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In order to facilitate the release of floods from the dams and to prevent their damage or collapse, a structure called a spillway is used. Due to the natural and variable flow of the input to the reservoirs of the dams, there are times when the river inflow exceeds the consumption amount in the downstream agricultural lands. In these cases, excess water is discharged over the crest of the weir and flows towards the spillway, which causes high velocities. This high velocity creates low pressure areas on the spillway concrete surface, which can cause major damage to the spillway or even endanger the integrity of the dam structure. Therefore, the dam spillway must safely dissipate the kinetic energy. One of the types of weirs is the stepped spillway to facilitate the passage of the flow over the dams. One of the most obvious practical features of stepped spillways compared to other spillways is the considerable energy dissipation along the spillway. Care should be taken in designing and selecting the type of spillway to prevent potential erosion and reduce kinetic energy as the water flow passes over the spillway. One possible solution is to use a stepped spillway instead of a smooth spillway. In this study, a numeral model of a stepped spillway with different steps and slopes is used. For this purpose, ANSYS software is used for modeling free surface with application of k-ε turbulence model. In the present study, numerical simulation using the Volume of Fluid (VOF) model was used to investigate the mixing phenomenon of two phases of air and water of the free surface flow. The flow field was continued until the residuals reached 10^-7. Compared to simpler models such as Mixture, which operates solely on the basis of averaging the properties of two phases, the VOF model, is separating the phases and considering the effects of the interface. The VOF model, is capable of more accurate simulation of phenomena such as fluid mixing, turbulent flows, and heat transfer in multiphase flows. A number of hydraulic specifications which are considered in designing the stepped spillways are the pressure on the surface of the steps, velocity distribution and energy dissipation. The results from the numerical models were compared with experimental studies. They showed acceptable agreement with physical simulations. Results show that discharge and spillway slope increment reduces the amount of energy loss. In the spillway with 5 steps, for a discharge of 0.063 m³/s, the amount of energy dissipation at a slope of 26.6 degrees changes from 85 to 82% at a slope of 45 degrees, which shows a decrease of 3%. With the increase in discharge, the flow depth increases and reduces the effect of the roughness of the steps on the upper layers of the flow. Increasing the height of the steps increases the rate of energy dissipation and also increases the occurrence of negative pressures in stepped spillway. In this case, the contact surface between the main flow and the eddy currents increases. With the increase in the height of the steps, the dimensions of the rotating vortices also increase and cause a larger radius of rotation on the steps. The presence of these large rotating vortices separates the flow from the bottom of the steps and reduces the pressure on the surfaces. The number and dimensions of steps can alter the energy dissipation rate. Increase in the number of steps in a spillway with constant height, reduces the energy loss as the result of steps dimensions being shrunk

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The flow at a channel bifurcation is turbulent, highly three-dimensional (3D) and has many complex features. There is transverse motion accompanying the main flow and an extensive separation zone that develops in the branch channel. There are two complex flow regions along the intake channel: one is the separation zone and the other is the region in which helical motion of water particles forms. This separation occurs because the flow entering the branch channel has considerable momentum in the direction of the main channel flow. This zone causes hydraulic and sedimentation problems that must be known before designing the system. This necessitates a deeper insight into the flow patterns and shear stress distributions near the solid boundaries. In this research, 3D flow patterns at lateral diversion were investigated experimentally and numerically. The experimental investigation was carried out at a T-junction, formed by two channels with rectangular cross-sections. The width of lateral intake to the main channel was 0.4. 3D velocity measurements were obtained using Acoustic Doppler Velocimeter at junction region for 11%, 16% and 21% discharge ratios. Fluent mathematical model was then used to investigate the dividing open-channel flow characteristics. Turbulence was modeled by Two Equation (k-ε, k-ω) and Reynolds Stress (RSM) turbulence models. The predicted flow characteristics were validated using experimental data and the proper model was selected for hydrodynamic and parametric studies. Within the main channel, good agreement was obtained between all models prediction and the experimental measurements, but within the lateral channel, the RSM predictions were in better agreement with the measured data, and k-ω predictions was better than those of k-ε. The comparison of experimental and numerical streamlines at different elevations showed that the selected model is capable to simulate the most important features of flow at diversions. The study of the velocity contours at different elevations showed that the velocity magnitude decreases at main channel, just downstream corner of lateral intake at the near bed levels and this causes the sedimentation in movable beds. The results showed that the width of separation zone at lateral intake will decrease and the distance of dividing stream surface from left bank of the main channel will increase by increasing of the discharge ratio. Investigation of the flow pattern at the entrance of the lateral intake showed that the secondary flow will form at this section. The dimension of the secondary flow at near bed elevation will increase by increasing of the discharge ratio and this causes entering of more bed load into the lateral channel.

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Non-Newtonian fluid flows experience turbulent regime in some industrial applications. Several approaches have been proposed for numerical simulation of turbulent flows that each one has specific features. RANS turbulence models have reasonable computational costs, while include several sources of uncertainties affecting simulation results. In addition, developed RANS models for non-Newtonian fluids are modified versions of available models for Newtonian fluids, therefore, they cannot provide reliable estimation for viscoplastic stress term. On the contrary, DNS delivers accurate results but with high computational costs. Consequently, use of DNS data for estimation of uncertainty in RANS models can provide better decision making for engineers based on RANS results. In the present study, a turbulence model based on for power-law non-Newtonian fluid is developed and employed for simulation of flow in a pipe. Then, an efficient method is proposed for quantification of available model-form uncertainty. Moreover, it is assumed that uncertainties originating from various sources are combined together in calculation of Reynolds stress as well as viscoplastic stress. Deviation of the stresses, computed using RANS turbulence model, from DNS data are modeled through Gaussian Random Field. Thereafter, Karhunen-Loeve expansion is employed for uncertainty propagation in simulation process. Finally, the effects of these uncertainties on RANS results are shown in velocity field demonstrating the fact that the presented approach is accurate enough for statistical modeling of model-form uncertainty in RANS turbulence models.

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In this study, a three-dimensional fluid field of an axial flow type micro hydro named Agnew has been investigated. The turbine installed at the Hydrulic Machines Laboratory (HML) of Iranian Research Organization for Science and Technology has been designed to generate 1 kw output power.All numerical simulations were performed using ANSYS CFX, a Computational Fluid Dynamic code, to investigate the performance parameters, such as efficiency and power, and results are validated against experimental data. Four different grid sizes are studied in accordance with the Grid Convergence Index (GCI) to investigate mesh independency of the solution. Results of several turbulence models were also examined to find out the Shear Stress Transport (SST) model in order to take into account the turbulence in the flow. Several turbulence models were also examined together with wall function in order to take into account the turbulence in the flow. A mixing plane interface plane was used to pass the disturbance of rotary domain to stationary domain. The obtained results show that a high resolution advection scheme, mixing plane to model the rotor-stator interaction together with a turbulence intensity of I=6% at the inlet, best matches with the experimental results. The difference between the efficiencies computed from both numerical approaches and experimental values may be ascribed to a numerical error, a model error or a systematic error.

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In order to assess the effect of turbulence models in prediction of flow structure with adverse pressure gradient, steady state Reynolds-averaged Navier-Stokes (RANS) equations in an annular axisymmetric diffuser are solved. After selection of the best turbulence model, an approach for the shape optimization of annular diffusers is presented. The goal in our optimization process is to maximize diffuser performance and, in this way, pressure recovery by optimizing the geometry. Our methodology is the optimization through wall contouring of a given two-dimensional diffuser length and area ratio. The developed algorithm uses the CFD software: Fluent for the hydrodynamic analysis and employs surrogate modeling and an expected improvement approach to optimization. The non-uniform rational basic splines (NURBS) are used to represent the shape of diffuser wall with two to ten design variables, respectively. In order to manage solution time, the Kriging surrogate model is employed to predict exact answers. The CFD software and the Kriging model have been combined for a fully automated operation using some special control commands on the Matlab platform. In order to seek a balance between local and global search, an adaptive sample criterion is employed. The optimal design exhibits a reasonable performance improvement compared with the reference design.

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Spillways have long been of practical importance to safety of dams, therefore these structures have to be built strong, reliable and highly efficient. Ski jump dissipator is one the flow energy dissipators which is applicable downstream of spillway chutes with velocity over 20 m/s. Flow over a flip-bucket is a two-phase and strongly turbulent flow. Turbulence modeling is one of the most limiting factors in accurate computer simulation of flows. By fixing the grid resolution and the discretization scheme, the difference of computation time is mainly attributed to the turbulence model. The choice of turbulence model depends on factors such as the physics encompassed in the flow, the level of accuracy required, the available computational resources, and the amount of time available for the simulation. It is a fact that no single turbulence model is universally accepted as being superior for all classes of problems.
The main purpose of the present study is numerical investigation of two-phase turbulent flow over a triangular flip-bucket to evaluate effects of different turbulence models in this type of flow. Hence, using FLUENT® software, two dimensional Reynolds averaged Navier-Stockes equations have been solved in unsteady state. Different turbulence models consist of k-ε, k-ω and RSM; have been used. To simulate two-phase flow, volume of fluid (VOF) method has been applied.
Standard k-ε and stress-omega RSM models with low-Reynolds number modifications have the best performance among the other turbulence models. In standard k-ε model when low-Reynolds number modification was activated, the effects of molecular viscosity were taken into account in near-wall regions. Therefore, in low-Reynolds number k-ε model, maximum dynamic pressure over the bucket was predicted more accurately in comparison with standard k-ε model. Regarding modification in strain-pressure terms in turbulence equations, effects of anisotropic Reynolds stress tensor were taken into account in stress-omega RSM model with low-Reynolds number modifications. Thus, compared to other turbulence models, numerical results of this model are in a better agreement with experimental results. Different k-ε models could not predict the jet trajectory after the bucket very well. Due to blending function in SST k-ω model, this turbulence model effectively blended the robust and accurate formulation of the k-ω model in near-wall regions with the free-stream independence of the k-ε model in the far field. In estimation of maximum dynamic pressure over the bucket, this model had a better performance than standard k-ω model and relatively similar results to k-ε model. In addition, SST k-ω model has shown the best prediction of the jet trajectory among other turbulence models. Eventually, with respect to computation cost and accuracy of results, SST k-ω turbulence model has been introduced as the most suitable turbulence model to predict the flow pattern of a triangular flip-bucket.

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The hydraulic jump phenomenon is one of the most common phenomena in open channels. Hydraulic jump is a transition state from supercritical to subcritical flow regime, which normally occurs in conjunction with hydraulic structures, such as spillways, weirs, and sluice gates. A hydraulic jump phenomenon serves a variety of purposes, for instance, to dissipate the energy of flow to prevent bed erosion and aerate water or to facilitate the mixing process of chemicals used for the purification of water. Stilling basins are one of the most common structures for energy dissipation of flow with high velocities.The stilling basin has been accepted to be the most powerful hydraulic structure for the dissipation of the flow energy. The size and geometry of the stilling basin affect the formation of flow patterns, which can be influential for hydraulic performance of the whole system. The depth of water after the jump is related to the energy content of the flow, and any reduction in energy content with increased energy dissipation in the jump will reduce the required depth of flow after the jump. Sometimes these basins are supplied with appurtenances that increase the overall roughness of the basins. This in turn increases the energy dissipation, decreases the sequent depth, and requires a shorter basin for the full development of the hydraulic jump. There are plenty of research studies in the literature regarding the classical hydraulic jump in the usual rectangular straight stilling basin, but less for the hydraulic jump in other cross section shape of basins. Expanding gradually basin with the rectangular cross section acts as two separate hydraulic structures including stilling basin and transition. In this type of structures not only the transition can be eliminated, but the length of the basin will be also much smaller than what is designed for the usual straight basins. Researchers’ studies show that divergence in stilling basins reduce the sequent depth and the length of the jump while increasing the energy losses compared to the classic jumps.
In this research, numerical simulation of the hydraulic jump was performed in divergence rectangular sections, and compared with the results of the laboratory, making use of the FLOW-3D software and the standard k-ԑ and RNG k-ԑ turbulence models. The effects of rectangular Strip roughness on the specification of hydraulic jump were evaluated.
The results showed that the standard k-ԑ turbulence model was able to predict the water level profiles in the hydraulic jump in divergence rectangular sections with appropriate and acceptable coincidence. Results showed that the mean relative error of water surface obtained from numerical model and measured values is about 3.55 percent. Also the numerical model showed the vortices that were accrued because of diverging walls as well as experiment investigations. The results show that creating the rectangular Strip roughness, reduces the sequent depth as much as 13.65 % and the length of the hydraulic jump as much as 11.39%, while increasing the energy loss as much as 9.12%, compared to Smooth divergent stilling basin. The results also show that creating the rectangular Strip roughness, reduces the sequent depth as much as 24.63 % and the length of the hydraulic jump as much as 17.64%, while increasing the energy loss as much as 14.46%, compared to the classic hydraulic jumps. Consequently, the use of roughness in stilling basins would be economical.

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In the present study, performance of nonlinear low Reynolds number k-ε model of turbulence has been investigated in order to predict turbulent flow field through three dimensional U bend channel of intercooling passage of gas turbine blade. Finite volume method is used to solve governing equations of mean fluid flow. In this study, linear low Reynold number model of turbulence and Zonal Eddy Viscosity model k-ε/1-eq. and cubic nonlinear low Reynolds number model has been used to model the turbulence field. Results of Computations show that the zonal model predicts the profiles of velocity and turbulent stress as same as linear model and overestimate the turbulent stresses in separated zones but results of nonlinear model shows improvement in prediction of velocity and turbulent stresses in separated zones. Also, linear, nonlinear and zonal models have similar prediction about separation point of flow but nonlinear model has been predicted the level of Reynolds stresses and its changes from inner side toward outer side and maximum level of Reynolds stresses more accurate in comparison with zonal and linear models specially on near-wall plane.

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The hydraulic jump phenomenon is one of the most common phenomena in open channels. Hydraulic jump is a transition state from supercritical to subcritical flow regime, which normally occurs in conjunction with hydraulic structures, such as spillways, weirs, and sluice gates. A hydraulic jump phenomenon serves a variety of purposes, for instance, to dissipate the energy of flow to prevent bed erosion and aerate water or to facilitate the mixing process of chemicals used for the purification of water. Stilling basins are one of the most common structures for energy dissipation of flow with high velocities. The stilling basin has been accepted to be the most powerful hydraulic structure for the dissipation of the flow energy. The size and geometry of the stilling basin affect the formation of flow patterns, which can be influential for hydraulic performance of the whole system. The depth of water after the jump is related to the energy content of the flow, and any reduction in energy content with increased energy dissipation in the jump will reduce the required depth of flow after the jump. Sometimes these basins are supplied with appurtenances that increase the overall roughness of the basins. This in turn increases the energy dissipation, decreases the sequent depth, and requires a shorter basin for the full development of the hydraulic jump. There are plenty of research studies in the literature regarding the classical hydraulic jump in the usual rectangular straight stilling basin, but less for the hydraulic jump in other cross section shape of basins. Expanding gradually basin with the rectangular cross section acts as two separate hydraulic structures including stilling basin and transition. In this type of structures not only the transition can be eliminated, but the length of the basin will be also much smaller than what is designed for the usual straight basins. Researchers’ studies show that divergence in stilling basins reduce the sequent depth and the length of the jump while increasing the energy losses compared to the classic jumps. In this research, numerical simulation of the hydraulic jump was performed in divergence rectangular sections, and compared with the results of the laboratory, making use of the FLOW-3D software and the standard k-ԑ and RNG k-ԑ turbulence models. The effects of Vertical and Curve blocks on the specification of hydraulic jump were evaluated. The results showed that the standard k-ԑ turbulence model was able to predict the water level profiles in the hydraulic jump in divergence rectangular sections with appropriate and acceptable coincidence. Results showed that the mean relative error of water surface obtained from numerical model and measured values is about 3.55 percent. Also the numerical model showed the vortices that were accrued because of diverging walls as well as experiment investigations. The results show that creating the vertical blocks, reduces the sequent depth as much as 46.27 % and the length of the hydraulic jump as much as 17.64%, while increasing the energy loss as much as 31.57%, compared to the classic hydraulic jumps. The results also show that creating the Curve blocks, reduces the sequent depth as much as 69.76 % and the length of the hydraulic jump as much as 35.29%, while increasing the energy loss as much as 32%, compared to the classic hydraulic jumps.

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In this paper, the performance of three turbulence models, zonal k-ε, linear low-Reynolds k-ε and nonlinear low-Reynolds k-ε in the prediction of flow and heat transfer through a dimpled channel is investigated. Furthermore, the effect of YAP term replacement with NYP length scale correction term is studied. Dimples are heat transfer devices which are employed in gas turbine blades to increase the heat transfer levels. These devices do not act as an obstacle for flow, and thus they produce low pressure losses. In this study, the governing equations on flow and energy are solved using the finite volume method together with the SIMPLE algorithm. The results obtained with YAP term indicate that the nonlinear model predicts larger recirculation flow inside the dimple than zonal and linear models. Also, the intensity of impingement and upwash flow in this model is greater than other models. Heat transfer results show that the zonal model predicts the heat transfer levels lower than experimental measurement. Using the linear model leads to a better prediction of heat transfer inside the dimples and their back rim. Compared to these models, the nonlinear model yields a better prediction not only for the smooth area between the dimples, but in the back rim of the dimple. The replacement of the YAP term with the NYP term in linear and nonlinear models leads to more accurate results for heat transfer in dimple span-wise direction and back rim.

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