Bluff body flow is a kind of internal flow in which fluid flows over an object totally immersed in the fluid. Practical examples include aircraft, heat exchangers, and parachutes.
Lift and Drag Forces
Bluff body flow is typically concerned with the effect of the fluid flow on the bluff body. As such we care about what kind of forces the flow will induce on the bluff body. The net force can be broken into two perpendicular forces, lift and drag.
- Lift: The force induced on the bluff body perpendicular to the flow direction.
- Drag: The force induced on the bluff body parallel to the flow direction.
Each force can be described with a coefficient, which provides an easy way to relate the fluid flow and lift/drag forces. For lift:
C_L=\dfrac{2F_L}{\rho U_\infty^2 A_p}
Where A_p is the platform area, the area of the objected projected on to a plane perpendicular to the lift force.
The drag coefficient:
C_D=\dfrac{2F_D}{\rho U_\infty^2 A_w}
Where A_w is the wetted area, the surface area of the object that is in contact with the fluid flow.
Pressure and Friction Drag
Drag can be interpreted as having two causes, pressure drag and friction drag.
- Pressure Drag: Caused by the geometry of the bluff body causing a pressure difference between the front and rear ends of the body.
- Friction Drag: Caused by friction between the fluid and the surface of the bluff body.
Viscous drag can be determined by:
\displaystyle F_{D_{viscous}}=\int_A\tau_wdA
Pressure drag can be determined by:
\displaystyle \overrightarrow{\bm{F}}_{D_{pressure}}=\int_ApdA\hat{\bm{n}}
Where \hat{\bm{n}} is the unit vector in the direction of flow.