Formation of the free surface of a viscous fluid volume inside a rotating horizontal cylinder

Шрагер, Г. Р.; Shtokolova, M. N.; Yakutenok, V. A.

doi:10.1134/s0015462809020161

Cited by 5 publications

(4 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…When a wider variety of cases than the present low-volume fraction regime are considered, there have been many studies in the literature [13][14][15]. As noted below, they show the richness of rimming flow with respect to rotation speed, various filling fractions and fluid phase used.…”

Section: Introductionmentioning

confidence: 97%

Characterization of patterns in rimming flow

Chicharro

Vázquez

Manasseh

2011

Experimental Thermal and Fluid Science

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 97%

Characterization of patterns in rimming flow

Chicharro

Vázquez

Manasseh

2011

Experimental Thermal and Fluid Science

View full text Add to dashboard Cite

“…The indirect boundary element method (IBEM) is an effective means to solve the fluid dynamics problems at low Reynolds numbers (Stokes flows) with a free surface. Its application in combination with the use of the constant elements made it possible to investigate a number of practically important flows [1][2][3][4]. In these papers the two-dimensional creeping flows whose characteristic feature is the presence of a free surface are considered.…”

Section: Introductionmentioning

confidence: 99%

The indirect boundary element method for the axisymmetric free surface Stokes flow

Ponomareva¹,

Yakutenok²

2015

WIT Transactions on Modelling and Simulation

Self Cite

View full text Add to dashboard Cite

The authors present the formulation of the indirect boundary element method (IBEM) for an axisymmetric Stokes flow with a free surface in the presence of gravity. The formulae of the fundamental solutions of the Stokes equations are found for velocities and tractions in the axisymmetric case. These expressions are written in the cylindrical coordinate system and contain the elliptic integrals of the first and second kind. For the integral equations discretization the constant elements are used. The necessary integrals are evaluated numerically except for the singular ones. The analytical formulae are obtained for them. Two boundaryvalue problems with mixed conditions are considered. The problem of the Poiseuille flow of a viscous fluid in a round tube with the exact solution was calculated to verify the IBEM algorithm and to demonstrate its approximation convergence. Another problem of the cylindrical tube filling by a viscous fluid with a free surface was calculated to prove the IBEM in the case of a moving boundary. The simulation in a steady-state formulation showed that the stationary advancing front shapes exist in both cases when the gravity acts against the flow (Stokes number St<0) and aids the flow (0

show abstract

“…In particular, a great number of viscous fluid flows with free surface have been investigated with low Reynolds numbers. Several practically important problems were discussed in papers [6][7][8][9][10]. Important results were successfully obtained by means of the indirect BEM for the flow of Newtonian fluid.…”

Section: Introductionmentioning

confidence: 99%

The indirect boundary element method for the two-dimensional pressure- and gravity-driven free surface Stokes flow

Ponomareva¹,

Filina²,

Yakutenok³

2014

WIT Transactions on Modelling and Simulation

Self Cite

View full text Add to dashboard Cite

The indirect boundary element method (IBEM) is formulated for a two-dimensional Stokes flow with moving boundary in the presence of gravity. For simulation of the non-Newtonian fluid flow an iterative scheme for solving a nonlinear system of algebraic equation is used to calculate nonlinear viscous terms. The selected scheme requires values of pseudo forces in each boundary element and each internal collocation point obtained from boundary conditions (for velocities and tractions) and velocity field found at the previous iteration. Boundary element integrals are calculated analytically with a singularity extraction and internal cells integrals are evaluated by using the standard Gaussian quadratures. Internal cells sources are estimated numerically within a finite difference approach to velocity derivatives calculation. The Poiseuille flow of power law fluid in a channel is calculated for a benchmark of the IBEM algorithm. The accuracy and convergence tests are presented for a wide range of power law index (0.2-1.2). In the presence of a free surface, no analytical solution is available. The problem of channel filling with power law fluid is analyzed. The shape and the movement of the free surface are investigated through a special numerical front tracking algorithm based on mesh refinement for the free surface and for the solution domain. Elements of high performance computing are presented. The obtained results coincide with those of other authors. It confirms that the presented algorithm and corresponding software can be applied to study a number of low Reynolds flows, for example in a mould filling technology.

show abstract

Formation of the free surface of a viscous fluid volume inside a rotating horizontal cylinder

Cited by 5 publications

References 11 publications

Characterization of patterns in rimming flow

Characterization of patterns in rimming flow

The indirect boundary element method for the axisymmetric free surface Stokes flow

The indirect boundary element method for the two-dimensional pressure- and gravity-driven free surface Stokes flow

Contact Info

Product

Resources

About