Lift and drag evaluation in external CFD

Evaluating forces from CFD

The aerodynamic force on a body is the integral of the surface pressure and wall shear stress over its surface $S$:

$$\vec F=\oint_S\left(-p\,\hat n+\vec\tau_w\right)dS$$

where $\hat n$ is the outward unit normal. The force is resolved relative to the free-stream direction:

• Drag $D$: component parallel to the free stream, made up of pressure (form) drag and skin friction drag.
• Lift $L$: component perpendicular to the free stream.

Non-dimensional coefficients:

$$C_L=\frac{L}{\tfrac12\rho U^2S},\qquad C_D=\frac{D}{\tfrac12\rho U^2S}$$

with $S$ = planform area (chord $\times$ span). In practice, the CFD code sums the force on each wall face and reports $C_L$ and $C_D$ through "force monitors"; the angle of attack is set by the flow direction. Accuracy requires a fine boundary-layer mesh ($y^+\approx1$ for k-$\omega$ SST), correct transition and separation modelling, and a mesh-independence check. A far-field distance of 10 to 20 chords is used.

Numerical

Planform area $S=0.5\times2=1.0$ m². Dynamic pressure:

$$q=\tfrac12\rho U^2=0.5\times1.2\times40^2=960\ \text{Pa}$$ $$L=C_LqS=0.9\times960\times1.0=864\ \text{N}$$ $$D=C_DqS=0.012\times960\times1.0=11.52\ \text{N}$$ $$\frac LD=\frac{C_L}{C_D}=\frac{0.9}{0.012}=75$$

Answer: $L=864$ N, $D=11.5$ N, $L/D=75$.