A study on the unsteady low-frequency oscillatory flow in a helical circular pipe is carried out based upon the blood flow in vessels, using the method of bi-parameter perturbation. The second order perturbation resul...A study on the unsteady low-frequency oscillatory flow in a helical circular pipe is carried out based upon the blood flow in vessels, using the method of bi-parameter perturbation. The second order perturbation results were obtained and the characteristics were analyzed at different time of the axial velocity, of the secondary flow, and of the wall shearing stress. Also done the analysis of above-mentioned variables that varied along with time and Womersley number. The results indicate that for a helical pipe, the torsion exerts the main influence on the distribution of secondary flow velocity, especially when the absolute value of axial press gradient is rather small. The severe variation of stream function takes place within a very short period, during which time the stream function develops from positive value to negative value and vice versa, while in most cases in a cycle, the variation is smooth. The wall shearing stress changes severely with theta too.展开更多
Without simplifying the N-S equations of Germano's[5], we study the flow in a helical circular pipe employing perturbation method. A third perturbation solution is fully presented. The first- second- and third-ord...Without simplifying the N-S equations of Germano's[5], we study the flow in a helical circular pipe employing perturbation method. A third perturbation solution is fully presented. The first- second- and third-order effects of curvature κ and torsion τ on the secondary flow and axial velocity are discussed in detail. The first-order effect of curvature is to form two counter-rotating cells of the secondary flow and to push the maximum axial velocity to the outer bend. The two cells are pushed to the outer bend by the pure second-order effect of curvature. The combined higher-order (second-, third-) effects of curvature and torsion, are found to be an enlargement of the lower vortex of the secondary flow at expense of the upper one and a clockwise shift of the centers of the secondary vortices and the location of maximum axial velocity. When the axial pressure gradient is small enough or the torsion is sufficiently larger than the curvature, the location of the maximal axial velocity is near the inner bend. The equation of the volume flux is obtained from integrating the perturbation solutions of axial velocity. From the equation the validity range of the perturbation solutions in this paper can be obtained and the conclusion that the three terms of torsion have no effect on the volume flux can easily be drawn. When the axial pressure gradient is less than 22.67, the volume flux in a helical pipe is larger than that in a straight pipe.展开更多
文摘A study on the unsteady low-frequency oscillatory flow in a helical circular pipe is carried out based upon the blood flow in vessels, using the method of bi-parameter perturbation. The second order perturbation results were obtained and the characteristics were analyzed at different time of the axial velocity, of the secondary flow, and of the wall shearing stress. Also done the analysis of above-mentioned variables that varied along with time and Womersley number. The results indicate that for a helical pipe, the torsion exerts the main influence on the distribution of secondary flow velocity, especially when the absolute value of axial press gradient is rather small. The severe variation of stream function takes place within a very short period, during which time the stream function develops from positive value to negative value and vice versa, while in most cases in a cycle, the variation is smooth. The wall shearing stress changes severely with theta too.
文摘Without simplifying the N-S equations of Germano's[5], we study the flow in a helical circular pipe employing perturbation method. A third perturbation solution is fully presented. The first- second- and third-order effects of curvature κ and torsion τ on the secondary flow and axial velocity are discussed in detail. The first-order effect of curvature is to form two counter-rotating cells of the secondary flow and to push the maximum axial velocity to the outer bend. The two cells are pushed to the outer bend by the pure second-order effect of curvature. The combined higher-order (second-, third-) effects of curvature and torsion, are found to be an enlargement of the lower vortex of the secondary flow at expense of the upper one and a clockwise shift of the centers of the secondary vortices and the location of maximum axial velocity. When the axial pressure gradient is small enough or the torsion is sufficiently larger than the curvature, the location of the maximal axial velocity is near the inner bend. The equation of the volume flux is obtained from integrating the perturbation solutions of axial velocity. From the equation the validity range of the perturbation solutions in this paper can be obtained and the conclusion that the three terms of torsion have no effect on the volume flux can easily be drawn. When the axial pressure gradient is less than 22.67, the volume flux in a helical pipe is larger than that in a straight pipe.
