Affiliation:
1. School of Engineering and Center for Bioenvironmental Research, Tulane University, New Orleans, LA 70118
Abstract
A finite-difference scheme is used to solve the Navier-Stokes equations for the steady flow inside and outside viscous spheres in a fluid of different properties. Hence, the hydrodynamic force and the steady-state drag coefficient of the spheres are obtained. The Reynolds numbers of the computations range between 0.5 and 1000 and the viscosity ratio ranges between 0 (inviscid bubble) and infinity (solid particle). Unlike the numerical schemes previously implemented in similar studies (uniform grid in a stretched coordinate system) the present method introduces a two-layer concept for the computational domain outside the sphere. The first layer is a very thin one [ORe−1/2] and is positioned at the interface of the sphere. The second layer is based on an exponential function and covers the rest of the domain. The need for such a double-layered domain arises from the observation that at intermediate and large Reynolds numbers a very thin boundary layer appears at the fluid-fluid interface. The computations yield the friction and the form drag of the sphere. It is found that with the present scheme, one is able to obtain results for the drag coefficient up to 1000 with relatively low computational power. It is also observed that both the Reynolds number and the viscosity ratio play a major role on the value of the hydrodynamic force and the drag coefficient. The results show that, if all other conditions are the same, there is a negligible effect of the density ratio on the drag coefficient of viscous spheres.
Reference21 articles.
1. Lovalenti, P. M., and Brady, J. F., 1995, “Force on a Body in Response to an Abrupt Change in Velocity at Small but Finite Reynolds Number,” J. Fluid Mech., 293, pp. 35–46.
2. Mei, R., Lawrence, C. J., and Adrian, R. J., 1991, “Unsteady Drag on a Sphere at Finite Reynolds Number with Small Fluctuations in the Free-Stream Velocity,” J. Fluid Mech., 233, pp. 613–631.
3. Mei, R., and Adrian, R. J., 1992, “Flow past a Sphere with an Oscillation in the Free-Stream and unsteady Drag at Finite Reynolds Number,” J. Fluid Mech., 237, pp. 323–341.
4. Feng, Z.-G., 1996, “Heat Transfer from Small Particles at Low Reynolds Numbers,” Sc. D. Dissertation, Tulane Univ.
5. Feng, Z. G., and Michaelides, E. E., 1998, “Transient Heat Transfer from a Particle with Arbitrary Shape and Motion,” ASME J. Heat Transfer, 120, pp. 674–681.
Cited by
135 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献