Renwei Mei

Viscous flow computations with the method of lattice Boltzmann equation

Abstract The method of lattice Boltzmann equation (LBE) is a kinetic-based approach for fluid flow computations. This method has been successfully applied to the multi-phase and multi-component flows. To extend the application of LBE to high Reynolds number incompressible flows, some critical issues need to be addressed, noticeably flexible spatial resolution, boundary treatments for curved solid wall, dispersion and mode of relaxation, and turbulence model. Recent developments in these aspects are highlighted in this paper. These efforts include the study of force evaluation methods, the development of multi-block methods which provide a means to satisfy different resolution requirement in the near wall region and the far field and reduce the memory requirement and computational time, the progress in constructing the second-order boundary condition for curved solid wall, and the analyses of the single-relaxation-time and multiple-relaxation-time models in LBE. These efforts have lead to successful applications of the LBE method to the simulation of incompressible laminar flows and demonstrated the potential of applying the LBE method to higher Reynolds flows. The progress in developing thermal and compressible LBE models and the applications of LBE method in multi-phase flows, multi-component flows, particulate suspensions, turbulent flow, and micro-flows are reviewed.

Vapor bubble departure in forced convection boiling

Abstract A forced convection boiling facility has been fabricated in which vapor bubble departure can be investigated. It has been observed that once a vapor bubble departs from its nucleation site, it typically slides along the heating surface and lifts off at some finite distance downstream. The probability density functions (pdfs) for bubble departure diameter, d , have been obtained for mass flux, C , ranging from 112 to 287 kg m −2 s −1 and heat flux, q w , ranging from 11.0 to 26.0 kW m −2 . The data indicate a systematic dependence of d on G and q w . A detailed analysis of various forces acting on the bubble is presented and is used to predict the mean departure diameter. The onset of imbalance between the quasi-steady drag, the unsteady component of the drag due to asymmetrical bubble growth, and the surface tension force in the flow direction is used as a criterion for departure and yields satisfactory agreement between the measured and predicted values of the mean departure diameter. The analytical prediction shows a strong influence of mean liquid velocity and wall superheat on the bubble departure diameter. At the point of departure the surface tension force in the flow direction is generally small.

A unified model for the prediction of bubble detachment diameters in boiling systems-II. Flow boiling

An improved model is proposed for the prediction of departure and lift-off diameters in saturated forced convection boiling. The model utilizes a force balance similar to that proposed by Klausner et al. (Int. J. Heat Mass Transfer 36, 651–662 (1993)). One significant improvement is that the inclination angle is determined on a dynamic basis and is not required as an input. Furthermore, it is hypothesized that the surface tension force is small compared to other forces acting on a vapor bubble at the points of departure and lift-off, and thus information on the bubble contact diameter and contact angles is not required. A new data set on mean vapor bubble lift-off diameters and probability density functions (pdfs) for flow boiling of refrigerant R113 on a nichrome heating strip has been obtained using the experimental facility described by Klausner et al. (Int. J. Heat Mass Transfer 36, 651–662 (1993)). The wall superheat and mean liquid velocity respectively range from 5.5 to 12.0 °C and 0.35 to 1.0 m s−1. It is demonstrated that over the limited range of flow boiling conditions considered, the predicted departure and lift-off diameters agree well with measured values.

A NOTE ON THE HISTORY FORCE ON A SPHERICAL BUBBLE AT FINITE REYNOLDS NUMBER

An approximate expression for the history force on a spherical bubble is proposed for finite Reynolds number, Re. At small time, the history‐force kernel is a constant, which decreases with increasing Re, and the kernel decays as t−2 for large time. For an impulsively started flow over a bubble, accurate finite difference results show that the history force on the bubble decays as t−2 at large time. Satisfactory agreement is observed between the presently proposed history force and the numerical solution.

An experimental investigation of bubble growth and detachment in vertical upflow and downflow boiling

A visual study of vapor bubble growth and departure in vertical upflow and downflow forced convection boiling is presented. A vertical flow boiling facility was constructed with a transparent, electrically-heated test section in which the ebullition process could be observed. High-speed digital images of flow boiling phenomena were obtained, which were used to measure bubble growth, departure diameters, and lift-off diameters. Experiments were conducted for flow of FC-87 over a commercially-finished nichrome heating surface, with mass flux ranging from 190 to 666 kg m−2 s−1 and heat flux ranging from 1.3 to 14.6 kW\m2. The flow was slightly subcooled (ΔTsub = 1.0–5.0°C), and boiling occurred at isolated nucleation sites. A major conclusion of this work is that the observed vapor bubble dynamics between upflow and downflow are significantly different. In the upflow configuration, bubbles departing the nucleation site slide along the heater wall, and typically do not lift off. In the downflow configuration, bubbles either lift off directly from the nucleation site or slide and then lift off, depending on flow and thermal conditions. The process of vapor bubble sliding appears to be responsible for enhanced energy transfer from the heating surface, as evidenced by larger heat transfer coefficients for upflow than for downflow under otherwise identical operating conditions.

Long-time behaviour of the drag on a body in impulsive motion

We consider the response of the hydrodynamic drag on a body in rectilinear motion to a change in the speed between two steady states, from U 1 to U 2 ≥0. We consider situations where the body generates no lift, such as occur for bodies with an axis of symmmetry aligned with the motion. At large times, the laminar wake consists of two quasi-steady regions - the new wake and the old wake - connected by a transition zone that is convected downstream with the mean speed U 2 . A global mass balance indicates the existence of a sink flow centred on the transition zone, and this is responsible for the leading-order behaviour of the unsteady force at long times. For the case of U 1 ≥0, the force is shown to decay algebraically with the inverse square of time for any finite Reynolds number (Re), and this result is also shown to hold for non-rectilinear motions. The cases of reversed flow (U 1 <0) and stopped flow (U 2 =0) are treated separately, and it is shown that the transient force is dominated by the effects of the old wake, leading to a slower decay as the simple inverse of time. The force is determined by the far regions of the flow field and so the results are valid for any (symmetric) particle, bubble or drop and (in an average sense) for any Re, provided τ»max {Re, Re -1 }, where the time τ is made dimensionless with the convection timescale. These are believed to be the first calculations which adequately resolve the transient far wake behind a bluff body at long times. The asymptotic result for the force is applied to determine that the approach to terminal velocity of a body in free fall is also as the inverse square of time

Vapor bubble growth in heterogeneous boiling—I. Formulation

Abstract A numerical analysis is carried out to study bubble growth in saturated heterogeneous boiling. The bubble growth is determined by considering the simultaneous energy transfer among the vapor bubble, liquid microlayer, and heater. Finite difference solutions for the temperature fields in the microlayer and heater are obtained on expanding coordinates as the bubble grows. The parameters characterizing the bubble shape and microlayer wedge angle are determined by matching the existing experimental data. The predicted bubble growth rate compares very well with the reported experimental data over a wide range of conditions.

Unsteady force on a spherical bubble at finite Reynolds number with small fluctuations in the free‐stream velocity

Unsteady flow over a stationary spherical bubble with small fluctuations in the free‐stream velocity is considered for Reynolds number ranging from 0.1 to 200. Solutions to the Navier–Stokes equations of both steady and unsteady components are obtained using a finite‐difference method and a regular perturbation scheme based on the amplitude of the fluctuations being small. The dependence of the unsteady drag on the frequency of the fluctuations is examined at finite Reynolds number. It is shown that the quasisteady drag can be represented by using the steady‐state drag coefficient and the instantaneous velocity. Numerical results indicate that the unsteady force at low frequency, ω, increases linearly with ω rather than increasing linearly with ω1/2, which results from the creeping flow solution of the Stokes equation. The added‐mass force at finite Reynolds number is found to be the same as in creeping flow and potential flow. The history force at finite Re is identified and carefully evaluated. The imaginary component of the history force increases linearly with ω when ω is small and decays as ω−1/2 as ω becomes large. The implication is that the history force has a much shorter memory in the time domain than predicted by the solution of the unsteady Stokes equation. Numerical results suggest that the history force, which is due to the combination of the viscous diffusion of the vorticity and the acceleration of the flow field, at low frequency is finite even at large Reynolds number.

A Flow Boiling Microchannel Evaporator Plate for Fuel Cell Thermal Management

In order to provide a high-power density thermal management system for PEM fuel cell applications, a flow boiling microchannel evaporator plate has been developed that operates in a closed loop two-phase thermosyphon. The flow is passively driven by gravity, and the flow rate initially increases with increasing evaporation rate and then decreases after reaching a peak flow rate. A microchannel plate has been fabricated with 56 square channels that have a 1 mm × 1 mm cross-section and are 115 mm long. The working fluid, HFE-7100, has been chosen due to its favorable saturation temperature at one atmosphere. Experiments have been conducted with the heat flux as the control variable. Measurements of mass flow rate, temperature field, and pressure drop have been made. The flow regimes are predominately bubbly and slug. The maximum heat flux observed, 32 kW/m2, is an order of magnitude greater than that required in current fuel cells and is limited by a Ledinegg instability. Two-phase thermal hydraulic models give a reasonable prediction for the mass flow rates and wall temperatures using standard flow boiling correlations. This paper will thoroughly describe the performance of the two-phase thermal management system over a wide range of operating conditions.

Vapor bubble growth in heterogeneous boiling II. Growth rate and thermal fields

In Part I of this study a numerical analysis for vapor bubble growth in heterogeneous boiling has been developed. Four dimensionless parameters governing the bubble growth have been identified : Jacob number, Fourier number, thermal conductivity ratio and thermal diffusivity ratio of the liquid to solid. A systematic investigation on the dependence of the bubble growth rate and the thermal fields of the microlayer and heater on these dimensionless parameters is presented. The results of this investigation assist in the basic understanding of bubble growth in heterogeneous boiling. The numerical study for the solid thermal field elucidates the detailed energy transfer beneath a rapidly growing bubble. In Part I of the present study (1) the governing equa- tions, the boundary conditions, and the initial con- ditions for the unsteady energy transfer from the solid heater through the liquid microlayer to the vapor bub- ble have been systematically formulated. A time vary- ing coordinate system is used to resolve the large tem- perature variations over a small area beneath the vapor bubble. The bubble shape parameter, c, was correlated with Jacob number based on experimental bubble shape protiles, and the microlayer wedge angle parameter, c1, was determined by matching the finite difference solution for the growth rate, R(t), with the existing experimental data over a large range of con- ditions. The numerical results for the bubble growth rate have compared very well with the existing data for the growth rate (2.-7) over a wide range of conditions. From the basic formulation, qualitative analysis, and the result for c~, it is observed that the Prandtl number has little effect on the growth process.