Developing and testing low cost LTD Stirling engines

THERMODYNAMICS
Revista Mexicana de Fı́sica S 59 (1) 199–203
FEBRUARY 2013
Developing and testing low cost LTD Stirling engines
G. Aragón-González∗ , M. Cano-Blanco, A. Canales-Palma, and A. León-Galicia
PDPA, Universidad Autónoma Metropolitana-Azcapotzalco,
Av. San Pablo # 180. Col. Reynosa. Azcapotzalco, 02200, D.F.
Teléfono y FAX: (55) 5318-9057.
∗
e-mail: [email protected]
Received 30 de junio de 2011; accepted 25 de agosto de 2011
The construction of miniature LTD Stirling engine prototypes, developed with low-cost materials and simple technologies is described. The
protypes follow the Ringbom motor array, without mechanical linkages to actuate the displacer piston. Different designs, sizes, materials and
mechanisms components have been tested. The power piston has been replaced with a flexible diaphragm and the mechanisms linkages were
constructed with piano steel wire. Power output and efficiency experimental measurements are presented for two miniature LTD Stirling
engines, the MM7 model from American Stirling Company and our simplest low cost model. A reasonable design to build low cost engines,
rendering brake power and thermal efficiencies about 40 % those obtained with similar commercial engines, but only 5 % the cost has been
obtained.
Keywords: Stirling cycle; LTD machines; Ringbom motors; power and thermal efficiency measurement.
Se describe la construcción de prototipos de máquinas Stirling LTD miniatura, desarrollados con materiales de bajo costo y tecnologı́as
sencillas. Se apegan al modelo de motor Ringbom, sin eslabones mecánicos para actuar el pistón de desplazamiento. Se han sometido a
prueba diferentes diseños, tamaños, materiales y componentes para los mecanismos. El pistón de potencia se remplazó con un diafragma
flexible y los eslabones de los mecanismos se construyeron con alambre cuerda de piano. Se presentan mediciones experimentales de la
potencia y la eficiencia para dos máquinas Stirling LTD miniatura, el modelo MM7 de American Stirling Company y del más sencillo de
nuestros modelos de bajo costo. Se obtuvo un buen diseño para construir máquinas de bajo costo, que entrega 40 % de potencia y eficiencia
térmica desarrollada por modelos comerciales semejantes, pero con sólo 5% del costo.
Descriptores: Ciclo Stirling; máquinas LTD; motores Ringbom; medición de potencia y eficiencia térmica.
PACS: 01.50.Kw; 01.50.Pa; 07.10.Pz; 07.20.Pe
1.
Introduction
The operation of several thermal machines, devices designed
to convert internal energy in mechanical work, is well described using the thermodynamic power cycle concept. One
of these engines is the Stirling motor, a device that follows a
four times closed regenerative cycle operating with an ideal
gas as the working substance
The main subject of Robert Stirling’s original design was
a heat exchanger, called originally “economiser” for its enhancement of fuel economy to run the engine. The heat exchanger takes up a part of the energy of hot gas leaving the
expansion chamber to deliver it when the cold gas goes back
to the chamber. Now it is generally known as ’regenerator’.
The ideal gas undergoes successive expansions and compressions, due to the heat exchanging from hot and cold temperature sources. The ideal Stirling cycle consists of four
thermodynamic processes (Fig. 1 below): 3-4, the gas is externally heated and undergoes an isothermal expansion; 4-1,
the gas transfers heat to the regenerator and follows an isochoric cooling process; 1-2, the gas undergoes an isothermal
compression, transferring with the cool temperature source;
2-3, the compressed gas receives heat from the regenerator
and follows an isochoric process [1].
A Stirling engine is not an internal combustion engine; it
receives the heat from any external high temperature source.
For example the waste heat rejected to the environment from
several industrial or manufacturing processes.
F IGURE 1. Ideal regenerative Stirling cycle.
200
G. ARAGÓN-GONZÁLEZ, M. CANO-BLANCO, A. CANALES-PALMA, AND A. LEÓN-GALICIA
where pm is the medium cycle pressure (bar), Vp the power
piston stroke (m3 ), f the cycle frecuency (Hz). This dimensionless parameter Bn is called Beale number [7]. Typical
values for the Beale number are 0.11 to 0.15 when considering high temperature differential engines [8].
3. Low temperature difference Stirling engines
F IGURE 2. Gamma engine with separate cylinders.
The net work output W (J) for the ideal cycle is, [2]:
W = mR ln
V1
(TH − TC )
V2
(1)
where m (kg) is the mass of the gas enclosed by the engine, R
(J/kgK) is the specific gas constant, V1 (m3 ) is the enclosed
gas volume with the power piston at highest position in its
cylinder, V2 (m3 ) is the gas volume with the power piston at
lowest point, TH (K) is the temperature of the engine hot-side
and TC (K) is the temperature of the engine cold-side.
2. Power production on a Stirling engine
The thermal efficiency of any Stirling engine is defined as the
ratio of the power output to the heat transferred from the high
temperature source. Schmidt developed a model to predict
the power output of a Stirling machine, [3-5]; the working
substance is treated as an ideal gas and the compression and
expansion as isothermal processes.
The gas changes of volume in any Stirling engine are
synchronized with the cyclic piston stroke, from the upper
to the lower dead point; they can be expressed with a sinusoidal function. The theoretical predictions from the Schmidt
model approach to the behaviour observed in real engines, for
any of the mechanical Stirling engines configurations. These
mechanical configurations are generally divided into three
groups known as α, β and γ arrangements.
Alpha engines have two pistons in separate cylinders
which are connected in series by a heater, regenerator and
cooler. Both Beta and Gamma engines use displacer-piston
arrangements, the Beta engine having both the displacer and
the piston in an in-line cylinder system, whilst the Gamma
engine uses separate cylinders (Fig. 2)
From the initial Schmidt analysis several other authors
have proposed mathematical models for Stirling engine thermodynamic analysis. Chen and Giffin [6] identified 25 different models. Beale proposed an empirical equation to calculate the power output of the Stirling engine, by:
Bn =
ẇ
pm Vp f
In 1982 Kolin developed a Stirling engine to produce mechanical work from a temperature source lower than the boiling water [9]. In 1992 James R. Senft received a request from
the National Aeronautics and Space Administration (NASA)
to build a Stirling engine operating with a very low temperature difference (LTD motors). Senft built the N-92 engine [10]; this Stirling engine runs with ∆T as low as 6◦ C
and even with the heat produced with a warm hand on a cold
day
Several researchers are developing new LTD Stirling engines [11-13], to fit them to some low temperature difference
or use several sources of waste heat. The Mexico City subway company has recently expressed his interest to build and
use 1 (kW) Stirling engines. The purpose is to make use of
the heat generated in the electric train systems or obtained
from solar collectors, to provide electric power for the lighting system in the train stations. Even though the initial financing may be expensive, this request may be satisfied with
LTD Stirling
(2)
F IGURE 3. Ringbom miniature engine (Carl Aero Co.).
Rev. Mex. Fis. S 59 (1) (2013) 199–203
DEVELOPING AND TESTING LOW COST LTD STIRLING ENGINES
201
Miniature LTD Ringbom γ engines develop power in the
order of 1 to 10 (mW), shaft torques below 3×10−4 (Nm),
angular speeds under 500 (rpm) with thermal efficiencies below 0.1% (Fig. 3). They are built sometimes as scientific
toys, but can be employed with didactic purposes and to explore the limits of useful low temperature difference. It is also
possible to measure its power output and thermal efficiency,
using simple methods and common instruments available in
almost any engineering school [15].
Equation (2) cannot be used to calculate the power output
of LTD Ringbom Stirling engines. Walker [16] proposed an
empirical equation for these engines, with BN in function of
the cold to hot engine temperatures ratio, τ = TC /TH :
BN = 0.034 − 0.052τ
(3)
Kongtragool [17] proposed the modified Beale number:
·
¸
(1 + τ )
ẇ
(4)
M Bn =
pm Vp f (1 − τ )
Typical MBN values for LTD engines are 0.25 to 0.35.
4.
Testing LTD Ringbom engines
There are not any other means to know the thermal efficiency
and real power output from any thermal engine, but performing measurements from primary variables. A testing facility
was built to measure LTD Ringbom miniature engine performance [15].
The very low power figures (no more than 10 mW), made
compulsory to adapt typical testing designs to measure brake
power and heat transferred from the high temperature source,
without using expensive laboratory instruments (Fig. 4).
The testing procedure consists of supplying the heat QH
(W) by electric means, measuring voltage and electric current (QH = ∆V i). An increasing torque M is applied to the
pulley on the flywheel shaft, until permanent state is achieved
with shaft constant speed ω (then ẇ= Mω).
F IGURE 4. MM7 LTD engine pointing downwards in the testing
facility. A Dynamometer; B Voltmeter; C Electric multimeter; D
Switch; E Variable voltage transformer; F Adiabatic recipient; G
Digital thermometer; H Fan; I LTD engine; J Optical tachometer;
K Weight.
motors; for example extending the Gaynor et al design for a
500 (W) prototype [2].
Senft [14] has improved his designs and built Ringbom
Gamma type engines, running with ∆T of only 0.5◦ C The
Ringbom Stirling engines have no mechanical linkage to actuate the displacer piston. Pressure changes inside the engine
caused by the movement of the power piston act on an oversized displacer pushrod to create movement of the displacer
piston.
F IGURE 5. Brake power (mW) vs shaft speed (rpm) and temperature difference (◦ C). MM-7 LTD engine.
Rev. Mex. Fis. S 59 (1) (2013) 199–203
202
G. ARAGÓN-GONZÁLEZ, M. CANO-BLANCO, A. CANALES-PALMA, AND A. LEÓN-GALICIA
F IGURE 6. Efficiency (%) vs shaft speed (rpm) and temperature
difference (◦ C). MM-7 LTD engine.
F IGURE 8. Small cost LTD ringbom engines.
F IGURE 9. Brake power (mW) vs shaft speed (rpm) and temperature difference (◦ C). Low cost LTD engine.
F IGURE 7. Testing procedure with the MM7 LTD engine from
American Stirling Company.
Brake power output ẇ (mW) and thermal efficiency
ηe = ẇ/qH are shown in Figs. 5 and 6, as functions of shaft
speed (rpm) and temperature difference (∆T = TH - TC ; ◦ C),
for the MM-7 LTD engine built by American Stirling Company (Fig. 7).
5. Low cost LTD Ringbom Stirling engines
Commercial LTD miniature engines like those shown in
Figs. 3 and 7, may be very expensive due to the manufactur-
ing processes required to construct them; not only to achieve
tight geometrical tolerances but to get a shining ornamental
appearance.
Usually miniature Ringbom LTD engines have a small
amount of components, but besides the manufacturing costs
some of them are constructed with expensive materials
(borosilicate glass and aluminium-clad graphite for the power
cylinder and piston, for example).
We have developed and tested several low cost miniature
Ringbom LTD prototypes (Fig. 8). Different designs, sizes,
materials and mechanisms components have been tested for
its construction. Artisan processes and short-lasting materials
have been avoided, alike expensive materials.
The power piston has been replaced with a flexible diaphragm and the power cylinder adapted from a small plastic
recipient. The displacer cylinder is manufactured with copper sheet with plastic glued walls. The flywheel is a compact
disc and the mechanisms linkages were constructed with piano steel wire.
These low cost engines may operate with temperature differences ∆T = TH -TC from 20 to 80◦ C. The smaller one in
Fig. 8 has only 0.36 the heat transfer surfaces of the MM7 engine in Fig. 7. A discarded steel vessel works like displacer
Rev. Mex. Fis. S 59 (1) (2013) 199–203
DEVELOPING AND TESTING LOW COST LTD STIRLING ENGINES
F IGURE 10. Efficiency (%) vs shaft speed (rpm) and temperature
difference (◦ C). Low cost LTD engine.
cylinder and the engine lacks of any refinement (like screwed
unions, bearings for the gyratory axes or machined parts).
This extremely simple engine was tested in the facility
shown in Fig. 4, developing brake power and thermal efficiencies about 10% those obtained with the commercial engines MM7 (with similar temperature differences applied to
both engines, Figs. 9 and 10).
6.
Conclusions
It seems very difficult to build any other device as inexpensive
and simple as the Stirling Ringbom LTD, in order to produce
mechanical work from a heat source. Nevertheless they show
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203
the full attributes of thermal engines and admit a thorough
testing.
Miniature Ringbom LTD engines have really small efficiencies, but allow making good use of very low temperature waste heat sources (fully unsuitable for other thermal
engines). Senft [14] proved the possibility to run continuously an engine with a temperature difference of only 0.5◦ C,
but ∆T of about 40◦ C is a good practical limit to produce
mechanical power (for example using solar energy or waste
heat from air conditioning systems).
Commercial Ringbom LTD engines have elevated costs,
highly related with its ornamental toy quality. These engines
may be successfully simplified, even to extremely plain designs and yet showing smooth running with regular speed.
We took these simplifications to the limit only for didactic
purposes. Now we have a reasonable design to build miniature Ringbom LTD engines, rendering brake power and thermal efficiencies about 40 % those obtained with similar commercial engines (but 5 % the cost).
The design of a Stirling engine to produce 1 (kW), using
waste heat from a low temperature source, may be resolved
with the Ringbom Gamma array. This motor has no mechanical linkages to actuate the displacer piston; the power output
would be achieved with several displacer cylinders and power
pistons linked to a common flywheel shaft
To continue this work with a theoretical approach, it
would be convenient comparing the miniature LTD efficiencies with a model like the Novikov-Chambadal-CurzonAhlborn one, as it was made for the Otto cycle in Ref. 18.
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desplazamiento. Bachelor’s thesis. (Universidad Autónoma
Metropolitana, Unidad Azcapotzalco, México, 2008). (in Spanish).
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Rev. Mex. Fis. S 59 (1) (2013) 199–203