published_or_final_version / Civil Engineering / Master / Master of Philosophy

Various sources of error can cause discrepancies among flight test results, experimental measurements and numerical predictions in the transonic regime. For unsteady flow, the effects of wind tunnel walls or a finite computational domain are the least understood and perhaps the most important. Although various techniques can be used in steady wind tunnel testing to minimize wall reflections, e.g., using slotted walls with ventilation, wind tunnel wall effects remain in unsteady wind tunnel testing even when they have been essentially eliminated from the steady flow. Even when the walls are ten chord lengths or more from the airfoil being tested, they can have a substantial effect on the unsteady aerodynamic response of the airfoil. In this study we compare numerical computations of two- and three-dimensional unsteady transonic flow with one another, and with experimental measurements, to isolate and examine the effects of tunnel walls. An extension of the time-linearized code developed by Fung, Yu and Seebass (1978) is used to obtain numerical results in two dimensions for comparison with one another and with the experimental measurments of Davis and Malcolm (1980). The steady flow which is perturbed by small unsteady airfoil motions is found numerically by specifying the pressure distribution rather than the airfoil coordinates using the procedure provided by Fung and Chung (1982). This provides results that are nearly free from effects caused by the small perturbation approximation; it also simulates the viscous effects present in the experimental measurements. A similar algorithm, developed especially for this study, is used for the related investigations in three dimensions. Different wall conditions are simulated numerically. Aside from a shift of frequency due to nonlinear effects, our numerical predictions of resonance conditions in two dimensions agree very well with those of linear acoustic theory. A substantial discrepancy between unconfined computations and wind tunnel experiments is observed in the low frequency range. This discrepancy highlights the importance of wall interference and wind tunnel measurements of unsteady transonic flows and delineates the conditions required to suppress them satisfactorily.

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