The University of the South Pacific

School of Engineering and Physics

MM301- Energy Supplies

Theoretical Performance of Heat Engine

NAME: ARON CHAND STUDENT ID: S11110303PROGRAM: BACHELORS OF ENGINEERING (MECHANICAL)SUPERVISOR: DR. ATUL RATURI

Aim

1. To demonstrate the working principle and theoretical analysis on two types of heat engines which are: Steam Engine Sterling Engine.

2. Compare the performance of a steam engine with the performance of a sterling engine

Objective

At the end of this project the group will be able to:

Understand the working principle of the steam engine and the sterling engine. Analyze the basic process in each cycle and compare the performance between the two cycles.

Acknowledgements

I would personally like to acknowledge this list of people, without whom, this project would not have been successful:

1. Ms. Shirleen Swapna (PH301 Tutor).2. Dr. Atul Raturi (Senior Lecturer and our project supervisor).3. Dr. Surendra Prasad (Senior Lecturer).4. Mesake Navunawa (Group Member).5. Isaiah Holmes (Group Member).

Lastly, I would like to acknowledge my sources in the reference section of this report, through which I have demonstrated my project more thoroughly.

Declaration of Originality

I would like to personally declare that this is my original piece of work, and all the information and resources which I have used in this project are properly referenced and acknowledged.

..Aron Chand(23rd May 2015) Introduction

This project is based on heat engines. There are a variety of heat engines and are categorized into two main branches and they are called internal combustion and external combustion. In an internal combustion engine, the combustion of fuel or cycle reaction occurs in a confined area. Such examples are Compression ignition engine [1], which is commonly known as Diesel engine and Spark ignition engine, also known as Petrol engine [2].

Figure 1: Animated design of a Compression ignition engine

Figure 1: Animated design of a Spark ignition engineExternal combustion engines are engines, where the combustion process does not always have a fixed confined area, they occur openly. Such examples are Gas turbine [3] and Steam turbine [4].

Figure 3: Animated design of a Gas Turbine (Jet engine)

Figure 4: Siemens steam Turbine.

This project focuses mainly on the performance analysis on steam engine and a sterling engine. Sterling engine [5] is a type of engine which requires gas as the working fluid and it does not has any by-product such as fume or any other harmful gas. Instead, there is only heat addition and heat rejection. The sterling engine works solely on gas expansion and compression, and is also an external combustion engine. This type of engine also follows the sterling cycle which is slight similar to Carnot cycle, but the efficiency is less compared to Carnot cycle. As the gas heats it expands inside the confined space, pushing the displacer upwards, cranking the flywheel rotation, , upon more expansion, it flows over the displacer and enters the cold region where it is cooled again and then contraction occurs and the whole cycle starts again with the same gas.

Secondly, the steam engine [6] works on the Rankine cycle process, where it uses water as a working fluid. Water is heated inside the boiler where it leaves the boiler as superheated steam, and upon flowing over the turbine or against piston at such high temperature and pressure, it causes the turbine to rotate or piston to reciprocate and thus mechanical work is produced. Upon passing over the turbine or again the piston, the steam loses heat and phase change occurs and finally it passes through a condenser where it rejects more heat and upon leaving the condenser it is in liquid state. Finally, it is pumped back up to the boiler where the cycle continues again.

Figure 5: Animated design of a Sterling Engine.

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Figure 6: Application of a Rankine Cycle.

Literature Review

Steam EngineSteam engines are of two types; piston type and turbine type

Reciprocating Piston Steam EngineIn a reciprocating piston steam engine, the water is heated in the boiler until state change occurs. Upon further heating of the water vapor, it changes into superheated steam. The steam is released into the piston cylinder where it pushes the piston upwards, causing the flywheel to rotate, this in turn creates a moment on the flywheel where upon continuous reciprocating motion the rotation continues and causes the shaft coupled with it to rotate. This in turn can generate electricity in a generator or other mechanical work. Figure [7] below demonstrates a simple piston driven steam engine.

Figure 7: Demonstration of Rankine Cycle with a piston.

Steam turbine In a steam turbine, the boiler converts the water into high pressure steam, after which it passes over the turbine. While it is passing through the turbine, the enthalpy of the steam decreases until it changes state from steam to liquid. Then it flows to the condenser or heat exchanger where upon more heat loss, it leaves as a liquid. Then it is pumped back up to the boiler. The figure [8] below demonstrates a Rankine cycle and also the basic component and cycle of the working fluid

Figure 8: Rankine Cycle with a Steam TurbineSterling EngineThere are three major types of sterling engine and they are classified as:

Alpha TypeIn this type of set-up, the hot and cold chambers where expansion and compression occurs, are separate from each other with a regenerator in between them. There are two pistons for each cylinder and both are connected to the same crankshaft. Regenerator takes away heat from the hot gas upon expansion and gives in heat to the cold gas upon compression.

Figure 9: Alpha type Sterling Engine.

Beta TypeIn a beta type configuration [10], there is only one chamber with one piston and a displacer. The displacer is loosely mounted so that it can force the flow of the working fluid inside the chamber between the clod and hot section.

Figure 10: Beta type Sterling Engine.

Gamma TypeThese types also function similar to beta type, expansion and compression occurs in same chamber where the displacer influences the fluid flow in the section. The major difference when compared to beta is that the power piston is not in-line with the displacer piston but in a different chamber which is jointed to the compression side of the first chamber. The advantage of this arrangement is that it prevents the power piston to be influenced by the size of the displacer or the orientation. But a major disadvantage of this type is that the compression is low thus low shaft power

Figure 11: Gamma type Sterling Engine.

Basic Parts and Component

Steam Engine

Engine frame Cylinder Steam chest Stuffing box and gland packing The crosshead guide is a link between the piston rod and the connecting rod. Main bearings support the engine crankshaft and are fitted on the engine frame. Piston Cam shaft( for valve opening and closing)

Sterling Engine Piston Displacer Heat source Heat sink Linkages Crankshaft Regenerator

Methodology Research, compile and evaluation of the analysis of steam engine and sterling engine. Findings on the efficiency for both and comparison, to determine the better performer.

Results and Discussion

Steam Engine

Hypothetical indicator diagram considering compression and clearance Figure 12: Hypothetical indicator diagram

Process 6-1 steam admissionProcess 1-2 hyperbolic expansionProcess 2-3 exhaust valve opens at 2 and the stroke reaches dead center at 3Process 3-4 Exhaust of steam into condenserProcess 4-5 Compression of remaining steam in the cylinderProcess 5-6 Fresh steam enters the boiler at the state 5 for the next cycle. Its pressure rises immediately to the boiler pressure

Work done

W = area of indicator diagramW = [1]

We define:r = v2/v1 (expansion ratio) = (V1-Vc)/Vs (cut off ratio) = (fraction of stroke volume completed at the start off)Compression

C = (clearance volume ratio)

Using the above defined terms we get:

and

Therefore Work done can be rewritten as:

Mean effective pressure

If neglecting the effect of compression = 0 and we get:

Steam consumptionThe steam consumption of a steam engine may be defined as the amount of steam in kg consumed by the engine per hour. The steam consumption for an engine can be obtained from the theoretical indicator diagram.Mass of steam admitted per cycle:

Where:d = bore of cylinderL = length of stroke of piston (m) = cut off ratiov = specific volume of steam at admission pressure (

For a single acting steam engine which makes N revolutions per minute:

This equation represents the steam consumption on one side of the piston. For single acting steam engine it represents the total steam consumption per hour. For a double acting steam engine the total steam engine is twice the above amount, provided: The cut off ratio on both sides is the same The volume occupied by the piston rod is negligibleThus for a double acting steam engine:

Power Output of Steam engine

Piston speed: It is the linear speed travelled by a piston per second and is expressed as follows: (m/s) .

Theoretical indicated power: The theoretical power developed by the engine inside the cylinder as shown by the area of an indicated diagram is known as indicated power. It is designated as and expressed as the product of force and velocity of the piston

Where:n = N for single acting cylinder = 2N, for double acting engineN = rotation per minute of the engine

Actual indicated powerThe actual indicated power developed by an engine:

Brake PowerIt is the power available (output) at the crank shaft of the engine. However, it is less than the power developed in the cylinder due to frictional losses. The brake power is measured by dynamometers like rope brake, prony brake or hydraulic dynamometers.

Figure 13: Rope brake dynamometer

Where:W = Weight applied on rope , (N=mg)S = spring balance reading (N)N = speed of the crank shaft, rpmR = effective radius of the brake drum

Then:

Frictional Power The frictional power is the difference between the indicated power and the brake power.FP = IP BP

Heat supplied by steam to engine

Where:

Indicated thermal efficiencyIt is defined as the ratio of actual indicated power developed in the engine cylinder to heat supplied by the steam

Brake thermal efficiencyThe ratio of brake power to energy supplied by steam

Mechanical efficiency

Overall efficiencyIt is defined as the ratio of the brake power to energy supplied by the fuel for steam generation in the boiler.

Where: = rate of fuel supplyCV = calorific value of fuel (KJ/kg)

Sterling Engine (Ideal)

The diagrams below show the typical cycle of an ideal sterling engine

Figure 14: Typical of an ideal sterling cycle diagram

The table below lists each phase with corresponding alphabets

State ChangeSterling Engine Heat Cycle Processes

A-BIsothermal Compression.

B-CConstant Volume Heat Transfer

C- DIsothermal Expansion

D-AConstant Volume Heat Rejection

Mean Effective Pressure: = [(P3-P2) V3 / (V1-V2)] ln (V1-V2)

Work Done: = Heat in(C-D) Heat out (A-B)

Torque:= Net Force acting on the flywheel * radius of flywheel

Shaft Power:= 2*pi*torque*angular speed (revs/s)

Thermal efficiency:= shaft power/ heat added to the system

Heat added to system:Heat added to system=heat released by fuel/source.

Heat released by source:= Efficiency of source * heat used by source

Heat used by source:= volume of fuel used by source* calorific value of the fuel

Discussion on Stirling Engine

In the P-v diagram of the sterling engine cycle; 1. From 1(A) to 2(B), the air is compressed at constant temperature and also during this time, heat is rejected to the cold sink. 2. From 2(B) to 3(C), partial heat is added by the regenerator at constant volume.3. From 3(C) to 4(D), air is expanded at constant temperature due to heat addition until it reaches 4(D)4. From 4(D) to 1(A), the heated air is cooled down by a regenerator at constant volume, and then the cycle repeats.

Heat released by fuel per volume can be determined by testing a fixed volume sample in a bomb calorimeter and then multiplying the volume of fuel used to the result obtained after testing the fixed sample volume tested in the bomb calorimeter.

Total heat released can be determined by multiplying the calorific value of the fuel used with the volume of fuel used and then dividing the product with the average time taken for the volume of fuel burnt. The results from here can be substituted into the given formulas to determine the final work done, efficiency and mean effective pressure of the sterling engine.

Discussion on Steam Engine

In the P-v diagram of the steam engine cycle;1. From 6-1; steam is transferred to the chamber at high pressure until the pressure is high enough to force the piston to take a stroke2. Process 1-2; is a hyperbolic expansion, where the steam is expanding in the cylinder while piston is displacing 3. Process 2-3; exhaust valve opens at 2 while the piston is moving to the dead center resulting in steam ejection from the chamber and at 3the stroke reaches dead center.4. Process 3-4; steam is exhausted out of the chamber.5. Process 4-5; the remaining steam in the cylinder is compressed as the piston comes back6. Process 5-6 Fresh steam enters the boiler at the state 5 for the next cycle. Its pressure rises immediately to the boiler pressure

The boiler can be either fire tube or water tube. In a fire tube boiler, the heat flows through the tube, which is submerged in the water. And in the water tube boiler, the water flows inside the tube and heat is added from outside. Fire tube boiler is more common in industries than water tube. And it is also very efficient.

The efficiency of the boiler can be calculated by the enthalpy of the steam released divided by the heat input into the boiler. The heat input into the boiler can be calculated by the same way as the Stirling engine, where the quantity of fuel used can be multiplied with the calorific value of the fuel and the result divided by the time consumed for that much quantity of fuel to burn.

Conclusion

After completion of this project, our objective was completed as we were able to grasp and thoroughly understand the working principle of different types of steam engines and sterling engines and also the theoretical analysis on how to calculate the performance of the stirling engine and the steam engine (piston) such as the efficiency, net-work, power output, mean effective working pressure and heat required to run the cycle. We also found out the limitation of the steam engines and the sterling engines, together with their maximum recorded efficiency.

Limitation of a steam engine: Requires superheated for a longer life span and optimum performance. Quality affects the system adversely, which means that if there is slight moisture content in the steam, it will be very harmful to the piston or turbine as it causes cavitation and pitting corrosion. Due to losses such as leakages, the exact quantity of water is not returned to the boiler, which was used to be converted to steam. This reduces the efficiency of the cycle. During stroke cycle, the early opening of the valves causes steam loss which again affects the efficiency. The cost of maintenance of the boiler and turbine is not very economical and the capital cost is high.

Limitation of a Stirling engine: Requires a regenerator to achieve higher efficiency External losses influence the efficiency of Stirling engine for example, imperfect transfer of heat from the source to the Stirling engine. And also friction within the Stirling engine chamber and pumping components reduce the efficiency of the steam. The capital cost is very high for installation and maintenance is high but not as high as for steam engine.

Finally, we also found out that the efficiency of the Stirling engine is much higher than the efficiency of the steam engine. Therefore, the performance of a Stirling engine is much better than steam engine and dependent with the efficiency.

Reference

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[8] Simple Performance Prediction Method -English-. 2015. Simple Performance Prediction Method -English-. [ONLINE] Available at: https://www.nmri.go.jp/eng/khirata/stirling/simple/simplee.htm. [Accessed 23 May 2015].[9] Mesake Navunawa (USP). Group member.MM301. Steam engine results.doc

[10] Stirling engine - Wikipedia, the free encyclopedia. 2015. Stirling engine - Wikipedia, the free encyclopedia. [ONLINE] Available at: http://en.wikipedia.org/wiki/Stirling_engine. [Accessed 23 May 2015].