# Blockage Effects

When a model is mounted in a wind tunnel, it partially blocks the flow of air going through the working section. The result is to increase the effective airspeed in way of the model over and above that recorded by the tunnel Pitot-static tube, which will lie in a region of the tunnel where there is no blockage. If the model is small compared to the tunnel and aerodynamically streamlined in shape, this effect will be small, but since aerodynamic forces are driven by the velocity squared, once the model starts to have a wing span of even 20% of the tunnel width or large AoAs with attendant stalled flows, the effects become important. Moreover, the variation in longitudinal velocity caused by blockage is not symmetrical forward and aft of the test specimen, and this gives rise to a longitudinal buoyancy force that impacts on the drag. Figure 16.2 illustrates the effect of theDecode-1 airframe at 6° AoA in our largest wind tunnel. The size of the blockage is readily apparent. The projected area of the aircraft is 0.233 m^{2},

**Figure 16.2 **AirCONICS model of Decode-1 airframe in a representation of the R.J. Mitchell 11’ X 8’ wind tunnel working section at Southampton University, illustrating degree of blockage.

while that of the tunnel is 8.174 m^{2}, that is, the area blockage is 2.85% without allowing for the wake.

Most tunnel operators will supply simple blockage correction factors for their tunnels based on frontal area of the specimen under test, tunnel speed and the type of flow regime being studied, and so on, which can be applied directly to lift and drag coefficients.^{[1]} These corrections only form a starting point, however, since bluff bodies with appreciable wakes will lead to greater blockage than smooth airfoils at low AoAs, even for the same frontal area. Therefore, whole aircraft at modest AoAs but including undercarriage elements will lie somewhere between these extremes, meaning that deducing the correct blockage correction is far from straightforward. Even then, the corrections for lift and drag are generally not the same.

One way of attempting to calculate accurate blockage factors is via CFD models where the tunnel walls are able to be included or removed from the simulation. Direct comparisons between the lift and drag forces seen between the two models will then allow blockage correction factors to be deduced, although some care has to be taken in deciding how to model the boundary layer growth on the tunnel walls themselves (and, of course, building a high-quality boundary layer mesh on the tunnel walls can massively increase the cell count in the CFD simulation). If using CFD in this way, it is also important to calculate the blockage impact on lift well away from the zero-lift condition of course; we chose to run calculations at 6° AoA because this typically lies halfway between zero lift and full stall. Figure 16.3 shows

Figure 16.3 AirCONICS half-model of Decode-1 airframe in the R.J. Mitchell 11’ X 8’ wind tunnel prior to mesh preparation.

an AirCONICS model of Decode-1 at this AoA placed in a representation of our Mitchell wind tunnel ready for analysis, while Figure 16.4 shows the boundary layer and how close it is becoming to the disturbed flow around the aircraft wingtip along with a section through the mesh used. Comparison of this CFD model with one with widely spaced symmetry far-field

Figure 16.4 Section through Fluent velocity magnitude results and Harpoon mesh for Decode-1 airframe in the R.J. Mitchell 11’ X 8’ wind tunnel.

Note the extent of the boundary layer on the tunnel walls and the fine boundary layer mesh needed to resolve this, along with the refinement zone near the wing tip.

boundary conditions shows that the ratio of the lift coefficients at 6° AoA is 0.918 and that for the drag coefficients is 1.037 (greater than 1 because of the aforementioned buoyancy effects that cause the drag calculated in the model with the tunnel in this case to be slightly less than that without it, but note that, as ever, the drag forces are an order of magnitude less than the lift forces and so the likely errors in this correction are much larger). This lift correction is broadly in line with the various approximations found in the literature and makes clear the importance of correcting wind tunnel data for blockage affects before they are used. Figure 13.32 given earlier includes experimental data for the Decode-1 airframe adjusted for blockage corrections calculated in this way.

- [1] See for example Road Vehicle Aerodynamic Design (p. 243) where the blockage correction for drag coefficients isgiven as (1A/S)1288, where A is the model frontal area, and S is the wind tunnel cross-sectional area, so for a modellike Decode-1 with a frontal area of 0.233 m2 at 6° AoA, in our large tunnel of 8.174 m2 cross-sectional area, thecorrection factor is 0.963 or around 3.7% on the drag coefficient.