基于径向基函数的冷却塔风场重构
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摘要
采用径向基函数法根据风洞试验结果对冷却塔的塔筒外表面进行风场重构,比较了重构前后喉部高度处迎风点和背风点的时程风压系数的相对误差,得出当体型常数C=0.5 C_(max)时(C_(max)为C值的最大取值),在整个采样时间内绝大多数时程风压系数的相对误差在5%以内;将若干子午线上和环线上的重构结果与刚性模型测压风洞试验结果进行对比,证明了重构前后风压系数分布一致;分析了径向基函数中3种不同的C值对重构风场的影响,得出在这3种C值重构的结果中,取C=0.5 C_(max)时重构的效果最好;最后比较了两种不同点集密度重构风场的风场特性,得出加密前后风场特性不变的结果,为优化后续的结构瞬态动力响应分析提供了依据。该文研究表明,基于径向基函数法进行冷却塔风场重构是一种简单、有效的方法。
The radial basis function was adopted to reconstruct the wind field on the outer surface of a cooling tower from the result of a wind tunnel test. The relative errors of wind pressure coefficients of windward and leeward points at throat height before and after the reconstruction were compared at every sample point. The results show that most relative errors are less than 5% when the shape parameter C is equal to 0.5 C_(max), where Cmax is the maximum value of C. The reconstruction results at several meridian lines and latitude lines were compared with those obtained from the rigid-model wind pressure test. The results show that the distribution of wind pressure coefficients is consistent before and after the reconstruction. The effect of three different values of C in the radial basis function on the reconstructed wind field is analyzed. The results show that among the reconstruction results obtained from the three values of C, the reconstruction effect is the best when C is equal to 0.5 C_(max). The reconstructed wind fields with two densities of reconstruction points were built up and compared with each other. The results in which the characteristics of reconstructed wind field is unchanged are obtained. This provides the basis for optimizing the transient structural dynamic response analysis in future studies. The research of this paper shows that the wind field reconstruction method based on the radial basis function is effective and simple.
The radial basis function was adopted to reconstruct the wind field on the outer surface of a cooling tower from the result of a wind tunnel test. The relative errors of wind pressure coefficients of windward and leeward points at throat height before and after the reconstruction were compared at every sample point. The results show that most relative errors are less than 5% when the shape parameter C is equal to 0.5 C_(max), where Cmax is the maximum value of C. The reconstruction results at several meridian lines and latitude lines were compared with those obtained from the rigid-model wind pressure test. The results show that the distribution of wind pressure coefficients is consistent before and after the reconstruction. The effect of three different values of C in the radial basis function on the reconstructed wind field is analyzed. The results show that among the reconstruction results obtained from the three values of C, the reconstruction effect is the best when C is equal to 0.5 C_(max). The reconstructed wind fields with two densities of reconstruction points were built up and compared with each other. The results in which the characteristics of reconstructed wind field is unchanged are obtained. This provides the basis for optimizing the transient structural dynamic response analysis in future studies. The research of this paper shows that the wind field reconstruction method based on the radial basis function is effective and simple.
引文
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[16]Wang L,Wang Z,Qian Z.A meshfree method for inverse wave propagation using collocation and radial basis functions[J].Computer Methods in Applied Mechanics&Engineering,2017,322(1):311―350.
[17]Wang L,Chu F,Zhong Z.Study of radial basis collocation method for wave propagation[J].Engineering Analysis with Boundary Elements,2013,37(2):453―463.
[18]Hu H Y,Chen J S,Hu W.Weighted radial basis collocation method for boundary value problems[J].International Journal for Numerical Methods in Engineering,2010,69(13):2736―2757.
[19]Madych W R.Miscellaneous error bounds for multiquadric and related interpolators[J].Computers&Mathematics with Applications,1992,24(12):121―138.
[2]Niemann H J,Kopper H D.Influence of adjacent buildings on wind effects on cooling towers[J].Engineering Structures,1998,20(10):874―880.
[3]Armitt J.Wind loading on cooling towers[J].Journal of the Structural Division,1980,106(3):623―641.
[4]Sun T F,Zhou L M.Wind pressure distribution around a ribless hyperbolic cooling tower[J].Journal of Wind Engineering&Industrial Aerodynamics,1983,14(1):181―192.
[5]Viladkar M N,Karisiddappa,Bhargava P,et al.Static soil-structure interaction response of hyperbolic cooling towers to symmetrical wind loads[J].Engineering Structures,2006,28(9):1236―1251.
[6]Cheng X,Zhao L,Ge Y,et al.Wind effects on rough-walled and smooth-walled large cooling towers[J].Advances in Structural Engineering,2017.20(6):843―864.
[7]田凯强,秦其伟,郑云飞,等.大型冷却塔表面风压分布特性的试验研究[J].工程力学,2017,34:269―272.Tian Kaiqiang,Qin Qiwei,Zheng Yunfei,et al.Experimental research on wind pressure distribution of cooling towers[J].Engineering Mechanics,2017,34:269―272.(in Chinese)
[8]李元齐,沈祖炎.本征正交分解法在曲面模型风场重构中的应用[J].同济大学学报(自然科学版),2006,34(1):22―26.Li Yuanqi,Shen Zuyan.Application of the proper orthogonal decomposition method to wind field reconstruction of models with curved surfaces[J].Journal of Tongji University(Natural Science),2006,34(1):22―26.(in Chinese)
[9]Huang D,He S,He X,et al.Prediction of wind loads on high-rise building using a BP neural network combined with POD[J].Journal of Wind Engineering&Industrial Aerodynamics,2017,170:1―17.
[10]陶天友,王浩.基于Hermite插值的简化风场模拟[J].工程力学,2017,34(3):182―188.Tao Tianyou,Wang Hao.Reduced simulation of the wind field based on Hermite interpolation[J].Engineering Mechanics,2017,34(3):182―188.(in Chinese)
[11]Hardy R L.Multiquadric equations of topography and other irregular surfaces[J].Journal of Geophysical Research,1971,76(8):1905―1915.
[12]Hardy R L.Theory and applications of the multiquadric-biharmonic method 20 years of discovery1968-1988[J].Computers&Mathematics with Applications,1990,19(8):163―208.
[13]Franke R.Scattered data interpolation:Tests of some method[J].Mathematics of Computation,1982,157(157):181―200.
[14]Micchelli C A.Interpolation of scattered data:Distance matrices and conditionally positive definite functions[J].Constructive Approximation,1986,2(1):11―22.
[15]Schaback R.A unified theory of radial basis functions:Native Hilbert spaces for radial basis functions II[J].Journal of Computational&Applied Mathematics,2000,121(1/2):165―177.
[16]Wang L,Wang Z,Qian Z.A meshfree method for inverse wave propagation using collocation and radial basis functions[J].Computer Methods in Applied Mechanics&Engineering,2017,322(1):311―350.
[17]Wang L,Chu F,Zhong Z.Study of radial basis collocation method for wave propagation[J].Engineering Analysis with Boundary Elements,2013,37(2):453―463.
[18]Hu H Y,Chen J S,Hu W.Weighted radial basis collocation method for boundary value problems[J].International Journal for Numerical Methods in Engineering,2010,69(13):2736―2757.
[19]Madych W R.Miscellaneous error bounds for multiquadric and related interpolators[J].Computers&Mathematics with Applications,1992,24(12):121―138.