The drag force, also known as hydrodynamic resistance, is a resistive force that opposes the motion of an object moving through a fluid. The magnitude of the drag force depends on the size and shape of the object, as well as the velocity of the surrounding currents or wind. When an object moves through a fluid, it experiences resistance due to both viscous effects and pressure effects. These two components act simultaneously, and their relative influence depends on the nature of the flow around the object. If the flow around the object is laminar, the drag is primarily caused by shear stresses, meaning that friction between the fluid and the object’s surface dominates. In contrast, when the flow becomes turbulent, pressure differences between the upstream and downstream sides of the object contribute significantly to the overall drag force. The combination of fluid velocity and the object's shape may result in a wake forming behind the object. This wake leads to pressure drag, which arises due to the difference in pressure across the object’s front and rear surfaces.
Drag force calculation
Most drag force data are obtained empirically through direct measurements. However, for an approximate estimation, the drag force can be calculated using (1).
| \( F = \frac{1}{2} C_{D} \rho A v^2 \) | (1) | |||
| \(F\) | - | drag force \( [\text{N}]\) | ||
| \( \rho\) | - | mass density of the fluid \( [\frac{\text{kg}}{\text{m}^3}]\) | ||
| \( C_D\) | - | drag coefficient | ||
| \(A\) | - | reference area \( [m^2]\) | ||
| \(v\) | - | flow velocity \( [\frac{m}{s}]\) | ||
The drag coefficient, \( C_D\) , can be further refined based on the flow conditions and body orientation. It can be calculated using (2).
| \( C_{D} = \frac{2F}{\rho A V^2} = f(Re, \alpha) \) | (2) | |||
| \(\alpha\) | - | angle between the flow direction and the specified body axis \( [^\circ]\) | ||
| \( Re\) | - | dimensionless Reynolds number, which is a dimensionless quantity that characterizes the type of flow around the object defined by (3) | ||
| \( Re = V~\frac{d}{v} \) | (3) | |||
| \(d\) | - | characteristic length scale of the object \( [m]\) | ||
| \(v\) | - | fluid's kinematic viscosity \( [\frac{m^2}{s}]\) | ||
The Reynolds number can be used to distinguish between different flow regimes. When Re is small (typically Re<1), viscosity dominates, leading to laminar flow around the object. In contrast, at higher Reynolds numbers ( Re>1000), the flow becomes turbulent, characterized by chaotic fluid motion and vortex formation. While these threshold values are approximate, they serve as a general guideline: turbulence is typically associated with Reynolds numbers significantly greater than unity. In turbulent conditions, vortex shedding may occur, causing additional unsteady forces on the mooring system.
Effects of drag on mooring systems
Drag forces impact mooring systems in two primary ways: mooring excursions and mooring inclination. When a mooring experiences significant drag, it can be displaced horizontally from its intended position, leading to errors in current measurements. This occurs because the mooring takes time to reach equilibrium after experiencing a shift in current conditions, during which the velocity measured by the instrument may not accurately represent the true current. Additionally, exposure to drag forces can cause the instrument to move deeper in the water column, altering the intended measurement location. This effect, known as drag-down, results in changes to parameters such as pitch, velocity, and pressure, which may become apparent in the recorded data. Excessive inclination can introduce measurement errors due to sensor tilt and distort the collected data.
Beyond the steady drag force, moored instruments may also experience fluctuating lift and drag forces due to vortex shedding. These oscillatory forces can further contribute to unwanted motion, increasing uncertainty in data collection. In order to predict changes in the excursion and inclination when designing a deployment, drag forces must be calculated for the expected current conditions. These can also be used to predict errors in the data, since a certain amount of movement cannot be avoided.
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