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46 observe the scour development. The evolution of the three- bed shear stress is required. The CPU time increases to dimensional scour hole with time was obtained by combining 20 hours when the scour hole development needs to be the scour profiles from all angles around the pier. simulated. 6. The output consists of the following parameters in 6.3 NUMERICAL METHOD USED three dimensions: velocity vectors, pressure, bed shear IN THIS STUDY stress, and turbulent kinetic energy. In the present study, the three-dimensional flow chimera 6.4 VERIFICATION OF RANS Method of Chen et al. (1993, 1995a, 1995b, 1997) was THE NUMERICAL METHOD used. First, the computational domain was divided into a num- ber of smaller grid blocks to allow complex configurations and This verification was achieved by comparing the shear flow conditions to be modeled efficiently through the judicious stresses predicted by the numerical method to those measured selection of different block topology, flow solvers, and bound- experimentally. The measurements were performed by Hjorth ary conditions. The chimera domain decomposition technique (1975) who investigated the distribution of shear stresses was used to connect the overlapped grids together by inter- around a circular pier. The experiment was conducted in a polating information across the block boundaries. The rigid boundary flume. Two circular piers were used (diameter Reynolds stresses were evaluated using the two-layer turbu- 0.05 m and 0.075 m). The study focused on two different lence model of Chen and Patel (1988). The mean flow and velocities (0.15 m/s and 0.20 m/s) and two different depths of turbulence quantities were calculated using the finite-analytical approach flow (0.1 m and 0.2 m). The shear stress was mea- method of Chen, Patel, and Ju (1990). The SIMPLER/PISO sured by using a stationary hot film probe through the bottom pressure-velocity coupling approach of Chen and Patel (1989) of the flume flush with the bottom, then moving the position and Chen and Korpus (1993) was used to solve for the pres- of the cylinder around the fixed probe. In that fashion, Hjorth sure field. A detailed description of the multiblock and chimera obtained the shear stress at 35 different locations around the RANS methods is given in Chen and Korpus (1993) and Chen, cylinder and created isostress lines by interpolation between Chen, and Davis (1997). A useful summary of that method the measurements. The numerical method was used to simu- can be found in Nurtjahyo (2002). This summary discusses the late the experiments performed by Hjorth. The output was the governing equations, turbulence modeling (RANS or RANS distribution of the shear stresses on the flume bottom around equations), the boundary conditions on the pier surface, the the cylinder. The result of the experiment and the numerical river bottom, the outer boundaries, and the free water surface. simulation for the 0.075-m-diameter cylinder are compared The computer code has the ability to simulate the develop- on Figures 6.1 and 6.2. The very favorable comparison gave ment of the scour hole around the pier as a function of time. confidence in the validity of the numerical results. This is done by including an erosion function linking the ver- tical erosion rate to the shear stress at the interface between the 6.5 SHALLOW WATER EFFECT: water and the soil. The program then steps into time by adjust- NUMERICAL SIMULATION RESULTS ing the mesh in the vertical direction after each time step as the scour hole develops. This option is not necessary to obtain the The objective of this parametric study was to obtain the maximum shear stress before scour starts, since in this case relationship between the maximum bed shear stress max and the bottom of the river is kept flat. water depth (Figure 6.3). A typical run consists of the following steps: One of the flume experiments was chosen to perform the simulation. The cylindrical pier with a diameter equal to 0.273 1. Obtain the information for the problem: water depth, m was placed vertically in a 1.5-m-wide flume. The velocity mean depth velocity at the inlet, pier size, and pier shape. was constant at 0.3 m/s and four different water depths were 2. Calculate the Reynolds Number and Froude Number simulated: H = 0.546 m (or H/ B = 2), H = 0.258 m (or H/ B = because they influence the size and distribution of the 0.95), H = 0.137 m (or H/ B = 0.5), and H = 0.060 m (or H/ B grid elements. = 0.22). The value of the Reynolds Number based on the 3. Generate the grid using a program called GRIDGEN diameter was Re = 81900 and the Froude Number based (about 4 days' worth of work). on the diameter was Fr = 0.1833. In order to reduce the 4. The input consists of the Reynolds Number, the Froude amount of CPU time, one-half of the symmetric domain was Number, and the boundary conditions on all surfaces. chosen. The grid was divided into four blocks as shown in The initial condition consists of the velocity profile at Figure 6.4. the inlet and is automatically generated by the program The grid was very fine near the pier and riverbed in order on the basis of the inlet mean depth velocity and the to apply the two-layer approach of the turbulence model. A geometry. few grid layers were placed within the viscous sublayer. The 5. Typical runs last 5 hours of CPU time on the Texas first step was to verify that the inlet velocity profile for the A&M University SGI supercomputer when only the numerical simulation matched the experiment. The result was