“…1 ), respectively. According to previous experimental investigations 19 , 24 , the total energy head in each section of the drop shaft is calculated using the following equations: Figure 1 Definition of vortex drop shaft: ( a ) side view, ( b ) tangential inlet plan view, ( c ) photograph of the physical model. in which, z = height from zero elevation (origin bed of the outlet channel), V z = vertical velocity, V t = tangential velocity, P ( r ) = pressure distribution at each section of the drop shaft, r = radial coordinate, R = radius of the vertical shaft, D = diameter of the vertical shaft, b = vortex flow thickness, t = relative flow thickness ( t = b / R ), C = circulation constant, Q = design discharge, e = inlet width at the junction of vertical shaft, g = gravity of acceleration, and β = angle of bottom slope.…”
Section: Flow Energy Dissipation Efficiency In the Vertical Shaftmentioning
confidence: 99%
“…From these investigations, it can be proved that the successful usability of DOE in analysis of experimental research demonstrated optimum values of design dimensionless parameters when constructing vortex structures in the practical applications. In addition, the most recent investigation in which effects of dissipation chamber on the energy losses in the vortex energy was studied 24 . Mahmoudi-Rad and Najafzadeh 24 found that the optimal values of effective parameters (i.e., F r and L / D ) yielded 2.32 and 13.901, respectively; so as to stand the efficiency of flow energy loss at its highest level.…”
Section: Introductionmentioning
confidence: 99%
“…In addition, the most recent investigation in which effects of dissipation chamber on the energy losses in the vortex energy was studied 24 . Mahmoudi-Rad and Najafzadeh 24 found that the optimal values of effective parameters (i.e., F r and L / D ) yielded 2.32 and 13.901, respectively; so as to stand the efficiency of flow energy loss at its highest level. Obviously, a great amount of flow energy in the vortex structures is dissipated in the vertical shaft section.…”
In urban wastewater collection and drainage networks, vortex structures are recruited to transfer fluid between two conduits with significant level differences. During the drop shaft, in addition to preventing the fluid from falling due to vortex flow formation, a significant amount of the fluid energy is dissipated due to wall friction of vertical shaft. In the present study, by constructing a physical model with a scale of 1:10 made of Plexiglas, the energy dissipation efficiency in the vertical shaft has been investigated. In this way, the performance of dimensional analysis indicates that the flow Froude number (Fr) and the ratio of drop total height to shaft diameter (L⁄D) are parameters affecting the efficiency of flow energy dissipation in the vertical shaft (ηs). This research considers four levels of Fr factor (1.77, 2.01, 2.18, and 2.32) and three levels of L⁄D factor (10, 13, and 16). Additionally, four replications for 12 possible combinations allow us to carry out 48 experiments and the full factorial method. The results demonstrated that the energy dissipation efficiency in the vertical shaft changes varies from 10.80 to 62.29%. Moreover, ηs values decrease with an increase in Fr whereas the efficiency increases with increasing L⁄D ratio. Furthermore, the regression analysis gave a second-order polynomial equation which is a function of Fr and L⁄D to accurately estimate the flow energy dissipation efficiency in the vertical shaft.
“…1 ), respectively. According to previous experimental investigations 19 , 24 , the total energy head in each section of the drop shaft is calculated using the following equations: Figure 1 Definition of vortex drop shaft: ( a ) side view, ( b ) tangential inlet plan view, ( c ) photograph of the physical model. in which, z = height from zero elevation (origin bed of the outlet channel), V z = vertical velocity, V t = tangential velocity, P ( r ) = pressure distribution at each section of the drop shaft, r = radial coordinate, R = radius of the vertical shaft, D = diameter of the vertical shaft, b = vortex flow thickness, t = relative flow thickness ( t = b / R ), C = circulation constant, Q = design discharge, e = inlet width at the junction of vertical shaft, g = gravity of acceleration, and β = angle of bottom slope.…”
Section: Flow Energy Dissipation Efficiency In the Vertical Shaftmentioning
confidence: 99%
“…From these investigations, it can be proved that the successful usability of DOE in analysis of experimental research demonstrated optimum values of design dimensionless parameters when constructing vortex structures in the practical applications. In addition, the most recent investigation in which effects of dissipation chamber on the energy losses in the vortex energy was studied 24 . Mahmoudi-Rad and Najafzadeh 24 found that the optimal values of effective parameters (i.e., F r and L / D ) yielded 2.32 and 13.901, respectively; so as to stand the efficiency of flow energy loss at its highest level.…”
Section: Introductionmentioning
confidence: 99%
“…In addition, the most recent investigation in which effects of dissipation chamber on the energy losses in the vortex energy was studied 24 . Mahmoudi-Rad and Najafzadeh 24 found that the optimal values of effective parameters (i.e., F r and L / D ) yielded 2.32 and 13.901, respectively; so as to stand the efficiency of flow energy loss at its highest level. Obviously, a great amount of flow energy in the vortex structures is dissipated in the vertical shaft section.…”
In urban wastewater collection and drainage networks, vortex structures are recruited to transfer fluid between two conduits with significant level differences. During the drop shaft, in addition to preventing the fluid from falling due to vortex flow formation, a significant amount of the fluid energy is dissipated due to wall friction of vertical shaft. In the present study, by constructing a physical model with a scale of 1:10 made of Plexiglas, the energy dissipation efficiency in the vertical shaft has been investigated. In this way, the performance of dimensional analysis indicates that the flow Froude number (Fr) and the ratio of drop total height to shaft diameter (L⁄D) are parameters affecting the efficiency of flow energy dissipation in the vertical shaft (ηs). This research considers four levels of Fr factor (1.77, 2.01, 2.18, and 2.32) and three levels of L⁄D factor (10, 13, and 16). Additionally, four replications for 12 possible combinations allow us to carry out 48 experiments and the full factorial method. The results demonstrated that the energy dissipation efficiency in the vertical shaft changes varies from 10.80 to 62.29%. Moreover, ηs values decrease with an increase in Fr whereas the efficiency increases with increasing L⁄D ratio. Furthermore, the regression analysis gave a second-order polynomial equation which is a function of Fr and L⁄D to accurately estimate the flow energy dissipation efficiency in the vertical shaft.
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