A Physical Model Study of the North Shore Wastewater Treatment Plant Pump Station

<div>Large scale water pumps with bell mouth intakes have been broadly used by municipal wastewater services to move sewage to wastewater treatment plants. Swirling of the flow when entering the suction bell of the pump intake can cause free-surface and/or sub-surface vortices, resulting in poor pump operation. In order to properly design, the wet well of sewage pump station both physical and numerical models are used to analyze the flow condition entering the pump intake and the associated flow pattern and potential vortex formation. In cooperation with WSP Canada Ltd., a physical modelling study of the First Narrows Sewage Pumping Station was conducted by the Ryerson research team at Ryerson University’s Centre of Urban Innovation Laboratory. During the physical model testing, uneven flow distributions including vortices were observed at the intake chamber under three pump-working conditions. To achieve an even flow distribution with minimal vortices, alternative slot designs at the entrance of the chamber were analyzed.</div><div>Additionally, a tapered design of the suction bell intake was tested for potential vortex formation. The results showed that a reduced area of the entrance slot could distribute the inflow evenly in the chamber. Moreover, no vortex formation around the tapered suction bell was found under (a) a low flow condition of 10 l/s at a water level -5.10 m below datum and (b) a cleaning cycle scenario of 16 l/s at a water level -4.9 m below the datum. However, there was observed water rotations at the backwall side. For tight and intense water rotations, it might cause vortex formation. This study has provided design changes that can smooth the flow and reduce vortices at the bell mouth intakes of the pump intake chamber.</div>

A Physical Model Study of the North Shore Wastewater Treatment Plant Pump Station

<div>Large scale water pumps with bell mouth intakes have been broadly used by municipal wastewater services to move sewage to wastewater treatment plants. Swirling of the flow when entering the suction bell of the pump intake can cause free-surface and/or sub-surface vortices, resulting in poor pump operation. In order to properly design, the wet well of sewage pump station both physical and numerical models are used to analyze the flow condition entering the pump intake and the associated flow pattern and potential vortex formation. In cooperation with WSP Canada Ltd., a physical modelling study of the First Narrows Sewage Pumping Station was conducted by the Ryerson research team at Ryerson University’s Centre of Urban Innovation Laboratory. During the physical model testing, uneven flow distributions including vortices were observed at the intake chamber under three pump-working conditions. To achieve an even flow distribution with minimal vortices, alternative slot designs at the entrance of the chamber were analyzed.</div><div>Additionally, a tapered design of the suction bell intake was tested for potential vortex formation. The results showed that a reduced area of the entrance slot could distribute the inflow evenly in the chamber. Moreover, no vortex formation around the tapered suction bell was found under (a) a low flow condition of 10 l/s at a water level -5.10 m below datum and (b) a cleaning cycle scenario of 16 l/s at a water level -4.9 m below the datum. However, there was observed water rotations at the backwall side. For tight and intense water rotations, it might cause vortex formation. This study has provided design changes that can smooth the flow and reduce vortices at the bell mouth intakes of the pump intake chamber.</div>

Characteristics of the Concentric Eyewall Structure of Super Typhoon Muifa during Its Formation and Replacement Processes

&lt;p&gt;To explore the characteristics of the concentric eyewall of a typhoon during its formation and replacement processes, with Super Typhoon Muifa in 2011 as the example case, the Weather Research and Forecast&amp;#160;(WRF) mode was used to carry out a numerical simulation to reproduce the entire formation and replacement processes of the concentric eyewall. The physical quantities such as the tangential&amp;#160;wind speed, radar echo, radial wind speed, vertical wind speed, and potential vortex were diagnosed and analyzed. The results of the analysis show that the outward expansion of the isovelocity in the lower troposphere was the early signal of the formation of the outer eyewall. After the outer eyewall formed, there was a center&amp;#160;of second-highest tangential wind speed in the corresponding area. The second-highest wind speed increased as the strength of the outer eyewall increased, and the position of the second-highest wind speed center&amp;#160;was retracted with the retraction of the outer eyewall. The tangential wind speed of the moat area was smaller than that corresponding to the concentric&amp;#160;eyewall and this feature gradually disappeared with the increase of the height. The echo in the moat area was weak, and this characteristic was particularly evident when the moat area was relatively wide and the outer eyewall was relatively strong. With the formation and development of the outer eyewall, the intensity of the inflow in the boundary layer corresponding to the inner eyewall was reduced, the intensity of the outflow in the upper layers declined, and the intensities of the inflow and outflow corresponding to the outer eyewall were enhanced. After the second outer eyewall matured, there was a significant inflow in the upper layer of the moat area. Once the outer eyewall formed, a large amount of hydrometeors appeared in the corresponding area, and there was a strong ascending motion inside that area. The strength of the ascending motion and the content of hydrometeors increased as the outer eyewall increased. When the moat area was relatively wide, the divergent airflow generated by the developed outer eyewall in the upper layer would produce a significant descending motion in the moat area.&lt;/p&gt;

Characteristics of the Concentric Eyewall Structure of Super Typhoon Muifa during Its Formation and Replacement Processes

To explore the characteristics of the concentric eyewall of a typhoon during its formation and replacement processes, with Super Typhoon Muifa in 2011 as the example case, the Weather Research and Forecast (WRF) mode was used to carry out a numerical simulation to reproduce the entire formation and replacement processes of the concentric eyewall. The physical quantities such as the tangential wind speed, radar echo, radial wind speed, vertical wind speed, and potential vortex were diagnosed and analyzed. The results of the analysis show that the outward expansion of the isovelocity in the lower troposphere was the early signal of the formation of the outer eyewall. After the outer eyewall formed, there was a center of second-highest tangential wind speed in the corresponding area. The second-highest wind speed increased as the strength of the outer eyewall increased, and the position of the second-highest wind speed center was retracted with the retraction of the outer eyewall. The tangential wind speed of the moat area was smaller than that corresponding to the concentric eyewall and this feature gradually disappeared with the increase of the height. The echo in the moat area was weak, and this characteristic was particularly evident when the moat area was relatively wide and the outer eyewall was relatively strong. With the formation and development of the outer eyewall, the intensity of the inflow in the boundary layer corresponding to the inner eyewall was reduced, the intensity of the outflow in the upper layers declined, and the intensities of the inflow and outflow corresponding to the outer eyewall were enhanced. After the second outer eyewall matured, there was a significant inflow in the upper layer of the moat area. Once the outer eyewall formed, a large amount of hydrometeors appeared in the corresponding area, and there was a strong ascending motion inside that area. The strength of the ascending motion and the content of hydrometeors increased as the outer eyewall increased. When the moat area was relatively wide, the divergent airflow generated by the developed outer eyewall in the upper layer would produce a significant descending motion in the moat area.

Multipole expansions for time-dependent charge and current distributions in quasistatic approximation

We propose a consistent approach to the definition of electric, magnetic and toroidal multipole moments. Electric and magnetic fields are split into potential, vortex and radiative terms, with the latter ones dropped off in the quasistatic approximation. The potential part of the electric field, the vortex parts of the magnetic field and vector potential contain gradients of scalar functions. Formally introducing magnetic and toroidal analogs of the electric charge, we apply multipole expansions for those scalars. Closed-form expressions are derived in an arbitrary order for electric, magnetic and toroidal multipoles, which constitute a full system for expansions of the electromagnetic field.

On the instabilities of a potential vortex with a free surface

In this paper, we address the linear stability analysis of a confined potential vortex with a free surface. This particular flow has been recently used by Tophøj et al. (Phys. Rev. Lett., vol. 110(19), 2013, article 194502) as a model for the swirling flow of fluid in an open cylindrical container, driven by rotating the bottom plate (the rotating bottom experiment) to explain the so-called rotating polygons instability (Vatistas J. Fluid Mech., vol. 217, 1990, pp. 241–248; Jansson et al., Phys. Rev. Lett., vol. 96, 2006, article 174502) in terms of surface wave interactions leading to resonance. Global linear stability results are complemented by a Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) analysis in the shallow-water limit as well as new experimental observations. It is found that global stability results predict additional resonances that cannot be captured by the simple wave coupling model presented in Tophøj et al. (2013). Both the main resonances (thought to be at the root of the rotating polygons) and these secondary resonances are interpreted in terms of over-reflection phenomena by the WKBJ analysis. Finally, we provide experimental evidence for a secondary resonance supporting the numerical and theoretical analysis presented. These different methods and observations allow to support the unstable wave coupling mechanism as the physical process at the origin of the polygonal patterns observed in free-surface rotating flows.

A vortex force study for a flat plate at high angle of attack

The vortex force is studied for a flat plate at arbitrarily large angle of attack. A suitable vortex force approach, adapted from a previous work, is used to study the vortex force and to build a vortex force line map to identify the force effect of any potential vortex. This map can be used exactly for a potential point vortex and approximately for a concentrated leading-edge vortex (LEV) or trailing-edge vortex (TEV); the latter are shown to have a non-potential vortex core. By means of this map, we identify a force-producing critical region, due to pressure suction, above the front and rear parts of the plate for an LEV and a TEV, respectively. The impulsively started flow problem is used as an application, with validation by computational fluid dynamics. The force variation in time is decomposed into four repeatable stages (force release, force enhancement, stall and force recovery) in close relation to the individual and combined effect by an LEV and a TEV. A pressure distribution analysis shows that force enhancement is due to pressure suction by an LEV, while stall and force recovery are respectively due to the upwash effect (which reduces the pressure below the plate) of a new TEV right off the plate and the pressure suction of this TEV having now moved above the plate. A viscous effect causes a small-amplitude oscillation on the force curves by promoting multiple small-scale LEVs.

Asymptotic theory for a bathtub vortex in a rotating tank

Fluid entering the periphery of a cylindrical tank mounted on a rotating table is pumped inwards toward a central, floor drain by a potential vortex that is established in the fluid interior. We present here an asymptotic theory for small Rossby and Ekman numbers, including detailed solutions in the vortex core. Results for azimuthal velocity variation with radius agree quite well with the experiments of Andersen et al. (J. Fluid Mech., vol. 556, 2006, pp. 121–146), in spite of their free upper boundary. Modifications of the flow are presented in the instance that a short cylinder is place on the tank axis as in the work of Chen et al. (J. Fluid Mech., vol. 733, 2013, pp. 134–157). The overall flow structure found here is exactly that noted by both Andersen et al. and Chen et al.

Decay of Potential Vortex and Diffusion of Temperature in a Generalized Oldroyd-B Fluid through a Porous Medium

Based on a modified Darcy law, the decay of potential vortex and diffusion of temperature in a generalized Oldroyd-B fluid with fractional derivatives through a porous medium is studied. Exact solutions of the velocity and temperature fields are obtained in terms of the generalized Mittag-Leffler function by using the Hankel transform and discrete Laplace transform of the sequential fractional derivatives. One of the solutions is the sum of the Newtonian solutions and the non-Newtonian contributions. As limiting cases of the present solutions, the corresponding solutions of the fractional Maxwell fluid and classical Maxwell fluids are given. The influences of the fractional parameters, material parameters, and the porous space on the decay of the vortex are interpreted by graphical results.