FLOW-3D Success Stories
Numerical Modeling of Spillway Flow Achieves Reduction in Time and Cost
By Dan Gessler, Alden Research Laboratory; Bernie Rasmussen, American Electric Power
American Electric Power (AEP) recently revised the probable maximum flood (PMF) study for the Smith Mountain Dam. As a result of that study, the PMF pool elevation significantly increased over the previous study, and concerns were raised regarding the performance of the dam for the increased elevations. AEP contracted Alden to model the flow characteristics of the dam’s spillways during the PMF event. Alden used a combination of historic physical modeling results and the computational fluid dynamics (CFD) program, FLOW-3D, to obtain reliable results while minimizing project costs and schedule. Since the estimated flow during a PMF greatly exceeds the dam’s original design flow, AEP was concerned that the increased flow during this event would cause the freefalling water to overshoot the catch chute and adversely affect the structures. Building a reduced scale physical model of the dam and implementing a laboratory test program would have cost AEP approximately $200,000 and required six to eight months to complete. Alternatively, engineers at Alden Research Laboratory (Alden) simulated the flow in a much shorter time period using the CFD software to efficiently compute the trajectory of the water through the air and predict the point of impaction. The simulation results, which closely correlated to physical model testing performed at Alden 45 years ago, showed that even the high flows associated with a PMF would not result in water trajectories that extend past the spillway’s catch chute.
Description of Smith Mountain Dam
Smith Mountain Dam is located on the Roanoke River, near Roanoke Virginia. It is a double arch concrete dam with a base thickness of 30 ft, a height of 235 ft, and top width of 816 ft. Construction of the project was completed in 1965 with 175,000 cubic yards of concrete. The dam is part of a hydroelectric pumped storage project that also includes Leesville Dam. Smith Mountain Lake is approximately 40 miles long, with 500 miles of shoreline and a full pool water surface elevation 795 ft above mean sea level (msl). Smith Mountain Dam has two ungated overtopping spillways, each with a total clear opening of 100 ft. A pier at the mid-span of each spillway supports the roadway across the spillway opening. The spillway crest has an elevation of 795 ft.
Looking upstream at Smith Mountain Dam
Water passing over the spillway free-falls through the air before entering the catch chute, which was structurally designed to minimize the force of the water’s impact. As part of a physical model study conducted over 45 years ago Alden evaluated the dam’s original spillway design and performance at lake levels up to 812 above msl, where the spillways pass 50,000 cubic feet of water per second (cfs). In 1960, Alden used this historic test data to determine optimum spillway geometry.
AEP computed the probable maximum flood (PMF), which is the largest flood that the dam would likely ever experience. The projected flows are as high as 120,000 cfs with an associated pool elevation of 821.9 feet. This would exceed the 812 ft pool level for which the dam had been originally tested. Based on the assessment, AEP asked Alden to determine the trajectory of the flow through the spillway openings at these higher flow rates.
Using Simulation Instead of Physical Modeling
Alden considered building a physical model, however, based on the model construction and testing cost Alden engineers decided to use CFD for the modeling with historic physical model data providing the necessary validation. The CFD simulation was very challenging, primarily because of the complexities involved in numerically modeling severely deformed free surfaces—i.e., the free flow of water through air. In this case, the water free-falls over 100 feet before entering the catch chute. Alden engineers revisited the photographs of the original reduced scale model tests of the dam and determined that the free-falling water largely remained in a coherent mass instead of breaking into clumps and droplets. This allowed Alden to disregard the effect of the air on the water, simplifying the necessary simulations.
Most CFD codes have the capability to model free surfaces. Typically, they require computation of both the water and air motion in order to simulate the deformation of the air/water interface. To obtain a sharp interface between the water and air, these codes require the use of very fine computational meshes and higher order numerical methods. Computing the flow in each cell over the extent of the solution domain, including air, requires significant computing resources and large computational time.
The CFD code that Alden used, FLOW-3D from Flow Science, Inc., (www.flow3d.com) models only the water component of the flow while ignoring the motion of the surrounding air. When the free-falling water passes through the computational cells, the code calculates its motion. The FLOW-3D code allows cells where no water is present to drop out of the computation, dramatically reducing the time it takes to reach the desired solution. FLOW-3D uses the volume of fluid (VOF) method to simulate free-surface fluid motion, surface tension, and other flow characteristics. The code includes algorithms that track sharp liquid interfaces through arbitrary deformations and applies accurate normal and tangential stress boundary conditions at both solid surfaces and along the air/water interface which was essential in accurately modeling the dynamics of the flow associated with this project.
Building and Validating the CFD Model
Alden engineers started with as-built drawings that AEP provided and created the geometry of the model using third-party CAD software. They imported the geometry as an STL file into FLOW-3D and then meshed the geometry three times: at low, medium, and high resolution. The models incorporated a total of about 13,000,000 computational cells. FLOW-3D uses a time-dependent solution scheme for all problems, including steady-state simulations. Alden initiated the simulation for a known condition and allowed it to develop through time (spin up) to the desired flow field. The grid resolution was increased at the end of the first simulation and the results of the previous solution were used as the starting point for calculations on the refined grid. Alden’s use of multiple grids reduced the total time required to complete the computation. Alden initiated model runs on a coarse grid and successively refined the grids when steady state conditions were achieved. The engineers refined the computational grid three times to obtain the final results. To determine the footprint of the impact zone as accurately as possible, engineers created a submodel for each spillway using a higher grid resolution of about 1 ft horizontally and less than 0.5 ft vertically.
Overview of Model Area
Alden assessed the results of the simulation by comparing the computed lake levels and flow rates with the discharge curve developed from the physical model data. The simulations predicted lake levels within 5% of those observed in the physical experiments for a given flow rate. Alden then generated visual representations of the spillway flow from simulation data that matched the camera angles of photographs from the physical model at each discharge condition. The physical model photographs incorporated horizontal marker lines on the catch chute to help gauge the impact zone, and Alden added corresponding lines to the visualizations of the simulated results. From this analysis it became apparent that, for equal flows, the water in the simulation was hitting the catch chute at nearly the same place as in the physical model. Furthermore, the general characteristics of the water were extremely similar in the physical and numerical models. In both models, the flow contracted as it left the dam and then spread out after it hit the spillway.
Visual Comparison of Laboratory and CFD Results at 50,000 cfs
Predicting Conditions During the PMF
Once they had validated the model, Alden’s engineers changed the inlet conditions to match the PMF determined by AEP’s other consultant. They raised the inlet flow to reach a lake level of 821.9 feet above msl, which resulted in a flow of about 120,000 cfs. At this point, the water overtopped the dam by 6 feet and the spillway crest by 27 feet. Alden then compared the trajectory of the previous design flow with the trajectory at the PMF. At the section shown below, near the center of the dam, the trajectory extended 5 to 10 feet vertically down the spillway past the impact point engineers observed at 50,000 cfs. This was still 30 vertical feet from where the change in catch chute slope begins, well within the area of the chute that was designed for the water impact. Engineers evaluated other sections of the dam and saw that the maximum movement in the trajectory was about 20 vertical feet and remained at least 20 feet above the bottom of the ideal landing area.
Comparison of flow trajectory at 50,000 cfs and PMF
Conclusions
Simulating the hydraulic performance of the Smith Mountain Dam provided many benefits for AEP. Beyond the wealth of technical information gained from the study, the costs associated with performing the numerical simulations were about 20% of the projected costs associated with the design, construction and testing of an equivalent physical model. Further, the numerical modeling was completed in eight weeks which was far less time than projected for building and testing an equivalent physical model.
The availability of the data from the original physical model to validate the FLOW-3D model made the use of computer simulations, rather than physical modeling, an acceptable alternative to AEP. Not only did the use of computer simulations reduce modeling costs, but this partnership between AEP, Alden, and FLOW-3D represents an exciting new frontier in the application of computational fluid dynamics.
For more information, contact Flow Science Inc., 683 Harkle Road, Suite A,
Santa Fe, NM 87505. Ph: (505) 982-0088, Fax: (505) 982-5551. Email: info@flow3d.com
