Volume 18, Issue 1, January 2006
Index of content:
- Interfacial Flows
18(2006); http://dx.doi.org/10.1063/1.2137358View Description Hide Description
Oscillations of a nominally hemispherical, inviscid drop on a solid plate are considered accounting for the contact line dynamics. Hocking boundary conditions hold on the contact line: the velocity of the contact line is proportional to the deviation of the contact angle from its equilibrium value. Natural oscillations of a drop are studied, and both eigenfrequencies and damping ratios are determined for the axisymmetric modes. The linear oscillations caused by normal vibration of the substrate are considered. Well-pronounced resonant phenomena are revealed. The nonlinear oscillations of a drop are studied.
18(2006); http://dx.doi.org/10.1063/1.2163810View Description Hide Description
Gravity-driven filmflow along an inclined periodic wall with transverse rectangular corrugations is studied experimentally. The effect of corrugation steepness is considered in detail and an interesting contrast emerges between properties of the flow that are apparently independent of corrugation steepness and properties that are strongly affected by it. The steady interaction between the wall and the flow leads to a statically deformed free surface, whose amplitude is independent of the corrugation heights tested. Beyond the maximum steady free-surface amplitude, a three-dimensional pattern is established (consisting of transverse arrays of depressions along corrugation valleys), again at conditions independent of corrugation height. On the contrary, steep corrugations expand significantly the stable region of steady flow. Also, fully developed traveling waves (emerging from ambient noise under unsteady conditions) are significantly larger and more regular than under the same conditions along a flat wall. This difference is attributed to the continuous interaction of traveling pulses with the steadily deformed substrate.
Transient and steady-state amplitudes of resonant three-dimensional sloshing in a square base tank with a finite fluid depth18(2006); http://dx.doi.org/10.1063/1.2160522View Description Hide Description
An adaptive asymptotic nonlinear modal system is used for systematic quantification of three-dimensional steady-state resonant sloshing in a square base tank with a finite fill depth. The depth/breadth ratios are . The tank is laterally excited with frequency close to the lowest natural frequency. The main emphasis is on the “swirling” wave regime and its special features, e.g., stability, feedback of higher modes, and regular and irregular switch of the apparent direction of rotation. Theoretical results are validated for both steady-state solutions and “beating” that does not die out in experimental investigations. Frequency domains with no stable steady-state waves and occurrence of “chaotic” waves are discussed.
18(2006); http://dx.doi.org/10.1063/1.2166642View Description Hide Description
Thermocapillary instability is one of the primary causes of a spontaneous rupture of thin films on heated walls. The film rupture may lead to an appearance of uncontrolled dry patches that significantly deteriorate the heat and mass transfer. In the present paper the thermocapillarity-induced film flow on a microstructured wall is studied in the framework of the long-wave theory. When the wall is heated or cooled, the solution predicts a film deformation caused by thermocapillarity. The linear stability analysis shows that the films on heated microstructured walls are less stable to the long-wave disturbances compared to the films on flat walls. The time-dependent film evolution is simulated and the effect of the wall structure on the film thinning and rupture is analyzed. It is shown that the wall topography exerts a profound effect on the dynamics of the film deformation and rupture, as well as on the size and the location of the dry patches. The full-scale direct volume-of-fluid simulations are used to verity the predictions of the long-wave theory. Good agreement is found for the small ratios between the groove depth and period. The agreement is further improved by including the effect of the convection heat transfer into the long-wave model.
- Viscous and Non-Newtonian Flows
18(2006); http://dx.doi.org/10.1063/1.2163913View Description Hide Description
Reoriented duct flows of generalized Newtonian fluids are an idealization of non-Newtonian fluid flow in industrial in-line mixers. Based on scaling analysis and computation we find that non-Newtonian duct flows have several limit behaviors, in the sense that such flows can become (nearly) independent of one or more of the rheological and dynamical control parameters, simplifying the general flow and mixing problem. These limit flows give several levels of modeling complexity to the full problem of non-Newtonian duct flow. We describe the sets of simplified flowmodels and their corresponding regions of validity. This flow-model decomposition captures the essential rheological and dynamical characteristics of the reoriented duct flows and enables a more efficient and systematic study and design of flow and mixing of non-Newtonian fluids in ducts. Key aspects of the flow-model decomposition are demonstrated via a specific, but representative, duct flow.
18(2006); http://dx.doi.org/10.1063/1.2164475View Description Hide Description
The mass transport of a pulsatile free-stream flow past a single circular cylinder is investigated as a building block for an artificial lung device. The free stream far from the cylinder is represented by a time-periodic (sinusoidal) component superimposed on a steady velocity. The dimensionless parameters of interest are the steady Reynolds number (Re), Womersley parameter , sinusoidal amplitude , and the Schmidt number . The ranges investigated in this study are , , , and . A pair of vortices downstream of the cylinder is observed in almost all cases investigated. These vortices oscillate in size and strength as and are varied. For , where , the vortex is always attached to the cylinder (persistent); while for , the vortex is attached to the cylinder only during part of a time cycle (intermittent). The time-averaged Sherwood number, , is found to be largely influenced by the steady Reynolds number, increasing approximately as . For , is less than the steady ( , ) value and decreases with increasing . For and , is greater than the steady value and increases with increasing . These qualitatively opposite effects of pulsatility are discussed in terms of quasisteady versus unsteady transport. The maximum increase over steady transport due to pulsatility varies between 14.4% and 20.9% for , , and .
- Particulate, Multiphase, and Granular Flows
18(2006); http://dx.doi.org/10.1063/1.2166125View Description Hide Description
The hydrodynamic interaction of two neutrally buoyant porous aggregates is investigated under creeping flow conditions for the case where the undisturbed velocity of the surrounding flow field is a linear function of position. In this framework, the relative velocity between two aggregates is given by the deformation of the undisturbed flow expressed through the rate of strain and the angular velocity of the flow field, and by two flow-independent hydrodynamic functions, typically referred to as and , which account for the disturbance of the flow field due to the presence of the particles [G. K. Batchelor and J. T. Green, J. Fluid Mech.56, 375 (1972)]. In the present paper, the analysis of the hydrodynamic interaction that is known for the case of two impermeable, solid particles is extended to the case of porous aggregates by applying Brinkman’s equation to describe the flow within the aggregates. A reflection scheme is applied to calculate and and the obtained expressions are applied to interpret the orthokinetic aggregation of aggregates in diluted suspensions, where the collision frequency is computed using the method of relative trajectories of a pair of aggregates.
- Laminar Flows
18(2006); http://dx.doi.org/10.1063/1.2148993View Description Hide Description
The effect of topography on the free surface and solvent concentration profiles of an evaporating thin film of liquid flowing down an inclined plane is considered. The liquid is assumed to be composed of a resin dissolved in a volatile solvent with the associated solvent concentration equation derived on the basis of the well-mixed approximation. The dynamics of the film is formulated as a lubrication approximation and the effect of a composition-dependent viscosity is included in the model. The resulting time-dependent, nonlinear, coupled set of governing equations is solved using a full approximation storage multigrid method. The approach is first validated against a closed-form analytical solution for the case of a gravity-driven, evaporating thin film flowing down a flat substrate. Analysis of the results for a range of topography shapes reveal that although a full-width, spanwise topography such as a step-up or a step-down does not affect the composition of the film, the same is no longer true for the case of localized topography, such as a peak or a trough, for which clear nonuniformities of the solvent concentration profile can be observed in the wake of the topography.
18(2006); http://dx.doi.org/10.1063/1.2158427View Description Hide Description
Comparison of recent experimental results for flow-induced drop coalescence[H. Yang, C. C. Park, Y. T. Hu et al. , “The coalescence of two equal-sized drops in a two-dimensional linear flow,” Phys. Fluids13, 1087 (Year: 2001)] with existing theory provides the motivation for an examination of the theory. Specifically, for head-on collisions, the experiments show a plateau in the dependence of drainage time versus capillary number at low capillary number that could not be explained by either the existing scaling analysis or the existing thin-film theory of the film drainage process previously described in the pioneering work of Davis and co-workers [S. G. Yiantsios and R. H. Davis, “Close approach and deformation of two viscous drops due to gravity and van der Waals forces,” J. Colloid Interface Sci.144, 412 (Year: 1991); R. H. Davis, J. A. Schonberg, and J. M. Rallison, “The lubrication force between two viscous drops,” Phys. Fluids A1, 77 (Year: 1989); M. A. Rother, A. Z. Zinchenko, and R. H. Davis, “Buoyancy-driven coalescence of slightly deformable drops,” J. Fluid Mech.346, 117 (Year: 1997);S. G. Yiantsios and R. H. Davis, “On the buoyancy-driven motion of a drop towards a rigid surface or a deformable interface,” J. Fluid Mech.217, 547 (Year: 1990)]. Both of these results indicate that the existing theories, while fundamentally correct in concept, are incomplete in providing a framework for a comprehensive explanation of the experimental results. In the present paper, we reexamine the thin-film theory of Davis et al. in the low capillary number limit. We find that a quasistatic model in which deformation is localized within the thin film is in general not sufficient to describe the leading-order asymptotic approximation of the flow-induced collision and coalescence of two slightly deformable drops at low capillary number. Instead, the overall deformation induced in the drops by the external flow plays a key role in determining the initial film thickness needed for numerical simulation of the thin-film dynamics via the existing theoretical framework. Also, we find that including retardation effects is important to be able to make quantitatively accurate predictions, especially at viscosity ratios below .
- Instability and Transition
18(2006); http://dx.doi.org/10.1063/1.2160523View Description Hide Description
The development of most amplified wavelength Görtler vortices is studied by means of varying the spanwise spacing of thin vertical wires located upstream of the leading edge of a concave surface. The free-stream velocity is set so as to provide the value of the dimensionless parameter of that for the most amplified vortex wavelength. The resulting uniform vortex wavelengths were determined by the wire spacings and they were preserved downstream prior to turbulence. The spectrum study of the fluctuating velocity component was able to detect the fundamental frequency of the secondary instability mode with the streamwise wavelengths comparable to the wire spacing, which confirm that the wavelength of the vortices observed is the most amplified one. The intermittency study of the boundary layerflow in the presence of the most amplified wavelength Görtler vortices of 15.0 mm using Turbulent Energy Recognition Algorithm method shows the transition onset in the upwash regions, which coincides with the onset of the secondary instability obtained from the spectrum method. The intermittency factor distributions obtained agree with the single universal distribution with an error of about 5%. The transition Görtler number was also found within the range of that of the boundary layers in the presence of naturally developed Görtler vortices reported earlier.
18(2006); http://dx.doi.org/10.1063/1.2148989View Description Hide Description
We study the dynamics of a rigid, symmetric wing that is flapped vertically in a fluid. The motion of the wing in the horizontal direction is not constrained. Above a critical flapping frequency, forward flight arises as the wing accelerates to a terminal state of constant speed. We describe a number of measurements which supplement our previous work. These include (a) a study of the initial transition to forward flight near the onset of the instability, (b) the separate effects of flapping amplitude and frequency, (c) the effect of wing thickness, (d) the effect of asymmetry of the wing planform, and (e) the response of the wing to an added resistance. Our results emphasize the robustness of the mechanisms determining the forward-flight speed as observed in our previous study.
18(2006); http://dx.doi.org/10.1063/1.2160524View Description Hide Description
The hydrodynamic stability of the flow in a solid rocket motor is revisited using a general linear stability approach. A harmonic perturbation is introduced into the linearized Navier-Stokes equations leading to an eigenvalue problem posed as a system of partial differential equations with respect to the spatial coordinates. The system is discretized by a spectral collocation method applied to each spatial coordinate and the eigenvalues are determined using Arnoldi’s procedure. A special emphasis is placed on the boundary conditions. The main result is the discrete nature of the eigenvalue set. According to the present theory and the obtained results, only some discrete frequencies may exist in the motor (as eigenmodes). These frequencies only depend on the Reynolds number based on the injection velocity and the radius of the pipe flow. They are compared to measurements that have been performed at ONERA in one case with a cold-gas setup and in another case with a reduced scale live motor. Due to the agreement obtained with both experiments, the biglobal stability approach seems to offer new insight into the unresolved thrust oscillations problem.
18(2006); http://dx.doi.org/10.1063/1.2166388View Description Hide Description
Nonlinear evolution of viscous and gravitational instability in two-phase immiscible displacements is analyzed with a high-accuracy numerical method. We compare our results with linear stability theory and find good agreement at small times. The fundamental physical mechanisms of finger evolution and interaction are described in terms of the competing viscous, capillary, and gravitational forces. For the parameter range considered, immiscible viscous fingers are found to undergo considerably weak interaction as compared to miscible fingers. The wave number of nonlinear fingers decreases rapidly due to the shielding mechanism and scales uniformly as at long times. We have observed that even a small amount of density contrast can eliminate viscous fingers. The dominant feature for these flows is the gravity tongue, which develops a “ridge instability” when capillary and gravity effects are of similar magnitude.
Holographic particle image velocimetry measurements of hairpin vortices in a subcritical air channel flow18(2006); http://dx.doi.org/10.1063/1.2158429View Description Hide Description
A holographic particle image velocimetry (HPIV) system is employed to study the evolution of coherent structures artificially generated in a plane Poiseuille air flow. As a first step the hot-wire technique and two-dimensional flow visualization are used to determine the generation conditions and dimensions of the coherent structures, their shedding frequency, trajectory, and convectionvelocity. Then, the HPIV method is utilized to obtain the instantaneous topology of the hairpin vortex and its associated three-dimensional distribution of the two (streamwise and spanwise) velocity components as well as the corresponding wall-normal vorticity. Finally, the experimental data are compared with results of related experimental and numerical studies. The present experimental results support the view that the generation of hairpins under various base flow conditions is governed by a basic mechanism, the important common elements of which are the shear of the base flow and an initial disturbance having a sufficiently large amplitude.
18(2006); http://dx.doi.org/10.1063/1.2159031View Description Hide Description
A three-dimensional flow transition behind a heated cylinder is analyzed at low Reynolds numbers:. Both visualizations and numerical simulations show that the transition manifests itself in the form of mushroom-type structures in the far wake and -shaped structures in the near wake. The legs of the -shaped structures coincide with streamwise vorticity regions. An intermediate stage is observed between the -shaped structures and the escaping mushroom-type structures. This intermediate step is characterized by a lift-up process, which takes place in the center region between the legs and head of the -shaped structures. As a result, hot fluid is being pulled out of the upper vortex core. Due to this lift-up process, mushroom-type structures are generated in the form of escaping vortex rings in the far wake.
- Turbulent Flows
18(2006); http://dx.doi.org/10.1063/1.2162186View Description Hide Description
The spatial development of turbulent thermal plumes under rotating conditions of the heat source has been investigated using large-eddy simulations. In order to analyze the rotation effect of the heat source in an otherwise quiescent environment, a range of rotation frequencies is considered in an intermediary Rossby number regime in which inertial and Coriolis forces strongly interact. Above a threshold Rossby number of about 1.82, the influence of heat source rotation is insignificant. Below the threshold heat source, rotation has a significant influence. In the region close to the heat source there is a strong interaction region between the plume development and heat source rotation. Radial transport across the plume is amplified and a mixing process through shear-layer development enhances engulfment of ambient fluid into the thermal plume. Farther above the plume the direct effect of source rotation decays and becomes insignificant. The plume continues to be wider, but this is due to the swirling effects imparted to the base of the plume at the heat source. Thus, after an initial enhancement of entrainment, the resulting flow field behaves as would a nonrotating plume driven by buoyancy, convection, and turbulent mixing.
18(2006); http://dx.doi.org/10.1063/1.2166454View Description Hide Description
Large eddy simulations of turbulent flow over a sphere are conducted at subcritical Reynolds numbers ( and ) based on the freestream velocity and sphere diameter. At , the separating shear layer persists downstream to form a cylindrical vortex sheet and its instability becomes manifest at . The flow right behind the sphere contains only a few vortices. On the other hand, at , the shear-layer instability occurs right behind the sphere in a form of vortex rings, and the flow becomes turbulent in the near wake. Therefore, at , the size of the recirculation region is smaller and the wake recovers more quickly than at . At both Reynolds numbers, large-scale waviness of vortical structures is observed in the wake and the plane containing the large-scale waviness changes quasirandomly in time. This waviness is more pronounced at than at . The mechanism responsible for this large-scale waviness of vortical structures is shown to be closely associated with the temporal evolution of vortices generated by the shear-layer instability.
18(2006); http://dx.doi.org/10.1063/1.2166455View Description Hide Description
Kolmogorov’s theory for turbulence, proposed in 1941, is based on a hypothesis that small-scale statistics are uniquely determined by the kinematicviscosity and the mean rate of energy dissipation. Landau remarked that the local rate of energy dissipation should fluctuate in space over large scales and hence should affect small-scale statistics. Experimentally, we confirm the significance of this large-scale fluctuation, which is comparable to the mean rate of energy dissipation at the typical scale for energy-containing eddies. The significance is independent of the Reynolds number and the configuration for turbulence production. With an increase of scale above the scale of largest energy-containing eddies, the fluctuation comes to have the scaling and becomes close to Gaussian. We also confirm that the large-scale fluctuation affects small-scale statistics.
- Compressible Flows
18(2006); http://dx.doi.org/10.1063/1.2166627View Description Hide Description
In the present study we examine Rayleigh flows of single-phase, nonreacting fluids. When the fluid is of the Bethe-Zel’dovich-Thompson type, it is shown that as many as three sonic points and extrema of the entropy,enthalpy, and heat supply can occur on a fixed Rayleigh line. Exact solutions for van der Waals gases are provided, as is a complete theory of shocked and unshocked flows subjected to strict heating or strict cooling. Further nonclassical results of interest include the occurrence of flow choking in unshocked and shocked strictly cooled flows, the occurrence of as many as three shock waves in cooled or heated flows, and shock splitting in both cooled and heated flows.
- Geophysical Flows
The motion of an internal solitary wave of depression over a fixed bottom boundary in a shallow, two-layer fluid18(2006); http://dx.doi.org/10.1063/1.2162033View Description Hide Description
The motion of a large-amplitude internal solitary wave of depression over a fixed bottom boundary in a shallow, two-layer fluid is investigated experimentally. Measurements of the velocity fields close to the bottom boundary are presented to illustrate the generation of an unsteady boundary jet along the bed. The formation of the jet, the structural characteristics of which show striking similarities with those predicted by recent numerical model studies by Diamessis and Redekopp [J. Phys. Oceanogr. (in press)], is attributed to boundary layer separation in the adverse pressure gradient region of the wave-induced flow.