Lateral Outflow from Supercritical Channels J. Coonrod 1, J. Ho 2 and N. Bernardo 3 1 Associate Professor, Department of Civil Engineering, University of New Mexico, Albuquerque, NM 87131; PH (505) 277-3233; FAX (505) 277-1988; email: jcoonrod@unm.edu 2 Post Doctoral Associate, Department of Civil Engineering, University of New Mexico, Albuquerque, NM 87131; email: jayho@unm.edu 3 Research Assistant, Department of Civil Engineering, University of New Mexico, Albuquerque, NM 87131; email: nbernard@unm.edu ABSTRACT Supercritical channels present a number of design issues as the flow is readily disturbed. Yet, the design of supercritical channels for storm water drainage is necessary in steep environments. Storm drains flowing into supercritical channels are typically aligned to minimize the angle between the drain and the channel. By doing so, standing waves are minimized. Channels are often designed with additional freeboard downstream to accommodate the standing wave. In contrast, flow can be removed from channels via storm drain pipes for the purpose of Best Management Practices consisting of storm water cleaning such as debris removal and/or natural filtration. Various lateral outflow structures have been used in Albuquerque, NM, USA. In some cases, low to moderate flows with lateral outflow result in undesirable hydraulics, while the effects of the lateral outflow are negligible at design flow rates. A physical model of a supercritical trapezoidal channel was built to assist in design guidance of lateral outflow. The angle and size of the outlet pipe were changed; various guiding vanes were employed; and a range of flow rates were tested. A numerical model was also developed to further the range of variables tested and to develop discharge coefficients for lateral outflow in supercritical channels. Preliminary results show that a 45 degree angled storm drain with a tapered vane can divert a reasonable amount of flow without adverse hydraulics for a range of flow rates. BACKGROUND Steep environments exist in many urban areas necessitating concrete lined supercritical flow channels for flood control. Storm water draining into channels through pipes results in standing waves as shown in Figure 1. Cities with such channels usually provide design guidance for associated freeboard.
flow Figure 1. Standing waves in supercritical channel with later inflow As large urban areas are required to utilize Best Management Practices (BMPs) for cleaner storm water, the need to consider lateral outflow from supercritical channels has risen. By diverting the first flush from a channel, the storm water can be run through debris removal structures and/or wetlands then routed back into the storm water channel such that receiving waters will be cleaner. Lateral outflow using weirs has been studied by a number of researchers (Hager, 1987; Singh, et al, 1994). However, weirs are not applicable in this case as they cannot be used to divert the first flush. Mizumura et.al. (2003) and Mizumura (2005) have investigated outflow from supercritical channels for the purpose of considering a breach and the impact on the floodplain. The Albuquerque Metropolitan Arroyo Flood Control Authority (AMAFCA) has designed and installed several lateral outflow structures for the purpose of BMPs in Albuquerque, NM, USA. One of their first such outlets consisted of a pipe coming from the bottom of the channel such that frequent storms and the first part of the hydrograph for less frequent storms were easily diverted. Laboratory experiments for design flow had shown the outlet to be effective. However, once built, low storm events resulted in a rooster tail shaped wave in the middle of the channel. For a different location in Albuquerque, physical modeling was performed of a large circular storm drain with outlets to the bottom and to the side. Both wye scenarios successfully diverted frequent flows. However, with low to moderate flows in the wye extending to the bottom, the potential energy resulted in a large hydraulic jump in the center of the pipe. The wye extending to the side had a slight disturbance in the flow for low to moderate flows. However, this separation was much more desirable than the rooster tail shaped wave produced by the wye diverting to the bottom. With higher flow rates the effects of the wye were drowned out (Coonrod, 2002).
PHYSICAL MODEL A typical flood control channel was built in the newly constructed Hydraulics Lab at the University of New Mexico. The 0.3 m bottom width, 2:1 side sloped channel was constructed of sheet metal on top of a 15 meter long tilting table as shown in Figure 2. flow Figure 2. Scaled model of supercritical channel with lateral outflow Different pipe diameters were tested with 30, 45, and 90 angles to the downstream flow. Flow rates were measured in the channel and diversion, as were depths and velocities. In general, diverted flow increased with increased pipe size. However, the results were not consistent due to wave action in the channel. Furthermore, for low flow rates, the 30 o angle resulted in more diverted flow. As flows were increased, wave action increased, and the angle of the diversion no longer made much difference in amount of diverted flow. To increase the amount of diverted flow, guiding vanes were added to the experiment. Three vanes were modeled: a) a vane perpendicular to the flow just downstream of the diversion; b) a vane placed at the same angle as the pipe just downstream of the diversion, and c) a tapered vane at the same angle as the pipe with increasing height closer to the pipe. For low flows, the vanes assisted in guiding more water into the diversion. As flow rate increased on these steep slopes, the effect of the vane became less evident. Although more streamlined, the angled vane resulted in similar hydraulics as the perpendicular vane. The tapered vane at an angle generally resulted in more water in the diversion. Photos of the tapered vane at an angle are shown in Figure 3 for three flow rates. At the lower flow rate, a hydraulic jump is induced by the vane, resulting in more head to push flow through the diversion.
Q=2500 cm 3 /s Q=6700 cm 3 /s Q=14,600 cm 3 /s Figure 3. Lateral outflow with 45 o tapered vane With increased flow rates, the increased momentum results in a very short distance between depth increasing and the vane; thus no additional head is provided to push the flow through the diversion. The experiments described are preliminary. A number of tests were run in expectation of a relationship between the ratio of diverted flow to channel flow and the Froude number. No relationship was shown in the data when three flow rates were used. Because the controlling variables change with increased flow rate, it is necessary to run the experiments with smaller changes in flow. Based on observation and flow measurement, the tapered vane results in increased diversion with no undesirable hydraulics. The rate of taper and height of the vane should be further investigated.
NUMERICAL MODEL Flow-3D, developed by Flow Sciences (2008), was used in this study to numerically model lateral outflow from a supercritical channel. This computer program solves the Reynolds-averaged Navier-Stokes equations including the Reynolds stress term, which approximates the random turbulent fluctuations using the finite volume formulation. The Volume Of Fluid (VOF) method, which is based on conservation of the volume fraction with respect to time and space, was used for fluid interfaces. With the VOF method, grid cells are defined as empty, full, or partially filled with fluid. In order to define mesh geometry on the finite control volume, the Fractional Area/Volume Obstacle Representation method, which defines an obstacle in a cell with a porosity value between zero and one as the obstacle fills in the cell, was used. To account for turbulent effects of eddy viscosity, the renormalization group (RNG) model (ASCE Task Committee, 1988), a widely used turbulence closure model, was adopted. The RNG model has shown reliable performance for flows with high streamline curvature. The Prandtl mixing length model was employed for the wall shear stress boundary. A hexahedral mesh, 508 cm long by 25.4 cm high by 132.3 cm wide, was built with 284 18 76 computational cells, respectively (Figure 4). To decrease computation time and memory, a variable grid size was used. Figure 4. Numerical model mesh and boundary conditions
On the surface of the obstacle, all velocity and pressure components are set to zero. For the model inflow boundary and outflow boundary, the specific velocity with fluid height and continuative conditions were employed, respectively. To simulate flow diversion at higher Froude numbers ( 4.0 Fr ), a velocity of 250.0 cm/s with 2.5 cm water depth were used for the inflow boundary condition. The continuative boundary condition consists of zero normal velocity derivatives; thus a smooth continuation of the flow discharge can be generated without impacting the outflow boundary. Atmospheric pressure was set at the top of the mesh, and a non-slip wall condition defined as having zero tangential and normal velocities was applied at the bottom and sidewalls of the mesh. Another continuative boundary condition was applied to the lateral diversion outlet. To impose friction on the structure surface, the non-slip wall shear boundary condition was used with a 1/7-power law velocity profile approximation. A successive over-relaxation iterative process, a fast converging implicit method in a wide range of flow conditions, was adopted to solve pressure. The computation time step was controlled by stability and convergence for the pressure iteration. Figure 5 shows computed transient flow rates in the upstream channel, diversion, and downstream channel. A 23,440 cm 3 /s of inflow was generated from the very beginning of the simulation, while the downstream flow rate reaches steady state after approximately 25 seconds. Figure 5. Diversion flow rate transient state computation Including a vane increases the diversion flow rate. The vane model (w/ vane, solid circle marked line) produces a steady 290 cm 3 /s diversion rate, almost 5.3 times more
effective than without the vane (w/o vane, hollow circle marked line). In addition, the vane model provides flow retention at the beginning of the flow, which is effective in diverting the first flush for storm water quality BMPs. The vane forces supercritical flow through a hydraulic jump to subcritical flow as shown in Figure 6. The jump occurs close to the vane resulting such that the increased water depth is not seen very far upstream. Time dependent streamwise velocity is shown with colored surface plots and streamlines in Figure 6. The results are consistent with the physical model Figure 6. Computed flow pattern of 45º angled lateral diversion with tapered vane CONCLUSION Physical and numerical models were developed to investigate lateral outflow from supercritical trapezoidal shaped channels. The physical and numerical models were in agreement. Models run with more flow rates are required to develop relationships between flow rate, percent diverted flow, and Froude number. Tapered vanes, placed at the same angle as the diversion, are effective in directing more flow to the diversion while minimizing disturbances to the flow. The controlling variables for effective diversion discharge change with flow rate.
ACKNOWLEDGEMENTS Partial funding of this project was provided by the Albuquerque Metropolitan Arroyo Flood Control Authority. Their support is appreciated. REFERENCES ASCE Task Committee. (1988). Turbulence modeling of surface water flow and transport: part I, II, III, IV, V. Journal of Hydraulic Engineering 114(9): 970-1073. Coonrod, J. (2002). North Domingo Baca Diversion Wye, Modeling Report, prepared for the Albuquerque Metropolitan Arroyo Flood Control Authority. Flow-3D user manual; excellence in flow modeling software, v 9.2. (2008). Flow Science, Inc., Santa Fe, NM. Hager, W. H. (1987). Lateral outflow over side weirs. Journal of Hydraulic Engineering, ASCE. Misumura, K. (2005). Discharge Ratio of Side Outflow to Supercritical Channel Flow, Journal of Hydraulic Engineering, ASCE. Mizumura, K; Yamasaka,M.; and Adachi, J. ;(2003). Side Outflow from Supercritical Channel Flow, Journal of Hydraulic Engineering, ASCE. Singh, R. M., Manivannan, D., and Satyanarayana, T. (1994). Discharge coefficient of rectangular side weirs. Journal of Irrigation and Drainage Engineering. ASCE.