Drag coefficient

Two important parameters in the study of flow past bluff bodies are drag coefficient and Strouhal number. Drag coefficient is the dimensionless form of the force acting on the body in the direction of flow. Strouhal number is the non-dimensional vortex shedding frequency. It is also indicative of the time scale of the unsteady forces and determines the nature of flow induced vibrations of the body in both stream-wise and transverse directions.

In the present study, drag coefficient has been calculated by a momentum integration approach over a control volume. It is also called the wake survey method, and has been extensively discussed (Schlichting, 1979). Generally, the method is used to calculate drag coefficient from velocity probe in the intermediate and far wakes, where there is no static pressure variation across the flow. In the present experiments of flow past a square cylinder in a closed channel, static pressure variation has been observed under some conditions even at twenty cylinder widths downstream. Therefore, it is necessary to consider the static pressure variation in the calculations. The drag coefficient is given by the formula (White, 1991)

Here is the velocity prole in the wake where x and y are coordinates parallel and perpendicular to the main flow direction. Additionally, is the approach velocity, is the projected area of the cylinder normal to the flow direction (per unit length along the cylinder axis) and is the static pressure drop between the free stream and the point under consideration. To maintain uniformity with the nomenclature in the published literature, the projected dimension has been taken to be equal to the edge of the cylinder for straight as well as inclined cylinders.

It is clear from the above expression that the drag coefficient cannot be determined exclusively from PIV images. Most experiments in which the pressure drop was measured using a static probe showed that the correction was to the extent of Hence, results can also be presented without the pressure correction term. For such data, the drag coefficient can be interpreted simply as a momentum loss coefficient.

The symbol in the formula for the drag coefficient is the width of the control volume over which the local velocity attains the free stream value. In external flow measurements, this location coincides with a boundary that has zero shear. Accordingly, the external force calculated from the momentum balance formula can be attributed entirely to drag on the cylinder. In channel flow, the asymptotic limit is not reached unambiguously; hence the value of has been selected by first examining the velocity vectors. A second approach employed was to set equal to the channel half-width and make corrections for the wall shear. Both of these approaches were found to give very similar drag coeffients.