6.2.1 Heat Engine Cycle

6.2.1.1 Define Heat Engine Cycle

A Heat-Engine Cycle is defined as a number of thermodynamic processes arranged in a given sequence and repeated over constant intervals of time.

Those thermodynamic processes (e.g., in a Carnot cycle) are as follows:

• Along AB an isothermal expansion occurs at temperature TH, with heat Q2 being absorbed.

• Along BC an adiabatic expansion occurs, and the temperature falls to TC.

• Along CD an isothermal compression occurs at temperature TC, with heat Q1 being rejected.

• Along DA an adiabatic compression occurs, and the temperature rises back to TH

In an isothermal process, the temperature is constant, meaning the internal energy in the cylinder is constant, and the net change in internal energy is ZERO. Adiabatic compression means that no heat is given to or taken from the cylinder walls of the engine.

6.2.1.2 The Practical Cycles and "Ideal" Theoretical Cycles

Real practical cycles are based on "ideal" theoretical cycles.

6.2.1.3 Most ideal cycles involve the following thermodynamic processes:

• Heating or cooling, at constant pressure.

• Heating or cooling, at constant volume.

• Adiabatic compression or expansion.

6.2.1.4 - 6.2.1.8 Working Fluid, Efficiency, and Energy Input

A cycle of thermodynamic processes (or operations) is carried out on a "working fluid." Ideally, the working fluid is "perfect" with constant physical properties and structure throughout the cycle (only in theoretical conditions). Working fluids used in practical engines change during the cycle of processes.

The function of a heat-engine cycle is to produce the maximum possible output of useful work (W) from a given quantity of energy supplied to the working fluid. In the majority of practical heat-engine cycles, the energy input is obtained from the energy released by the combustion of a fuel with air.

The "efficiency" of the cycle is measured by the energy output obtained per unit of energy supplied to the working fluid. In the "ideal" case, the energy output will be the difference between the energy supplied during the cycle (Q1) and the energy rejected at the end of the cycle (Q2).

6.2.2 Ideal Gas Cycle

6.2.2.1 Define Ideal Gas Cycle

Ideal / Theoretical Gas Cycles

 are the most efficient cycles for reciprocating engines. These cycles occur under the following theoretical conditions:

• The working fluid is assumed to be ideal.

• The working fluid never leaves the system; it remains within the closed system from cycle to cycle.

• Heat supplied to the working fluid converts completely to work.

• Heat is rejected from the working fluid to the surrounding.

• All compression and expansion processes are carried out adiabatically (without heat transfer).

6.2.2.2 Ideal Cycle Models

6.2.2.2.1 Constant Volume or Otto Cycle

The Otto cycle is a description of what happens to a mass of gas as it is subjected to changes of pressure, temperature, volume, heat addition, and heat removal. The process steps are:

• 1-2: Rapid adiabatic compression of the air by the piston moving quickly into the Top Dead Centre (TDC). This raises the pressure and temperature.

• 2-3: Whilst the piston remains at (TDC), heat energy is supplied to the air at constant volume, further increasing the pressure and temperature to the maximum values.

• 3-4: The hot, high-pressure air forces the piston rapidly down, causing work energy to be transferred to the surroundings (power stroke).

• 1-4: When the piston reaches the Bottom Dead Centre (BDC), heat energy flows from the air to the surroundings at constant volume, until the air reaches its original position at 1.

Practically, the above cycle is modelled in an internal combustion reciprocating engine using gas or petrol as a fuel, with spark ignition.

6.2.2.2.2 Diesel Cycle

The Diesel cycle is a combustion process where fuel is ignited by heat generated during the compression of air. The process steps are:

At 1 with the piston at BDC, cylinder is full of air.

• 1-2: Represents the adiabatic compression of air as the piston moves from BDC to TDC

• 2-3: Heat energy is supplied at constant pressure as the piston starts to return to BDC, resulting in a further increase in temperature.

• 3-4: The supply of heat is cut off, and the air expands adiabatically until the piston reaches BDC

• 4-1: Heat energy flows from the air to the surroundings at constant volume until the air returns to its original condition.

Practically, the above cycle is modelled in a compression-ignition reciprocating engine using diesel or heavier fuel oil, where ignition is by transfer of heat energy from compressed air.

6.2.2.2.3 Dual Cycle

The Dual Combustion Cycle is a thermal cycle that combines the Otto cycle and the Diesel cycle. Heat is added partly at constant volume and partly at constant pressure. This is the cycle that modern diesel engines tend to approach.

At 1 the Piston is at BDC, cylinder is full of air.

• 1-2: Air is compressed adiabatically (isentropically), raising pressure and temperature.

• 2-3: Heat is supplied at constant volume to further increase temperature and pressure (reaching maximum pressure).

• 3-4: Further heat energy is supplied at constant pressure, causing an increase in volume and temperature (reaching maximum temperature).

• 4-5: The air then expands adiabatically until the piston reaches BDC.

• 5-1: Heat energy is rejected at constant volume until the air returns to its original condition.

6.2.2.2.4 Joule (Constant Pressure) Cycle (Brayton Cycle)

The Brayton cycle (or Joule cycle) represents the operation of a gas turbine engine. The cycle consists of four processes:

• a - b: Adiabatic compression in the inlet and compressor.

• b - c: Constant pressure fuel combustion (idealized as constant pressure heat addition).

• c - d: Adiabatic expansion in the turbine and exhaust nozzle, where work is extracted.

• d - a: Cool the air at constant pressure back to its initial condition.

  

Practically, the above cycle is modelled in a rotary gas turbine.

6.2.2.5 Explain the meaning of single and double acting as applied to reciprocating engines

Single acting

A single-acting cylinder is a cylinder in which the working fluid acts on one side of the piston only. A single-acting cylinder relies on the load of other cylinders, or the momentum of a flywheel, to push the piston back in the other direction. They are almost universal in internal combustion engines.

Double acting

A double-acting cylinder is a cylinder in which the working fluid acts alternately on both sides of the piston. Double-acting cylinders are common in steam engines but unusual in other engine types. They are used where an external force is not available to retract the piston or where high force is required in both directions of travel.

6.2.2.6 Describe the processes which take place in each stroke of the two stroke and four stroke cycle in diesel and petrol engines

(Please refer to section 6.1.3 for the detailed description of the two-stroke and four-stroke cycle processes.)

6.2.3 Rankin Cycle

6.2.3.1 Definition of the Rankine Cycle

The Rankine cycle is the ideal cycle where the working fluid is used in both liquid and vapor phases such as in a steam power plant or refrigeration plant. It is the fundamental operating cycle where an operating fluid is continuously evaporated and condensed.

steam power plant cycle

Refrigeration plant cycle

6.2.3.2 Describe the four main components of steam plant

The marine steam plant consists of four main components

1. Boiler: Produces superheated steam from feed water, with the required energy supplied from the combustion of fuel in air.

2. Turbine (HP/LP): High-Pressure and Low-Pressure turbines adiabatically expand the high-pressure superheated steam to obtain useful output work (W).

3. Condenser (Main/Auxiliary): Receives low-pressure exhaust steam from the turbine, interacts with a cooling medium (usually seawater) for heat transfer, and condenses the steam back into water.

4. Feed Pump: Raises the pressure of the condensate to the boiler pressure and pumps it back into the boiler, ensuring positive flow.

6.2.3.3 State the Rankine Cycle Efficiency

The Rankine cycle efficiency is the ratio of Energy derived from the cycle as useful work to the Energy supplied to the cycle.

6.2.4 Reciprocating Internal Combustion Engines

6.2.4.1 Swept Volume

When the piston moves from one end of the cylinder to the other, it will sweep or displace air equal to the cylinder volume between TDC and BDC. This full stroke movement is known as the swept volume or the piston displacement.

Swept volume can be defined as the volume swept by the engine piston during one complete stroke. It is the product of piston area and stroke. In the following diagram, swept volume is V2.

6.2.4.2 Mean Effective Pressure (MEP)

The Mean Effective Pressure (MEP) is the average pressure exerted on the piston during each power stroke. It is an equivalent constant pressure that would do the same work as the varying pressure within the cylinder.

The units used for MEP may be either kilo Newton per square meter (kN/m^2) or bars.

The diagram on the left represents the pressure variation inside the cylinder during one revolution of a two-stroke engine, which is called a Power Card Diagram.

The Mean Effective Pressure (MEP) is the equivalent constant pressure acting on the piston over one stroke that would do the same work as the actual changing pressure over the whole cycle.

In order to find the mean effective pressure in the cylinder, a rectangular area is produced on the indicator diagram, having the same stroke (L) and area (A) as the indicator diagram. The pressure at the top of this rectangular area is the mean effective pressure within the cylinder.

6.2.4.3 Energy Transfer from Combustion Gas to Piston

In an Internal Combustion Engine (ICE), the expansion of the high-pressure gases produced by combustion applies force to the piston, causing it to push downward. This force moves the piston over a distance, transforming chemical energy into useful mechanical energy by turning the engine.

6.2.4.4 Energy Transferred from the Combustion Gas to the Piston is MEP X Swept Volume.

MEP is defined as the average pressure that the gas exerts on the piston (S) through one complete cycle of the engine.

Work is defined using the fundamental equations:

F=P x A

 

F = Force

P = Pressure

A = Area.

 

Work = Force x Distance

 

Work = P x A x Distance

 

As the distance is the stroke length, above A x Distance = Swept volume

 

So, Work = P x Swept volume (Unit is Joule)

 

Work per Operating Cycle = (Mean Effective Pressure) x (Swept Volume per                                                                                       .                                                                                                 Operating cycle)

                                                =   [bar]                                     X   [m] x [m²]

                                                   =    [10⁵N/m²]                               X    [m³]

                                                   =  J

 

6.2.4.5 The power produced by one cylinder of an engine is found by using the expression power = Work per Cycle x Number of Cycles per Second and is measured in Watts.

If engine revolutions per second is , the Power is: 

Power = Work done per cycle x Number of cycles per second

This is measured in Watts (Joules per second).

6.2.4.6 State that the number of cycles per second

The number of cycles per second is calculated based on the engine type:

• Two-Stroke Engine: The number of cycles per second is equal to the Revolutions Per Minute (RPM) divided by 60, as there is one cycle per revolution.

• Four-Stroke Engine: The number of cycles per second is the RPM divided by 60 and divided again by 2. This is because a cycle occurs every two revolutions.

• Double-Acting Engine (Steam or Two-Stroke Oil): The number of cycles per second is 2 x  N, ( N= revolutions per second)

         Because there are two working strokes in each revolution.

6.2.4.7 Describes an Indicator Diagram and Obtains M.E.P.s from Indicator Diagrams

There are mainly two types of indicator diagrams taken from the engine cylinder to assess engine condition and performance:

Power Card / Power Indicator Diagram: Taken with the indicator drum rotating in phase with the piston movement. The area within this diagram represents the work done during one complete cycle to scale. Mean Indicated Pressure (MIP) is obtained from this diagram to calculate the power produced in the cylinder.

Draw Card / Out of Phase Diagram: Taken using the same mechanism, but the barrel movement is amplified over a short period to magnify the topmost part (end of compression and peak pressure area) of the power diagram.

A. Ignition

B. Pressure-Volume working diagram

C. Ignition stroke

D. Draw diagram

E. Top dead center

F. Bottom dead center 

G. Pcomp

H. Pmax

F. Opening exhaust valve

• The indicator diagram is very important to know the combustion in the cylinder and also to adjust the engine.
• The diagram is taken periodically from the indicator valve equipped on the cylinder head and combustion condition is to be confirmed.
• The compression pressure and maximum pressure in the cylinder can be taken from the indicator diagram.
• Engine indicator is the device used to take the indicator diagram.
• Indicator diagrams give efficiency of combustion in the cylinder, condition of the running gear, irregularities in fuel pumping and injection and a lot of things.

The indicator diagram is crucial for confirming combustion efficiency, adjusting the engine, and confirming compression and maximum cylinder pressure.

Obtain MEPs from Indicator Diagrams

An indicator diagram taken from a six cylinder two-stroke engine is shown in Figure. The spring constant for the indicator mechanism is 65kPa mm

The diagram is divided into l0 equal parts and within each a mid-ordinate is positioned.

Therefore.

Mean height of diagram = sum of mid- ordinates

                                           Number of parts in diagram

                                       = 3+4+5+7+8+9+11+14+26+42

                                                        10

                                       = 129/10

                                       =12.9mm

 

Mean effective pressure = mean height of diagram × spring constant

                                        = 12.9× 65

                                        = 838.5 kPa

6.2.4.8 Definition of Engine Power Terms

6.2.4.8.1 Indicated Power (IP)

Indicated Power (IP) is the theoretical power developed inside the cylinder and is measured by an indicator instrument that records the gas pressure throughout the piston travel.

6.2.4.8.2 Brake Power (BP)

The $\text{IP}$ is the theoretical power. The actual, usable power obtained at the output shaft of the engine is the Brake Power (BP). It is less than the (IP) due to various losses.

6.2.4.8.3 Friction Power (FP)

The difference between the (IP) and the (BP) is the Friction Power (FP), which is the power required to overcome the frictional resistance of the engine parts (e.g., pistons, bearings, and auxiliary drives).

Friction Power = Indicated Power - Brake Power

6.2.4.9 Explain that the energy is also transferred to the Exhaust gas and Engine cooling system

The energy released in the combustion chamber is dissipated in three different ways:

1. Useful Mechanical Work: Approximately 30% to 40% is converted into useful mechanical work.

2. Exhaust Gases: Approximately 30% to 40% is lost as waste heat through the exhaust gases.

3. Engine Cooling System: Approximately 30% is lost as waste heat to the engine cooling system.

6.2.4.10 Mechanical Efficiency

Mechanical Efficiency tells us how much of the indicated power is converted into brake power. It is the ratio between the Brake Power and the Indicated Power.