A compact dynamic model for household vapor compression refrigerated systems

https://doi.org/10.1016/j.applthermaleng.2011.08.005Get rights and content

Abstract

In this study, a very simplified dynamic lumped model for the simulation of small-scale single-temperature vapor compression refrigerators working between two thermal sources with finite thermal capacity is presented. The model is compact enough to be employed in actual regulation systems, but adequate to describe the basic underlying physical phenomena relevant to the transient response of the refrigerated cell. The dynamic behavior of the system is simulated taking into account the main heat capacities involved in the heat transfer processes between the system, the refrigerating fluid and the outside.

The numerical model has been validated by comparing the calculated results with transient experimental data coming from an instrumented chest-freezer. After a steady state tuning phase, the model was able to predict the transient temperature response of the cell with good accuracy.

Highlights

▸ In this study we propose a simple dynamic lumped model for household refrigerators. ▸ The model results able to describe the actual behavior of commercial chest-freezers. ▸ Although less than perfect, the model is suitable for embedded control applications.

Introduction

The growing concern for the environment urged towards environmentally safe refrigerants and reduced energy consumption in refrigeration technology developments since early 1990s. The field of small commercial and domestic refrigeration contributes for the 26% to the total global warming impact due to refrigeration and air conditioning in Europe [1]. In the field of small refrigeration devices, the vapor compression refrigerator/freezer is one of the most important energy-consuming domestic appliances [2], [3] and it represent 8% of the residential electricity consumption in USA [4]. The operating energy consumption is strongly affected by both the employed refrigerant fluid and the control strategy applied to the system. The application of an effective control strategy requires a system model that allows a real time implementation.

Despite the large amount of available literature sources concerning the dynamic modeling of generic vapor compression inverse cycles [5], little has been made in order to adapt the complexity of such models to the implementation, in actual refrigeration systems, of the very last model-based control techniques, especially in the field of very low capacity, down to less than 100 W [6], [7], [8], [9], [10], [11].

The increasing use of these sophisticated techniques in order to obtain “optimal performance” from a system is quickly diffusing also in the field of refrigeration and in particular in the vapor compression refrigeration technology.

Such algorithms, in their deterministic or stochastic embodiments, are characterized by the minimization of a cost function, achieved by means of LQC (Linear Quadratic Control) techniques, generally coupled to suitable estimators of the state variables, such as a Kalman filter.

The complexity of this approach places severe constraints to the modeling of the process, due both to cost considerations during the software development and to the high computational burden occurring during the use of the numerical model embedded in the regulation system. These requirements ask for an accurate, though compact, description of the interested physical phenomena, advisably based on a lumped representation of the system.

In recent times some authors [12], [13], [14], [15], [16] used indeed a lumped parameter approach, still suffering however from a too much detailed description of the two-phase processes taking place inside the refrigeration fluid. With reference to the Kalman algorithm, if the computational burden required by the numerical integration of a lumped model of, say, N nodes is proportional to N2, that required by the evolution of the error variance/covariance matrix needed by the control algorithm will be proportional to N3. As a consequence, the reduction of the number of thermal inertias describing the system is a critical point.

The aim of this study is the formulation of a dynamic model based on a simplified lumped description of a refrigerator operated by means of a vapor compression inverse cycle, working between thermal sources with finite thermal capacity, where the external work is provided by means of a reciprocating compressor.

The model is compact enough to be employed in actual regulation systems, but adequate to describe all the relevant underlying physical phenomena. Indeed, the proposed approach just accounts for the differential equations governing the time-temperature history of the various devices (evaporator and condenser, refrigerated cell) involving heat transfer (with the refrigerant fluid or with the outside).

This approach is validated by comparing the numerical results to transient experimental data. To this aim, the dynamic model has been adapted to simulate at best the behavior of a commercial chest-freezer (one kind of small refrigerator often used in domestic and super-market applications) properly instrumented by means of several thermocouples and electrical heaters for the simulation of given thermal loads.

We do not make use of “real food” tests in our campaign, nor with respect to latent heat nor to sensible heat dynamics, since the food presence, due to its thermal response, might mask the refrigerator alone behavior.

The constructive solution taken into consideration presents smooth walls on all of the four sides of the refrigerator with the condenser and evaporator operating inside the insulating walls of the cabinet. The condenser, a single tube wound all around the casing of the refrigerator, is placed inside the casing (stuck in good thermal contact to the external refrigerator plate) to form the so-called hot-wall condenser or “skin” condenser. The same solution is adopted for the evaporator, which again is a single tube inside the wall, wound all around the refrigerator. A schematic view of the “hot-wall” solution, with internal condenser and evaporator, is shown in Fig. 1.

In this hot-wall configuration most of the heat transfer leaving the condenser tube is transferred to the external metallic plate of the refrigerator (which operates in a way very similar to a fin added to the tube), and thereafter to the ambient air. However a small amount of extra heat qcd–ev is directly recycled back to the evaporator (which is located on the opposite side of the insulating foam layer) by thermal conduction through the insulating foam. This “useless heat transfer rate” qcd–ev gives rise to a significant increase in the energy consumption of the appliance, when working temperatures and capacity are kept the same [17]. The thermal and dynamic model of the whole system accounts for all the possible heat paths existing in the system, as shown in Fig. 2.

Based on actual geometrical and operating measured data [18], the lumped model here presented resulted to be sufficiently reliable to describe the system both in steady state and in dynamic operations.

Section snippets

Main assumptions

With reference to the plant sketch of Fig. 2 and the corresponding thermodynamic cycle of the refrigeration fluid of Fig. 3, a model is proposed with the purpose to describe the dynamic behavior of systems based on the inverse cycle. Only the dynamics of the thermal inertias associated to the cell, the refrigerator case, the evaporator and the condenser will be described. Such simplification works well, as shown by a preliminary suite of tests [19], when applied to small size household

Steady state results

The reference geometrical characteristics and thermal working parameters of the refrigerator are listed in Table 1 and the working boundary conditions assumed for the calculations, based on data measured in several experimental tests are reported in Table 2.

All of the above mentioned thermal characteristics have been calculated on the basis of steady-state measurements obtained introducing a proper electrical heater inside the refrigerator volume and operating it with variable heating power in

Conclusions

A compact dynamic model based on three first-order ordinary differential equations and describing the transient behavior of a chest freezer has been implemented. Despite the assumed simplifications, the results achieved by the model are in good agreement with experimental data related to test carried out on an actual refrigerator (chest-freezer) suitably instrumented.

All the tests, both static and dynamic, show a good agreement between simulated and measured behavior, although some differences

Acknowledgements

The present work was supported by Genuense Atheneum.

References (28)

Cited by (0)

View full text