A flow in the depth of infinite annular cylindrical cavity

2012 ◽  
Vol 711 ◽  
pp. 667-680 ◽  
Author(s):  
Vladimir Shtern
Keyword(s):  
Eigenvalue Problem ◽  
Viscous Fluid ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Cylindrical Cavity ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Asymptotic Solutions

AbstractThe paper describes an asymptotic flow of a viscous fluid in an infinite annular cylindrical cavity as the distance from the flow source tends to infinity. If the driving flow near the source is axisymmetric then the asymptotic pattern is cellular; otherwise it is typically not. Boundary conditions are derived to match the asymptotic axisymmetric flow with that near the source. For a narrow cavity, the asymptotic solutions for the axisymmetric and three-dimensional flows are obtained analytically. For any gap, the flow is described by a numerical solution of an eigenvalue problem. The least decaying mode corresponds to azimuthal wavenumber $m= 1$.

Axisymmetric flow near the critical point on the moving boundary

2010 ◽  
Vol 7 ◽  
pp. 182-190
Author(s):  
I.Sh. Nasibullayev ◽  
E.Sh. Nasibullaeva
Keyword(s):  
Fluid Flow ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Axial Velocity ◽  
Moving Boundary ◽  
Axisymmetric Flow ◽  
Boundary Motion ◽  
Newton Raphson ◽  
Raphson Method

In this paper the investigation of the axisymmetric flow of a liquid with a boundary perpendicular to the flow is considered. Analytical equations are derived for the radial and axial velocity and pressure components of fluid flow in a pipe of finite length with a movable right boundary, and boundary conditions on the moving boundary are also defined. A numerical solution of the problem on a finite-difference grid by the iterative Newton-Raphson method for various velocities of the boundary motion is obtained.

ASYMPTOTIC BEHAVIOR OF A VISCOUS FLUID WITH SLIP BOUNDARY CONDITIONS ON A SLIGHTLY ROUGH WALL

2010 ◽  
Vol 20 (01) ◽  
pp. 121-156 ◽  
Author(s):  
J. CASADO-DÍAZ ◽  
M. LUNA-LAYNEZ ◽  
F. J. SUÁREZ-GRAU
Keyword(s):  
Asymptotic Behavior ◽  
Viscous Fluid ◽  
Boundary Conditions ◽  
Critical Size ◽  
Three Dimensional ◽  
Plane Boundary ◽  
Limit Equation ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Oscillating Boundary

For an oscillating boundary of period and amplitude ε, it is known that the asymptotic behavior when ε tends to zero of a three-dimensional viscous fluid satisfying slip boundary conditions is the same as if we assume no-slip (adherence) boundary conditions. Here we consider the case where the period is still ε but the amplitude is δε with δε/ε converging to zero. We show that if [Formula: see text] tends to infinity, the equivalence between the slip and no-slip conditions still holds. If the limit of [Formula: see text] belongs to (0, +∞) (critical size), then we still have the slip boundary conditions in the limit but with a bigger friction coefficient. In the case where [Formula: see text] tends to zero the boundary behaves as a plane boundary. Besides the limit equation, we also obtain an approximation (corrector result) of the pressure and the velocity in the strong topology of L2 and H1 respectively.

Mass transport in three-dimensional water waves

1991 ◽  
Vol 231 ◽  
pp. 417-437 ◽  
Author(s):  
Mohamed Iskandarani ◽  
Philip L.-F. Liu
Keyword(s):  
Mass Transport ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Steady Flow ◽  
Water Waves ◽  
Numerical Scheme ◽  
Three Dimensional ◽  
Langmuir Circulation ◽  
Circulation Patterns ◽  
Wave Trains

A spectral scheme is developed to study the mass transport in three-dimensional water waves where the steady flow is assumed to be periodic in two horizontal directions. The velocity–vorticity formulation is adopted for the numerical solution, and boundary conditions for the vorticity are derived to enforce the no-slip conditions. The numerical scheme is used to calculate the mass transport under two intersecting wave trains; the resulting flow is reminiscent of the Langmuir circulation patterns. The scheme is then applied to study the steady flow in a three-dimensional standing wave.

Modelling solid transport in building drainage systems

1996 ◽  
Vol 33 (9) ◽  
pp. 9-16 ◽  
Author(s):  
John A. Swaffield ◽  
John A. McDougall
Keyword(s):  
Decision Making ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Water Conservation ◽  
Transient Flow ◽  
Drainage System ◽  
System Model ◽  
Flow Depth ◽  
Flow Conditions ◽  
Solid Transport

The transient flow conditions within a building drainage system may be simulated by the numerical solution of the defining equations of momentum and continuity, coupled to a knowledge of the boundary conditions representing either appliances discharging to the network or particular network terminations. While the fundamental mathematics has long been available, it is the availability of fast, affordable and accessible computing that has allowed the development of the simulations presented in this paper. A drainage system model for unsteady partially filled pipeflow will be presented in this paper. The model is capable of predicting flow depth and rate, and solid velocity, throughout a complex network. The ability of such models to assist in the decision making and design processes will be shown, particularly in such areas as appliance design and water conservation.

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