Calculation Of Surface Tension Force Research Articles

Numerical simulations of thermal capillary migration of a droplet on a temperature gradient wall with smoothed particle hydrodynamics method

Thermal capillary migration is a phenomenon due to the Marangoni effect, which refers to the spontaneous motion of a liquid on a non-isothermal surface. Numerical simulation of thermal capillary migration of a droplet is extremely difficult due to the multi-physics field coupling and the violent motion of the droplet surface. In this paper, an improved smooth particle hydrodynamics (SPH) method is developed for simulating thermal capillary migration of a droplet driven by thermal gradient. In improved SPH model, an improved continuous surface force model is proposed to enhance the accuracy and stability of surface tension force calculation by introducing an improved surface tangential force. The contact angle model is utilized to model the surface wettability. The SPH method for simulating the thermal fluid flow is developed based on the continuum, momentum, and energy equations. In addition, kernel gradient correction and particle shifting technique are utilized to improve the accuracy and stability of the SPH method. The correctness and effectiveness of the improved SPH method are verified by numerical examples. Moreover, the motions of a droplet driven by thermal gradient under different conditions are investigated. Comparing with the results obtained by experiments and other resources, we can conclude that the improved SPH model is effective in modeling the thermal capillary migration of a droplet.

Conjugate heat transfer effects on flow boiling in microchannels

• Heat distributes nonuniformly around the perimeter of microchannels in evaporators. • In single-phase flow, low aspect-ratio channels yield best heat transfer. • In two-phase flow, the Nusselt number trends vs. aspect-ratio are mixed. • High aspect-ratio channels exhibit larger thermal resistance and higher evaporator temperatures. • Conjugate heat transfer should be included in design models for evaporators. This article presents a computational study of saturated flow boiling in non-circular microchannels. The unit channel of a multi-microchannel evaporator, consisting of the fluidic channel and surrounding evaporator walls, is simulated and the conjugate heat transfer problem is solved. Simulations are performed using OpenFOAM v2106 and the built-in geometric Volume Of Fluid method, augmented with self-developed libraries to include liquid-vapour phase-change and improve the surface tension force calculation. A systematic study is conducted by employing water at atmospheric pressure, a channel hydraulic diameter of D h = 229 µm, a uniform base heat flux of q b = 100 kW / m 2 , and by varying the channel width-to-height aspect-ratio and channel fin thickness in the range ϵ = 0.25 –4 and W f = D h / 8 − D h , respectively. The effects of conjugate heat transfer and channel aspect-ratio on the bubble and evaporative film dynamics, heat transfer, and evaporator temperature are investigated in detail. This study reveals that, when the flow is single-phase, higher Nusselt numbers and lower evaporator base temperatures are achieved for smaller channel aspect-ratios, from Nu ≃ 4 and T b − T s a t ≃ 9 K when ϵ = 4 , to Nu ≃ 6 and T b − T s a t ≃ 2 K when ϵ = 0.25 , for same fin thickness W f = D h / 8 . In the two-phase flow regime, Nusselt numbers in the range Nu = 12 − 36 are achieved. The trends of the Nusselt number versus the aspect-ratio are non-monotonic and exhibit a marked dependence on the channel fin thickness. For small fin thicknesses, W f = D h / 8 and W f = D h / 4 , an overall ascending trend of Nu for increasing aspect-ratios is apparent, although in the narrower range ϵ = 0.5 –2 the Nusselt number appears weakly dependent on ϵ . For thicker fins, W f = D h / 2 and W f = D h , the Nusselt number decreases slightly when increasing the aspect-ratio in the range ϵ = 0.5 –2, although this trend is not monotonic when considering the entire range of aspect-ratios investigated. Nonetheless, due to conjugate heat transfer, Nusselt numbers and evaporator base temperatures follow different trends when varying the aspect-ratio, and channels with ϵ < 1 seem to promote lower evaporator temperatures than higher aspect-ratio conduits.

An accurate interface reconstruction method using piecewise circular arcs

SummaryA novel piecewise circular interface construction (PCIC) method for accurate reconstruction of interface in a two‐phase flow problem is proposed. This is under the framework of a fixed grid, volume of fluid approach applied on a two‐dimensional semistaggered structured grid. Fluid interface in each mixed cell is represented using a geometric template of piecewise circular arc. Data corresponding to arc center coordinates and radius are first predicted using curve fitting methods and corrected with the help of volume fraction constraints. Further corrections are carried out to achieve function (c0) continuity at cell boundaries. The proposed method does not require additional calculations for the determination of curvature (for calculation of surface tension force), since it is obtained as part of reconstruction process itself. For dynamic interface construction, simple analytical expressions are derived to construct edge matched flux polygons. Area of intersection of flux polygons with area covered by primary fluid is determined to effect geometric advection across a PCIC interface. Accuracy of this method is demonstrated by the reconstruction of standard static and dynamically evolving interface problems. Accuracy levels superior to most interface reconstruction methods using PLIC and schemes using higher order curves are established. Finally, the capability to handle a complex two‐phase flow problem simulation viz the four‐vortex flow field, where interface undergoes breakage and coalescence, is also demonstrated.

Coalescence of two initially spherical bubbles: Dual effect of liquid viscosity

The coalescence and interaction of two inline bubbles in viscous ambient liquids are explored using axisymmetric computations. The incompressible Navier–Stokes equations for gas-liquid flow are solved numerically through a tree-based finite volume method. Starting from spherical shape, the deformation and evolution of bubbles are simulated by a volume-of-fluid (VOF) method that combines a balanced surface tension force calculation and a height function curvature estimation. High mesh resolution is achieved by dynamic, adaptive mesh refinement to finely resolve the local topological evolutions during coalescence. The influence of liquid viscosity, for which Galilei number Ga ranges from 1 to 150, is studied under different Eötvös numbers Eo. It is discovered that the outcome of coalescence is determined by the competition between the two liquid circulations (vortex rings) around bubbles. We find that the inter-bubble interaction is always enhanced by reducing liquid viscosity. However, the effect of liquid viscosity on bubble coalescence is dual and the minimum coalescence time is obtained at a moderate Ga with other parameters fixed. A comprehensive map of coalescence regime is provided, where four distinct coalescence regimes are identified and three critical Galilei numbers are defined. The motion of bubbles in different coalescence regimes are also analyzed and compared. Our work contributes to a further understanding of the coalescence and interaction of bubbles.

A CFD model for the coupling of multiphase, multicomponent and mass transfer physics for micro-scale simulations

This paper presents a CFD model that couples the physics of multiphase and multicomponent flow involving mass transfer for micro-scale simulations. The volume-of-fluid (VOF) model is utilised to capture the multiphase physics, and smoothing operations are applied in the surface tension force calculation to minimise spurious velocities. For multicomponent tracking of the species transport, the α-factor and expulsion operation methods are implemented to ensure that the species are tracked within the correct phase. Three different mass transfer models were adopted with modifications to the original models. The developed coupled multiphase-multicomponent model was assessed via a series of validation cases: a simple one-dimensional (1D) diffusion problem, horizontal vapour flow over a smooth stationary liquid where Sherwood number was used to measure mass transfer performance, and the dissolution of a two-dimensional (2D) droplet. In all the test cases, the model was able to yield reasonably close results with the analytical solution or empirical correlations used in the validation, thus establishing its accuracy and reliability of the developed model. Simulations using the coupled multiphase-multicomponent model represent a cost-effective approach to obtaining insights into the flow physics for a variety of applications: dissolution of droplets in microchannels, transport of drugs in blood vessels that entails mass transfer and simulations of carbon dioxide enhanced oil recovery at the pore-scale.

Algebraic coupled level set-volume of fluid method for surface tension dominant two-phase flows

In this study, an Algebraic Coupled Level Set-Volume of Fluid (A-CLSVOF) method is proposed for the simulation of interfacial capillary flows. The Volume of Fluid (VOF) method is utilized to incorporate one-way coupling with the Level Set (LS) function in order to improve the accuracy of the surface tension force calculation and to reduce the presence of parasitic currents. In this method, both VOF and LS functions are transported where the new volume fraction determines the interface seed position utilized by the reinitialization procedure for the LS field. Computational efficiency is enhanced through the use of the advected LS field, serving as an initial condition for the reinitialization procedure. The Hamilton–Godunov function is used with a second order (in space and time) discretization scheme to produce a signed distance function. In order to evaluate the performance of the methodology implemented here for capillary dominant flows, four different cases were considered: 1. static droplet; 2. capillary wave relaxation; 3. Rayleigh–Taylor instability and 4. droplet impact on a liquid pool. The simulations demonstrated reduction in spurious currents, accurately predicted capillary pressure and demonstrated overall improvements in efficiency and error reduction owing to the addition of LS advection. The present methodology is tested against previously published experimental results for a droplet impact on a deep liquid pool. Simulation results demonstrate excellent agreement with measured interface height up to and beyond the formation of a Rayleigh–Jet and break-up formation of a secondary daughter drop.

On the combined effects of surface tension force calculation and interface advection on spurious currents within Volume of Fluid and Level Set frameworks

This paper deals with the comparison of Eulerian methods to take into account the capillary contribution in the vicinity of a fluid–fluid interface. Eulerian methods are well-known to produce additional vorticity close to the interface that leads to non-physical spurious currents. Numerical equilibrium between pressure gradient and capillary force for the static bubble test case within a VOF framework has been reached in [35] with the height-function technique [14,35]. However, once the bubble is translated in a uniform flow, spurious currents are maintained by slight errors induced by translation schemes. In this work, two main points are investigated: the ability of Volume of Fluid and Level Set methods to accurately calculate the curvature, and the magnitude of spurious currents due to errors in the calculation of the curvature after advection in both translating and rotating flows. The spurious currents source term is expressed from the vorticity equation and used to discuss and compare the methods. Simulations of gas–liquid Taylor flow at low capillary number show that the flow structure and the bubble velocity can be significantly affected by spurious currents.

Numerical simulation of droplet deposition onto a liquid film by VOF–MPS hybrid method

Droplet entrainment and deposition are a couple of significant mechanisms for the heat transfer in annular two-phase flows existing in some heat exchange systems. The basic physics include the peeling of droplets from the liquid film due to high friction with the gas phase and the collision of droplets with the liquid film or deposition into the liquid film. Droplet deposition particularly plays a crucial role in the course of film dryout events which might have a vital importance for particular systems. In this study, a new numerical method (named as VOF–MPS hybrid method) based on the moving particle semi-implicit (MPS) method was developed to analyze the droplet deposition onto a stagnant thin liquid film. That proposed method combines the volume of fluid (VOF) solver of the open-source CFD code OpenFOAM with the MPS method. VOF–MPS technique introduces the surface tension force calculation of VOF model into the MPS method. MPS method formerly employed the continuum surface force (CSF) approach based on the particles. Three-dimensional (3D) VOF–MPS simulation with the novel surface tension modeling addition to the MPS-based modeling provides a smoother liquid–gas interface on the crown formed after the impact. Droplet deposition experiments were also carried out for the validation and comparison of two models. VOF–MPS method could predict the crown parameters such as crown thickness relatively better than the MPS method employing the CSF. However, the instabilities formed at the tip of the crown, observed in the experiments, could not be resolved with both methods.

Simulation of surface-tension-driven interfacial flow with smoothed particle hydrodynamics method

The method for simulation of surface-tension-driven interfacial flow with smoothed particle hydrodynamics is developed. The calculation of surface tension force is based on the interface reconstruction. The boundary particles for each fluid are detected dynamically. The position of the interface particles are specified in the middle of the boundary particles of each fluid. According to the positions of the interface particles, the interface can be reconstructed. The normal vector and curvature of the interface can be obtained. Then the surface tension force is calculated according to the reconstructed interface. Finally the surface tension force is transferred to the SPH particles near the interface. The accuracy and efficiency of the developed method are investigated. Drop deformation in shear flow, oscillation of square drop, head-on binary collision, and off-center binary collision are simulated. The developed method can be applied to the simulation of surface-tension-driven interfacial flow with high density ratio of up to 797.88 and high viscosity ratio of up to 55.56.

Phase-Field simulation of small capillary-number two-phase flow in a microtube

Accurate calculation of surface tension force is critically important for numerical simulation of gas–liquid two-phase flows at small capillary number. It is well known that the errors in the surface tension calculation would cause considerable parasitic flow with conventional continuum surface force method. In the present simulation, Phase-Field method is employed to capture local two-phase interface. The surface tension force is represented by a chemical potential gradient. The numerical results show that the chemical potential formulation of surface tension force can reduce the magnitude of parasitic flow to the level of truncation error. This is because exchange between kinetic and surface energy is appropriately calculated. The method is applied to the simulations of air–water two-phase bubbly and slug flows in a microtube of 600 μ m . The Reynolds numbers are 60–200, and the capillary number is O ( 10 - 3 ) . The simulated gas bubble shape and two-phase flow patterns are in good agreement with experimental results. The pressure drop, represented by Lockhart–Martinelli correlation, is found larger than that proposed for tubes in millimeter.