2584

Table 1 shows that modeling the cone surfaces referenced to the surface floor overestimates the drag for both cone surfaces. As expected, this model is adequate for the Deposit Cone surface because it is sparse. For the closely-packed cones of the Erosion Cone surface, this method greatly overestimates the drag.

Table 1 shows that modeling the cone surfaces referenced to the surface floor overestimates the drag for both cone surfaces. As expected, this model is adequate for the Deposit Cone surface because it is sparse. For the closely-packed cones of the Erosion Cone surface, this method greatly overestimates the drag.

If a 10% uncertainty in the experimental data is assumed, then setting a datum at the mean hydraulic surface and adding shear on the area at the datum not blocked by flow models the surfaces well. Modeling the surfaces referenced to the mean hydraulic elevation and adding the wall shear to the skin friction coefficient on the area of the reference surface not blocked by flow has a very low percentage difference for the Deposit Cone surface and barely exceeds the assumed uncertainty bands for the Erosion Cone surface.

Random Surface Skin Friction Results

Acknowledging the cone surface results, the random surfaces were modeled as roughness elements placed at the mean hydraulic elevation of the real surface for the skin friction coefficient predictions. After the boundary-layer equations were solved using the "no-slip" condition at the surface, surface shear was added to the skin friction coefficient on the area of the mean hydraulic elevation not blocked by roughness elements. For each blockage element at a given height above the mean hydraulic surface, the maximum width of the blockage element was extracted and used as the diameter. The total drag at a given height in the boundary layer was then calculated with the following expression for circular blockages as suggested by Taylor (1983).

2 LxLz i=1

The above model was applied to each of the randomly-rough surfaces and to the layered-analog surfaces of the randomly-rough surfaces. The results are presented in Table 2. Table 2 shows that the surface that is most like the model, which assumes circular blockages on a flat surface with large spacings relative to the diameter of the blokcages, is accurately predicted. The Erosion 2 Layered surface is a very sparse surface with circular blockages and a flat surface beneath the mean hydraulic elevation. For the Erosion 2 Layered surface, the model prediction is within 2% of the experimentally measured value of the average skin friction coefficient. Table 2. Random Roughness and Layered Ellipsoidal Surface Results

Surface

Average Rex

Measured Cf

Predicted Cf

% Difference

Erosion 2

0 0

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