Method of Determining a Nominal Index Value for the Polytropic Expansion Process of Supercritical Carbon Dioxide in Piston-Cylinder Devices

Year 2014, , 275 - 282, 18.03.2014

Kevin Anderson

https://doi.org/10.5541/ijot.582

Abstract

The polytropic process is a widely used pressure model for predicting the nature of pressure and volume states in expansion and compression systems. The two variable nature of this model typically leads to an open ended approach with heavy reliance on mechanism evaluation and potential extended design iterations in the prototyping phase. Through a fundamental examination of the polytropic derivation from the energy transfer ratio assumption, in conjunction with repeated application of elementary thermodynamic principles, including First Law analysis, moving boundary work, and substance property evaluation, a solution to a refined nominal polytropic index can be found. The derivation can provide valuable insight to the polytropic process itself and address the issue of bounding a complex system with a reasonable choice of theoretical system input. With the aid of the method outlined in this paper, researchers will be enabled with a tool to better predict the polytropic expansion coefficient which finds widespread use in thermodynamic modeling and analysis. To this end, the method is used herein to predict a polytropic index of n = 1.306 and k = 1.615 for the specific heat ratio for a SCO2 expansion engine operating between 20 MPa and 9.2 MPa.

Keywords

Polytropic Expansion; Supercritical Carbon Dioxide; Thermodynamics Modeling; Cycle Analysis

References

• Anderson, K., Devost, M., Wells, T., Forgette, D., Okerson, R., Stuart, M., Cunningham, M. Waste Heat Energy Regenerative Supercritical Carbon Dioxide Rankine Cycle Thermodynamic Analysis and Design. Adv. Renewable Energy , ARE-2013-11-291 Feb. 2014.
• Anderson, K., Clark, A., Forgette, D., Devost, M., Okerson, R., Wells, T., Cunningham, S., Stuart, M. (2013) Analysis and Design of a Lightweight High Specific Power Two-Stroke Polygon Engine. J. Eng. Gas Turbines Power 136, 041508 (Dec 12, 2013)doi:10.1115/1.4026049.
• Heiser, W. , Huxley, T. , & Bucey, J. (2011). The Brayton Cycle Using Real Air and Polytropic Component Efficiencies. J. Eng. for Gas Turbines Power, 133, 111702-111710, doi: 10.1115/1.4003671.
• Lapuerta, M. , Armas, O., Molina, S. Study of the Compression Cycle of a Reciprocating Engine through the Polytropic Coefficient. Applied Thermal Engineering, 23, 313-323, 2003.
• Zhao, W. , Ye, Q., Meng, G. Measurement of Flow Rate Characteristics of Pneumatic Components Based on the Dynamic Regularity of Polytropic Exponents. Flow Measurement and Instrumentation, 22, 331-337, 2011.
• Chang, H. , Zhang, Y., Chen, L. An Applied Thermodynamic Method for Correction of TDC in the Indicator Diagram and its Experimental Confirmation. Applied Thermal Engineering, 25, 759768, 2005.
• Stone, R. The Internal Combustion Engine, SAE Press. 20 Heywood, J. Internal Combustion Engine Fundamentals. New York, NY, McGraw-Hill, 1998.
• Faires, V. Thermodynamics, (6 th ed.). New Jersey, Macmillan, 1978.
• Taylor, C. The Internal Combustion Engine in Theory and Practice, Volume 1: Thermodynamics, Fluid Flow, Performance (2 nd ed.). Cambridge, MIT Press, 1985.
• Christians, J. Approach for Teaching Polytropic Processes Based on the Energy Transfer Ratio. Int. J. Mechanical Engineering Education., 40, 53-65, 2012.