AN EXPERIMENTAL SETUP TO TEST LINEAR ALTERNATORS:
DESIGN, OPERATION AND PRELIMINARY RESULTS
Moamen Abdou, A.Y. AbdelWahed and A.H. Ibrahim*
The American University in Cairo, School of Sciences & Engineering, 11835 New Cairo, Egypt
*On leave from Mechanical Power Department, Faculty of Engineering, Cairo University, Giza,
Egypt
Ehab Abdel-Rahman
Associate Provost for Research and acting Director of Yousef Jameel Science and Technology
Research Center, The American University in Cairo, 11835 New Cairo, Egypt
e-mail:ehab_ab@aucegypt.edu
A thermoacoustic power converter consists of a thermoacoustic engine driving a linear alternator connected to a matched electric load. Accordingly, linear alternators are essential parts
of thermoacoustic power converters. However, integration of a linear alternator in a thermoacoustic power converter is complicated since it requires acoustic matching with the thermoacoustic engine as well as electrical matching with the off-grid electric load connected to it
and fast protection against piston over-stroking. In order to simplify the integration process,
an experimental setup is designed and built in which the acoustic power generated by a
thermoacoustic engine is simulated by an acoustic driver. This setup provides a platform to
test and evaluate the performance of a linear alternator in a controlled environment in isolation of thermoacoustic engines and allows identification and resolution of potential problems
in a linear alternator separately. A control circuit is designed and built to protect the alternator’s piston against over-stroking. A non-linear electric load is connected to the alternator to
provide a stable operating point of the complete system. In this setup, instrumentation are
used to monitor the main variables (input and output currents, input and output voltages, dynamic gas pressure at exit of acoustic driver and inlet of linear alternator, acoustic driver
stroke, linear alternator stroke, air and coil temperatures). The setup allows use of different
resonators to simulate the effects of different front volumes on the performance of linear alternators and allows alterations in the enclosure volumes housing the acoustic driver and/or
alternator to control their resonance frequencies. Results showing the performance of a given
linear alternator under different operating frequencies are presented and discussed
1. Introduction
A thermoacoustic power converter (TAPC) consists of a thermoacoustic engine that converts
heat energy into acoustic energy, a linear alternator that converts acoustic energy into electricity and
an electric load. The integration of a linear alternator into a thermoacoustic power converter is not
straightforward and requires attention to several important issues in order to achieve matching beICSV22, Florence (Italy) 12-16 July 2015
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tween the thermoacoustic engine and the linear alternator as well as matching between the linear
alternator and the electric load in addition to protection against potential over-stroking in the linear
alternator’s piston. Proper matching results in large conversion efficiency on the alternator itself
(acoustic to electric conversion) as well as to large overall conversion efficiency on the thermoacoustic power converter as a whole (thermal to electric conversion). Thermoacoustic engines are
explained in details in [1]. Details on linear alternators can be found in[2].
Linear alternators are attractive power converters in TAPC’s because of their small size and
weight, reasonable power handling capacity, reasonable stroke limit, high acoustic-to-electric conversion efficiency, operation without sliding seals or lubrication with demonstrated reliability and
long maintenance-free lifetimes [2].
Corey and Martin [3]summarized the acoustic matching conditions between an acoustic driver
and an acoustic load (e.g., a linear alternator) in an acoustic resonator. These conditions require the
operator to be able to control the frequency of operation, provide the proper acoustic impedance and
be able to have the linear alternator operate at its full design stroke when operated at its full rated
power, which requires complete understanding of how to control the alternator’s stroke.
Stroke control in linear alternators is essential in order to avoid over-stroking (a catastrophic
condition that occurs when the piston exceeds the stroke limits causing permanent deformation and
system failure) and to achieve full rated power at the rated stroke. Protection against over-stroking
is implemented in this work by a control circuit that feeds the measured piston displacement into
analog comparators and solid-state relays to provide a control action at a time scale much faster
than the time scale corresponding to the operating frequency of the TAPC. The control logic is presented in the experimental setup.
The setup allows use and control of different electric loads to study the matching between the
linear alternator and the load. The electric load controls the stroke of the linear alternator and the
acoustic-to-electric conversion efficiency of the linear alternator. Moreover, the combined system
made of the thermoacoustic engine, linear alternator and load must have a single intersection point
between the power produced by the engine versus stroke and the power absorbed by the load versus
stroke. The power produced by the thermoacoustic engine running on a Striling cycle is a quadratic
function with voltage (and hence approximately quadratic with stroke). A load made of simple resistors has its power absorption also quadratic with voltage (and therefore also with stroke) and thus
no stable intersection point exists between the alternator and a simple resistive load since both have
quadratic dependence with voltage and stroke.
If the combined system is perfectly balanced, then it will run in a stable mode. However, a perfect balance is not possible or sustainable, especially in the start-up and shutdown operation modes
of the combined system. The imperfect balance gives rise to two possible scenarios: either the power produced by the engine is slightly higher than the power absorbed by the load (with respect to
stroke) because of higher temperature at the hot end, cooler rejection or lower friction, then the
stroke will increase until it exceeds the safe stroke limits or the over-stroke protection circuit forces
the system to stop. If the opposite happens, then the stroke will decrease until the engine stalls and
operation ceases.
One of the methods that can be used to resolve this issue is to use a non-linear load, in which the
absorbed power is not in proportion to the square of the voltage. Systems built with purely resistive
loads suffered from instability of operation and inability to properly test the thermoacoustic engine
and the linear alternator (e.g., Telez M.Sc.[4]).
It should be noted that non-linear loads are needed only during initial testing in laboratories because once the thermoacoustic engine and the linear alternator are connected to the grid, the output
voltage (and hence the stroke) are imposed by the grid and no special loads are needed then.
Non-linear loads can be made using back-to-back zener diodes, as suggested by [5], or by using
an electronic load device that allows constant voltage or constant current operations. The described
experimental setup allows the operator to adjust the operating conditions (gas mixture composition,
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mean gas pressure, input acoustic power, operating frequency and load value) in order to satisfy
both proper acoustic matching between the linear alternator and the input acoustic power as well as
proper matching with the load, which should translate into stable operation with high conversion
efficiency at the desired stroke.
2.
Experimental setup
The experimental setup system consists of an acoustic driver (model 1S102D, supplied by Qdrive, with a rated power of 125 W) that generates acoustic power at a controlled rate at the required frequency to simulate the acoustic power resulting from a thermoacoustic engine. This
acoustic power drives a linear alternator (model model1S102D, supplied by Q-drive, with a rated
power of 100 W) to generate electricity. An electric load is connected in parallel to the linear alternator to dissipate the generated electric power. The acoustic driver and the alternator are housed
inside enclosures and are connected together using an acoustic resonator. The system is designed in
a modular form to allow ease of change of different components to study different effects. A schematic of the setup is shown in Figure 1 below.The acoustic design of the system was tested prior to
implementation via a numerical simulation carried-out using DeltaEC[6].
Figure 1: Schematic showing the linear alternator under test and the accessories and instrumentation used.
The acoustic driver is operated using a function generator (Tektronix AFG 3021B) that generates
a sine-wave at the required frequency. The generated wave then is amplified by a power amplifier
(Bruel and Kjaermodel 2734) and then fed into the acoustic driver. The acoustic driver is protected
against excessive current (by a fast acting 2.25-A fuse), over-stroking (by a control circuit described
below) and against over-heating (by monitoring its coil temperature via a thermocouple).
Three different acoustic resonators are available of different lengths (250 mm, 150 mm and 50
mm) to simulate the effects of different front volume in TAPC’s on linear alternator performance.
The resonators are made of steel to withstand operation at 40 bar and are tested hydro-statically
(with the enclosure volumes as well) at 60 bar. Mechanical design followed the standards in [7].
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The acoustic driver and alternator are housed inside enclosures (AKA back volumes). Enlarging
the enclosure volume reduces the pressure wave in the back space, which in turn reduces the thermal relaxation loss and the seal loss causing an improvement in the conversion efficiency. However, the volume increase should be balanced by the corresponding decrease in the TAPC’s power
density.
The non-linear electric load used in this work consists of a set of back-to-back zener diodes of
different break-down voltages connected in series to a high-power rheostat.
The control logic used to prevent against over-stroking on the acoustic driver and/or linear alternator is shown in Figure 2. The stroke of each of the acoustic driver and the alternator is measured
using Linear Variable Differential Transducers (LVDT’s). Each LVDT signal is fed into a precision
rectifier in order to get the absolute value of the LVDT signal, to provide over-stroking protection
in either positive or negative directions. The output signal then is fed into an analog comparator
(LM324 Op-amp) in which it is compared against a preset voltage that corresponds to the maximum
stroke limit where the result of the analog comparison controls a control action to prevent overstroking.
Figure 2:Control logic used to protect against over-stroking in the linear alternator and the acoustic driver
If the alternator stroke exceeds the set point, two control actions occur: the input electric power
supply to the acoustic driver is turned-off via a normally-closed solid state relay and a stall circuit is
introduced parallel to the electric load via a normally-open solid-state relay. The latter provides a
protection fast enough in TAPC’s since the linear alternator will continue to operate for a significant time after the heat input is turned-off. The stall circuit is designed in such a way that it has a
resistance lower than that of the load and a power rating capable of dissipating the full generated
electric power. The introduction of the stall circuit in parallel to the load reduces the overall resistance seen by the load causing the current generated by the linear alternator to increase and the
voltage generated by the alternator to decrease, which forces the alternator stroke to decrease. In
this work the stall circuit is simply a 2-Ω 100-W resistance.
Additionally, if the driver stroke exceeds the set point, the input electric power is turned-off via
the same normally-closed solid state relay. This operation is made using an analog OR gate.
Once any of these control actions is initiated, it remains in effect until a manual reset is made by
a human action, to avoid further operation until the cause of over-stroking is identified and resolved.
The working gas is a gas mixture of helium and argon gases with different molar fractions. This
gas mixture allows different combinations of speeds of sound and mixture densities and thus covers
a wide range of conversion efficiencies, power densities and acoustic impedances. The helium and
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argon gases are supplied from high-pressure gas cylinders. Dalton's law is used to introduce a certain gas mixture composition. To check that the gases are well mixed, the system is filled to a mean
pressure 5% higher than the set value and the operating frequency is monitored. The excess gas is
then released and the frequency is observed again. If both values are the same, then the gases are
well mixed. This technique was utilized in [8].
The working gas is introduced to the system through three different ports (the resonator, the
acoustic driver and the alternator enclosures) simultaneously to avoid large internal pressure differentials inside the system during the pressurization or de-pressurization of the system. A flow regulator is used to control the filling rate since quick filling of the system may result in a large pressure
difference over the alternator which may cause damage. For example, the filling rate used inwas 12
mbar/s[9]. The alternators used in this work can be subjected vacuum during mixture
introduction[10].
The mean gas pressure is measured using a Bourdon-tube gage installed at the middle of the resonator. A vacuum pressure gauge is used, with a vacuum pump, to remove the used working gases
in order to introduce a fresh mixture. These gauges are isolated from the resonator via stain-less
steel valves in order to protect them from exposure to acoustic oscillations and to prevent acoustic
power from flowing out of the system in the direction of the gauges and confusing the data.
The dynamic gas pressure is measured at several locations close to the exit of acoustic driver and
the input of linear alternator (PAD and PLA, respectively) inside the setup using piezo-resistive pressure microphones (MeggittModel 8530C-500M5) and a programmable-gain DC amplifier (Meggitt
Model DC 136).
The mean gas temperature inside the resonator is measured using a thermocouple. All thermocouples are connected to the setup using feedthroughs and are then connected to data acquisition
(NI USB-6225, 16-bit, 250 kS/s).
The piston displacement of both the acoustic driver and the linear alternator are measured using
LVDT (Measurement Specialtiesmodel XS-C 499 and LDM-1000 signal conditioning module). The
LVDT is installed such that it reads zero when the pistons are at their equilibrium positions and this
zero reading is checked before and after operation to make sure that the pistons retain their original
positions.
The piston velocity on the acoustic driver and on the linear alternator (UAD and ULA, respectively) can be estimated from the displacement’s signal by numerical differentiation of the captured
time signal with respect to time. The simultaneous acquisition of piston displacement and dynamic
gas pressure allows estimation of the acoustic power as shown in equation 3 and 4.
The input voltage (Vin) to the acoustic driver, the output voltage (Vout) on the electric load, and
the open-circuit voltage (VOC) on the linear alternator are measured using a digital storage oscilloscope via a voltage probe (10-X attenuation).
Acquiring the input volt and current at the open-circuit condition allows estimation of all the
losses involved in the complete system (except the copper losses I2R losses in the alternator coils,
which can be estimated at any load setting). Simultaneous measurements of the LVDT signal and
the dynamic pressure in the enclosure volume allows estimation of the alternator-space thermal hysteresis.
The input and output current (Iin and Iout, respectively) are measured by monitoring the voltage
drop on a 1-Ω 100-W series resistance. Multi-meters are used to provide visual monitoring of the
input and output voltages and currents.
The system is allowed to operate for approximately five minutes until steady-state operation is
achieved before measurements are taken.
Special attention is used to ensure signal integrity to isolate the measurement signals from the
magnetic fields associated with the power cords carrying the input/output electric currents. The path
of these power cords is kept away from the path of the shielded signal wires and the length of the
signal wires is kept to a minimum.
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Data acquisition of the dynamic pressure, LVDT signals, input and output voltages and currents
are made using two digital storage oscilloscopes (Tektronix TDS2024B) running simultaneously
and synchronized using LabVIEW with a sampling rate 5E4 Samples/s for 50ms (corresponding to
about two acoustic cycles). This setting is used to analyze the data in time domain with a time resolution of 20E-6 s.
Prior to operation, the function generator is set to produce a sinusoidal wave at the desired frequency. This wave is fed into a power amplifier in order to be amplified to the value that causes the
acoustic driver to generate the required acoustic power. Operation is only possible within a narrow
range of operating conditions to avoid over-stroking, excessive current, excessive heating or poor
electro-acoustic conversion efficiency on either the acoustic driver and/or the linear alternator. The
experimental setup presented in this work allows the operator to adjust the operating conditions
(frequency, gas mixture composition, mean gas pressure, input voltage to the acoustic driver and
electric load) in order to test the linear alternator behavior and monitor its performance at any required condition, as indicated by its acoustic-to-electric conversion efficiency, output electric power
and stroke.
The linear alternator is protected against over-stroking (by the control circuit described above)
and against over-heating (by monitoring its coil temperature by a thermocouple).
3.
Data analysis
The input electric power Pin is estimated using the dot product of the input current and voltage to
the acoustic driver, where the bracket denotes averaging made after the dot product operation of the
two waves:
(1)
= ⟨ ( ). ( )⟩
Similarly, the output electric power Pout is estimated as:
( ).
(2)
=⟨
( )⟩
The acoustic power produced by the acoustic driver is estimated using the average of the dot
product of the dynamic pressure at the acoustic driver exit and the acoustic driver’s piston velocity:
(3)
= ⟨ ( ).
( )⟩
Similarly, the acoustic power received by the linear alternator is estimated as:
(4)
= ⟨ ( ).
( )⟩
The electro-acoustic conversion efficiency (AD) of the acoustic driver is estimated as:
(5)
η =
The acoustic-to-electric conversion efficiency (LA) of the linear alternator is estimated as:
(6)
η = ̇
The overall conversion efficiency overall is estimated as:
(7)
η
=
4.
Sample of raw data
Figure 3 presents a sample of the captured raw data, namely the input volt and current, dynamic
pressure, piston strokes of acoustic driver and linear alternator, and output volt and current. All the
data presented are captured simultaneously, providing information of the phase relation-ship between the different data. This data set corresponds to a working gas mixture of 50% helium, 50%
argon, a mean pressure of 10 bar, operating frequency of 54 Hz, input voltage of 20 VRMS to the
acoustic driver and an electric load consisting of back-to-back zener diodes of 6-V break-down
voltage and a resistance of 22 Ω.
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Figure 3: A Sample of the raw data all captured simultaneously
5.
Preliminary results
Some of the preliminary results are presented in Figure 4. This data set corresponds to the same
operating conditions of Figure 3 in the frequency range of 45 Hz to 70 Hz. This set of results focuses on the dependence on the frequency, which is one of the main parameters in a TAPC.
Figure 4: Sample of preliminary results
The maximum output electric power occurs at 57 Hz, because this is the point of maximum conversion efficiency of the linear alternator.
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The point of maximum input power (60 Hz) is of special interest, since it allows loading of the
acoustic driver without excessive current and overheating, which provides a large acoustic input to
the linear alternator.
Optimization of the conversion efficiency of the linear alternator and its output electric power
can be implemented by adjusting the acoustic impedance (through different mixture compositions
and different mean gas pressures) as well as optimization of the electric load, which will be presented in a later publication.
6.
Summary and conclusions
An experimental setup is presented in which the acoustic power flow from a thermoacoustic engine is simulated using an acoustic driver in order to be able to test linear alternators separately
from thermoacoustic engines. The issues related to the integration between linear alternators and
thermoacoustic engines and electric loads are presented. A control logic is presented to protect linear alternators against over-stroking. The input and out variables necessary to document the performance of the linear alternator are measured and presented in a range of operating frequencies.
7.
Acknowledgements
This project is funded by the European Union. Eng. MoamenAbdou is thankful to the Egyptian
Academy of Scientific Research and Technology for his M.Sc. fellowship
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