Evaluation of a hybrid method for refrigerant flow balancing in multi-circuit evaporators

A companion paper [Kim, J.-H., Braun, J.E., Groll, E.A., 2009. A hybrid method for refrigerant flow balancing in multi-circuit evaporators: upstream versus downstream control. International Journal of Refrigeration doi:10.1016/j.ijrefrig.2009.01.013 presented a hybrid approach for providing control of refrigerant flow distribution in evaporators that involves the use of small balancing valves in each circuit along with a primary expansion device to control the overall superheat from the evaporator. Furthermore, the companion paper demonstrated that the flow balancing valves should be located upstream rather than downstream of the evaporator in order to realize significant benefits. The current paper utilizes the model presented in the companion paper to more fully evaluate the effects of uneven air and refrigerant flow distributions and the benefits of upstream hybrid control in response to these effects.     

A generalized moving-boundary model for transient simulation of dry-expansion evaporators under larger disturbances

A generalized model based on the moving-boundary approach is developed to describe the transient behavior of dry-expansion evaporators in the vapor-compression refrigeration system. To improve the robustness of the traditional moving-boundary model under larger disturbances, the time-variant mean void fraction is employed instead of the constant. Numerical integration is applied to get the mean properties in the two-phase region and the superheated region. The interface wall temperature between the two-phase and the superheated regions is also evaluated by a new weighted mean. Qualitative case study shows that the present model can well predict the transient behaviors of evaporators under larger disturbances and keep the robustness whenever superheated region appears or disappears.     

Development of a design tool for display case evaporators

A model for simulating a fin-and-tube display case evaporator has been developed to serve as a design tool for improving performance in frosting conditions. It is capable of simulating cross-counterflow evaporators with multiple modules having completely different geometries. Quasi-steady heat and mass transfer calculations provide local values of all relevant variables, including heat and mass transfer coefficients, air and refrigerant-side pressure drops and fin and tube frost thicknesses. A multi-lump method enables the model to simulate both tube and fin frost thicknesses and surface temperatures. The results presented in this paper reflect interactions with the display case and its air curtains and predict local and overall effects of frost accumulation, to facilitate optimization of the larger display case system.     

Modeling absorption of pure refrigerants and refrigerant mixtures in lubricant oil

This paper addresses the problem of absorption of refrigerant vapor in a stagnant layer of lubricant oil. The bulk motion of the solute is described in terms of apparent diffusion coefficients that encompass both molecular diffusion and possible macroscopic motion induced by liquid density instability and surface tension. In absorption of refrigerant mixtures, diffusion in the vapor and liquid phases are coupled with a thermodynamic model for interfacial equilibrium. Results are compared with experimental data available in the literature for absorption of several refrigerants in polyol ester oil (POE68). The adequacy of the formulation is assessed in the light of its basic assumptions and performance of the model.     

Modeling, identification and control of air-conditioning systems

In this paper, feedback controller design for the air-conditioning system is addressed through systematic modeling and identification. Particularly, the physical model of the system reveals the key parameter that dictates energy efficiency, and the identification procedure produces a low-order, linear model suitable for controller design. The feedback controller employed is multi-input–multi-output-based and possesses a cascade structure for dealing with the fast and slow dynamics in the system. To determine appropriate control parameters, conditions that establish performance and stability of the cascade design are given. Experiments show that the controller can simultaneously achieve satisfactory transient response in the indoor temperature, and improve energy efficiency at steady state.     

A numerical simulation model for plate-type, roll-bond evaporators

This study presents a first-principles mathematical model developed to investigate the thermal behavior of a plate-type, roll-bond evaporator. The refrigerated cabinet was also taken into account in order to supply the proper boundary conditions to the evaporator model. The mathematical model was based on the mass, momentum and energy conservation principles applied to each of the following domains: (i) refrigerant flow through the evaporator channels; (ii) heat diffusion in the evaporator plate; and (iii) heat transmission to the refrigerated cabinet. Empirical correlations were also required to estimate the shear stresses, and the internal and external heat transfer rates. The governing partial differential equations were discretized through the finite-volume approach and the resulting set of algebraic equations was solved by successive iterations. Validation of the model against experimental steady-state data showed a reasonable level of agreement: the cabinet air temperature and the evaporator cooling capacity were predicted within error bands of ±1.5 °C and ±6%, respectively.     

A novel special distributed method for dynamic refrigeration system simulation

A novel dynamic mathematical model based on spatially distributed approach has been developed and validated in this paper. This model gives good agreement in predicting the system COP and other parameters. The validated model has been used to enhance the prediction of the micro variations of superheat and sub-cooling. The novel spatial distributed model for the condenser and evaporator in refrigeration system, calculates the two-phase region in gas and liquid field separately since the gas and liquid in the two-phase region have different velocities. Previous researchers have used a pre-defined function of the void fraction in their spatially distributed model, based on experimental results. This approach results in the separate solution of the mass and energy equations, and less calculation is required. However, it is recognized that the mass and energy equations should be coupled during solving for more accurate solution. Based on the energy and mass balance, the spatial distribution model constructed here solves the velocity, pressure, refrigerant temperature, and wall temperature functions in heat exchangers simultaneously. A novel iteration method is developed and reduces the intensive calculations required. Furthermore, the condenser and evaporator models have shown a parametric distribution along the heat exchanger surface, therefore, the spatial distribution parameters in the two heat exchangers can be visualised numerically with a two-phase moving interface clearly shown.     

An improved method for analyzing a fin and tube evaporator containing a zeotropic mixture refrigerant with air mal-distribution

A new program was developed to analyze the heat transfer characteristics of fin and tube evaporators that use a zeotropic mixture refrigerant, R-407C, as the working fluid. The calculation algorithm is based on EVSIM (NIST), but a tube is segmented into several sections to provide a base unit for the calculations in this study. Therefore, two-dimensional air mal-distribution in the tube-length (horizontal) and vertical directions of the evaporator can be considered. The temperature gradient in the flow direction is traced using a discrete pattern to simulate the continuous variation found in actual evaporators. To validate the simulation results, 45 test cases in a real evaporator were performed with two different refrigerant flow path configurations using R-22 and R-407C refrigerants. The deviation between the simulations and test data was a maximum of 5.4%, and the trends were similar. The local heat transfer predictions were verified by comparing the numerical and test wall temperatures along the refrigerant flow path. Local temperature difference and the heat transfer contributions from each row are also analyzed along refrigerant flow path. And more, the impact of air mal-distribution is studied with two-dimensional four different types of velocity profiles and the significant difference in heat transfer is analyzed. The program developed in this study will be a useful tool to know all of information related with heat and mass transfer at any local point and can be used for improving the efficiency of zeotropic mixture refrigerant evaporators.     

Analysis of refrigerant flow and deformation for a flexible short-tube using a finite element model

A finite element model was used to simulate single-phase flow of R-22 through flexible short-tubes. The numerical model included the fluid-structure interaction between the refrigerant and the deformation of the short-tube as upstream pressure was varied. The finite element model was developed using a commercially available finite element package. Short-tubes with moduli of elasticity ranging from 5513 to 9889 kPa were studied. Four upstream and downstream pressures were applied and the upstream subcooling was held at a constant value of 16.7 °C. Mass flow rates from the numerical model were compared to available published experimental results. The study showed that upon deformation the short-tube resembled the shape of a converging-diverging nozzle. Both tube inlet and outlet had a chamfered-like shape after deformation which reduced the pressure drop at the tube inlet. The smaller the modulus of the tube, the larger the chamfered-like angle at the inlet and the higher the pressure drop along the tube due to the higher tube contraction. The results illustrated that as the upstream pressure was increased by 45%, there was almost a 60% decrease in the flow area. The more flexible (5513 kPa) short-tube restricted the mass flow rate more than the most rigid (9889 kPa) short-tube used in this study. The mass flow rates estimated with the finite element model were as much as 14% higher than those from experimental results reported in the literature.     

Dynamic behavior of a direct expansion evaporator under frosting condition. Part I. Distributed model

A general distributed model with two-phase flow for refrigerant coupled with a frost model is developed for studying the dynamic behavior of an evaporator. The equations are derived in non-steady-state manner for the refrigerant and a quasi-steady state model with permeation for the frost. The complex flow and geometry of the finned tube evaporator lead to uneven wall and air temperature distributions, which in turn affect the rate of frost growth and densification along the coil depth. Results include frost accumulation and its effect on energy transfer, air off-coil temperature, refrigerant liquid dry-out position and propagation of frost formation along the coil.     

Development and validation of “grey-box” models for refrigeration applications: A review of key concepts

“Grey-box” modelling combines the use of first-principle based “white-box” models and empirical “black-box” models, offering particular benefits when: (a) there is a lack of fundamental theory to describe the system or process modelled; (b) there is a scarcity of suitable experimental data for validation or (c) there is a need to decrease the complexity of the model. The grey-box approach has been used, for example, to create mathematical models to predict the shelf life of chilled products or the thermal behaviour of imperfectly mixed fluids, or to create models that combine artificial neural networks and dynamic differential equations for control-related applications. This paper discusses the main characteristics of white-box, black-box and their integration into grey-box models, the requirements and sourcing of accurate data for model development and important validation concepts and measures.     

Real-time measurement of mixing ratio of refrigerant/refrigeration oil mixture

The mixing of refrigeration oil with refrigerant in a refrigeration cycle has great influence on cycle performance. A sampling method is the most general way to measure the mixing ratio of refrigerant and refrigeration oil. Since the sampling method is time-consuming and reduces the amount of refrigerant and oil in the cycle, a real-time measurement is desirable. In this study, a refractive index measurement was applied to measure the mixing ratio of refrigerant/oil mixture. A laser displacement sensor was used to detect any change in optical path which results from changes of the refractive index of refrigerant/oil mixture. For the practical application of real-time measurement of the oil circulation ratio (OCR) in the refrigeration cycle, a correlation between the refractive index and the mixing ratio was developed. In addition, the changes of the refractive index in a range of a few percentages of the oil concentration and under subcooled conditions were measured. Finally, a transient measurement of the OCR in a practically operating refrigeration cycle was carried out successfully.     

Experimental and numerical study on microchannel and round-tube condensers in a R410A residential air-conditioning system

The effect of different type of condensers on the performance of R410A residential air-conditioning systems was investigated in this study. Two R410A residential air-conditioning systems, one with a microchannel condenser and the other with a round-tube condenser, were examined experimentally, while the other components of the two systems were identical except the condensers. Two condensers had almost same package volumes. The two systems were operated in separate environmental chambers and their performance was measured in ARI A, B, and C conditions. Both the COP and cooling capacity of the system with the microchannel condenser were higher than those for the round-tube condenser in all test conditions. The refrigerant charge amount and the refrigerant pressure drop were measured; the results showed a reduction of charge and pressure drop in the microchannel condenser. A numerical model for the microchannel condenser was developed and its results were compared with the experiments. The model simulated the condenser with consideration given to the non-uniform air distribution at the face of the condenser and refrigerant distribution in the headers. The results showed that the effect of the air and refrigerant distribution was not a significant parameter in predicting the capacity of the microchannel condenser experimentally examined in this study. Temperature contours, generated from the measured air exit temperatures, showed the refrigerant distribution in the microchannel condenser indirectly. The temperature contours developed from the model results showed a relatively good agreement with the contours for measured air exit temperatures of the microchannel condenser.     

Modified neural network correlation of refrigerant mass flow rates through adiabatic capillary and short tubes: Extension to CO2 transcritical flow

This paper presents a modified dimensionless neural network correlation of refrigerant mass flow rates through adiabatic capillary tubes and short tube orifices. In particular, CO₂ transcritical flow is taken into account. The definition of neural network input and output dimensionless parameters is grounded on the homogeneous equilibrium model and extended to supercritical inlet conditions. 2000 sets of experimental mass flow-rate data of R12, R22, R134a, R404A, R407C, R410A, R600a and CO₂ (R744) in the open literature covering capillary and short tube geometries, subcritical and supercritical inlet conditions are collected for neural network training and testing. The comparison between the trained neural network and experimental data reports 0.65% average and 8.2% standard deviations; 85% data fall into ±10% error band. Particularly for CO₂, the average and standard deviations are −2.5% and 6.0%, respectively. 90% data fall into ±10% error band.     

Optimization of counter flow Ranque–Hilsch vortex tube performance using Taguchi method

This study discusses the application of Taguchi method in assessing maximum temperature gradient for the Ranque–Hilsch counter flow vortex tube performance. The experiments were planned based on Taguchi's L27 orthogonal array with each trial performed under different conditions of inlet pressure, nozzle number and fluid type. Signal-to-noise ratio (S/N) analysis, analysis of variance (ANOVA) and regression analysis were carried out in order to determine the effects of process parameters and optimal factor settings. Finally, confirmation tests verified that Taguchi method achieved optimization of counter flow Ranque–Hilsch vortex tube performance with sufficient accuracy.     

Modeling and performance analyses of evaporators in frozen-food supermarket display cabinets at low temperatures

This paper presents modeling and experimental analyses of evaporators in “in situ” frozen-food display cabinets at low temperatures in the supermarket industry. Extensive experiments were conducted to measure store and display cabinet relative humidities and temperatures, and pressures, temperatures and mass flow rates of the refrigerant. The mathematical model adopts various empirical correlations of heat transfer coefficients and frost properties in a fin-tube heat exchanger in order to investigate the influence of indoor conditions on the performance of the display cabinets. The model is validated with the experimental data of “in situ” cabinets. The model would be a good guide tool to the design engineers to evaluate the performance of supermarket display cabinet heat exchangers under various store conditions.     

Numerical study of electroosmotic (EO) flow in microfabricated EO pump with overlapped electrical double layer (EDL)

Micropump is an important component for the development of micro absorption heat pump systems. To study the performance of microfabricated EO pump with the dimension comparable to the electrical double layer (EDL), a model avoiding the use of the Boltzmann equation was developed to investigate the EO flow instead of using the Poisson–Boltzmann (PB) equation. Generally used Debye–Huckle approximation and symmetric condition are also not involved so this model can be applied in the more complicated EO micropumps. Numerical simulation was carried out to study the distributions of potential, ions and net charge density in the EO micropump. Comparison between the present model and the PB equation was conducted. Using the present model, the EO flow in the EO micropump with overlapped EDL was investigated. It shows that the flow is quite different from the channel with dimension much larger than the EDL, which exhibits plug-like flow characteristics. The errors induced by the PB equation for the pumps with different depths were evaluated. It shows that the accuracy of the PB equation is not good when the EO pump is very thin.     

Use of ejectors in a multi-evaporator refrigeration system for performance enhancement

In this study, an improved cooling cycle for a conventional multi-evaporators simple compression system utilizing ejector for vapour precompression is analyzed. The ejector-enhanced refrigeration cycle consists of multi-evaporators that operate at different pressure and temperature levels. A one-dimensional mathematical model of the ejector was developed using the equations governing the flow and thermodynamics based on the constant-area ejector flow model. The model includes effects of friction at the constant-area mixing chamber. The energy efficiency and the performance characteristics of the novel cycle are theoretically investigated. The comparison between the novel and conventional system was made under the same operating conditions. Also, a comparison of the system performances with environment friendly refrigerants (R290, R600a, R717, R134a, R152a, and R141b) is made. The theoretical results show that the COP of the novel cycle is better than the conventional system.     

Optimization of finned-tube condensers using an intelligent system

The refrigerant circuitry influences a heat exchanger's attainable capacity. Typically, a design engineer specifies a circuitry and validates it using a simulation model or laboratory test. The circuitry optimization process can be improved by using intelligent search techniques. This paper presents experiments with a novel intelligent optimization module, ISHED (Intelligent System for Heat Exchanger Design), applied to maximize capacity through circuitry design of finned-tube condensers. The module operates in a semi-Darwinian mode and seeks refrigerant circuitry designs that maximize the condenser capacity for specified operating conditions and condenser slab design constraints. Examples of optimization runs for six different refrigerants are included. ISHED demonstrated the ability to generate circuitry architectures with capacities equal to or superior to those prepared manually, particularly for cases involving non-uniform air distribution.     

Prediction of the heat transfer rate of a single layer wire-on-tube type heat exchanger using ANFIS

In this paper, we applied an Adaptive Neuro-Fuzzy Inference System (ANFIS) model for prediction of the heat transfer rate of the wire-on-tube type heat exchanger. Limited experimental data was used for training and testing ANFIS configuration with the help of hybrid learning algorithm consisting of backpropagation and least-squares estimation. The predicted values are found to be in good agreement with the actual values from the experiments with mean relative error less than 2.55%. Also, we compared the proposed ANFIS model to an ANN approach. Results show that the ANFIS model has more accuracy in comparison to ANN approach. Therefore, we can use ANFIS model to predict the performances of thermal systems in engineering applications, such as modeling heat exchangers for heat transfer analysis.