基于高阶动力学模态分解和本征正交分解方法的受扰建筑表面随机风压场研究

Study on random wind pressure field of interfered building surface using HODMD and POD method

受扰建筑表面风压场是一个复杂、随机的高维动态系统,依据风压分布难以完全呈现和复刻其流动机理。为此,基于刚性模型测压风洞试验,采用本征正交分解(POD)方法和高阶动力学模态分解(HODMD)方法,对串列布置干扰下的方形高层建筑表面随机风压场进行分解与重构。结果表明:上游建筑对下游受扰建筑迎风面风压的影响主要是遮挡作用,使得下游建筑迎风面出现负压区,受扰建筑两个侧风面最小平均风压系数出现在靠近迎风面的边缘区域,且随着距上游建筑距离增加,遮挡效应减弱,串列布置对下游建筑背风面风压的影响不大;通过POD方法分析可知,3倍迎风宽度是串列布置的临界间隙,当受扰建筑位于施扰建筑后方3倍迎风宽度内,受扰建筑不会发生明显的漩涡脱落;POD和HODMD方法分解得到的模态均可以反映脉动风压特征,但由于风压数据的高度非线性,POD模态反映多个频率的耦合,而HODMD方法能分解出每个模态的增长率和频率,单频的HODMD模态能够捕捉到不同尺度漩涡运动作用在建筑表面形成的相干结构,模态系数的周期性变化反映湍流的能量级联,且单体和干扰间距为2、3、4倍迎风宽度的4种工况都是以低频的漩涡运动为主导,建筑的干扰使得含有高能量的低频模态增多。因此,在揭示随机风压场的流动机理方面,采用HODMD方法更准确合理。

The wind pressure field on the surface of a interfered building is a complex,stochastic,high-dimensional dynamic system,and it is difficult to fully present and replicate the flow mechanism from the wind pressure distribution.Accompany with the wind tunnel test result of rigid model pressure measurement,the proper orthogonal decomposition(POD)method and high-order dynamic mode decomposition(HODMD)method are used to decompose and reconstruct the random wind pressure field on the surface of square high-rise building under the interference of tandem arrangement.The results show that the influence of the upstream building on the windward wind pressure of the downstream interfered building is mainly the shielding effect,which leads to the negative pressure area on the windward side of the downstream building,and the minimum mean pressure coefficient of the two side wind surfaces appears in the edge area close to the windward side.With the increasement of the upstream building placement distance,the shielding effect weakens,and the serial arrangement has little effect on the leeward wind pressure of downstream buildings.Through the analysis of POD method,it can be known that 3B(B is the windward width)is a critical gap of tandem arrangement,and when the interfered building located in the rear 3B from the interfered building,the interfered building has not obvious vortex shedding.The modes obtained by POD and HODMD can reflect the characteristics of fluctuating wind pressure,but because of the high nonlinearity of wind pressure data,POD modes reflect the coupling of multiple frequencies,while HODMD method can decompose the growth rate and frequency of each mode.The single-frequency HODMD mode can capture the coherent structure formed by the vortex motion of different scales on the building surface.The periodic change of the mode coefficient reflects the turbulent energy cascade.The low-frequency vortex motion dominates under four cases,of which are principle building and the windward width is 2B,3Band 4B.The interference of buildings increases the number of low-frequency modes containing high energy.HODMD method has more advantages in revealing the flow mechanism of the random wind pressure field.