Numerical Simulation And Mathematical Theoretical Analysis Of Taylor-Couette Flow Field

In this paper,two research methods include of numerical simulation and PIV measurement are used to measure and analyze the flow field of Taylor-Couette with the same geometry.Vortex intensity method is used to identify the vortex structure in flow field obtained by PIV measurement and numerical simulation separately.The characteristics of the flow field obtained by the two methods are compared and analyzed.The feasibility and accuracy of using numerical simulation to explore the flow field of Taylor Couette are demonstrated.At the same time,the flow field generated by Taylor Couette vortex generator with different radius ratio and gap width is simulated under the same rotating Reynolds number.The effects of radius ratio and gap width on the flow field shape characteristics and angular momentum,speed in all directions,turbulent kinetic energy,fluctuating velocity gradient on each characteristic line in the annular gap,as well as the characteristic parameters of flow field change with radius ratio and gap width are explored,in order to further explore the relevant flow mechanism.It provides a reference for the rational and effective use of Taylor vortex for the subsequent study of vortex flocculation kinetics.Through the analysis of flow field shape under different radius ratio,it is found that the length of the vortex grows with the increase of the radius ratio,and the width of the vortex is limited by the boundary conditions.At a proper Reynolds number,the width of the vortex increases with the increase of the Reynolds number.When it exceeds a certain Reynolds number,it does not change much.At the same time,the number of the vortex decreases gradually.The distribution of turbulent kinetic energy,vorticity and velocity gradient in Taylor Couette flow field under different radius ratio is similar.Their isoline nephogram are similar to a continuous vortex structure.The turbulent kinetic energy,vorticity and velocity gradient in the vortex pair are symmetrically distributed.With the increase of radius ratio,the distribution of vorticity,velocity gradient and turbulent kinetic energy in the flow field is more uniform.Compared with the velocity and the identified vortex structure,it is found that the maximum value of the combined velocity is 0.18m/s,the minimum value is 0.01m/s,and the absolute value of vortex strength is mostly between 1.4-1.6 under different radius ratio.With the increase of the radius ratio,the vortex structure changes from high aspect ratio to low aspect ratio,and the vortex structure is slowly elongated until it is finally destroyed.By comparing the velocity in all directions,angular momentum and turbulent kinetic energy of each feature line under different radius ratios,it is found that,the tangential velocity of each point on each feature line increases with the increase of radius ratio while the radial velocity and axial velocity of each point on each feature line decrease with the increase of radius ratio except for the inner and outer cylinder walls..In the range of 0.002m-0.01 m radial distance,the tangential velocity of each characteristic radial line changes little with the radial distance,especially on the radial line 2 and 4 are more obvious.In addition to the inner andouter cylinder walls,the angular momentum of each point on each characteristic radial line decreases gradually with the increase of radius ratio,and the change of radius ratio on the same radial line has little influence on the angular momentum of each point near the outer cylinder wall and vortex center,but has great influence on the angular momentum of other positions.On the central axis,the angular momentum of each point is basically the same under different radius ratio,and the influence of radius ratio on the angular momentum is relatively large Small.In addition,it is found that the change of radius ratio has little effect on the turbulent kinetic energy near the vortex center by analyzing the turbulent kinetic energy of each point on each characteristic line.Through the analysis of the fluctuating velocity gradients on each characteristic line under different radius ratios,it is found that on the same characteristic line,the fluctuating velocity gradients of the flow field in the vortex center area under different radius ratios change little,while the fluctuating velocity gradients near the outer wall are less affected by the radius ratio,and the radius ratio near the inner wall has the greatest influence on the fluctuating velocity gradients in the flow field.Based on the theoretical analysis of the axial velocity on the radial line 2,it is found that when the gap width of the model is 12.5mm,the height of the cylinder is 440 mm,the radius ratio is between 0.667-0.909,rotating Reynolds number is 2342 and the radial distance is between 0.00125m-0.01125 m,the axial velocity increases linearly with the increase of the radial distance,while the angular momentum under different radial ratio all show parabola relationship with the radial distance.Through the analysis of the flow field shape under the same radius ratio,it is found that when d equals 8mm,the width to length ratio of the vortex is 0.5,when d equals 10 mm,the width to length ratio of the vortex is 0.567,when d equals 20 mm,the width to length ratio of the vortex is 0.622.It can be seen that with the increase of the gap width,the geometry of the vortex tends to be elongated.At the same radius ratio,the distribution of turbulent kinetic energy,vorticity and velocity gradient in Taylor Couette flow field is similar.Their isoline nephogram are similar to a continuous vortex structure,and the turbulent kinetic energy,vorticity and velocity gradient in the vortex pair are symmetrical with each other.Comparing the velocity and the identified vortex structure,it is found that the distribution of combined velocity is similar under different gap width,but with the increase of gap width,the maximum combined velocity decreases gradually,while the absolute value of vortex strength is 0-1.6,and with the increase of gap width,the shape and structure of vortex also increases.And when the gap width is 20 mm,the vortex structure is quite different from that of the first two gaps,which are 8 mm and 10 mm in width.The former has full vortex shape and moderate aspect ratio,the shape of the latter vortex is close to the strip shape,and the outer curve of the vortex is relatively straight.By studying the velocity in all directions of each characteristic line under the same radius ratio,it is found that with the increase of the gap width,except for some special points,thevelocity in all directions of each point on the feature line decreases gradually.The tangential velocity of each characteristic radial line is greatly affected by the change of gap width in the area where the inner and outer cylinder walls are removed,while the radial velocity of each characteristic radial line,such as radial line 1 and radial line 3 is less affected by the gap width near the inner and outer cylinder walls,while radial line 2 and radial line 4 are less affected by the gap width on the inner and outer cylinder walls and at the center of the annular gap.In addition,on each characteristic radial line,the axial velocity of each point under different gap width is also less affected by the gap width near the inner and outer cylinder walls and the area near the center of the annular gap,and the other locations are more affected by the gap width.By analyzing the turbulent kinetic energy and angular momentum of each characteristic line under the same radius ratio,it is found that the turbulent kinetic energy of each point on each characteristic line decreases gradually with the increase of gap width.On the same characteristic radial line,the turbulent kinetic energy on the inner and outer wall of the cylinder is greatly affected by the change of gap width,while on the meridian axis,the change of gap width only affects the maximum value of turbulent kinetic energy and has weak impact on the minimum value of turbulent kinetic energy.In addition,under different gap width,except for the inner wall and vortex center,the angular momentum of each point on each radial line increases with the increase of the gap width.In this region,the change of the gap width of the model has a greater impact on the flow field angular momentum,while the impact of the gap width on the flow field angular momentum on the central axis is weak.By studying the fluctuating velocity gradients of each feature line under the same radius ratio,it is found that the fluctuating velocity gradients of each point on each feature line decrease with the increase of gap width.In addition,in the same characteristic line,the area which is greatly affected by the gap width is mainly concentrated near the inner and outer cylinder walls,but in the range of 0.4-0.8 of the normalized radial distance of the flow field,the influence of the gap width on the fluctuating velocity gradient of each point on the characteristic diameter line is relatively small.By increasing the gap width,the fluctuating velocity gradient of the flow field can be evenly distributed.