Abstract
A novel approach to correcting the effects of wall interference has been developed for closed-wall wind tunnels using a nonlinear least squares optimisation process that is independent of model geometry. Potential flow singularities are used to represent the test object and the method of images is used to represent the tunnel walls. The present approach makes use of trust-region reflective optimisation to allow the locations and strengths of singularities to be determined iteratively with only wall pressure measurements as independent inputs. The technique has been validated using CFD simulations of flow around canonical shapes in both free and wall-bounded conditions at blockages of 5 % to 20 %. Comparisons are drawn to the two-variable method, with demonstrated improvements across the range of bodies considered. A major source of error in wind tunnel testing arises from the interference effects between the wind tunnel walls and the test model. In a closed-wall tunnel, boundary layer growth along the walls results in a pressure gradient along the length of the tunnel referred to as horizontal buoyancy [1]-although the effects of this are typically mitigated through facility design. For a lifting model, the general redirection of the flow downwards is constrained by the tunnel floor, resulting in an induced upwash known as lift interference. The walls also impose a flow constraint in the region around the model and its wake, causing a local increase in streamwise velocity, affecting the aerodynamic forces and moments experienced by the model. It is imperative that wind tunnel test data be corrected for these effects, as aircraft design demands very low uncertainty from wind tunnel data [2]. One of the most widely-used correction techniques in wind tunnel testing is the two-variable (2V) method [3]. By defining a control volume bounded by the tunnel walls and by arbitrary upstream and downstream planes, the strength of all sources and sinks representing the tunnel walls can be obtained from the potential flux using the divergence theorem. To obtain a unique solution, two independent flow variables at the bounding surface are needed: for closed wall tunnels this may be taken as the streamwise velocity, and wall-normal velocity equal to zero due to the assumed imper-meability of the walls. The key advantage of this technique is that it can determine the interference flow field independently of any model representation. However, in order to do this, this technique normally requires a large number of wall pressure measurements (typically n ≈ 100) in order to obtain a sufficiently resolved solution. Contrary to the approach taken by the 2V method, the wall pressure signature technique provides estimates of the interference flow field by modelling the object in the wind tunnel and its wake as the superposition of source, sink and doublet elements centrally located along the tunnel axis [4]. This technique has the advantage of requiring significantly fewer measurements to obtain a unique solution (typically, n ≲ 20 [5]). However, the wall pressure-signature technique does not capture upwash corrections particularly well, as the blockage is assumed to be axisymmetric. The technique