scholarly journals The temporal evolution of neutral modes in the impulsively started flow through a circular pipe and their connection to the nonlinear stability of Hagen–Poiseuille flow

2002 ◽  
Vol 457 ◽  
pp. 339-376 ◽  
Author(s):  
ANDREW G. WALTON
Keyword(s):  
Poiseuille Flow ◽  
Multiple Scales ◽  
Stability Boundary ◽  
Circular Cross Section ◽  
Flow Characteristics ◽  
Internal Flow ◽  
Bypass Transition ◽  
Flow Through ◽  
High Reynolds ◽  
Wave Limit

The linear stability of the impulsively started flow through a pipe of circular cross-section is studied at high Reynolds number R. A crucial non-dimensional time of O(R7/9) is identified at which the disturbance acquires internal flow characteristics. It is shown that even if the disturbance amplitude at this time is as small as O(R−22/27) the subsequent evolution of the perturbation is nonlinear, although it can still be followed analytically using a multiple-scales approach. The amplitude and wave speed of the nonlinear disturbance are calculated as functions of time and we show that as t → ∞, the disturbance evolves into the long-wave limit of the neutral mode structure found by Smith & Bodonyi in the fully developed Hagen–Poiseuille flow, into which our basic flow ultimately evolves. It is proposed that the critical amplitude found here forms a stability boundary between the decay of linear disturbances and ‘bypass’ transition, in which the fully developed state is never attained.

Impact of Print Parameters on Pressure Drop in Turbulent Flow Through 3-D Printed Pipes

2020 ◽  
Author(s):  
Thomas G. Shepard ◽  
John Wentz ◽  
Tucker Bender ◽  
Derek Olmschenk ◽  
Alex Gutenberg
Keyword(s):  
Surface Roughness ◽  
Additive Manufacturing ◽  
Flow Characteristics ◽  
Internal Flow ◽  
Acrylonitrile Butadiene Styrene ◽  
Industrial Applications ◽  
Relative Pressure ◽  
Fused Filament Fabrication ◽  
Pressure Drops ◽  
Flow Through

Abstract Flow conduits made via additive manufacturing, commonly referred to as 3-D printing, are of increasing interest for a variety of industrial applications due to the ability to create unique and conformal flow paths that would not be possible with other fabrication techniques. Fused filament fabrication (FFF) is an additive manufacturing technique that is seeing new interest in the creation of internal flow channels with its ability to print high-temperature polymers and soluble supports. Printing parameter choices in the FFF printing process result in surfaces that can have significant profile differences that may significantly impact the flow characteristics within the conduits. In this study, two print parameters were experimentally studied for turbulent water flow through circular pipes created by fused filament fabrication out of acrylonitrile butadiene styrene (ABS). The print layer orientation relative to the flow was investigated for printing layers parallel, perpendicular, and at 45 degrees from the flow axis. Layer thickness were varied from 0.254 mm to 0.330 mm and all channels were created using soluble support structures. Pressure drops were measured for fully developed flow through pipes with an inside diameter of 5 mm and Reynolds numbers up to 62,000. Results are presented in terms of relative pressure drops as well as the wall surface roughness that would lead to such impacts. These flow-determined grain surface roughnesses are then compared against measurements of print surface roughness.

Amplitude-dependent neutral modes in the Hagen-Poiseuille flow through a circular pipe

1982 ◽  
Vol 384 (1787) ◽  
pp. 463-489 ◽  
Keyword(s):  
Phase Shift ◽  
Poiseuille Flow ◽  
Relative Size ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Reynolds Numbers ◽  
Critical Layer ◽  
Amplitude Dependence ◽  
Small Phase ◽  
Flow Through

An investigation is described for the nonlinear stability, at large Reynolds numbers R , of the Hagen-Poiseuille flow through a pipe of circular cross section when subjected to three-dimensional disturbances of typical relative size δ large enough to yield only a vanishingly small phase shift across the critical layer. A crucial size is δ = O ( R -⅓ ) since then this small phase shift is in tune with the small phase shift produced by the viscous wall layers. The critical layer, which is fully nonlinear and three-dimensional, and the wall layers, where the disturbance is greater than the basic flow and flow reversal occurs, are discussed in detail. Neutral solutions are then found to exist in the range c 01 < c 0 < 1 with N = 1, where c 0 is the non-dimensional wavespeed, c 01 = 0.284 and N is the azimuthal wavenumber; there is also evidence to suggest that no similar neutral solutions exist outside that range. The amplitude-dependence of the neutral modes follows and it is such that the cut-off value c 0 = c 01 + is approached as the amplitude shrinks, whereas centre modes with c 0 → 1 - are produced as the amplitude becomes relatively large.

Internal laminar flow

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Poiseuille Flow ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Concentric Cylinder ◽  
Navier Stokes Equations ◽  
Concentric Cylinders ◽  
Constant Viscosity ◽  
Pressure Driven Flow

In this chapter it is shown that solutions to the Navier-Stokes equations can be derived for steady, fully developed flow of a constant-viscosity Newtonian fluid through a cylindrical duct. Such a flow is known as a Poiseuille flow. For a pipe of circular cross section, the term Hagen-Poiseuille flow is used. Solutions are also derived for shear-driven flow within the annular space between two concentric cylinders or in the space between two parallel plates when there is relative tangential movement between the wetted surfaces, termed Couette flows. The concepts of wetted perimeter and hydraulic diameter are introduced. It is shown how the viscometer equations result from the concentric-cylinder solutions. The pressure-driven flow of generalised Newtonian fluids is also discussed.

scholarly journals Effect of Air Injection on the Internal Flow Characteristics in the Draft Tube of a Francis Turbine Model

Processes ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 1182
Author(s):  
Seung-Jun Kim ◽  
Yong Cho ◽  
Jin-Hyuk Kim
Keyword(s):  
Flow Rate ◽  
Draft Tube ◽  
Pressure Fluctuations ◽  
Flow Characteristics ◽  
Internal Flow ◽  
Air Injection ◽  
Low Flow ◽  
Francis Turbine ◽  
Navier Stokes ◽  
Vortex Rope

Under low flow-rate conditions, a Francis turbine exhibits precession of a vortex rope with pressure fluctuations in the draft tube. These undesirable flow phenomena can lead to deterioration of the turbine performance as manifested by torque and power output fluctuations. In order to suppress the rope with precession and a swirl component in the tube, the use of anti-swirl fins was investigated in a previous study. However, vortex rope generation still occurred near the cone of the tube. In this study, unsteady-state Reynolds-averaged Navier–Stokes analyses were conducted with a scale-adaptive simulation shear stress transport turbulence model. This model was used to observe the effects of the injection in the draft tube on the unsteady internal flow and pressure phenomena considering both active and passive suppression methods. The air injection affected the generation and suppression of the vortex rope and swirl component depending on the flow rate of the air. In addition, an injection level of 0.5%Q led to a reduction in the maximum unsteady pressure characteristics.

Effects of Reynolds Number and Free-Stream Turbulence on Boundary Layer Transition in a Compressor Cascade

2000 ◽  
Author(s):  
Heinz-Adolf Schreiber ◽  
Wolfgang Steinert ◽  
Bernhard Küsters
Keyword(s):  
Boundary Layer ◽  
Free Stream ◽  
Reynolds Numbers ◽  
Boundary Layer Transition ◽  
Bypass Transition ◽  
Layer Transition ◽  
Free Stream Turbulence ◽  
High Reynolds Numbers ◽  
High Turbulence ◽  
High Reynolds

An experimental and analytical study has been performed on the effect of Reynolds number and free-stream turbulence on boundary layer transition location on the suction surface of a controlled diffusion airfoil (CDA). The experiments were conducted in a rectilinear cascade facility at Reynolds numbers between 0.7 and 3.0×106 and turbulence intensities from about 0.7 to 4%. An oil streak technique and liquid crystal coatings were used to visualize the boundary layer state. For small turbulence levels and all Reynolds numbers tested the accelerated front portion of the blade is laminar and transition occurs within a laminar separation bubble shortly after the maximum velocity near 35–40% of chord. For high turbulence levels (Tu > 3%) and high Reynolds numbers transition propagates upstream into the accelerated front portion of the CDA blade. For those conditions, the sensitivity to surface roughness increases considerably and at Tu = 4% bypass transition is observed near 7–10% of chord. Experimental results are compared to theoretical predictions using the transition model which is implemented in the MISES code of Youngren and Drela. Overall the results indicate that early bypass transition at high turbulence levels must alter the profile velocity distribution for compressor blades that are designed and optimized for high Reynolds numbers.

On the modulation of water waves on shear flows

1976 ◽  
Vol 347 (1651) ◽  
pp. 537-546 ◽  
Keyword(s):  
Water Waves ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Vries Equation ◽  
Harmonic Wave ◽  
Short Wave ◽  
Long Wave ◽  
Stokes Waves ◽  
The Stability ◽  
Wave Limit

The method of multiple scales is used to examine the slow modulation of a harmonic wave moving over the surface of a two dimensional channel. The flow is assumed inviscid and incompressible, but the basic flow takes the form of an arbitrary shear. The appropriate nonlinear Schrödinger equation is derived with coefficients that depend, in a complicated way, on the shear. It is shown that this equation agrees with previous work for the case of no shear; it also agrees in the long wave limit with the appropriate short wave limit of the Korteweg-de Vries equation, the shear being arbitrary. Finally, it is remarked that the stability of Stokes waves over any shear can be examined by using the results derived here.

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