Lift and drag

From CFD-Wiki

The force on a body immersed in a fluid is decomposed into lift and drag. Lift is the component of the force normal to the freestream velocity while drag is the force in the direction of the freestream velocity.

The force on a body $B$ can be obtained by integrating the stress on the surface $\partial B$ of the body and is given by

$F_i = \int_{\partial B} \sigma_{ij} n_j dS$

where

$\sigma_{ij} = -p\delta_{ij} + \tau_{ij}$ is the total stress
$p$ is the static pressure
$\tau_{ij}$ is the shear stress
$n_i$ is the unit normal vector to $\partial B$

If $U_i$ is the freestream velocity with $U = \sqrt{U_i U_i}$ then the drag force ( $D$ ) is given by

$D := F_i U_i / U$

The remaining force can be considered as lift force. For a 3-D slender body the lift force may be broken into a normal force and a side force.

In 2-D, the lift ( $L$ ) and drag are given by

$L = -F_1 \sin\alpha + F_2 \cos\alpha$

$D = F_1 \cos\alpha + F_2 \sin\alpha$

where $\alpha$ is the angle of attack, that is the angle between the freestream velocity and the $x_1$ axis.

Lift and drag

From CFD-Wiki

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