# A Review of Small-Scale Vapor Compression Refrigeration Technologies
## 3 Small-Scale Vapor Compression Refrigeration (VCR) Systems
### Modeling  
Modeling is a useful tool for system design and optimization, especially considering that the proliferation of experimental prototypes has provided considerable opportunity for validation. Models predict component and system behavior ahead of manufacture, thereby providing guidance for improving existing designs, even if model results do not closely match experimental results. Types of models include mathematical, physical, numerical, dynamical, empirical, black box, etc. [PERSON] [68] presented a steady-state model of the performance of a CPU cooling system employing a mathematical multi-zone formulation for the condenser and evaporator, along with a physics-based efficiency model for the free piston linear compressor, and an empirical correlation for modeling the flow rate through the capillary tube. The model enables the evaluation of the effect of design parameters such as evaporating and condensing temperatures on system components and overall efficiency. The results showed an increase in system efficiency and a decreasing condenser heat load as evaporating temperature increases under a fixed junction temperature (the operating temperature of the semiconductor) and evaporator load. On the other hand, the rise in condenser temperature leads to a reduction in system COP when evaporating temperature, junction temperature, and evaporator load remain constant. The model also allows evaluation of different refrigerants. The authors selected R134a based on thermodynamic, physical, chemical, and safety and environmental aspects, leading to a COP equal to 3. Other refrigerants (ammonia, R22, R290, R718, R404A, R504A) were also evaluated. Other authors focused their modeling work on improving the overall thermal performance of miniaturized vapor compression systems by finding optimum component designs [69]. Through a COOLPACK [70] simulation for a system with 100 W of cooling capacity, 10 \({}^{\circ}\)C evaporating temperature, 55 \({}^{\circ}\)condensing temperature, and a scroll-type compressor with 90% isentropic efficiency, the authors optimized evaporator and condenser dimensions, leading to a COP as high as 4.5. Considering the relative scarcity of dynamic and control models applied to meso-scale VCR systems, [PERSON] et al. [71] presented an empirical model and robust control system of a prototype developed in a previous study [57], with the purpose of maintaining the heat source temperature constant as the cooling load changes. This was accomplished with a black-box model developed to predict dynamic behavior under varying cooling load. After some tests, the 2 nd order empirical Box-Jenkins (BI) model was selected as it successfully reproduced the transient behavior of the system for the given cooling load. The model has two inputs: compressor speed and cooling load, and one output: the temperature of the heat source. In addition, the authors developed a robust control system based on the black-box model to ensure acceptable performance for variable or unknown cooling loads, to develop a future multi-input multi-output (MIMO) control system. The results show that the robust controller can adjust the temperature of the heat source to the desired value within 70 s, with oscillations between 1.25-2.5 \({}^{\circ}\)C.  
A methodology for designing a meso-scale VCR system using a novel model capable of assessing the effects of downscaling vapor compression systems uses thermodynamic and empirical correlations and considers the impact of component interactions on system performance [72]. The system comprises a roll-bond-plate-type evaporator, an air-cooled louvered fin-and-plate multi-layered condenser, a fixed orifice as expansion device, and a reciprocating compressor. A 3D heat conduction model calculates heat leakage from the condenser to the evaporator, 2D heat conduction models calculate temperature distribution and heat transfer rates at the cold and hot ends, and the fluid flow was modeled as 1D considering both the momentum and the energy conservation equations on heat exchanger design.