stirling rhombic
Post on 06-Apr-2018
221 Views
Preview:
TRANSCRIPT
8/2/2019 Stirling Rhombic
http://slidepdf.com/reader/full/stirling-rhombic 1/15
11/10/07
1
Rhombic drive for β type
Stirling enginesGuide :
Prof. S.L. Bapat
Siddhartha Ghosh, Deep Gupta and Rajat Goyal.
8/2/2019 Stirling Rhombic
http://slidepdf.com/reader/full/stirling-rhombic 2/15
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
8/2/2019 Stirling Rhombic
http://slidepdf.com/reader/full/stirling-rhombic 3/15
11/10/07 Rhombic Drive for Stirling Engines 3
Schematic of a Stirling engine
8/2/2019 Stirling Rhombic
http://slidepdf.com/reader/full/stirling-rhombic 4/15
11/10/07 Rhombic Drive for Stirling Engines 4
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.
8/2/2019 Stirling Rhombic
http://slidepdf.com/reader/full/stirling-rhombic 5/15
11/10/07 Rhombic Drive for Stirling Engines 5
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.
8/2/2019 Stirling Rhombic
http://slidepdf.com/reader/full/stirling-rhombic 6/15
11/10/07 Rhombic Drive for Stirling Engines 6
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
8/2/2019 Stirling Rhombic
http://slidepdf.com/reader/full/stirling-rhombic 7/15
11/10/07 Rhombic Drive for Stirling Engines 7
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.
8/2/2019 Stirling Rhombic
http://slidepdf.com/reader/full/stirling-rhombic 8/15
11/10/07 Rhombic Drive for Stirling Engines 8
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.
8/2/2019 Stirling Rhombic
http://slidepdf.com/reader/full/stirling-rhombic 9/15
11/10/07 Rhombic Drive for Stirling Engines 9
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
8/2/2019 Stirling Rhombic
http://slidepdf.com/reader/full/stirling-rhombic 10/15
11/10/07 Rhombic Drive for Stirling Engines 10
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
8/2/2019 Stirling Rhombic
http://slidepdf.com/reader/full/stirling-rhombic 11/15
11/10/07 Rhombic Drive for Stirling Engines 11
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.
8/2/2019 Stirling Rhombic
http://slidepdf.com/reader/full/stirling-rhombic 12/15
11/10/07 Rhombic Drive for Stirling Engines 12
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
8/2/2019 Stirling Rhombic
http://slidepdf.com/reader/full/stirling-rhombic 13/15
11/10/07 Rhombic Drive for Stirling Engines 13
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
8/2/2019 Stirling Rhombic
http://slidepdf.com/reader/full/stirling-rhombic 14/15
11/10/07 Rhombic Drive for Stirling Engines 14
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..!!)
8/2/2019 Stirling Rhombic
http://slidepdf.com/reader/full/stirling-rhombic 15/15
11/10/07 Rhombic Drive for Stirling Engines 15
top related