A method that includes the use of modified equations of state has been developed to enable noniterative, efficient computation of the thermodynamic behaviors of gases and liquids at temperatures >100 K and pressures from 1 to 100 MPa. The method is intended to be particularly useful for calculating such quantities as partial molar volumes, enthalpies, entropies, compressibilities, and thermal expansivities of oxidant/fuel mixtures at given pressures, temperatures, and mass fractions in gas turbine and rocket engines.
The method is based partly on the concept of a reference state of a real gas, which state is similar to that of a perfect gas at the same temperature and pressure and is defined with respect to the condition of the real gas at a relatively low reference pressure. The method is also based partly on the use of departure functions to represent the deviations of thermodynamic functions of the real gas at high pressure from reference-state values of those functions.
The form of the departure functions is obtained from the Peng-Robinson equation of state:
p=RT/(v-bm)-am/(v²+2bmv-b²m),
where p is the absolute pressure, R is the molar ideal-gas constant,T is the absolute temperature, and v is the molar volume. The parameters am and bm are semiempirical terms calculated from critical-state properties; these parameters follow conventional mixing rules; namely,
am=ΣΣxixjaij and bm=Σxibi,
where xi is the mole fraction of the ith molecular species.
One first applies the departure-function formalism to each of the pure constituents of a mixture, then reuses this formalism for the mixture as a whole. In the application to each pure constituent, one expresses the reference-state enthalpy and entropy as finite series of temperature- and pressure-dependent terms, the coefficients of which are established by least-squares fits to the best available empirical data on enthalpy and entropy (see table). This method follows the standard practice in calculating the properties of nonideal mixtures by use of accurately known properties of the pure constituents along with excess Gibbs energy and/or fugacity coefficients, which are defined by use of conventional mixing rules.
This work was done by Josette Bellan, Richard S. Miller, and Kenneth G. Harstad of Caltech for NASA's Jet Propulsion Laboratory. For further information, access the Technical Support Package (TSP) free on-line at www.techbriefs.com under the Physical Sciences category, or circle no. 128 on the TSP Order Card in this issue to receive a copy by mail ($5 charge).
NPO-20066
This Brief includes a Technical Support Package (TSP).
Equations of state for fluid mixtures at high pressures
(reference NPO20066) is currently available for download from the TSP library.
Don't have an account?
Overview
The document is a technical support package from NASA, specifically a NASA Tech Brief, detailing advancements in the equations of state for fluid mixtures at high pressures. It was prepared by the Jet Propulsion Laboratory (JPL) and is associated with research conducted for high-pressure gas turbine and rocket engines. The primary focus is on developing a computationally efficient method for calculating the thermodynamic properties of various gases, particularly hydrogen, oxygen, and methane, under high-pressure and high-temperature conditions.
The proposed method utilizes the Peng-Robinson equation of state (EOS), which is a widely recognized model for predicting the behavior of fluids. This approach allows for non-iterative calculations of pure substance properties, which can be extended to mixtures, making it suitable for practical applications in aerospace engineering. The document emphasizes the importance of accurate thermodynamic data for the design and operation of propulsion systems, where understanding the behavior of gases under varying conditions is crucial.
The research highlights the range of reference fits for different substances, including hydrogen (80-400 K, 0.1-100 MPa), nitrogen (100-2000 K, 0.1-100 MPa), oxygen (0.1-100 MPa), and methane (100-600 K, 1-30 MPa). These ranges indicate the temperatures and pressures over which the equations of state can be reliably applied, providing engineers with essential data for simulations and design processes.
The document also acknowledges the support from NASA's Marshall Space Flight Center and the Lewis Research Center, indicating a collaborative effort in advancing aerospace technology. The findings are intended to enhance the understanding of fluid dynamics in high-pressure environments, which is vital for improving the efficiency and performance of rocket engines and gas turbines.
In summary, this NASA Tech Brief presents a significant advancement in the computational methods for analyzing fluid mixtures at high pressures, with a focus on practical applications in aerospace propulsion systems. The work aims to provide engineers with reliable tools for predicting the behavior of gases, ultimately contributing to the development of more efficient and effective propulsion technologies.
