Modelling the unsteady axial forces on a finite-length circular cylinder in cross-flow

A semi-empirical model for unsteady axial forces is developed to predict the spectral features of the force generated by the flow over the end-caps on a finite-length, right circular cylinder in cross-flow. In general, the model consists of two parts: the spatial variation of r.m.s. wall pressure on the cylinder end-caps, and the correlation lengths and areas, which describe the spatial extent of the correlation of the unsteady wall pressures. Experiments were conducted in a low-noise wind tunnel as a function of cylinder diameter Reynolds number (19 200<Re<32 000) and the Strouhal number (0.05<St<3.33) to measure the statistics of the unsteady wall pressures on a model cylinder. These results are incorporated into the theoretical models, and prediction of the spectral characteristics of the axial force are made. The r.m.s. wall pressures on the end-caps are found to have the largest amplitude at circumferential locations (from the forward stagnation point) in the 90-120° range. The high levels at these locations are attributed to reattachment of the separated flow over the end-cap. The radial and circumferential correlation areas have a maximum value at St=0.21. Due to the 3-D flow over the end-caps, the radial correlation areas are found to depend on the circumferential measurement reference location, and the circumferential correlation lengths are found to depend on the radial measurement location. The unsteady axial force predictions using the model show a very broad spectral character.