We have to rewrite the previous equation (to include ηK) using the term (+h1 – h1) to: Qadd = h3 – h2 = h3 – h1 – (h2s – h1)/ηK [kJ/kg]. Moreover we know, that the compressor receives gas (point 1) at the figure: The heat capacity ratio, , for helium is equal to =cp/cv=1.66. (T3-T2s), but in this case we do not know the temperature (T2s) at the outlet of the compressor. The turbine outlet temperature of the gas, T4,is, can be calculated using the same p, V, T Relation as in 2) but between states 3 and 4:eval(ez_write_tag([[300,250],'nuclear_power_net-medrectangle-4','ezslot_7',104,'0','0'])); From the previous equation follows that the outlet temperature of the gas, T4,is, is: The work done by gas turbine in the isentropic expansion is then: WT,s = cp (T3 – T4s) = 5200 x (1190 – 839) = 1.825 MJ/kg. Glasstone, Sesonske. Entire website is based on our own personal perspectives, and do not represent the views of any company of nuclear industry. 2) You may not distribute or commercially exploit the content, especially on another website. Our Website follows all legal requirements to protect your privacy. Addison-Wesley Pub. (424-299)/0.87 = 4.633 MJ/kg – 0.747 MJ/kg = 3.886 MJ/kgeval(ez_write_tag([[300,250],'nuclear_power_net-box-3','ezslot_2',103,'0','0'])); The work done on the gas by the compressor in the isentropic compression process is: WC,s = cp (T2s – T1) = 5200 x (424 – 299) = 0.650 MJ/kg. In this turbine the high-pressure stage receives gas (point 3 at the figure) from a heat exchanger: and exhaust it to another heat exchanger, where the outlet pressure is (point 4): Thus the compressor pressure ratio is equal to PR = 2.41. Finally, the thermal efficiency including isentropic turbine/compressor efficiency is: ηth,real = (WT,real – WC,real) / Qadd = (1.661 – 0.747) / 3.886 = 0.235 = 23.5%. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2. DOE Fundamentals Handbook, Volume 1 and 2. In this case assume a helium gas turbine with single compressor and single turbine arrangement. This website does not use any proprietary data. Glasstone, Sesonske. DOE Fundamentals Handbook, Volume 1 and 2. The non-ideal processes of the Brayton Cycle points out a problem; that the work used to raise entropy is thus a leak in the amount of work that could have been used for useful mechanical energy. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2. 8-1-5 [heat-8000kW] A gas turbine power plant operates on a simple Brayton cycle with air as the working fluid. From the first law of thermodynamics, the net heat added is given by Qadd,ex = H3 – H2 [kJ] or Qadd = Cp. The real work done on the gas by the compressor in the adiabatic compression is then: WC,real = cp (T2s – T1). Nuclear and Particle Physics. Thermal Engineering, Copyright 2020 Thermal Engineering | All Rights Reserved |, What is Example of Rankine Cycle – Problem with Solution - Definition, What is Diesel Cycle – Problem with Solution - Definition, What is Otto Cycle - Problem with Solution - Definition, What is Four Stroke Diesel Engine – Definition, What is Boiler and Condenser Pressure – Rankine Cycle – Definition, the heat added by the heat exchanger (between 2 → 3), the compressor outlet temperature of the gas (T, the real work done on this compressor, when the isentropic compressor efficiency is η, the turbine outlet temperature of the gas (T, the real work done by this turbine, when the isentropic turbine efficiency is η. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983). W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1. 1/M (molar weight of helium) = 20.8 x 4.10-3 = 5200 J/kg K. Qadd = cp(T3-T1) – (cp(T2s-T1)/ηK) = 5200. We assume no responsibility for consequences which may arise from the use of information from this website. One of key parameters of such engines is the maximum turbine inlet temperature and the compressor pressure ratio (PR = p2/p1) which determines the thermal efficiency of such engine. Physics of Nuclear Kinetics. Then we will calculate the temperature, T2s, using p, V, T Relation (from Ideal Gas Law) for adiabatic process between (1 → 2). Entire website is based on our own personal perspectives, and do not represent the views of any company of nuclear industry. It explains how we use cookies (and other locally stored data technologies), how third-party cookies are used on our Website, and how you can manage your cookie options. ηC = 5200 x (424 – 299) / 0.87 = 0.747 MJ/kg. Brayton Cycle – Turbine Engine. The Cookies Statement is part of our Privacy Policy. Calculate for the closed Brayton cycle key thermodynamic parameters such as temperatures, pressures and heat transfers. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4. If you want to get in touch with us, please do not hesitate to contact us via e-mail: The information contained in this website is for general information purposes only. From the previous equation follows that the compressor outlet temperature, T2s, is: Cv = 3/2R = 12.5 J/mol K and Cp = Cv + R = 5/2R = 20.8 J/mol K. We transfer the specific heat capacities into units of J/kg K via: cp = Cp . The real work done on the gas by the compressor in the adiabatic compression is then: WC,real = cp (T2s – T1). Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317, W.S.C. Introductory Nuclear Physics, 3rd Edition, Wiley, 1987, ISBN: 978-0471805533, G.R.Keepin. In a Brayton Refrigeration Cycle, air is compressed adiabatically from 100 kPa and 540 K to 500 kPa. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317, W.S.C. The mention of names of specific companies or products does not imply any intention to infringe their proprietary rights. This website was founded as a non-profit project, build entirely by a group of nuclear engineers. Cycle A is an ideal Brayton Cycle. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4. We have to rewrite the previous equation (to include ηK) using the term (+h1 – h1) to: Qadd = h3 – h2 = h3 – h1 – (h2s – h1)/ηK [kJ/kg]. Air enters the internally reversible turbine at 510 K and expands adiabatically to 100 kPa. We hope, this article, Example of Brayton Cycle – Problem with Solution, helps you. Homework # 1 (Gas Power Cycles Do problems (from the 6th edition): 9-23 (Carnot Cycle) 9-38 (Otto Cycle) 9-62 (Diesel Cycle) 9-77 (Ericsson Cycle) 9-98 (Simple Brayton Cycle) 9-105 (Simple Brayton Cycle) Problem 9-23: Carnot cycle with the specified temperature limits is considered. In this case assume a helium gas turbine with single compressor and single turbine arrangement. 1) You may use almost everything for non-commercial and educational use. Main purpose of this website is to help the public to learn some interesting and important information about thermal engineering. 10E-2 : Brayton Refrigeration Cycle : 8 pts. If you want to get in touch with us, please do not hesitate to contact us via e-mail: Example of Brayton Cycle – Problem with Solution. Moreover we know, that the compressor receives gas (point 1) at the figure: The heat capacity ratio, , for helium is equal to =cp/cv=1.66. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467, Kenneth S. Krane. Let assume the closed Brayton cycle, which is the one of most common thermodynamic cycles that can be found in modern gas turbine engines. Copyright 2020 Nuclear Power for Everybody | All Rights Reserved | Powered by. Engineering Thermodynamics: Chapter-8 Problems. Main purpose of this project is to help the public learn some interesting and important information about the peaceful uses of nuclear energy. Example Problem with Complete Solution . Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988. Williams. In this case assume a helium gas turbine with single compressor and single turbine arrangement. In this equation the factor for helium is equal to =cp/cv=1.66. Our Privacy Policy is a legal statement that explains what kind of information about you we collect, when you visit our Website. The mention of names of specific companies or products does not imply any intention to infringe their proprietary rights. January 1993. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988. U.S. Department of Energy, Nuclear Physics and Reactor Theory. Main purpose of this project is to help the public learn some interesting and important information about engineering and thermal engineering. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4. For Everybody | all rights Reserved | Powered by T3-T2s ), but in case! Cycle is to help the public learn some interesting and important information about peaceful. Helps you Reserved | Powered by by public relations departments and allowed for.. Reactor Engineering: Reactor Systems Engineering, 3d ed., Prentice-Hall, 2001 ISBN! ) / 0.87 = 0.747 MJ/kg views of any company of Nuclear engineers about thermal Engineering is... Information about you we collect, when you visit our website, us... 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