Three-Dimensional Modelling of Density Variation Due to Phase Change in Complex Free Surface Flows

A three-dimensional model of droplet impact and solidification has been modified to include the effects of density variation during phase change. The governing equations for conservation of mass, momentum, and energy, and a volume-of-fluid (VOF) equation are derived by assuming different but constant solid and liquid densities. The equations are solved numerically using a control-volume approach. The model is validated against the Stefan and planar solidification problems. It is then applied to simulate the effects of density variation during solidification of molten tin in a mold and also of an impacting tin droplet on a substrate.     

低熔点熔融盐管内强迫对流换热的实验研究

利用课题组自行配制的二元混合熔融盐(KNO3-Ca(NO3)2)开展导热油与低熔点熔融盐的管内强制对流实验研究。通过实验得到导热油与低熔点熔融盐的总换热系数,并通过最小二乘法和Wilson分离法得到了管内低熔点熔融盐侧的对流换热系数及其准则关联式。与不同的经典传热关联式对比,最大偏差为+23%。考虑高温熔融盐的变物性特征,利用黏度项对Dittus-Boelter方程关联式进行修正。经过修正后的Dittus-Boelter方程与实验测试结果最大偏差为-15%,偏差值明显减小。过渡流实验数据和Hausen方程及Gnielinski方程的最大偏差均为10%,实验结果验证了传热关系式仍适用于高温熔融盐的结论。     

A three-dimensional model of droplet impact and solidification

A three-dimensional model has been developed to simulate the fluid dynamics, heat transfer and phase-change that occur when a molten metal droplet falls onto a flat substrate. The model is an extension of one developed by Bussmann et al. [Phys. Fluids 11 (1999) 1406] and combines a fixed-grid control volume discretization of the fluid flow and energy equations with a volume-tracking algorithm to track the droplet free surface, and an improved fixed velocity method to track the solidification front. Surface tension is modeled as a volume force acting on fluid near the free surface. Contact angles are applied as a boundary condition at liquid-solid contact lines. The energy equations in both the liquid and solid portions of the droplet are solved using the Enthalpy method. Heat transfer within the substrate is by conduction alone. Thermal contact resistance at the droplet-substrate interface is included in the model. We studied the deposition of tin droplets on a stainless steel surface using both experiments and numerical simulations. The results of two different scenarios are presented: the normal impact of a 2.7 mm tin droplet at 1 m/s, and of the oblique impact of a 2.2 mm tin droplet at 2.35 m/s onto a surface inclined at 45° to the horizontal. Images obtained from numerical model were compared with experimental photographs and found to agree well.     

Thermodynamic model of viscosity of hydrocarbons and their mixtures

Activation hypothesis suggested by Eyring for modeling viscosity of liquids is generalized for calculation coefficient of dynamic viscosity of pure hydrocarbons and their mixtures in wide region of temperature, pressure and concentrations. Energy of vacancy activation is modeled as difference between enthalpy of ideal gas and enthalpy of real substance. Enthalpy and other thermodynamic parameters for pure substances and mixtures are calculated on the base of well-known Lee–Kesler equation of state. Thermodynamics of mixture calculated in the frame of pseudofluid hypothesis with pseudocritical thermodynamic constants. Pseudocritical thermodynamic constants are estimated with the help of mixing rules offered also by Lee–Kesler. Two additional constants are including in the suggested model of viscosity. For normal paraffin these constant have universal value. For other substances, for example, oxygen containing hydrocarbons values of the constant are installed in accordance to the experimental data. The model with sufficiently accuracy reproduces viscosity experimental data as pure substances in vapor and liquid phases and also solutions in the wide regions of thermodynamical parameters and concentrations. Calculation results are compared with the literature experimental data.     

Momentum interaction in buoyancy-driven gas–liquid vertical channel flows

Drag coefficient correlations for bubbles in buoyancy-driven two-phase flows have generally been derived from data on low-viscosity media and within the bubbly flow regime. In a number of applications, e.g. evaporative crystallizers, there is a need to extend this correlation to higher viscosity flows and slug regimes. In this paper, the momentum interaction in gas–liquid vertical channel flow has been studied experimentally over a wide range of void fractions using a circulation loop facility where the buoyancy is the only driving force for liquid circulation. A model for the drag in gas–liquid buoyant flows has been developed, and is applicable for a wide range of viscosity and void fractions.     

Thermal interactions of a molten tin drop with water triggered by a low-pressure shock

Thermal interactions of a molten tin drop with water were studied with a dropping contact mode in a shock tube geometry. The interaction was triggered by collapsing the initial vapor/gas bubble with a low-pressure (s< 0.8 MPa) shock. The hollow, porous, shell-like debris indicates that violent boiling, or homogeneous nucleation, of penetrated water, followed by turbulent mixing, might be a dominant mechanism for fragmentation of tin drops. An empirical correlation was obtained for the fragmentation time scale. The average heat transfer rate during the interaction was found to be in the range 1–10kW. The conversion efficiency of thermal energy to mechanical energy of the water column above the tin drop was found to be in the range 0.1%–1.0%.     

Modeling of Flow and Heat Transfer in a Molten Glass Mini-Film for High Temperature Heat Collection in a Falling-Film Solar Central Receiver

ABSTRACT

In concentrating solar power plants, there is a strong incentive to increase the collection temperature and the overall exergy efficiency of the system. Some molten glass mixtures are attractive working fluids for high temperature solar thermal heat collection because optimized glass mixtures can be more stable, less-toxic, and less-corrosive than, for example, molten salts at high temperatures (≥1000°C). A specific phosphorous pentoxide glass mixture is considered in this study to explore its performance in a molten glass falling film central receiver design for collection of heat at conditions resulting in a mini-film with a thickness less than 3mm. In our falling molten glass thin film, the phosphate glass flow is treated as a laminar, Newtonian and gravity-driven flow over a slightly inclined flat plate using an explicit finite difference scheme to evaluate its heat transfer performance for a direct absorption receiver concept. One of the main challenges of modeling transport in the molten glass is the strong dependence of its viscosity on temperature. To incorporate this effect in our numerical analysis, a temperature-dependent viscosity model is used in the momentum equation to model the fluid behavior as it flows down the surface and is progressively heated. An exponential function is used to model the viscosity as it changes with temperature to properly fit the measured the viscosity data provided by Halotechnics. Also, a variable film thickness model analysis is implemented to treat the variation in film thickness that results from the viscosity variation with temperature. In order to avoid stability issues, the finite difference scheme is organized in terms of nondimensional parameters that include all important properties that govern the system. The results of our model indicate that thinning of the film as it flows over the heated surface enhances the heat transfer performance on the lower portion of the receiver system. The heat transfer coefficient increases instead of remaining constant (as normally expected for fully developed laminar flows) on the lower portion of the heated surface. The results further indicate that using a thin mini-film of molten glass for solar thermal heat collection provides high heat transfer performance and enhances the exergy collection.     

A new model of mass flow characteristics in electronic expansion valves considering metastability

This paper presents an experimental study on the mass flow characteristics of electronic expansion valves in a wide operating condition range. It was found that flow choking always occurs under common operating conditions in refrigeration systems. Based on metastability in EEVs, a new model predicting mass flow rate was proposed under flow choking conditions. Different from the conventional models using Bernoulli equation which employed downstream pressure at the EEV exit and a corrected mass flow coefficient, the present model considered metastable liquid flow caused by rapid depressurization, and employed single-phase incompressible flow coefficient and metastable pressure at the throat. An empirical correlation of the metastable pressure, based on the experimental data for R22 and its substitutes, R407C and R410A, was developed in a power law form of dimensionless parameters including upstream operating parameters and refrigerant thermophysical properties and throat area. The predictions of the present model were found to be in good agreement with the measured data, and approximately 95% of the measured data fall within a relative deviation of ±7.0%. The comparison with a prior model shows that, in terms of flashing mechanism application and predicting accuracy, the present model is better than the conventional model without considering metastability.     

NaCl-MgCl2-CaCl2相图计算方法研究

为满足规模化太阳能热发电中对传热蓄热的要求,针对储能材料开展探究。以熔融盐热物性及经济性作为筛选条件,选定来源广泛、价格低廉、工作温度范围宽、黏度低、相变潜热大的NaCl、MgCl₂和CaCl₂三元熔盐体系开展深入研究。应用修正的准化学溶液模型,在子二元系基础上推导计算三元混合熔盐NaCl-MgCl₂-CaCl₂相图。结果表明,该熔盐混合物共晶点温度为412.45 ℃,NaCl、MgCl₂和CaCl₂的摩尔分数分别为50.99%、22.78%和26.23%,与已有文献数据相比,误差在3%以内,验证了方法的准确性,为构建熔盐氯化物相图数据库奠定了部分基础。     

An analytical model for gas absorption in open-channel flow

An analytical model is developed for gas absorption in open-channel flow. It is solved in closed-form by the integration of the boundary layer diffusion equation for prescribed four liquid film layers and assumed universal velocity profile across the liquid film. A model is expressed in a form of an algebraic correlation for the prediction of mass transfer coefficient at the liquid surface. The comparison between the model predictions and the experimental data of CO₂ absorption in open-channel flow shows good agreement.     

The meshless analog equation method for solving heat transfer to molten polymer flow in tubes

In this paper, we proposed a meshless analog equation method (MAEM) to solve a heat transfer problem of molten polymer flow, which is considered to be a generalized Newtonian viscous flow. The MAEM, free from mesh generation and numerical integration, is a powerful meshless method. The numerical solutions are expressed by a linear combination of the derived radial basis functions (RBFs). This paper considers two different viscosity models for the molten polymer; one is temperature-independent power-law model and the other is temperature-dependent power-law model. The viscous dissipation term is included in the energy equation to capture the relevant physical phenomena. From the comparisons of numerical simulation, the meshless solutions are in good agreement with some analytical solutions and other finite element solutions. Moreover, the MAEM uses much less CPU-time and computer memory to simulate molten polymer flows. Therefore, it is believed that the RBF-based meshless method of the MAEM is a promising and flexible numerical scheme for molten polymer flow simulation.     

Non-equilibrium solidification of the molten metal droplets impacting on a solid surface

A measuring method for the kinetic coefficient and activation energy of molten metals has been developed. This method is based on a splat thickness measurement of a molten metal droplet deposited on a polished metal substrate. An analytical solution of a non-equilibrium crystallization of a molten metal droplet impacting on a solid substrate relates the thickness of the splat to the kinetic coefficient. The dimensionless number showing the departure of the equilibrium phase transition from the non-equilibrium transition follows from the theory. The predicted values of the kinetic coefficient and activation energy agree well with the existing literature data.     

Liquid-based high-temperature receiver technologies for next-generation concentrating solar power: A review of challenges and potential solutions

To reduce the levelized cost of energy for concentrating solar power (CSP), the outlet temperature of the solar receiver needs to be higher than 700 °C in the next-generation CSP. Because of extensive engineering application experience, the liquid-based receiver is an attractive receiver technology for the next-generation CSP. This review is focused on four of the most promising liquid-based receivers, including chloride salts, sodium, lead-bismuth, and tin receivers. The challenges of these receivers and corresponding solutions are comprehensively reviewed and classified. It is concluded that combining salt purification and anti-corrosion receiver materials is promising to tackle the corrosion problems of chloride salts at high temperatures. In addition, reducing energy losses of the receiver from sources and during propagation is the most effective way to improve the receiver efficiency. Moreover, resolving the sodium fire risk and material compatibility issues could promote the potential application of liquid-metal receivers. Furthermore, using multiple heat transfer fluids in one system is also a promising way for the next-generation CSP. For example, the liquid sodium is used as the heat transfer fluid while the molten chloride salt is used as the storage medium. In the end, suggestions for future studies are proposed to bridge the research gaps for > 700 °C liquid-based receivers.     

A simplified model for bi-component droplet heating and evaporation

A simplified model for bi-component droplet heating and evaporation is developed and applied for the analysis of the observed average droplet temperatures in a monodisperse spray. The model takes into account all key processes, which take place during this heating and evaporation, including the distribution of temperature and diffusion of liquid species inside the droplet and the effects of the non-unity activity coefficient (ideal and non-ideal models). The effects of recirculation in the moving droplets on heat and mass diffusion within them are taken into account using the effective thermal conductivity and the effective diffusivity models. The previously obtained analytical solution of the transient heat conduction equation inside droplets is incorporated in the numerical code alongside the original analytical solution of the species diffusion equation inside droplets. The predicted time evolution of the average temperatures is shown to be reasonably close to the measured one, especially in the case of pure acetone and acetone-rich mixture droplets. It is shown that the temperatures predicted by the simplified model and the earlier reported vortex model are reasonably close. Also, the temperatures predicted by the ideal and non-ideal models differ by not more than several degrees. This can justify the application of the simplified model with the activity coefficient equal to 1 for the interpretation of the time evolution of temperatures measured with errors more than several degrees.     

Wake Flow and Heat Transfer Due to a Spherical Viscous Droplet

A numerical study on the buoyancy-assisted flow and heat transfer from a liquid spherical droplet falling in fluid medium is made. The investigation is based on the solution of the Navier-Stokes equations together with the energy equation inside and outside the droplet, along with a suitable interface condition. The governing equations for three-dimensional flow and heat transfer are solved through the pressure correction based iterative algorithm, SIMPLE. The Reynolds number for the exterior flow is considered below 300 with the Richardson number in the range 0 ≤ Ri ≤ 1.5. The form of the wake due to the viscous droplet and its influence on heat transfer and drag coefficient are analyzed for a wide range of physical parameters. It is found that by increasing the Reynolds number, the predicted rate of heat transfer is significantly increased for a liquid droplet compared to a solid sphere. The increment of viscosity of the droplet increases the drag experienced by the droplet but reduces the rate of heat transfer. An increase in Richardson number produces an increment in drag coefficient as well as in heat transfer. In order to establish a simplified model for heat transfer due to a viscous droplet, we compared our computed solutions with several empirical correlations for conjugate heat transfer and proposed a model (in absence of buoyancy). We have also investigated the validity of several empirical correlations for the drag coefficient.     

A step-by-step methodology to construct a model of performance of molten carbonate fuel cells with internal reforming

This work is divided into two main sections. First, a review of the most frequently used approaches to molten carbonate fuel cell modelling is presented. The models available in literature are found to be classified in three different groups which are carefully described in the paper. Then the models are compared and their ability to predict fuel cell performance far from the design point is tested. It is concluded that even though some models seem to be accurate close to a reference point, their estimates differ largely far from these working conditions.Accordingly, a model is selected amongst those previously reviewed and its capacity to replicate real fuel cell performance is checked against experimental data available in open literature. Such validation confirms that the model is fully satisfactory as it is able to predict fuel cell performance within less than 1.0-1.5% deviation for a wide variety of test setups. This remarkable accuracy is further reinforced by the fact that the model does not rely on experimental information (known a priori) about the system being modelled.The work also introduces an interesting approach to estimate average gas compositions to be used when evaluating Nernst potential. This approach is based on arithmetic and logarithmic means for cathode and anode respectively and it proves to yield accurate results.Overall, the work provides researchers willing to construct their own models of performance with a valuable guide to assess them in such process.     

不同状态方程对R134a摩擦理论黏度模型的比较分析

为了考察不同状态方程对摩擦理论黏度模型拟合结果的影响,以制冷剂R134a为例,分别采用工程上常用的PR(Peng-Robinson)方程、MBWR(modified benediet-webbrubin)方程和R134a的专用状态方程Span-Wagner方程建立了R134a的摩擦理论黏度模型.计算结果表明,用这三个方...     

A momentum integral model for prediction of steady operation and flooding in thermosyphons

An analytical momentum integral model is developed for the prediction of the steady operation of closed two-phase thermosyphons over a wide range of temperatures, pressures and heat inputs. Using a new proposed velocity distribution for the flow of the liquid film, differential equations for mass, momentum, and energy balances have been solved simultaneously to obtain the continuous solution for the thickness of the liquid film, mass flow rate, and heat transfer along the length of the condenser. The interfacial shear due to phase-change at the liquid–vapor interface, as well as acceleration of the condensate film in the momentum balance equation, has been taken into account. The current model uses minimal number of semi-empirical correlations for interfacial shear and heat transfer coefficient and utilizes self-consistent assumptions. The current model is able to accurately predict the essential performance parameters of the system including local and overall mass flow and heat transfer rates through the length of the condenser for a wide range of low to medium heat inputs, up to the flooding limit. Despite the simplicity of the model in comparison to previous studies, the predictions for local mass flow rates and heat fluxes are in excellent agreement with available experimental data.     

Performance model of molten carbonate fuel cell

A performance model of a molten carbonate fuel cell (MCFC), an electrochemical energy conversion device for electric power generation, is discussed. The presumptive ability of the MCFC model is improved and the impact of MCFC characteristics in fuel cell system simulations is investigated. Basic data are obtained experimentally by single-cell tests. A correlation formula based on the experimental data is derived for the cell voltage and the oxygen and carbon dioxide partial pressures. Three types of MCFC systems are compared. With regard to fuel utilization, system characteristics using the proposed correlation are very similar to those obtained using a previous model. However, the amount of decrease predicted by the proposed model with respect to system efficiency is larger than that obtained by the previous model at high air utilization     

Observations of initiation stage of spontaneous vapor explosions for droplet scale

In this study, the initiation stage of spontaneous vapor explosions generated by single droplets of molten tin submerged in water was investigated using a high‐ speed video camera operated with a reflected light system. Photographs of the formation process of vapor film, the process of vapor film disturbance, and the initiation process of the vapor explosions for different masses of molten tin and different nozzle diameters were obtained. The results demonstrate that partial thermal interaction between tin and water does not cause a vapor explosion with fragmentation. The vapor film disappears locally during the formation of the vapor film around the hot liquid droplet. Direct contact between the hot molten tin surface and water is thereby generated. However, the local disappearance of the vapor film does not progress and the vapor film is reconstructed. A vapor explosion occurs when the vapor film collapses at the local area of the bottom or edge of the disk‐shaped droplet. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(1): 41–55, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20185