A Level-Set Method for the Direct Numerical Simulation of Particle Motion in Droplet Evaporation

A sharp-interface level-set (LS) method is presented for direct numerical simulation (DNS) of particle motion in droplet evaporation. The LS formulation for liquid–gas flows is extended to liquid–gas–solid flows by treating the moving solid region as a high-viscosity fluid phase. The evaporation effect is accurately implemented by imposing the coupled temperature and vapor fraction conditions at the interface. The LS method is tested through computations of particle sedimentation in single-phase and two-phase fluids. The DNS of particle motion in droplet evaporation demonstrates the pinning phenomena of the liquid–gas–solid contact line.     

A Numerical Method for Bubble Motion with Phase Change

A numerical method for computing the motion of bubbles undergoing liquid?vapor phase change is presented. The method is based on a level set technique for capturing the phase interface, which is modified to include the effect of phase change at the interface as well as to achieve mass conservation during the whole calculation procedure. The modified level set method is applied for numerical simulation of bubble rise and growth in a stationary liquid. The numerical results are found to compare well with the data reported in the literature and the analytical solutions.     

Direct simulation of spray cooling: Effect of vapor bubble growth and liquid droplet impact on heat transfer

Numerical modeling of multiphase flow using level set method is discussed. The 2-D model considers the effect of surface tension between liquid and vapor, gravity, phase change and viscosity. The level set method is used to capture the movement of the free surface. The detail of incorporating the mechanism of phase change in the incompressible Navier–Stokes equations using the level set method is described. The governing equations are solved using the finite difference method. The computer model is used to study the spray cooling phenomenon in the micro environment of about 40 μm thick liquid layer with vapor bubble growing due to nucleation. The importance of studying the heat transfer mechanism in thin liquid film for spray cooling is identified. The flow and heat transfer details are presented for two cases: (1) when the vapor bubble grows due to nucleation and (2) merges with the vapor layer above the liquid layer and when a liquid droplet impacts the thin liquid layer with vapor bubble growing.     

Numerical Modeling for Multiphase Incompressible Flow with Phase Change

ABSTRACT

A general formula for the second-order projection method combined with the level set method is developed to simulate unsteady, incompressible multifluid flow with phase change. A subcell conception is introduced in a modified mass transfer model to accurately calculate the mass transfer across the interface. The third-order essentially nonoscillatory (ENO) scheme and second-order semi-implicit Crank-Nicholson scheme is employed to update the convective and diffusion terms, respectively. The projection method has second-order temporal accuracy for variable-density unsteady incompressible flows as well. The level set approach is employed to implicitly capture the interface for multiphase flows. A continuum surface force (CSF) tension model is used in the present cases. Phase change and dynamics associated with single bubble and multibubbles in two and three dimensions during nucleate boiling are studied numerically via the present modeling. The numerical results show that this method can handle complex deformation of the interface and account for the effect of liquid–vapor phase change.     

Lattice Boltzmann Simulation of Growth and Deformation for a Rising Vapor Bubble Through Superheated Liquid

Combining with a lattice Boltzmann thermal model, a lattice Boltzmann multiphase model with a large density ratio can be extended to describe phase change with mass and heat transferring through the interface. Based on the Stefan boundary condition, the phase change is considered as a change of phase order parameter and is disposed as a source term of the Cahn-Hilliard equation. This hybrid model is applied to simulate the motion and growth of a rising vapor bubble through a uniformly superheated liquid. Meanwhile, the parametric effect on the bubble growth, deformation and rising in the different surface tension forces and kinetic viscosities are also presented.     

A sharp-interface level-set method for compressible bubble growth with phase change

A sharp-interface level-set method is presented for simulating the growth and collapse of a compressible vapor bubble. The interface tracking method is extended to include the effects of bubble compressibility and liquid-vapor phase change by incorporating the ghost fluid method to efficiently implement the matching conditions of velocity, stress and temperature at the interface. The numerical results for one-dimensional compressible flows and spherical bubble growth show good agreement with the exact solutions. The level-set method is applied to investigate the effects of phase change, ambient temperature and wall on the compressible bubble growth and collapse.     

Numerical analysis of the dynamics of moving vapor bubbles

Bubbles have been observed rapidly sweeping along very fine heated wires during subcooled nucleate boiling with jet flows emanating from the tops of the vapor bubbles. This paper analyzes the physical mechanisms driving the bubble and the jet flows from the tops of these moving bubbles. The flows are analyzed by numerically solving the governing equations for the velocity and temperature distributions around the bubble and the heated wire as the bubble moves along the wire. The bubble motion is due to the non-uniform temperature distribution in the liquid and in the wire caused by the bubble as it moves along the wire. The flow is driven by the horizontal Marangoni flow induced by the temperature difference across the bubble which thrusts the bubble forward. Comparisons with experimental observations suggest that the condensation heat transfer at the bubble interface is restricted by non-condensable gases that increases the surface temperature gradient and the resulting Marangoni flow.     

A Level Set Method for Analysis of Film Boiling on an Immersed Solid Surface

A numerical method is presented for simulating film boiling on an immersed (or irregularly shaped) solid surface. The level set formulation for tracking the phase interfaces is modified to include the effect of phase change at the liquid–vapor interface and to treat the no-slip condition at the fluid–solid interface. The boundary or matching conditions at the phase interfaces are accurately imposed by incorporating the ghost fluid approach based on a sharp-interface representation. The numerical method is tested through computations of bubble rise in a stationary liquid, single-phase fluid flow past a circular cylinder, and film boiling on a horizontal cylinder.     

Dynamics of a vapor bubble on a heated substrate

The dynamics of a vapor bubble between its liquid phase and a heated plate is studied in relation to the breakdown and recovery of the film boiling. By examining the expansion and the contraction of the vapor bubble the film boiling and transition boiling states are predicted. Conservation laws in the vapor, solid, and liquid phases are invoked along with fully nonlinear, coupled, free boundary conditions. These coupled system of equations are reduced to a single evolution equation for the local thickness of the vapor bubble by using a long-wave asymptotics, which is then solved numerically to yield the transient motion of the vapor bubble. Of the numerous parameters involved in this complex phenomenon we focus on the effects of the degree of superheat from the solid plate, that of the supercooling through the liquid, and the wetting/dewetting characteristics of the liquid on the solid plate. A material property of the substrate thus is incorporated into the criteria for the film boiling based on hydrodynamic models.     

Numerical Simulation of Bubble Growth and Heat Transfer During Flow Boiling in a Surface-Modified Microchannel

Flow boiling in a microchannel without or with surface modifications, such as fins, grooves, and cavities, has received significant attention as an effective cooling method for high-power microelectronic devices. However, a general predictive approach for the boiling process has not yet been developed because of its complexity involving the bubble dynamics coupled with boiling heat transfer in a microscale channel. In this study, direct numerical simulations for flow boiling in a surface-modified microchannel are performed by solving the conservation equations of mass, momentum, and energy in the liquid and vapor phases. The bubble surfaces are determined by a sharp-interface level-set method, which is modified to include the effect of phase change at the liquid–vapor interface and to treat the no-slip and contact-angle conditions on immersed solid surface of microstructures. This computation demonstrates that the surface-modified microchannel enhances boiling heat transfer significantly compared to a plain microchannel. The effects of various surface modifications on the bubble growth and heat transfer are investigated to find better conditions for boiling enhancement.     

Simulation of heat transfer with the growth and collapse of a cavitation bubble near the heated wall

The growth and collapse behaviors of a single cavitation bubble near a heated wall and its effect on the heat transfer are numerically investigated. The present study is designed to reveal the mechanism of cavitation enhanced heat transfer from a microscopic perspective. In the simulation, the time-dependent Navier-Stokes equations are solved in an axisymmetric two-dimensional domain. The volume of fluid (VOF) method is employed to track the liquid-gas interface. It is assumed that the gas inside the bubble is compressible vapor, and the surrounding liquid is incompressible water. Mass transfer between two phases is ignored. The calculated bubble profiles were compared to the available experimental data, and a good agreement was obtained. Then, the relationship among bubble motion, flow field and surface heat transfer coefficient was analyzed. On this basis, the effects of such factors as the initial distance between the bubble and the wall, the initial vapor pressure and the initial bubble nucleus size on the heat transfer enhancement are discussed. The present study is helpful to understand the heat transfer phenomenon in presence of cavitation bubble in liquid.     

Direct numerical simulation of flow boiling in a finned microchannel

Direct numerical simulations of bubble growth and heat transfer associated with flow boiling in a finned microchannel are performed by solving the conservation equations of mass, momentum and energy in the liquid and vapor phases. The phase interfaces are determined by a sharp-interface level-set method which is modified to include the effect of phase change at the liquid–vapor interface and to treat the no-slip and contact-angle conditions on the immersed solid surface of fins. The effects of fin height, spacing, and length on the flow boiling in a microchannel are investigated to find the better conditions for heat transfer enhancement.     

Dynamic Behavior of Bubble Interface During Boiling

A brief review with discussions is conducted for some pertinent works, done and ongoing in the Laboratory of Phase-Change and Interfacial Phenomena at Tsinghua University, on interfacial behavior of vapor bubbles and interfacial transport phenomena during liquid nucleation boiling. From a sequence of experimental investigations, some new phenomena, particularly, the visually observed interfacial transport phenomena or processes including jet-like flows, bubble interaction and spatial scale effect, were described in this article. The interfacial effects and transport phenomena associated with surface tension gradients caused by temperature and concentration variations were theoretically analyzed to reveal the marked influence on bubble interfacial shape and dynamic behavior, the bubble dynamics including nucleation, bubble motion and coalescence. Several theoretical models and methods were proposed to describe the dynamic characteristics and explain the physics of interfacial phenomena/processes. The spe     

Numerical Analysis of Bubble Growth and Departure from a Microcavity

A numerical approach is presented for analysis of bubble growth and departure from a microcavity during nucleate boiling. The level-set formulation for tracking the phase interfaces is modified to include the effect of phase change on the liquid–vapor interface and to treat the no-slip and contact angle conditions on the immersed (or irregularly shaped) solid surface of the microcavity. Also, the formulation is coupled with a simple and efficient model for predicting the evaporative heat flux from the liquid microlayer on an immersed solid surface. The effects of cavity size and geometry on the bubble growth and departure in nucleate boiling are investigated.     

High speed bubbly nozzle flow with heat, mass, and momentum interactions

The characteristics of high speed bubbly flows through convergent-divergent nozzles are studied theoretically. A steady, one-dimensional flow is considered. The liquid phase is water, whereas the gaseous phase consists of a mixture of both non-condensable (air) and condensable (water vapor) components. The comprehensive physical model allows for momentum and thermal lags as well as mass transfer between the gaseous and liquid phases due to evaporation and condensation. The parametric analysis reveals that choked flow with supersonic speeds along the diverging section of the nozzle, similar to the behavior of a compressible gas flow, may be obtained under appropriate conditions. Effects of flow parameters such as wall friction, interphase heat transfer, initial bubble size and void fraction are demonstrated.     

Unidirectional bubble growth in microchannels with asymmetric surface features

The growth of vapor bubbles is studied numerically in a microchannel with asymmetric surface features. The channel design is chosen such that evaporation results in vapor bubbles growing only along a predefined direction. The principle relies on capillary forces and the pinning/depinning of three-phase contact lines at sharp edges of the wall geometry. Analytical expressions are derived predicting the direction of bubble growth and allowing to assess the robustness of a specific channel geometry in terms of supporting unidirectional bubble growth. From these expressions design rules for microchannels incorporating geometrical parameters and the wall contact angle of the liquid phase can be derived. The numerical calculations are performed based on an extended Volume-of-Fluid method accounting for phase change. The results confirm that under specific conditions, vapor bubbles only expand in one direction, thereby corroborating the analytical model. The presented concept may find applications in designing microchannels for stabilized flow boiling or micropumps/-actuators relying on phase change.     

Numerical Study on Phase Change of Water Flowing Across Two Heated Circular Cylinders in Tandem Arrangement

This paper focuses on fluid flow and heat transfer analysis over two heated cylinders arranged in tandem. The flow of water over heated cylinders faces a phenomenon of phase change from liquid (water) to vapor phase (steam). The mechanism of this phase change is studied through a numerical simulation supplemented with verification and validation of the code. The problem is simulated when flows from two cylinders in a tandem arrangement become interacting and noninteracting. The Eulerian model is used during simulation to comprehend the multiphase phenomena. The effect of spacing between these two cylinders and the Reynolds number effect are studied in this paper. The volume fractions of both the water and vapor phases and the heat transfer coefficients of both the cylinders have been computed and presented as findings of the problem.     

Computation of practical flow problems with release of latent heat

Practical flow problems with condensation due to phase change from water vapor to water liquid are numerically investigated. Fundamental equations solved in this study consist of conservation laws of mixed gas, water vapor, water liquid, and the number density of water droplets, coupled with the momentum equations and the energy equation. The classical condensation theory is employed for modeling homogeneous nucleation and nonequilibrium condensation. Heterogeneous nucleation is approximately modeled by assuming a constant radius and a constant number density of droplets. These equations are solved by a high-order high-resolution finite-difference method. As external flows, condensate transonic flows around NACA0012 airfoil in atmospheric flow conditions are calculated, and as internal flows, steady and unsteady transonic wet-steam flows through a steam turbine cascade channel are also calculated.     

Coupled level-set and volume-of-fluid method for two-phase flow calculations

In simulating two-phase flows, the volume-of-fluid (VOF) method has the advantage of mass conservation while with the level-set (LS) method, the surface tension force can be calculated more accurately. In this study, we present a coupling method which combines the advantages of both methods. The volume-of-fluid (VOF) method adopted in the calculation is the conservative interpolation scheme for interface tracking method proposed recently by the authors. Based on the location of the interface calculated from the VOF, the LS function is obtained by solving the equation used in the LS method for re-initialization without needing to solve its advection equation. A high-resolution-bounded scheme within the frame of finite-volume methods is used to solve the re-initialization equation. This scheme is verified by considering a variety of interface geometries. A circular bubble at equilibrium is used to assess the coupled LS and VOF method by examining the spurious currents generated in the bubble. Three-dimensional calculations are conducted to study the rising of a bubble in the quiescent water.