考虑模型抖振力跨向不完全相关性效应的气动导纳识别

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

首先通过考虑节段模型上抖振力跨向不完全相关性效应推导了节段模型风洞试验中作用在模型断面上的分布抖振力谱和由底支式天平测到的模型总抖振力谱之间的关系。然后,以准平板断面为例,进行了格栅湍流场节段模型的测力和同步测压试验,获得了模型总抖振力谱以及模型抖振力跨向相关性函数。接着,采用等效导纳法以及抖振力自谱和抖振力脉动风速交叉谱综合残量最小二乘法分别识别了准平板节段模型等效气动导纳和六分量气动导纳,讨论了模型抖振力跨向不完全相关性效应对气动导纳识别结果的影响,并把识别得到的准平板断面气动导纳与平板断面气动导纳的理论结果——Sears函数进行了比较。结果表明:忽略抖振力跨向不完全相关性效应(即假设节段模型分布抖振力沿跨向完全相关)而直接采用平均抖振力作为断面上分布抖振力的传统方法会导致气动导纳识别结果偏小,并且,其偏小程度会随着频率的增加而增加;此外,相对于抖振升力和扭矩相关的气动导纳分量而言,由于抖振阻力的跨向相关性比抖振升力和扭矩的跨向相关性显得更弱,因此抖振力跨向不完全相关性效应对阻力相关气动导纳分量识别结果的影响更大;利用识别得到的六分量气动导纳反算的作用在模型上的分布抖振力谱与试验中实测结果非常接近,经抖振力跨向不完全相关性效应修正后的竖向脉动风速对应的升力和扭矩气动导纳分量的识别结果与Sears函数也比较接近,从而验证了用于六分量气动导纳识别的自谱-交叉谱综合最小二乘法的可靠性。

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-supported force balance in wind tunnel test of sectional model was derived first in this paper by considering 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 turbulent 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 admittance 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, abbreviated as ＂colligated least square approach of auto and cross spectra＂. The effect of the spanwise 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 buffeting 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 admittance 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 buffeting drag related components of aerodynamic admittance is more remarkable than that on the buffeting 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 torsional 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 vertical 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.