Finally, the net values of the pressure, viscous, and total forces and coefficients for all of the selected wall zones are also computed. The total moment vector about a specified center is computed by summing the cross products of the pressure and viscous force vectors for each face with the moment vector , which is the vector from the specified moment center to the force origin see Figure The terms in this summation represent the pressure and viscous moment vectors: Direction of the total moment vector follows the right hand rule for cross products.
Along with the actual components of the pressure, viscous, and total moments, the moment coefficients are computed for each of the selected wall zones, using the reference values as described in this section in the separate User's Guide. The moment coefficient is defined as the moment divided by , where , , , and are the density, velocity, area, and length. The coefficient values for the individual wall zones are also summed to yield the net values of the pressure, viscous, and total moments and coefficients for all of the selected wall zones.
There was virtually no reduction in flow velocity beneath the bridge. The PIV results, however, display a significant zone of very slow flow in the cavity on the underside of the streamlined deck shown in figure Even minute differences in the flow fields or non-visible flow parameters, however, could lead to significant differences in the simulated force values.
The next sections highlight the deck force results. Figure PIV velocity profile for the six-girder bridge. PIV velocity profile for the three-girder bridge. PIV velocity profile for the streamlined bridge. The six-girder bridge deck represented the dimensions of a typical highway bridge deck.
The scale of the model allowed the range of Fr used in the experimentation to correspond well with realistic Fr for actual flood flows interacting with bridges. Figure 28 depicts the relationship of the inundation ratio with the drag coefficient, C D , for the six-girder bridge.
The experimental data are shown in four series of points. Drag coefficient versus inundation ratio for the six-girder bridge. This corresponds to a case when the bridge was slightly more than halfway inundated, perhaps as the water level was reaching the top of the girders and was beginning to transition to overtopping the deck.
The fitting equations enclose the experimental data generally well over the whole range of inundation ratios. The CFD models did not show any dependence on Fr, so agreement with experimental data should not be overstated. Figure 29 displays the lift coefficient plot for the six-girder bridge. Experimental data, fitting equations, and CFD simulation results are displayed in the same manner as in the drag coefficient plot. The experimental results revealed that the lift coefficient was negative for all the cases tested.
A negative lift coefficient means that the flow was actually exerting a pull-down force on the bridge. The lift coefficient slowly returned to 0 as the inundation ratio exceeded 3. As shown in figure 29, the fitting equations are generally representative of the experimental data but break down at higher inundation ratios and higher Fr. Lift coefficient versus inundation ratio for the six-girder bridge.
The CFD model results did not closely follow the experimental results. The moment coefficient plot is shown in figure The experimental results demonstrate a similar shape no matter the Fr but are intriguing for their relative positions on the moment coefficient axis.
This corresponds to a moment rotating the bridge counterclockwise rotating the upstream side of the bridge down and the downstream side up. The peak moment coefficient came during the study when the bridge was roughly halfway inundated, and the flow was pushing almost entirely on the first girder and thus below the center of gravity.
At higher Fr , the effect was less pronounced. Additionally, in the 1. As shown in the figure, the CFD results demonstrate only fair agreement with the experimental results for the moment coefficient. They also show reasonable agreement with some of the experimental results at high inundation ratios, but the moment coefficients are near 0 anyway. The model represents the reduction in the moment coefficient and stabilization but somewhat more aggressively than in the experimental results.
Moment coefficient versus inundation ratio for the six-girder bridge. The three-girder bridge deck represented another common highway bridge design. The bridge-deck height was somewhat larger than the height for the six-girder, and the girders were rectangular and proportionally more massive.
The increased deck height meant that the bridge could be tested for a narrower range of inundation ratios since the water depth remained at 0.
Figure 31 shows the drag coefficient plot for the three-girder bridge. The experimental results display a shape similar to the results of the six-girder bridge, and the minimum point occurs at roughly the same inundation ratio.
The two higher Fr cases 0. The CFD results for the three-girder bridge are also displayed on the plot in figure Unlike the simulations for the six-girder bridge, the flow conditions in the CFD model are not calibrated based on the experimental results. Instead, the configuration of the six-girder model is used, and only the bridge deck model is changed.
Next, open the appropriate dialog box using the Monitors task page. Note that you can only access one of these monitor dialog boxes at a time, though all three monitors can be used during the same simulation. Monitors Drag Edit Monitors Lift Edit Monitors Moment Edit Figure
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