Numerical Research On Turbulent Pipe Flow

The objective of present work is to explore the fully developed turbulent flow in a cylindrical smooth pipe by means of direct numerical simulation. Spectral method and spectral element method are both used in the present DNS. The flow is developed from an initial velocity field whose mean and root mean square values are fitted to the experimental data. The Reynolds number of the flow is 2250 based on the mean velocity and the radius of the pipe. The length of the pipe is . The velocity and pressure data bank of smooth pipe at low Reynolds number has been set up for further investigation.Firstly, discrete methods of time and space in the DNS are introduced in the present paper. And the procedure of solving the Navier-Stokes equation is also presented. In addition, ways of correcting time-splitting error and removing aliasing error in pesudospectral transform method are introduced too.Some statistical features of turbulent pipe flow including mean velocity profile, turbulence intensity, Reynolds shear stress, skewness and flatness are studied based on the pipe flow data bank. Comparing the results with experimental data and other DNS results shows that our computation is correct and credible. In order to research the burst period in turbulent pipe flow, burst detection methods are studied in the present paper. Detection methods including ulevel, mulevel and VITA methods are analyzed in detail. The threshold value of each method is discussed. And the conclusion is that VITA method is a more reasonable method in burst detection when the threshold value is between 0.7 to 1.0. In order to investigate the influence of transverse curvature of the wall, the direct numerical simulated data bank of turbulent channel flow is also analyzed. The mean velocity profile in pipe and channel flow is compared. The result shows that the karman constant in pipe and channel is different. This is consistent with experimental results. Power law for mean velocity profile isalso studied. And the power of the power law is different in pipe and channel too. The relationship of this difference and the intermittency is discussed. Turbulence intensity is compared. The result shows that turbulence intensity in the pipe is lower than that in the channel. Same result is obtained with Reynolds shear stress, which means Reynolds shear stress in the pipe is smaller than that in the channel. The difference in friction coefficient attribute to Reynolds shear stress according to theoretical analysis. This is demonstrated by the analysis of the both data banks. Streak structures are studied and compared in pipe and channel flows. The streak width of pipe flow is smaller than that of channel flow. Burst events are also investigated in pipe and channel flows. The result shows that there is no remarkable difference in burst period between both flows. But the burst intensity is very different. Burst intensity in pipe flow in smaller than that in channel flow. Detailed analysis shows that the main difference between pipe and channel flow in burst events is in the normal direction. So the conclusion is that transverse curvature has little influence in stream-wise direction. Its main influence is in the normal direction.