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An Analysis of the Brayton Cycle As a Cryogenic Refrigerator

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An Analysis of the Brayton Cycle As a Cryogenic Refrigerator jbrary, E-01 Admin. BJdg. OCT 7 1968 NBS 366 An Analysis of the Brayton Cycle As a Cryogenic Refrigerator ITATIONAL BURSAL' OF iTANDABD8 LIBRABT MAR 6 J973 V* 0F c J* 0a <5 Q \ v S. DEPARTMENT OF COMMERCE in Q National Bureau of Standards %. *^CAU 0? * : NATIONAL BUREAU OF STANDARDS The National Bureau of Standards 1 was established by an act of Congress March 3, 1901. Today, in addition to serving as the Nation's central measurement laboratory, the Bureau is a principal focal point in the Federal Government for assuring maxi- mum application of the physical and engineering sciences to the advancement of tech- nology in industry and commerce. To this end the Bureau conducts research and provides central national services in three broad program areas and provides cen- tral national services in a fourth. These are: (1) basic measurements and standards, (2) materials measurements and standards, (3) technological measurements and standards, and (4) transfer of technology. The Bureau comprises the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology, and the Center for Radiation Research. THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United States of a complete and consistent system of physical measurement, coor- dinates that system with the measurement systems of other nations, and furnishes essential services leading to accurate and uniform physical measurements throughout the Nation's scientific community, industry, and commerce. The Institute consists of an Office of Standard Reference Data and a group of divisions organized by the following areas of science and engineering Applied Mathematics—Electricity—Metrology—Mechanics—Heat—Atomic Phys- 2 2 ics—Cryogenics-—Radio Physics-—Radio Engineering —Astrophysics —Time and Frequency. 2 THE INSTITUTE FOR MATERIALS RESEARCH conducts materials research lead- ing to methods, standards of measurement, and data needed by industry, commerce, educational institutions, and government. The Institute also provides advisory and research services to other government agencies. The Institute consists of an Office of Standard Reference Materials and a group of divisions organized by the following areas of materials research: Analytical Chemistry—Polymers—Metallurgy — Inorganic Materials — Physical Chemistry. THE INSTITUTE FOR APPLIED TECHNOLOGY provides for the creation of appro- priate opportunities for the use and application of technology within the Federal Gov- ernment and within the civilian sector of American industry. The primary functions of the Institute may be broadly classified as programs relating to technological meas- urements and standards and techniques for the transfer of technology. The Institute consists of a Clearinghouse for Scientific and Technical Information, 3 a Center for Computer Sciences and Technology, and a group of technical divisions and offices organized by the following fields of technology: Building Research—Electronic Instrumentation — Technical Analysis — Product Evaluation—Invention and Innovation— Weights and Measures — Engineering Standards—Vehicle Systems Research. THE CENTER FOR RADIATION RESEARCH engages in research, measurement, and application of radiation to the solution of Bureau mission problems and the problems of other agencies and institutions. The Center for Radiation Research con- sists of the following divisions: Reactor Radiation—Linac Radiation—Applied Radiation—Nuclear Radiation. 'Headquarters and Laboratories at fiakhersbuiK, Maryland, unless otherwise noted; mailing address Washington, D. C. 20234. rado 80302. Royal Road, Springfield, Virginia 22151. UNITED STATES DEPARTMENT OF COMMERCE C. R. Smith, Secretary NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director NBS TECHNICAL NOTE 366 ISSUED AUGUST 1968 AN ANALYSIS OF THE BRAYTON CYCLE AS A CRYOGENIC REFRIGERATOR R. C. MUHLENHAUPT AND T. R. STROBRIDGE Cryogenics Division Institute for Basic Standards National Bureau of Standards Boulder, Colorado 80302 NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be listed or referred to in the open literature. For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 20402 Price $1.25 TABLE OF CONTENTS Page ABSTRACT 1 1. Introduction 1 2. Refrigerants „ . 2 3. Nomenclature List . 2 4. Discussion of Process 4 5. Parameter Values 4 6. Ideal Gas Calculations 8 7. Real Gas Calculations 15 8. Pressure Drop „ 16 9. Results 18 10. Discussion of Results 19 11. Conclusions 30 12. References 33 13. Appendix 34 List of Figures Figure 1. Schematic Flow Diagram of the Modified Brayton Refrigeration Cycle „ 5 Figure 2. Temperature-Entropy Diagram of the Modified Brayton Refrigeration Cycle 6 Figure 3. Temperature-Entropy Diagram of an Ideal Brayton Refrigerator 7 in TABLE OF CONTENTS (CONTINUED) Page Figure 4. Schematic Diagram of the Brayton Refrigerator Performance with an Ideal Gas as the Working Fluid . 12 Figure 5. Schematic Diagram of the Brayton Refrigerator Performance Showing a Double Minimum Curve ..... 22 Figure 6. Schematic Diagram of Enthalpy Difference as a Function of High Pressure For Parahydrogen 24 Figure 7. Schematic Diagram of Brayton Refrigerator Performance with an Ideal Gas as the Working Fluid - Single and Double Minimum Curves . 25 Figure 8. Brayton Refrigerator Performance - Helium Refrigerant - 300 K Cycle Inlet Temperature - 100% Expander Efficiency - No Pressure Drop 39 Figure 9« Brayton Refrigerator Performance - Helium Refrigerant - 300 K Cycle Inlet Temperature - 90% Expander Efficiency - No Pressure Drop 40 Figure 10. Brayton Refrigerator Performance - Helium Refrigerant - 300 K Cycle Inlet Temperature - 70% Expander Efficiency - No Pressure Drop ...... 41 Figure 11. Brayton Refrigerator Performance - Helium Refrigerant - 300 K Cycle Inlet Temperature - 50% Expander Efficiency - No Pressure Drop ...... 42 Figure 12. Brayton Refrigerator Performance - Helium Refrigerant - 77. 36 K Cycle Inlet Temperature - 100% Expander Efficiency - No Pressure Drop ..... 43 Figure 13. Brayton Refrigerator Performance - Helium Refrigerant - 77. 36 K Cycle Inlet Temperature - 90% Expander Efficiency - No Pressure Drop 44 Figure 14. Brayton Refrigerator Performance - Helium Refrigerant - 77. 36 K Cycle Inlet Temperature - 70% Expander Efficiency - No Pressure Drop 45 IV TABLE OF CONTENTS (CONTINUED) Page Figure 15. Brayton Refrigerator Performance - Helium Refrigerant - 77. 36 K Cycle Inlet Temperature - 50% Expander Efficiency - No Pressure Drop . 46 Figure 16. Brayton Refrigerator Performance - Helium Refrigerant - 20. 27 K Cycle Inlet Temperature - 100% Expander Efficiency - No Pressure Drop .... 47 Figure 17. Brayton Refrigerator Performance - Helium Refrigerant - 20. 27 K Cycle Inlet Temperature - 90% Expander Efficiency - No Pressure Drop ..... 48 Figure 18. Brayton Refrigerator Performance - Helium Refrigerant - 20. 27 K Cycle Inlet Temperature - 70% Expander Efficiency - No Pressure Drop 49 Figure 19. Brayton Refrigerator Performance - Helium Refrigerant - 20. 27 K Cycle Inlet Temperature - 50% Expander Efficiency - No Pressure Drop ..... 50 Figure 20. Brayton Refrigerator Performance - Parahydrogen Refrigerant - 300 K Cycle Inlet Temperature - 100% Expander Efficiency - No Pressure Drop .... 51 Figure 21. Brayton Refrigerator Performance - Parahydrogen Refrigerant - 300 K Cycle Inlet Temperature - 90% Expander Efficiency - No Pressure Drop 52 Figure 22. Brayton Refrigerator Performance - Parahydrogen Refrigerant - 300 K Cycle Inlet Temperature - 70% Expander Efficiency - No Pressure Drop 53 Figure 23. Brayton Refrigerator Performance - Parahydrogen Refrigerant - 300 K Cycle Inlet Temperature - 50% Expander Efficiency - No Pressure Drop 54 Figure 24. Brayton Refrigerator Performance - Parahydrogen Refrigerant - 77. 36 K Cycle Inlet Temperature - 100% Expander Efficiency - No Pressure Drop .... 55 TABLE OF CONTENTS (CONTINUED) Page Figure 25. Brayton Refrigerator Performance - Para hydro gen Refrigerant - 77. 36 K Cycle Inlet Temperature - 90% Expander Efficiency - No Pressure Drop 56 Figure 26. Brayton Refrigerator Performance - Parahydrogen Refrigerant - 77. 36 K Cycle Inlet Temperature - 70% Expander Efficiency - No Pressure Drop 57 Figure 27. Brayton Refrigerator Performance - Parahydrogen Refrigerant - 77. 36 K Cycle Inlet Temperature - 50% Expander Efficiency - No Pressure Drop 58 Figure 28. Brayton Refrigerator Performance - Nitrogen Refrigerant - 300 K Cycle Inlet Temperature - 100% Expander Efficiency - 2 K Heat Exchanger Temperature Difference - No Pressure Drop 59 Figure 29. Brayton Refrigerator Performance - Nitrogen Refrigerant - 300 K Cycle Inlet Temperature - 90% Expander Efficiency - 2 K Heat Exchanger Temperature Difference - No Pressure Drop ..... 60 Figure 30. Brayton Refrigerator Performance - Nitrogen Refrigerant - 300 K Cycle Inlet Temperature- 70% Expander Efficiency - 2 K Heat Exchanger Temperature Difference - No Pressure Drop 61 Figure 31. Brayton Refrigerator Performance - Nitrogen Refrigerant - 300 K Cycle Inlet Temperature - 50% Expander Efficiency - 2 K Heat Exchanger Temperature Difference - No Pressure Drop ..... 62 Figure 32. Brayton Refrigerator Performance - Nitrogen Refrigerant - 300 K Cycle Inlet Temperature - 100% Expander Efficiency - 4 K Heat Exchanger Temperature Difference - No Pressure Drop ..... 63 VI TABLE OF CONTENTS (CONTINUED)
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