Force Coefficients From Wave Project I and II Data Including Free Surface Effects

Abstract

Abstract Wave force data, obtained by Chevron Oil Field Research Co. in conjunction with Shell Development Co. and Exxon Production Research Co., have been reanalyzed for drag and inertia coefficients. These data are the field results of Wave Projects l and II and consist of water surface elevations and forces on piles of various sizes at different elevations within the water column. The analysis here is based on the stream function wave theory and Morison's equation, resulting in drag (CD) and inertia (CM) coefficients including a dependency on Reynolds number. Principal findings are a somewhat higher value for CD at large Reynolds numbers than that obtained by Aagaard and Dean. Free surface effects include a run-up on the piling and an associated local modification in drag coefficients. resulting in reductions in overall forces and moments. Using a large data set of 349 waves (digitized at 0.1 second), variances between predicted and measured forces also were obtained that followed a normal probability distribution. Introduction The two wave projects (WP) discussed in this paper represent the best field data generally available to the engineering and scientific community. The first of these projects, WP I, obtained wave and force data in 33 ft (10 m) of water from Dec. 1954 to Nov. 1958. WP II was carried out from Sept. 1960 to Nov. 1963 in 99 ft (30.2 m) of water to obtain data for larger waves of greater depth. The wave project data have been analyzed in the past by Evans, Aagaard and Dean, and Wheeler. For each of the reported analyses, water wave theories were necessary to predict velocities and accelerations since no reliable water particle kinematics were measured, and the differences in the results of the analysis are due largely to the choice of the theory used as well as the method for obtaining force coefficients. For example. Wheeler used a "stretched" linear wave theory that allowed for the variability of the measured free surface (yet the method failed for WP I as the shallow water depth and resulting wave nonlinearities precluded the use of a linearized theory). Evans, on the other hand, used several theoretical wave theories such as Airy, Stokes V, and the numerical Chappelear theory, all of which are symmetric in form about the crest. Aagaard and Dean applied the irregular form of the stream function wave theory to obtain kinematics. Dean has shown that the stream function theory provides the best fit to the mathematical problem posed for water waves, and the use of the irregular form of the theory allowed for the influence of the irregular free surface to be included. Aagaard and Dean's analysis included 255 WP I and 100 WP II waves. Data from each wave, taken from the most forceful one-third of the waves, were grouped into Reynolds number ranges and a least-squares procedure was used to find the best CD and CM for each Reynolds number (NRe) range for both the inline and the resultant direction. These directions were established as the directions of the highest mean square force as the wave passed and the instantaneous vector sum of the measured forces over the depth. A reasonable trend with Reynolds numbers occurred for CD, while CM was found to be a constant, 1.33. This paper reports the analysis of 263 WP I waves and 86 WP II waves, which represent the highest waves in each project. Compared with earlier analyses of these data, the principal difference is a somewhat higher drag coefficient at high Reynolds numbers due to free surface effects. SPEJ P. 779^