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.     

Numerical simulation of non-adiabatic capillary tubes considering metastable region. Part I: Mathematical formulation and numerical model

A detailed one-dimensional steady and transient numerical simulation of the thermal and fluid-dynamic behavior of capillary tube–suction line heat exchangers has been carried out. The governing equations (continuity, momentum, energy and entropy) for fluid flows, together with the energy equation in solids, are solved iteratively in a segregated manner. The discretized governing equations in the zones with fluid flow are coupled using a fully implicit step-by-step method. An implicit central difference numerical scheme and a line-by-line solver were used in solids. A special treatment has been implemented in order to consider transitions (subcooled liquid region, metastable liquid region, metastable two-phase region and equilibrium two-phase region). All the flow variables (enthalpies, temperatures, pressures, mass fractions, heat fluxes, etc.) together with the thermophysical and transport properties are evaluated at each point of the grid in which the domain is discretized. The numerical model allows analysis of aspects such as geometry, type of fluid, critical or non-critical flow conditions, metastable regions and transient cases. Comparison of the numerical simulation with experimental data presented in the technical literature will be shown in Part II of the present paper.     

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.     

A hybrid method for refrigerant flow balancing in multi-circuit evaporators: Upstream versus downstream flow control

A hybrid method for optimizing refrigerant distribution in evaporators is presented 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. The flow balancing valves could be located upstream or downstream of the evaporator. This paper presents the results of a study to investigate the benefits of this hybrid scheme for both upstream and downstream flow balancing for the case of air flow mal-distribution. In order to perform this investigation, a simulation model was developed to consider evaporator flow mal-distributions for a 10.55 kW residential R410A heat pump and then validated through comparisons of predicted results with measurements. Simulation results show that there are significant benefits in controlling the superheat of each circuit of evaporators through the hybrid–individual superheat control method. Furthermore, the upstream refrigerant flow control consistently outperforms the downstream refrigerant flow control, and recovers most of the loss in cooling capacity and COP due to non-uniform air flow distribution.     

A dynamic simulation model for transient absorption chiller performance. Part I: The model

This paper is the first of two which presents the development of a dynamic model for single-effect LiBr/water absorption chillers. The model is based on external and internal steady-state enthalpy balances for each main component. Dynamic behaviour is implemented via mass storage terms in the absorber and generator, thermal heat storage terms in all vessels and a delay time in the solution cycle. A special feature is that the thermal capacity is partly connected to external and partly to internal process temperatures.In this paper, the model is presented in detail. For verification, the model has been compared to experimental data. The dynamic agreement between experiment and simulation is very good with dynamic deviations around 10 s. General functionality of the model and a more detailed comparison with experimental data are presented in Part II of this paper.     

Numerical simulation of non-adiabatic capillary tubes considering metastable region. Part II: Experimental validation

A detailed one-dimensional steady and transient numerical simulation of the thermal and fluid-dynamic behavior of capillary tube–suction line heat exchangers considering metastable region and separated flow has been developed in Part I of this paper. The developed numerical model allows analysis of aspects such as geometry, type of fluid, critical or non-critical flow conditions and metastable region. The accuracy of the detailed simulation model is demonstrated in this part (Part II) of the paper by comparing simulation results with a wide range of steady state experimental data from the technical literature, which include the refrigerant mass flow rate, outlet suction line temperature, and temperature profile along concentric and lateral capillary tube–suction line heat exchangers. Of the 196 data points evaluated for mass flow rate 96.4% are within an error of ±15%, 81.1% are within ±10% with a mean deviation of ±6.3%. Of the 143 data points evaluated for outlet suction line temperature 89.5% are within an error of ±2 °C, with a mean deviation of ±0.98 °C.The numerical results obtained are used to understand the refrigerant flow behavior inside non-adiabatic capillary tubes. Some divergence problems in the numerical solution process is found to be the discontinuity in non-adiabatic capillary tube flow characteristics caused by re-condensation of the refrigerant within the heat exchanger zone; this aspect needs special attention while modeling the non-adiabatic capillary tube flow. Other important parameter to be evaluated experimentally with special care is the capillary tube internal diameter due to its strong influence on the refrigerant flow results (results of any study based on the nominal diameter are to be used with caution).     

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.     

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.     

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.     

A dynamic simulation model for transient absorption chiller performance. Part II: Numerical results and experimental verification

This paper is the second paper out of two which present the development of a dynamic model for single-effect LiBr/water absorption chillers. The first part describes the model in detail with respect to the heat and mass balances as well as the dynamic terms. This second part presents a more detailed investigation of the model performance, including performance analysis, sensitivity checks and a comparison to experimental data. General model functionality is demonstrated.A sensitivity analysis gives results which agree very well to fundamental expectations: it shows that an increase in both external and internal thermal mass results in a slower response to the step change but also in smaller heat flow oscillations during the transient period. Also, the thermal mass has been found to influence the heat flow transients more significantly if allocated internally. The time shift in the solution cycle has been found to influence both the time to reach steady-state and the transients and oscillations of the heat flow. A smaller time shift leads to significantly faster response.A comparison with experimental data shows that the dynamic agreement between experiment and simulation is very good with dynamic temperature deviations between 10 and 25 s. The total time to achieve a new steady-state in hot water temperature after a 10 K input temperature step amounts to approximately 15 min. Compared to this, the present dynamic deviations are in the magnitude of approximately 1–3%.     

A continuous/discrete simulation of controlled atmosphere (CA) cool storage systems: evaluation of plant performance/design and product quality evolution

In this paper, a controlled atmosphere storage model, developed earlier, is validated using an industrial CA cool storage facility with stepwise product loading strategy. The proposed combined continuous and discrete CA cool storage simulation model was able to represent the step response transients and continuous events, with accuracy less than the observed variability or at best with accuracy level as set by the measurement instrument. Moreover, the handling of discrete/continuous events enabled the implementation of practical operational procedures and to investigate their implication on plant performance/design and directly on the product quality. The model is a valid working model for design and optimization of CA cool storage facilities both with respect to plant performance and final quality of the stored product.     

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.     

An experimental and numerical study of hunting in thermostatic-expansion-valve-controlled evaporators

The dynamic behaviour of a thermostatic-expansion–valve (TEV)-controlled dry-evaporator is studied experimentally and numerically. Although the linear model of the TEV together with the distributed model of the evaporator is able to predict the stable dynamic response of the system adequately, it fails to reproduce the hunting behaviour that is observed under certain operating conditions. A scrutiny of the experimental data reveals the possible existence of hysteresis in the system. The distributed model including the experimentally determined input-output characteristics of the TEV is able to reproduce the main features of the hunting oscillations well. The amplitude and frequency of these oscillations depend on the static superheat setting, the heat load of the evaporator and the time constant of the TEV bulb.     

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.     

Modelling and transient simulation of CO2-refrigeration systems with Modelica

This paper presents the current results of the development of a Modelica library for CO₂-refrigeration systems based on the free Modelica library ThermoFluid. The development of the library is carried out in a research project of Airbus Deutschland and the TUHH and is focused on the aim to obtain a library for detailed numerical investigations of refrigeration systems with the rediscovered refrigerant carbon dioxide (CO₂). A survey of the concept of an integrated on-board cooling system of airliners, the modelling language Modelica™ and the CO₂-library is given and the modelling of CO₂-heat exchangers is described. A comparison with steady state results of heat exchangers shows a fair agreement. The presented transient simulation results are compared with experimental data showing also a fair agreement.     

Numerical simulation of a variable speed refrigeration system

This work presents two numerical models to simulate the transient and steady state behavior of a vapor compression refrigeration system. The condenser and the evaporator were divided into a number of control volumes. Time dependent partial differential equations system was obtained from the mass, energy and momentum balances for each control volume. As the expansion valve and the compressor both have very small thermal inertia, the steady state models were applied for these components. Transient and steady state models numerical predictions were compared and good agreement was found. Further simulations were performed with the objective of verifying the possibility of controlling the refrigeration system and the superheating of the refrigerant in the evaporator outlet by varying the compressor speed and the throttling valve sectional area. The results indicate that the proposed models can be used to formulate an algorithm for controlling a refrigeration system.     

Hot gas defrost model development and validation

This paper describes the development, validation, and application of a transient model for predicting the heat and mass transfer effects associated with an industrial air-cooling evaporator during a hot gas defrost cycle. The inputs to the model include the space dry bulb temperature, space humidity, coil geometry, frost thickness, frost density, and hot gas inlet temperature. The model predicts the time required for a complete frost melt as well as the sensible and latent loads transferred back to the conditioned space during the defrost period. The model is validated by comparing predicted results to actual defrost cycle field measurements and to results presented in previously published studies.A unique contribution of the present model is its ability to estimate parasitic space loads generated during a defrost cycle. The parasitic energy associated with the defrost process includes thermal convection, moisture re-evaporation, and extraction of the stored energy in the coil mass following a defrost cycle. Each of these factors contribute to the parasitic load on compressors connected to the defrost return. The results from the model provide quantitative information on evaporator operation during a defrost cycle which forms the basis to improve the energy efficiency of the defrost process.     

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.     

A general dynamic simulation model for evaporators and condensers in refrigeration. Part II: simulation and control of an evaporator

A mathematical model of an evaporator based on one-dimensional partial differential equations representing mass conservation, and tube wall energy has been formulated. These equations are then restructured and linked to a program data base of all major refrigerants and refrigerant mixtures. The result is a simulation model of an evaporator that is general and flexible. The model is tested over a wide range of operating conditions and a simple controller is implemented to demonstrate the effectiveness of the model for controller and systems design.

Résumé

On a établi un modèle mathématique d'un évaporateur basé sur des équations aux dérivés partielles unidimensionnelles qui représentent la conservation de masse et l'énergie de la paroi du tube. Ces équations ont été restructurées ensuite, puis reliées à une base de données sur les principaux frigorigènes purs et en mélanges. De cette manière, on obtient un modèle d'évaporateur d'application générale et souple. Ce modèle a été éprouvé dans des conditions de fonctionnement très variées et on a employé un système de régulation simple pour montrer l'efficacité du modèle pour la conception et la régulation des systèmes.     

Piston-cylinder work producing expansion device in a transcritical carbon dioxide cycle. Part I: experimental investigation

A simulation model for a piston-cylinder type expansion device in which the linear motion of the piston is converted to the rotational motion of a crank via a connecting rod was developed for its use in a transcritical CO₂ cycle. The model is based on lubrication theory with an assumption that the piston ring is a slippery bearing. This model has been used to verify the proper operation of the device in a prototype application and to identify the loss mechanisms of the device in the design stage. In addition, an analysis of the device has been conducted using this theoretical model for the device as installed in a prototype cycle as reported in a companion part I paper.