed with the one of a diesel pump. The pressure gauge showed 12 bars at the middle-pumping station, which could cause a failure of the ring equipment. Conclusion In this research, the middle ring of the fire water network of Ilam gas refinery was tested and evaluated using the WaterGEMS hydraulic simulation software. Different scenarios related to this ring, which included the simultaneous operation of several hydrants and deluge valve in different areas, were simulated. Sensitivity analysis was performed on changes in the roughness coefficient of pipes and the required flow rate in the network. With an increase of roughness by 20%, the average pressure in the middle ring decreased by as much as 3.5%. In the case of increasing the required flow, the pumping pressure and deluge valve pressure drop by 3.2 and 12.2%, respectively. The results of the study indicate the proper operation of the firefighting water network, but in some cases the pressure generated at the pumping station is higher than the recommended values in the design, which in the long period could result in inappropriate performance.

Introduction Different types of drainage systems are used for seepage control through earth dams; including: horizontal toe drain, triangular toe drain, chimney drain and combined toe drain. Earth dams are constructed by soil compaction, so horizontal permeability is more than vertical permeability. As a result, hydraulic performance of chimney drain is better than triangular toe drain and operation of triangular toe drain is more suitable than horizontal toe drain. On the other hand, triangular toe drain can be repaired due to the more accessible position, if necessary, and is easier to implement than chimney drain. In this research, a combined drain, as a replacement for triangular toe drain is introduced, and its hydraulic performance is studied and compared with triangular toe drain. In order to achieve this goal, first, the hydraulic efficiency of the combined drain is investigated through physical modeling. After assuring the positive performance of combined drain and acceptable comparing of numerical and physical modeling results, sensitivity analyses of seepage and stability were performed numerically. For this, the height of triangular toe drain was decreased from 20 to 50%, and a part of the saved material was attached to triangular toe drain as horizontal toe drain. This kind of drain called combined drain. Methodology In this study, first, hydraulic performance of 3 physical models with different drainage system (without drain, with triangular toe drain, and with combined drain) is studied. Models were constructed in a box with 11 piezometers and 2 spillways in upstream and downstream which are used to keep the water level fixed in reservoirs. Height, length and width of this box are 1m, 1.1m, and 0.15m, respectively. Height of physical models, considering the dimensional constraints of box considered 49 cm. The slopes angles were kept about 45 degrees and the crest width was dictated 21 cm. The height of triangular toe drain, considering Creager’s recommendation was choosed 17 cm. In models with combined toe drain, height of triangular part, considering 15% reduction, was assumed to be 14.5 cm and length and thickness of the horizontal part of combined drain were held to be 11.5 and 5 cm respectively. Upstream and downstream water level were set as 47 and 4 cm for all models. Piezometric water level as a representative of phereatic surface, and volumetric flux were recorded from physical models. Then numerical models were run using Geo-studio software. Hydraulic performance comparison between these two physical and numerical analyses illustrated acceptable agreement; In the following, additional analyses were performed just numerically in order to assurance the adequacy of combined drain. The size and characteristics of numerical models were assumed based on real earth dams characteristics. Seepage analyses were performed for both steady state and rapid drawdown conditions, then stability analyses were done for downstream slope (end of construction, steady flow condition and quasi-static condition) and upstream slope (drawdown condition) for these mpdels. Results and discussion Comparison between models having triangular toe drain and combined toe drain, in whih half of the remaining material from toe triangular drain height reduction were horizontally atached to toe drain, showed an increase in cover length of downstream on phreatic line, and also noticeable rise in amount of discharged water; so in the next step, models having combined toe drain, with the same hydraulic performance as models with triangular toe drain were compared. Also, stability performance of these two models were evaluated. Stability analyses of models, showed ignorable difference in factors of safety, due to little share of drain area in slip surface in which causes slight change in shear strength, and also, phreatic surface dropping down in which causes an increase in dry area of earth dam downstream and induces an increase in unit weight of soil and subsequently, expansion of slope stability. Conclusion. The process described in the previous parts, approved proper performance of combined drain when it is used as a replacement for triangular toe drain. It was revealed that when a triangular toe drain substitute with combined drain, it will improve the hydraulic performance of the earth dam and will also result in a noicable reduction in drain material usage in which is more expensive than body material. In addition, this replacement will have a negligible effect on the static and quasi-static stability of the reservoir slopes. Therefore, the proposed drainage system’s adequacy is confirmed as a suitable alternative for triangular toe drain in homogeneous soil dams. Results indicated 11 to 157% increase in cover length on downstream phreatic line and 25 to 50% reduction in drain material compared with triangular toe drain, in models which half of the saved drain material, was used as horizontal toe drain. On the other hand, using combined drain with the same hydraulic performance instead of triangular toe drain results in 17 to 60% decrease in volume of drain material.

Sand mining, especially from places with lower potential, impacts on the hydraulically and sedimentary properties around the bridge piers. The creation of the turbulence causes to the negative effects on the scouring depth and width around the piers. In the present study, the consequences of the mining material, the hydraulical, and sedimentary parameters on the scouring patterns of the piers group were investigated. In order to investigate the scouring of a bridge pier group, 22 experiments were carried out in a rectangular canal with a dimensions of 13 m length, 1.2 m width and 0.8 m depth. The experimental facility is housed at the Hydraulic Lab of Maragheh University. Two false glass floors were installed upstream and downstream at a distance of 4.25 m relative to each other and with a height of 22 cm in the middle of the canal. Sandy movable bed with a height of 22 cm was placed between the aprons. Two pier groups were located upstream and downstream of the bed a specified distance from the aprons. The pier groups with the same arrangement (three consecutive piers in the direction of flow and at the center of the canal's width) were located with center-to-center distances of 21 cm. To eliminate the effect of the canal wall on local scour, the ratio of the pier center-canal wall distance to the pier diameter was greater than 6.25 (Raudkivi and Ettema (1983)). Consequently, piers of diameter of 9 cm were used. To prevent the formation of a ripple, the average diameter of the bed particles should be greater than 0.7 mm and the ratio of the pier diameter to the average particle should exceed 20-25 (Raudkivi and Ettema (1983)). Therefore, the experiments were tested in two different beds, grading ꞌAꞌ with =0.78 mm and grading ꞌBꞌ with =1.7 mm. In order to investigate the effect of the mining pit hole on scouring rate, the mining was done between the upstream and downstream pier groups. The results showed that granulation with coarse particles (B) had lower scour depth than substrate with fine grain size (A). So that the maximum scour depth for B aggregate for Froud number equal to 0.5 and 0.25, was respectively, 14.14 and 47.58 percent less than A. By mining of bed from the downstream and upstream of the group piers, the scouring depth has been increased and reduces respectively. In the Froude number of 0.5 with the mining of materials from the upstream of the groups in the grain size A, the scour depth was 12 to 10.9 cm. However, taking off the bottom of the bases in the same Froude and grading number increased the maximum scour depth from 15 to 15.6 cm. Also, the maximum scour depth in a discharge of 15 liters per second was less for B, compared with A, for gravel A, in Froud number of 0.25 and 0.5 respectively, 44.87% at the fourth base and 61.86% at the first pier, less observation. Although the ratio values in the Froude number of 0.25 for grain size A in the downstream bed is approximately 4 times the grain size of B. Also, the lowest ratio in the Froude number of 0.25 is for the B model with the non-pit hole mining material, while the grain size A with the downstream bed is one of the most scouring models in this Froude number. The phenomenon of scouring in addition to depth dimension, can be studied along the transverse and longitudinal direction. Scouring area is another dimension of the scouring phenomenon that can be affected by parameters. Therefore, the extent of scour area changes in two parts of the scour pattern and bed topography were investigated. In this research, nonlinear regression method is used to predict scour depth around bridges. The relationship between experimental data and empirical of other researchers has been verified using experimental data of this study. In the present study, the scour area around the pier group, along the flow direction for two bed and pit hole was investigated. The effect of this impression on the pattern and depth of scouring showed that the mining of materials from the upstream of the pier groups led to a decrease and this withdrawal from the downstream, increased the depth and extent of scouring. Therefore, it was observed that the pier groups were more sensitive to the mining of materials from their downstream, and it would be better to take this impression upstream of the pier group. Increasing the number of Froude from 0.25 to 0.5 has increased the depth of scouring around the pier group. This increase is higher in larger discharges. Increasing the Froude number in mining of material mode will affect the downstream bed more than the no-pit. So, increasing the Froud number in the bed with the pit hole compared with the non-pit hole bed increases the scour maximum for A, 33% and for B, 73.5%.

Numerical Investigation of Column separation and Bubbles Growth in Water Hammer Maryam Mousavifard‎, Assistant Professor, Department of Civil Engineering‎, Faculty of engineering‎, Fasa University, Fasa, Iran Reza Roohi‎, Assistant Professor, Department of Mechanical Engineering‎, Faculty of engineering‎, Fasa University, Fasa, Iran Introduction In modern hydraulic systems, when a sudden change occurs in fluid velocity because of any reasons (sudden pump stroke, valve closure, etc.), it will be followed by intense pressure fluctuations in the system, which is referred to water hemmer. If the fluctuations decrease to less than the vapor pressure of the fluid, the separation column will occur. In general, two cases can be distinguished: either the pressure drops below the saturation pressure but keeps above the vapor pressure, or the pressure drops to the vapor pressure of the liquid. In the former case, gaseous cavitation takes place, characterized by the presence of a large number of gas nuclei. When the pressure drops suddenly, a significant gas release may occur. In the latter case, vaporous cavitation takes place, and when the fluid pressure drops to its vapor pressure, a sudden growth of the nuclei containing vapor occurs. In general, there are two basic assumptions to describe the phenomenon of cavitation: discrete and distributed cavitation. In discrete cavitation, the vapor or gas cavities create discontinuity in fluid. In this case, it is assumed that the vapor and gas cavities occur at computational nodes, when the pressure reaches less than the vapor pressure of the fluid or the saturation pressure. In distributed cavitation, the two phases of the liquid and the vapor (or the gas) are simultaneously solved, and the vapor (or gas) cavities are continuously exist all over the fluid. Methodology In this paper, the column separation in pressurized pipes affected by water hammer is numerically investigated using one-dimensional and quasi-two-dimensional models of gas cavity. A one-dimensional model is modeled based on the method of characteristics, and the energy dissipation is simulated using the summation of the Brunone unsteady friction and quasi-steady friction. In the proposed quasi-two-dimensional model, the characteristic equations along the pipeline axis and the finite difference equations along the pipe radius are used to simulate water hammer, and then the governing equations of discrete gas cavity model is coupled with the primary model, and the five-layer turbulence model was also used to simulate the energy dissipation. It should be noted that, in the quasi two dimensional model of separation column, like the one-dimensional model, the velocity on the upstream and downstream of each computing node will not be equal. Free gas distribution throughout liquid in a homogeneous mix in a pipeline yields a wave propagation velocity that is strongly pressure dependent. Results and Discussion After verifying the developed models by experimental data, the total shear stress is studied in some initial cycles of water hammer. In the second part of the paper, the dynamics of bubble growth and the process of temperature and pressure variation within the bubbles are also analyzed using the Rayleigh-Plesset equation. The growth of bubbles in the fluid is a function of a variety of variables such as applied pressure, fluid surface tension, evaporation pressure in fluid temperature and viscosity. Conclusion - the quasi-two-dimensional model has been more successful in calculating energy depreciation, especially in the final cycles of water hammer. - Regarding the head oscillation shape, it can be evaluated that the quasi 2D DGCM improved the energy losses reproduction, and reproduces the experimental spikes successfully even in final cycles of experimental runs. - The 1D model of DGCM reproduce the first oscillations of the experimental data successfully, but in final cycles, does not predict the shape of head oscillations successfully and does not stay in phase with experimental data. - According to the shear stress diagrams it can be concluded that in high pressure pulses, the total shear stress is negative and it is positive in low pressure pulses. - The difference between the minimum and maximum radius is about 0.5 μm. Considering the average radius of the bubbles and the relationship between the radius of the bubbles and the gas phase volume, the 85 to 125% increase in the volume of the gas phase in the fluid during the periodic pressure fluctuations process, is visible. - It should be noted that in spite of the fact that the maximum pressure inside the bubbles (the driving force for the growth of bubbles) is greater than the external pressure, the high dependence of the internal gas pressure on the radius of the bubbles and the dynamic behavior of the system, lead to periodic changes. In other words, the strong growth of the resistive force by reducing the radius of the bubbles prevents significant contraction in them, and again, by reducing the pressure head in the fluid, the growth of the bubbles will be renewed to reach the initial radius. Keywords: Water hammer; Column separation; unsteady friction; quasi two Dimensional model; shear stress; Rayleigh Plesset equation