图  1  两种布置方柱的示意图

Figure  1.  Two kinds of square column layout diagram

图  2  X-Y平面上的单方柱计算网格

Figure  2.  Computational grids in the X-Y plane for a single square cylinder

图  3  无量纲平均流向速度在中心线的流向演化

Figure  3.  Streamwise evolution of the normalized mean stream-wise velocity u₁/U_in along the centerline

图  4  均方根速度沿中心线的流向演化

Figure  4.  Streamwise evolution of all three rms velocities along the centerline

图  5  不同雷诺数Re_in下的平均阻力系数C_D

Figure  5.  Mean drag coefficient C_D at different Re_in

图  6  单方柱4个面上的平均压力系数C_P分布

Figure  6.  Distribution of the mean pressure coefficient C_P over 4 sides of a single square cylinder

图  7  不同雷诺数Re_in下的平均阻力系数与平均升力系数均方根值之比$C_D' / C_L'$

Figure  7.  The ratio of the mean drag coefficient to the mean lift coefficient rms $C_D' / C_L' $ at different Re_in

图  8  观测点处的声压级功率谱密度

Figure  8.  Power spectral density of sound pressure level at observation points

图  9  X-Y平面上的瞬时涡量等值面云图

Figure  9.  Contour plots of the magnitude of instantaneous vorti-city in the X-Y plane

图  10  Q值瞬时等值面图（Q$T_{\mathrm{Bar}}^2 /U_{\mathrm{in}}^2 $=1）

Figure  10.  Instantaneous isosurfaces of Q-value (Q$T_{\mathrm{Bar}}^2 /U_{\mathrm{in}}^2 $=1)

图  11  无量纲平均流向速度场$u_{1} / U_{{\mathrm{in}}}$云图

Figure  11.  Contour plots of the normalized mean streamwise velocity field ($u_{1} / U_{{\mathrm{in}}}$)

图  12  无量纲均方根速度$u_{1}'/ U_{{\rm{in}}}$云图

Figure  12.  Contour plots of the normalized RMS velocity ($u_{1}'/ U_{{\rm{in}}}$)

图  13  无量纲平均压力场（P−P_in）/（0.5ρ$U_{{\mathrm{in}}}^2 $）云图

Figure  13.  Contour plots of the normalized mean pressure field (P−P_in)/(0.5ρ$U_{{\mathrm{in}}}^2 $)

图  14  无量纲化平均流向速度u₁/U_in的法向分布

Figure  14.  Vertical distribution of the normalized mean stream-wise velocity u₁/U_in

图  15  无量纲化平均法向速度u₂/U_in的法向分布

Figure  15.  Vertical distribution of the normalized mean vertical velocity u₂/U_in

图  16  无量纲速度均方根值（$u_{1}^{\prime} / U_{{\rm{in}}}$, $u_{2}^{\prime} / U_{{\rm{in}}}$, $u_{3}^{\prime} / U_{{\rm{in}}}$）的法向分布

Figure  16.  Vertical distribution of the normalized mean squares velocity ($u_{1}^{\prime} / U_{{\rm{in}}}$, $u_{2}^{\prime} / U_{{\rm{in}}}$, $u_{3}^{\prime} / U_{{\rm{in}}}$)

图  17  规则布置4个方柱的升力系数C_L和阻力系数C_D时程曲线

Figure  17.  Time trace curves of the lift coefficient C_L and the drag coefficient C_D behind four cylinders for the regular array

图  18  规则布置方柱中选定方柱的升力系数C_L和阻力系数C_D功率谱密度

Figure  18.  Power spectral density of the lift coefficient C_L and drag coefficient C_D of the chosen square cylinders for the regular array

图  19  分形布置方柱升力系数C_L和阻力系数C_D时程曲线

Figure  19.  Time trace curves of the lift coefficient C_L and the drag coefficient C_D of square cylinders for the multiscale array

图  20  分形布置方柱中选定方柱的升力系数C_L和阻力系数C_D功率谱密度

Figure  20.  Power spectra density of the lift coefficient C_L and the drag coefficient C_D of the chosen square cylinder in the multiscale case

图  21  规则布置和分形布置各方柱体的平均阻力系数C_D

Figure  21.  Mean drag coefficient C_D of different square cylinders for the regular array and the multiscale array

图  22  远场声压级指向分布图（r/T_Bar=32）

Figure  22.  Directivity of SPL at r/T_Bar=32

图  23  规则与分形布置方柱在选定观测点（0, 32T_Bar, 0）处不同柱体引起的瞬时声压随时间变化曲线

Figure  23.  Time variation curves of the instantaneous acoustic pressure of different square cylinders at the observation point (0, 32T_Bar, 0) for the regular array and the multiscale array

图  24  规则布置和分形布置方柱在选定观测点（0, 32T_Bar, 0）处的声压级功率谱密度

Figure  24.  Power spectral density of the sound pressure level at the receiver point (0, 32T_Bar, 0) for the regular array and the multiscale array