تحلیل حساسیت برای توابع هدف توان، بازده‏، اتلاف حرارتی و هزینة سیال عامل بر مبنای متغیرهای ورودی در ‏موتور استرلینگ

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشکده مهندسی مکانیک، دانشگاه سمنان، سمنان، ایران

2 شرکت تحقیق، طراحی و تولید موتور ایران‌خودرو (ایپکو)، تهران، ایران

10.22034/er.2023.2006618.1008

چکیده

موتور استرلینگ یک موتور برونسوز است که کار مکانیکی را به برق تبدیل می‌کند. موتور استرلینگ برای کار کردن نیاز به سیال عامل دارد و معمولاً از هوا، هلیوم، هیدروژن، نیتروژن و غیره استفاده می‌شود. در میان سیال عامل‌های نام برده شده فقط هوا رایگان است اما متأسفانه نسبت به سیال عامل‌های دیگر توان و بازدهی ضعیف‌تری دارد، پیش‌بینی می‌شود با ترکیب دو سیال عامل مانند هوا و هلیوم بتوان با هزینه کمتر توان و بازدهی مورد نظر دریافت کرد. اما برای بررسی این موضوع نیاز است تا به تحلیل حساسیت متغیرهای مختلف ورودی بر روی متغیرهای خروجی پرداخته شود. از این‌رو در این مطالعه به بررسی مدل ترمودینامیک غیرایده‌ال پرداخته است و نتایج الگوی ارائه شده با آزمایش تجربی صحه‌‏گذاری می‌شود. سپس با کمک نرم­‌افزار دیزاین اکسپرت، 1260 آزمون طراحی شده و درنهایت، تأثیر تغییرات متغیرهای ورودی مانند سرعت، فشار تزریق گاز، دما و درصد هلیوم بر روی متغیرهای خروجی مانند توان، بازدهی، اتلاف حرارتی و هزینه بررسی شد. در ادامه مشخص شد هزینه فقط تابعی از فشار تزریق گاز و مقدار درصد ترکیب سیال‌ها است. همچنین نتایج نشان دادند که با افزایش دما، فشار، سرعت و درصد هلیم، توان بترتیب 189 درصد، 178 درصد، 82 درصد و 54 درصد افزایش می‌یابد. با افزایش دما، سرعت و فشار، بازدهی بترتیب 42 درصد افزایش، 23 درصد کاهش و 17 درصد کاهش می‌یابد. با افزایش دما، سرعت و فشار، اتلاف حرارتی بترتیب 85 درصد، 71 درصد و 357 درصد افزایش داشت.

کلیدواژه‌ها


عنوان مقاله [English]

Sensitivity analysis for objectives of power, efficiency, heat loss, and working fluid cost based on input parameters in the Stirling engine

نویسندگان [English]

  • Bahram Vaziri 1
  • Mohammad Azadi 1
  • Mojtaba Biglari 1
  • Seyed Navid Madani 2
1 Faculty of Mechanical Engineering, Semnan University, Semnan, Iran
2 Irankhodro Powertrain Company (IPCo), Tehran, Iran
چکیده [English]

The Stirling engine is a combustion engine that converts mechanical work into electricity. Stirling engine needs a working fluid to work and usually, air, helium, hydrogen, nitrogen, etc. are used. Among the mentioned operating fluids, only air is free, but unfortunately, it has lower power and efficiency compared to other working fluids. It is expected that the desired power and efficiency can be obtained at a lower cost by combining two working fluids such as air and helium. However, to check this issue, it is needed to analyze the sensitivity of different input parameters on the outputs. Therefore, in this study, the non-ideal thermodynamic model was investigated, and the results of the presented model were validated by experiments, and then with the help of Design Expert software, 1260 designs were considered. Finally, the effect of changes in input parameters such as the speed, gas injection pressure, temperature, and helium percentage on outputs such as power, efficiency, heat loss, and cost were investigated. It was found that the cost was only a function of the gas injection pressure and the percentage of the fluid composition. Moreover, the results showed that with the increase of the temperature, pressure, speed, and percentage of helium, the power increased by 189%, 178%, 82%, and 54%, respectively. With increasing the temperature, speed, and pressure, efficiency increased by 42%, decreased by 23%, and decreased by 17%, respectively. With the increase in the temperature, speed, and pressure, the heat loss increased by 85%, 71%, and 357%, respectively.

کلیدواژه‌ها [English]

  • Stirling Engine
  • Sensitivity Analysis
  • Power
  • Efficiency
  • Heat Loss
  • Working Fluid Cost
[1] Hooshang M. Improvement of gas displacer control parameters in solar Stirling engine to increase performance, MSc thesis, Faculty of New Science and Technology, Iran, 2013. [In Persian]
[2] Thimsen D. Stirling Engine Assessment, Electric Power Research Institute, Palo Alto, CA, Technical Report 2002;1007317.
[3] García MT, Trujillo EC, Godiño JAV, Martínez DS. Thermodynamic model for performance analysis of a Stirling engine prototype. Energies. 2018;11. doi: 10.3390/en11102655
[4] Topgül T, Okur M, Şahin F, Çınar C. Experimental investigation of the effects of hot-end and cold-end connection on the performance of a gamma type Stirling engine. Engineering Science and Technology, an International Journal. 2022;36. doi: 10.1016/j.jestch.2022.101152
[5] Kim DJ, Park JS, Sim K. Development and performance measurements of a 2.5 kW-class free-piston stirling converter with detailed design and fabrication processes. Energy Reports. 2022;8,15011–15026. doi: 10.1016/j.egyr.2022.11.046
[6] Bataineh KM, Maqableh MF. A new numerical thermodynamic model for a beta-type Stirling engine with a rhombic drive. Thermal Science and Engineering Progress. 2022;28. doi: 10.1016/j.tsep.2021.101071
[7] Yang HS, Cheng CH, Ali MA. Performance and operating modes of a thermal-lag Stirling engine with a flywheel. Applied Thermal Engineering. 2022;205. doi: 10.1016/j.applthermaleng.2022.118061
[8] Thomas S, Barth EJ. Active Stirling Thermocompressor: Modelling and effects of controlled displacer motion profile on work output. Applied Energy. 2022;327. doi: 10.1016/j.apenergy.2022.120084
[9] Sripakagorn A, Srikam C. Design and performance of a moderate temperature difference Stirling engine. Renewable Energy. 2011;36:1728–1733. doi: 10.1016/j.renene.2010.12.010
[10] Hooshang M, Askari Moghadam R, Alizadeh Nia S, Masouleh MT. Optimization of Stirling engine design parameters using neural networks. Renewable Energy. 2015;74:855–866. doi: 10.1016/j.renene.2014.09.012
[11] Toghyani S, Kasaeian A, Hashemabadi SH, Salimi M. Multi-objective optimization of GPU3 Stirling engine using third order analysis. Energy Conversion and Management. 2014;87:521–529. doi: 10.1016/j.enconman.2014.06.066
[12] Ahmadi MH, Sayyaadi H, Dehghani S, Hosseinzade H. Designing a solar powered Stirling heat engine based on multiple criteria: Maximized thermal efficiency and power. Energy Conversion and Management. 2013;75:282–291. doi: 10.1016/j.enconman.2013.06.025
[13] Cheng CH, Yang HS. Optimization of geometrical parameters for Stirling engines based on theoretical analysis. Applied Energy. 2012;92:395–405. doi: 10.1016/j.apenergy.2011.11.046
[14] Patel V, Savsani V. Multi-objective optimization of a Stirling heat engine using TS-TLBO (tutorial training and self learning inspired teaching-learning based optimization) algorithm. Energy. 2016;95:528–541. doi: 10.1016/j.energy.2015.12.030
[15] Ahmadi MH, Hosseinzade H, Sayyaadi H, Mohammadi AH, Kimiaghalam F. Application of the multi-objective optimization method for designing a powered Stirling heat engine: Design with maximized power, thermal efficiency and minimized pressure loss. Renewable Energy. 2013;60:313–322. doi: 10.1016/j.renene.2013.05.005
[16] Punnathanam V, Kotecha P. Effective multi-objective optimization of Stirling engine systems. Applied Thermal Engineering. 2016;108,61–276. doi: 10.1016/j.applthermaleng.2016.07.029
[17] Hosseinzade H, Sayyaadi H. CAFS: The Combined Adiabatic-Finite Speed thermal model for simulation and optimization of Stirling engines. Energy Conversion and Management. 2015;91:32–53. doi: 10.1016/j.enconman.2014.11.049.
[18] Hassanzadeh E, aliehyaei M, Jafari Mehrabadi S, Mohammadi A, Mazaheri H. Experimental investigation on the gamma model Stirling engine for cooling production using various gases. The Journal of Engine Research. 2020;59:17-28. [In Persian]
[19] Vaziri B, Azadi M, Biglari M, Madani SN. Sensitivity analysis of dependency of working fluid thermo-dynamics properties to temperature on performance of Gama-type Stirling engine. The Journal of Engine Research. 2019,54:3-12. [In Persian]
[20] Shufat SA, Kurt E, Cinar C, Aksoy F, Hançerlioğulları A, Solmaz H. Exploration of a Stirling engine and generator combination for air and helium media. Applied Thermal Engineering. 2019;150:738–749. doi: 10.1016/j.applthermaleng.2019.01.053
[21] Ahmed F, Zhu S, Yu G, Luo E. A potent numerical model coupled with multi-objective NSGA-II algorithm for the optimal design of Stirling engine. Energy. 2022;247. doi: 10.1016/j.energy.2022.123468
[22] Yang HS, Aon Ali M, Venkata Ravi Teja K, Yen YF. Parametric study and design optimization of a kW-class beta-type Stirling engine. Applied Thermal Engineering. 2022;215. doi: 10.1016/j.applthermaleng.2022.119010
[23] Alfarawi S, Al-Dadah R, Mahmoud S. Enhanced thermodynamic modelling of a gamma-type Stirling engine. Applied Thermal Engineering. 2016;106:1380–1390. doi: 10.1016/j.applthermaleng.2016.06.145.
[24] Vaziri B, Azadi M, Biglari M, Madani SN. Performance study of helium-air hybrid Stirling engine under parameters effect of temperature , pressure , rotational speed and working fluid composition. Applied Energy Conversion. 2021;1. doi: 10.22077/aec.2021.4711.1007. [In Persian]
[25] Ahmadi MH, Ahmadi MA, Pourfayaz F. Thermal models for analysis of performance of Stirling engine: A review. Renewable and Sustainable Energy Reviews. 2017;68:168–184, doi: 10.1016/j.rser.2016.09.033.
[26] Hosseinzade H, Sayyaadi H, Babaelahi M. A new closed-form analytical thermal model for simulating Stirling engines based on polytropic-finite speed thermodynamics. Energy Conversion and Management. 2015;90:395–408. doi: 10.1016/j.enconman.2014.11.043
[27] Babaelahi M, Sayyaadi H. Analytical closed-form model for predicting the power and efficiency of Stirling engines based on a comprehensive numerical model and the genetic programming. Energy. 2016;98:324–339. doi: 10.1016/j.energy.2016.01.031
[28] Sayyaadi H, Ghasemi H. A novel second-order thermal model of Stirling engines with consideration of losses due to the speed of the crack system. Energy Conversion and Management. 2018;505–521. doi: 10.1016/j.enconman.2018.05.021
[29] Babaelahi M, Sayyaadi H. Modified PSVL: A second order model for thermal simulation of Stirling engines based on convective-polytropic heat transfer of working spaces. Applied Thermal Engineering. 2015;85:340–355. doi: 10.1016/j.applthermaleng.2015.03.018
[30] Ahadi F, Azadi M, Biglari M, Madani SN. Study of coating effects on the performance of Stirling engine by non-ideal adiabatic thermodynamics modeling. Energy Reports. 2021;7:3688–3702. doi: 10.1016/j.egyr.2021.06.063
[31] Vaziri B. Optimization of working fluid type and combination percent in order to improve power and efficiency of Gamma Stirling Engine, MSc thesis, Semnan University, Iran, 2020. [In Persian]
[32] Li R, Grosu L, Li W. New polytropic model to predict the performance of beta and gamma type Stirling engine. Energy. 2017;12862–76. doi: 10.1016/j.energy.2017.04.001
[33] Cheng CH, Yang HS, Keong L. Theoretical and experimental study of a 300-W beta-type Stirling engine. Energy. 2013;59:590–599. doi: 10.1016/j.energy.2013.06.060