| Using U-shaped flume test method,the flow around three square cylinders in positive and negative triangular arrangement with different spacing ratios is studied.Because the flow mechanism of the three square cylinders in triangular arrangement is more complex with different spacing ratios,and there are some effects on the side walls of the flume,the non-submerged and submerged single square cylinder near the wall test groups are added.The flow structure near the three square cylinders in positive and negative triangular arrangement was measured by Partical Image Velocity(PIV)measurement system.The flow field,turbulence intensity,Reynolds stress,enstrophy and deformation energy were obtained.The following conclusions were drawn from the analysis of the experimental results:I.Flow around a square cylinder near the wall:(1)Non-submerged square cylinder(1)Structural characteristics of flow fieldWhen the near-wall distance of the square cylinder is 0(equivalent to spur dike),behind the square cylinder forms a larger vortex;when the distance is 1-3 cm,behind the square cylinder forms a pair of parallel vortexes,and with the increase of the near-wall distance of square cylinder,the two vortexes gradually becoming symmetrical.(2)Distribution characteristics of turbulence intensityThe high turbulence intensity is distributed the area at the left side of the square cylinder,near the wall of the flume behind the square cylinder and the area a certain distance behind the left side of the square cylinder.In addition,with the increase of the near-wall distance of square cylinder,the turbulence intensity is getting stronger.(3)Distribution characteristics of Reynolds stressA positive Reynolds stress region is formed on the left side of the square cylinder,and a negative Reynolds stress region is formed along the left side of the square cylinder and extending downstream for a certain distance from the mainstream area.When the near-wall distance of square cylinder is 2-3 cm,a positive Reynolds stress region is formed near the wall of the flume behind the square cylinder.(2)Submerged square cylinder(1)Structural characteristics of flow fieldWhen the near-wall distance of the square cylinder is 0,behind the square cylinder forms a small vortex;when the distance is 1 cm,behind the square cylinder forms two vortexes which distributed up and down;when the distance of the square cylinder is 2-3 cm,behind the square cylinder forms a pair of parallel vortexes,and with the increase of the near-wall distance of square cylinder,the two vortexes gradually becoming symmetrical.(2)Distribution characteristics of turbulence intensityThe high turbulence intensity is distributed the area on the left side of the square cylinder and the area a certain distance behind of it which near the mainstream area.Meanwhile,with the increase of the near-wall distance of square cylinder,the turbulence intensity and range constantly increasing.(3)Distribution characteristics of Reynolds stressA positive Reynolds stress region is formed on the left side of the square cylinder,and a negative Reynolds stress region is formed along the left side of the square cylinder downstream in a certain range near the mainstream area.When the near-wall distance of square cylinder is 2-3 cm,a positive Reynolds stress region is formed at a certain distance from the side wall of the flume behind the square cylinder.II.Flow around three square cylinders:(1)Flow around three square cylinders in positive triangular arrangement(1)Structural characteristics of flow fieldWhen the spacing ratio is 1.2-1.4,there are no vortices behind the upstream single square cylinder and four vortices behind the downstream two square cylinders;when the spacing ratio is 1.6,there is one vortex behind the upstream single square cylinder and three vortices behind the downstream two square cylinders;when the spacing ratio is 1.8-3.5,there is a pair of vortices behind the upstream single square cylinder,when the spacing ratio is 1.8-2.5,there are two vortices behind the downstream two square cylinders,and when the spacing ratio is 3.0-3.5,the vortex behind the two downstream square cylinders disappears.(2)Distribution characteristics of turbulence intensityWhen the spacing ratio is 1.2-1.6,a high turbulence intensity region is formed at a certain distance between the left and right sides of upstream single square cylinder and the rear of downstream two square cylinders,with the increase of spacing ratio,the variation of turbulent intensity and range behind upstream columns is not obvious,while the turbulence intensity and range of downstream two square cylinders at a certain distance from the two square cylinders gradually decrease,and the turbulent intensity and range between two square cylinders gradually increases;when the spacing ratio is 1.8-3.5,the three square cylinders will have higher turbulence intensity and range.The middle area of downstream square cylinders forms a high turbulence intensity region,and the turbulence intensity and range increase with the increase of spacing ratio.(3)Distribution characteristics of Reynolds stressWhen the spacing ratio is 1.2-1.6,there are positive and negative Reynolds stress regions on the left and right sides of upstream single square cylinder,and the relationship between Reynolds stress and range and spacing ratio is not obvious,when the spacing ratio is 1.6-3.5,the positive and negative Reynolds stress regions formed behind square cylinders gradually increase with the increase of spacing ratio;when the spacing ratio is 1.2-1.4,the downstream two square cylinders are at a certain distance from the two square cylinders.When the spacing ratio is 1.6-2.0,there is a pair of positive and negative Reynolds stress regions forms at the outlet of the gap between the two square cylinders,and its Reynolds stress and range increase with the increase of spacing ratio.When the spacing ratio is 2.5-3.5,the positive and negative Reynolds stress regions behind the two square cylinders have the tendency of forming a pair of poles,the range increases with the increase of spacing ratio.(4)Distribution characteristics of enstrophyWhen the spacing ratio is 1.2-1.4,there is no high enstrophy region around the upstream single square cylinder,when the spacing ratio is 1.6-3.0,there are two high enstrophy regions behind the square cylinder.The enstrophy increases with the increase of spacing ratio,and it decreases when the spacing ratio is 3.5;when the spacing ratio is 1.2-1.8,there are two high enstrophy regions on both sides of the downstream two square cylinders,and the average enstrophy increases with the increase of spacing ratio,when the spacing ratio is 1.8-3.5,the average enstrophy decreases.The total enstrophy in the high enstrophy region of three square cylinders in positive triangular arrangement also has a good response relationship with the change of spacing ratio,and the fitting accuracy is as high as 0.8477.(5)Distribution characteristics of deformation energyWhen the spacing ratio is 1.2-1.6,there is no high deformation energy region around the upstream single square cylinder,when the spacing ratio is 1.8-3.5,there are two high deformation energy regions behind the square cylinder,and the deformation energy increases with the increase of the spacing ratio;when the spacing ratio is 1.2-1.8,there are two high deformation energy regions on both sides of the downstream two square cylinders,and the average deformation energy of the two square cylinders increases with the increase of the spacing ratio,when the ratio is 1.8-3.5,the average deformation energy decreases with the increase of spacing ratio.The total deformation energy in the high deformation energy region of three square cylinders in positive triangular arrangement also has a good response relationship with the change of spacing ratio,and the fitting accuracy is as high as 0.8538.(2)Flow around three square cylinders in negative triangular arrangement(1)Structural characteristics of flow fieldWhen the spacing ratio is 1.2-1.8,there are no vortex behind the upstream two square cylinders,when the spacing ratio is 2.0-2.5,there are 1-2 vortices behind the two square cylinders,when the spacing ratio is 3.0-3.5,there are 4 vortices behind the two square cylinders,and there are a pair of larger vortices behind the downstream single square cylinder with different spacing ratios.(2)Distribution characteristics of turbulence intensityWhen the spacing ratio is 1.2-1.6,the turbulent intensity and range of the high turbulent intensity region around the upstream two square cylinders increase with the increase of spacing ratio,when the spacing ratio is 1.8-3.5,the turbulent intensity and range of the high turbulent intensity region around the two square cylinders decrease with the spacing ratio increasing;when the spacing ratio is 1.2-1.4,there is a high turbulent intensity area behind the downstream square cylinder,when the spacing ratio is 1.4-3.5,with the increase of spacing ratio,the turbulence intensity and turbulence range of the region of high turbulence intensity are decrease gradually.(3)Reynolds stress distribution characteristicsWhen the spacing ratio is 1.2-1.6,there are small positive and negative Reynolds stress regions on the left and right sides of the upstream square cylinders.The relationship between the Reynolds stress and the range and spacing ratio is not obvious,when the spacing ratio is 1.8,there is a pair of positive and negative Reynolds stress regions behind the upstream square cylinders,when the spacing ratio is 2.0,a pair of positive and a negative Reynolds stress regions opposites to the original Reynolds stress regions is formed behind the two square cylinders,and its Reynolds stress is small,when and the spacing ratio is 2.5-3.5,a pair of larger positive and negative Reynolds stress regions are formed behind the two each square cylinder,they tends to form two pairs of poles;when the spacing ratio is 1.2,a larger positive and negative Reynolds stress region is formed at a certain distance between the downstream single square cylinder,wWith the increase of the spacing ratio,the Reynolds stress region gradually moves upward,the Reynolds stress and range decrease gradually,when the spacing ratio is 3.0-3.5,the positive and negative Reynolds stress regions tend to form a pair of poles.(4)Distribution characteristics of enstrophyWhen the spacing ratio is 1.2-1.6,two high enstrophy regions appear on the left and right sides of the upstream two square cylinders,the average enstrophy decreases with the increase of the spacing ratio,when the spacing ratio is 1.6-2.0,the average enstrophy increases with the increase of the spacing ratio,when the spacing ratio is 2.5-3.5,the high enstrophy regions appear on the left,right sides and middle of the two square cylinders,the average enstrophy increases gradually and then decreases with the increase of the spacing ratio;when the spacing ratio is 1.2-2.5,there is no high enstrophy regions around the downstream single square cylinder,when the spacing ratio is 3.0-3.5,there are two high enstrophy regions around the single square cylinder and the enstrophy is very small.The total enstrophy in the high enstrophy region of three square cylinders in negative triangular arrangement has a good response relationship with the change of spacing ratio,and the fitting accuracy is as high as 0.905.(5)Distribution characteristics of deformation energyWhen the spacing ratio is 1.2-1.8,two high deformation energy regions appear on the left and right sides of the upstream square cylinders,and the average deformation energy decreases gradually with the increase of spacing ratio,when the spacing ratio is 2.0-3.0,the high deformation energy regions are formed on both sides and in the middle of the two square cylinders.The average deformation energy increases with the increase of spacing ratio,and when the spacing ratio is3.5,it decreases;when the spacing ratio is 1.2-3.5,there is no high deformation energy region around the downstream single square cylinder.The total deformation energy in the high deformation energy region of three square cylinders in negative triangular arrangement also has a good response relationship with the change of spacing ratio,and the fitting accuracy is as high as 0.8005.This paper reveals the mechanism of flow around three square cylinders in positive and negative triangular arrangement with different spacing ratios,which has high academic value and engineering application significance.The innovation of this paper is mainly embodied in the research content.Based on the analysis of the flow field structure,turbulence intensity and Reynolds stress,the distribution and variation characteristics of enstrophy and deformation energy are analyzed,which has important theoretical guiding significance in practice. |
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