A simple model for falling film absorption on vertical tubes in the presence of non-absorbables

Most water–lithium bromide (LiBr) absorption chillers have a purge system to remove non-absorbable gases that cause a reduction in cooling capacity. Generally, the non-absorbables are originated in corrosion/passivation processes inside the machine, but leaks can also be a source of concern. However, since leaks must be corrected immediately to avoid machine deterioration, this study is mostly aimed at the non-absorbables evolved during operation. This paper analyses the effect of inlet non-absorbable air concentration, outlet purge velocity, absorber pressure and cooling water temperature on the falling film absorption process inside a vertical tube absorber, based on a simple transport coefficient model. This model consists of three ordinary differential equations solved with as method for initial-value problem, and a set of auxiliary equations. The study shows that the effect of non-absorbables can be significant, and furthermore provides a quantitative framework to aid in purge design. The nominal working conditions in this study were a solution Reynolds number of 100, an absorber pressure of 1.3 kPa, a cooling water temperature of 35 °C and an inlet solution concentration of 62% LiBr by weight. The results indicate that a minimum vapour velocity is required to sweep the non-absorbables along the absorber towards the purge, thus preventing reduced absorption fluxes. At a cooling water temperature of 35 °C, an inlet air concentration of 20% (by mole) resulted in a 61% reduction in mass absorption flux.     

Gravity-driven flow of liquid films and droplets in horizontal tube banks

Liquid films falling over banks of internally cooled horizontal tubes are often used to absorb mass from a surrounding vapor. This arrangement is particularly suitable for absorption processes where the vapor has a high heat of absorption and where high transfer rates and low pressure drops are required, as is the case of absorption heat pumps and other chemical processes. When the liquid film presents a significant resistance to heat and mass transfer, understanding the motion of the film is critical. However, mathematical models of these types of systems in the literature have generally made use of many simplifying assumptions about the behavior of the falling liquid. The formation, detachment, and impact of droplets and the associated waves and film disturbances can all affect the mixing of the liquid and can enhance transfer rates accordingly. The objective of this paper is to identify and visually document these deviations from idealized film behavior and discuss their implications on the heat and mass transfer processes, which are important to consider in the development of mechanistic models of the absorption process.     

Analytical investigation of two different absorption modes: falling film and bubble types

The objectives of this paper are to analyze a combined heat and mass transfer for an ammonia–water absorption process, and to carry out the parametric analysis to evaluate the effects of important variables such as heat and mass transfer areas on the absorption rate for two different absorption modes — falling film and bubble modes. A plate heat exchanger with an offset strip fin (OSF) in the coolant side was used to design the falling film and the bubble absorber. It was found that the local absorption rate of the bubble mode was always higher than that of the falling film model leading to about 48.7% smaller size of the heat exchanger than the falling film mode. For the falling film absorption mode, mass transfer resistance was dominant in the liquid flow while both heat and mass transfer resistances were considerable in the vapor flow. For the bubble absorption mode, mass transfer resistance was dominant in the liquid flow while heat transfer resistance was dominant in the vapor region. Heat transfer coefficients had a more significant effect on the heat exchanger size (absorption rate) in the falling film mode than in the bubble mode, while mass transfer coefficients had a more significant effect in the bubble mode than in the falling film mode.     

Falling-film evaporation on horizontal tubes—a critical review

A state-of-the-art review of horizontal-tube, falling film evaporation is presented; the review is critical, in an attempt to uncover strengths and weaknesses in prior research, with the overall purpose of clearly identifying gaps in our understanding. The review covers flow-pattern studies, and the experimental parameters that affect the heat transfer performance on plain single tubes, enhanced surfaces and tube bundles. In addition, this paper presents a comprehensive review of the significant efforts to develop mathematical models, and empirical correlations for the heat transfer coefficient. Emphasis is placed on studies that are related to refrigeration applications.     

An elemental NTU- model for vapour-compression liquid chillers

This paper presents a steady-state model for predicting the performance of vapour-compression liquid chillers over a wide range of operating conditions. The model overcomes the idealisations of previous models with regard to modelling the heat exchangers. In particular, it employs an elemental NTU- methodology to model both the shell-and-tube condenser and evaporator. The approach allows the change in heat transfer coefficients throughout the heat exchangers to be accounted for, thereby improving both physical realism and the accuracy of the simulation model. The model requires only those inputs that are readily available to the user (e.g. condenser inlet water temperature and evaporator water outlet temperature). The outputs of the model include system performance variables such as the compressor electrical work input and the coefficient of performance (COP) as well as states of the refrigerant throughout the refrigeration cycle. The methodology employed within the model also allows the performance of chillers using refrigerant mixtures to be modelled. The model is validated with data from one single screw chiller and one twin-screw chiller where the agreement is found to be within ±10%.     

Two-dimensional turbulent film condensation of vapours flowing inside a vertical tube and between parallel plates: a numerical approach

Film condensation of vapour flowing inside a vertical tube and between parallel plates is treated. A methodology is presented to determine numerically the heat transfer coefficients, the film thickness and the pressure drop. The analysis is based on the resolution of the full coupled boundary layer equations of the liquid and vapour phases and does not neglect inertia and convection terms in the governing equations. Turbulence in the vapour and condensate film is taken into account using mixing length turbulence models. An explicit method and an implicit finite difference procedures are described. The calculated results for the condensation of steam in a 24 mm diameter tube are compared with those obtained from Chen's correlation. The heat flow rate for the condensation of R123 flowing between parallel plates obtained from numerical solution are compared with experimental values. The mean heat transfer coefficients for the condensation of vapour mixture R123/R134a are also presented.     

An experimental and numerical study of the dynamic behaviour of a counter-flow evaporator

The dynamic behaviour of a counter-flow, water-heated evaporator is studied experimentally and numerically. The frequency distribution of the random oscillations of the mixture-vapour transition point and the superheat temperature at the exit of the evaporator is obtained for steady operation of the system. These oscillations are well correlated. The transition point movement is found to cause fluctuations in the refrigerant temperature over 1 m downstream of its range of motion. Step changes in the refrigerant flow rate and the heating water flow rate demonstrate the non-linear characteristics of the evaporator where the time constants for step increases and step decreases of the same magnitude differ significantly. The distributed model predicts the variation of the superheat temperature and the evaporator pressure following step changes in the inputs with good accuracy.     

Time-dependent behavior of gas absorption in lubricant oil

Gas absorption behavior in liquid with time has been studied by applying a simple mathematical model. The model is based on a one-dimensional mass diffusion process due to the concentration difference in dissolving gas. In order to examine the model validity, selected experimental data in the literature have been analyzed with the present model. The model has faithfully reproduced the experimental transient behavior of dissolving gases, and physically meaningful model parameters, diffusion constant and solubility limit, have been obtained for dissolving gas (water and refrigerant) in various lubricant oils. The validity and the significance of the model are discussed.     

Evaluation of heat and mass transfer coefficients for falling-films on tubular absorbers

A coupled heat and mass transfer model is developed to extract the transfer coefficients for falling-films from the measurements on a tubular absorber. The mass transfer coefficients obtained from the coupled model and the log-mean-difference approach agree within about 10%. For the heat transfer coefficient, the values given by the two models can differ quite significantly. The cooling water temperature distribution predicted by the coupled model agrees well with measurements. The transfer coefficients obtained from experimental measurements using the various methods reported in the literature show wide variations.     

Wave characteristics of falling liquid film on a vertical circular tube

A falling film with waves on a vertical circular tube has been analyzed using the integral approach. A theoretical model of free surface deflection has been developed. The nonlinear equation obtained in the present work is similar to the deflection equation of a wave on a flat plate. It becomes exactly the same as the wave equation on a flat plate in the case of an infinite radius. This study shows that the wave characteristics depend on the parameters such as wave number, dimensionless wave velocity, tube radius and Reynolds number. As the tube radius decreases, the intensity of the wavy processes increases. The velocity distribution of the falling film was investigated in the present work. The cylindrical model appears to be more appropriate over the Cartesian model when the film thickness to tube diameter ratio is large. Calculated values are in good agreement with other published data.     

Experimental correlation of falling film absorption heat transfer on micro-scale hatched tubes

The objectives of this paper are to investigate the effect of surface roughness of micro-hatching tubes on the absorption performance and to develop an experimental correlation of Nusselt number as a function of the roughness. Two different micro-scale hatched tubes and a bare tube are tested to quantify the effect of the surface roughness on the absorption performance. The roughness of the micro-scale hatched tubes ranges 0.386–11.359 μm. The working fluid is H₂O/LiBr solution with inlet concentration of 55, 58 and 61 wt.% of LiBr. The absorber heat exchanger consists of 24 horizontal tubes in a column, liquid distributor at the liquid inlet and the liquid reservoir at the bottom of the absorber. It was found that absorption performance of micro-hatching tubes was improved up to two times compared with the bare tube. An experimental correlation of Nusselt number was developed as a function of the film Reynolds number and the roughness with an error band of ±25%.     

Testing the computer assisted solution of the electrical analogy in a heat transfer process with a phase change which has an analytical solution

A new method has been developed for the computer assisted solution of electrical analogies. The method, relatively simple in comparison with other methods, allows the study of heat transfer problems, including the change of phase. The aim of this work has been to apply this technique to the study of a heat transfer problem with change of phase, which has an analytical solution, in order to test its validity. The results obtained by both methods, analytical and analogical, are compared, and they are observed to agree satisfactorily. It makes it possible to establish that the technique developed is suitable for the study of processes with a phase change present.     

Interfacial mass transfer and mass transfer coefficient in aqua ammonia packed bed absorberTransfert de masse à l'interface et coéfficient de transfert de masse dans un absorbeur à matelas dispersant eau–ammoniac

A mathematical model was given to predict the mass transfer between flow of a mixture of ammonia vapor and water vapor and a flow of aqua ammonia solution at any interface within a packed bed absorber (PBA). The model used the molal mass and heat transfer coefficients in both the liquid and gas phases, the interface molal solution concentration, interface molal vapor mixture concentration, interface temperature, and the heat transfer coefficients in the liquid and gas phases in both sides of the interface. The heat transfer coefficient was corrected to account for the mass transfer. The model was also used to derive a convenient mass transfer coefficient which was based on the bulk mass concentration, not on the molal concentration, and not directly dependent on the concentration at the interface. To complete the model, mathematical correlations were derived for several thermodynamic and physical properties of aqua ammonia solution and vapor mixture. A computer program was developed to demonstrate the use of the model to predict the rate of absorption of ammonia vapor at an interface within the packed bed at various operating conditions.     

Thermodynamic modeling of an ammonia–water absorption chiller

This article develops a general thermodynamic framework for the modeling of an irreversible absorption chiller at the design point, with application to a single-stage ammonia–water absorption chiller. Component models of the chiller have been assembled so as to quantify the internal entropy production and thermal conductance (UA) in a thermodynamically rigorous formalism, which is in agreement with the simultaneous heat-and-mass transfer processes occurring within the exchangers. Local thermodynamic balance (viz. energy, entropy, and mass balance) and consistency within the components is respected, in addition to the overall thermodynamic balance as determined by the inlet and outlet states of the components. For the absorbers, Colburn-and-Drew mass transfer equations are incorporated to describe the absorption process. Furthermore, the impact of various irreversibilities on the performance of chiller is also evaluated through the use of a general macroscopic equation.     

Heat and mass transfer enhancement of binary nanofluids for H2O/LiBr falling film absorption process

The objectives of this study are to measure the vapor absorption rate and heat transfer rate for falling film flow of binary nanofluids, and to compare the enhancement of heat transfer and mass transfer under the same conditions of nanofluids. The key parameters are the base fluid concentration of LiBr, the concentration of nanoparticles in weight %, and nanoparticle constituents. The binary nanofluids are H₂O/LiBr solution with nanoparticles of Fe and Carbon nanotubes (CNT) with the concentrations of 0.0, 0.01 and 0.1 wt %. The vapor absorption rate increases with increasing the solution mass flow rate and the concentration of Fe and CNT nanoparticles. It is found that the mass transfer enhancement is much more significant than the heat transfer enhancement in the binary nanofluids with Fe and CNT. It is also found that the mass transfer enhancement from the CNT nanoparticles becomes higher than that from the Fe nanoparticles. Therefore, the CNT is a better candidate than Fe nanoparticles for absorption performance enhancement in H₂O/LiBr absorption system.     

The effect of micro-scale surface treatment on heat and mass transfer performance for a falling film H2O/LiBr absorber

The objectives of this paper are to develop a new method of wettability measurement, to study the effect of micro-scale surface treatment on the wettability across horizontal tubes and to apply it for numerical analysis of heat and mass transfer in a H₂O/LiBr falling film absorber. Three types of tubes with roughness are tested in a test rig. Inlet solution temperature (30–50 °C), concentration (55–62 wt.% of LiBr) and mass flow rate (0.74–2.71 kg/min) are considered as key parameters. Reynolds number ranged from 30 to 120 by controlling the inlet mass flow rate. The wettability on the roughened tubes was higher than that for the smooth tubes. The wettability decreased linearly along the vertical location but was proportional to the solution temperature and mass flow rate. The experimental correlations of the wettability for the smooth and the roughened tubes were developed with error bands of ±20 and ±10%, respectively. These are used for the heat and mass transfer analysis of absorbers with micro-scale hatched tubes.     

Effect of axial conduction on the ice crystal growth in laminar falling filmsEffet de la conduction axiale sur la vitesse de formation de cristaux de glace à l'intérieur de films tombants laminaires

A finite volume numerical code has been developed to numerically approximate the rate of ice crystal growth in a laminar falling film flowing down a cooled vertical plate. The governing energy equation contains the phase energy as the source term. Enhancement of heat transfer as a result of suspended ice crystals is accounted for in the use of effective values of thermal conductivity, viscosity, thermal diffusivity, and specific heat as function of volumetric concentration of ice crystals in the falling film. Nusselt number, overall heat transfer coefficients between the fluid and cooled plate, and ice crystal growth rate were calculated for different film thicknesses with and without axial diffusion. Nusselt number and ice crystal growth rates were found to be dependent on film thickness. Axial diffusion effects were found to be negligible for larger film thickness (large flowrate).     

Transient simulation of vapour-compression packaged liquid chillers

This paper presents a transient simulation model that is useful for predicting the dynamic performance of vapour-compression liquid chillers over a wide range of operating conditions. The model employs a thermal capacitance approach for specific state variables to account for the dynamics of the chiller and ancillaries. The model accounts for the change in heat transfer coefficients throughout the heat exchangers thereby improving both physical realism and the accuracy of the simulation model. The model requires only a select few initial conditions (eg. the chilled water and condenser water temperatures). A simple compressor model based on empirical regression has been employed in the simulation. The outputs of the model include system performance variables such as the compressor electrical work input and the coefficient of performance (COP) as well as states of the refrigerant throughout the refrigeration cycle with respect to time. The model is validated with data from two in -situ screw chillers. Predictions are found to be within ±10%, although for one of the chillers a degree of empiricism was employed for the evaporator tube wall mass in order to give satisfactory results for the start-up process.     

A numerical model for thermal mapping in a hermetically sealed reciprocating refrigerant compressor

In a refrigerant compressor, improvement in performance such as reduction of various electrical and mechanical losses, reduction of gas leakage, better lubrication, reduction of suction gas heating etc. can be achieved by maintaining a low temperature rise inside the compressor. Proper selection and location of an internal over load protector relay, estimation of heat transfer coefficient and winding insulation coefficient are also vital in enhancing the performance. In this context it is necessary to understand the temperature distribution inside a compressor for an optimal design. In this paper, a numerical model has been created and a heat transfer analysis for a hermetically sealed reciprocating refrigerant compressor is presented. The temperature distribution inside the compressor has been obtained taking into consideration the various heat sources and sinks and compared with experimental results. The maximum temperature was observed at the rotor which was 427.5 K. The deviation of the predicted rotor temperature from that of experimental value is 5.5% only. A good agreement was found between experimental results and that predicted in the numerical analysis.