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
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
In terms of tensor analysis technique, the Navier-Stokes equations in helical coordinate system were derived. A steady incompressible flow of power-law fluid in helical pipes at low Reynolds number was investigated by...In terms of tensor analysis technique, the Navier-Stokes equations in helical coordinate system were derived. A steady incompressible flow of power-law fluid in helical pipes at low Reynolds number was investigated by the perturbation method. A second order solution of secondary flow was worked out. The secondary flow characteristics in helical pipes are analyzed. The effects of the number Dn, curvature and torsion on the secondary flow at different flow parameters were discussed. The results show that the secondary flow pattern changes from a single vortex to two vortices as the number Dn increases at a given curvature and a given torsion. Because of the effect of torsion, the secondary flow pattern changes from two almost symmetrical vortices to a single vortex as the torsion of the helical pipe increases while the Reynolds number and curvature hold constant. The secondary flow pattern cannot be affected by the curvature of the helical pipe at a given Dn number.展开更多
The low frequency oscillatory flow in a rotating curved pipe was studied by using the method of bi parameter perturbation. Perturbation solutions up to the second order were obtained and the effects of rotation on th...The low frequency oscillatory flow in a rotating curved pipe was studied by using the method of bi parameter perturbation. Perturbation solutions up to the second order were obtained and the effects of rotation on the low frequency oscillatory flow were examined in detail. The results indicated that there exists evident difference between the low frequency oscillatory flow in a rotating curved pipe and in a curved pipe without rotation. During a period, four secondary vortexes may exist on the circular cross section and the distribution of axial velocity and wall shear stress are related to the ratio of the Coriolis force to centrifugal force and the axial pressure gradient.展开更多
The 3-D turbulent flows in a valve pipe were described by the incompressibleReynolds-averaged Navier-Stokes equations with an RNG k-ε turbulence model. With the finite volumemethod and a body-fitted coordinate system...The 3-D turbulent flows in a valve pipe were described by the incompressibleReynolds-averaged Navier-Stokes equations with an RNG k-ε turbulence model. With the finite volumemethod and a body-fitted coordinate system, the discretised equations were solved by the SIMPLESTalgorithm. The numerical result of a cut-off valve with curved inlet shows the flow characteristicsand the main cause of energy loss when fluid flows through a valve. And then, the boundaries ofvalve were modified in order to reduce the energy loss. The computational results of modified valveshow that the numerical value of turbulent kinetic energy is lower, and that the modified design ofthe 3-D valve boundaries is much better. The analysis of the result also shows that RNG k-εturbulence model can successfully be used to predict the 3-D turbulent separated flows and thesecondary flow inside valve pipes.展开更多
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.
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In terms of tensor analysis technique, the Navier-Stokes equations in helical coordinate system were derived. A steady incompressible flow of power-law fluid in helical pipes at low Reynolds number was investigated by the perturbation method. A second order solution of secondary flow was worked out. The secondary flow characteristics in helical pipes are analyzed. The effects of the number Dn, curvature and torsion on the secondary flow at different flow parameters were discussed. The results show that the secondary flow pattern changes from a single vortex to two vortices as the number Dn increases at a given curvature and a given torsion. Because of the effect of torsion, the secondary flow pattern changes from two almost symmetrical vortices to a single vortex as the torsion of the helical pipe increases while the Reynolds number and curvature hold constant. The secondary flow pattern cannot be affected by the curvature of the helical pipe at a given Dn number.
文摘The low frequency oscillatory flow in a rotating curved pipe was studied by using the method of bi parameter perturbation. Perturbation solutions up to the second order were obtained and the effects of rotation on the low frequency oscillatory flow were examined in detail. The results indicated that there exists evident difference between the low frequency oscillatory flow in a rotating curved pipe and in a curved pipe without rotation. During a period, four secondary vortexes may exist on the circular cross section and the distribution of axial velocity and wall shear stress are related to the ratio of the Coriolis force to centrifugal force and the axial pressure gradient.
文摘The 3-D turbulent flows in a valve pipe were described by the incompressibleReynolds-averaged Navier-Stokes equations with an RNG k-ε turbulence model. With the finite volumemethod and a body-fitted coordinate system, the discretised equations were solved by the SIMPLESTalgorithm. The numerical result of a cut-off valve with curved inlet shows the flow characteristicsand the main cause of energy loss when fluid flows through a valve. And then, the boundaries ofvalve were modified in order to reduce the energy loss. The computational results of modified valveshow that the numerical value of turbulent kinetic energy is lower, and that the modified design ofthe 3-D valve boundaries is much better. The analysis of the result also shows that RNG k-εturbulence model can successfully be used to predict the 3-D turbulent separated flows and thesecondary flow inside valve pipes.
