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.     

基于有限元方法的溴化锂降膜吸收传热传质的数值研究

吸收器是吸收式制冷系统的重要部件.溴化锂溶液的降膜吸收是吸收器中最常见的传质传热形式之一.通过对溴化锂溶液在降膜吸收过程中传质和传热特性的分析,使用基于有限元法的COMSOL Multiphysics软件,建立了溴化锂溶液和水蒸汽降膜吸收的物理数学模型,计算了液膜内部温度和质量分数的分布、界面处传质通量、界面处传热通量...     

Étude numérique de l'évaporation dans un courant d'air humide laminaire d'un film d'eau ruisselant sur une plaque inclinée

Numerical study of the evaporation in laminar humid air flow of a liquid film flowing over an inclined plate. By using an implicit centered finite differences method with a non-uniform grid, the authors study numerically the evaporation of a thin liquid film flowing over an inclined plate in a forced humid-air flow. They consider the existence of two-dimensional laminar boundary-layers with variable physical properties and show that the term of enthalpy diffusion is always negligible, whether the plate is adiabatic, isothermal or heated by a constant heat flux density. By using in the liquid film transfer equations which are one-dimensional, partially two-dimensional and two-dimensional, the authors additionally show the following features. If the plate is adiabatic, the liquid mass flow rate is without influence on the transfers and the gas–liquid interface behaves like an isotherm surface at rest. In this case, one may use a one-dimensional model in the film whatever liquid mass flow rate is. If the wall is isotherm or heated by a constant heat flux and when the liquid mass flow rate is less than 10⁻³ kg·m⁻¹·s⁻¹, the one-dimensional model is sufficient; if it is included in the interval [10⁻³ kg·m⁻¹·s⁻¹, 10⁻² kg·m⁻¹·s⁻¹[, the partially two-dimensional model is useful; if it is superior to 10⁻² kg·m⁻¹·s⁻¹, it is necessary to use the two-dimensional model. Generally, whatever the thermal conditions on the plate are, heat transfer is dominated by the liquid-vapor transition.     

Effects of film evaporation on laminar mixed convection heat and mass transfer in a vertical channel

A numerical study of finite liquid film evaporation on laminar mixed convection heat and mass transfer in a vertical parallel plate channel is presented. The influences of the inlet liquid mass flow rate and the imposed wall heat flux on the film vaporization and the associated heat and mass transfer characteristics were examined for air-water and air-ethanol systems. Predicted results obtained by including transport in the liquid film are contrasted with those where liquid film transport is neglected, showing that the assumption of an extremely thin film made by Tsay and Yan (Wärme- und Stoffübertragung 26, 23–31 (1990)) is only valid for a system with a small liquid mass flow rate. Additionally, it is found that the heat transfer between the interface and gas stream is dominated by the transport of latent heat associated with film evaporation. The magnitude of the evaporative latent heat flux may be five times greater than that of sensible heat flux.     

Effects of Aspect Ratio on the Turbulent Heat Transfer of Regenerative Cooling Passage in a Liquid Rocket Engine

Turbulent flows and related heat transfer in a regenerative cooling passage of liquid rocket engine are investigated by turbulence models. At a constant mass flow rate, three-dimensional characteristics of flow and heat transfer are studied by changing the aspect ratio under constant or variable heat flux conditions. The cooling passage shows different flow structures, which cannot be found in a straight duct, because the heated wall has a convex-concave-convex curvature. So, the streamwise velocity and secondary flows are varied by the geometrical feature of curvature inversion. From these characteristics the thermal field in the cooling passage is discussed depending on the variation of cross-sectional area and the aspect ratio. Also, the influences of aspect ratio coupled to the thermal boundary condition are investigated. Finally, the geometric effects on the local heat transfer and the change of flow structure are scrutinized.     

Effects of inlet conditions on film evaporation along an inclined plate

The evaporation of falling water liquid film in air flow is used in different solar energy applications as drying, distillation and desalination, and desiccant systems. The good understanding of the hydrodynamics and heat exchange in falling liquid film and gas flow, with interfacial heat and mass transfer, can be applied in improving solar systems performance. The solar system performance is dependent on the operating conditions, system conception and related to several physical parameters, where the effects of some of these parameters are not completely clarified. In the present numerical study, we examine the effects of inlet conditions on the evaporation processes along the gas–liquid interface. The liquid film streams over an inclined plate subjected to different thermal conditions. Liquid and gas flows are approached by two coupled laminar boundary-layers. The numerical solution is obtained by utilizing an implicit finite-difference box method. In this analysis an air–water system is considered and the coupled effects of inclination, inlet liquid mass flow rate and gas velocity are examined. The results show that, for imposed heat flux or uniform wall temperature, the effect of inclination is highly dependent on the liquid mass flow rate and gas velocity. An increase in the liquid mass flow rate causes an enhancement of the effect of inclination on the heat and mass transfer. The inclination affects the heat and mass transfer, especially at lower gas velocities. In the range of inclination angles of 0–10°, an increase in the inclination improves the evaporation by increasing the vapor mass flow rate. The maximum effect of inclination is nearly achieved at an inclination angle of 10°.     

Simultaneous measurement of local film thickness and temperature distribution in wavy liquid films using a luminescence technique

Heat transfer in falling liquid film systems is enhanced by waviness. Comprehension of the underlying kinetic phenomena requires experimental data of the temperature field with high spatiotemporal resolution. Therefore a non-invasive measuring method based on luminescence indicators is developed. It is used to determine the temperature distribution and the local film thickness simultaneously. First results are presented for the temperature distribution measurement in a laminar-wavy water film with a liquid side Reynolds number of 126 flowing down a heated plane with an inclination angle of 2°. The measured temperature distributions are used to calculate the local heat transfer coefficient and the convective heat flux perpendicular to the wall for different points in the development of a solitary wave.     

Laminar flow and heat transfer of non-newtonian falling liquid film on a horizontal tube with variable surface heat flux

An analysis is performed to study the laminar flow and heat transfer of non-Newtonian falling liquid film on a horizontal tube for the case of variable surface heat flux. The inertia and convection terms are taken into account. The governing boundary layer equations are solved numerically using an implicit finite difference method. Of particular interest are the effects of the mass flow rate Γ, the concentration C of carboxymethylcellulose (CMC) solutions, the exponent m for the power-law surface heat flux, and the tube diameter D on the film thickness profiles, as well as on the local and average Nusselt numbers. It was found that an increase in the mass flow rate Γ and exponent value m increases the local and average heat transfer rates. Finally, the present simulation is found to be in good agreement with previous experimental and numerical results for Newtonian films.     

Numerical simulation and experimental results of horizontal tube falling film generator working in a NH3–LiNO3 absorption refrigeration system

This paper describes the work made at the Centro de Investigación en Energía in the development of an absorption refrigeration system for cooling and refrigeration applications with a capacity of 10 kW. The single effect unit utilizes ammonia-lithium nitrate as working pair and it is air cooled. The generator is a falling film type with horizontal tubes where the heating oil flows inside the tube bank and the ammonia-lithium nitrate solution flows as a falling film on the tube outside, where it is heated and ammonia vapor is generated. The generator consists of tree columns and four rows per column of horizontal tubes. The system was tested at controlled conditions with heating oil obtained from an electric resistance heating loop. A numerical model of the horizontal falling film generator was developed that divided the system into three different thermal elements: the flow inside the tube, the heat conduction in the tube wall and the falling film solution flow. The mathematical model was tested and validated with experimental data and a study of the influence of the heat transfer coefficient for ammonia-lithium nitrate solution in the numerical model was carried out. A comparison between experimental and numerical data for the heat flux in the system and the temperature profiles in the oil and solution flows shown a good degree of correlation.     

Heat transfer characteristics of falling film evaporation on horizontal tube arrays

A falling film heat transfer test facility has been built for the measurement of falling film evaporation in a vacuum of about 1000 Pa. At this condition, only convective evaporation occurred in the liquid film. The Reynolds numbers of falling film over a range from 21.6 to 108.1 were tested on six-tube arrays made of enhanced or smooth tubes. Results show that the tubes with both enhanced outer and inner surfaces give high heat flux. Besides, as the Reynolds number increases, the heat transfer enhancement ratio of falling film evaporation decreases. A semi-analytical correlation is established to predict the heat transfer coefficients of falling film evaporation on smooth tube arrays, considering the contributions of partially dryout and fully wet regimes, respectively. For enhanced tubes, the heat transfer enhancement ratios to the smooth tubes were also correlated.     

Numerical investigation of effective parameters of falling film evaporation in a vertical-tube evaporator

Wastewater treatment is one of the most effective solutions to manage the problem of water scarcity. Falling film evaporators are excellent technology in wastewater treatment plants. These wastewater evaporators provide high heat transfer, short residence time in the heating zone, and high-purity distilled water. In the present study, the mechanism of turbulent falling film evaporation in a vertical tube has been investigated. A model has been developed for symmetrical two-dimensional pure and saline water flow in a vertical tube under constant wall heat flux. The numerical simulation has been carried out by a commercial computational fluid dynamics code. The evaporation of saturated liquid film is simulated utilizing a two-phase volume of fluid method and Tanasawa phase-change model. The main objective of this study is to evaluate the effects of water salinity, liquid Reynolds number, wall heat flux, and liquid film thickness on the two-phase heat transfer coefficient and vapor volume fraction. The numerical heat transfer coefficients are compared with the obtained results by Chen's empirical correlation. With a MAPE ≤ 11%, this study proves that the numerical method is highly effective at predicting the heat transfer coefficient. Moreover, the empirical coefficient of the Tanasawa model and the minimum thickness of the falling film are determined.     

自由表面摩擦和蒸发对过冷下降液膜传热的影响

从理论上对下降液膜在自由表面上存在反向剪切力和蒸发散热情况下的换热特性进行了分析,得到了膜厚、换热系数的无量纲关系式,讨论了剪切力、液膜雷诺数、壁面热流、蒸发率对流动和传热的影响。     

Local and instantaneous distribution of heat transfer rates through wavy films

Heat transfer through a laminar-wavy falling silicon oil film on a vertical plate has been investigated. The film flows down an electrically heated metal foil which delivers a constant heat flux. The temperature field at the backside of the foil is measured by a very sensitive infrared camera with high temporal resolution. Local and instantaneous heat transfer rates through the film are evaluated from the temporal development of the local wall temperature. Investigations in two-dimensional waves show the influence of the Prandtl number on the transport processes even in the laminar region. The experimental data confirm the results of numerical calculations with a spectral element method. Furthermore, the temporal averaged heat transfer has been investigated in thermally developed three-dimensional wavy films over a film Reynolds number range of 10–129 and a Prandtl number range of 10–45. The Prandtl number dependency of the heat transfer in the laminar-wavy region of the film agrees well with a recently published experimental study.     

Natural convection flows in a vertical,open tube resulting from combined buoyancy effects of thermal and mass diffusion

This study aims to investigate theoretically the role of latent heat transfer, in connection with the vaporization of a thin liquid film on a tube's inside surface, in natural convection flows driven by the simultaneous presence of combined buoyancy effects of thermal and mass diffusion. Results are specifically presented for an air-water system under various conditions. The effects of tube length and system temperatures on the momentum, heat and mass transfer in the flow are examined in great detail. The important role that the liquid film plays under the situations of buoyancy-aiding and opposing flows is clearly demonstrated.     

Conjugate heat transfer measurements with single-phase and water flow boiling in a single-side heated monoblock flow channel

Optimized and robust designs of one-side heated plasma-facing components and other heat flux removal components are dependent on conjugate heat transfer. In the present case, the conjugate heat transfer involved measuring the local distributions of the inside wall temperature and heat flux in a single-side heated monoblock flow channel with: (1) peripheral (radial and circumferential) heat transfer; and, (2) coupled internal turbulent, forced convective single-phase flow and flow boiling. For the first time, multi-dimensional boiling curves have been measured for a single-side heated monoblock flow channel. Using a thermal hydraulic diameter as the characteristic dimension in select correlations for the highest mass velocity (3.2 Mg/m² s), good agreement was obtained. At lower mass velocities, only the single-phase correlations agreed better with the data for the averaged net incident heat flux vs the inside channel wall temperature. Hence, additional correlation development and adaptation are needed for single-side heated monoblocks with peripheral heat transfer.     

Shear-driven flows of locally heated liquid films

This paper considers the flow of a liquid film sheared by gas flow in a channel with a heater placed at the bottom wall. A one-sided 2D model is considered for weakly heated films. The heat and mass transfer problem is also investigated in the framework of a two-sided model. The exact solution to the problem of heat transfer is obtained for a linear velocity profile. The double effect of Marangoni forces is demonstrated by the formation of a liquid bump in the vicinity of the heater’s upper edge and film thinning in the vicinity of the lower edge. The criterion determining the occurrence of “ripples” on the film surface upstream from the bump is found. Numerical analysis reveals that evaporation dramatically changes the temperature distribution, and hence, thermocapillary forces on the gas–liquid interface. All transport phenomena (convection to liquid and gas, evaporation) are found to be important for relatively thin films, and the thermal entry length is a determining factor for heaters of finite length. The thermal entry length depends on film thickness, which can be regulated by gas flow rate or channel height. The influence of the convective heat transfer mechanism is much more prominent for relatively high values of the liquid Reynolds number. The liquid–gas interface Biot number is shown to be a sectional-hyperbolic function of a longitudinal axis variable. Some qualitative and quantitative comparisons with experimental results are presented.     

Experimental investigation of falling film evaporation on horizontal tubes

This paper presents the results of an experimental investigation relating to heat transfer during evaporation of thin liquid films falling over horizontal tubes. Experiments were conducted using 25 mm o.d. copper tubes heated by internal electrical cartridge heaters so that a uniform heat flux was generated on the outside tube surface. Five heated tubes were arrayed on a vertical plane with a pitch of 50 mm. Freon R-11 preheated to the saturation temperature at 0.2 MPa was supplied to the topmost heated tube through feeding tubes. Heat transfer characteristics on each heated tube were clarified in a range of film Reynolds number from 10 to 2000 and the measured data are presented in the form of correlations. Deterioration of heat transfer due to film break down was also considered. © 1999 Scripta Technica, Inc. Heat Trans Jpn Res, 27(8): 609–618, 1998     

A coupled level set and volume-of-fluid simulation for heat transfer of the double droplet impact on a spherical liquid film

A coupled level set and volume-of-fluid method is applied to investigate the double droplet impact on a spherical liquid film. The method focuses on the analysis of surface curvature, droplet diameter, impact velocity, double droplets vertical spacing, the thickness of the liquid film of two liquid droplets after the impact on a spherical liquid film, and the influence of flow and heat transfer characteristics. The results indicate that the average wall heat flux density of the double liquid droplet impact on a spherical liquid film is greater than that of a flat liquid film. Average wall heat transfer coefficient increases with the increase in the liquid film’s spherical curvature. When the liquid film thickness is smaller, the average wall heat flux density of the liquid film is significantly reduced by the secondary droplets generated from the liquid film. When the liquid film thickness is larger, the influence of liquid film thickness on the average wall heat flux density gradually decreases. The average wall heat flux density increases with the increase in impact velocity and the droplet diameter; it also decreases with the increase in double droplets vertical spacing.     

Experimental Study on Heat Transfer of Heated Falling Film Under Gas–Liquid Cross-Flow Condition

With the influence of the different gas Reynolds numbers and liquid Reynolds numbers on heated falling film heat transfer, an experiment was performed by noncontact thermal infrared imaging technology under the gas–liquid cross-flow condition. The results indicated that during the increase of liquid Reynolds number the thickness and thermal resistance of liquid film increased in the determined temperature of the heating water, which weakened the heat transfer of the liquid film. However, the increase of liquid Reynolds number strengthened liquid film turbulence and therefore enhanced heat transfer. Under the synergistic effect of these two factors, there should be an optimal liquid Reynolds number that minimizes thermal resistance and maximizes the heat transfer coefficient of the liquid film. Temperature plays an important role in heat transfer of laminar liquid film flow. However, the heat transfer of turbulent liquid film flow is not sensitive to liquid film inlet temperature.     

Effects of Non-Darcian and Inlet Conditions on the Forced Convection Along a Vertical Plate With Film Evaporation

The present study analyzes theoretically the non-Darcian effects and inlet conditions of forced convection flow with liquid film evaporation in a porous medium. The physical scheme includes a liquid–air streams combined system; the liquid film falls down along the plate and is exposed to a cocurrent forced moist air stream. The axial momentum, energy, and concentration equations for the air and water flows are developed based on the steady two-dimensional (2-D) laminar boundary layer model. The non-Darcian convective, boundary, and inertia effects are considered to describe the momentum characteristics of a porous medium. The paper clearly describes the temperature and mass concentration variations at the liquid–air interface and provides the heat and mass transfer distributions along the heated plate. Then, the paper further evaluates the non-Darcian effects and inlet conditions on the heat transfer and evaporating rate of liquid film evaporation. The numerical results show that latent heat transfer plays the dominant heat transfer role. Carrying out a parametric analysis indicates that higher air Reynolds number, higher wetted wall temperature, and lower moist air relative humidity will produce a better evaporating rate and heat transfer rate. In addition, a non-Darcy model should be adopted in the present study. The maximum error for predictions of heat and mass transfer performance will be 21% when the Darcy model is used.