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.

Deviations Due to Non-Newtonian Influences Within a Miniature Viscous Disk Pump

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Phil Ligrani ◽  
Hui Jiang ◽  
Benjamin Lund ◽  
Jae Sik Jin
Keyword(s):  
Newtonian Fluid ◽  
Flow Rate ◽  
Rotational Speed ◽  
Stokes Equations ◽  
Sucrose Concentration ◽  
Pure Water ◽  
Pressure Rise ◽  
Volumetric Flow Rate ◽  
Newtonian Flow ◽  
Newtonian Behavior

A miniature viscous disk pump (VDP) is utilized to characterize and quantify non-Newtonian fluid deviations due to non-Newtonian influences relative to Newtonian flow behavior. Such deviations from Newtonian behavior are induced by adding different concentrations of sucrose to purified water, with increasing non-Newtonian characteristics as sucrose concentration increases from 0% (pure water) to 10% by mass. The VDP consists of a 10.16 mm diameter disk that rotates above a C-shaped channel with inner and outer radii of 1.19 mm, and 2.38 mm, respectively, and a channel depth of 200 μm. Fluid inlet and outlet ports are located at the ends of the C-shaped channel. Within the present study, experimental data are given for rotational speeds of 1200–2500 rpm, fluid viscosities of 0.001–0.00134 Pa s, pressure rises of 0–220 Pa, and flow rates up to approximately 0.00000005 m3/s. The theory of Flumerfelt is modified and adapted for application to the present VDP environment. Included is a new development of expressions for dimensionless volumetric flow rate, and normalized local circumferential velocity for Newtonian and non-Newtonian fluid flows. To quantify deviations due to the magnitude non-Newtonian flow influences, a new pressure rise parameter is employed, which represents the dimensional pressure rise change at a particular flow rate and sucrose concentration, as the flow changes from Newtonian to non-Newtonian behavior. For 5% and 10% sucrose solutions at rotational speeds of 1200–2500 rpm, this parameter increases as the disk dimensional rotational speed increases and as the volumetric flow rate decreases. Associated magnitudes of the pressure difference parameter show that the fluid with the larger sucrose concentration (by mass) produces significantly larger differences between Newtonian and non-Newtonian fluid flow, for each value of dimensional volumetric flow rate. For each disc rotational speed, compared to Newtonian data, dimensional pressure rise variations with dimensional volumetric flow rate, which are associated with the non-Newtonian data, are generally lower when compared at a particular volumetric flow rate. Agreement with analytic results, for any given flow rate, rotational speed, and flow passage height, validates the shear stress model employed to represent non-Newtonian behavior, as well as the analytic equations and tools (based upon the Navier–Stokes equations) which are employed to predict measured behavior over the investigated range of experimental conditions.

Numerical Simulation of Effect of Slip Conditions on PVC Co-Rotating Twin-Screw Extrusion

2011 ◽  
Vol 189-193 ◽  
pp. 1946-1954 ◽  
Author(s):  
Ying Han Cao ◽  
Jin Nan Chen
Keyword(s):  
Flow Rate ◽  
Volumetric Flow Rate ◽  
Wall Slip ◽  
Slip Condition ◽  
Twin Screw Extruder ◽  
Slip Coefficient ◽  
Twin Screw Extrusion ◽  
Screw Extruder ◽  
Slip Conditions ◽  
Twin Screw

The effect of wall conditions on the co-rotating parallel twin-screw extrusion of rigid polyvinyl chloride (RPVC) is studied. The relationship between the shear stress at the screw wall and the slip velocity of the flowing melt obeys Navier’s linear law. At zero pressure difference between the entrance and exit of the melting section of twin-screw extruder, the volumetric flow rate and 3D isothermal flow fields of RPVC are calculated under different wall slip conditions in the metering section of the twin-screw extruder by using the evolution technique in POLYFLOW. The results show that when the slip coefficient is smaller than 104Pa*s/m , the volumetric flow rate of the melt is constant, corresponding to the full slip condition. When the slip coefficient is larger than 104Pa*s/m , with the slip coefficient decreasing, the volumetric flow rate and viscosity increase, but the gradients of velocity, pressure, and shear rate decrease. The residual stress of the product is thus reduced. Therefore, increasing wall slip is good for the stability of polymer extrusion and the product quality. The dispersive and the distributive mixing of the twin-screw extruder under full slip and no slip conditions are also studied. Results show that the mixing performance under no-slip condition is better than under full-slip condition, but slip at the wall is good for the extrusion of heat-sensitive materials.

Periodic flows through curved tubes: the effect of the frequency parameter

1990 ◽  
Vol 210 ◽  
pp. 353-370 ◽  
Author(s):  
Costas C. Hamakiotes ◽  
Stanley A. Berger
Keyword(s):  
Flow Field ◽  
Flow Rate ◽  
Stokes Equations ◽  
Volumetric Flow Rate ◽  
Frequency Parameter ◽  
Dean Number ◽  
Single Vortex ◽  
Curved Pipe ◽  
Periodic Flows ◽  
Axial Pressure Gradient

In a previous paper we reported on the effect of Dean number, κm, on the fully developed region of periodic flows through curved tubes. In this paper we again consider a sinusoldally varying volumetric flow rate in a curved pipe of arbitrary curvature ratio, δ, and investigate the effect of frequency parameter α, and Reynolds number Rem on the flow. Specifically, we report on the flow-field development for the range 7.5 [les ] α [les ] 25, and 50 [les ] Rem [les ] 450. The results, obtained by numerical integration of the full Navier–Stokes equations, reveal a number of characteristics of the flow previously unreported. For low values of Rem the secondary flow consists of a single vortex (Dean-type motion) in the half-cross-section at all times and for all values of α studied. For higher Rem we observe inward ‘centrifuging’ (Lyne-type motion) at the centre. This motion always occurs during the accelerating period of the volumetric flow rate. It appears at lower α for higher Rem and, for the given Rem at which it appears, it occurs at earlier times in the cycle for lower a. A striking feature is observed for α = 15 for the range 315 [les ] Rem [les ] 400: period tripling. The flow field varies periodically with time for the duration of three volumetric-flow-rate cycles then repeats for the subsequent three cycles, and so on. The computed axial pressure gradient also varies periodically with time but with the same period as the volumetric flow rate.

The pumping characteristics of screw rotors. I. The theory of calculation of the pumping capacity of screw rotors

1987 ◽  
Vol 52 (2) ◽  
pp. 357-371 ◽  
Author(s):  
František Rieger
Keyword(s):  
Present State ◽  
Flow Rate ◽  
Volumetric Flow Rate ◽  
Screw Rotor ◽  
Screw Rotors

This paper summarizes the present state of the theory of calculation of the pumping capacity of screw rotors. The calculation starts from the equation for the volumetric flow rate of the flow between two unconfined plates modified by correction coefficients obtained from the relationships for the flow rate in simpler geometrical configurations to which the screw rotor may be, under certain circumstances, reduced.

scholarly journals Local Well-Posedness for Free Boundary Problem of Viscous Incompressible Magnetohydrodynamics

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 461
Author(s):  
Kenta Oishi ◽  
Yoshihiro Shibata
Keyword(s):  
Free Surface ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Stokes Equations ◽  
Mhd Flow ◽  
Transmission Conditions ◽  
Well Posedness ◽  
Anisotropic Space ◽  
Free Boundary Conditions ◽  
Incompressible Magnetohydrodynamics

In this paper, we consider the motion of incompressible magnetohydrodynamics (MHD) with resistivity in a domain bounded by a free surface. An electromagnetic field generated by some currents in an external domain keeps an MHD flow in a bounded domain. On the free surface, free boundary conditions for MHD flow and transmission conditions for electromagnetic fields are imposed. We proved the local well-posedness in the general setting of domains from a mathematical point of view. The solutions are obtained in an anisotropic space Hp1((0,T),Hq1)∩Lp((0,T),Hq3) for the velocity field and in an anisotropic space Hp1((0,T),Lq)∩Lp((0,T),Hq2) for the magnetic fields with 2<p<∞, N<q<∞ and 2/p+N/q<1. To prove our main result, we used the Lp-Lq maximal regularity theorem for the Stokes equations with free boundary conditions and for the magnetic field equations with transmission conditions, which have been obtained by Frolova and the second author.

scholarly journals Steady flow separation patterns in a 45 degree junction

2000 ◽  
Vol 411 ◽  
pp. 1-38 ◽  
Author(s):  
C. ROSS ETHIER ◽  
SUJATA PRAKASH ◽  
DAVID A. STEINMAN ◽  
RICHARD L. LEASK ◽  
GREGORY G. COUCH ◽  
...  
Keyword(s):  
Flow Separation ◽  
Stokes Equations ◽  
Bypass Graft ◽  
Three Dimensional ◽  
Symmetry Plane ◽  
Axial Flow ◽  
Reynolds Numbers ◽  
Secondary Flows ◽  
Measured Velocity ◽  
Curved Tube

Numerical and experimental techniques were used to study the physics of flow separation for steady internal flow in a 45° junction geometry, such as that observed between two pipes or between the downstream end of a bypass graft and an artery. The three-dimensional Navier–Stokes equations were solved using a validated finite element code, and complementary experiments were performed using the photochromic dye tracer technique. Inlet Reynolds numbers in the range 250 to 1650 were considered. An adaptive mesh refinement approach was adopted to ensure grid-independent solutions. Good agreement was observed between the numerical results and the experimentally measured velocity fields; however, the wall shear stress agreement was less satisfactory. Just distal to the ‘toe’ of the junction, axial flow separation was observed for all Reynolds numbers greater than 250. Further downstream (approximately 1.3 diameters from the toe), the axial flow again separated for Re [ges ] 450. The location and structure of axial flow separation in this geometry is controlled by secondary flows, which at sufficiently high Re create free stagnation points on the model symmetry plane. In fact, separation in this flow is best explained by a secondary flow boundary layer collision model, analogous to that proposed for flow in the entry region of a curved tube. Novel features of this flow include axial flow separation at modest Re (as compared to flow in a curved tube, where separation occurs only at much higher Re), and the existence and interaction of two distinct three-dimensional separation zones.

Pahoehoe and aa in Hawaii: volumetric flow rate controls the lava structure

1990 ◽  
Vol 52 (8) ◽  
pp. 615-628 ◽  
Author(s):  
Scott K Rowland ◽  
George PL Walker
Keyword(s):  
Flow Rate ◽  
Volumetric Flow Rate
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