Ericsson Cycle – Components, Steps and Efficiency derivation

Ericsson Cycle is a thermodynamic cycle that consists of constant pressure heat addition and rejection.
The Ericsson Cycle is named after its Swedish inventor John Ericsson. Many heat engines based on various thermodynamic cycles were but by him.
Ericsson was also responsible for the early use of the screw propellor for ship propulsion built in 1842.
The first cycle invented by him is known as the Brayton Cycle and the second one is Ericsson Cycle.

The working principle of the Ericsson Engine is based on this Ericsson Cycle. Ericsson Engine is an external combustion engine. This engine works on either air or any other monophasic gas.
Ericsson Cycle with ideal components can reach the thermal efficiency of the Carnot cycle.

In Ericsson cycle heat is added and rejected at constant pressure.
Also, compression and extension will take place at a constant temperature.
Ericsson Cycle consists of a regenerator and a heat exchanger.
In this cycle, a regenerator is used. A regenerator is used to add and remove heat from the working fluid.

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Components:

The main components for the operation Ericsson Cycle are hot cylinder, regenerator, a cold cylinder, and 2 crankshafts to drive the piston of the hot and cold cylinder.

1) Hot Cylinder:
The hot cylinder is used to receive heated working fluid from the regenerator. In this cylinder working fluid expands and work is done by working fluid.

2) Cold Cylinder:
The cold cylinder is used to receive cooled working fluid from the regenerator. In the cold cylinder, the working fluid is compressed using the work done produced in the hot cylinder.

3) Crankshafts:
Two crankshafts are connected to the hot cylinder and cold cylinder. These two crankshafts are connected using a gear so that the work done in the hot cylinder can be easily transferred to the cold cylinder and the working fluid in the cold cylinder can be compressed.

4) Regenerator:
The regenerator is used to heat and cool the working fluid based on whether the working fluid is received from the hot cylinder or the cold cylinder and then transfer heated fluid to the hot cylinder and cooled fluid to the cold cylinder.

Components Of Regenerator:

1 Wire gauge system:
It is used to pass the air slowly through it so that air can be heated easily and uniformly.

2 Furnace:
In this fuel is burnt and heat is produced and this heat is used to increase the temperature of the air trapped below the wire gauge system. So the air below the wire gauge system has a high temperature as it is present near the furnace.

4 Cold water inlet and outlet:
Cold water inlet and outlet are present for the passage of cold water. Pipelines are also present for the passage of cold water. Cold water is passed to decrease the temperature of air present above the wire gauge system. So the air above the wire gauge system has a low temperature.

Openings for Engine Cylinder:
There are two openings in the regenerator to pass the air to the engine cylinder. One opening is for cold air and is present near the top of the regenerator and another opening is for hot air and is present near the bottom of the regenerator.

The regenerator is used both for heating and cooling the air. Heat is given to air when it moves down towards the furnace and heat is taken from the air when it moves upwards towards the top of the regenerator.

Steps in Ericsson cycle:

There are four steps in the Ericsson Cycle.

Step 1-2: Constant Pressure Heat Addition

At first, the air or working fluid will be sent to the regenerator. When air enters the regenerator, it will flow downwards towards the furnace and heat will be added to it. In this process, it is assumed that heat is added in constant pressure. So, constant pressure heat addition takes place in this process.
In PV diagram, the temperature will increase and pressure will remain constant. So this process graph plot will be parallel to the temperature axis.
In TS diagram, the temperature will increase and the entropy will also increase.

Step 2-3: Isothermal Expansion

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After that, the heated air from the regenerator is sent to the hot cylinder. When the heated reaches the hot cylinder, it will expand and will exert a force on the piston and will push the piston backward. In this step, the isothermal expansion will take place. Simultaneously, the cooled air in the cold cylinder will be compressed using the work produced in the hot cylinder. The work done is transferred between crankshafts of two engine cylinder using a gear.
In PV diagram, the volume will increase and pressure will decrease in this step.
In TS diagram, entropy (S) will increase and temperature (T) will remain constant.

Step 3-4: Constant Pressure Heat Rejection:
After pushing the piston, the hot air is sent back to the regenerator. The air in the regenerator will flow upwards towards the cold water pipe. When the air flows upwards in the regenerator, its temperature will decrease because it will come in contact with the cold water pipe. After that, it will be again sent to the engine cylinder. So in this step heat will be rejected at constant pressure. This step will be the opposite of Step 1-2.

In PV diagram, volume (V) will decrease due to a decrease in temperature but the pressure (P) will remain constant as this process is done at constant pressure.
In TS diagram, the temperature (T) and entropy (S) both will decrease as there is heat rejection in this process.

Step 4-1: Isothermal Compression
After constant pressure heat rejection, the cooled air is again sent to the cold Engine Cylinder. In this step, the piston will move inside towards the working fluid using the work produced in the hot cylinder. As the piston will move towards the working fluid, the working fluid will get compressed and due to compression the pressure and temperature will increase.
But we will assume that temperature will remain constant and this process will be isothermal and only pressure will rise in this process.

In the PV diagram, we see that pressure (P) will increase and the volume (V) will decrease.
In the TS diagram, we will see that temperature (T) will remain constant and entropy (S) will decrease.

After the last step 4-1, the process will reach its initial stage 1 and in this way, this cycle will repeat itself continuously.

Efficiency of Ericsson Cycle:

The efficiency of the Ericsson Cycle is the ratio of net work output to the heat input.
Now, let us calculate the heat supplied in different steps of the Ericsson Cycle.

1 Heat addition in Step 1-2( Constant Pressure Heating )
Q_1-2
= MC_P (T₂ – T₁)

2 Heat addition in Step 2-3 (Isothermal Expansion)
Q_2-3
= P₂V₂ ln[V₃/V₂]
= P₂V₂ ln( R ) ( Since, V₃/V₂ = R , which is compression ratio )
= mRT₂ln (R) …………… (i)

3 Heat addition in Step 3-4 ( Constant Pressure Cooling )
Q_3-4
= MC_P (T₃ – T₄)


4 Heat addition in Step 4-1 (Isothermal Compression)
Q_4-1
= P₄V₄ ln[V₄/V₁]
= P₄V₄ ln( R ) ( Since, V₄/V₁ = R , which is compression ratio )
= mRT₄ln (R) …………… (ii)

Now, the efficiency of Ericsson Cycle:

Efficiency (η_{Ericsson Cycle} )
= Heat Supplied – Heat Rejection / Heat Supplied
= mRT₂ln (R) – mRT₄ln (R) / mRT₂ln (R)
= mRln(R) [ T₂ – T₄ ] / mRln(R) T₂
= T₂ – T₄ / T₂
= 1 – T₄ / T₂ (This is same as efficiency of carnot cycle)
= 1 – T_lower / T_upper

(Step 2-3 and Step 4-1 are not considered as both are isothermal process and no heat rejection or addition takes place during this step. )