Bubble Boundary Layer Research Articles

Nucleation bubble boundary layer theory for ultra-fast electrochemical polishing of additive manufacturing components

The application of electrochemical-based polishing techniques, including electrochemical polishing (ECP) and plasma electrolytic polishing (PEP), to improve the surface quality of additive manufacturing (AM) components is challenged by the high amplitudes and long spatial wavelengths of roughness, which cause pre-polishing procedures to be indispensable. In this study, a nucleation bubble boundary layer (NBBL) mechanism for enhanced electrochemical-based polishing performance is revealed to solve this problem, namely nucleation bubble electrochemical polishing (NBEP). The NBBL is constructed on the anode surface via electrolytic oxygen evolution and nucleate boiling, and is activated by regulating the temperature and electric potential. The experiments verify a model of NBBL consisting of an inner adherent layer and outer diffusion layer (ODL). Simulations and experiments demonstrate that the polishing mechanism is based on the combined current-limiting effect of individual adherent bubbles and the ODL, which differentiates the anodic dissolution rates at the peaks and valleys of a wide range of spatial wavelengths with their electrical resistance. The bubble dynamics also enhance mass transfer, further improving the polishing efficiency. The experimental results show that NBEP is capable of reducing the surface roughness of AM stainless steel 316 L from Ra of 10.22 μm to 0.71 μm, and eliminating the spatial wavelengths of 200–400 μm in 8 min, which cannot be achieved by either ECP or PEP. The polishing current density also increased from 0.25 (ECP) and 0.48 (PEP) to 2 A/cm2 in NBEP. Finally, a prediction model that accurately describes the ultimate roughness achieved by NBEP as a function of the minimum cavity size is established. The NBEP can be directly followed by PEP or ECP to achieve an optimal surface finish of Ra <70 nm for AM parts. The NBEP method considerably enhances the polishing performance of electrochemical-based systems for AM components, as well as expands the application range of electrochemical-based polishing techniques.

A data-driven polynomial chaos method for uncertainty quantification of a subsonic compressor cascade with stagger angle errors

The probability-based uncertainty quantification (UQ) methods require a large amount of sampled data to construct the probability distribution of uncertain input parameters. However, it is a common situation that only limited and scarce sampled data are available in engineering applications due to expensive tests. In the present paper, the Data-Driven Polynomial Chaos (DDPC) method is adopted, which can propagate input uncertainty in the case of scarce sampled data. The calculation accuracy and convergence of the self-developed DDPC method are validated by a nonlinear test function. Subsequently, the DDPC method is applied to investigate the uncertain impact of stagger angle errors on the aerodynamic performance of a subsonic compressor cascade. A family of manufacturing error data of stagger angles was obtained from the real compressor blades. Based on the limited measurement data, the DDPC method combined with Computational Fluid Dynamics (CFD) simulation is employed to quantify the performance impact of the compressor cascade. The results show that the performance dispersion under off-design conditions is more prominent than that under design conditions. The actual aerodynamic performance deviating from the nominal performance is not a small probability event, and the probability of deviating from the nominal loss coefficient and exit flow angle by more than 1% can reach up to 47.6% and 36.8% under high incidence i = 7°. Detailed analysis shows that stagger angle errors have a significant effect on the flow state near the leading edge, resulting in variations in separation bubble size and boundary layer thickness.

Nanobubble boundary layer thickness quantified by solvent relaxation NMR

HypothesisThe boundary layer holds the key to solve the puzzle of the unusual stability of the nanobubbles in solution. The quantitative determination on its mechanical and structural properties has not been achieved due to its diffusive and dynamic nature, lack of distinctive interfaces, and difficult differentiation from bulk background. Therefore, it is necessary to investigate this boundary using more sensitive interface analysis technologies to effectively differentiate the water molecules at the interface from those in the bulk. ExperimentsAn in-situ and non-deconstructive method, solvent relaxation nuclear magnetic resonance, was used to investigate the boundary layer on bulk nanobubbles, where the relaxation rate of the water in the layer and its thickness were measured by solvent relaxation NMR and the ratio between the water molecules at the bubble interfaces and those in the bulk and the corresponding boundary layer thickness were determined. FindingsThe spin–spin relaxation time for the water in the layer (∼101ms) is found to be two orders of magnitude lower than that of the free water (∼103ms). As the first attempt, the determined boundary layer thickness is around 35–45 nm and 17.0 %–8.7 % of the effective gaseous size of the nanobubbles, which increases with the decrease of the bubble diameter. As a result, a quantitative measurement model for bubble boundary layer has been established in order to better understand the interfacial properties and stabilization mechanism for bulk nanobubbles.

Deformation and breakup of bubbles interacting with single vortex rings

The turbulent breakup of bubbles is a complex phenomenon present in a large number of engineering applications and natural processes. Simplified models are essential to better understand the interaction between turbulent eddies and bubbles. Probably the simplest one is that given by a vortex ring colliding with a single bubble. With this motivation, in the present work we perform three-dimensional numerical simulations of a single vortex ring of initial circulation Γ0, radius R0 and Reynolds number Re=Γ0/νl=15,000, interacting with a bubble of radius Rb immersed in a liquid of kinematic viscosity νl. The temporal evolution of the vortex ring is compared with analytical models for the size of the vortex core, a(t), the kinetic energy, Ek(t), and the enstrophy Ω(t), looking for a concurrence of this magnitude with the rate of dissipation of Ek. The dynamics of the bubble-vortex interaction process is described varying the vortex-to-bubble size ratio, R0/Rb, and the Weber number, We=ρl(Γ0/2πR0)2/(σ/Rb). With respect to the bubble, the simulations show that vortices smaller or of the same size as the bubble are not able to break it up. However, vortices slightly larger, although of comparable sizes, can efficiently break the bubble after trapping it inside the vortex core. In these cases, if the Weber number is sufficiently large, the bubble migrates to the vortex core, where the strain is maximum, and elongates along the azimuthal direction to eventually break by a Rayleigh-Plateau mechanism. In fact, we observe that the bubbles always break if We⪆1 when R0/Rb>1. The numerical results are corroborated experimentally for vortex-to-bubble diameter ratios in the range 2.28≤R0/Rb≤7.5. Regarding the vortex ring, it is observed that when the vortex decelerates the bubble while they interact, the vorticity contained in the bubble boundary layer is engulfed by the vortex core, destabilizing the vortex ring. This makes the total enstrophy to suddenly increase due to the vorticity generation by the vortex stretching mechanism that follows the lost of axial symmetry. This increase in enstrophy is associated to a rapid decrease of kinetic energy, especially at low Weber numbers.

Lattice Boltzmann Simulation of Ferrofluids Film Boiling

In the present investigation, two phase film boiling of ferrofluids under an external field delivered around a two-dimensional square cross-section heater was investigated using the lattice Boltzmann technique. The purpose of this work is to find the effect of magnetic field magnitude and direction on the Nusselt number in single and double heater geometry. The improving thermal efficiency in the horizontal and vertical placement of heaters is also presented. The governing equations of mass conservation, momentum conservation, and energy conservation are solved by using a central-moments-based Lattice Boltzmann scheme. The air pocket generated around heater raised incorporating magnetic effects. The heat transfer through this advancement has been explored quantitatively and abstractly. The results shows that with the development in the volumetric applied force at the bubble-fluid interface, the bubble boundary layer thickness around the square heater lessened which cause the Nusselt number augmented. Through the parameter study it found that the Nusselt number can be essentially extended by altering the course of magnet shafts, and that film rising outwardly of the bubble. The improvement and advancement of vapour phase in various heater arrangement made two column of bubble rises at the same time, which rose above each heater and in the end changed into one column of bubble. A correlation considering magnitude and angle of the magnetic field on time-averaged Nusselt number is presented. Finally, the Nusselt number can be controlled with the help of the incorporation of other heaters.

Modeling Interfacial Interactions and Turbulence in the Near-Wall Region of a Vertical Bubbly Boundary Layer

Abstract A two-fluid model with second-order turbulence closure is used for the simulation of a turbulent bubbly boundary layer. The turbulence model is based on the decomposition of the Reynolds stress tensor in the liquid phase into two parts: a turbulent part and a pseudo-turbulent part. The reduction in second-order turbulence closure in the near-wall region is interpreted according to a modified wall logarithmic law. Numerical simulations of bubbly boundary layer developing on a vertical flat plate were performed in order to analyze the bubbles effect on the liquid turbulence structure and to evaluate the respective roles of turbulence and of interfacial forces in the near-wall distribution of the void fraction. The two-fluid model with the second-order turbulence closure succeeds in reproducing the diminution of the turbulent intensity observed in the near-wall region of bubbly boundary layer and the increase in turbulence outside the boundary layer. The analysis of the interfacial force in the near-wall zone has led to the development of relatively simple formulation of the lift-wall force in the logarithmic zone that depends on dimensionless distances to the wall. After appropriate adjustment, this formulation makes it possible to reproduce the shape of the near-wall void fraction peaking observed in bubbly boundary layer experiments.

Bubble clustering in a horizontal turbulent channel flow investigated by bubble-tracking velocimetry

We investigated bubble clustering in a horizontal turbulent channel flow experimentally. Accurate image processing was used to detect individual bubble centroids with a 100% success rate. The successful detections realize bubble tracking velocimetry for Lagrangian mapping of bubble-bubble interaction both visually and quantitatively. The bubble-bubble interaction becomes explicit as the channel Reynolds number (Re) increases in the range 5,000 < Re < 11,000, incorporating streamwise attraction, lateral repulsion, and tandem circulation within a space narrower than 3 bubble diameters. We attribute this to the turbulent boundary layer where wall-sliding bubbles display streamwise velocity differences due to size. The resulting clustering can be attributed to poly-dispersed bubbles. This idea is verified by experimental data classified by bubble size. The present findings offer an explanation for the initiation of void waves in a bubbly two-phase boundary layer at a scale larger than that of the original coherent structures involved in the turbulence.

Bubbly drag reduction accompanied by void wave generation inside turbulent boundary layers

Frictional drag reduction, a technique by which bubbles are injected into the turbulent boundary layer surrounding the hull of a marine vessel, is now at the stage of practical applications. In achieving drag reduction, void waves often stand out naturally, the reason for which still remains unclear. The present study aims at an experimental characterization of void waves along a flat-bottom ship. A 100-m-long water reservoir is used in which a 4-m-long fully transparent experimental model ship, equipped with wall shear stress sensors and cameras, is towed by a train at speeds of up to 3 m/s. From measurements of the transition of the bubble distribution from random to wavy accumulated swarms downstream, the accompanying intrinsic passing frequency of void waves is examined. A 30% drag reduction rate was recorded with the appearance of void waves in the boundary layer at an average void fraction of 4%. This is much greater than the trivial inertia effect from drag reduction. To clarify the characteristics of the measured void waves, we compare the void wave frequency range to those of several flow instabilities that may occur in bubbly two-phase boundary layer flows.

Quiescent Prominence Dynamics Observed with the Hinode Solar Optical Telescope. II. Prominence Bubble Boundary Layer Characteristics and the Onset of a Coupled Kelvin–Helmholtz Rayleigh–Taylor Instability

Abstract We analyze solar quiescent prominence bubble characteristics and instability dynamics using Hinode/Solar Optical Telescope data. We measure the bubble expansion rate, prominence downflows, and the profile of the boundary layer brightness and thickness as a function of time. The largest bubble analyzed rises into the prominence with a speed of about 1.3 km s − 1 until it is destabilized by a localized shear flow on the boundary. Boundary layer thickness grows gradually as prominence downflows deposit plasma onto the bubble with characteristic speeds of 20 – 35 km s − 1 . Lateral downflows initiate from the thickened boundary layer with characteristic speeds of 25 – 50 km s − 1 , “draining” the layer of plasma. Strong shear flow across one bubble boundary leads to an apparent coupled Kelvin–Helmholtz Rayleigh–Taylor (KH–RT) instability. We measure shear flow speeds above the bubble of 10 km s − 1 and infer interior bubble flow speeds on the order of 100 km s − 1 . Comparing the measured growth rate of the instability to analytic expressions, we infer a magnetic flux density across the bubble boundary of ∼10−3 T (10 Gauss) at an angle of ∼ 70 ° to the prominence plane. The results are consistent with the hypothesis that prominence bubbles are caused by magnetic flux that emerges below a prominence, setting up the conditions for RT, or combined KH–RT, instability flows that transport flux, helicity, and hot plasma upward into the overlying coronal magnetic flux rope.

State dynamics of bubbly cavitation in a vicinity of quasi-empty rupture at its collapse

The presentation deals with one of the experimental models of a quasi-empty rupture which is formed in the liquid layer of a distilled cavitating fluid under shock loading. It is shown that the rupture is shaped as a spherical segment, which retains its topology during the entire process of its evolution and collapsing. The dynamic behavior of the quasi-empty rupture and of the structure of cavitating flow on its surface are analyzed. It is shown that rupture implosion is accompanied by the SW radiation and a transformation of the bubble boundary layer to a cavitating cluster, which takes the form of a ring-shaped vortex floating upward to the free surface of the liquid layer.

Formation of a cavitation cluster in the vicinity of a quasi-empty rupture

The presentation deals with one of the experimental and numerical models of a quasi-empty rupture in the magma melt. This rupture is formed in the liquid layer of a distilled cavitating fluid under shock loading within the framework of the problem formulation with a small electromagnetic hydrodynamic shock tube. It is demonstrated that the rupture is shaped as a spherical segment, which retains its topology during the entire process of its evolution and collapsing. The dynamic behavior of the quasi-empty rupture is analyzed, and the growth of cavitating nuclei in the form of the boundary layer near the entire rupture interface is found. It is shown that rupture implosion is accompanied by the transformation of the bubble boundary layer to a cavitating cluster, which takes the form of a ring-shaped vortex floating upward to the free surface of the liquid layer. A p-κ mathematical model is formulated, and calculations are performed to investigate the implosion of a quasi-empty spherical cavity in the cavitating liquid, generation of a shock wave by this cavity, and dynamics of the bubble density growth in the cavitating cluster by five orders of magnitude.

Use of a rotating cylinder to induce laminar and turbulent separation over a flat plate

An innovative and easy technique using a rotating cylinder system has been implemented in a water tunnel experiment to generate an adverse pressure gradient (APG). The strength of the APG was varied through adjustment in the rotation speed and location of the cylinder. Then the technique was used for inducing a laminar separation bubble (LSB) and turbulent boundary layer (TBL) separation over a flat plate. A theoretical model to predict the pressure variation induced on the plate consists of an inviscid flow over a reverse doublet-like configuration of two counter rotating cylinders. This model quantified the pressure distribution with changes of cylinder speed and location. The dimensionless velocity ratio (VR) of the cylinder rotation rate to the mainstream velocity and gap to diameter ratio were chosen as the two main ways of varying the strength of the APG, which affects the nature and extent of the LSB as well as TBL separation. The experimental parametric study, using time-resolved digital particle image velocimetry, was then conducted in a water tunnel. The variation in height (h), length (l), and the separation point (S) of the LSB was documented due to the variation in the APG. The similar type of experimental parametric study was used to explore the unsteady, turbulent separation bubble in a 2D plane aligned with the flow and perpendicular to the plate. The mean detachment locations of TBL separation are determined by two different definitions: (i) back-flow coefficient (χ) = 50%, and (ii) location of start of negative mean skin friction coefficient (Cf). They are in good agreement and separation bubble characteristics agreed well with results obtained using different methods thus proving the validity of the technique.

気液二相流の特徴を利用した摩擦抵抗低減

Drag reduction using bubbles are now in operation for marine vessels, and recorded significant fuel saving. Beside it, fluid mechanics inside high-speed bubbly turbulent boundary layer is highly complex. Efforts by scientists and engineers in Japan straggled in the last 30 years and recently reached the goal. They found further potential of technical improvement with recent experimental discovery on bubbles’ organizing behaviors.

Void waves propagating in the bubbly two-phase turbulent boundary layer beneath a flat-bottom model ship during drag reduction

The injection of bubbles into a turbulent boundary layer can reduce the skin friction of a wall. Conventionally, the drag reduction rate is evaluated using time-averaged quantities of the mean gas flow rate or mean void fraction. Actually, as bubbles are subject to strong shear stresses near the wall, void waves and local bubble clusters appear. For pipe and channel flows, such wave-like behavior of the dispersed phase has been investigated intensely as an internal two-phase flow problem. We investigate how this wavy structure forms within the boundary layer as an external spatially developing two-phase flow along a horizontal flat plate. We describe how our model ship is designed to meet that purpose and report bubble-traveling behavior that accompanies unexpectedly strong wavy oscillations in the streamwise direction. A theoretical explanation based on a simplified two-fluid model is given to support this experimental fact, which suggests that void waves naturally stand out when drag reduction is enhanced through the local spatial gradient of the void fraction.

New Two-Fluid Model Near-Wall Averaging and Consistent Matching for Turbulent Bubbly Flows

A new two-fluid model averaging in the near-wall region is proposed to ensure consistent matching of the two-phase k–ε turbulence model with the two-phase logarithmic law of the wall (Marie J. L., Moursali, E., and Tran-Cong, S., 1997, “Similarity Law and Turbulence Intensity Profiles in a Bubbly Boundary Layer,” Int. J. Multiphase Flow, 23(2), pp. 227–247). The void fraction distribution obtained with the averaging procedure is seen to conform to the two-phase wall function approach which is based on a double step function void fraction distribution. In particular, the proposed averaging technique is shown to achieve grid convergence in the near-wall region, which could not be obtained otherwise. Computational fluid dynamics (CFD) results with the proposed technique are in good agreement with experiments on upward bubbly flows over a flat plate, and upward and downward flows in pipes. An additional advantage of the proposed technique is that it replaces the wall force model, which has a significant degree of uncertainty in turbulent flow modeling, with a simpler geometric constraint.

Ignition and combustion characteristics of jet fuel liquid film containing graphene powders at meso-scale

At meso-scale, ignition and combustion characteristics of jet fuel liquid film containing graphene powders were investigated. Jet fuel/graphene suspensions were prepared, and sprayed to produce the liquid film. Liquid film was ignited by optical tweezers, five distinctive stages including graphene trap, ignition and combustion of graphene, bubble formation, jet fuel vaporization and bubble growth, bubble rupture and combustion of liquid film were identified. Ignition of graphene is prior to jet fuel. The combustion heat of graphene serves a heat source to accelerate the vaporization of jet fuel. The graphene serves as a nucleation point to form a bubble. Expansion of both combustion products and jet fuel vapor result in the bubble growth. The thickness of bubble boundary layer depends on graphene concentration. As the bubble escaped, liquid film ruptured and micro-explosion occurred. Jet fuel was then ignited, and combusted sustainably till burnt out. During combustion, the flame front fluctuated slightly, indicating good flame stability. Finally, a schematic physical model was presented to analyze the inductive mechanism of graphene for ignition and combustion of jet fuel liquid film by optical tweezers.

CFD simulation of upward subcooled boiling flow of refrigerant-113 using the two-fluid model

In this paper, a modified two-fluid model considering temperature dependent properties and saturation temperature variation was adapted to accurately simulate the process of subcooled boiling flow. The calculations were performed by a CFD code CFX-10 with an extended user defined FORTRAN. The refrigerant-113 boiling flow experiments in a vertical concentric annulus from reference were used to validate the modified two-fluid model of subcooled boiling flow. Compared with the previous published predicted results, the results in the present model show better and reasonable approximation with the experimental data, including the local distribution of void fraction, liquid temperature, axial liquid and vapor velocity. Results show that with increasing the wall heat flux, the bubble boundary layer will become thicker, the liquid temperature gradient at the near-wall region will be smoother and the profiles of axial liquid velocity will gradually depart from those of single-phase flow. Decreasing the inlet liquid subcooling or the mass flux will obtain the same results.

Bubble migration in a turbulent boundary layer

The wall void peaking distribution observed in an upward turbulent bubbly boundary layer along a flat plate is generated by bubbles that move towards the plate, come into contact with the wall and then slide along it. This transverse ‘migration’ has been studied using flow visualization, high speed video and particle tracking techniques to measure the trajectories of mono-disperse air bubbles at very low void fractions. Investigations have been performed at four Reynolds numbers in the range 280 < Re θ < 3000, covering both the laminar and turbulent regimes, with mono-disperse bubbles of mean equivalent diameter between 2 mm and 6 mm. Lagrangian statistics calculated from hundreds of trajectories show that the migration only occurs in the turbulent regime and for bubble diameters below some critical value: 3.5 mm < d eqcrit < 4 mm. Above this size ( We > 3), the interface deformation is such that bubbles do not remain at the wall, even when they are released at the surface. Also, bubble migration is shown to be non-systematic, to have a non-deterministic character in the sense that trajectories differ significantly, to increase with Reynolds number and to take place on a short time scale. A series of experiments with isolated bubbles demonstrates that these results are not influenced by bubble–bubble interactions and confirm that two-way coupling in the flow is limited. Flow visualizations show that the migration originates with the capture of bubbles inside the large turbulent structures of the boundary layer (‘bulges’). The bubbles begin to move towards the wall as they cross these structures, and the point at which they reach the wall is strongly correlated with the position of the deep ‘valleys’ which separate the turbulent ‘bulges’. The analysis of the mean Lagrangian trajectories of migrating bubbles confirms these observations. Firstly, the average time of migration calculated from these trajectories coincides with the mean transit time of the bubbles across the structures. Secondly, once the trajectories have been scaled by this transit time and the boundary layer thickness δ, they all have the same form in the region y/ δ < 0.4, independent of the Reynolds number.

Mass Transfer from a Single Bubble in the Presence of Surfactants

Oxygen transfer from a single bubble is studied experimentally. A mechanism of surfactant effect on the mass transfer of sparingly soluble gases is suggested. A simplified model is constructed for surfactant adsorption and gas absorption in the bubble boundary layer. The effect of turbulence and surfactant concentration on mass transfer from a single bubble is analyzed.

Calculation of a two-phase dynamic laminar boundary layer and a thermal laminar boundary layer on a plate

The approximate method of calculation of a bubble boundary layer based on the integral relations for momentum and energy is proposed. The corresponding equations are derived and results of the numerical investigation of heat exchange are given.