See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/334657385
Thermodynamic analysis, performance numerical simulation and losses
analysis of a low cost Stirling engine V-Type, and its impact on social
development in remote areas
Conference Paper · June 2011
CITATIONS
READS
0
2,936
4 authors:
Walter Arias
Daniel Flórez-Orrego
University of Maryland, College Park
École Polytechnique Fédérale de Lausanne
14 PUBLICATIONS 56 CITATIONS
110 PUBLICATIONS 485 CITATIONS
SEE PROFILE
SEE PROFILE
Hector I. Velasquez
Silvio De Oliveira Junior
National University of Colombia
University of São Paulo
38 PUBLICATIONS 438 CITATIONS
220 PUBLICATIONS 2,142 CITATIONS
SEE PROFILE
Some of the authors of this publication are also working on these related projects:
Worldwide Exergy Community: aeronautics View project
Integration and Optimization in the Chemical Process Industry View project
All content following this page was uploaded by Daniel Flórez-Orrego on 24 July 2019.
The user has requested enhancement of the downloaded file.
SEE PROFILE
Proceedings of ECOS 2011
Novi Sad, Serbia
July 4–7, 2011
Thermodynamic analysis, performance
numerical simulation and losses analysis of a
low cost Stirling engine V-Type, and its impact
on social development in remote areas
W. Ariasa, H.I. Velásqueza, D. Floreza and Oliveira Junior S b
a
b
Universidad acional de Colombia, Sede Medellín, Colombia, wariasr@unal.edu.co, CA
Mechanical Engineering Department, Polytechnic School, University of São Paulo, Brazil
Abstract:
This study is aimed to develop an analysis and numerical simulation on the performance of a
low cost Stirling Engine V-type, built with locally available technology, with the goal of being an
alternative energy technology for its implementation in non-interconnected rural areas, based on
renewable sources. The detailed method includes an energy and exergy analysis for each
process of the cycle and numerical simulation in MATLAB®. The selected model was the
adiabatic model, due to better approximation to real engine performance compared to the
isothermal model. To increase the accuracy, the internal irreversibilities caused by pressure
drops, incomplete (non-ideal) regeneration, heating, and cooling processes were included. The
actual efficiency result was 34%, being the effectiveness of the regeneration process the one
that most impact generated on it (approximately 80% of total losses). In addition, based on the
measuring of energy sources (radiation and biomass), technical feasibility was predicted.
Finally, to simulate the evolution in the social development of the area since the incorporation of
energy technologies, a system dynamics model was used with a holistic approach. The result
was the necessity of including other parameters in addition to technical and economic feasibility,
such as monitoring and accompaniment in the early stages and subsequent assimilation of their
management and operation to the entire community, allowing them to present a sustainable
development based on the use and value generation.
Keywords: Numerical Simulation, Stirling Engine, Exergy Analysis.
1. Introduction
Due to the growth in energy demand,
environmental issues and high dependence on
fossil fuels, the need to find sustainable
alternative sources of energy conversion
emerges. Stirling engine performance meets
these demands, which has one theoretical
efficiency equivalent to that of Carnot, it also
uses any heat sources (biomass, solar energy,
combustion gases) and the pollution generated
is smaller than the conventional engines [1-4].
The simple construction, and its manufacture
being the same as the reciprocating internal
combustion engine, and when produce in a large
number of units per year, the Stirling engine
would obtain the economy of scale and could be
built as a cheap power source for developing
countries. For solar electric generation in the
range of 1–100 kWe, the Stirling engine was
considered to be the cheapest, Although the
Stirling engine efficiency may be low, reliability
is high and costs are low [5].
Moreover, the International Energy Agency
estimates that in 2008, 1.5 billion people, or
22% of the world’s population, had no access to
electricity, of whom 85% live in rural areas
[20]. In Colombia, there are geographically
isolated regions, not connected to the National
Transmission System, these areas represent 66%
of the territory, and about 15% (3'000 .000
people) of the total population [6,7]. In 2008,
service coverage in non-interconnected areas
was 76% [7]. State policy has focused on
promoting fossil fuel-based projects reaching
more than 96% of total generation in diesel
plants [6.8]. Two studies [9.10] carried out on
the potential availability of agricultural and
agro-industrial residues, found that in Colombia
the Stirling micro-generators implement
3767
alternative is economically viable, especially in
non-interconnected and/or rural areas, there is a
similarly strong solar energy potential, reaching
averages of radiation throughout their territory,
with a daily multi-year average close to 4.5
kWh/m2, suitable for proper utilization [11].
This paper presents a Stirling engine as a
technical alternative, economically and socially
viable in the search for energy solutions in such
areas, using its natural resources. Because of
this, the thermodynamic analysis and numerical
simulation of a low-cost Stirling engine
prototype is done. And finally we will analyze
the incorporation of this new technology in
social development in the area.
2. Thermodynamics of Stirling
cycle engine
The Stirling engine uses a compressible fluid as
the working fluid (Hydrogen, Helium or Air) in
a closed system, Fig. 1a and Fig. 1b show the
classic diagram of the Stirling cycle PressureVolume and Temperature –Entropy, which
consists of four processes: an isothermal
expansion (heat addition from the external
source), isothermal compression (heat rejection
to the external sink), a rejection (internal heat
transfer from the working fluid to the
regenerator) and heat addition (internal heat
transfer from the regenerator back to the
working fluid at constant volume).
Aside from having an equal theoretical
efficiency to Carnot efficiency, the Stirling
engine has the advantage to work with two
constant volume processes, instead of two
isentropic processes; increasing the p-v diagram
area and therefore the work done (Fig. 1a), also
it has the maximum mechanical performance
compared with another reciprocating thermal
engines at the same working conditions[5,15].
The analysis using the first and second laws of
thermodynamics to the four ideal Stirling cycle
processes is taken into account to establish the
ideal adiabatic model used to simulate the
performance of the prototype in the four
processes mentioned before, in which,
additionally, a decoupled analysis of the
irreversibilities due to pumping losses and
imperfect heat exchanger was performed
(regenerator, heater and cooler) [13, 14]
Fig.1. Thermodynamic Stirling cycle: a) P-V
diagram, b) T-S diagram. [12]
3. Mathematical model of the
Stirling engine
There are three widely detailed mathematical
and documented analysis, discriminated
according to the methodology proposed by
Martini, Dyson and Chen [14,17,18], a first
analysis or the Zero Order was proposed by W.
Beale, he noted that the output of many Stirling
engines with similar specifications is given by
(1) [17], although this method cannot analyze
the power loss and heat, is used as a first design
approach [3,18].
Pot= b P*f*Vswe
(1)
An analysis of first order was made by G.
Schmidt called isothermal analysis, which is the
most complicated it can be solved analytically
due to its closed-form solution is to approximate
the sinusoidal volumetric variations, see Fig. 2
[14,17,18].
Fig. 2. Sinusoidal volume variation [19]
However, the given results by this analysis are
incongruous, indicating that the heater and
cooler are redundant, because all the heat is
transferred through the working spaces. This
paradox is due to the compression and
expansion spaces are kept at the respective
cooler and heater temperature, prompting the
3768
calculated efficiency equals the Carnot
efficiency, which is usually 2 or 3 times the
actual
efficiency
of
Stirling
engines
[1,13,14,19].
A second order analysis was developed by
Finkelstein. He modified the Schmidt analysis,
changing the isothermal to adiabatic conditions,
allowing the heat transfer to occur only through
the heater and cooler. Furthermore, this analysis
has the feature to be decoupled, i.e. the
irreversibilities are treated separately from the
ideal model; e.g. the losses due to pressure
drops and heat losses, are calculated and
subtracted from the adiabatic ideal work,
increasing the accuracy of work done and
efficiency calculated, compared to the actual
engine, and allows to detail and quantify the
power losses [13,14].
3.1. Adiabatic Analysis
To carry out the prototype numerical simulation,
the adiabatic analysis model was selected, due
to the above mentioned advantajes, also it was
taking into account the aproximations and
assumptions indicated by Finkeltein [14] and
later by Urieli [19] and Herzog [20]:
• Leakage of gas to the outside of the engine,
including crank case, is assumed to be zero.
• Any pressure drops due to flow resistances
and pressure differentials needed to
accelerate the working gas are neglected.
Hence, the pressure has at a given instant the
same value everywhere inside the engine and
varies only with time.
• Equal to the schmidt model, to simulate the
prototype by the adiabatic model, it is
necesary to approach the expansion and
compresion volume variation to sinusoidal
form (Fig. 3), since the drive mechanism is a
crankshaft (Eq. 2,3) 1 [13,14,19,20].
Ve = Vcle + 1/ 2 Vswe ( 1+ cos (θ + α + π) ) (2)
dVe
= - 1/2 Vswe sin(θ + α + π )
dθ
(3)
• The engine turns at constant speed.
Therefore, time and crank angle are
proportional to each other.
• Both, the compression and expansion space,
volumes, are adiabatic. The temperature in
these spaces is uniform but varies during a
cycle due to changes in pressure, volume and
gas coming from/leaving to the adjacent
cooler and heater space, respectively
• The heat transfer conditions for the cooler
space are sufficiently good to keep the gas
inside the cooler space, volume Vk, at
constant uniform temperature Tc at all times.
The same holds true for the heater space,
volume Vh and uniform temperature Th.
• The heat transfer conditions are sufficient to
keep the temperature distribution inside the
regenerator, volume Vr , linear, varying from
Tc where the regenerator is connected to the
cooler to Th at the heater side.
• An ideal gas is used as working fluid and the
ideal gas law :
PV = mRT
(4)
Cp − Cv = R
(5)
K = Cp
Cv
du = Cv (T ) dT
dh = Cp (T ) dT
(6)
(7)
(8)
This model split the engine into five parts:
heater, regenerator, cooler and expansion and
compression spaces as is showd in Fig 3
furthermore the gas temperature in each of the
control volumes is shown, the graphic also
shows the control limits through which the
enthalpy passes given the mass flow.
3.1.1. Mass and energy conservation
laws
Additionally to the restrictions or aproximations
given in numeral 3.1, the mass and energy
conservation laws were used to formulate the
governing diferential
Relevant equations to each part of the Fig. 3
initially, thermodynamics basic equations are
applied to a volume control for a piston/cylinder
device and a heat exchanger with one inlet and
one outlet mass flux, como se muestra en Fig. 4.
1
The
equations shown
are
for the expansion
space, these are similar to the compression space
3769
dV
dm
e =
dθ
p=
p
V
e + e dp
dθ
γ dθ
RT
he
(11)
MR
 Vc Vk Vh Ve Vr ln ( Tr Tc
 + + + +
Tr − Tc
 Tc Tk Th Te
 1 dVc
1 dVe 

− γp
+
+
T
dθ
T
dθ
he
 ck

dp =
 Vc
V V V  V 
+ γ k + r + h  + e 

 Tk Tr Th  The 
 Tck
Fig. 3. Ideal Adiabatic Model [1]
Fig. 4. Generic volume control [13]
To deduce the governing equations is
convenient derivate in function of the crankshaft
angle (dθ) instead of the time. To find the
pressure equation (13) in function to the angle,
as well as its differential (14), natural logarithm
is applied to the ideal gas equation (4) and
afterwards it is derived in function of the
crankshaft angle to obtain (9). this equation is
applied to the three heat exchangers, where the
volume and the temperature are constant,
obtaining the mass differential in these spaces
(10). Similarly to find the mass differential on
expansion and compression spaces(11, 12), the
energy conservation equation is applied in
conjunction with the ideal gas relations (5-8).
Finally these five equations are replaced into the
mass conservation equation, obtaining (12) and
(13).
1 dp 1 dV
1 dm 1 dT
+
=
+
p dθ V dθ m dθ T dθ
dmhx dp
=
mhx
p
(9)
)


(12)
(13)
The mass flows equations in a control volume
are found through the mass conservation
principle, applying this equation to each one of
the volumes described by the Fig 4, (14-17) are
obtained.
dm
mck = − c
(14)
dθ
dmc
mkr = mck −
(15)
dθ
dm
mhe = mrh − h
(16)
dθ
dmh
mrh = mhe +
(17)
dθ
The equations for temperature (18) into the
compression and expansion spaces were found
by deriving in function of the crankshaft angle
the ideal gas equation (4).
dTe
1 dp 1 dVe
1 dme
= Te(
+
−
)
dθ
p dθ Ve dθ me dθ
(18)
To determinate the heat transference in the
heater, cooler and regenerator, the energy
equation is applied to each of the spaces along
with the ideal gas equation (4) and the relation
of the calorific capacities equations (5-8):
dQ r Vr C v dp
(19)
=
− C p (Tkr m kr − Trh m rh )
dθ
R dθ
dQ h V h C v dp
=
− C p (Trh m rh − The m he )
dθ
R dθ
(10)
(20)
The equations that describe the work differential
for the compression and expansion spaces and
the total are:
3770
dWe
dV
=p e
dθ
dθ
(21)
dW dWe dWc
=
+
dθ
dθ
dθ
(22)
of the Reynolds number and the fanning friction
factor).
St * Awgr
TU =
(23)
2 Ar
Due to the non-linearity of the temperature
differential equations (18), it is necessary to
apply numeric methods to solve them as well as
the whole equations system here detailed.
4. Losses Analysis
The power loss analysis assesses the heat
transference effectiveness as well as the
pressure drop in the three heat exchangers. The
advantage of this decoupled method is that a
detailed accounting of the losses is produced
which is useful in design modifications, sin
embargo however, it has a disadvantage in front
of the coupled method, since the relationships
between the various subsystems are neglected,
even though the coupled analysis is generally
more complex, makes also significant
assumptions and some decoupling occurs by
the use of this method [13,17]. West claims
that the simpler decoupled analysis is not
established to be inferior to the more complex
"third order" or coupled analysis [13]. Creswick,
Qvale, Rios, Walker, Senft, and Smith were
some pioneers using this approach [1,5,13].
In general, both, the coupled and decoupled
approaches are valid; the decoupled method
was selected given that it fits to the
requirements of this project because it has been
supported and validated with empirical data
[3,13,16,21], and verges the calculated results
to the ones given by a real engine, letting
parametrize the power losses .
In this analysis, the process is approximated to a
Quasi-steady flow (since the real nature of the
flow in a Stirling Engine is oscillatory), in
which it is assumed that on each stage of the
cycle, the flow behaves as a stable fluid. The
effect of the non-ideal regenerator is modeled
by the Number of transfer Units (NTU), which
it is in function of the Stanton number (23). In
order to calculate the Stanton number, the
modified analogy of Reynolds had to be
considered, which can be used even in presence
of pressure gradients (24) [22,23] where fr is the
Reynolds friction factor (equals to the product
St =
fr
2 Re Pr 0 .67
(24)
The Reynolds friction factor (fr) depends on the
regimen of the flow which is given by the
Reynolds number, for laminar Flow (Re<2000),
it is calculated using the annular flow laminar
equation; for turbulent flow (it is assumed from
Re>2000), it is calculated using the Blasius
equation [22]. So the effectiveness of the
regenerator can be calculated by (25) and the
heat lost by (26).
TU
ε=
(25)
1 + TU
Qrloss = ( 1 − ε)(Qr max − Qr min )
(26)
The heater and the cooler effectiveness is
related with the temperature reached by the fluid
when passing through it, which for the real case
( < 1), is lower than the temperature of the
walls of the exchangers, decreasing the
performance of the engine, when operating
between temperature limits lower than the
heater and cooler walls temperatures (Fig. 5).
This analysis determinates the difference
between temperatures using heat transference
equations by convection (27), taking into
account the heat lost due to the imperfect
regenerator and the heat transference coefficient
for each of the spaces (28).
Th = Twh −
h=
(Qh − Qrloss ) * freq
hh Awgh
fr µCp
2d h Pr
2
(27)
(28)
3
The fluid friction associated with the flow
through the heat exchangers will in fact result in
a pressure drop across all the heat exchangers
which has the effect of reducing the power
output of the engine [21]. The actual work is
found subtracting the lost work to the ideal
adiabatic work (29-31) [19, 21, 22]:
3771
parameters such as the expansion phase advance
angle advance equal 90°, for the regenerator
was inserted a stainless steel foil (it was took
thermal conductivity as 25 W ), for detail
m*K
specifications of the Stirling engine prototype
see Table 1.
Fig. 5. Actual performance of Stirling Engine
[22]
W = ∫ p ( dVe + dV c ) − ∫ ∑ ∆pdV e
(29)
2π
dV 
 3
∆W = ∫  ∑i =1 ∆pi e dθ
dθ 
0
∆p =
− 2 frµuV
2
d hid A
(30)
(31)
Where u is the speed fluid, V is the void
volume, A is the internal free flow area, µ is the
gas dynamic viscosity, calculated through the
Sutherland equation[21,22]
5. Prototype
The objective of this study is to design a Stirling
engine as micro-generation alternative (power
about 0,5kW – 1kW). Because of that, the
construction of the Stirling engine has to be
attached to the local restrictions. The V-type
Stirling engine is easier to build than other types
of configuration, given that its construction can
be commenced from a commercial V-type
compressor. Equation (1) was used, with the
goal to dimension the compressor [3], the
compressor operating frequency was selected as
the engine operating frequency factor in (1) and
the reference pressure factor in (1) was the 80%
of the maximun operating pressure. Power
output was 605W for a 1,5KW compressor and
its price is the half price of another compressor
(2.2- 3.8 KW), besides the increase in power is
not equivalent to the price increase, because of
that, 1.5KW compressor was selected. Figure 6
shows the prototype, in the heater and cooler
were attached seven internal fin (due to space
restriction), to increase the wetted area of each
one. also the expansion piston and the
regenerator were insulated to decreased the heat
losses. The compressor has established
6. Energy Potential in Remote
Areas
Two studies [9,10] concerning the availability
potential of agricultural and agro-industrial
waste, concluded that the implementation of
Stirling micro-generator in Colombia is
economically feasible. Specially
in noninterconected and/or rural areas, since the
agricultural waste of harvest (rice husk, sugar
cane harvest waste, pulp of coffee and cocoa,
among others), besides the planted and natural
forests waste is 12.968 MWh/year. However
this is not entirely usable, there are limitations
on use, such as competition, i.e. the energy
product (waste) has a specific destination, the
knowledge involved to the transformation in
energy, and the availability, indicating the
amount, timing of cultivation and processing
technology in energy. This limitations define the
actual, useful and available energy (Fig. 7).
To determinate the gained temperature from the
agricultural and forest waste combustion was
necessary to resort to previous studies, for the
case of the direct combustion of cane bagasse
was obtained a stack gas temperature of 517°C
and a furnace temperature of 841°C (16%
bagasse cane moisture) [24]. For rice husk was
obtained a bed temperature of 600°C – 800°C
[25], for wood and bark (sawdust of pine and
spruce), temperature of 680°C was achieved
(measured at a distance of 70 mm from the
burner).
Similarly Colombia count with a high solar
energy potential, reaching a multiannual diary
average close to 4,5kW/ m2 (highlighting the
peninsula of La Guajira with a daily average of
6.0 kWh/ m2 and the Orinoco, with a value
slightly lower), suitable for proper exploitation
[11].
It was selected a specific area (Latitude 12.5 and
Longitude -71.5), to analyze the solar radiation
potential.
3772
with a projected area of 2 m2 and built with
commercial aluminum rings, and similar
climatic conditions, the focus achieved a
temperature of 450 ±20°C. Other studies show
focus temperature between 675°C and 800°C
[28].
12000
Gross energy
potential
10000
MWh/Year
8000
Available energy
potential
6000
4000
Useful or
additional energy
(effic 55%)
2000
0
Fig. 6. Low cost Stirling Engine V-type
Fuel oil
production
Figure 8 show the results, with a minimum and
maximum radiation of 0.24KW/m2 and
0.90KW/m2, respectively and a diary average of
0.66KW/m2 [26]. Based on an experimental
study [27] about a parabolic solar concentrator
Waste
Forest waste
Fig. 7 agricultural waste useful energy [10]
Insolation KW/m2
Table 1.Technical feature and operating
conditions of the Stirling engine prototype.
Parameter
Value/Type
Engine type
Alpha
Drive type
Sinusoidal
Working fluid
Air/Hydrogen
Compression / Expansion space
0.0
clearance volume (m3)
Compression/Expansion space
7.10 × 10-5
swept volume (m3)
expansion phase angle advance
90
(degrees)
Cooler /Heater type
Slots
Width of slot (m)
2.45 × 103
Height of slot (m)
3.40 × 102
Heat exchanger length (m)
6.77 × 102
Number of slots
7
Regenerator configuration
Tubular
Housing external diameter(m)
4.4 ×102
Housing internal diameter (m)
3.8 ×102
Regenerator length (m)
0.177
Operating frequency (Hz)
90
Regenerator material
Stainless steel
wrapped foil
Matrix type
matrix
Unrolled length of foil (m)
2.025
Foil thickness (m)
2×10-4
Mean pressure (Pa)
8.6 × 105
Charging pressure(Pa)
6.2 × 105
Cold sink temperature (K)
320.15
Hot source temperature (K)
773.15
Alcohol
production
1
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
Experimental
Data
y = -0,0292x 2 + 0,6878x - 3,1472
R² = 0,9998
0
2
4
6
8
10 12 14 16 18
Hour GMT -5:00
Fig. 8 Insolation Incident on a horizontal
surface (KW/m2)[26]
6. Numerical Simulation and
Results
The prototype was analysed by using
MATLAB®, through the Isothermal, adiabatic
and Simple routines presented by Urieli and
Berchowitz [19,21]. To determinate the heater
temperature, the energy potential in rural and
non-interconnected areas was taking into
account, listed in Table 1. It also was used the
four order Runge Kutta (RK4) method to solve
the differential equations. This numerical
simulation method was validated with the D90
(90cc) Andy Ross Stirling engine [21], similarly
this method was used by Scollo [3].
Prior to perform the numeric integration, the
method stabilizes the gas temperature
calculating them by RK4 and comparing them
before and after a complete cycle, achieving the
steady state when their difference is lower than
1°C. Then it calculates the volumes and their
derivates for each crankshaft angle by means of
(2) and (3) for the compression and expansion,
3773
Table 2 shows that the real power using air and
hydrogen as working gas is respectively 24%
and 71% of the ideal power, noticing the
inefficiency of the air, due to the greater amount
of heat lost through the regenerator, plus the
least amount of heat transferred to the cooler
and the heater and therefore a lower rate of
temperature compared to hydrogen.
The pressure limits were increased in the nonideal model, due to the temperature ratio (Th/Tc)
decreased, from 2.23 to 1.39, being the pressure
function of this ratio (Eq. 12). This is observed
in Fig. 10.
11.5
11
Pressure (bar [1bar = 100kPa])
then together with the total mass value and the
temperatura in each part of the engine, pressure
in calculated (12) for each crankshaft angle.
With these values, it calculated the mass
changes in each space and thus the mass flow
rat through (14-17), with the pressure, volume
and mass flow rate values for a given crankshaft
angle, it used the RK4 method to calculate the
variation of temperatures in the compression
and expansion spaces (18), heat flux in each
heat exchanger (19-20), and finally the
expansion and compression spaces (21, 22)
Table 2 show the adiabatic and non-ideal model
results. Non-ideal regenerator, heater and cooler
as well as pumping losses caused by fluid
friction are considered. Air and Hydrogen were
considered as working gas. The P-V diagram
shown in Fig. 9, compare the engine
performance with and without losses. This
figure shows that the temperature difference
was reduced, therefore the enclosed area of the
cycle.
10.5
Non-ideal Analysis
(Working gas: Air)
Adiabatic Analysis
10
9.5
9
8.5
8
7.5
7
pressu re (ba r)
6.5
Table 2. 8umerical results comparison.
220
240
260
280
300
320
340
Volume (cc)
Parameter
Adiab Nonideal Nonideal
Fig. 9 P-V diagram comparison
atic
(Air)
(Hydrogen)
Total power
943.9 231.4
675.6
The heat transfer coefficient calculated trough
output (W)
(Eq. 27) in the cooler, using air and hydrogen
Heat transferred 1736
2683.5
1946.8
are respectively 567.45 y 965.50 (W/m2K).
to the heater(W)
Although the Reynolds number calculated for
-906.4
Heat transferred -796.4 -1140.7
hydrogen was lower than the calculated for air,
to the cooler(W)
4573.1 and 24436.5 respectively, the hydrogen
Gas temperature 772.5 618.8
697.8
has larger calorific capacity than the air (ratio
in heater
14-1).
Gas temperature 345.3 444.1
358.1
in cooler
11.5
Non-ideal Analysis
Regenerator net 0
1205.7
316.7
11
heat loss(W)
10.5
Regenerator
1
0.797
0.964
10
P-mean Non-ideal
analysis
effectiveness
9.5
Regenerator wall 0
24.7
24.7
P-mean Adiabatic
9
analysis
heat leakage(W)
8.5
Pressure drop
0
85.5
27.9
8
Adiabatic Analysis
available work
7.5
loss(KPa)
7
Thermal ideal
54.4
21.8
43.8
6.5
efficiency (%)*
0
50
100
150
200
250
300
350
400
crank angle (deg)
8.6
34.7
Actual efficiency Fig. 10. Pressure – Crank angle
(%)**
* Power losses are not taken into account, only considers
the temperature ratio.
** This value does not take into account the power loss in
shaft bearings.
Figure 11 describe the temperatures in
expansion and compression spaces, checking
3774
the above. It is observed the imperfect heat
transfer in the cooler and heater, obtaining
temperatures of 100°C below the wall
temperature in the worst case.
Equal to cooler, the heat transfer coefficient in
heater and regenerator are larger for hydrogen
than air. The opposite occurs with the Reynolds
friction factor, since it decreased when using
hydrogen as working gas instead of air (ratio 14).
800
750
Mean heater gas temperature
X: Hydrogen
O: Air
Heater wall temperature=773 K
this due to their wetted area is 23 times higher
compared to the heater and cooler.
Figure 14 show the involved energy in function
of crank angle, in each heat exchanger, as well
as the net work, in Fig.14 is noticeable the
difference between the energy involved for
regenerator and heater or cooler, being the first
two or three time larger than the last two.
This result is in accordance to Thombare [1].
Also is remarkable that the net energy involved
in the regenerator is zero for a complete cycle
(Ideal case).
700
4
1.5
Expansion space temperature
600
550
H eat exchang er pressure drop [P a]
T e m p e ra tu re (K )
650
Regenerator space temperature
500
450
400
Compression space temperature
Mean cooler gas temperature
350
Cooler wall temperature =320 K
300
0
50
100
150
200
Crank angle (degrees)
250
300
350
Fig.11. Expansion, Regenerator and
Compression temperature – Crank angle.
x 10
1
0.5
0
-0.5
-1
-1.5
0
50
100
150
200
250
Crank angle (degrees)
300
350
Fig. 13 Heat exchanger pressure drop –Crank
angle (Air)
80
Work W
60
Energy [Joules]
Figure 12 show the power losses caused by
imperfect functioning regenerator and pressure
drops in the engine. This figure show that there
are less heat losses for hydrogen than air, due to
= 26,5
larger heat transfer coefficient (
to hydrogen, and 3,9 to air). The fewer amounts
of losses for hydrogen is due to the mass flux
are lower than calculated for air (ratio 14 – 1).
Cooler
Heater
Regenerator
40
Heater heat Qh
20
0
Cooler heat Qk
-20
Regenerator heat Qr
600
-40
0
400
Power (W)
200
50
100
150
200
250
Crank angle (degrees)
300
350
400
Fig. 14. Energy – Crank angle (Air)
0
-200
-400
-600
-800
0
7. Impact on social
development in remote
areas
Loss heat by Non-ideal Regenerator
(working gas= air)
Power loss by pressure drop
(working gas=air)
Loss heat by Non-idea Regenerator
(Working gas=Hydrogen)
Power loss by pressure drop
(Working gas=Hydrogen)
50
100
150
200
250
Crank angle (degrees)
300
350
Fig. 12 Power loss –Crank angle diagram
Figure 13shows in detail the pressure drop for
each of the heat exchangers for air (hydrogen
has similar behaviour). It is noticeable that in
the regenerator has the highest amount of losses,
This analysis is based on a work done to
simulate the behaviour of remote areas of
Colombia after the incorporation of energy
technologies through a holistic simulation,
validated with real data [29].
The general
problem is that only the initial
training does not hold an energy technology
3775
implemented (renewable or not) for a long
time, this is called disabilities appropriation
The results (Fig. 15) shows the real power
available, i.e. the use of installed capacity; in
baseline scenario (without any kind of training
or guided learning),
the misuse of the
infrastructure and the inability to efficiently
exploit energy availability, implies that this
becomes obsolete.
due to the community lacks adequate learning
processes regarding the operation and
maintenance, however picks up when these
impossibilities
are
overcome.
In
the technological learning scenario there is a
clear trend, based on the effectiveness of
investment in education and social investment.
This allows an aggregate value of it and
makes efficient operation.
Fig. 15 real power available [29]
When the technology operators through learning
processes, overcome the difficulty of operating
the technology and means productions, the
scenario is operational learning. Taking into
account that there is an barrier in learning, i.e.
operating appropriation, which is overcome
after years of operation. The available power
decreased due to the misuse at the first years.
The technological learning scenario consists of
a knowledge and innovation of technology,
beyond its operation and maintenance, this type
of knowledge can increase the operational
capacities of energy production of Goods and
Services; it is satisfactory the performance in
this scenario, due to different processes of
exploitation of energy and innovation in the
means of production, demonstrating a
community development.
The behaviour of human and social capital (Fig.
16), on baseline scenario tend to decrease,
based on the ineffectiveness of social and
educational investment, since the community
lacks the means to make the investment
necessary to allow sustained growth of capital.
On operational learning scenario shows a clear
trend toward lowering them in the early years,
Fig. 16 Human and Social Capital.[29]
7. Conclusions
The objective of this analysis was to simulate
the performance of a low cost Stirling engine,
obtaining the power output and real efficiency,
also know under which scenario is feasible its
implementation in a non-interconnected area of
the country. The results show that the actual
power was 675.6 W in the best of cases,
achieving an actual efficiency of 34.6%,
equivalent to 60%of the theoretical efficiency.
Similarly this technology is susceptible to be
implemented due to the 30% of the installed
capacity in the areas is within the range of 020KW [8].
The numerical simulation allows on a first
approach to analyze the temperatures and power
losses behaviour in the three heat exchangers. It
3776
was found that the regenerator losses are 80% of
the total losses, also due to imperfect heat
transfer in the three heat exchangers and
pressure drops was necessary to increase the
heat furnished by 54% using air and 12% using
hydrogen, being capable of optimization,
similarly this simulation allows perform a
sensitivity analysis in order to increase power
and efficiency.
The efficiency achieved with air as working gas
was four times lower than that achieved with
hydrogen, however the last one is more
expensive and difficult to pressurize.
The rural and non-interconnected areas have a
large energy potential even without using, and
together with a learning process which allows
accumulate operational and technological
capabilities, would make them self-sustainable
in the long term.
8. Future perspective
The next target is to realize the laboratory
tests to validate the simulation and then test it
in a remote area, to meet in the medium-term
the social and human impact generated.
Nomenclature
A:
C:
D:
F:
Fr:
M:
N:
P:
Pot:
Pr:
Q:
R:
Re:
S:
St:
T:
V:
W:
Area
Heat capacity (kJ/kg-K)
Diameter (m)
Frecuency (Hz)
Reynolds friction factor
Mass (kg)
Referred to particular number
Pressure (Pa)
Power (W)
Prandtl number
Heat (W)
Ideal gas constant (kJ/kmol-K)
Reynolds number
Specific entropy (kJ/kg-K)
Stanton Number
Temperature (K)
Volume (m3)
Work (J)
Greek letter
µ:
Dynamic viscosity (kg/m-s)
α:
Expansion phase angle advance (°)
γ:
Heat capacity relation
ε:
Effectiveness
θ:
Crank angle (°)
ϕ:
Specific exergy (kJ/kg)
Subscripts and Superscripts
b:
c:
ck:
cle:
e:
h:
he:
hid:
hx:
k:
kr:
p:
r:
rh:
swe:
v:
wg:
Beale Number
Compression
Compression-cooler
Clearance
Expansion
Heater
Heater-expansion
Hydraulic
Heat exchanger
Cooler
Cooler-Regenerator
Constant pressure
Regeneration
Regenerator-Heater
Swept
Constant volume
Wetted area
Reference
[1] Thombare D, Verma S.Technological
development in the Stirling cycle engines.
Renew Sust Energ Rev 2006; 12 : 1–38.
[2] Timoumi Y, Tlili I, Nasrallah S.
Performance
optimization
of
Stirling
engines,RenewEnerg2008;33:2134–2144.
[3] Scollo L, Valdez P, Baron J. Design and
construction of a Stirling engine prototype. Int J
Hydrogen Energ 2008; 33(13) : 3506-3510.
[4] Berchowitz D. Stirling Engines in
Developing Countries. Conference on Small
Engine and Their Fuels in Developing
Countries1984Sept;Ohio, USA
[5] Kongtragool B, Wongwises S. A review of
solar-powered Stirling engine and low
3777
temperature difference Stirling engines. Renew
Sust Energ Rev
2003;7:131-154.
[6] DNP
Departamento
Nacional
de
Planeación. Programa de energización para
zonas no interconectadas. Documento del
Consejo Nacional de Política Económica y
Social. Bogotá, Colombia: 2001 Apr. Tech.
Report 3108.
[7] Alliance of Rural Electrification [Internet].
Belgium
–
Available
at:
Brussels,
<http://www.ruralelec.org/9.0.html> [accesed:
12.12.2010]
[8] CREG Comisión de Regulación de Energía
y Gas. Bases conceptuales para la regulación de
la prestación del servicio de electricidad en las
zonas no interconectadas. Bogotá, Colombia:
2003, Sept. Tec.Report CREG073.
[9] Naso,
Vincenzo.
Microgeneradores
“Stirling” alimentados con biomasa, Revista
Palmas 1997; 18 (1): 68-73.
[10] UPME Unidad de Planeación Minero
Energética. Potencialidades de los cultivos
energéticos y residuos agrícolas en Colombia.
Bogotá, Colombia: 2003, Jul. Technical Report
ANC-631 – 03
[11] IDEAM Instituto de Hidrología,
Meteorología y Estudio Ambientales. Atlas de
radiación solar de Colombia. Bogota, Colombia:
2005.
[12] Cengel Y, Boles M. Thermodynamics an
engineering approach. Reno USA. McGrawHill; 2003.
[13] Malroy E. Solution of the ideal adiabatic
Stirling model with coupled first order
differential equations by the pasic method. [MS
dissertation]. Ohio, USA: Ohio University; 1998
[14] Martini W. Nasa Stirling Engine Design,
CR-168088, NASA 1983
[15] Senft J. Mechanical efficiency of heat
engines. Cambridge, UK: Cambridge University
Press; 2007.
[16] Snyman H, Harms T, Strauss J. Design
analysis method for Stirling engines. J Energy
in Southern Africa 2008; 19 (3): 1-19
[17] Dyson RW, Wilson SD, Tew RC.
Review of computational Stirling analysis
methods.
Second
International
Energy
Conversion Engineering Conference; 2004 Aug
16-19.NASA; Cleveland, Ohio, USA.
[18] Chen N, Griffin F. A review of Stirling
engine mathematical models. Oak Ridge,
Tennessee
:
Oak
Ridge
National
Laboratory;
1983
Aug.Technical
Report:ORNL/CON 135.
[19] Urieli I, Berchowitz D. Stirling cycle
engine analysis. Bristol, UK: Adam Hilger:
1984.
[20] Herzog
Siegfried,
Mathematical
simulation of Stirling engines. Available
at:<http://mac6.ma.psu.edu/stirling/simulations/
IdealAdiabatic/index.html>[accessed
09.11.2010].
[21] Urieli Israel, Stirling Cycle Machine
Analysis.
Available
at:
<http://www.ohio.edu/people/urieli/stirling/me4
22.html> [accesed 01.03.2010]
[22] Urieli Israel, A computer simulation of
Stirling cycle machine. [PhD Dissertation].
Johannesburg, South Africa: University of
Witwatersrand; 1977.
[23] Cengel Y. Heat and mass transfer: a
practical approach. Reno USA. McGraw-Hill;
2003.
[24] Cundy V, Maples D, Tauzin C.
Combustion of bagasse, use of an agricultural –
derived waste. Fuel 1983; 62: 775-780.
[25] Kuprianov V, Janvijitsakul K, Permchart
W. Co-firing of sugar cane bagasse with rice
husk in a conical fluidized-bed combustor. Fuel
2006; 85: 434-442.
[26] Atmospheric science data center,
Surface meteorology and Solar Energy.
Available at:<http://eosweb.larcnasa .gov/sse/ >
[accesed 01.04.2010]
[27] Franco J, Cadena C, Saravia L. Multiple
use comunal cookers. Sol Energy 2004; 77:
217-223.
[28] Stine W, Diver R. A compendium of
solar/dish Stirling technology. Pomona,
California: California State Polytechnic
University, Sandia National Laboratories.
Technical Report: SAND93-7026UC-236.
[29] Ceballos F. El proceso de incorporación
de tecnologías energéticas en comunidades
rurales aisladas bajo un enfoque de dinámica de
sistemas [MS dissertation], Medellín, Colombia:
Universidad Nacional de Colombia Sede
Medellín: 2006
3778
View publication stats