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68 CHAPTER 8 THE SRICOS-EFA METHOD FOR INITIAL SCOUR RATE AT CONTRACTED CHANNELS 8.1 BACKGROUND 8.2 CONTRACTION RATIO EFFECT: NUMERICAL SIMULATION RESULTS The existing knowledge on numerical methods for scour studies was presented at the beginning of Chapter 6 (Section One of the flume experiments was chosen to perform the 6.2) and the existing knowledge on contraction scour in numerical simulation. The width of the flume used was 0.45 m. cohesive soils was presented at the beginning of Chapter 7 The upstream flow was a steady flow with a velocity V1 of (Section 7.1). 0.45 m/s and the upstream water depth H was 0.12 m. Three The initial scour rate is an integral part of the SRICOS different contraction ratios were chosen: B2/B1 = 0.25, 0.5, and Method to predict contraction scour as a function of time 0.75. In order to reduce the CPU time, a half domain was used because it is one of the two fundamental parameters used to based on the symmetry of the problem. For numerical purposes, describe the scour depth versus time curve. The other funda- the characteristic length B was defined as half of the flume mental parameter is the maximum depth of contraction scour width. Based on this definition, the value of the Reynolds that was studied in Chapter 7. The initial rate of scour for a Number (Re = VB/) was 101250 and the Froude Number given contraction scour problem is obtained by first calculat- (Fr = V gB) was 0.303. The grid was made of four blocks as shown in Figure 8.1. ing the maximum shear stress max existing in the contracted The bed shear stress contours around the abutment and in channel before the scour starts (flat river bottom) and then the contracted zone are shown in Figures 8.2 to 8.4. The reading the initial scour rate on the erosion function obtained maximum bed shear stress is found around the abutment but in the EFA test. Therefore, the problem of obtaining the ini- the maximum contraction bed shear stress max is found tial rate of contraction scour is brought back to the problem of along the centerline of the channel in the contracted section. obtaining the maximum shear stress in the contracted channel As expected, it is found that the magnitude of max increases before scour starts. This problem was solved by numerical when the contraction ratio (B2/B1) decreases. It is also simulations that use the chimera RANS method. This method observed that the distance Xmax between the beginning of the was described in Section 6.3 and a verification of its reliabil- fully contracted section and the location of max increases ity was presented in Section 6.4. This chapter describes the when the contraction ratio (B2/B1) increases. simulations performed and the associated results. The goal was to develop an equation for the maximum shear stress max existing in the contraction zone. 8.3 TRANSITION ANGLE EFFECT: The equation for the maximum shear stress max at the bot- NUMERICAL SIMULATION RESULTS tom of an open channel without contraction is given by (Munson et al., 1990) as Again, one of the flume experiments was chosen to per- form the numerical simulation. The width of the flume used was 0.45 m. The upstream flow was a steady flow with a 1 - velocity of 0.45 m/s, the contracted length L was such that max = n 2 V 2 Rh 3 (8.1) L/(B1 - B2) = 6.76 and the water depth was 0.12 m. Four dif- ferent transition angles were chosen for the simulations: = where is the unit weight of water, n is Manning's rough- 15, 30, 45, and 90 degrees. The width (B1 - B2) was chosen ness coefficient, V is the mean depth velocity, and Rh is the as the characteristic length B. The Reynolds Number was hydraulic radius defined as the cross-section area of the flow 101250 and the Froude Number was 0.303. divided by the wetted perimeter. The equation obtained for the The bed shear stress contours around the abutment and in contracted channel case should collapse to the open channel the contracted zone are shown in Figures 8.5 to 8.7. As can case when the contraction ratio B2/B1 becomes equal to 1. The be seen, the magnitude of the maximum bed shear stress max objective of the numerical simulations was to obtain correction along the center of the channel in the contracted section factors that would introduce the effect of the contraction ratio, increases when the transition angle increases. However the the transition angle, and the length of the contracted zone. transition angle does not have a major influence on max. It is