REAL-TIME MEASUREMENTS OF LINEAR ALTERNATOR PERFORMANCE INDICES UNDER THERMOACOUSTIC- POWER-CONVERSION CONDITIONS

Transcription

1 REAL-TIME MEASUREMENTS OF LINEAR ALTERNATOR PERFORMANCE INDICES UNDER THERMOACOUSTIC- POWER-CONVERSION CONDITIONS A.H. Ibrahim 1, A.Y. Abdelwahed and M. Abdou The American University in Cairo, School of Sciences & Engineering, New Cairo, Egypt 1 On leave from Mechanical Power Department, Faculty of Engineering, Cairo University, Giza, Egypt Ehab Abdel-Rahman Professor of Physics, Department of Physics, The American University in Cairo, New Cairo, Egypt ehab_ab@aucegypt.edu A thermoacoustic power converter consists of a thermoacoustic heat engine and a linear alternator. Integration of linear alternators into thermoacoustic power converters is complicated since it requires acoustic matching with the thermoacoustic engine and matching with the load connected to it. In order to fully understand this process, this work presents an experimental setup designed and built to test linear alternators under different thermoacoustic-power-conversion conditions. The setup supplies the acoustic power to the linear alternator in a controllable and stable form, using an acoustic driver. Results indicate that introduction of a low-resistance in parallel to the linear alternator can provide over-stroke protection on a time scale of few milliseconds. Results on how the key performance indices (mechanical stroke, acoustic-to-electrical conversion efficiency, mechanical-motion loss, fluid-seal loss and Ohmic loss) of the linear alternator are affected by the operating frequency, the mean gas pressure and the working gas mixture composition are presented and discussed. Under the conditions employed, the proportionality constant between the mechanical stroke and the generated voltage is found to increase linearly with the operating frequency (even across the mechanical resonance frequency point) and to decreases linearly with the mean gas pressure and to be almost independent on the gas mixture composition. The effects of the acoustic gas impedance at different mean gas pressures and different gas mixture compositions on the acoustic matching between the acoustic power supplied and the linear alternator are quantified. 1. Introduction A thermoacoustic power converter converts thermal energy into acoustic energy using a thermoacoustic engine and then into electrical energy using a linear alternator. Recent thermoacoustic power converters have been reported in [1-3]. The matching between the thermoacoustic engine, linear alternator and the driven load is essential for efficient and stable operation but is also complicated. The matching conditions between an acoustic driver and an acoustic load in an acoustic resonator are reported in [4], and require that the acoustic driver is operated at the design frequency of the acoustic load, is operated at its mechanical resonance frequency, delivers the proper acoustic power to the acoustic load, and operates at its rated mechanical stroke when operated at its rated power. Additionally, the values of the pressure and volumetric flow rate amplitudes and phases supplied by the acoustic driver must be matched to a design point of the acoustic load. Simultaneous satisfaction of all the above conditions requires deep understanding of the matching issues as well as quantitative understanding of how to control the mechanical stroke at different operating conditions, because if full acoustic power is delivered at less than the rated mechanical stroke, excessive current will be required while if the full rated power is delivered at more than the rated 1

2 mechanical stroke, the thermoacoustic power converter will never achieve its rated power capacity. From the efficiency view-point, operating at rated mechanical stroke at less than the rated output power implies carrying the full mechanical-motion loss while operating at only a fraction of that power, which will necessarily lead to a reduced acoustic-to-electric conversion efficiency. Achieving all the above conditions requires designing and implementation of a platform to test linear alternators under different operating conditions, which is one of the objectives of this work. The presented setup was upgraded over that presented in [5], to allow testing under different thermoacoustic key conditions. For example, the setup allows testing at the linear alternator s mechanical and/or electrical resonance frequency, or under impedance matching conditions with the source of acoustic power, or under travelling wave thermoacoustic operating conditions, or under balanced or unbalanced mechanical/electrical losses in the alternator, as well as under different loads that dissipate the generated electric power. Results using a resistive load are presented in [6] while results using a passive non-linear load are presented in [5] and results using a constant-voltage electronic load are presented here. Comparison between the linear alternator performance under linear and nonlinear loads is carried-out in [7]. Additionally, the setup calculates the key performance indices from the measured signals in real-time using LabView, allowing identification of the value of any required performance index immediately after the data acquisition is completed. The experimental conditions used in this article are selected to match the conditions typically encountered in thermoacoustic power-conversion conditions, which are in the frequency range of Hz, with working gases/gas mixtures made of argon and helium, and operating at a mean gas pressure in the range of bar [1-3]. The objectives of this work are to 1- present the setup and explain its relevance to thermoacoustic power conversion, 2- present the performance of the linear alternator in a reference experiment carried-out at conditions typical in thermoacoustic power converters, 3- to carry-out a parametric study to quantify the effects of the operating frequency, the mean gas pressure and the working gas mixture composition on the performance indices of the linear alternator. In this work, the key performance indices selected to monitor the linear alternator s performance are the mechanical stroke, the acoustic-to-electric conversion efficiency, the mechanical motion loss, the fluid seal loss and the Ohmic loss. Further work made by the authors to understand this part of thermoacoustic power converters is carried-out using this setup: an experimental investigation of the effects of mechanical stroke on the acoustic impedance is presented in [6]; a novel method developed to allow testing using passive nonlinear loads to achieve stable and controllable operation under off-grid conditions is introduced and its effects on the performance indices are compared to linear loading in [7]; and a sensitivity analysis on how the operating conditions affect the key performance indices is presented in [8]. 2. Experimental setup Fig. 1 shows a schematic of the experimental setup. The setup consists of a function generator (Tektronix AFG3021B) that supplies a sine wave of a controlled frequency and amplitude to a power amplifier (model 2734, Bruel and Kjaer). This wave is supplied to an acoustic driver (model 1S102D, Chart Industries). The generated acoustic power is fed to the linear alternator under test at the required frequency and intensity through an acoustic resonator (5-cm long and 50.8-mm inside diameter). The technical details of the linear alternator used in this work are presented in [6]. The use of the acoustic driver to deliver acoustic power to the linear alternator in lieu of thermoacoustic heat engine results in supplying stable and controllable acoustic power to the linear alternator while decoupling all potential problems related to thermoacoustic engines like overheating, streaming, turbulence as well as non-uniformity and limited intensity and frequency ranges of the acoustic power delivered to the linear alternator during the test. The electric power produced by the linear alternator is dissipated using an electronic-load (model 8540, rated at 150 W, BK precision) operated at constant-voltage mode, for better simulation of the load presented by the grid (which operates under a constant-voltage mode) in real applications. 2 ICSV23, Athens (Greece), July 2016

3 Figure 1: Schematic of the experimental setup. The dynamic pressures are measured using pressure microphones (model 8530B-500M5, piezoresistive, range PSI absolute, individually calibrated by the supplier, Meggitt). The pressure microphones receive bridge excitation from a signal conditioner unit (amplifier Model 136, Meggitt). Measurements of the dynamic pressure take place at three different key points: inside the acoustic driver s enclosure, upstream of the linear alternator s piston (hereinafter referred to as the resonator pressure), and at the back of the linear alternator s piston, inside the linear alternator s enclosure (hereinafter referred to as the enclosure pressure). The mechanical strokes of the acoustic driver and of the linear alternator pistons are measured using Linear Variable Differential Transformers (LVDT s) (model XS-C 499, sensitivity of 1.27 mm/v, Measurement Specialties), which receive excitation from a signal conditioner (Model LDM1000) powered by a power supply (Zhaoxin-RXN305D). The input voltage to the acoustic driver and the generated voltage from the linear alternator are reduced in amplitude using phase-preserving transformers and then are digitized using a data-acquisition card. The input current to the acoustic driver and the output current from the linear alternator are measured by capturing the voltage drop on a known precise high-power resistance and then are digitized as well. All the data is captured simultaneously using a data acquisition card (Model NI 6225, 40 differential-input analog channels, 16-bit resolution, maximum sampling rate of 250,000 Samples/S, supplied by National Instruments). The sampling parameters are selected to ensure sampling of an integer large number of cycles with fine time and spectral resolutions without aliasing and without significant amplitude leakage. The sampling parameters used in this work are a sampling rate of 20,000 Samples/s applied for 400 complete cycles at 400 Samples/cycle with a total number of samples of 160,000 samples and a total sampling time of 8.0 seconds. This yields a quantization resolution of 0.3 mv, a time resolution of 50 s and a spectral resolution of 0.15 Hz. A digital image of the setup is shown in Fig. 2. To prevent the linear alternator s piston from over-stroking, the presented setup utilizes an overstroke protection methodology. This is based on measuring the piston s stroke using the LVDT and comparing the LVDT output voltage to a set voltage using an analog comparator (Model LM324N). If the measured stroke voltage reaches 95% of the voltage corresponding to the rated stroke, then the analog comparator issues two digital signals simultaneously: the first signal activates a normallyclosed solid-state relay to open and to disconnect the power from the acoustic driver and the second signal activates a normally-open solid-state relay to close and thus to connect a high-power low resistance (2- in this work) in parallel to the linear alternator, causing the alternator s output voltage to drop instantly with a corresponding drop in its mechanical stroke, thus providing fast protection against potential over-stroke. ICSV23, Athens (Greece), July

4 Figure 2: Digital image of the setup showing the digital storage oscilloscopes (1 and 13), function generator (2), power amplifier (3), signal conditioner of the pressure microphone (4 and 12), data acquisition card (5), over-stroke protection circuit (6), LVDT signal conditioner (7 and 11), acoustic driver enclosure (8), acoustic resonator (9), linear alternator enclosure (10), power-factor-correcting capacitor and rectifier (14), resistive load (15) and LVDT power supply. Figure 3: Measurements of the time response of the over-stroke protection methodology. The over-stroke control circuit is invoked to send a digital signal to introduce a 2- resistance in parallel to the linear alternator, forcing the mechanical stroke to decrease in less than 10 ms. This methodology prevents over-stroking protection under any operating conditions on a time scale of few milliseconds, which is fast-enough for the frequencies typically encountered in thermoacoustic power conversion, as shown in Fig. 3. This time response is electric in nature since the low resistance introduced in parallel to the linear alternator withdraws a large current from it, forcing the generated voltage to drop. The mechanical stroke generally is proportional to the generated voltage (as shown in Fig. 4), where the proportionality constant depends strongly on the mean gas pressure and the operating frequency and to a less extent on the gas composition [5]. Thus, the reduction in the output voltage is accompanied by a reduction in the mechanical stroke. This fast response would not be possible if the only control action was to switch-off the heat input in a thermoacoustic power converter (e.g., de-focusing of the solar concentrator) and this methodology would be needed in addition to turning-off the heat source. This over-stroke protection is particularly helpful when trying to identify the operating conditions that lead to delivering the rated output power at the rated mechanical stroke. Different conditions related to thermoacoustic power conversion are readily achievable in this setup, and include 1- testing under mechanical resonance condition, where the mechanical resonance frequency is measured in situ to account for the gas spring effect that takes place in the enclosure volume housing the linear alternator (56.3 Hz at the 30-bar mean gas pressure used in this work), 2- testing under electric resonance condition (where a power-factor-correcting capacitor is inserted in series with the load to balance the effective coil inductance s at different mechanical stroke amplitudes), 3- testing under impedance matching with the source of acoustic power (where the acoustic impedances of the acoustic driver and the linear alternator pistons are equal, which corresponds to a frequency of 52 Hz in this work), 4- testing under travelling wave operating mode (by operating at a frequency where the angle between the resonator s dynamic pressure and the piston s velocity is low, which corresponds to a frequency of nearly 52 Hz in this work), an 5- testing at equal mechanical motion loss and Ohmic loss, which represents an operating point of balanced losses of the linear alternator. This concludes the first objective of this work. 3. Results and analysis 3.1 Estimating the performance indices of a reference experiment A reference experiment is carried-out using a working gas mixture made of 60% helium and 40% argon, which is the helium/argon gas mixture that enjoys the minimum Prandtl number of 0.4 of all helium/argon gas mixtures [9] and thus has a minimum ratio of the viscous penetration depth to the thermal penetration depth. The molar fractions of the different gases are adjusted by controlling their 4 ICSV23, Athens (Greece), July 2016

5 partial gas pressures using Dalton s law. The mean gas pressure is 30 bar, which is typical in thermoacoustic power converters. At this mean gas pressure, the mechanical resonance frequency of the acoustic driver is measured in situ and found to be 56.3 Hz, which is close to the travelling-wave frequency of 52 Hz. The operating frequency is 52 Hz, which is the frequency that corresponds to nearly travelling-wave mode of operation under the conditions used. The load connected to the linear alternator consists of a power-factor-correcting capacitor (polypropylene film capacitor, run type, maximum operating voltage of 450 V, a capacitance of F) connected in series to a rectifier and then to an electronic load operated at a constant voltage of 13 V. The main alternator signals are presented in Fig. 4, showing the mechanical stroke, S, in mm; the resonator pressure, Pres, in kpa; the enclosure pressure, Penc, in kpa; the generated voltage, VLA in V and the generated current, ILA in A. This figure also shows the linear relationship between the generated voltage and the generated current with respect to the mechanical stroke. Figure 4: Time domain of the linear alternator signals. The signals are the mechanical stroke (mm), resonator dynamic pressure (kpa), enclosure dynamic pressure (kpa), generated voltage (V) and generated current (A). This data is for a gas mixture made of 60% helium/40% argon, a mean gas pressure of 30 bar, an input pressure ratio to the linear alternator of 0.67%, an operating frequency of 52 Hz, a load made of 95.3-µF power factor correcting capacitor, a rectifier and a constant-voltage electronic load set at 13 V. The linear relationship between the mechanical stroke and output voltage and current is shown at the bottom right curve, where different points on the curve correspond to different load voltages. In Fig. 4, the output voltage and current are not sinusoidal in shape because of the non-linear nature of the load used on the linear alternator. This non-linear constant-voltage electric load gives rise to odd harmonics at decreasing amplitudes in the output voltage and current signals. These harmonics are not propagated significantly into the mechanical stroke or dynamic pressure signals. The output current and voltage signals acquired with the electronic load used in this work are contrasted to those obtained using a linear (resistive) load in [6]. Generally, the piston s velocity, u, can be estimated by time-differentiation of the piston stroke. The mechanical stroke amplitude S is written as S = B sin ( t + ), (1) where B and are the amplitude and phase of the mechanical stroke signal, respectively and is the angular frequency. Then, the piston velocity amplitude, u, can be written as u = B cos ( t + ) = B sin ( t + +90), (2) allowing analytical estimation of the piston velocity from the mechanical stroke signal, without numerical differentiation. The acoustic impedance, Z, at the linear alternator s can be estimated as Z = P res/(ua), (3) where Pres is the resonator pressure and A is the alternator piston s area. The output electric power of the linear alternator, PLA, is calculated as the dot product of the output current, ILA, and the output voltage signal, VLA, over a large integer large number of cycles P LA =<I LA.V LA>. (4) The acoustic power delivered to the linear alternator, ELA, can be estimated as the dot product of resonator pressure and the alternator s piston s velocity over a larger integer number of cycles E LA = <P res.ua>. (5) ICSV23, Athens (Greece), July

6 The acoustic-to-electric conversion efficiency, LA, of the linear alternator can be estimated as: LA = P LA/E LA, (6) and the mechanical motion loss can be estimated as mechanical-motion loss = R m u 2, (7) where Rm is the damping coefficient of the linear alternator (4.55 N.S/m). Similarly, the Ohmic loss can be estimated as: Ohmic loss = I LA 2 R e, (8) where Re is the stator resistance of the linear alternator (6.72 ). The fluid-seal loss at the linear alternator s piston can be estimated as: [10] fluid seal loss = d 3 P max 2 /12µL, (9) where Pmax is the maximum root mean square difference between the pressure difference across the linear alternator s piston, µ is the dynamic gas viscosity, L is the seal length (12.7 mm), d is the piston diameter (2 inch) and is the piston s seal gap (19.1 m). Using equations [1-9] above, the performance indices are obtained in real time using LabView software and are presented in Table 1. Linear alternator mechanical stroke, mm (peak-peak) Acoustic driver mechanical stroke, mm (peak-peak) Acoustic-driver to linear-alternator stroke ratio Linear alternator output electric power, W Linear alternator acoustic-to-electric conversion efficiency, % Table1: Performance indices of the reference experiment Angle between resonator pressure and piston s velocity, degree Linear alternator 0.43 mechanical-motion loss, W 1.23 Linear alternator Ohmic loss, W Ratio of mechanical-motion loss to 0.28 Ohmic loss 52.5 Linear alternator fluid-seal loss, W This concludes the second objective of this work, where a reference experiment is presented at conditions typical in thermoacoustic power conversion conditions, with simultaneous realization of the following factors: 1- travelling-wave mode (at 52 Hz); 2- the linear alternator is operating close to its mechanical resonance frequency of 56 Hz; 3- the linear alternator is driving a constant voltage load (better simulation of real load imposed by the grid); 3- the linear alternator is operating close to impedance matching condition with the source (ratio of acoustic-driver stroke to linear-alternator stroke is 1.23); 4- the linear alternator is operated at nearly balanced mechanical/electric losses (mechanical and electric losses are same order of magnitude) and 5- the linear alternator is operated at electric resonance (the 95.3-µF capacitor balances the effective inductance of the alternator s coil at the mechanical stroke amplitude observed [6]). 3.2 Effects of the operating conditions on the linear alternator performance indices This section presents and discusses the effects of the operating frequency, mean gas pressure and gas mixture composition on the linear alternator performance indices, which is the third objective of this work. The performance indices are presented for a frequency range of Hz, a mean gas pressure of bar, a helium molar fraction in the range of 0% to 100% in helium/argon working gas mixture. This concludes the third objective of this work Effects of operating frequency The frequency range presented in Fig. 5 covers the range encountered in impedance matching operation, pure travelling-wave mode operation and operation at the mechanical resonance frequency of the linear alternator. The variation in mechanical stroke at a constant imposed voltage occurs because the proportionality constant between the mechanical stroke and the generated voltage is a function of the operating frequency and the mean gas pressure. The proportionality constant increases linearly with the operating frequency, even across the mechanical resonance frequency point (56 Hz 6 ICSV23, Athens (Greece), July 2016

7 in this work). The increase in mechanical stroke results in an increase in mechanical-motion loss as well (Eq. 7). Figure 5: Linear alternator performance for a range of operating frequency (45 to 65 Hz). The mean gas pressure, the gas mixture composition, and the load voltage are the same as in Fig. 4, except that the dynamic pressure ratio at the inlet of the linear alternator is 0.3%. As the frequency increases, the linear alternator moves towards a point in which the pressure difference across the sides of the alternator s piston (enclosure pressure and resonator pressure) is a maximum, causing the acoustic-to-electric conversion efficiency to increase and the generated current to increase as well. The later causes the Ohmic loss to increase Effects of mean gas pressure Operating at different mean gas pressures (Fig. 6) causes the linear alternator to face different acoustic impedances ( C), where and C are the density and speed of sound in the working gas, respectively. The acoustic impedance increases with the mean gas pressure causing a reduction in the mechanical stroke. Because the linear alternator is facing a constant-voltage load with a decreasing mechanical stroke, the output alternator s current exercises a non-monotonic behaviour, giving rise to a non-monotonic Ohmic loss as well. The negative impact of the decrease in the mechanical stroke overcomes the benefit from the decrease in Ohmic loss causing the acoustic-to-electric conversion efficiency to decrease at a low rate. Figure 6: Linear alternator performance for a range of mean gas pressures (10 to 30 bar). The operating frequency, the gas mixture composition, and the load voltage are the same as in Fig. 4, except that the dynamic pressure ratio at the inlet of the linear alternator is 0.3% Effects of working gas mixture composition In Fig. 7, the mechanical stroke is nearly constant, since the output voltage is set to be constant. The proportionality between the generated voltage and mechanical stroke is not affected by changes in mean gas pressure or frequency. This yields a nearly-constant mechanical motion loss. Figure 7: Linear alternator performance for a range of helium molar fractions (0% to 100%) in a helium/argon working gas mixture. The operating frequency, mean gas pressure and the load voltage are the same as in Fig. 4, except that the dynamic pressure ratio at the inlet of the linear alternator is 0.3%. ICSV23, Athens (Greece), July

8 The acoustic impedance ( C) is the product of the speed of sound (maximum at 100% helium molar fraction) and the gas density (maximum at 100% argon molar fraction). In the range of low acoustic impedance (helium molar fraction in the range of 10-50%), the system is severely mismatched with the source of acoustic power and the acoustic-to-electric conversion is inefficient, yielding low output current, low Ohmic loss and low acoustic-to-electric conversion efficiency with respect to larger acoustic impedances at either pure helium or pure argon conditions. A similar behaviour is observed in [7]. 4. Summary and conclusions A setup designed and built to test linear alternators under conditions similar to those encountered in thermoacoustic power conversion is presented and the results of a reference experiment are presented. A methodology to prevent over-stroking on a time base fast-enough of thermoacoustic purposes is presented and tested. Quantitative data on how the mechanical stroke, acoustic-to-electric conversion efficiency, mechanical motion loss and Ohmic loss are affected by the operating frequency, the mean gas pressure and the working gas mixture composition is provided and discussed. Under the conditions employed, the proportionality constant between the mechanical stroke and the generated voltage is found to increase linearly with the operating frequency (even across the mechanical resonance frequency point) and to decrease linearly with the mean gas pressure and to be almost insensitive to the working gas mixture composition used. The effects of the acoustic impedance mismatch between the linear alternator and the source of acoustic power on the mechanical stroke and the acoustic-to-electric conversion efficiency are quantified. 5. Acknowledgements This publication has been produced with the financial assistance of the European Union. The contents of this document are the sole responsibility of the authors and can under no circumstances be regarded as reflecting the position of the European Union. REFERENCES 1 Wang, K., Sun, D., Zhang, J., Xu, Y., Zou, J., Wu, K., Qiu, L. and Huang, Z. Operating characteristics and performance improvements of a 500-W traveling-wave thermoacoustic electric generator, Journal of Applied Energy, 160, , (2015). 2 W, Z., Yu, G., Zhang, L., Dai, W. and Luo, E. Development of a 3 kw double-acting thermoacoustic Stirling electric generator, Journal of Applied Energy, 136, , (2014). 3 Wu, Z., Dai, W., Man, M. and Luo, E. A solar-powered traveling-wave thermoacoustic electricity generator, Journal of Solar Energy, 86(9), , (2012). 4 Corey, J., and Martin, J. United States Patent US Patent 6,604,363 B2, Matching an acoustic driver to an acoustic load in an acoustic resonant system, (2003). 5 Abdou, M., Abdelwahed, A.Y., Ibrahim, A. H. and Abdel-Rahman, E. An experimental setup to test linear alternators: design, operation and preliminary results, Proceedings of the 22 nd International Congress on Sound and Vibration, Florence, Italy, July, (2015). 6 Abdelwahed, A. Y., Ibrahim, A. H. and Abdel-Rahman, E. Experimental investigation of the effects of mechanical stroke on the acoustic impedance of linear alternators under thermoacoustic-power-conversion conditions, Proceedings of the 23 rd International Congress on Sound and Vibration, Athens, Greece, July, (2016). 7 Abdelwahed, A. Y., Ibrahim, A. H. and Abdel-Rahman, E. Performance of linear alternators with passive linear and non-linear loads under thermoacoustic-power-conversion conditions, Proceedings of the 23 rd International Congress on Sound and Vibration, Athens, Greece, July, (2016). 8 Ibrahim, A. H., Abdelwahed, A. Y. and Abdel-Rahman, E. Sensitivity analysis of linear alternator performance indices under thermoacoustic-power-conversion conditions, Proceedings of the 23 rd International Congress on Sound and Vibration, Athens, Greece, July, (2016). 9 Tijani, M. E. H., Zeegres, J. C. H. and de Waele, A. T. A. M. Prandtl number and thermoacoustic refrigerators, The Journal of the Acoustical Society of America, 112(1), , (2002). 10 Gonen, E. and Grossman, G. Gap seal dissipation in linear alternators, The Journal of the Acoustical Society of America, 173(4), , (2015). 8 ICSV23, Athens (Greece), July 2016