scholarly journals Wave Characteristics of Falling Film on Inclination Plate at Moderate Reynolds Number

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Chuan Lu ◽  
Sheng-Yao Jiang ◽  
Ri-Qiang Duan
Keyword(s):  
Reynolds Number ◽  
Solitary Wave ◽  
Film Flow ◽  
Three Dimensional ◽  
Wave Pattern ◽  
Two Dimensional ◽  
Irregular Wave ◽  
Moderate Reynolds Number ◽  
Pulse Spacing ◽  
Primary Pulse

Falling water film on an inclined plane is studied by shadowgraphy. The ranges of inclination angle and the film Reynolds number are, respectively, up to 21° and 60. Water is used as working fluid. The scenario of wave regime evolution is identified as three distinctive regimes, namely, initial quiescent smooth film flow, two-dimensional regular solitary wave pattern riding on film flow, and three-dimensional irregular wave pattern. Three characteristic parameters of two-dimensional solitary wave pattern, namely, inception length, primary pulse spacing, and propagation velocity, are examined, which are significant in engineering applications for estimation of heat and mass transfer on film flow. The present experimental data are well in agreement with the Koizumi correlations, the deviation from which is limited to 20% and 15%, respectively, for primary pulse spacing and propagation velocity. Through the scrutiny of the present experimental observation, it is concluded that wave evolution on film flow at the moderate Reynolds number is controlled by gravity and drag and the Rayleigh-Taylor instability that occurred on the steep front of primary pulse triggers the disintegration of continuous two-dimensional regular solitary wave pattern into three-dimensional irregular wave pattern.

scholarly journals Controlling the dual cascade of two-dimensional turbulence

2010 ◽  
Vol 668 ◽  
pp. 202-222 ◽  
Author(s):  
M. M. FARAZMAND ◽  
N. K.-R. KEVLAHAN ◽  
B. PROTAS
Keyword(s):  
Reynolds Number ◽  
Energy Spectrum ◽  
Three Dimensional ◽  
Careful Analysis ◽  
Space Structure ◽  
Inertial Range ◽  
Two Dimensional ◽  
Control Approach ◽  
Time Space ◽  
Moderate Reynolds Number

The Kraichnan–Leith–Batchelor (KLB) theory of statistically stationary forced homogeneous isotropic two-dimensional turbulence predicts the existence of two inertial ranges: an energy inertial range with an energy spectrum scaling of k−5/3, and an enstrophy inertial range with an energy spectrum scaling of k−3. However, unlike the analogous Kolmogorov theory for three-dimensional turbulence, the scaling of the enstrophy range in the two-dimensional turbulence seems to be Reynolds-number-dependent: numerical simulations have shown that as Reynolds number tends to infinity, the enstrophy range of the energy spectrum converges to the KLB prediction, i.e. E ~ k−3. The present paper uses a novel optimal control approach to find a forcing that does produce the KLB scaling of the energy spectrum in a moderate Reynolds number flow. We show that the time–space structure of the forcing can significantly alter the scaling of the energy spectrum over inertial ranges. A careful analysis of the optimal forcing suggests that it is unlikely to be realized in nature, or by a simple numerical model.

Direct numerical simulations of bubbly flows Part 2. Moderate Reynolds number arrays

1999 ◽  
Vol 385 ◽  
pp. 325-358 ◽  
Author(s):  
ASGHAR ESMAEELI ◽  
GRÉTAR TRYGGVASON
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Direct Numerical Simulations ◽  
Dimensional System ◽  
Two Dimensional ◽  
Reynolds Stresses ◽  
Bubble Distribution ◽  
Moderate Reynolds Number

Direct numerical simulations of the motion of two- and three-dimensional finite Reynolds number buoyant bubbles in a periodic domain are presented. The full Navier–Stokes equations are solved by a finite difference/front tracking method that allows a fully deformable interface between the bubbles and the ambient fluid and the inclusion of surface tension. The rise Reynolds numbers are around 20–30 for the lowest volume fraction, but decrease as the volume fraction is increased. The rise of a regular array of bubbles, where the relative positions of the bubbles are fixed, is compared with the evolution of a freely evolving array. Generally, the freely evolving array rises slower than the regular one, in contrast to what has been found earlier for low Reynolds number arrays. The structure of the bubble distribution is examined and it is found that while the three-dimensional bubbles show a tendency to line up horizontally, the two-dimensional bubbles are nearly randomly distributed. The effect of the number of bubbles in each period is examined for the two-dimensional system and it is found that although the rise Reynolds number is nearly independent of the number of bubbles, the velocity fluctuations in the liquid (the Reynolds stresses) increase with the size of the system. While some aspects of the fully three-dimensional flows, such as the reduction in the rise velocity, are predicted by results for two-dimensional bubbles, the structure of the bubble distribution is not. The magnitude of the Reynolds stresses is also greatly over-predicted by the two-dimensional results.

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.

Aerodynamics of a two-dimensional bluff body with the cross-section of a train

2020 ◽  
Vol 23 (12) ◽  
pp. 2679-2693 ◽  
Author(s):  
Huan Li ◽  
Xuhui He ◽  
Hanfeng Wang ◽  
Si Peng ◽  
Shuwei Zhou ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Large Amplitude ◽  
High Speed ◽  
Bluff Body ◽  
Mean Amplitude ◽  
Two Dimensional ◽  
Aerodynamic Forces ◽  
Moderate Reynolds Number ◽  
Amplitude Mode

Experiments on the aerodynamics of a two-dimensional bluff body simplified from a China high-speed train in crosswinds were carried out in a wind tunnel. Effects of wind angle of attack α varying in [−20°, 20°] were investigated at a moderate Reynolds number Re = 9.35 × 104 (based on the height of the model). Four typical behaviors of aerodynamics were identified. These behaviors are attributed to the flow structure around the upper and lower halves of the model changing from full to intermittent reattachment, and to full separation with a variation in α. An alternate transition phenomenon, characterized by an alteration between large- and small-amplitude aerodynamic fluctuations, was detected. The frequency of this alteration is about 1/10 of the predominant vortex shedding. In the intervals of the large-amplitude behavior, aerodynamic forces fluctuate periodically with a strong span-wise coherence, which are caused by the anti-symmetric vortex shedding along the stream-wise direction. On the contrary, the aerodynamic forces fluctuating at small amplitudes correspond to a weak span-wise coherence, which are ascribed to the symmetric vortex shedding from the upper and lower halves of the model. Generally, the mean amplitude of the large-amplitude mode is 3 times larger than that of the small one. Finally, the effects of Reynolds number were examined within Re = [9.35 × 104, 2.49 × 105]. Strong Reynolds number dependence was observed on the model with two rounded upper corners.

Two- and Three-Dimensional Simulations of the Flow Around a Cylinder Fitted With Strakes

2012 ◽  
Author(s):  
Bruno S. Carmo ◽  
Rafael S. Gioria ◽  
Ivan Korkischko ◽  
Cesar M. Freire ◽  
Julio R. Meneghini
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Free Stream ◽  
Three Dimensional ◽  
The Body ◽  
Vortex Wake ◽  
Two Dimensional ◽  
Flow Around A Cylinder ◽  
Three Dimensional Simulations ◽  
Angle Of Rotation

Two- and three-dimensional simulations of the flow around straked cylinders are presented. For the two-dimensional simulations we used the Spectral/hp Element Method, and carried out simulations for five different angles of rotation of the cylinder with respect to the free stream. Fixed and elastically-mounted cylinders were tested, and the Reynolds number was kept constant and equal to 150. The results were compared to those obtained from the simulation of the flow around a bare cylinder under the same conditions. We observed that the two-dimensional strakes are not effective in suppressing the vibration of the cylinders, but also noticed that the responses were completely different even with a slight change in the angle of rotation of the body. The three-dimensional results showed that there are two mechanisms of suppression: the main one is the decrease in the vortex shedding correlation along the span, whilst a secondary one is the vortex wake formation farther downstream.

Flow past a rotationally oscillating cylinder

2013 ◽  
Vol 735 ◽  
pp. 307-346 ◽  
Author(s):  
S. Kumar ◽  
C. Lopez ◽  
O. Probst ◽  
G. Francisco ◽  
D. Askari ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Three Dimensional ◽  
Far Field ◽  
Two Dimensional ◽  
Flow Past ◽  
Vortex Shedding Frequency ◽  
Shedding Frequency ◽  
Flow Visualizations ◽  
Hydrogen Bubble Technique

AbstractFlow past a circular cylinder executing sinusoidal rotary oscillations about its own axis is studied experimentally. The experiments are carried out at a Reynolds number of 185, oscillation amplitudes varying from $\mathrm{\pi} / 8$ to $\mathrm{\pi} $, and at non-dimensional forcing frequencies (ratio of the cylinder oscillation frequency to the vortex-shedding frequency from a stationary cylinder) varying from 0 to 5. The diagnostic is performed by extensive flow visualization using the hydrogen bubble technique, hot-wire anemometry and particle-image velocimetry. The wake structures are related to the velocity spectra at various forcing parameters and downstream distances. It is found that the phenomenon of lock-on occurs in a forcing frequency range which depends not only on the amplitude of oscillation but also the downstream location from the cylinder. The experimentally measured lock-on diagram in the forcing amplitude and frequency plane at various downstream locations ranging from 2 to 23 diameters is presented. The far-field wake decouples, after the lock-on at higher forcing frequencies and behaves more like a regular Bénard–von Kármán vortex street from a stationary cylinder with vortex-shedding frequency mostly lower than that from a stationary cylinder. The dependence of circulation values of the shed vortices on the forcing frequency reveals a decay character independent of forcing amplitude beyond forcing frequency of ${\sim }1. 0$ and a scaling behaviour with forcing amplitude at forcing frequencies ${\leq }1. 0$. The flow visualizations reveal that the far-field wake becomes two-dimensional (planar) near the forcing frequencies where the circulation of the shed vortices becomes maximum and strong three-dimensional flow is generated as mode shape changes in certain forcing parameter conditions. It is also found from flow visualizations that even at higher Reynolds number of 400, forcing the cylinder at forcing amplitudes of $\mathrm{\pi} / 4$ and $\mathrm{\pi} / 2$ can make the flow field two-dimensional at forcing frequencies greater than ${\sim }2. 5$.

The Three-Dimensional Turbulent Boundary Layer on an Infinite Yawed Wing

1971 ◽  
Vol 22 (4) ◽  
pp. 346-362 ◽  
Author(s):  
J. F. Nash ◽  
R. R. Tseng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Lift Coefficient ◽  
Three Dimensional ◽  
Numerical Representation ◽  
Two Dimensional ◽  
Incompressible Turbulent Boundary Layer ◽  
Displacement Thickness ◽  
Attachment Line

SummaryThis paper presents the results of some calculations of the incompressible turbulent boundary layer on an infinite yawed wing. A discussion is made of the effects of increasing lift coefficient, and increasing Reynolds number, on the displacement thickness, and on the magnitude and direction of the skin friction. The effects of the state of the boundary layer (laminar or turbulent) along the attachment line are also considered.A study is made to determine whether the behaviour of the boundary layer can adequately be predicted by a two-dimensional calculation. It is concluded that there is no simple way to do this (as is provided, in the laminar case, by the principle of independence). However, with some modification, a two-dimensional calculation can be made to give an acceptable numerical representation of the chordwise components of the flow.

Three-dimensional instabilities in the boundary-layer flow over a long rectangular plate

2011 ◽  
Vol 681 ◽  
pp. 411-433 ◽  
Author(s):  
HEMANT K. CHAURASIA ◽  
MARK C. THOMPSON
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Vortical Flow ◽  
Forced Flow ◽  
Recirculation Region ◽  
Two Dimensional ◽  
Optimal Perturbation ◽  
Dimensional Instability

A detailed numerical study of the separating and reattaching flow over a square leading-edge plate is presented, examining the instability modes governing transition from two- to three-dimensional flow. Under the influence of background noise, experiments show that the transition scenario typically is incompletely described by either global stability analysis or the transient growth of dominant optimal perturbation modes. Instead two-dimensional transition effectively can be triggered by the convective Kelvin–Helmholtz (KH) shear-layer instability; although it may be possible that this could be described alternatively in terms of higher-order optimal perturbation modes. At least in some experiments, observed transition occurs by either: (i) KH vortices shedding downstream directly and then almost immediately undergoing three-dimensional transition or (ii) at higher Reynolds numbers, larger vortical structures are shed that are also three-dimensionally unstable. These two paths lead to distinctly different three-dimensional arrangements of vortical flow structures. This paper focuses on the mechanisms underlying these three-dimensional transitions. Floquet analysis of weakly periodically forced flow, mimicking the observed two-dimensional quasi-periodic base flow, indicates that the two-dimensional vortex rollers shed from the recirculation region become globally three-dimensionally unstable at a Reynolds number of approximately 380. This transition Reynolds number and the predicted wavelength and flow symmetries match well with those of the experiments. The instability appears to be elliptical in nature with the perturbation field mainly restricted to the cores of the shed rollers and showing the spatial vorticity distribution expected for that instability type. Indeed an estimate of the theoretical predicted wavelength is also a good match to the prediction from Floquet analysis and theoretical estimates indicate the growth rate is positive. Fully three-dimensional simulations are also undertaken to explore the nonlinear development of the three-dimensional instability. These show the development of the characteristic upright hairpins observed in the experimental dye visualisations. The three-dimensional instability that manifests at lower Reynolds numbers is shown to be consistent with an elliptic instability of the KH shear-layer vortices in both symmetry and spanwise wavelength.

scholarly journals Linear stability of confined flow around a 180-degree sharp bend

2017 ◽  
Vol 822 ◽  
pp. 813-847 ◽  
Author(s):  
Azan M. Sapardi ◽  
Wisam K. Hussam ◽  
Alban Pothérat ◽  
Gregory J. Sheard
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Base Flow ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
The Stability

This study seeks to characterise the breakdown of the steady two-dimensional solution in the flow around a 180-degree sharp bend to infinitesimal three-dimensional disturbances using a linear stability analysis. The stability analysis predicts that three-dimensional transition is via a synchronous instability of the steady flows. A highly accurate global linear stability analysis of the flow was conducted with Reynolds number $\mathit{Re}<1150$ and bend opening ratio (ratio of bend width to inlet height) $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 5$. This range of $\mathit{Re}$ and $\unicode[STIX]{x1D6FD}$ captures both steady-state two-dimensional flow solutions and the inception of unsteady two-dimensional flow. For $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 1$, the two-dimensional base flow transitions from steady to unsteady at higher Reynolds number as $\unicode[STIX]{x1D6FD}$ increases. The stability analysis shows that at the onset of instability, the base flow becomes three-dimensionally unstable in two different modes, namely a spanwise oscillating mode for $\unicode[STIX]{x1D6FD}=0.2$ and a spanwise synchronous mode for $\unicode[STIX]{x1D6FD}\geqslant 0.3$. The critical Reynolds number and the spanwise wavelength of perturbations increase as $\unicode[STIX]{x1D6FD}$ increases. For $1<\unicode[STIX]{x1D6FD}\leqslant 2$ both the critical Reynolds number for onset of unsteadiness and the spanwise wavelength decrease as $\unicode[STIX]{x1D6FD}$ increases. Finally, for $2<\unicode[STIX]{x1D6FD}\leqslant 5$, the critical Reynolds number and spanwise wavelength remain almost constant. The linear stability analysis also shows that the base flow becomes unstable to different three-dimensional modes depending on the opening ratio. The modes are found to be localised near the reattachment point of the first recirculation bubble.

Stability of flow in a channel with longitudinal grooves

2014 ◽  
Vol 757 ◽  
pp. 613-648 ◽  
Author(s):  
H. V. Moradi ◽  
J. M. Floryan
Keyword(s):  
Reynolds Number ◽  
Small Amplitude ◽  
Arbitrary Shape ◽  
Critical Reynolds Number ◽  
Critical Role ◽  
Three Dimensional ◽  
Travelling Wave ◽  
Two Dimensional ◽  
Wave Instability ◽  
Long Wavelength

AbstractThe travelling wave instability in a channel with small-amplitude longitudinal grooves of arbitrary shape has been studied. The disturbance velocity field is always three-dimensional with disturbances which connect to the two-dimensional waves in the limit of zero groove amplitude playing the critical role. The presence of grooves destabilizes the flow if the groove wavenumber $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\beta $ is larger than $\beta _{tran}\approx 4.22$, but stabilizes the flow for smaller $\beta $. It has been found that $\beta _{tran}$ does not depend on the groove amplitude. The dependence of the critical Reynolds number on the groove amplitude and wavenumber has been determined. Special attention has been paid to the drag-reducing long-wavelength grooves, including the optimal grooves. It has been demonstrated that such grooves slightly increase the critical Reynolds number, i.e. such grooves do not cause an early breakdown into turbulence.

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