Boundary Conditions For an Open Wind Tunnel

An open wind tunnel is a wind tunnel that takes in air from the surroundings, and outputs it to the surroundings. This is in contrast to a closed wind tunnel, which recirculates the air (i.e. the outlet is connected to the inlet). The difference is mainly power savings.

This article will describe the boundary conditions necessary to simulate an open wind tunnel.

An important thing to realize is that static pressure in a wind tunnel is not constant from upstream to downstream, as it is for an actual vehicle in flight. The small but significant pressure gradient is required to create a flow and  is created by the fan powering the wind tunnel (fans produce a pressure gradient, which is how they provide thrust).

Often in aerodynamics, because the air is invisible, many flow properties are indirectly measured. Wind tunnel velocity is typically measured by dynamic pressure, which is the additional pressure generated when a moving flow comes to a halt. For incompressible flows (below about Mach 0.3), the dynamic pressure can be calculated by 0.5*density*velocity^2.

Knowing this we can set up proper boundary conditions for an open wind tunnel. The following are the boundary conditions for U (velocity) and p (pressure). Set the desired wind tunnel velocity to V.

Walls: U = 0, p = zero gradient
Inlet: U = zero gradient, p = zero gradient, p0 (total pressure) = 1/2*density*V^2
Outlet: U = zero gradient, p = 0