Numerical analysis of the rotating viscous flow approaching a solid sphere

Wang, Yan-Xing; Lu, Xi‐Yun; Zhuang, Lixian

doi:10.1002/fld.683

Cited by 10 publications

(11 citation statements)

References 38 publications

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“…The present results are in quite good agreement with those experimental and numerical data. Further, the present computational code has also been verified in our previous study (Lu et al, 2002;Wang et al, 2004).…”

Section: Resultssupporting

confidence: 65%

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Numerical investigation of the non-Newtonian pulsatile blood flow in a bifurcation model with a non-planar branch

Chen

2006

Journal of Biomechanics

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119

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The pulsatile flow of non-Newtonian fluid in a bifurcation model with a non-planar daughter branch is investigated numerically by using the Carreau-Yasuda model to take into account the shear thinning behavior of the analog blood fluid. The objective of this study is to deal with the influence of the non-Newtonian property of fluid and of out-of-plane curvature in the non-planar daughter vessel on wall shear stress (WSS), oscillatory shear index (OSI), and flow phenomena during the pulse cycle. The non-Newtonian property in the daughter vessels induces a flattened axial velocity profile due to its shear thinning behavior. The non-planarity deflects flow from the inner wall of the vessel to the outer wall and changes the distribution of WSS along the vessel, in particular in systole phase. Downstream of the bifurcation, the velocity profiles are shifted toward the flow divider, and low WSS and high shear stress temporal oscillations characterized by OSI occur on the outer wall region of the daughter vessels close to the bifurcation. Secondary motions become stronger with the addition of the out-of-plane curvature induced by the bending of the vessel, and the secondary flow patterns swirl along the non-planar daughter vessel. A significant difference between the non-Newtonian and the Newtonian pulsatile flow is revealed during the pulse cycle; however, reasonable agreement between the non-Newtonian and the rescaled Newtonian flow is found. Calculated results for the pulsatile flow support the view that the non-planarity of blood vessels and the non-Newtonian properties of blood are an important factor in hemodynamics and may play a significant role in vascular biology and pathophysiology.

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Section: Resultssupporting

confidence: 65%

“…A time-accurate finite element method based on a fractional-step velocity correction (Kovacs and Kawahara, 1991;Lu et al, 2002;Chen and Lu, 2004;Wang et al, 2004) is applied to solve Eqs. (1) and (2).…”

Section: Methodsmentioning

confidence: 99%

Numerical investigation of the non-Newtonian pulsatile blood flow in a bifurcation model with a non-planar branch

Chen

2006

Journal of Biomechanics

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119

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“…Perhaps not surprisingly, this regime turns out to correspond to that in which inertial waves can propagate through the fluid. That is to say, it is observed that inertial waves can propagate in a quasi-linear manner through a still fluid (still in the rotating frame) whenever is less than , but nonlinear effects become very evident in the range and indeed no waves are observed whenever exceeds a value of around (Maxworthy 1970, Wang, Lu & Zhuang 2004, Sreenivasan & Davidson 2008). Of course, the exact value of at which waves cease to propagate depends on the precise definitions of and .…”

Section: The Role Of Inertial Waves In Columnar Vortex Formationmentioning

confidence: 99%

Are planetary dynamos driven by helical waves?

Davidson

Ranjan

2018

J. Plasma Phys.

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In most numerical simulations of the Earth’s core the dynamo is located outside the tangent cylinder and, in a zero-order sense, takes the form of a classical $\unicode[STIX]{x1D6FC}^{2}$ dynamo. Such a dynamo usually requires a distribution of helicity, $h$, which is asymmetric about the equator and in the simulations it is observed that, outside the tangent cylinder, the helicity is predominantly negative in the north and positive in the south. If we are to extrapolate the results of these simulations to the planets, we must understand how this asymmetry in helicity is established and ask if the same mechanism is likely to operate in a planet. In some of the early numerical dynamos, which were too viscous by a factor of at least $10^{9}$, as measured by the Ekman number, the asymmetric helicity distribution was attributed to Ekman pumping. However, Ekman pumping plays much less of a role in more recent, and less viscous, numerical dynamos, and almost certainly plays no significant role in the core of a planet. So the question remains: what establishes the asymmetric helicity distribution in the simulations and is this mechanism likely to carry over to planetary cores? In this paper we review the evidence that planetary dynamos, and their numerical analogues, might be maintained by helical waves, especially inertial waves, excited in and around the equatorial regions. This cartoon arises from the observation that there tends to be a statistical bias in the buoyancy flux towards the equatorial regions, and so waves are preferentially excited there. Moreover, upward (downward) propagating inertial waves carry negative (positive) helicity, which leads naturally to a segregation in $h$.

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“…Many numerical studies of single-particle dynamics in rotating flows have been concerned with the motion of a particle in a fluid-filled cylinder rotating about a vertical axis (Minkov, Ungarish & Israeli 2000Wang, Lu & Zhuang 2004). Fewer studies exist on the single-particle dynamics in a fluid-filled cylinder rotating about a horizontal axis (see figure 1), (see for example, Annamalai & Cole 1986;Roberts, Kornfeld & Fowlis 1991;Gao et al 1997;Coimbra & Kobayashi 2002;Lee & Ladd 2002;Ramirez et al 2004).…”

Section: Introductionmentioning

confidence: 99%

The dynamics of two spherical particles in a confined rotating flow: pedalling motion

Mukundakrishnan

Ayyaswamy

2008

J. Fluid Mech.

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We have numerically investigated the interaction dynamics between two rigid spherical particles moving in a fluid-filled cylinder that is rotating at a constant speed. The cylinder rotation is about a horizontal axis. The particle densities are less than that of the fluid. The numerical procedure employed to solve the mathematical formulation is based on a three-dimensional arbitrary Larangian-Eulerian (ALE), moving mesh finiteelement technique, described in a frame of reference rotating with the cylinder. Results are obtained in the ranges of particle Reynolds number, 1<Re p ≤60, and shear Reynolds number, 1≤Re s <10. Two identical particles, depending on initial conditions at release, approach each other ('drafting' and 'kissing'), tumble in the axial direction, and axially migrate towards opposing transverse planes on which they 'settle' (settling planes). Under some other initial conditions, the particles migrate directly onto their settling planes. For two identical particles, the settling planes are equidistant from the mid-transverse plane of the cylinder and the locations of the planes are determined by particle-particle and particle-wall force balances. Furthermore, for identical particles and given values of Re p and Re s , the locations of such settling planes remain the same, independent of the initial conditions at release. While located on these settling planes, as viewed in an inertial frame, the particles may attain three possible distinct states depending on the values of the Reynolds numbers. In one state (low Re p , high Re s ), the particles attain and remain at fixed equilibrium points on their settling planes. In the second (all Re p , low Re s ), they execute spiralling motions about fixed points on their respective settling planes. These fixed points coincide with the locations of the equilibrium point which would occur on the mid-axial plane in the case of a single particle. In the third state (low Re p , moderate Re s or high Re p , moderate to high Re s ), they execute near-circular orbital motion on their respective settling planes, again about fixed points. These fixed points also coincide with the locations of the equilibrium points corresponding to single-particle dynamics. Both the spiral and near-circular motions of the particles occur in an out-of-phase manner with regard to their radial positions about the fixed point; the near-circular out-of-phase motion resembles bicycle pedalling. Also, in the second and third states, the particles simultaneously experience very weak axial oscillations about their settling planes, the frequency of such oscillations coinciding with the frequency of rotation of the circular cylinder. The behaviours of two non-identical particles (same density but different sizes, or same size but different densities) are different from those of identical particles. For example, non-identical particles may both end up settling on the mid-axial plane. This occurs when the locations of their corresponding single-particle equilibrium points are far ap...

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Numerical analysis of the rotating viscous flow approaching a solid sphere

Cited by 10 publications

References 38 publications

Numerical investigation of the non-Newtonian pulsatile blood flow in a bifurcation model with a non-planar branch

Numerical investigation of the non-Newtonian pulsatile blood flow in a bifurcation model with a non-planar branch

Are planetary dynamos driven by helical waves?

The dynamics of two spherical particles in a confined rotating flow: pedalling motion

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