Simple Predictions for the Sonic Conditions in a Real Gas

1977 ◽  
Vol 99 (1) ◽  
pp. 217-225 ◽  
Author(s):  
P. A. Thompson ◽  
D. A. Sullivan
Keyword(s):  
Equation Of State ◽  
Closed Form ◽  
Thermodynamic Parameters ◽  
Ideal Gas ◽  
Accurate Prediction ◽  
Bernoulli Equation ◽  
Real Gas ◽  
Similarity Principle ◽  
Isentropic Flow ◽  
The Ideal

The steady isentropic flow of a fluid which satisfies an arbitrary equation of state is treated, with emphasis on the prediction of pressure, density, velocity, and massflow at the sonic state. The isentrope P(v) is described by a limited number of thermodynamic parameters, the most important ones being the soundspeed c and fundamental derivative Γ. Using this description, an application of the Bernoulli equation and appropriate thermodynamic relations yields simple closed-form predictions for the sonic state. These predictions are recognizable as generalizations of well-known ideal gas formulas, but are applicable to fluids very far removed from the ideal gas state, even including liquids. Comparisons in several cases for which precise independent solutions are available suggest that the methods found here are accurate. A derived similarity principle allows the accurate prediction of sonic properties from any single given sonic property.

Supercooling in hypersonic nitrogen wind tunnels

1994 ◽  
Vol 269 ◽  
pp. 283-299 ◽  
Author(s):  
Wayland C. Griffith ◽  
William J. Yanta ◽  
William C. Ragsdale
Keyword(s):  
Vibrational Energy ◽  
Ideal Gas ◽  
Wind Tunnels ◽  
Pure Nitrogen ◽  
Real Gas ◽  
Absolute Limit ◽  
Real Gas Effects ◽  
Supercooled Region ◽  
The Ideal

Recent experimental observation of supercooling in large hypersonic wind tunnels using pure nitrogen identified a broad range of non-equilibrium metastable vapour states of the flow in the test cell. To investigate this phenomenon a number of real-gas effects are analysed and compared with predictions made using the ideal-gas equation of state and equilibrium thermodynamics. The observed limit on the extent of supercooling is found to be at 60% of the temperature difference from the sublimation line to Gibbs’ absolute limit on phase stability. The mass fraction then condensing is calculated to be 12–14%. Included in the study are virial effects, quantization of rotational and vibrational energy, and the possible role of vibrational relaxation and freezing in supercooling. Results suggest that use of the supercooled region to enlarge the Mach–Reynolds number test envelope may be practical. Data from model tests in supercooled flows support this possibility.

scholarly journals Compressible flow at high pressure with linear equation of state

2018 ◽  
Vol 843 ◽  
pp. 244-292 ◽  
Author(s):  
William A. Sirignano
Keyword(s):  
Equation Of State ◽  
Compressible Flow ◽  
Sound Speed ◽  
Ideal Gas ◽  
Real Gas ◽  
Cubic Equation Of State ◽  
Cubic Equation ◽  
Wide Range ◽  
Real Gas Effects ◽  
Flow Configurations

Compressible flow varies from ideal-gas behaviour at high pressures where molecular interactions become important. It is widely accepted that density is well described through a cubic equation of state while enthalpy and sound speed are functions of both temperature and pressure, based on two parameters, $A$ and $B$, related to intermolecular attraction and repulsion, respectively. Assuming small variations from ideal-gas behaviour, a closed-form approximate solution is obtained that is valid over a wide range of conditions. An expansion in these molecular interaction parameters simplifies relations for flow variables, elucidating the role of molecular repulsion and attraction in variations from ideal-gas behaviour. Real-gas modifications in density, enthalpy and sound speed for a given pressure and temperature lead to variations in many basic compressible-flow configurations. Sometimes, the variations can be substantial in quantitative or qualitative terms. The new approach is applied to choked-nozzle flow, isentropic flow, nonlinear wave propagation and flow across a shock wave, all for a real gas. Modifications are obtained for allowable mass flow through a choked nozzle, nozzle thrust, sonic wave speed, Riemann invariants, Prandtl’s shock relation and the Rankine–Hugoniot relations. Forced acoustic oscillations can show substantial augmentation of pressure amplitudes when real-gas effects are taken into account. Shocks at higher temperatures and pressures can have larger pressure jumps with real-gas effects. Weak shocks decay to zero strength at sonic speed. The proposed framework can rely on any cubic equation of state and can be applied to multicomponent flows or to more complex flow configurations.

Numerical Approach for Real Gas Simulations: Part I — Tabular Fluid Properties for Real Gas Analysis

2017 ◽  
Author(s):  
Francisco Moraga ◽  
Doug Hofer ◽  
Swati Saxena ◽  
Ramakrishna Mallina
Keyword(s):  
Equation Of State ◽  
Error Analysis ◽  
Critical Point ◽  
Ideal Gas ◽  
Phase Region ◽  
System Level ◽  
Component Level ◽  
Power Cycles ◽  
Real Gas ◽  
Fluid Properties

Recently there has been increased interest in the use of carbon dioxide (CO2) in closed loop power cycles. As these power cycles capitalize on the non-ideal gas behavior of CO2, their analysis both at the system level and at the detailed component level requires an advanced equation of state. Commonly used analytical equations of state as BWRS (BenedictWebbRubin equation of State) or Peng-Robinson are known to have high errors near the critical point and are thus unsuitable for the analysis of cycles or components where the flow conditions approach the critical point. An accurate equation of state is required at all phases of the development process from high level cycle calculations to the detailed component CFD. The NIST RefProp software package provides accurate CO2 fluid properties across the thermodynamic space but suffers from high computational over-head. This study is presented in two parts. Part I (this part) of this paper describes an approach to creating a tabular representation of the equation of state that is applicable to any fluid. This approach is applied to generating an accurate, fast and robust tabular representation of the RefProp CO2 properties and an error analysis is performed to meet the accuracy requirements. The paper also discusses two approaches used to define speed of sound in the two-phase region and their sensitivity analysis on the 3D compressor flow. Part II of the paper details the numerical simulations of a supercritical CO2 centrifugal compressor using the tabular approach. This paper shows that table resolution can be tailored to match the accuracy requirements while minimizing the time used to evaluate the tabulated thermo-physical functions. Error analysis are shown to demonstrate the level of accuracy possible with this approach.

scholarly journals Design of a Centrifugal Compressor Stage and a Radial-Inflow Turbine Stage for a Supercritical CO2 Recompression Brayton Cycle by Using 3D Inverse Design Method

2017 ◽  
Author(s):  
Jiangnan Zhang ◽  
Pedro Gomes ◽  
Mehrdad Zangeneh ◽  
Benjamin Choo
Keyword(s):  
Centrifugal Compressor ◽  
Supercritical Co2 ◽  
Design Method ◽  
Ideal Gas ◽  
Inverse Design ◽  
Brayton Cycle ◽  
Real Gas ◽  
Radial Inflow Turbine ◽  
Inverse Design Method ◽  
The Ideal

It is found that the ideal gas assumption is not proper for the design of turbomachinery blades using supercritical CO2 (S-CO2) as working fluid especially near the critical point. Therefore, the inverse design method which has been successfully applied to the ideal gas is extended to applications for the real gas by using a real gas property lookup table. A fast interpolation lookup approach is implemented which can be applied both in superheated and two-phase regimes. This method is applied to the design of a centrifugal compressor blade and a radial-inflow turbine blade for a S-CO2 recompression Brayton cycle. The stage aerodynamic performance (volute included) of the compressor and turbine is validated numerically by using the commercial CFD code ANSYS CFX R162. The structural integrity of the designs is also confirmed by using ANSYS Workbench Mechanical R162.

Extremes in Dependences of Enthalpy and Entropy of Saturated Vapour on Temperature

1997 ◽  
Vol 62 (5) ◽  
pp. 679-695
Author(s):  
Josef P. Novák ◽  
Anatol Malijevský ◽  
Jaroslav Dědek ◽  
Jiří Oldřich
Keyword(s):  
Heat Capacity ◽  
Equation Of State ◽  
Ideal Gas ◽  
Corresponding States ◽  
Saturated Vapour ◽  
Enthalpy And Entropy ◽  
The Ideal

It was proved that the enthalpy of saturated vapour as a function of temperature has a maximum for all substances. The dependence of the entropy of saturated vapour on temperature can be monotonous, has a minimum and a maximum, or has only a maximum. The thermodynamic relations were derived for the existence of the extremes which enable their computation from the knowledge of dependence of the ideal-gas heat capacity on temperature and an equation of state. A method based on the theorem of corresponding states was proposed for estimating the extremes, and its results were compared with literature data. The agreement between the literature and estimated temperatures corresponding to the extremes is very good. The procedure proposed can serve for giving precision to the H-p and T-S diagrams commonly used in applied thermodynamics.

A comparative study of thermodynamic models to describe the VLE of the ternary electrolytic mixture H2O–NH3–CO2

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Licianne P. S. Rosa ◽  
Natan Cruz ◽  
Glória M. N. Costa ◽  
Karen V. Pontes
Keyword(s):  
Experimental Data ◽  
Liquid Phase ◽  
Equation Of State ◽  
Activity Coefficient ◽  
Vapor Phase ◽  
Large Scale ◽  
Optimization Problems ◽  
Ideal Gas ◽  
Simultaneous Optimization ◽  
The Ideal

Abstract This study aims to ascertain the influence of the activity coefficient model and equation of state for predicting the vapor–liquid equilibrium (VLE) of the multi-electrolytic system H2O–NH3–CO2. The non-idealities of the liquid phase are described by the eUNIQUAC and eNRTL models. The vapor phase is modeled with the Nakamura equation, which is compared with the ideal gas assumption. The models are validated with experimental data from literature on total pressure and ammonia partial pressure. Results show that the models UNIQUAC and NRTL without dissociation can only reproduce the experimental conditions in the absence of CO2. When the electrolytic term is considered, the eUNIQUAC model is able to reproduce the experimental data with greater accuracy than the eNRTL. The equation of state which describes the vapor phase plays no major role in the accuracy of the VLE prediction in the operational conditions evaluated here. Indeed, the accuracy relies on the activity coefficient, therefore the ideal gas equation can be considered if the non-idealities of the liquid phase are described by a well-tuned model. These findings could be useful for equipment design, flowsheet simulations and large-scale simultaneous optimization problems.

scholarly journals Analysis of the application of ideal gas equation of state

2021 ◽  
Vol 252 ◽  
pp. 03019
Author(s):  
Yarong Wang ◽  
Peirong Wang
Keyword(s):  
Equation Of State ◽  
Molecular Motion ◽  
Interaction Force ◽  
Ideal Gas ◽  
Real Gas ◽  
Mathematical Relation

In nature, the molecules of real gas have a certain volume and have interaction force with each other. It is difficult to find the molecular motion law of real gas because of its complex properties. An ideal gas is an imaginary substance that does not exist in reality. Its molecules are elastic, non volume particles, and there is no interaction among them. This kind of gas is simple in nature and easy to be analyzed and calculated by simple mathematical relation. The introduction of the concept of ideal gas greatly simplifies the analysis of some thermodynamic problems.

Thermodynamic Property Models for Moist Air and Combustion Gases

2002 ◽  
Vol 125 (1) ◽  
pp. 374-384 ◽  
Author(s):  
D. Bu¨cker ◽  
R. Span ◽  
W. Wagner
Keyword(s):  
Ideal Gas ◽  
Moist Air ◽  
Combustion Gas ◽  
Real Gas ◽  
New Model ◽  
Combustion Gases ◽  
Dissociation Model ◽  
The Individual ◽  
Ideal Gas Model ◽  
The Ideal

A new model for the prediction of caloric properties of moist air and combustion gases has been developed. The model very accurately predicts ideal gas caloric properties of undissociated gas mixtures at temperatures from 200 K to 3300 K. In addition, a simple model has been developed to account for caloric effects of dissociation at temperatures up to 2000 K. As a part of the project, scientific equations for the ideal gas isobaric heat capacity of the individual combustion gas components have been established. Based on this reference, an assessment and comparison of the new model with the most common technical models have been carried out. Results of the simplified dissociation model are compared to the results of complex chemical equilibrium programs. To mark out the limits of the ideal gas hypothesis, some sample calculations are given, which compare results of the new ideal gas model to results from sophisticated real gas models.

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