ALBERT

Description: A fully nonlinear solution for bi-chromatic progressive waves in water of finite depth in the framework of the homotopy analysis method (HAM) is derived. The bi-chromatic wave field is assumed to be obtained by the nonlinear interaction of two monochromatic wave trains that propagate independently in the same direction before encountering. The equations for the mass, momentum, and energy fluxes based on the accurate high-order homotopy series solutions are obtained using a discrete integration and a Fourier series-based fitting. The conservation equations for the mean rates of the mass, momentum, and energy fluxes before and after the interaction of the two nonlinear monochromatic wave trains are proposed to establish the relationship between the steady-state bi-chromatic wave field and the two nonlinear monochromatic wave trains. The parametric analysis on ε 1 and ε 2 , representing the nonlinearity of the bi-chromatic wave field, is performed to obtain a sufficiently small standard deviation S d , which is applied to describe the deviation from the conservation state ( S d = 0) in terms of the mean rates of the mass, momentum, and energy fluxes before and after the interaction. It is demonstrated that very small standard deviation from the conservation state can be achieved. After the interaction, the amplitude of the primary wave with a lower circular frequency is found to decrease; while the one with a higher circular frequency is found to increase. Moreover, the highest horizontal velocity of the water particles underneath the largest wave crest, which is obtained by the nonlinear interaction between the two monochromatic waves, is found to be significantly higher than the linear superposition value of the corresponding velocity of the two monochromatic waves. The present study is helpful to enrich and deepen the understanding with insight to steady-state wave-wave interactions.

Description: A numerical investigation of the vortex-induced vibration (VIV) in a side-by-side circular cylinder arrangement has been performed in a two-dimensional laminar flow environment. One of the cylinders is elastically mounted and only vibrates in the transverse direction, while its counterpart remains stationary in a uniform flow stream. When the gap ratio is sufficiently small, the flip-flopping phenomenon of the gap flow can be an additional time-dependent interference to the flow field. This phenomenon was reported in the experimental work of Bearman and Wadcock [“The interaction between a pair of circular cylinders normal to a stream,” J. Fluid Mech. 61 (3), 499–511 (1973)] in a side-by-side circular cylinder arrangement, in which the gap flow deflects toward one of the cylinders and switched its sides intermittently. Albeit one of the two cylinders is free to vibrate, the flip-flop of a gap flow during VIV dynamics can still be observed outside the lock-in region. The exact moments of the flip-flop phenomenon due to spontaneous symmetry breaking are observed in this numerical study. The significant characteristic vortex modes in the near-wake region are extracted via dynamic modal analysis and the interference between the gap flow and VIV is found to be mutual. In a vibrating side-by-side arrangement, the lock-in region with respect to reduced velocity becomes narrower due to the interference from its stationary counterpart. The frequency lock-in occurs and ends earlier than that of an isolated vibrating circular cylinder subjected to an identical flow environment. Similar to a tandem cylinder arrangement, in the post-lock-in region, the maximum vibration amplitudes are escalated compared with those of an isolated circular cylinder configuration. On the other hand, subjected to the influence from VIV, the biased gap flow deflects toward the vibrating cylinder quasi-stably during the frequency lock-in process. This behavior is different from the reported bi-stable regime in a stationary side-by-side arrangement. The analyses show that the flip-flop is associated with a characteristic low flip-flopping frequency, which is dependent upon the values of gap ratio, Reynolds number and the symmetry of the gap flow strength in a time-averaged sense. The disappearance of the flip-flop during the frequency lock-in of vibrating side-by-side arrangements is further investigated through a critical-point concept and a critical vortex merging distance.

Description: The non-isothermal extrudate swell of a high molecular weight high-density polyethylene (HDPE) in long capillary and slit dies is studied numerically (ANSYS POLYFLOW ® ) using an integral K-BKZ constitutive model including crystallization kinetics, determined experimentally. The Nakamura model is used for crystallization of the HDPE, where the crystallization rate parameter is evaluated by using the well-known Ziabicki equation. This non-isothermal extrudate swell phenomenon is simulated using the pseudo-time integral K-BKZ model with the Wagner damping function along with the differential form of the Nakamura model to account for the crystallization of the extrudate. The swell measurements were carried out under non-isothermal conditions by extruding the polymer melt at 200 °C through long capillary and slit dies to ambient air at 25 °C, 110 °C, and 200 °C. The numerical results are found to be in excellent agreement with experimental observations.

Description: The sedimentation of a pair of rigid circular particles in a two-dimensional vertical channel containing a Newtonian fluid is investigated numerically, for terminal particle Reynolds numbers (Re T ) ranging from 1 to 10, and for a confinement ratio equal to 4. While it is widely admitted that sufficiently inertial pairs should sediment by performing a regular DKT oscillation (Drafting-Kissing-Tumbling), the present analysis shows in contrast that a chaotic regime can also exist for such particles, leading to a much slower sedimentation velocity. It consists of a nearly horizontal pair, corresponding to a maximum effective blockage ratio, and performing a quasiperiodic transition to chaos while increasing the particle weight. For less inertial regimes, the classical oblique doublet structure and its complex behavior (multiple stable states and hysteresis, period-doubling cascade and chaotic attractor) are recovered, in agreement with previous work [Aidun, C. K. and Ding, E.-J., “Dynamics of particle sedimentation in a vertical channel: Period-doubling bifurcation and chaotic state,” Phys. Fluids 15 , 1612 (2003)]. As a consequence of these various behaviors, the link between the terminal Reynolds number and the non-dimensional driving force is complex: it contains several branches displaying hysteresis as well as various bifurcations. For the range of Reynolds number considered here, a global bifurcation diagram is given.

Description: We study thermally induced atomization modes in contact free (acoustically levitated) nanoparticle laden fuel droplets. The initial droplet size, external heat supplied, and suspended particle concentration (wt. %) in droplets govern the stability criterion which ultimately determines the dominant mode of atomization. Pure fuel droplets exhibit two dominant modes of breakup namely primary and secondary. Primary modes are rather sporadic and normally do not involve shape oscillations. Secondary atomization however leads to severe shape deformations and catastrophic intense breakup of the droplets. The dominance of these modes has been quantified based on the external heat flux, dynamic variation of surface tension, acoustic pressure, and droplet size. Addition of particles alters the regimes of the primary and secondary atomization and introduces bubble induced boiling and bursting. We analyze this new mode of atomization and estimate the time scale of bubble growth up to the point of bursting using energy balance to determine the criterion suitable for parent droplet rupture. All the three different modes of breakup have been well identified in a regime map determined in terms of Weber number and the heat utilization rate which is defined as the energy utilized for transient heating, vaporization, and boiling in droplets.

Description: Ice disks were released at the surface of a thermalised aluminium plate. The fusion of the ice creates a lubrication film between the ice disk and the plate. The situation is similar to the Leidenfrost effect reported for a liquid droplet evaporating at the surface of a plate which temperature is above the boiling temperature of the liquid. An analogy is depicted between the Leidenfrost phenomenon and the rapid fusion of a solid at the contact of a hot plate. Similarly to Leidenfrost droplet, we observe that, while the ice disks were melting, the disks were very mobile: translation and rotation. A hole was drilled in the plate and allowed the canalising of the melted liquid. Under these conditions, we discover that the rotation of the ice disk is systematic and persistent. Moreover, the rotation speed increases with the temperature of the plate and with the load put on the ice disk. A model is proposed to explain the spontaneous rotation of the ice disk. We claim that the rotation is due to the viscous drag of the liquid that flows around the ice disk.

Description: In this work we report the results of DNSs and LESs of the turbulent flow through hexagonal ducts at friction Reynolds numbers based on centerplane wall shear and duct half-height Re τ , c ≃ 180, 360, and 550. The evolution of the Fanning friction factor f with Re is in very good agreement with experimental measurements. A significant disagreement between the DNS and previous RANS simulations was found in the prediction of the in-plane velocity, and is explained through the inability of the RANS model to properly reproduce the secondary flow present in the hexagon. The kinetic energy of the secondary flow integrated over the cross-sectional area 〈 K 〉 yz decreases with Re in the hexagon, whereas it remains constant with Re in square ducts at comparable Reynolds numbers. Close connection between the values of Reynolds stress u w ¯ on the horizontal wall close to the corner and the interaction of bursting events between the horizontal and inclined walls is found. This interaction leads to the formation of the secondary flow, and is less frequent in the hexagon as Re increases due to the 120 ∘ aperture of its vertex, whereas in the square duct the 90 ∘ corner leads to the same level of interaction with increasing Re . Analysis of turbulence statistics at the centerplane and the azimuthal variance of the mean flow and the fluctuations shows a close connection between hexagonal ducts and pipe flows, since the hexagon exhibits near-axisymmetric conditions up to a distance of around 0.15 D H measured from its center. Spanwise distributions of wall-shear stress show that in square ducts the 90 ∘ corner sets the location of a high-speed streak at a distance z v + ≃ 50 from it, whereas in hexagons the 120 ∘ aperture leads to a shorter distance of z v + ≃ 38 . At these locations the root mean square of the wall-shear stresses exhibits an inflection point, which further shows the connections between the near-wall structures and the large-scale motions in the outer flow.

Description: By replacing the “heavy” silicone oil used in the oil phase of Saksena, Christensen, and Pearlstein [“Surrogate immiscible liquid pairs with refractive indexes matchable over a wide range of density and viscosity ratios,” Phys. Fluids 27 , 087103 (2015)] by one with a twentyfold higher viscosity, and replacing the “light” silicone oil in that work by one with a viscosity fivefold lower and a density about 10% lower, we have greatly extended the range of viscosity ratio accessible by index-matching the adjustable-composition oil phase to an adjustable-composition 1,2-propanediol + CsBr + H 2 O aqueous phase and have also extended the range of accessible density ratios. The new system of index-matchable surrogate immiscible liquids is capable of achieving the density and viscosity ratios for liquid/liquid systems consisting of water with the entire range of light or medium crude oils over the temperature range from 40 °F (4.44 °C) to 200 °F (93.3 °C) and can access the density and viscosity ratios for water with some heavy crude oils over part of the same temperature range. It also provides a room-temperature, atmospheric-pressure surrogate for the liquid CO 2 + H 2 O system at 0 °C over almost all of the pressure range of interest in sub-seabed CO 2 sequestration.

Description: The wave excited motion of a body floating on water confined between two semi-infinite ice sheets is investigated. The ice sheet is treated as an elastic thin plate and water is treated as an ideal and incompressible fluid. The linearized velocity potential theory is adopted in the frequency domain and problems are solved by the method of matched eigenfunctions expansion. The fluid domain is divided into sub-regions and in each sub-region the velocity potential is expanded into a series of eigenfunctions satisfying the governing equation and the boundary conditions on horizontal planes including the free surface and ice sheets. Matching is conducted at the interfaces of two neighbouring regions to ensure the continuity of the pressure and velocity, and the unknown coefficients in the expressions are obtained as a result. The behaviour of the added mass and damping coefficients of the floating body with the effect of the ice sheets and the excitation force are analysed. They are found to vary oscillatorily with the wave number, which is different from that for a floating body in the open sea. The motion of the body confined between ice sheets is investigated, in particular its resonant behaviour with extremely large motion found to be possible under certain conditions. Standing waves within the polynya are also observed.

Description: In this paper, we present a novel method for vortex generation and control in a resonator-shaped microfluidic chamber with actuations. By varying the actuation conditions, including the working transducers, frequency, and voltage, two regimes of vortices, clockwise vortex (CW vortex) and counter-clockwise vortex (CCW vortex), are generated in the chamber. We show that the direction of the vortex can be conveniently shifted from clockwise to counterclockwise by switching the working transducers without interrupting the flow, and the intensity of the vortex can be regulated by the actuation frequency and voltage. It is proposed that the vortex generation in the present case is due to the instability of the actuation-induced pulsatile flow through the sudden expansion part at the outlet of the chamber, while the vortex control is realized through the asymmetric flows in the chamber induced by the upper or lower transducers. The reported method of vortex generation and control can be applied in microfluidic operations for mixing enhancement of multiple reagents and distribution of microparticles and nanoparticles.