Analysis of pipe flow with free surface. Part II. Theoretical analysis and experiment

1994 ◽  
Vol 13 (5) ◽  
pp. 249-260
Author(s):  
Amane Tanaka ◽  
Ryuji Takaki
Keyword(s):  
Free Surface ◽  
Theoretical Analysis ◽  
Pipe Flow ◽  
Surface Part

The Effect of Slip on the Discharge From Partially Filled Circular and Fully Filled Lens and Figure 8 Shaped Pipes

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Samuel Irvine ◽  
Luke Fullard
Keyword(s):  
Free Surface ◽  
Analytical Solution ◽  
Flow Rate ◽  
Pipe Flow ◽  
Stokes Equations ◽  
Symmetry Plane ◽  
Volumetric Flow Rate ◽  
Wall Slip ◽  
Circular Pipe ◽  
Gravity Driven Flow

In this work, we examine the effect of wall slip for a gravity-driven flow of a Newtonian fluid in a partially filled circular pipe. An analytical solution is available for the no-slip case, while a numerical method is used for the case of flow with wall slip. We note that the partially filled circular pipe flow contains a free surface. The solution to the Navier–Stokes equations in such a case is a symmetry of a pipe flow (with no free surface) with the free surface as the symmetry plane. Therefore, we note that the analytical solution for the partially filled case is also the exact solution for fully filled lens and figure 8 shaped pipes, depending on the fill level. We find that the presence of wall slip increases the optimal fill height for maximum volumetric flow rate, brings the “velocity dip” closer to the free surface, and increases the overall flow rate for any fill. The applications of the work are twofold; the analytical solution may be used to verify numerical schemes for flows with a free surface in partially filled circular pipes, or for pipe flows in lens and figure 8 shaped pipes. Second, the work suggests that flows in pipes, particularly shallow filled pipes, can be greatly enhanced in the presence of wall slip, and optimal fill levels must account for the slip phenomenon when present.

The stability of unsteady axisymmetric incompressible pipe flow close to a piston. Part 2. Experimental investigation and comparison with computation

1971 ◽  
Vol 50 (4) ◽  
pp. 645-655 ◽  
Author(s):  
M. D. Hughes ◽  
J. H. Gerrard
Keyword(s):  
Free Surface ◽  
Pipe Flow ◽  
Critical Reynolds Number ◽  
Reynolds Numbers ◽  
Radial Component ◽  
Tube Diameter ◽  
Ring Vortex ◽  
Tracer Particles ◽  
The Stability ◽  
Cylindrical Reservoir

Flow visualization has been used quantitatively to determine the flow relative to a piston and a free surface started from rest. The discharge of water from a cylindrical reservoir was investigated. Flow with a free surface started from rest was found to have a critical Reynolds number (based on tube diameter and surface speed) of about 450 above which a ring vortex was produced just below the surface.Measurements at Reynolds numbers of 525 and 1200 were compared with computations made by the methods described in Part 1. The computed drift of tracer particles agreed well with observed values. The largest discrepancies occurred in the radial component of the drift in the early stages of the motion and amounted to 2½% of the tube diameter.

A theoretical analysis of free-surface flows of saturated granular–liquid mixtures

2008 ◽  
Vol 608 ◽  
pp. 393-410 ◽  
Author(s):  
D. BERZI ◽  
J. T. JENKINS
Keyword(s):  
Free Surface ◽  
Theoretical Analysis ◽  
Eddy Viscosity ◽  
Numerical Solutions ◽  
Liquid Mixtures ◽  
Free Surface Flows ◽  
Two Phase ◽  
Surface Flows ◽  
Physical Experiments ◽  
Analytical Expressions

A simple two-phase model for steady fully developed flows of particles and water over erodible inclined beds is developed for situations in which the water and particles have the same depth. The rheology of the particles is based on recent numerical simulations and physical experiments, the rheology of the fluid is based on an eddy viscosity, and the interaction between the particles and the fluid is through drag and buoyancy. Numerical solutions of the resulting differential equations and boundary conditions provide velocity profiles of the fluid and particles, the concentration profile of the particles, and the depth of the flow at a given angle of inclination of the bed. Simple approximations permit analytical expressions for the flow velocities and the depth of flow to be obtained that agree with the numerical solutions and those measured in experiments.

The Flat Solitary Waves Due to a Submerged Moving Body in a Two-Layer Fluid With a Free Surface

2005 ◽  
Author(s):  
Gang Wei ◽  
Xiao-Bing Su ◽  
Yun-Xiang You
Keyword(s):  
Free Surface ◽  
Theoretical Analysis ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Experimental Results ◽  
Stable System ◽  
Weakly Nonlinear ◽  
Submerged Body ◽  
Moving Body

The flat solitary wave with the behavior of conjugate flow, generated by a submerged body moving in a two-layer fluid, is investigated. A criteria about the existence of weakly nonlinear weakly dispersive flat solitary wave is given. The condition of the stable system of conjugate flow is obtained. The solution of the flat solitary wave satisfying the criteria is numerically verified to be unique. Theoretical analysis is qualitatively consistent with the experimental results obtained by the authors.

Sign in / Sign up

Export Citation Format

Share Document