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OCR for page 69
69 Z X Y Block 4 Block 3 0 Block 1 -0.2 Z/(0.5B1) -2 -0.4 0 2 0 1) Block 2 0.25 4 0. 5B X /( Y /( 0.5 0 .5 6 B1 0.75 ) 8 Center of the channel 1 Figure 8.1. Grid system for the simulation in the case of B2/B1 = 0.25. also observed that the distance xmax between the beginning of was 0.45 m. The upstream flow was a steady flow with a the fully contracted section and the location of max increases velocity of 0.45 m/s, the contraction channel ratio (B2/B1) when increases was equal to 0.5, the transition angle was 90 degrees, and the water depth was 0.12 m. Four different contraction lengths 8.4 CONTRACTED LENGTH EFFECT: were simulated: L/(B1 - B2) = 0.25, 0.5, 1.0 and 6.76. The NUMERICAL SIMULATION RESULTS difference (B1 - B2) was chosen as the characteristic length B. The Reynolds Number was 101250 and the Froude Number Again, one of the flume experiments was chosen to per- was 0.303. The initial bed shear stress distribution around the form the numerical simulation. The width of the flume used contracted zone is shown in Figures 114 to 116 for various 1 8.50 4.51 6.92 8.12 6.92 Center of channel 3.31 5.71 9.32 4.51 0.91 0.75 2.11 = 0.91 Y/(0.5B1) 0.5 Abutment Flow 0.25 0 -1 -0.5 0 0.5 X/(0.5B1) Figure 8.2. Initial bed shear stress distribution (N/m2) for B2/B1 = 0.25 and V = 0.45m/s.

OCR for page 69
70 1 3.29 Center of channel 3.11 3.29 2.49 0.75 1.25 1.70 2.49 1.70 Y/(0.5B1) = 0.91 4.08 0.91 0.5 Abutment 0.25 Flow 0 -1 -0.5 0 0.5 X/(0.5B1) Figure 8.3. Initial bed shear stress distribution (N/m2) for B1/B2 = 0.50 and V = 0.45m/s. 1 2.18 Center of channel 0.75 1.54 1.78 2.03 = 1.29 2.33 Y/(0.5B1) 0.5 2.03 2.66 1.78 1.54 3.00 1.29 0.91 Flow 0.25 0.91 Abutment 0 -1 -0.5 0 0.5 X/(0.5B1) Figure 8.4. Initial bed shear stress distribution (N/m2) for B2/B1 = 0.75, and V = 0.45m/s. 1 1.83 Center of channel 1.68 1.68 1.06 1.52 0.75 1.37 1.68 = 0.91 1.22 1.99 Y/(B1-B2) 2.45 0.5 Flow 0.25 Abutment 0 -3 -2 -1 0 1 2 X/(B1-B2) Figure 8.5. Initial bed shear stress distribution (N/m2) for B2/B1 = 0.5, V = 0.45 m/s, L/(B1 B2) = 6.76, and = 15 degrees).

OCR for page 69
71 1 2.06 1.49 Center of channel 1.10 1.87 1.68 1.49 1.87 0.75 2.06 = 0.91 2.25 Y/(B1-B2) 3.17 0.5 Flow 0.25 Abutment 0 -3 -2 -1 0 1 2 X/(B1-B2) Figure 8.6. Initial bed shear stress distribution (N/m2) for B2/B1 = 0.5, V = 0.45 m/s, L/(B1 B2) = 6.76, and = 30 degrees). 1 2.27 2.02 1.36 2.27 Center of channel 1.82 2.02 0.75 2.62 Y/(B1-B2) = 0.91 3.76 0.5 0.25 Flow Abutment 0 -3 -2 -1 0 1 2 X/(B1-B2) Figure 8.7. Initial bed shear stress distribution (N/m2) for B2/B1 = 0.5, V = 0.45 m/s, L/(B1 B2) = 6.76, and = 45 degrees). 1 3.25 Center of channel 3.25 1.97 3.02 2.49 0.75 1.44 3.02 3.44 = 0.91 3.75 1.97 Y/(B1-B2) 4.04 0.91 0.5 Flow 0.25 Abutment 0 -1 -0.5 0 0.5 X/(B1-B2) Figure 8.8. Initial bed shear stress distribution (N/m2) for B2/B1 = 0.5, V = 0.45 m/s, and L/(B1 B2) = 0.25).