Experimental evidence of convective and absolute instabilities in rotating Hagen–Poiseuille flow

2013 ◽  
Vol 716 ◽  
Author(s):  
K. Shrestha ◽  
L. Parras ◽  
C. Del Pino ◽  
E. Sanmiguel-Rojas ◽  
R. Fernandez-Feria
Keyword(s):  
Experimental Evidence ◽  
Poiseuille Flow ◽  
Pipe Flow ◽  
Reynolds Numbers ◽  
Hydrodynamic Instabilities ◽  
Theoretical Predictions ◽  
Rotating Pipe Flow ◽  
Theoretical Results ◽  
Good Agreement ◽  
Swirl Parameter

AbstractExperimental results for instabilities present in a rotating Hagen–Poiseuille flow are reported in this study through fluid flow visualization. First, we found a very good agreement between the experimental and the theoretical predictions for the onset of convective hydrodynamic instabilities. Our analysis in a space–time domain is able to obtain quantitative data, so the wavelengths and the frequencies are also estimated. The comparison of the predicted theoretical frequencies with the experimental ones shows the suitability of the parallel, spatial and linear stability analysis, even though the problem is spatially developing. Special attention is focused on the transition from convective to absolute instabilities, where we observe that the entire pipe presents wavy patterns, and the experimental frequencies collapse with the theoretical results for the absolute frequencies. Thus, we provide experimental evidence of absolute instabilities in a pipe flow, confirming that the rotating pipe flow may be absolutely unstable for moderate values of Reynolds numbers and low values of the swirl parameter.

Stability of Hagen-Poiseuille flow with superimposed rigid rotation

1976 ◽  
Vol 73 (1) ◽  
pp. 153-164 ◽  
Author(s):  
P.-A. Mackrodt
Keyword(s):  
Poiseuille Flow ◽  
Pipe Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Neutral Curve ◽  
Rigid Rotation ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Navier Stokes Equations

The linear stability of Hagen-Poiseuille flow (Poiseuille pipe flow) with superimposed rigid rotation against small three-dimensional disturbances is examined at finite and infinite axial Reynolds numbers. The neutral curve, which is obtained by numerical solution of the system of perturbation equations (derived from the Navier-Stokes equations), has been confirmed for finite axial Reynolds numbers by a few simple experiments. The results suggest that, at high axial Reynolds numbers, the amount of rotation required for destabilization could be small enough to have escaped notice in experiments on the transition to turbulence in (nominally) non-rotating pipe flow.

Spin-down in rotating Hagen–Poiseuille flow: a simple criterion to detect the onset of absolute instabilities

2016 ◽  
Vol 793 ◽  
pp. 316-334 ◽  
Author(s):  
A. Miranda-Barea ◽  
C. Fabrellas-García ◽  
L. Parras ◽  
C. del Pino
Keyword(s):  
Poiseuille Flow ◽  
Wave Packets ◽  
Reynolds Numbers ◽  
Finite Amplitude ◽  
Gradual Transition ◽  
Initial State ◽  
Mode Shift ◽  
Through Flow ◽  
Reliable Procedure ◽  
Swirl Parameter

We conduct experiments in a circular pipe with rotating Hagen–Poiseuille flow (RHPF) to which we apply spin-down or impulsive spin-down to rest, in order to analyse the threshold between convective and absolute instabilities through flow visualisations in the inlet region of the pipe. For a constant value of the Reynolds number,$Re$, the finite-amplitude wave packets generated by the arbitrary perturbation that results by reducing the swirl parameter, propagate upstream or downstream depending on the initial value of the swirl parameter,$L_{0}$. In fact, the main characteristic of the flow is that the velocity front of these wave packets changes from negative to positive when absolutely unstable modes are present in the initial state. The experimental results show that spin-down becomes a precise, reliable procedure to detect the onset of absolute instabilities. In addition, we give evidence of a gradual transition for Reynolds numbers ranging from 300 to 500 where a mode shift from$n=-1$to$n=-2$appears in the absolutely unstable region.

The steady flow due to a rotating sphere at low and moderate Reynolds numbers

1980 ◽  
Vol 101 (2) ◽  
pp. 257-279 ◽  
Author(s):  
S. C. R. Dennis ◽  
S. N. Singh ◽  
D. B. Ingham
Keyword(s):  
Reynolds Number ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Finite Set ◽  
Flow Variables ◽  
Theoretical Results ◽  
Radial Variable ◽  
Good Agreement

The problem of determining the steady axially symmetrical motion induced by a sphere rotating with constant angular velocity about a diameter in an incompressible viscous fluid which is at rest at large distances from it is considered. The basic independent variables are the polar co-ordinates (r, θ) in a plane through the axis of rotation and with origin at the centre of the sphere. The equations of motion are reduced to three sets of nonlinear second-order ordinary differential equations in the radial variable by expanding the flow variables as series of orthogonal Gegenbauer functions with argument μ = cosθ. Numerical solutions of the finite set of equations obtained by truncating the series after a given number of terms are obtained. The calculations are carried out for Reynolds numbers in the range R = 1 to R = 100, and the results are compared with various other theoretical results and with experimental observations.The torque exerted by the fluid on the sphere is found to be in good agreement with theory at low Reynolds numbers and appears to tend towards the results of steady boundary-layer theory for increasing Reynolds number. There is excellent agreement with experimental results over the range considered. A region of inflow to the sphere near the poles is balanced by a region of outflow near the equator and as the Reynolds number increases the inflow region increases and the region of outflow becomes narrower. The radial velocity increases with Reynolds number at the equator, indicating the formation of a radial jet over the narrowing region of outflow. There is no evidence of any separation of the flow from the surface of the sphere near the equator over the range of Reynolds numbers considered.

Hydrodynamic instabilities in the developing region of an axially rotating pipe flow

2015 ◽  
Vol 47 (3) ◽  
pp. 035514 ◽  
Author(s):  
A Miranda-Barea ◽  
C Fabrellas-García ◽  
L Parras ◽  
C del Pino
Keyword(s):  
Pipe Flow ◽  
Hydrodynamic Instabilities ◽  
Developing Region ◽  
Rotating Pipe Flow

Thermal Behavior and Friction in Journal Bearings

1970 ◽  
Vol 92 (3) ◽  
pp. 373-380 ◽  
Author(s):  
Al. Nica
Keyword(s):  
Experimental Data ◽  
Thermal Behavior ◽  
Heat Dissipation ◽  
Journal Bearings ◽  
Friction Torque ◽  
Operating Characteristics ◽  
Lubricant Flow ◽  
Theoretical Predictions ◽  
Theoretical Results ◽  
Good Agreement

This paper deals with friction and the field of temperature in the lubricant film of journal bearings. Theoretical results regarding the thermal behavior are checked with experimental data and good agreement is found. Emphasis is put on the variation of temperature and lubricant flow with the operating characteristics of the bearing and it is seen that theoretical predictions for minima of friction torque are backed by temperature measurements. Further on, the friction torque and the mechanism of heat dissipation in bearings are dealt with, in order to verify the assumptions used in the calculation schemes. The means of efficiently cooling the bearing are also discussed, as well as the part played by the divergent zone in this process.

Eigenvalue Sensitivity to Base Flow Variations in Hagen-Poiseuille Flow

2002 ◽  
Author(s):  
Isabella M. Gavarini ◽  
Alessandro Bottaro ◽  
Frans T. M. Nieuwstadt
Keyword(s):  
Poiseuille Flow ◽  
Pipe Flow ◽  
Reynolds Numbers ◽  
Base Flow ◽  
Transient Growth ◽  
Cylindrical Pipe ◽  
Low Reynolds Numbers ◽  
Parabolic Profile ◽  
Eigenvalue Sensitivity ◽  
The Ideal

Transition in a cylindrical pipe flow still eludes thorough understanding. Most recent advances are based on the concept of transient growth of disturbances, but even this scenario is not fully confirmed by DNS and/or experiments. Based on the fact that even the most carefully conducted experiment is biased by uncertainties, we explore the spatial growth of disturbances developing on top of an almost ideal, axially invariant Poiseuille flow. The optimal deviation of the base flow from the ideal parabolic profile is computed by a variational tecnique, and unstable modes, driven by an inviscid mechanism, are found to exist for very small values of the norm of the deviation, at low Reynolds numbers.

Beam-foil spectroscopy of oxygen in the wavelength region from 270 to 490 Å

1978 ◽  
Vol 56 (5) ◽  
pp. 508-516 ◽  
Author(s):  
Eric H. Pinnington ◽  
Keith E. Donnelly ◽  
J. Anthony Kernahan ◽  
David J. G. Irwin
Keyword(s):  
Satisfactory Agreement ◽  
Wavelength Region ◽  
Theoretical Predictions ◽  
The Mean ◽  
Theoretical Results ◽  
Beam Foil ◽  
Foil Technique ◽  
Good Agreement

We have used the beam-foil technique to study the spectrum of oxygen between 270 and 490 Å. We have measured the mean lives of the 3d2F, 3d4P, 3d4D, 3d′ 2D, 3d′ 2F, 4d4P, and 4d4D terms of O II, the 3s1P0, 3s3P0, 3S5P, 3s′ 3D, 3d3P, 3d3D, 3d3F, and 3d5P terms of O III, and the 3S2S, 3P2P0, and 3s4P0 terms of O IV. All cascade components are adequately explained. Good agreement is found with previous measurements in most cases, but significant discrepancies are found with some earlier results obtained using branches above 2000 Å. Generally satisfactory agreement is also found with theoretical predictions, although disagreement is found for several members of the 2p3–2p23d array in O II f-Values are computed for 18 individual lines, and compared with other experimental and theoretical results. Finally, we discuss briefly the f-value trends along the 2p23P–2p3s3P0 (O III), 2p21D–2p3s1P0 (O III), 2s2p24P–2s2p(3P0)3s4P0 (O IV), and 2p2P0–3s2S (O IV) isoelectronic sequences.

scholarly journals Energy spectrum in the dissipation range of fluid turbulence

1997 ◽  
Vol 57 (1) ◽  
pp. 195-201 ◽  
Author(s):  
D. O. MARTÍNEZ ◽  
S. CHEN ◽  
G. D. DOOLEN ◽  
R. H. KRAICHNAN ◽  
L.-P. WANG ◽  
...  
Keyword(s):  
Energy Spectrum ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Fluid Turbulence ◽  
Theoretical Predictions ◽  
Dissipation Range ◽  
Good Agreement

High-resolution, direct numerical simulations of three-dimensional incompressible Navier–Stokes equations are carried out to study the energy spectrum in the dissipation range. An energy spectrum of the form A(k/kd)α exp[−βk/kd] is confirmed. The possible values of the parameters α and β, as well as their dependence on Reynolds numbers and length scales, are investigated, showing good agreement with recent theoretical predictions. A ‘bottleneck’-type effect is reported at k/kd≈4, exhibiting a possible transition from near-dissipation to far-dissipation.

scholarly journals Generalized Softened Variable Angle Truss Model for RC Hollow Beams under Torsion

Materials ◽  
2019 ◽  
Vol 12 (13) ◽  
pp. 2209
Author(s):  
Luís Bernardo
Keyword(s):  
Solution Procedure ◽  
Pure Torsion ◽  
Specific Behavior ◽  
Torsional Response ◽  
Truss Model ◽  
Variable Angle ◽  
Theoretical Predictions ◽  
Hollow Beams ◽  
Theoretical Results ◽  
Good Agreement

In recent studies, a new softened truss model called Generalized Softened Variable Angle Truss Model (GSVATM) has been proposed to compute the full torsional response of reinforced concrete (RC) rectangular solid beams under pure torsion. In this article, the GSVATM is extended to cover RC hollow beams under torsion. The modification of the calculation procedure, in order to account for the specific behavior of RC hollow beams for low loading levels, as well as the final solution procedure, is presented. The theoretical predictions from the extended GSVATM are compared with experimental results of RC hollow beams under torsion found in the literature. Good agreement is observed between the experimental and theoretical results, for both high and low loading levels.

A swirling spiral wave solution in pipe flow

2013 ◽  
Vol 737 ◽  
Author(s):  
K. Deguchi ◽  
A. G. Walton
Keyword(s):  
Poiseuille Flow ◽  
Pipe Flow ◽  
Wave Solution ◽  
Asymptotic Theory ◽  
Spiral Wave ◽  
Reynolds Numbers ◽  
Quantitative Agreement ◽  
Travelling Wave ◽  
Navier Stokes ◽  
Nonlinear Solution

AbstractA numerically exact full Navier–Stokes counterpart of the asymptotic nonlinear solution in Hagen–Poiseuille flow proposed by Smith & Bodonyi (Proc. R. Soc. A, vol. 384, 1982, pp. 463–489) is discovered. The solution takes the form of a spiral travelling wave, with a novel feature being a strong induced component of swirl. Our solution shows excellent quantitative agreement with the asymptotic theory at Reynolds numbers of the order of $1{0}^{8} $.

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