Consider a two-stage cascade refrigeration system operating...

Consider a two-stage cascade refrigeration system operating between the pressure limits of 0.8 and 0.14 MPa. Each stage operates on the ideal vapor-compression refrigeration cycle with refrigerant-134a as the working fluid. Heat rejection from the lower cycle to the upper cycle takes place in an adiabatic counterflow heat exchanger where both streams enter at about 0.4 MPa. If the mass flow rate of the refrigerant through the upper cycle is $0.24 \mathrm{kg} / \mathrm{s}$, determine (a) the mass flow rate of the refrigerant through the lower cycle, $(b)$ the rate of heat removal from the refrigerated space and the power input to the compressor, and $(c)$ the coefficient of performance of this cascade refrigerator.

Key Concepts

Coefficient of Performance (COP)

The coefficient of performance is a measure of the efficiency of a refrigeration cycle, defined as the ratio of the cooling effect achieved to the work input required. In cascade systems, the overall COP is influenced by the performance of each individual stage, making it a key parameter for assessing and optimizing refrigeration system efficiency.

Mass Flow Rate Balancing

The mass flow rate of the working fluid in each stage of a multi-stage or cascade system is a critical parameter. Analyzing and balancing these flow rates is necessary to ensure that the heat exchange process between the cycles is effective, and that the overall system operates efficiently. This involves applying conservation of mass and energy principles to interrelate the performance of the different stages.

Adiabatic Counterflow Heat Exchanger

In the context of cascade refrigeration, an adiabatic counterflow heat exchanger facilitates the transfer of heat between two refrigerant streams from different cycles without any heat loss to the surroundings. It allows the lower cycle’s refrigerant to precool or subcool before entering the evaporator, thereby optimizing the operating conditions and recalibrating the thermodynamic properties as the two streams interact.

Cascade Refrigeration System

A cascade refrigeration system uses multiple refrigeration cycles or stages, each operating at different pressure and temperature levels, to achieve a lower overall evaporator temperature than would be possible with a single cycle. This configuration improves efficiency, allows for more flexible operation, and is particularly useful in applications requiring very low temperatures.

Vapor-Compression Refrigeration Cycle

This is the fundamental thermodynamic cycle used for cooling applications, where a refrigerant is circulated through stages of compression, condensation, expansion, and evaporation. In its ideal form, it provides a basic framework for analyzing the performance and efficiency of refrigeration systems by focusing on energy transfers and state changes during each process.

Transcript

00:01 Hi friends here it is given two states.

00:16 Gascold refrigeration system.

00:31 Each stage is operating on vapor compression cycle with r134a working fluid.

01:13 We have to find mass flow rate through lower cycle.

01:36 Rate of heat removal from refrigerated place the power input to the compression and coefficient of performance of refrigeration.

02:14 Let us see here.

02:19 For the solution we have to analyze using fluid properties of r134a using the tables a11 to a13.

03:00 Each stage of the cascade refrigeration cycle is set to operate on ideal vapor compression so compression processes isentrophic and refrigerant enter as saturated vapor at a vapor pressure refrigerant leaves the condenser at saturated liquid at condensual pressure and thalphies of refrigerant at all eight stages are h1 239 .19 kilojoule per kg as to 260 .61 kilojoule per kg all these values i am writing using the table as mentioned above h3 is 63 .92 kilojoule per kg h4 63 .92 kilojoule per kg h5 255 .651 kilo jule per kg as 6 269 .96 kilo jules per kege and ax h8, sorry, h7, 95 .48 kilojoule per kg and h8 95 .48 kilojoule per kg.

07:58 The mass flow rate of refrigerant through the lower cycle is calculated from an energy balance equation on their heat exchanger.

09:06 Rate of flow of heat in minus rate of flow of heat out is equal to net change of heat of the system and that must be zero so rate net rate flow of heat in is called to rate of flow of heat out it will be rate of flow of fluid here m .e is the rate of flow of refrigerant out this is the rate of flow of refrigerant in rate of flow of fluid a that is out h5 minus s6 sorry h8 is called to rate of flow of refrigerant in to h2 minus h3 so rate of flow of refrigerant in you will get h5 minus h8 upon h2 minus h3 into mass flow rate out substitute the value 255 .61 minus 95 .48 divided by 260 .61 minus 63 .92 into 0 .24 kg per second...

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