Hydrodynamic lift and drag fluctuations of a sphere

A semi-empirical model is developed to estimate the unsteady force induced on a spherical body subjected to a steady, uniform flow. An open-ended wind tunnel is built to measure the statistics of the surface pressure fluctuations on the sphere. The experiments are performed for Reynolds numbers of 17,800, 25,600, and 31,700. The measurement results are incorporated into the model for predicting the unsteady force induced on the sphere.; The model is based on the separable assumption of the cross-power spectral densities of the surface pressure fluctuations. This assumption is shown to be a proper engineering approximation except in low frequency ranges. The model functions are obtained using least mean-square curve fits of the data.; Experiments are performed where the flow-induced unsteady side force and drag force are measured independently of each other on towed spheres in a basin of water. These experiments are performed for Reynolds numbers of 6,680, 10,020, 13,360, and 16,700.; The semi-empirical model and the tow tank measurements show that the dimensionless power spectral densities of unsteady lift and drag forces are St0 (St is abbreviation for Strouhal number) dependent for St < 1, and St−3 dependent for 1 ≤ St ≤ 100. The model predicts that the levels of the dimensionless power spectral densities of the unsteady lift force are about 5 dB higher than that of the unsteady drag force, while this level difference is about 3 to 7 dB from the tow tank measurements.; The predicted unsteady lift and drag forces are then used to determine the flow noise induced on underwater inertial sensors subjected to a steady, uniform flow. For a given frequency, flow noise is estimated to be higher for a smaller sensor than for a larger one. The flow noise response is about 5 dB higher in the side force direction than in the drag force direction.