Identification of aerodynamic admittances by considering the effect of incomplete span-wise correlation of buffeting forces on sectional model

The relationship between the spectra of the distributed buffeting forces on a model cross section and the total buffeting forces on the whole sectional model measured by a base-sup-ported force balance in wind tunnel test of sectional model was derived first in this paper by consider-ing the span-wise incomplete correlation of distributed buffeting forces on the sectional model.By taking a quasi-flat plate cross section as an example,sectional model wind tunnel tests of force measurement and simultaneous pressure measurement were carried out in a grid-generated turbu-lent wind field to obtain the spectra of the total buffeting forces and the span-wise correlation functions of the distributed buffeting forces.On this basis,the equivalent aerodynamic admit-tance functions of the quasi-flat plate were calculated in the light of the equivalent admittance method whilst the six-component aerodynamic admittance functions of the quasi-flat plate were identified by using a least square approach based on a colligated residue of the auto spectrum of buffeting force and the cross-spectra between buffeting force and fluctuating wind velocities,ab-breviated as “colligated least square approach of auto and cross spectra”.The effect of the span-wise incomplete correlation on the identification results of the aerodynamic admittance were then discussed and the identified results were compared with Sears function,the theoretical solution of the aerodynamic admittance function of flat plate under the vertical fluctuating velocity of w.The results show that the ignorance of the span-wise incomplete correlation of the distributed buffe-ting forces on the sectional model,namely the direct employment of the averaged buffeting force as the distributed one based on the assumption of complete correlation of distributed buffeting forces along the model span,will lead to underestimated values of the identified aerodynamic ad-mittance functions,and the extent of the underestimation will rise with the increase of frequency. Furthermore,the effect of the span-wise incomplete correlation of buffeting force on the buffe-ting drag related components of aerodynamic admittance is more remarkable than that on the buf-feting lift force or torsional moment related components of aerodynamic admittance because the span-wise correlation of buffeting drag is much weak than those of the buffeting lift force and tor-sional moment.It can also be found that the back-calculated spectra of distributed buffeting forces acting on the model obtained by using the six-component aerodynamic admittance functions identified with the colligated least square approach of auto and cross spectra are quite close to those measured in the test.The two components of aerodynamic admittance related to the verti-cal fluctuating wind velocity (w)as well as the buffeting lift force and torsional moment are also rather close to the Sears function.These two facts verify the reliability of the colligated least square approach of auto and cross spectra for the identification of aerodynamic admittance.