This paper offers an improvement to the Morison, O"Brien, Johnson, and Schaaf (MOJS, 1950) representation of the in-line force for a sinusoidally oscillating flow. The modification proposed herein consists of the addition of a third term, without the introduction of additional empirical coefficients. The three-term model is expected to offer greater universality and higher engineering reliability, particularly in the inertia-drag regime where the original MOJS equation fails.


Unsteady flows over bluff bodies arise in many engineering situations and the prediction of the fluid/structure interaction (forces and dynamic response) presents monumental mathematical, numerical and experimental challenges (Stokes, 1851; Wang, 1968; Sarpkaya, 1985, 1986a, 1992). Stokes classical solutions (1851) formed the basis of many subsequent models where the oscillations are presumed to be small enough to allow convective accelerations to be ignored. An extensive review (Mei, 1994) of the existing force models for flows at relatively small Reynolds numbers has shown that the degree of empiricism increases with increasing Reynolds number and some measure of the unsteadiness of the motion. As yet a theoretical analysis of the problem for separated flow is difficult and much of the desired information must be obtained experimentally and, if possible, numerically. The computational representation of a turbulent motion, without proper physics, is a major roadblock to the ultimate promises of the Computational Fluid Dynamics (CFD). Equally important is the fact that in highly complex, separated, timedependent turbulent flows with large-scale unsteadiness about small bodies (with negligible diffraction effects), such as those considered herein, the Reynolds number varies between zero and a desired maximum during a given cycle and the flow is three dimensional. Even if one were to develop rationally-constructed, two-or higher-order-equation turbulence models, there is no assurance that they will yield reliable results for time-dependent flows.

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