Drop fall-off from pendent rivulets

1997 ◽  
Vol 338 ◽  
pp. 173-201 ◽  
Author(s):  
ALEXANDRA INDEIKINA ◽  
IGOR VERETENNIKOV ◽  
HSUEH-CHIA CHANG
Keyword(s):  
Critical Value ◽  
Finite Amplitude ◽  
Mean Flow ◽  
Capillary Length ◽  
Lubrication Equation ◽  
Long Wave ◽  
Static Contact ◽  
Axial Curvature ◽  
Good Agreement ◽  
Matched Asymptotic Analysis

Drops fall off a viscous pendent rivulet on the underside of a plane when the inclination angle θ, measured with respect to the horizontal, is below a critical value θc. We estimate this θc by studying the existence of finite-amplitude drop solutions to a long-wave lubrication equation. Through a partial matched asymptotic analysis, we establish that fall-off occurs by two distinct mechanisms. For θ>ϕ, where ϕ is the static contact angle, a jet mechanism results when a mean-flow steepening effect cannot provide sufficient axial curvature to counter gravity. This fall-off mechanism occurs if the rivulet width B, which is normalized with respect to the capillary length H=(σ/ρg cosθ)1/2, exceeds a critical value defined by β=−cosB>1/4. For θ<ϕ, the normal azimuthal curvature is the dominant force against fall-off and the azimuthal capillary force. The corresponding critical condition is found to be 1.5β1/6>tanθ/tanϕ. Both criteria are in good agreement with our experimental data.

Stability of plane Poiseuille flow to periodic disturbances of finite amplitude

1969 ◽  
Vol 39 (3) ◽  
pp. 611-627 ◽  
Author(s):  
C. L. Pekeris ◽  
B. Shkoller
Keyword(s):  
Poiseuille Flow ◽  
Subsequent Development ◽  
Critical Value ◽  
Finite Amplitude ◽  
Higher Order ◽  
Initial Disturbance ◽  
Plane Poiseuille Flow ◽  
Mean Flow ◽  
Linear Ordinary Differential Equations ◽  
Sommerfeld Equation

A disturbance of finite amplitude λ, which is periodic in the direction of the axis of the channel, is superimposed on plane Poiseuille flow, and the subsequent development of the disturbance is studied. The disturbance is represented by an expansion in the eigenfunctions of the Orr-Sommerfeld equation with coefficients which are functions of the time, and an accurate numerical solution of the truncated system of non-linear ordinary differential equations for the coefficients is obtained.It is found that even for Reynolds numbers R less than the critical value Rc, the flow breaks down when λ exceeds a critical value λc(R). This is shown in figure 11 for the case when the initial disturbance is represented by the first mode of the Orr-Sommerfeld equation. The development of this type of disturbance is illustrated in figures 1, 3 and 13 and, for the case of a higher-order mode initial disturbance, in figure 14. Near the time of breakdown, the curvature of the modified mean flow changes sign (figure 15), but a disturbance may die down even after a reversal in the sign of the curvature has taken place (see figure 2).The stability of plane Poiseuille flow to disturbances of finite amplitude is affected by the characteristics of the higher-order modes of the Orr-Sommerfeld equation. As shown in figures 4, 10, and 12, and in figures 5, 6, and 7, these modes are either of a ‘boundary type’, characteristic of the region near the wall, or of an ‘interior type’, characteristic of the centre of the channel. The modes in the transition zone, where the two types merge, are easily amplified through mutual constructive interference, even though individually they have high damping coefficients. It is these transition modes which are mainly responsible for the breakdown through finite amplitude effects.

Long-wave instabilities of heated falling films: two-dimensional theory of uniform layers

1991 ◽  
Vol 230 ◽  
pp. 117-146 ◽  
Author(s):  
S. W. Joo ◽  
S. H. Davis ◽  
S. G. Bankoff
Keyword(s):  
Evolution Equation ◽  
Wave Breaking ◽  
Finite Amplitude ◽  
Two Dimensional ◽  
Mean Flow ◽  
Dimensional Theory ◽  
Inclined Plate ◽  
Long Wave ◽  
Wave Instabilities ◽  
Gravity Surface

A layer of volatile viscous liquid drains down a uniformly heated inclined plate. Long-wave instabilities of the uniform film are studied by deriving an evolution equation for two-dimensional disturbances. This equation incorporates viscosity, gravity, surface tension, thermocapillarity, and evaporation eifects. The linear theory derived from this describes the competition among the instabilities. Numerical solution of the evolution equation describes the finite-amplitude behaviour that determines the propensity for dryout of the film. Among the phenomena that appear are the tendency to wave breaking, the creation of secondary structures, and the preemption of dryout by mean flow.

Experimental and Theoretical Investigation of the Supersonic Boundary Layer Stability on the Swept Wing

2008 ◽  
Vol 3 (3) ◽  
pp. 34-38
Author(s):  
Sergey A. Gaponov ◽  
Yuri G. Yermolaev ◽  
Aleksandr D. Kosinov ◽  
Nikolay V. Semionov ◽  
Boris V. Smorodsky
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Leading Edge ◽  
Supersonic Boundary Layer ◽  
Mean Flow ◽  
Swept Wing ◽  
Wing Model ◽  
Dimensional Boundary ◽  
The Stability ◽  
Good Agreement

Theoretical and an experimental research results of the disturbances development in a swept wing boundary layer are presented at Mach number М = 2. In experiments development of natural and small amplitude controllable disturbances downstream was studied. Experiments were carried out on a swept wing model with a lenticular profile at a zero attack angle. The swept angle of a leading edge was 40°. Wave parameters of moving disturbances were determined. In frames of the linear theory and an approach of the local self-similar mean flow the stability of a compressible three-dimensional boundary layer is studied. Good agreement of the theory with experimental results for transversal scales of unstable vertices of the secondary flow was obtained. However the calculated amplification rates differ from measured values considerably. This disagreement is explained by the nonlinear processes observed in experiment

Stability and collapse of holes in liquid layers

2018 ◽  
Vol 855 ◽  
pp. 1130-1155 ◽  
Author(s):  
Cunjing Lv ◽  
Michael Eigenbrod ◽  
Steffen Hardt
Keyword(s):  
Liquid Film ◽  
Power Laws ◽  
Theoretical Models ◽  
Liquid Volume ◽  
Capillary Length ◽  
Minimum Thickness ◽  
The Stability ◽  
Film Profile ◽  
Hole Closure ◽  
Good Agreement

We investigate experimentally and theoretically the stability and collapse of holes in liquid layers on bounded substrates with various wettabilities. It is shown that for a liquid layer with a thickness of the order of the capillary length, a stable hole exists when the hole diameter is bigger than a critical value $d_{c}$. Consequently, a further increase of the liquid volume causes the hole to collapse. It is found that$d_{c}$increases with the size of the container, but its dependence on the contact angle is very weak. The experimental results are compared with theory, and good agreement is obtained. Moreover, we present investigations of the dynamics of the hole and the evolution of the liquid film profile after the collapse. The diameter of the hole during collapse and the minimum thickness of the liquid film shortly after the collapse obey different power laws with time. Simple theoretical models are developed which indicate that the collapse of the hole is triggered by surface tension and the subsequent closure process results from inertia, whereas the growth of the liquid column after hole closure results from the balance between the capillary force and inertia. Corresponding scaling coefficients are determined.

Propagation of finite-amplitude long-wave disturbances in aerosols

1981 ◽  
Vol 21 (5) ◽  
pp. 602-606 ◽  
Author(s):  
A. A. Borisov ◽  
A. F. Vakhgel't ◽  
V. E. Nakoryakov
Keyword(s):  
Finite Amplitude ◽  
Wave Disturbances ◽  
Long Wave

scholarly journals Stability and Sensitivity Analysis of Hydrodynamic Instabilities in Industrial Swirled Injection Systems

2017 ◽  
Author(s):  
Thomas L. Kaiser ◽  
Thierry Poinsot ◽  
Kilian Oberleithner
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Vortex Core ◽  
Large Eddy Simulations ◽  
Mode Shapes ◽  
Mean Flow ◽  
Precessing Vortex Core ◽  
Large Eddy ◽  
Good Agreement

The hydrodynamic instability in an industrial, two-staged, counter-rotative, swirled injector of highly complex geometry is under investigation. Large eddy simulations show that the complicated and strongly nonparallel flow field in the injector is superimposed by a strong precessing vortex core. Mean flow fields of large eddy simulations, validated by experimental particle image velocimetry measurements are used as input for both local and global linear stability analysis. It is shown that the origin of the instability is located at the exit plane of the primary injector. Mode shapes of both global and local linear stability analysis are compared to a dynamic mode decomposition based on large eddy simulation snapshots, showing good agreement. The estimated frequencies for the instability are in good agreement with both the experiment and the simulation. Furthermore, the adjoint mode shapes retrieved by the global approach are used to find the best location for periodic forcing in order to control the precessing vortex core.

scholarly journals Numerical Bifurcation Analysis of a Film Flowing over a Patterned Surface through Enhanced Lubrication Theory

Fluids ◽  
2021 ◽  
Vol 6 (11) ◽  
pp. 405
Author(s):  
Nicola Suzzi ◽  
Giulio Croce
Keyword(s):  
Contact Angle ◽  
Bifurcation Analysis ◽  
Dynamic Contact Angle ◽  
Flow Characteristics ◽  
Dynamic Contact ◽  
Contact Angles ◽  
Inclined Plate ◽  
Lubrication Equation ◽  
Static Contact ◽  
Numerical Bifurcation

The bifurcation analysis of a film falling down an hybrid surface is conducted via the numerical solution of the governing lubrication equation. Instability phenomena, that lead to film breakage and growth of fingers, are induced by multiple contamination spots. Contact angles up to 75∘ are investigated due to the full implementation of the free surface curvature, which replaces the small slope approximation, accurate for film slope lower than 30∘. The dynamic contact angle is first verified with the Hoffman–Voinov–Tanner law in case of a stable film down an inclined plate with uniform surface wettability. Then, contamination spots, characterized by an increased value of the static contact angle, are considered in order to induce film instability and several parametric computations are run, with different film patterns observed. The effects of the flow characteristics and of the hybrid pattern geometry are investigated and the corresponding bifurcation diagram with the number of observed rivulets is built. The long term evolution of induced film instabilities shows a complex behavior: different flow regimes can be observed at the same flow characteristics under slightly different hybrid configurations. This suggest the possibility of controlling the rivulet/film transition via a proper design of the surfaces, thus opening the way for relevant practical application.

scholarly journals INTERACTION OF IDEALIZED URBAN INFRASTRUCTURE AND LONG WAVES DURING RUN-UP AND ON-LAND FLOW PROCESS IN COASTAL REGIONS

2012 ◽  
Vol 1 (33) ◽  
pp. 18 ◽  
Author(s):  
Nils Goseberg ◽  
Torsten Schlurmann
Keyword(s):  
Shock Wave ◽  
Urban Infrastructure ◽  
Coastal Regions ◽  
Flow Process ◽  
Long Wave ◽  
Roughness Elements ◽  
Shock Wave Generation ◽  
Run Up ◽  
Sloping Beach ◽  
Good Agreement

This paper reports experimental results of long wave run-up climbing up a 1:40 sloping beach. The resulting maximum run-up is compared with analytical results and a good agreement is found for single sinusoidal waves with uniform wave period and varying amplitude. Subsequently, the interaction with macro-roughness elements on the beach is investigated for different long-shore obstruction ratios. The reduction in wave run-up is expressed by means of a nomogram relating the wave run-up without macro-roughness elements present to those cases where on-land flow is modified by macro-roughness. The presented results mainly focus on a non-staggered and non-rotated macro-roughness configuration. In addition to the run-up reduction, surface elevation profiles on the shore are presented, that address the shock wave generation when the wave tongue approaches the first row of macro-roughness elements.

Abstract P531: Cerebral Blood Flow Analysis Using Flow Wire Measurements and CFD Analysis

Stroke ◽  
2021 ◽  
Vol 52 (Suppl_1) ◽  
Author(s):  
Aichi Chien ◽  
Huy Dinh ◽  
Viktor Szeder ◽  
Fernando Vinuela
Keyword(s):  
Blood Flow ◽  
Cerebral Blood Flow ◽  
Flow Velocity ◽  
Cfd Simulation ◽  
Cfd Analysis ◽  
Flow Data ◽  
Velocity Data ◽  
Mean Flow ◽  
Good Agreement ◽  
Cerebral Vascular

Introduction: Clinical reports show that cerebral blood flow conditions are indicative of cerebral vascular disease. While methods for characterizing cerebral vascular flow have been extensively reported in the past, comparative analyses between direct flow measurements (DM) and computational flow dynamic (CFD) analysis remain limited. We hypothesize that flow data can be reliably measured both directly and through CFD in normal vessels. Methods: A left heart replicator was used as a realistic cardiac pump which maintained systolic pressure at 120 mmHg and diastolic pressure at 80 mmHg. A stenotic model with 50% stenosis for the ICA was connected to the replicator. A ComboWire was used for DM and recorded flow pressure and velocity. CFD was used to study flow. Results: In areas at the proximal end of the stenosis, the pressure and flow velocity derived from DM and CFD were in good agreement. At the end of systole and diastole, DM pressure were 145.42 mmHg and 73.53 mmHg, respectively. CFD simulation for the same system obtained the pressure at the end of systole and diastole of 147.16 mmHg and 74.64 mmHg, respectively. The velocity data collected from DM was at 15.40 cm/s and 7.74 cm/s for systolic flow and mean flow velocity. CFD measured flow was 17.85 cm/s and 11.37 cm/s, respectively. In areas at the distal end of the stenosis, pressure data showed good agreement between DM and CFD analysis. The DM were 138 and 70.81 mmHg at the end of systole and diastole, respectively; CFD simulation yielded 145.95 and 74.51 mmHg, respectively. Variations in the velocity data were observed at this location (Fig, pink arrows). Conclusion: DM of pressure showed good agreement with CFD simulation in all areas of the vessel. DM of velocity using the flow wire were highly affected by location of the measurement. CFD analysis can provide more consistent flow data for flow information collection along the vasculature.

scholarly journals Self-consistent triple decomposition of the turbulent flow over a backward-facing step under finite amplitude harmonic forcing

2019 ◽  
Vol 475 (2225) ◽  
pp. 20190018
Author(s):  
E. Yim ◽  
P. Meliga ◽  
F. Gallaire
Keyword(s):  
Turbulent Flow ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Backward Facing Step ◽  
Eddy Viscosity Model ◽  
Coherent Interaction ◽  
Self Consistent ◽  
The Mean

We investigate the saturation of harmonically forced disturbances in the turbulent flow over a backward-facing step subjected to a finite amplitude forcing. The analysis relies on a triple decomposition of the unsteady flow into mean, coherent and incoherent components. The coherent–incoherent interaction is lumped into a Reynolds averaged Navier–Stokes (RANS) eddy viscosity model, and the mean–coherent interaction is analysed via a semi-linear resolvent analysis building on the laminar approach by Mantič-Lugo & Gallaire (2016 J. Fluid Mech. 793 , 777–797. ( doi:10.1017/jfm.2016.109 )). This provides a self-consistent modelling of the interaction between all three components, in the sense that the coherent perturbation structures selected by the resolvent analysis are those whose Reynolds stresses force the mean flow in such a way that the mean flow generates exactly the aforementioned perturbations, while also accounting for the effect of the incoherent scale. The model does not require any input from numerical or experimental data, and accurately predicts the saturation of the forced coherent disturbances, as established from comparison to time-averages of unsteady RANS simulation data.

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