Computational Mechanics Research and Support for Aerodynamics ...
Computational Mechanics Research and Support for Aerodynamics ... Computational Mechanics Research and Support for Aerodynamics ...
[ ( ) ] (2.3) Differentiating Equation (2.3) gives the bed recession rate at the point of maximum scour: [ ] (2.4) One problem with this fitted function is that the bed recession rate approaches infinity at time zero, which is physically unrealistic. The function fits the experimental data reasonably well after the first ½ hour, however, the actual bed recession rate at time zero in the TFHRC pressure flow scour experiments is a finite value that is a small fraction of a meter per second. Because over one third of the final depth of the scour hole may be reached in the first half hour, that time period is important in a CFD simulation that starts from time zero with a flat bed. Currently alternatives for dealing with a lack of data for the scour rate during the first half hour are being investigated. Assuming that the entrainment rate is independent of time and a function of the local bed shear stress and bed slope, then Equations (2.3) and (2.4) can be used to fit an entrainment rate that is a function of shear stress at the point of maximum shear and that function can be applied anywhere on the bed. Three candidate functions are proposed. One by Xie [4] has the form: in which τ m denotes the maximum bed shear stress. E b denotes the recession rate or sediment pickup rate. An initial fit yields the parameters: a = 2.933e-011, b = 4.034, c = -0.001206, d = -4.645. Initial testing of this function fit found that the scour away from the point of greatest depth was too slow and did not match the bed profiles at intermediate times. The entrainment function by Van Rijn and a chemical kinetic rate law analogy proposed by Lottes [1] have been considered, and initial testing of these model functions for clear water pressure flow scour has begun. The Van Rijn function is a power law function of the form: (2.5) ( ) (2.6) where E b is the sediment pickup rate in units of mass per unit sediment bed area and per unit time, kg/(m 2 s). Initial tests using the constants given by Van Rijn yielded scour rates that were too fast and a pressure flow scour hole that was too deep, two or more times the experimental scour depth. The rate law as proposed by Lottes [1] has the form: (2.7) TRACC/TFHRC Y1Q3 Page 12
( ) ( ) (2.8) where A 0, A 1, and n are fitting parameters. An initial fit of these parameters to the reduced experimental results by Guo yields ( ) ( ) ( ) (2.9) 2.2. Initial Test of Mesh Morphing Applied to Transient Clear Water Pressure Flow Scour An initial simulation using the bed recession rate given by Equation (2.9) was performed. The initial bed shear is shown in Figure 2.1. The bridge deck extends from 3.83 m to 4.09 m. The peak in shear is 9 cm from the trailing edge of the deck. The lower peak near x = 0.0 is due to a honeycomb at the inlet that straightens the flow, helps to ensure a uniform velocity across the flume, and strips off the boundary layer at the bed. The reforming boundary layer generates locally high bed shear extending to approximately x = 0.7 m. In that upstream zone the bed is fixed and cannot be eroded. Figure 2.1: Initial bed shear profile along flume with flooded bridge deck at 3.83 m to 4.09 m Figure 2.2 shows that the local peak in bed shear stress under the submerged bridge deck has dropped as flow area under the deck is increased through the erosion of bed material to a plateau that is near the critical value to initiate motion of stationary sediment particles on the bed. TRACC/TFHRC Y1Q3 Page 13
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[ ( ) ] (2.3)<br />
Differentiating Equation (2.3) gives the bed recession rate at the point of maximum scour:<br />
[ ]<br />
(2.4)<br />
One problem with this fitted function is that the bed recession rate approaches infinity at time zero,<br />
which is physically unrealistic. The function fits the experimental data reasonably well after the first ½<br />
hour, however, the actual bed recession rate at time zero in the TFHRC pressure flow scour experiments<br />
is a finite value that is a small fraction of a meter per second. Because over one third of the final depth<br />
of the scour hole may be reached in the first half hour, that time period is important in a CFD simulation<br />
that starts from time zero with a flat bed. Currently alternatives <strong>for</strong> dealing with a lack of data <strong>for</strong> the<br />
scour rate during the first half hour are being investigated.<br />
Assuming that the entrainment rate is independent of time <strong>and</strong> a function of the local bed shear stress<br />
<strong>and</strong> bed slope, then Equations (2.3) <strong>and</strong> (2.4) can be used to fit an entrainment rate that is a function of<br />
shear stress at the point of maximum shear <strong>and</strong> that function can be applied anywhere on the bed.<br />
Three c<strong>and</strong>idate functions are proposed. One by Xie [4] has the <strong>for</strong>m:<br />
in which τ m denotes the maximum bed shear stress. E b denotes the recession rate or sediment pickup<br />
rate. An initial fit yields the parameters: a = 2.933e-011, b = 4.034, c = -0.001206, d = -4.645. Initial<br />
testing of this function fit found that the scour away from the point of greatest depth was too slow <strong>and</strong> did<br />
not match the bed profiles at intermediate times.<br />
The entrainment function by Van Rijn <strong>and</strong> a chemical kinetic rate law analogy proposed by Lottes [1]<br />
have been considered, <strong>and</strong> initial testing of these model functions <strong>for</strong> clear water pressure flow scour<br />
has begun. The Van Rijn function is a power law function of the <strong>for</strong>m:<br />
(2.5)<br />
( ) (2.6)<br />
where E b is the sediment pickup rate in units of mass per unit sediment bed area <strong>and</strong> per unit time,<br />
kg/(m 2 s). Initial tests using the constants given by Van Rijn yielded scour rates that were too fast <strong>and</strong> a<br />
pressure flow scour hole that was too deep, two or more times the experimental scour depth.<br />
The rate law as proposed by Lottes [1] has the <strong>for</strong>m:<br />
(2.7)<br />
TRACC/TFHRC Y1Q3 Page 12
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