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)
![](images/image175.png)
Here is the velocity prole 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.
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