Experimental assessment of Theodorsen's function for uncoupled pitch–plunge motion

Abstract

The accuracy of Theodorsen's lift model for pure-pitch, pure-plunge and combined pitch–plunge oscillations of a two-dimensional model is compared with wind tunnel results. The reduced frequency of the oscillation was in the range of 0.01<k<0.15, and the freestream Reynolds number was in the range of 130 000<Re<400 000. The lift response to an uncoupled combined pitch–plunge motion (for which the frequency of pitch and plunge motions were not the same) is discussed using experimental results. The Theodorsen’s lift model is rewritten for the general uncoupled pitch–plunge motions by a linear superposition of all components of the airfoil bound circulation. Both amplitude and phase from the Theodorsen's function are compared with those of the wind tunnel data, and the results are discussed. The Theodorsen’s function is found to be a good estimator for both pure-pitch and pure-plunge motions. It further appropriately estimates the lift amplitude for the case of coupled pitch–plunge motion; however, the prediction is not accurate for the uncoupled pitch–plunge motion. A motion amplitude ratio is defined, which shows the level of aperiodicity of the motion. Discrepancy between experimental and analytical results increase with the reduction of the lift amplitude ratio and with the deviation of frequency ratio from unity.