GATE 2022 | I C Engines | Various Air standard Cycle notes for Mechanical Engineering

Introduction: An engine is a device that transforms one form of energy into another form. Normally, most of the engines convert thermal energy into mechanical work and therefore they are called 'heat engines'. Heat engines can be broadly classified into two categories:

(i). Internal Combustion Engines (IC Engines)

(ii). External Combustion Engines (EC Engines)

Classification of heat engine:

Engines whether Internal Combustion or External Combustion can be classified into two types,

(i) Rotary engines

(ii) Reciprocating engines

BASIC ENGINE COMPONENTS

An engine is made up of by combining several components out of which some important components are discussed below.

NOMENCLATURE

 (i) Cylinder Bore(d)

The nominal inner diameter of the working cylinder is called the cylinder bore and is designated by ‘d’.

(ii) Piston Area (A)

The cross-sectional area of a cylinder is called the piston area and is designated by ‘A’.

(iii) Stroke (L)

The nominal distance through which a working piston moves between two successive reversals of its direction of motion is called the stroke.

 (iv) Dead Centre

The position of the working piston at the moment when the direction of the piston motion is reversed at either end of the stroke is called the dead centre. There are two dead centres in the engine

 (a) Top Dead Centre       

 (b) Bottom Dead Centre

(a) Top Dead Centre (TDC): Dead centre when the piston is farthest from the crankshaft or nearest to the cylinder head is known as Top Dead centre.

(b) Bottom Dead Centre (BDC): Dead centre when the piston is nearest to the crankshaft or farthest from the cylinder head is known as Bottom dead centre.

(v). Displacement or Swept Volume (V_s): The volume swept by the piston when travelling between both dead centres is called the displacement volume.

(vi). Compression Ratio (r): It is the ratio of the total cylinder volume when the piston is at the bottom dead centre, V_Total, to the clearance volume, V_c.

The three cycles of great practical importance in the analysis of piston engine performance are

(i). Constant Volume or Otto Cycle

(ii). Constant Pressure or Diesel Cycle

(iii). Dual Combustion or Limited pressure Cycle.

1. Constant Volume or Otto Cycle:

           Fig: P-V & T-S diagram of Otto Cycle

Working of Otto cycle:

When the engine is working on full throttle, the processes 0→1 and 1→0 on the p-V diagram represents suction and exhaust processes and their effect is nullified.

Process 1→2: represents isentropic compression of the air when the piston moves from bottom dead centre to top dead centre and charge (mixture of fuel and air) is compressed to a higher pressure.

Process 2→3: heat is supplied reversibly at constant volume. This process corresponds to spark ignition and combustion in the actual engine starts.

Processes 3→4: represent isentropic expansion where the product of expands & piston moves from top dead centre to bottom centre.

Process 4→1: represent constant volume heat rejection in which piston stays at the bottom dead centre.

Thermal Efficiency: The thermal efficiency of the Otto cycle can be written as:

From the above expression, we can see that the thermal efficiency of the Otto cycle is a function of compression ratio r and the ratio of specific heats γ.

Further, the efficiency is independent of heat supplied and pressure ratio.

The use of gases with higher γ values would increase the efficiency of the Otto cycle.

Effect of γ and r on the efficiency:

Work Output

Thus, it can be seen that the work output is directly proportional to the pressure ratio, r_p.        

The mean effective pressure of the cycle is given by:

The mean effective pressure which is an indication of the work output increases with a pressure ratio at a fixed value of compression ratio and the ratio of specific heats.

Constant pressure cycle or Diesel Cycle:

Process 1→2: represents isentropic compression of the air when the piston moves from bottom dead centre to top dead centre and the air is compressed to a higher pressure.

Process 2→3: heat is supplied reversibly at constant pressure. This process corresponds to the injection of fuel through fuel injector and combustion due to the self-ignition of fuel.

Processes 3→4: represent isentropic expansion where the product of expands & piston moves from top dead centre to bottom centre.

Process 4→1: represent constant volume heat rejection in which piston stays at the bottom dead centre.

The difference between Otto and Diesel cycles is in the process of heat addition.

In the Otto cycle, the heat addition takes place at constant volume whereas in the Diesel cycle it is at constant pressure.

For this reason, the Diesel cycle is often referred to as the constant-pressure cycle.

Thermal Efficiency:

From the above expression, we can see that the efficiency of the Diesel cycle is different from that of the Otto cycle only in the bracketed factor.

This factor is always greater than unity. Hence for a given compression ratio. the Otto cycle is more efficient.

In diesel engines, the fuel cut-off ratio, r_c, depends on output, for maximum output r_c maximum.

Therefore, unlike the Otto cycle, the air-standard efficiency of the Diesel cycle depends on the output.

Work Output: The network output for a Diesel cycle is given by:

Mean effective pressure: The mean effective pressure of the cycle is given by:

Dual combustion Or Mixed OR Limited Pressure Cycle:

The name dual combustion is derived from the fact that it incorporates into it the features of both Otto and Diesel cycles.

Heat addition at constant volume tends to increase the efficiency of the cycle whereas switching over to constant pressure heat addition limits the maximum pressure. Hence, this cycle is also called the limited pressure cycle.

Fig.: P-V & T-S diagram of Dual cycle

Comparison of Otto, Diesel and dual cycles:

In order to compare the performance of the Otto, Diesel and Dual combustion cycles some of the variable factors must be fixed.

(i). For the same compression ratio and same heat addition:

(ii). Same Compression Ratio and Heat Rejection:

(iii). Same Peak Pressure, Peak Temperature and Heat Rejection:

(iv). Same Maximum Pressure and Heat Input:

(v). For the same maximum pressure and work output:

Other cycles:

1. Stirling cycles:

2. Ericsson cycle: The Ericsson cycle consists of two isothermal and two constant pressure processes. 

3. The Lenoir Cycle:

The efficiency of Lenoir cycle is given by:

The efficiency of the Lenoir cycle depends upon the pressure ratio as well as the ratio of specific heats, γ.

4. Atkinson cycle:

Where r_e is the expansion ratio.

Relation between r, r_e and rc:

r = r_e × r_c

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