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.

Numerical Investigation of the Flow Behavior Inside a Supercritical CO2 Centrifugal Compressor

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Alireza Ameli ◽  
Teemu Turunen-Saaresti ◽  
Jari Backman
Keyword(s):  
Critical Point ◽  
Centrifugal Compressor ◽  
Supercritical Co2 ◽  
Flow Behavior ◽  
Liquid Density ◽  
Flow Solver ◽  
Real Gas ◽  
Fluid Behavior ◽  
Test Loop ◽  
Fluid Properties

Centrifugal compressors are one of the best choices among compressors in supercritical Brayton cycles. A supercritical CO2 centrifugal compressor increases the pressure of the fluid which state is initially very close to the critical point. When the supercritical fluid is compressed near the critical point, wide variations of fluid properties occur. The density of carbon dioxide at its critical point is close to the liquid density which leads to reduction in the compression work. This paper explains a method to overcome the simulation instabilities and challenges near the critical point in which the thermophysical properties change sharply. The investigated compressor is a centrifugal compressor tested in the Sandia supercritical CO2 test loop. In order to get results with the high accuracy and take into account the nonlinear variation of the properties near the critical point, the computational fluid dynamics (CFD) flow solver is coupled with a look-up table of properties of fluid. Behavior of real gas close to its critical point and the effect of the accuracy of the real gas model on the compressor performance are studied in this paper, and the results are compared with the experimental data from the Sandia compression facility.

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.

A Robust Iterative Method for Flash Calculations Using the Soave-Redlich-Kwong or the Peng-Robinson Equation of State

1983 ◽  
Vol 23 (03) ◽  
pp. 521-530 ◽  
Author(s):  
L.X. Nghiem ◽  
K. Aziz ◽  
Y.K. Li
Keyword(s):  
Equation Of State ◽  
Iterative Method ◽  
Critical Point ◽  
Newton’S Method ◽  
Newton's Method ◽  
Single Phase ◽  
Saturation Pressure ◽  
Phase Region ◽  
Single Phase Region ◽  
Poor Convergence

Abstract A robust algorithm for flash calculations that uses an equation of state(EOS) is presented. It first uses a special version of the successive substitution(SS) method and switches to Powell's method if poor convergence is observed. Criteria are established for an efficient switch from one method to the other. Experience shows that this method converges near the critical point and also detects the single-phase region without computing the saturation pressure. The Soave-Redlich-Kwong (SRK) and the Peng-Robinson (PR) EOS's are used in this work, but the method is general and applies to any EOS. Introduction The calculation of vapor/liquid equilibrium using an EOS in multicomponent systems yields a system of nonlinear equations that must be solved iteratively. The SS method is commonly used, but it exhibits poor rate of convergence near the critical point. To overcome convergence problems, Newton's method has been used by Fussell and Yanosik to solve the equations. The drawback of Newton's method is the necessity of computing a complicated Jacobian matrix and its inverse at every iteration. Hence, for systems removed from their critical point it involves more work to arrive at the solution than the SS method. Furthermore, the radius of convergence of Newton's method is relatively small when compared to that of the SS method; hence, a good initial guess is required before convergence can be achieved. The single-phase region usually is determined by computing the saturation pressure and comparing it with the pressure of the system. This requires additional work, pressure of the system. This requires additional work, and it is sometimes difficult to decide whether a dewpoint or bubblepoint pressure, which involve different equations, should be computed. This paper presents a robust iterative method for flash calculations using either the SRK or the PR EOS, both of which have received much interest in recent years. The proposed method combines SS with Powell's iteration, proposed method combines SS with Powell's iteration, which is a hybrid algorithm consisting of a quasi-Newton method and a steepest-descent method. The SS method is used initially and is replaced by Powell's method if it demonstrates poor convergence, thus taking advantage of the simplicity of the former method and the robustness of the latter. The SS method has been modified so that the single-phase region can be detected without having to compute the saturation pressure. The nonlinear equations to be solved by an iteration scheme could behave differently, depending on their form and the variables for which they are solved. In this paper three different approaches are considered with paper three different approaches are considered with Powell's method. One of the three approaches is based Powell's method. One of the three approaches is based on the minimization of the Gibbs free energy. The convergence properties of the proposed schemes are demonstrated by three example problems. SPEJ P. 521

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 Investigation of the Flow Behavior Inside a Supercritical CO2 Centrifugal Compressor

2016 ◽  
Author(s):  
Alireza Ameli ◽  
Teemu Turunen-Saaresti ◽  
Jari Backman
Keyword(s):  
Critical Point ◽  
Centrifugal Compressor ◽  
Supercritical Co2 ◽  
Flow Behavior ◽  
Lookup Table ◽  
Liquid Density ◽  
Flow Solver ◽  
Real Gas ◽  
Fluid Behavior ◽  
Fluid Properties

Centrifugal compressors are one of the best choices among compressors in supercritical Brayton cycles. A supercritical CO2 centrifugal compressor increases the pressure of the fluid which state is initially very close to the critical point. When the supercritical fluid is compressed near the critical point, wide variations of fluid properties occur. The density of carbon dioxide at its critical point is close to the liquid density which leads to reduction in compressor work. The investigated compressor is a centrifugal compressor tested in the Sandia supercritical CO2 compression loop. In order to get results with the high accuracy and take into account the non-linear variation of the properties near the critical point, the CFD flow solver is coupled with a lookup table of properties of fluid. Behavior of real gas close to its critical point and the effect of the accuracy of the real gas model on the compressor performance are studied in this paper and the results are compared with the experimental data from the Sandia compression facility.

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.

scholarly journals Method for constructing the fundamental equation of state that takes into account the peculiarities of the substance behaviour in a wide vicinity of the critical point

2021 ◽  
Vol 2057 (1) ◽  
pp. 012112
Author(s):  
S V Rykov ◽  
I V Kudryavtseva
Keyword(s):  
Heat Capacity ◽  
Free Energy ◽  
Equation Of State ◽  
Critical Point ◽  
Fundamental Equation ◽  
Virial Coefficients ◽  
Phenomenological Theory ◽  
Phase Region ◽  
Scale Functions ◽  
Fundamental Equation Of State

Abstract On the basis of the phenomenological theory of the critical point and the Benedek hypothesis, an expression for the Helmholtz free energy F with scale functions in the density-temperature variables has been developed. The proposed free energy equation has been tested on the example of constructing the fundamental equation of state of 2,3,3,3-tetrafluoropropene (R1234yf). By comparison with the known experimental data on the equilibrium properties of R1234yf – density and pressure on the phase equilibrium line, p-ρ-T-data in the single-phase region, the second and third virial coefficients, isochoric heat capacity, isobaric heat capacity and the sound velocity – the operating range of the equation of state of R1234yf has been established according to temperature from 220 K to 420 K and pressure up to 20 MPa.

scholarly journals Modification of the Redlich-Kwong-Aungier Equation of State to Determine the Degree of Dryness in the CO2 Two-phase Region

2021 ◽  
Vol 24 (4) ◽  
pp. 17-27
Author(s):  
Hanna S. Vorobieva ◽  
Keyword(s):  
Experimental Data ◽  
Equation Of State ◽  
Gas Phase ◽  
Saturated Vapor ◽  
Phase Region ◽  
Working Fluid ◽  
Two Phase ◽  
Real Gas ◽  
Liquid Phases ◽  
Good Agreement

The degree of dryness is the most important parameter that determines the state of a real gas and the thermodynamic properties of the working fluid in a two-phase region. This article presents a modified Redlich-Kwong-Aungier equation of state to determine the degree of dryness in the two-phase region of a real gas. Selected as the working fluid under study was CO2. The results were validated using the Span-Wanger equation presented in the mini-REFPROP program, the equation being closest to the experimental data in the CO2 two-phase region. For the proposed method, the initial data are temperature and density, critical properties of the working fluid, its eccentricity coefficient, and molar mass. In the process of its solution, determined are the pressure, which for a two-phase region becomes the pressure of saturated vapor, the volumes of the gas and liquid phases of a two-phase region, the densities of the gas and liquid phases, and the degree of dryness. The saturated vapor pressure was found using the Lee-Kesler and Pitzer method, the results being in good agreement with the experimental data. The volume of the gas phase of a two-phase region is determined by the modified Redlich-Kwong-Aungier equation of state. The paper proposes a correlation equation for the scale correction used in the Redlich-Kwongda-Aungier equation of state for the gas phase of a two-phase region. The volume of the liquid phase was found by the Yamada-Gann method. The volumes of both phases were validated against the basic data, and are in good agreement. The results obtained for the degree of dryness also showed good agreement with the basic values, which ensures the applicability of the proposed method in the entire two-phase region, limited by the temperature range from 220 to 300 K. The results also open up the possibility to develop the method in the triple point region (216.59K-220 K) and in the near-critical region (300 K-304.13 K), as well as to determine, with greater accuracy, the basic CO2 thermodynamic parameters in the two-phase region, such as enthalpy, entropy, viscosity, compressibility coefficient, specific heat capacity and thermal conductivity coefficient for the gas and liquid phases. Due to the simplicity of the form of the equation of state and a small number of empirical coefficients, the obtained technique can be used for practical problems of computational fluid dynamics without spending a lot of computation time.

Development and Commissioning of a Blowdown Facility for Dense Gas Vapours

2019 ◽  
Author(s):  
Miles C. Robertson ◽  
Peter J. Newton ◽  
Tao Chen ◽  
Ricardo F. Martinez-Botas
Keyword(s):  
Test Section ◽  
Waste Heat ◽  
Pressure Ratio ◽  
Ideal Gas ◽  
Helmholtz Energy ◽  
System Level ◽  
Low Grade ◽  
Dense Gas ◽  
Real Gas ◽  
Real Gas Effects

Abstract The Organic Rankine Cycle is a candidate technology for low grade heat recovery, from sources as diverse as geothermal, solar and industrial/vehicle waste heat. The organic working fluids used within these systems often display significant real-gas effects, especially in proximity of the thermodynamic critical point. Significant research has therefore been performed on the design of real-gas expansion devices, including both positive displacement and rotordynamic machinery. 3D Computational Fluid Dynamics (CFD) is commonly used for performance prediction and flow field analysis within expanders, and experimental validation of these simulations within a real-gas environment are scarce within the literature. This paper therefore presents a dense-gas blowdown facility constructed at Imperial College London, for the purpose of experimentally validating numerical simulations of these fluids. The system-level design process for the blowdown rig is detailed within this paper, including the sizing and specification of major components. A hemispherically-ended 3.785 L cylinder was selected as the main blowdown vessel, allowing a designpoint pressure and temperature of 3751 kPa and 477 K, respectively. Regulating valves were placed either side of the test section, allowing a Pressure Ratio to be fixed across the measurement section. The primary design focus of this paper is that of the test section — a converging-diverging nozzle producing an expansion of Mach 2 at the nozzle exit plane. The nozzle profile is generated by Method of Characteristics (MoC) modified to account for real-gas effects. Both mechanical and fluid dynamic design are discussed, along with location and thermal management of the nine pressure transducers, located along the nozzle centreline. A series of blowdown tests are conducted, firstly for a fluid conforming closely to the ideal gas Equation of State - Nitrogen (N2) at room temperature. A comparison between the experimental measurements and a CFD analysis of these results is taken as a benchmarking example. A second set of tests with refrigerant R1233zd(E) are run, across multiple inlet pressures - CFD simulations are subsequently performed, with the refrigerant modeled by Ideal Gas, Peng-Robinson, and Helmholtz energy (via REF-PROP) Equations of State. An error analysis is conducted for each, identifying that an increase in fluid model fidelity leads to reduced deviation between simulation and experiment. An average discrepancy of 11.1% in nozzle Pressure Ratio with the Helmholtz energy EoS indicates an over-prediction of expander power output within the CFD simulation.

Sensitivity Study of S-CO2 Compressor Design for Different Real Gas Approximations

2016 ◽  
Author(s):  
Jekyoung Lee ◽  
Seong Kuk Cho ◽  
Jae Eun Cha ◽  
Jeong Ik Lee
Keyword(s):  
Thermodynamic Property ◽  
Critical Point ◽  
Technology Development ◽  
Static Condition ◽  
Sensitivity Study ◽  
Ideal Gas ◽  
Brayton Cycle ◽  
Real Gas ◽  
Compressor Design ◽  
Turbomachinery Design

With the efforts of many researchers and engineers on the Supercritical CO2 (S-CO2) Brayton cycle technology development, the S-CO2 Brayton cycle is now considered as one of the key power technologies for the future. Since S-CO2 Brayton cycle has advantages in economics due to high efficiency and compactness of system, various industries have been trying to develop technologies on the design and analysis of S-CO2 Brayton cycle components. Among various technical issues on the S-CO2 Brayton cycle technology development, treatment of thermodynamic property near the critical point of S-CO2 is very important since the property shows non-linear variation which causes large error on design and analysis results for ideal gas based methodologies. Due to the special behavior of thermodynamic property of CO2 near the critical point, KAIST research team has been trying to develop a S-CO2 compressor design and analysis tool to reflect real gas effect accurately for better design and performance prediction results. The main motivation for developing an in-house code is to establish turbomachinery design methodology based on general equations to improve accuracy of design and analysis results for various working fluids including S-CO2. One of the key improvements of KAIST_TMD which is an in-house tool for S-CO2 turbomachinery design and analysis is the conversion process between stagnation condition and static condition. Since fluid is moving with high flow velocity in a compressor, the conversion process between stagnation and static condition is important and it can have an impact on the design and analysis results significantly. A common process for the conversion is based on the specific heat ratio which is typically a constant from ideal gas assumption. However, specific heat ratio cannot be assumed as a constant for the case of S-CO2 compressor design and analysis because it varies dramatically near the critical point. Thus, in this paper, sensitivity study results on the state condition conversion between stagnation and static conditions with different approaches will be presented and further analysis on impact of the selected approaches on the final impeller design results will be discussed.

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