What is Ideal Reverse Brayton Cycle ?

In general, the Brayton cycle describes the workings of a constant-pressure heat engine. Today, modern gas turbine engines and air-breathing jet engines are also a constant-pressure heat engines.

A Brayton cycle that is driven in reverse direction is known as the reverse Brayton cycle. Its purpose is to move heat from colder to hotter body, rather than produce work. In compliance with the second law of thermodynamics, heat cannot spontaneously flow from cold system to hot system without external work being performed on the system. Heat can flow from colder to hotter body, but only when forced by an external work. This is exactly what refrigerators and heat pumps accomplish. These are driven by electric motors requiring work from their surroundings to operate. One of possible cycles is a reverse Brayton cycle, which is similar to the ordinary Brayton cycle but it is driven in reverse, via net work input. This cycle is also known as the gas refrigeration cycle or Bell Coleman cycle. This type of cycle is widely used in jet aircrafts for air conditioning systems using air from the engine compressors. It is also widely used in the LNG industry where the largest reverse Brayton cycle is for subcooling LNG using 86 MW of power from a gas turbine-driven compressor and nitrogen refrigerant.

Fig : 1.1. Reverse Brayton Cycle

This is an important cycle frequently employed in gas cycle refrigeration systems. This may be thought of as a modification of reversed Carnot cycle, as the two isothermal processes of Carnot cycle are replaced by two isobaric heat transfer processes. This cycle is also called as Joule or Bell-Coleman cycle. Figure 1.2(a) and (b) shows the schematic of a closed, reverse Brayton cycle and also the cycle on T-s diagram. As shown in the figure, the ideal cycle consists of the following four processes:

Fig : 1.2 (b). Reverse Brayton cycle

Process 1-2: Reversible, adiabatic compression in a compressor
Process 2-3: Reversible, isobaric heat rejection in a heat exchanger
Process 3-4: Reversible, adiabatic expansion in a turbine
Process 4-1: Reversible, isobaric heat absorption in a heat exchanger

Fig : 1.2 (b) . Reverse Brayton Cycle on T-s Diagram

Process 1-2: Gas at low pressure is compressed isentropically from state 1 to state 2. Applying steady flow energy equation and neglecting changes in kinetic and potential energy, we can write:

where rp = (P2/P1) = pressure ratio

Process 2-3: Hot and high pressure gas flows through a heat exchanger and rejects heat sensibly and isobarically to a heat sink. The enthalpy and temperature of the gas drop during the process due to heat exchange, no work transfer takes place and the entropy of the gas decreases. Again applying steady flow energy equation and second T ds equation:

Process 3-4: High pressure gas from the heat exchanger flows through a turbine, undergoes isentropic expansion and delivers net work output. The temperature of the gas drops during the process from T3 to T4. From steady flow energy equation:

where rp = (P3/P4) = pressure ratio

Process 4-1: Cold and low pressure gas from turbine flows through the low temperature heat exchanger and extracts heat sensibly and isobarically from a heat source, providing a useful refrigeration effect. The enthalpy and temperature of the gas rise during the process due to heat exchange, no work transfer takes place and the entropy of the gas increases. Again applying steady flow energy equation and second T ds equation:

using the relation between temperatures and pressures, the COP can also be written as:

From the above expression for COP, the following observations can be made:
a). For fixed heat rejection temperature (T3) and fixed refrigeration temperature (T1), the COP of reverse Brayton cycle is always lower than the COP of reverse Carnot cycle (Fig. 1.3), that is

Fig : 1.3. Comparison of reverse Carnot and reverse Brayton cycle in T-s plane

b). COP of Brayton cycle approaches COP of Carnot cycle as T1 approaches T4 (thin cycle), however, the specific refrigeration effect [cp(T1-T4)] also reduces simultaneously.
c). COP of reverse Brayton cycle decreases as the pressure ratio rp increases

Actual Reverse Brayton Cycle :

The actual reverse Brayton cycle differs from the ideal cycle due to:
i. Non-isentropic compression and expansion processes
ii. Pressure drops in cold and hot heat exchangers

Fig : 1.4. Comparison of ideal and actual Brayton cycles T-s plane

Figure 1.4 shows the ideal and actual cycles on T-s diagram. Due to these irreversibilities, the compressor work input increases and turbine work output reduces. The actual work transfer rates of compressor and turbine are then given by:

where ηc,isen and ηt,isen are the isentropic efficiencies of compressor and turbine, respectively. In the absence of pressure drops, these are defined as:

thus the net work input increases due to increase in compressor work input and reduction in turbine work output. The refrigeration effect also reduces due to the irreversibilities. As a result, the COP of actual reverse Brayton cycles will be considerably lower than the ideal cycles. Design of efficient compressors and turbines plays a major role in improving the COP of the system.

In practice, reverse Brayton cycles can be open or closed. In open systems, cold air at the exit of the turbine flows into a room or cabin (cold space), and air to the compressor is taken from the cold space. In such a case, the low side pressure will be atmospheric. In closed systems, the same gas (air) flows through the cycle in a closed manner. In such cases it is possible to have low side pressures greater than atmospheric. These systems are known as dense air systems. Dense air systems are advantageous as it is possible to reduce the volume of air handled by the compressor and turbine at high pressures. Efficiency will also be high due to smaller pressure ratios. It is also possible to use gases other than air (e.g. helium) in closed systems.

Heat Pump – How does it work

The term heat pump is usually reserved for a device that can heat a house in winter by using an electric motor that does work W to take heat Qcold from the outside at low temperature and delivers heat Qhotto the warmer inside of the house.

The operating principle of refrigeratorsair conditioners, and heat pumps is the same and it is just the reverse of a heat engine. In general, a heat pump is a device that transfers heat energy from a heat source to a “heat sink“, but in this case the transfer occurs in the opposite direction of spontaneous heat transfer by absorbing heat from a cold space and releasing it to a warmer one. As diagrammed in the figure, by doing external work W, heat is taken from a low-temperature region (heat source) and a greater amount of heat is exhausted at a higher temperature (heat sink).

The most widely used thermodynamic cycle or method for heating, air-conditioning, refrigerators and heat pumps is the vapor compression cycle. But the Brayton cycle can be also used to drive the heat pumps.

12 thoughts on “What is Ideal Reverse Brayton Cycle ?”

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