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DESIGN AND FABRICATION OF ALPHA STIRLING ENGINE A PROJECT REPORT Submitted by

BHARANIDHARAN.N GOUTHAM.R GOVENDAN.N HARIRAGUL.K

(211414114061) (211414114107) (211414114109) (211414114118)

In partial fulfilment for the award of the degree Of

BACHELOR OF ENGINEERING IN MECHANICAL ENGINEERING

PANIMALAR ENGINEERING COLLEGE

ANNA UNIVERSITY : CHENNAI 600 025 APRIL 2017

DESIGN AND FABRICATION OF ALPHA STIRLING ENGINE A PROJECT REPORT Submitted by

BHARANIDHARAN.N GOUTHAM.R GOVENDAN.N HARIRAGUL.K

(211414114061) (211414114107) (211414114109) (211414114118)

In partial fulfilment for the award of the degree Of

BACHELOR OF ENGINEERING IN MECHANICAL ENGINEERING

ANNA UNIVERSITY :: CHENNAI 600 025 APRIL 2017

ACKNOWLEDGEMENT

Our

sincere

thanks

to

Honorable

Late.Col.Dr.JEPPIAAR.M.A,B.L.,PhD

for

Founder providing

and us

with

Chairman necessary

infrastructure to carry out this project. We would like to express our deep gratitude to Our Secretary andcorrespondent Dr.P.CHINNADURAI.M.A,M.Phil.PhDfor his enthusiastic motivation which inspired us a lot in completing this project. We also express our sincere thanks to Directors Mrs.C.VIJAYARAJESWARI and Mr.C.SAKTHIKUMAR. M.E,for facilitating the speedy completion of this project. We also express our gratitude to Our Principal Dr.K.MANI M.E.,Ph.D, Who has been a source of constant encouragement and support. We would also express our gratitude to Our Head of department Dr.L.KARTHIKEYAN.M.E,M.B.A.,Ph.D.,

Department

of

Mechanical

Engineering , Also we thank our guide Mr.S.DHANASEKAR M.E., Department of Mechanical Engineering, for their valuable guidance and encouragement to complete this project successfully. Finally we extend our thanks to all our faculty members and non teaching staff of Mechanical Engineering Department for their continuous support in completing this project. We would like to heart fully thank our PARENTS who gave us encouragement and guidance to complete this project successfully.

ANNA UNIVERSITY : CHENNAI 600 025 BONAFIDE CERTIFICATE Certified that this project report “DESIGN AND FABRICATION OF ALPHA STIRLING ENGINE” is the bonafide work of BHARANIDHARAN.N211414114061 GOUTHAM.R 211414114107 GOVENDAN.N 211414114109 HARIRAGUL.K 211414114118

SIGNATURE

SIGNATURE

Dr. L.KARTHIKEYAN,ME,MBA,Ph.D

Mr. S.DHANASEKAR.,ME

HEAD OF THE DEPARTMENT,

SUPERVISOR,

PROFESSOR

ASSISTANT PROFESSOR,

Dept of Mechanical Engineering,

Dept of Mechanical Engineering,

Panimalar Engineering College,

Panimalar Engineering College,

Poonamallee ,

Poonamallee ,

Chennai - 600 123.

Chennai – 600 123.

Submitted for Anna University Viva – Voce held on __________ during the year 2016-2017

EXTERNAL EXAMINER

INTERNAL EXAMINER

Abstract

In recent year’s usage of energy is very high. Researches are being done to find alternative sources for energy. There are many ways by which modifying existing techniques will help to reduce the usage. The paper proposes the way to build and utilize the low cost Stirling engine for the green energy applications. The research on Stirling engine is being increased, many inventions reveals the suitability of engine for low power applications that includes an alternative for motors in industries. As it knows that Stirling engine has closer theoretical Carnot cycle efficiency. This theoretical efficiency of engine provides an alternative for various industrial low duty applications. Finally this paper will outline theoretical background of Stirling cycle; various design parameters, innovative use of fabrication works and industrial implementation ways. The design process involves the design of cylinders, its mass flow rate, amount of heat addition, heat rejection, efficiency and many more. These sub design parameters helps in finding out power outcome of the engine. The fabricated work involves usage of available materials in and around effectively. As a result final assembly of the engine meets the objective. Alpha, Beta and Gamma an Alpha configuration was Chosen because of its ease of fabrication. Parabolic solar concentrator is used to provide Heat to the Engine. The main objective was to determine how much work can be extracted from a 49cc Stirling Engine..

APPENDIX 3 (A typical specimen of table of contents) TABLE OF CONTENTS CHAPTER NO. TITLE PAGE NO. ABSTRACT iii LIST OF TABLE xvi LIST OF FIGURES xviii LIST OF SYMBOLS xxvii 1. INTRODUCTION 1 1.1 GENERAL 1 1.2 . . . . . . . . . . . . . 2 1.2.1 General 5 1.2.2 . . . . . . . . . . . 12 1.2.2.1 General 19 1.2.2.2 . . . . . . . . . . 25 1.2.2.3 . . . . . . . . . . 29 1.2.3 . . . . . . . . . . . . 30 1.3 . . . . . . . . . . .. . . . . . . 45 1.4 . . . . . . . . . . . . . . . . . . 58 2. LITERATURE REVIEW 69 2.1 GENERAL 75 2.2 . . . . . . . . . . 99 2.2 ……………. 100

Introduction A Stirling engine is a heat engine that operates by cyclic compression and expansion of air or other gas(the working fluid) at different temperatures, such that there is a net conversion of heat energy to mechanical work. More specifically, the Stirling engine is a closed-cycle regenerative heat engine with a permanently gaseous working fluid. Closed-cycle, in this context, means a thermodynamic system in which the working fluid is permanently contained within the system, and regenerative describes the use of a specific type of internal heat exchanger and thermal store, known as the regenerator. The inclusion of a regenerator differentiates the Stirling engine from other closed cycle hot air engines. Originally conceived in 1816 as an industrial prime mover to rival the steam engine, its practical use was largely confined to low-power domestic applications for over a century. The Stirling engine is noted for high efficiency compared to steam engines, quiet operation, and its ability to use almost any heat source. The heat energy source is generated external to the Stirling engine rather than by internal combustion as with the Otto cycle or Diesel cycle engines. Because the Stirling engine is compatible with alternative and renewable energy sources, it could become increasingly significant as the price of conventional fuels rises, and also in light of concerns such as peak oil and climate change. This engine is currently exciting interest as the core component of micro combined heat and power(CHP) units, in which it is more efficient and

safer than a

comparable steam engine. However, it has a low power-to-weight ratio rendering it more suitable for use in static installations where space and weight are not at a premium. The modern Stirling engine is more efficient than the early engines and can use any high temperature heat source. The Stirling engine is an external combustion engine. Therefore, most sources of heat can power it, including combustion of any combustible material, field waste, rice husk or the like, biomass methane and solar energy. In principle, the Stirling engine is simple in design and construction, and can be operated easily.

ILLUSTRATION:

LITERATURE REVIEW HISTORICAL INFORMATION The Stirling engine has attracted much attention over the years. Its potential for high efficiency and the ability to use a wide variety of fuels has made it a serious contender for alternative power sources, especially in automotive applications. The potential for Stirling engines to replace the Internal Combustion engine (ICE) in automobiles was explored in the late nineteenth century A technical report was released by NASA outlining the development of the MOD I, and MOD II automotive Stirling engine (see Appendix E for details and pictures). The engine used pressurized hydrogen as the working gas. It was developed and produced by a collaborative effort between NASA and MTI (Mechanical Technology Incorporated). The MOD II engine in particular could reach a thermal efficiency of 38.5% (significantly higher than a spark ignition ICE), and with power comparable to an ICE of the same size (83.5 hp). It burned fuel with cleaner emissions than an ICE due to the fact that it burns fuel externally to the engine. It also produced much less noise during operation. Therefore, no muffler or catalytic converter would be needed for the tailpipe. The technical problems were for the most part related to the high-pressure requirements of the engine (up to 15 MPa), which requires bulky components and specialized seals. Nevertheless, it was projected that the cost of production due to economics of scale would be competitive with an ICE. Unfortunately, it failed to attract large investment in the automotive industry mainly because it was still in its infancy development-wise, and it couldn't compete with an ICE on the basis of responsiveness. Stirling engines do not respond as quickly to

The Purpose of Stirling Engine: Stirling engine design and optimization is not a trivial matter. At its core, it’s an area that requires an understanding of thermodynamics, fluid mechanics, heat transfer, and material science. This takes time and effort to become familiar with and is surely the reason that most people get discouraged. From this point of view it would then seem that Stirling engine design is more involved than ICE design, even though it requires none of the complex mechanisms such as valves and timing mechanisms. But in reality it’s just a different kind of engine. Nevertheless, people tend not to have an intuitive feel for how to make a Stirling engine. The problem is that good design (optimization) requires the balancing of several conflicting variables, and it can be difficult to keep them straight. The solution to this is often experimentation, which unfortunately can be time and resource intensive. The alternative is to model the physics of the engine as accurately as possible, and reduce the trial and error in the construction stage, as a result. This project is the result of a year of learning about Stirling engines; both from reading lots of information found online, such as research papers, and from my own design efforts. Admittedly, even though I have a background in mechanical engineering I have found it challenging to make sense of a lot of what I read. One reason for this is because I believe that the richness in information available is somewhat diminished by less than clear or contradictory explanations. One of the reasons for this, as I see it, is that Stirling engine theory (given its inherent physical complexity) is many times reduced to simplifications, which are incomplete.

Stirling Engine Basics A Stirling engine is a heat engine that works on the basis of an external applied temperature difference. By maintaining a hot and cold temperature difference the engine is able to run and produce mechanical power. It is different from the Internal Combustion Engine (ICE) in that it is a closed cycle; that is, the working gas is enclosed (sealed) inside the engine. This is in contrast to the ICE in which the working gas (air) is drawn in from the environment, combusted with fuel, and expelled as exhaust. In such an engine valves and timing mechanisms are necessary. But in a Stirling engine, no such components are required. In addition, the Stirling engine is not restricted to the type of fuel used. It is indifferent to the source of heat, which opens up many possibilities, including non-polluting solar energy, or the burning of biomass (wood, husks, ethanol, etc), which are carbonneutral. Carbon-neutral means they absorb as much carbon dioxide (during their growth - due to photosynthesis) as they emit when burned. This is unlike fossil fuels, which add a net amount of carbon dioxide to the atmosphere when burned. The basic principle of the Stirling engine is this. The engine is filled (under pressure), with a gas such as air, helium, or hydrogen. This is called the “working gas”. Inside the engine the gas is heated. This increases its pressure and moves pistons as a result. The gas is then cooled, lowering its pressure. It is then heated again, and the cycle repeats. In a real engine this typically happens very fast, on the same order of speed as an ICE. The working gas is shuttled back and forth very quickly inside the engine, between the hot and cold ends, continuously gaining and losing heat and producing power as a result. The working gas inside the engine is heated with a heater, and cooled with a cooler. The heater and cooler are typically compact heat exchangers consisting of narrow tubes (or passageways) in which the working gas flows. It is through these passageways that the working gas either gains heat (becoming hotter), or loses heat (becoming cooler). The outside surface of the heater is exposed to a

source of high temperature, such as the flame of a burner, or concentrated solar energy. The outside surface of the cooler is exposed to a source of cold temperature such as ambient air, or water. In between the heater and cooler is a regenerator. A regenerator increases the efficiency of a Stirling engine by lowering the heat input requirement of the heater and the heat removal requirement of the cooler. It is not necessary to have a regenerator for the engine to run but in the interest of cost-reduction, especially where the cost of heater fuel is concerned, it is wise to have one. The way the regenerator works is by storing some of the heat energy of the working gas as it moves from the heater to the cooler, thereby reducing the cooling demand on the cooler. And on the return path, as the working gas moves from the cooler to the heater, it “gains” back some of that heat energy, thereby reducing the heating requirement of the heater. A regenerator basically pre-heats the working gas before it enters the heater, and pre-cools the working gas before it enters the cooler. The regenerator is usually made of an intricate matrix material, made of stacked metal screens or metal felt, woven from fine wire. This provides the large surface area necessary for efficient heat exchange with the working gas.

Designing factors of stirling engine

(1) Keep dead volume to a minimum. Dead volume decreases engine power. Dead volume is the volume that is “unswept” by the motions of the pistons. This is the volume contained in the heater, cooler, regenerator, and all the clearance spaces. This volume is constant at all times. (2) Design the heater to maximize heating of the working gas, i.e. once the gas exits the heater its temperature must be as close as possible to that of the heater walls. This can be accomplished by using narrow and long tubes/passageways for the gas to flow through. (3) Design the cooler to maximize cooling of the working gas, i.e. once the gas exits the cooler its temperature must be as close as possible to that of the cooler walls. This can be accomplished by using narrow and long tubes/passageways for the gas to flow through. (4) Design the regenerator to maximize heat exchange with the working gas. This can be accomplished by using a sufficiently dense matrix material with large surface area. (5) Keep pumping losses to a minimum. Pumping losses are the friction (flow) losses caused by the working gas as it “pushes” through the narrow tubes/passageways of the heater and cooler, and the regenerator matrix.

The Three Stirling Engine Configurations  Alpha Stirling Engine  Beta Stirling Engine  Gamma Stirling Engine The most basic engine consists of a set of pistons, heat exchangers, and a device called a ‘regenerator’. The engine is filled with a working fluid (gas) which is commonly Air, but some more advanced engines may use Nitrogen, Helium or Hydrogen. The pistons are arranged such that they create both a change in volume of the working fluid and create a net flow of the fluid through the heat exchangers. Heat is absorbed from an external source in the ‘hot’ end, creating mechanical energy, and rejected in the ‘cold’ end to the environment. 1. The alpha configuration has two power pistons, one in a hot cylinder, one in a cold cylinder, and the gas is driven between the two by the pistons; it is typically in a V-formation with the pistons joined at the same point on a crankshaft. 2. The beta configuration has a single cylinder with a hot end and a cold end, containing a power piston and a 'displacer' that drives the gas between the hot and cold ends. It is typically used with a rhombic drive to achieve the phase difference between the displacer and power pistons, but they can be joined 90 degrees out of phase on a crankshaft. 3. The gamma configuration has two cylinders: one containing a displacer, with a hot and a cold end, and one for the power piston; they are joined to form a single space with the same pressure in both cylinders; the pistons are typically in parallel and joined 90 degrees out of phase on a crankshaft.

Alpha Engine The figure below shows a standard alpha engine.

In the alpha-configuration a displacer is not used. Two pistons, called the hot and cold pistons, are used on either side of the heater, regenerator, and cooler. These pistons move uniformly in the same direction to provide constant-volume heating or cooling processes of the working fluid. When all the working fluid has been transferred into one cylinder, one piston will be fixed and the other piston moves to expand or compress the working fluid. The expansion work is done by the hot piston while the compression work is done by the cold piston. The working gas inside the engine is repeatedly “shuttled” back and forth between the expansion and compression space, due to the up-and-down motion of the two pistons. This repeatedly forces the working gas back and forth through the heater,

regenerator and cooler. As a result, the gas is repeatedly heated and cooled, and power is produced. Alpha engines are the simplest to understand, and are the easiest to construct. It’s also easy to minimize the dead (clearance) volume in the expansion and compression spaces. But one of their main disadvantages is that they can require temperature resistant seals for the piston exposed to high temperature (shown on the right). The seals for the other piston (on the left) don’t have to be temperature resistant because it is constantly exposed to cool temperatures, due to its physical proximity to the compression space. The efficiency is proved to be maximum (50% of its theoretical efficiency unlike other engines). Limitations which doesn’t permit this engine to be used commercially in automotive applications are briefly analyzed and a study to overcome this limitations are made. A transient variation in engine working is explained by the alterations in engine’s components and via the coupling of an venturi based working fluid control system. An extensive parametric study of effects of different operating and geometric parameters has been performed and proved that the engine can be used successfully for commercial applications. Beta Engine The figure below shows a standard beta engine.

In the beta-configuration, a displacer and a power piston are incorporated in the same cylinder. The displacer moves working fluid between the hot space and the cold space of the cylinder through the heater, regenerator, and cooler. The power piston, located at the cold space of the cylinder, compresses the working fluid when the working fluid is in the cold space and expands the working fluid when the working fluid is moved into the hot space. Beta engines are compact in size. They use a power piston and displacer, which are in line with each other. Unlike an alpha engine that uses two pistons, the beta engine uses one power piston and displacer. The purpose of the power piston is to generate power, while the purpose of the displacer is to move the working gas back and forth through the heater, regenerator, and cooler. As a result, the pushing force experienced by the displacer is very little compared to that of the power piston. The power piston, displacer, and displacer rod are sealed around their gaps to prevent the leakage of working gas. The seal for the displacer is placed on the end closest to the compression space, in order to avoid direct contact with the hot working gas (in the expansion space). As a result, this seal does not need to be temperature resistant. The seals for the displacer rod and power piston do not need to be temperature resistant either since they are constantly exposed to cool engine temperatures. This is due to their physical proximity to the compression space. A disadvantage of the beta engine is that it can be difficult to minimize the dead (clearance) volume in the expansion and compression space, given that there must be enough clearance to allow the working gas to “feed in” unobstructed from the heater and cooler.

Gamma Engine The figure below shows a standard gamma engine.

The gamma-configuration uses separated cylinders for the displacer and the power pistons, with the power cylinder connected to the displacer cylinder. The displacer moves working fluid between the hot space and the cold space of the displacer cylinder through the heater, regenerator, and cooler. In this configuration, the power piston both compresses and expands the working fluid. The

gamma-configuration

with

double-acting

piston

arrangement

has

theoretically the highest possible mechanical efficiency. This configuration also shows good self pressurization.

Gamma engines are the same as beta engines, except that the power piston is “shifted” down. This can make it easier to construct the mechanical drive and linkages since the power piston and displacer are a certain distance apart (instead of aligned with each other). For this reason, the gamma configuration is often the preferred choice by Stirling engine enthusiasts. A disadvantage of the gamma engine is that it unavoidably introduces dead volume in the compression space due to the physical separation of the displacer and power piston. Other types Other Stirling configurations continue to interest engineers and inventors. The rotary Stirling engine seeks to convert power from the Stirling cycle directly into torque, similar to the rotary combustion engine. No practical engine has yet been built but a number of concepts, models and patents have been produced for example the Quasi turbine engine The hybrid between piston and rotary configuration is a double acting engine. This design rotates the displacers on either side of the power piston. In addition to giving great design variability in the heat transfer area, this layout eliminates all but one external seal on the output shaft and one internal seal on the piston. Also both sides can be highly pressurized as they balance against each other. Top view of two rotating displacer powering the horizontal piston. Regenerators and radiator removed for clarity

Another alternative is the Fluidyne engine (Fluidyne heat pump), which uses hydraulic pistons to implement the Stirling cycle The work produced by a Fluidyne engine goes into pumping the liquid. In its simplest form, the engine contains a working gas, a liquid and two non-return valves. The Ringbom engine concept published in 1907 has no rotary mechanism or linkage for the displacer. This is instead driven by a small auxiliary piston, usually a thick displacer rod, with the movement limited by stops. The two-cylinder Stirling with Ross yoke is a two-cylinder stirling engine (not positioned at 90°, but at 0°) connected with a special yoke. The engine configuration/yoke setup was invented by Andy Ross The Franchot engine is a double acting engine invented by Charles-Louis-Félix Franchot in the nineteenth century. A double acting engine is one where both sides of the piston are acted upon by the pressure of the working fluid. One of the simplest forms of a double acting machine, the Franchot engine consists of two pistons and two cylinders and acts like two separate alpha machines. In the Franchot engine, each piston acts in two gas phases, which makes more efficient use of the mechanical components than a single acting alpha machine.

THEORETICAL pv DIAGRAM:

It includes the four process: 1. Isothermal expansion process 2. Constant volume heat transfer process 3. Isothermal compression process 4. Constant volume heat removal process

Isothermal Expansion Process 1, 2: • Heat addition from high temperature heat sink. • Work is done by the working fluid (energy exchange to flywheel). The heat

source causes the air in the hot cylinder to expand and thus pushes both the cylinders outward.this process is defined as process 1 in the cycle.

Constant Volume Heat Addition Process 2, 3: • Heat addition (energy exchange from regenerator). • No work is done. • 2W3 = 0. The gas has expanded (about 3 times in this example). Most of the gas (about 2/3) is still located in the hot cylinder. Flywheel momentum carries the crankshaft the next 90 degrees, transferring the bulk of the gas to the cool cylinder. Isothermal Contraction Process 3, 4: • Heat rejection to low temperature heat sink. • Work is done on the working fluid (energy exchange from flywheel).The majority of the expanded gas has shifted to the cool cylinder. It cools and contracts, drawing both pistons inward. Constant Volume Heat Rejection Process 4, 1: • Heat rejection (energy exchange to regenerator). • No work is done. • 4W1 = 0. The contracted gas is still located in the cool cylinder. Flywheel momentum carries the crank another 90 degrees, transferring the gas to back to the hot cylinder to complete the cycle.

WORK OUTPUT

The net work done over the cycle is given by: Wnet= (W3-4 +W1-2).

where the compression workW1-2 is negative (work done on the system) AS INDICATED IN THE P-V DIAGRAM A measure of the regenerator effectiveness is given by Equation, with the value of e = 1 being ideal. e = (TR –TL)/(TH –TL) ...(1)

where,

TH = Temperature of high thermal sink. TL = Temperature of low thermal sink. TR = Mass averaged gas temperature of regenerator leaving during heating.

The cannot efficiency is denoted by Equation (2) and the real cycle efficiency with regenerator is denoted by Equation (3). Though regeneration is not required for a Stirling cycle, its inclusion can help improve the efficiency if applied properly. The regenerator efficiency does not tend to zero as the regenerator effectiveness tends to zero.

DESIGN OF ENGINE COMPONENTS Design of Frame  The frame is used to support piston cylinders, flywheel connected shaft and other rotating parts. The frame was constructed using wooden plate which is easier to machine and light weight. Frame is bought to its shape with the help of lathe and circular holes are drilled by means of drilling machines.

Design of Cylinders

 Two cylinders (Hot and cold chambers) are of same dimension. The two cylinders are made up of glass fibre material which has high tensile strength and high melting point.The glass fibre also has good surface finish. Aesthetics an external combustion engine the material selection plays a vital role.

Design of Piston  The piston is also made up of glass fibre in order to reduce friction between the piston and cylinder walls. This plays an important role as in case of tolerances between the piston and cylinder walls. To have a greater efficiency the surface finish should be very high so that losses will be minimum, but due to machining complication it’s good to buy a machined product which suits the design requirements.

Design of Crankshaft and Connecting rod  The crankshaft and connecting rod are made up of same material(steel rod).The material of the crankshaft and connecting rod are selected in such a way that they would not fail at high at high rotating speeds. These materials posses high compressive and tensile stresses. Design of transfer Tube  The transfer tube is made up of rubber tube so that they have high insulation properties and will not allow the heat from the hot cylinder to escape into the atmosphere and helps in transferring the fluid from hot cylinder to cold cylinder.

Design calculations Calculation of torque produced T=F*D Where, T- Torque F-Force acting on piston D-Radius of flywheel F=m*a Where, m-mass of the flywheel a-acceleration of the flywheel m=0.05kg a=v/t Where, v-velocity of the flywheel t-time taken (ie) for 1 second v=π*D*N/60 Where, N-speed of the flywheel. Required speed is 50rpm

v=π*0.105*50/60 v=0.2749 m/s a=0.2749/1 =0.2749m/s2 now applying the values for the main equation, F=0.040*0.2749 F=0.0109N T=0.0109*0.0525 T=5.77*10-4Nm Design calculation for piston Calculation of inertia force FI=mR*Ѡ2*r[cos 𝜃 + 𝑐𝑜𝑠2𝜃/𝑛] Where, FI-Inertia force of the piston mR-mass of the piston r-radius of the flywheel Ѡ-angular acceleration of flywheel Ө-angle of the flywheel Ѡ=2*π*N/60 Ѡ=5.236rad/s

n=l/r n=1.714 By substituting the above and required values, we get FI=0.040*(5.2362)*0.0525[cos60+cos120/1.714] FI=0.119N Design of the flywheel Flywheel effort (T) Turning moment T=FT*r Where, FT-effort of the flywheel FT=T/r FT=0.011N To find the angle Ф, l*sin Ф=r*sinӨ sin Ф=r*sinӨ/l

[

Ф=sin-1 r*sinӨ/l

[

]

Ф=sin-1 0.0525*sin60/0.09 Ф=30.340

]

Crank pin effort FT=Fp/cos Ф*sin[Ө+ Ф] Where, Fp-effort of the crank pin Fp= FT* cos Ф/[sin(Ө+ Ф)]

To find the length of the stroke FP=IP-BP Where, FP-frictional power IP-indicated power BP-brake power

BP=2*π*N*W*r Where, W-load factor in N Since there is no load factor W=0 So, BP=0

IP=Pm*l*a*n*k Where, Pm-mean effective pressure l-length of the stroke a-area of the flywheel k-number of cylinder IP=1.5*l*π/4*(0.105)2*1.714*2 IP=0.04452*l FP=IP-BP FP=(0.04452*l)-(16.49) Assume, FP=0.2W 0.2=(0.04452*l)-BP BP=0 0.2=(0.04452*l)-0 l=0.2/0.04452 l=0.04m l=4cm Hence The Total Stroke Length For The Designed Alpha Stirling Engine Is 4cm

Yet to do Photos of model Cost estimation Advantage Limitation Scope of improvement Conclusion Reference