stirling rhombic

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11/10/07

1

Rhombic drive for β type

Stirling enginesGuide :

Prof. S.L. Bapat

Siddhartha Ghosh, Deep Gupta and Rajat Goyal.



11/10/07 Rhombic Drive for Stirling Engines 2

Stirling Engines

Stirling engine is a closed cycle engine.

Power generated by heating and cooling

of working gas (usually hydrogen,

helium or air).

External combustion engine.

• Works on stirling cycle

which consists of 2

isotherms and 2 isochors.

• A real stirling cycle is

quasi-elliptical accounting

for smooth motion




Schematic of a Stirling engine




Advantages of a Stirling engine

Most efficient engine till date. It works on anykind of heat source, including solar energy,Stirling engines using palm heat have also beendeveloped.

The only practical machine with a theoreticalefficiency equal to Carnot efficiency.

Minimum pollution, heat rejected to theenvironment is very low in comparison to Otto,Diesel or Rankine cycle engines. Low

emissions in case of fossil fuels burning. Very simple in design compared to other types

of engines.




Types of Stirling engine,

Introduction to Rhombic drive There are 3 types of Stirling engines – α type, two pistons in separate cylinders, connected in

series by a heater, regenerator and cooler

– β type, displacer-piston arrangement, in-line cylinder system, this uses a Rhombic drive

– γ type, displacer-piston arrangement, separate cylinders.

Though α type is the simplest, it faces the disadvantage of sealing problems. β and γ types are usually used inpractical applications. In these two, β has more specificpower than γ type.




Rhombic Drive

Pink - Hot cylinder wall

Dark grey - Cold cylinder wall

(with coolant inlet and outlet

pipes in Yellow)Dark Green - Thermal

insulation separating the two

cylinder ends

Light Green – Displacer pistonDark Blue - Power piston

Light Blue - Flywheels




The Task

Design and development of a Rhombicdrive for β type stirling engine.

The task includes

– Listing of various design andthermodynamic parameters associated withthe engine and drive.

– Deriving an analytical formula for the overlapvolume in this type of engine and finding out

the overlap for optimum efficiency. – Determining the specifications of various

components of the drive and designingthem.




Analysis of a Simple Rhombic Drive

The Fig. shows the schematics of a rhombic drive.

The bars 12, 1'2', 13, and 1'3' have

identical length,, and are

connected to the cross-bars 22'

and 33' by pin/ hole connections.

The crank throws 01 and 0'1' haveidentical length, r, and the crank

centers 0 and 0' are at equal

distance, d+e, from the piston axis.

Analysis of the variation of the

height of the expansion space, Ve ,

and the compression space, Vc, as

the angle α changes.

The cranks turn at the same

angular velocity which can be

accomplished by two intermeshing

counter-rotating gears.




Analysis Of Rhombic Drive (Cont.) Modeling the Expansion

space height Ve, we get

……..(1)

where

Similarly, for Compression

space height Vc,

………(2)

where

Also, from the Geometrical

Constraints,

=constt..(3)Now, using the fact that

min.(Ve) =min(Vc)=0, and using

the above 3 eqns., eliminating

the constants,

We finally get,

and,

sin sine e

V C R L

e eC h

2 s inc c

V C L

c e cC h h

cos cose R L

2( ) 1 ( ) sin sine

eV L R R L

L R

22 { 1 ( ) sin }c

e RV L

L




Analysis of Rhombic Drive (Cont.)

Volume Overlap The volume of the cylinder which is used both by

the movement of the displacer and the piston. The overlap length , as can be seen from the

figure, can be written as,

which is again obtained by using the previous

eqns. Values of R,L and e have to be chosen such that

we get maximum possible overlap ensuring that

the cylinder volume is properly utilized.

2 2 2 2max{ } min{ } 2{ ( ) ( ) }e c e

V V V R L e L e R




Analysis Of Volume Overlap Developed a surface plot for the volume

overlap in MATLAB

Deduced the Maximum overlap from the

surface plot.

Chosen R>1.1L to account for any faults inthe actual design.




Compression & Expansion Volumes

•The Non-

Sinusoidal nature

of one volume w.r.t.

other shown by the

graphs

•Volume phase lag

between the two

volumes deducted

from the graphs ata particular

instance of time

(since it changes

continuously)

• The compression and the expansion volumes plots

were generated in MATLAB




Schmidt’s Analysis

Isothermal analysis of Stirling engines

Assumption: P constant throughout,perfect gas, T const. in each space

The general Schmidt’s analysis assumessinusoidal variation for both volumes

Average Pressure, Work done, Efficiencyare deduced from the analysis

Optimization of efficiency based on theparameters like Temperature of cold andhot space, volumes and optimal volumephase lag is done




Future Goals

To perform the modified

Schmidt’s analysis for

our engine, also taking

into account the

regenerator and other

losses.

To analyze the

stresses/forces in the

bars and finally reach to aworking model. (If time

permits..!!)

stirling rhombic

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