Numerical Example Analysis Of New Flow Theory And Improved Design Of Precisive Experiment Of Laminar Flow

Since the Navier-Stokes(N-S)equation was finally established to be the foundation of fluid mechanics in 1845,the understanding of flow as deformation has become unshakable.Professor Wennan Zou proposed the understanding of flow as slip and so built up a new theory of flow.For the straight flow,the new theory becomes the same as the N-S equation.But for the curved flow,their solutions are different.In this paper,the differences are studied from the viewpoints of theoretical analysis and numerical experiment,namely the numerical calculation of laminar flow in coil pipe and the improved design of the existing Taylor-Couette(TC)laminar flow experiment.The main results and conclusions are listed as follows:(1)When the curvature ratio,namely the ratio of the pipe radius to the coiling radius,of the coil pipe is 1/15,the friction factors of the coil obtained by the new flow theory,the classical theory of the N-S equation and the experimental data are not much different.The friction factor calculated by the new flow theory is 0.0643,the friction factor calculated by the N-S equation is 0.0640,and the experimental result is 0.0631.(2)When the curvature ratio of the coil is 1/50,the friction factor calculated by the new flow theory is 0.054,the result calculated by the N-S equation is 0.0359,and the result given by the experimental data is 0.0570.When the curvature ratio of the coil is 1/100,the friction factor calculated by the new flow theory is 0.0434,the result calculated by the N-S equation is 0.0212,and the result given by the experimental data is 0.0433.It can be seen that the results of the new flow theory in these two cases are closer to the experimental results.(3)In addition,the relative inlet length,namely the ratio of the inlet length to the pipe diameter,obtained by the new flow theory is closer to the relative inlet length obtained by the experimental data under all the coil curvature ratios.When the coil curvature ratio is 1/15,the relative inlet length of the new flow theory is 188-235,the result of the N-S equation is 60,and the experimental data is 173-346.When the coil curvature ratio is 1/50,the relative inlet length of the new flow theory is 314-471,the result of the N-S equation is 107,and the experimental data is 211-422.When the coil curvature ratio is 1/100,the relative inlet length of the new flow theory is 314-628,the result of the N-S equation is 181,and the experimental data is 224-448.Overall,the results of the new theory of flow are closer to the experimental results.The TC flow platform established by the research group exists some factors of internal disturbance in practice,which have caused large dispersion of analyzed data.In this paper,the existing problems of TC flow platform were checked,and by virtue of the newly bought Laser Doppler Velocimetry(LDV)and high-speed camera system,a new experimental scheme is renewed to achieve better data.Though the calculation and experiment are not well done now,the effort of this work would be helpful for a successful experiment of TC layer flow in the future.