The important role of atherosclerosis in pathophysiology of Alzheimer's Disease has become evident.Mechanisms such as hyperlipidemia,inflammation,abdominal obesity and insulin resistance are important yet they may...The important role of atherosclerosis in pathophysiology of Alzheimer's Disease has become evident.Mechanisms such as hyperlipidemia,inflammation,abdominal obesity and insulin resistance are important yet they may not fully explain the specific involvement of the Circle of Willis in these pathologies.The Circle of Wills is a complex geometrical structure which has several areas with different curvature as well as various branching angles of vessels composing the circle.The hemodynamics in this region should take into account the Dean number which indicates the influence of curvature on the resistance to blood flow.Thus,areas with various curvature and angles may have different hemodynamics and there are certain areas in the Circle of Willis that are more likely to develop atherosclerotic changes.Therefore,this could suggest the novel pathophysiological pathway resulting from the geometric peculiarities of the Circle of Willis.One of the directions of future research is to examine whether specific areas of the Circle of Willis are more likely to develop atherosclerotic changes compared to other ones.Selective areas of the Circle of Willis affected by atherosclerotic changes could indicate the primary role of atherosclerosis promoting Alzheimer's disease although other pathophysiological mechanisms suggesting the opposite direction should be also examined in prospective studies.展开更多
The effects of the aspect ratio on unsteady solutions through the curved duct flow are studied numerically by a spectral based computational procedure with a temperature gradient between the vertical sidewalls for the...The effects of the aspect ratio on unsteady solutions through the curved duct flow are studied numerically by a spectral based computational procedure with a temperature gradient between the vertical sidewalls for the Grashof number 100 ≤ Gr ≤ 2 000. The outer wall of the duct is heated while the inner wall is cooled and the top and bottom walls are adiabatic. In this paper, unsteady solutions are calculated by the time history analysis of the Nusselt number for the Dean numbers Dn = 100 and Dn = 500 and the aspect ratios 1≤γ≤ 3. Water is taken as a working fluid （Pr =7.0）. It is found that at Dn = 100, there appears a steady-state solution for small or large Gr. For moderate Gr, however, the steady-state solution turns into the periodic solution if γ is increased. For Dn = 500, on the other hand, it is analyzed that the steady-state solution turns into the chaotic solution for small and large Gr for any γ lying in the range. For moderate Gr at Dn = 500, however, the steady-state flow turns into the chaotic flow through the periodic oscillating flow if the aspect ratio is increased.展开更多
In this paper, A method, consisted of perturbation method, Garlerkin method and finite-difference method, is designed to calculate fully developed flows in curved tubes of rectangular cross-section. It costs less comp...In this paper, A method, consisted of perturbation method, Garlerkin method and finite-difference method, is designed to calculate fully developed flows in curved tubes of rectangular cross-section. It costs less computation than that of direct solving N-S equations, and prevents from building high-order difference equations and extra dealing with the boundary conditions. Numerical results in the situation of small curvature and low Dean number is in accordance with former's numerical and experimental results in quality, and it shows the feasibility of this paper's method.展开更多
The incompressible viscous steady flow through a rotating curved pipe of circular cross-section with magnetic field is investigated numerically to examine the combined effects of rotation (Coriolis force), magnetic fi...The incompressible viscous steady flow through a rotating curved pipe of circular cross-section with magnetic field is investigated numerically to examine the combined effects of rotation (Coriolis force), magnetic field and curvature (centrifugal force) on the flow. The curvature of the pipe has been assumed to be small, that is, the radius of the circle in which the central line of the pipe is coiled is large in comparison with the radius of the cross section. Spectral method is applied as a main tool for the numerical technique, where Fourier series, Chebyshev polynomials, Collocation methods, and Iteration method are used as secondary tools. The flow depends on the Taylor number (Tr), Dean Number (Dn), Magnetic Parameter (M) and the dimensionless curvature of the pipe δ. When Tr > 0, the rotation is in the direction so that the Coriolis force enforces the curvature effect. When Tr −1500 ≤ Tr ≤ 1500, Dn ≥ 1000 (large Dean number), M ≥ 0 and δ = 0.01. Due to high magnetic field four-vortex solution is observed in a rotating curved pipe system. Visualization is attained with MAPLE software.展开更多
Combined effects of centrifugal and coriolis instability of the flow through a rotating curved duct with rectangular cross section have been studied numerically by using a spectral method, and covering a wide range of...Combined effects of centrifugal and coriolis instability of the flow through a rotating curved duct with rectangular cross section have been studied numerically by using a spectral method, and covering a wide range of the Taylor number ?for a constant Dean number. The rotation of the duct about the center of curvature is imposed in the positive direction, and the effects of rotation (Coriolis force) on the flow characteristics are investigated. As a result, multiple branches of asymmetric steady solutions with two-, three-and multi-vortex solutions are obtained. To investigate the non-linear behavior of the unsteady solutions, time evolution calculations as well as power spectrum of the unsteady solutions are performed, and it is found that the unsteady flow undergoes through various flow instabilities in the scenario “chaotic?→ multi-periodic?→ periodic?→ steady-state”, if Tr is increased in the positive direction. The present results show the characteristics of both the secondary flow and axial flow distribution in the flow.展开更多
文摘The important role of atherosclerosis in pathophysiology of Alzheimer's Disease has become evident.Mechanisms such as hyperlipidemia,inflammation,abdominal obesity and insulin resistance are important yet they may not fully explain the specific involvement of the Circle of Willis in these pathologies.The Circle of Wills is a complex geometrical structure which has several areas with different curvature as well as various branching angles of vessels composing the circle.The hemodynamics in this region should take into account the Dean number which indicates the influence of curvature on the resistance to blood flow.Thus,areas with various curvature and angles may have different hemodynamics and there are certain areas in the Circle of Willis that are more likely to develop atherosclerotic changes.Therefore,this could suggest the novel pathophysiological pathway resulting from the geometric peculiarities of the Circle of Willis.One of the directions of future research is to examine whether specific areas of the Circle of Willis are more likely to develop atherosclerotic changes compared to other ones.Selective areas of the Circle of Willis affected by atherosclerotic changes could indicate the primary role of atherosclerosis promoting Alzheimer's disease although other pathophysiological mechanisms suggesting the opposite direction should be also examined in prospective studies.
文摘The effects of the aspect ratio on unsteady solutions through the curved duct flow are studied numerically by a spectral based computational procedure with a temperature gradient between the vertical sidewalls for the Grashof number 100 ≤ Gr ≤ 2 000. The outer wall of the duct is heated while the inner wall is cooled and the top and bottom walls are adiabatic. In this paper, unsteady solutions are calculated by the time history analysis of the Nusselt number for the Dean numbers Dn = 100 and Dn = 500 and the aspect ratios 1≤γ≤ 3. Water is taken as a working fluid （Pr =7.0）. It is found that at Dn = 100, there appears a steady-state solution for small or large Gr. For moderate Gr, however, the steady-state solution turns into the periodic solution if γ is increased. For Dn = 500, on the other hand, it is analyzed that the steady-state solution turns into the chaotic solution for small and large Gr for any γ lying in the range. For moderate Gr at Dn = 500, however, the steady-state flow turns into the chaotic flow through the periodic oscillating flow if the aspect ratio is increased.
文摘In this paper, A method, consisted of perturbation method, Garlerkin method and finite-difference method, is designed to calculate fully developed flows in curved tubes of rectangular cross-section. It costs less computation than that of direct solving N-S equations, and prevents from building high-order difference equations and extra dealing with the boundary conditions. Numerical results in the situation of small curvature and low Dean number is in accordance with former's numerical and experimental results in quality, and it shows the feasibility of this paper's method.
文摘The incompressible viscous steady flow through a rotating curved pipe of circular cross-section with magnetic field is investigated numerically to examine the combined effects of rotation (Coriolis force), magnetic field and curvature (centrifugal force) on the flow. The curvature of the pipe has been assumed to be small, that is, the radius of the circle in which the central line of the pipe is coiled is large in comparison with the radius of the cross section. Spectral method is applied as a main tool for the numerical technique, where Fourier series, Chebyshev polynomials, Collocation methods, and Iteration method are used as secondary tools. The flow depends on the Taylor number (Tr), Dean Number (Dn), Magnetic Parameter (M) and the dimensionless curvature of the pipe δ. When Tr > 0, the rotation is in the direction so that the Coriolis force enforces the curvature effect. When Tr −1500 ≤ Tr ≤ 1500, Dn ≥ 1000 (large Dean number), M ≥ 0 and δ = 0.01. Due to high magnetic field four-vortex solution is observed in a rotating curved pipe system. Visualization is attained with MAPLE software.
文摘Combined effects of centrifugal and coriolis instability of the flow through a rotating curved duct with rectangular cross section have been studied numerically by using a spectral method, and covering a wide range of the Taylor number ?for a constant Dean number. The rotation of the duct about the center of curvature is imposed in the positive direction, and the effects of rotation (Coriolis force) on the flow characteristics are investigated. As a result, multiple branches of asymmetric steady solutions with two-, three-and multi-vortex solutions are obtained. To investigate the non-linear behavior of the unsteady solutions, time evolution calculations as well as power spectrum of the unsteady solutions are performed, and it is found that the unsteady flow undergoes through various flow instabilities in the scenario “chaotic?→ multi-periodic?→ periodic?→ steady-state”, if Tr is increased in the positive direction. The present results show the characteristics of both the secondary flow and axial flow distribution in the flow.
