Wall interference calculation in a transonic wind tunnel with discrete slots

A computational simulation of a transonic wind-tunnel test section with longitudinally slotted walls is developed. The slot model includes nonlinear slot-discreteness and dynamic-pressure effects as well as a plenum pressure constraint. The solution is performed using a finite-difference method which solves an extended transonic small disturbance equation. The walls serve as the outer boundary conditions in the relaxation technique with an interaction procedure used at the slotted walls. The technique is predictive in that measured boundary pressures are not required in establishing the wall conditions. Measured wall pressures are only used to assess the accuracy of the simulation. The method is also capable of calculating a free-air solution as well as solutions employing the classical homogeneous wall conditions. Wall interference effects are determined by comparing test-section and free-air calculations. The simulation is used to examine two commercial transport aircraft models at both zero-lift and cruise conditions. Although the plenum pressure has a significant effect on the solution, little effect of slot discreteness is found with the models currently considered. At cruise conditions the wall interference results in errors on the order of one percent in the lift, drag, and pitching moment. The three-dimensional nature of the interference is shown by examining the wing pressure distributions. The walls induce an error in the position of the wing shock wave which is found to vary along the wing. It is concluded that the traditional concept of wall-interference corrections to Mach number and angle of attack may not be suitable for transonic conditions.