Mount Etna and the 1971 eruption - Rheological features of the 1971 Mount Etna lavas

1973 ◽  
Vol 274 (1238) ◽  
pp. 99-106 ◽  
Keyword(s):  
Surface Roughness ◽  
Reynolds Number ◽  
Laminar Flow ◽  
Mechanical Energy ◽  
Critical Value ◽  
Heat Energy ◽  
Mount Etna ◽  
Two Dimensional ◽  
Spiral Motion ◽  
Rapid Transition

Rheological studies on the 1971 M ount Etna lavas indicate they underwent rapid transition from Newtonian to non-Newtonian fluids near their point of emission and that the non-Newtonian regime may be coincidental with high mechanical energy/low heat energy regime further from the boccas. Darcy’s equation quantifies the surface roughness of channels using the Chezy coefficient and is plotted against Reynolds number on a Stanton diagram. The relation is linear, and the critical value Re0 is not exceeded, proving wholly laminar flow. The lava underwent a divergent, twin spiral motion involving two dimensional laminar flow. Convergent, twin spiral motion occurred only where lava passed through a constriction at a relatively high velocity.

Bifurcation Characteristics of Flows in Rectangular Sudden Expansion Channels

2005 ◽  
Author(s):  
Francine Battaglia ◽  
George Papadopoulos
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Expansion Ratio ◽  
Sudden Expansion ◽  
Two Dimensional ◽  
Effective Expansion ◽  
Three Dimensional Simulations

The effect of three-dimensionality on low Reynolds number flows past a symmetric sudden expansion in a channel was investigated. The geometric expansion ratio of in the current study was 2:1 and the aspect ratio was 6:1. Both experimental velocity measurements and two- and three-dimensional simulations for the flow along the centerplane of the rectangular duct are presented for Reynolds numbers in the range of 150 to 600. Comparison of the two-dimensional simulations with the experiments revealed that the simulations fail to capture completely the total expansion effect on the flow, which couples both geometric and hydrodynamic effects. To properly do so requires the definition of an effective expansion ratio, which is the ratio of the downstream and upstream hydraulic diameters and is therefore a function of both the expansion and aspect ratios. When the two-dimensional geometry was consistent with the effective expansion ratio, the new results agreed well with the three-dimensional simulations and the experiments. Furthermore, in the range of Reynolds numbers investigated, the laminar flow through the expansion underwent a symmetry-breaking bifurcation. The critical Reynolds number evaluated from the experiments and the simulations was compared to other values reported in the literature. Overall, side-wall proximity was found to enhance flow stability, helping to sustain laminar flow symmetry to higher Reynolds numbers in comparison to nominally two-dimensional double-expansion geometries. Lastly, and most importantly, when the logarithm of the critical Reynolds number from all these studies was plotted against the reciprocal of the effective expansion ratio, a linear trend emerged that uniquely captured the bifurcation dynamics of all symmetric double-sided planar expansions.

scholarly journals Experimental Study on Liquid Flow and Heat Transfer in Rough Microchannels

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Xuan Zhang ◽  
Taocheng Zhao ◽  
Suchen Wu ◽  
Feng Yao
Keyword(s):  
Heat Transfer ◽  
Surface Roughness ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Laminar Flow ◽  
Cross Section ◽  
Liquid Flow ◽  
Flow And Heat Transfer ◽  
Section Shape ◽  
Poiseuille Number

Although roughness is negligible for laminar flow through tubes in classic fluid mechanics, the surface roughness may play an important role in microscale fluid flow due to the large ratio of surface area to volume. To further verify the influence of rough surfaces on microscale liquid flow and heat transfer, a performance test system of heat transfer and liquid flow was designed and built, and a series of experimental examinations are conducted, in which the microchannel material is stainless steel and the working medium is methanol. The results indicate that the surface roughness plays a significant role in the process of laminar flow and heat transfer in microchannels. In microchannels with roughness characteristics, the Poiseuille number of liquid laminar flow relies not only on the cross section shape of the rough microchannels but also on the Reynolds number of liquid flow. The Poiseuille number of liquid laminar flow in rough microchannels increases with increasing Reynolds number. In addition, the Nusselt number of liquid laminar heat transfer is related not only to the cross section shape of a rough microchannel but also to the Reynolds number of liquid flow, and the Nusselt number increases with increasing Reynolds number.

A nonlinear instability burst in plane parallel flow

1972 ◽  
Vol 51 (4) ◽  
pp. 705-735 ◽  
Author(s):  
L. M. Hocking ◽  
K. Stewartson ◽  
J. T. Stuart ◽  
S. N. Brown
Keyword(s):  
Differential Equation ◽  
Reynolds Number ◽  
Critical Value ◽  
Three Dimensions ◽  
Parabolic Differential Equation ◽  
Nonlinear Instability ◽  
Two Dimensional ◽  
Slowly Varying Function ◽  
Plane Poiseuille Flow ◽  
Long Time

An infinitesimal centre disturbance is imposed on a fully Ldveloped plane Poiseuille flow at a Reynolds numberRslightly greater than the critical valueRcfor instability. After a long time,t, the disturbance consists of a modulated wave whose amplitudeAis a slowly varying function of position and time. In an earlier paper (Stewartson & Stuart 1971) the parabolic differential equation satisfied byAfor two-dimensional disturbances was found; the theory is here extended to three dimensions. Although the coefficients of the equation are coinples, a start is made on elucidating the properties of its solutions by assuming that these coefficients are real. It is then found numerically and confirmed analytically that, for a finite value of (R-Rc)t, the amplitudeAdevelops an infinite peak at the wave centre. The possible relevance of this work to the phenomenon of transition is discussed.

A Simple Device for Preventing Turbulent Contamination on Swept Leading Edges

1965 ◽  
Vol 69 (659) ◽  
pp. 788-789 ◽  
Author(s):  
M. Gaster
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Laminar Flow ◽  
Leading Edge ◽  
Critical Value ◽  
Stagnation Line ◽  
Naturally Occurring ◽  
Swept Wings ◽  
Laminar State ◽  
Attachment Line

On unswept wings, or wings with small amounts of sweep, the favourable pressure gradient round the leading edge, where the flow is rapidly accelerated away from the stagnation line, ensures a certain amount of laminar flow, provided the wing surface is sufficiently smooth. On highly swept wings, however, it has been found that turbulent flow can exist on the attachment line itself and there are therefore no naturally occurring regions of laminar flow. This trouble arises from the turbulence at the root of the wing, which sweeps along the attachment line. If the Reynolds number of this turbulent attachment line boundary layer is greater than some critical value, the whole attachment line boundary layer remains turbulent and the complete wing is contaminated. But if the Reynolds number is below the critical value, the turbulence decays along the leading edge and the boundary layer on the attachment line reverts back to the laminar state. This situation arises when the leading edge radius is small and the wing is only slightly swept. The attachment line boundary layer Reynolds number, Rθ, is given by the following equation:

The dynamics of a laminar flow in a symmetric channel with a sudden expansion

2001 ◽  
Vol 436 ◽  
pp. 283-320 ◽  
Author(s):  
T. HAWA ◽  
Z. RUSAK
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Numerical Simulations ◽  
Direct Numerical Simulations ◽  
Sudden Expansion ◽  
Asymptotically Stable ◽  
Two Dimensional ◽  
Stable Mode ◽  
Symmetric States ◽  
Asymmetric Equilibrium

Bifurcation analysis, linear stability study, and direct numerical simulations of the dynamics of a two-dimensional, incompressible, and laminar flow in a symmetric long channel with a sudden expansion with right angles and with an expansion ratio D/d (d is the width of the channel inlet section and D is the width of the outlet section) are presented. The bifurcation analysis of the steady flow equations concentrates on the flow states around a critical Reynolds number Rec(D/d) where asymmetric states appear in addition to the basic symmetric states when Re [ges ] Rec(D/d). The bifurcation of asymmetric states at Rec has a pitchfork nature and the asymmetric perturbation grows like √Re − Rec(D/d). The stability analysis is based on the linearized equations of motion for the evolution of infinitesimal two-dimensional disturbances imposed on the steady symmetric as well as asymmetric states. A neutrally stable asymmetric mode of disturbance exists at Rec(D/d) for both the symmetric and the asymmetric equilibrium states. Using asymptotic methods, it is demonstrated that when Re < Rec(D/d) the symmetric states have an asymptotically stable mode of disturbance. However, when Re > Rec(D/d), the symmetric states are unstable to this mode of asymmetric disturbance. It is also shown that when Re > Rec(D/d) the asymmetric states have an asymptotically stable mode of disturbance. The direct numerical simulations are guided by the theoretical approach. In order to improve the numerical simulations, a matching with the asymptotic solution of Moffatt (1964) in the regions around the expansion corners is also included. The dynamics of both small- and large-amplitude disturbances in the flow is described and the transition from symmetric to asymmetric states is demonstrated. The simulations clarify the relationship between the linear stability results and the time-asymptotic behaviour of the flow. The current analyses provide a theoretical foundation for previous experimental and numerical results and shed more light on the transition from symmetric to asymmetric states of a viscous flow in an expanding channel. It is an evolution from a symmetric state, which loses its stability when the Reynolds number of the incoming flow is above Rec(D/d), to a stable asymmetric equilibrium state. The loss of stability is a result of the interaction between the effects of viscous dissipation, the downstream convection of perturbations by the base symmetric flow, and the upstream convection induced by two-dimensional asymmetric disturbances.

Characterization of Surface Roughness Effects on Laminar Flow in Microchannels by Using Fractal Cantor Structures

2009 ◽  
Author(s):  
Chengbin Zhang ◽  
Yongping Chen ◽  
Panpan Fu ◽  
Mingheng Shi
Keyword(s):  
Surface Roughness ◽  
Reynolds Number ◽  
Fractal Dimension ◽  
Pressure Drop ◽  
Laminar Flow ◽  
Flow Direction ◽  
Roughness Effects ◽  
Relative Roughness ◽  
Smooth Channel

The fractal characterization of the topography of rough surfaces by using Cantor set structures is introduced in this paper. Based on the fractal Cantor surface, a model of laminar flow in rough microchannels is developed and numerically analyzed to study the characterization of surface roughness effects on laminar flow. The effects of Reynolds number, relative roughness, and fractal dimension on laminar flow are all discussed. The results indicate that the presence of roughness leads to the form of the detachment, and eddy generation is observed at the shadow of the roughness elements. The pressure drop in the rough channel along the flow direction is no longer in a linear fashion and larger than that in the smooth channel. The fluctuation characteristic of pressure drop along the stream, which is due to the vortex formation at the wall, is found. Differing from the smooth channel, the Poiseuille number for laminar flow in rough microchannels is no longer only dependent on the cross-sectional shape of the channel, but also strongly influenced by the Reynolds number, relative roughness and fractal dimension of the surface.

A study of laminar flow in low aspect ratio lid-driven cavities

2002 ◽  
Vol 29 (3) ◽  
pp. 436-447 ◽  
Author(s):  
Y Yang ◽  
A G Straatman ◽  
R J Martinuzzi ◽  
E K Yanful
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Aspect Ratio ◽  
Numerical Solutions ◽  
Cavity Flow ◽  
Momentum Equation ◽  
Laser Doppler Velocimeter ◽  
Countercurrent Flow ◽  
Two Dimensional ◽  
Low Aspect Ratio

The evolution to fully developed laminar flow in low aspect ratio, two-dimensional, lid-driven cavities has been studied experimentally and numerically. Velocity measurements were made in water in a moving-lid apparatus using a laser Doppler velocimeter (LDV). Numerical solutions for the cavity flow were obtained by solving the two-dimensional mass-momentum equation set in a finite-volume framework. The measured and predicted results were in excellent agreement. Fully developed cavity flow is said to exist when the main regions of the flow field become independent of the aspect ratio. When fully developed conditions prevail, a region of countercurrent flow (CCF) separates the end structures, which are decoupled. The extent of the end regions is shown to grow linearly with increasing Reynolds number Re, based on the lid speed and the cavity height. Consequently, the critical aspect ratio for the onset of fully developed flow is also linearly dependent on Re. Above a critical Reynolds number, Re [Formula: see text] 300, the flow becomes unsteady, and a lower-wall, tertiary vortex appears, which is thought to be associated with the onset of hydrodynamic instability.Key words: lid-driven cavity, laminar flow, shallow water cover, countercurrent flow.

Laminar Flow in a Uniformly Porous Channel

1964 ◽  
Vol 15 (3) ◽  
pp. 299-310 ◽  
Author(s):  
Thein Wah
Keyword(s):  
Differential Equation ◽  
Reynolds Number ◽  
Laminar Flow ◽  
Numerical Solutions ◽  
Large Reynolds Number ◽  
Two Dimensional ◽  
Series Solutions ◽  
Porous Walls ◽  
Linear Differential ◽  
Good Agreement

SummaryThe flow in a two-dimensional channel with porous walls through which fluid is uniformly injected or extracted is considered. Following Berman, a solution is obtained giving a fourth-order non-linear differential equation which depends on a suction Reynolds number R. Numerical solutions of this equation have been obtained. Series solutions of this equation for small and large Reynolds number are given and are shown to give good agreement with the numerical solutions.

scholarly journals Lyapunov dimension of elastic turbulence

2017 ◽  
Vol 822 ◽  
Author(s):  
Emmanuel Lance Christopher VI M. Plan ◽  
Anupam Gupta ◽  
Dario Vincenzi ◽  
John D. Gibbon
Keyword(s):  
Reynolds Number ◽  
Constitutive Model ◽  
Numerical Simulations ◽  
Mathematical Analysis ◽  
Critical Value ◽  
Weissenberg Number ◽  
Direct Numerical Simulations ◽  
Chaotic Behaviour ◽  
Two Dimensional ◽  
Lyapunov Dimension

Low-Reynolds-number polymer solutions exhibit a chaotic behaviour known as ‘elastic turbulence’ when the Weissenberg number exceeds a critical value. The two-dimensional Oldroyd-B model is the simplest constitutive model that reproduces this phenomenon. To make a practical estimate of the resolution scale of the dynamics, one requires the assumption that an attractor of the Oldroyd-B model exists; numerical simulations show that the quantities on which this assumption is based are bounded. We estimate the Lyapunov dimension of this assumed attractor as a function of the Weissenberg number by combining a mathematical analysis of the model with direct numerical simulations.

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