THERMAL AND CALORIC EQUATIONS OF STATE FOR NITROGEN: APPLICATION TO CRYOGENIC INJECTION CONDITIONS

2020 ◽  
Author(s):  
N. M. KUZNETSOV ◽  
◽  
S. N. MEDVEDEV ◽  
S. M. FROLOV ◽  
F. S. FROLOV ◽  
...  
Keyword(s):  
Equation Of State ◽  
Triple Point ◽  
Equations Of State ◽  
Applicability Domain ◽  
Analytical Equation ◽  
Nitrogen Application ◽  
Real Gas ◽  
The Real ◽  
Turbulent Reactive Flows ◽  
Wide Range

The real-gas analytical equation of state (EoS) for nitrogen is developed. The applicability domain of the EoS is verified in a wide range of density (from 0 to the value at the triple point, 0.867 g/cm3) and temperature (from 100 to 5000 K). The obtained EoS is introduced into the gasdynamic code for calculating multidimensional turbulent reactive flows.

Thermal equation of state for real gas in a wide range of state parameters, including the critical region

2008 ◽  
Vol 15 (3) ◽  
pp. 359-368 ◽  
Author(s):  
A. B. Kaplun ◽  
B. I. Kidyarov ◽  
A. B. Meshalkin ◽  
A. V. Shishkin
Keyword(s):  
Equation Of State ◽  
Critical Region ◽  
Thermal Equation ◽  
Real Gas ◽  
Thermal Equation Of State ◽  
Wide Range

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.

The Evaluation of the Equations of State Used for the Joule-Thomson Effect Analysis in the Dry Gas Seal

2015 ◽  
Vol 752-753 ◽  
pp. 391-395 ◽  
Author(s):  
Cheng Xiang Deng ◽  
Peng Yun Song
Keyword(s):  
Experimental Data ◽  
Carbon Dioxide ◽  
Equation Of State ◽  
Equations Of State ◽  
Gas Flows ◽  
Thomson Effect ◽  
Effect Analysis ◽  
Real Gas ◽  
Dry Gas Seal ◽  
Thomson Coefficient

The Joule-Thomson (JT) effect will occur when the gas flows through the components of filters, valves, orifices and end faces in the system of the dry gas seal, which may cause the temperature of the seal gas to decrease, and even the emergence of liquid condensation. Generally, the Joule-Thomson effect is reflected by the Joule-Thomson coefficient. As to the hydrogen, nitrogen, carbon dioxide and air, which are often met in the dry gas seal, the corresponding Joule-Thomson (JT) coefficients were calculated by four classical equations of state (EOS) of VDW, RK, SRK and PR, which are compared with the experimental data in the literature. The results show that the JT coefficients calculated by RK equation are most close to the experimental data in the literature, whose relative error is lowest and less than 4%. When the JT effect of real gas in the dry gas seal is analyzed, the RK equation of state is recommend.

scholarly journals Development and Experimental Validation of Real Fluid Models for CFD Calculation of ORC and Steam Turbine Flows

Materials ◽  
2021 ◽  
Vol 14 (22) ◽  
pp. 6879
Author(s):  
Andrii Rusanov ◽  
Roman Rusanov ◽  
Piotr Klonowicz ◽  
Piotr Lampart ◽  
Grzegorz Żywica ◽  
...  
Keyword(s):  
Experimental Data ◽  
Equation Of State ◽  
Steam Turbine ◽  
Thermodynamic Parameters ◽  
Equations Of State ◽  
Computational Cost ◽  
Organic Rankine Cycle ◽  
Rankine Cycle ◽  
Large Power ◽  
Wide Range

The article describes an interpolation–analytical method of reconstruction of the IAPWS-95 equations of state and the modified Benedict–Webb–Rubin equations of state with 32 terms (mBWR32). The method enables us to provide the thermodynamic closure in 3D computational fluid dynamics (CFD) calculations of turbomachinery flows with real working media, such as steam and Organic Rankine Cycle (ORC) fluids. The described approach allows for the sufficient accuracy of 3D flow calculations and does not require a significant increase in computational cost over perfect gas calculations. The method is validated against experimental data from measurements and compared with computational results from the model using the Tammann equation of state. Three turbine blading systems are considered—a multi-stage configuration from a low-pressure cylinder of a large-power steam turbine and two ORC microturbines working with organic media HFE7100 and R227ea. The calculation results obtained using the described method of approximation of the IAPWS-95 and mBWR32 equations exhibit satisfactory agreement with the experimental data, considering pressures, temperatures and enthalpies in key sections, as well as turbine power and efficiency in a wide range of changing thermodynamic parameters. In contrast, the Tammann equation of state provides acceptable results only for relatively small changes of thermodynamic parameters.

scholarly journals Ab initio based equation of state of dense water for planetary and exoplanetary modeling

2019 ◽  
Vol 621 ◽  
pp. A128 ◽  
Author(s):  
S. Mazevet ◽  
A. Licari ◽  
G. Chabrier ◽  
A. Y. Potekhin
Keyword(s):  
Equation Of State ◽  
First Principles ◽  
Equations Of State ◽  
Pure Water ◽  
Analytical Form ◽  
Quantum Molecular Dynamics ◽  
Dense Water ◽  
Wide Range ◽  
Dynamical Simulations ◽  
Dynamics Simulations

Context. The modeling of planetary interiors requires accurate equations of state (EOSs) for the basic constituents with proven validity in the difficult pressure–temperature regime extending up to 50 000 K and hundreds of megabars. While EOSs based on first-principles simulations are now available for the two most abundant elements, hydrogen and helium, the situation is less satisfactory for water where no wide-range EOS is available despite its requirement for interior modeling of planets ranging from super-Earths to planets several times the size of Jupiter. Aims. As a first step toward a multi-phase EOS for dense water, we develop a temperature-dependent EOS for dense water covering the liquid and plasma regimes and extending to the super-ionic and gas regimes. This equation of state covers the complete range of conditions encountered in planetary modeling. Methods. We use first-principles quantum molecular dynamics simulations and the Thomas-Fermi extension to reach the highest pressures encountered in giant planets several times the size of Jupiter. Using these results, as well as the data available at lower pressures, we obtain a parametrization of the Helmholtz free energy adjusted over this extended temperature and pressure domain. The parametrization ignores the entropy and density jumps at phase boundaries but we show that it is sufficiently accurate to model interior properties of most planets and exoplanets. Results. We produce an EOS given in analytical form that is readily usable in planetary modeling codes and dynamical simulations (a fortran implementation is provided). The EOS produced is valid for the entire density range relevant to planetary modeling, for densities where quantum effects for the ions can be neglected, and for temperatures below 50 000K. We use this EOS to calculate the mass-radius relationship of exoplanets up to 5000 MEarth, explore temperature effects in the wet Earth-like, ocean planets and pure water planets, and quantify the influence of the water EOS for the core on the gravitational moments of Jupiter.

Experimental Research of Combustion Chamber With Hybrid Burner and Variable Regulation of Primary Air

2007 ◽  
Author(s):  
S. Vesely´ ◽  
S. Pary´zek ◽  
E. Vinogradov ◽  
Y. Zakharov ◽  
A. Soudarev
Keyword(s):  
Combustion Chamber ◽  
Gas Turbine ◽  
Gas Turbines ◽  
Combustion Process ◽  
The European Union ◽  
Real Gas ◽  
The Real ◽  
Wide Range ◽  
Emission Limits ◽  
Turbine Output

The environmentally friendly modification of gas turbine combustion chambers is a process for altering the structure of combustion, mainly in the primary zone in order to reduce the emission of NOx, CO, and solids into the atmosphere. The ecological modernization of gas turbines that are currently in operation is a continually topical subject because there are several thousand turbine units in Europe that do not meet current emission limits. At the same time, it can be expected that the emission limits for these turbines operating in the European Union will be reduced to NOx≤75 mg/m3, CO≤100 mg/m3 in working range of 40–100% of the gas turbine output after the year 2010. The authors have developed a new construction of a hybrid low-emission natural gas burner. Developmental work was performed both on one burner and also in a burner group consisting of seven hybrid burners. Results will be presented in this paper for model conditions for the atmospheric test rig and their re-calculation to the operational parameters on the real gas turbine. A conception with variable primary section combustion chamber geometry has been used to achieve low emissions in a wide range of gas turbine output allowing the organization of the combustion process with a constant gas/air mixing ratio coefficient. A prototype of a combustion chamber with a hybrid burner group with control of the primary air mass flow has been manufactured and tested in a 6 MW gas turbine operating in a gas pipeline compressor plant. The achieved emission characteristics will be presented and compared with precalculations. The experiments made on the real gas turbine have proven the possibility of meeting the target emission limit performance of NOx≤50 mg/m3, CO≤50 mg/m3. Other possibilities how to reduce harmful emissions for this burner type will be presented in this paper.

Reference correlations for the viscosity and thermal conductivity of fluids over an extended range of conditions: hexane in the vapor, liquid, and supercritical regions (IUPAC Technical Report)

2015 ◽  
Vol 87 (3) ◽  
pp. 321-337
Author(s):  
Richard A. Perkins ◽  
Marcia L. Huber ◽  
Marc J. Assael ◽  
Efthimia K. Mihailidou ◽  
Sofia K. Mylona ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Equation Of State ◽  
Thermodynamic Properties ◽  
Equations Of State ◽  
Reliable Data ◽  
Theoretical Knowledge ◽  
Technical Report ◽  
Wide Range ◽  
Extended Range ◽  
Vapor Liquid

AbstractThis article summarizes the correlation procedures developed for IUPAC Project 2012-040-1-100 [Reference correlations for the thermal conductivity and viscosity of fluids over extended range of conditions (vapor, liquid and supercritical regions)]. This project is focused on the development of wide-range reference correlations for the thermal conductivity and viscosity of fluids that incorporate as much theoretical knowledge of these properties as possible. The thermal conductivity and viscosity correlations developed here for pure fluids are functions of temperature and density. The best available equations of state for a given fluid are used to calculate the thermodynamic properties required for these correlations, often from measured temperatures and pressures. The correlation methodology developed during this project has been applied to hexane in this report but can be applied to any pure fluid with a reliable equation of state and reliable data for the thermal conductivity and viscosity over a significant range of temperatures and densities.

scholarly journals An anisotropic equation of state for high pressure, high temperature applications

2021 ◽  
Author(s):  
Robert Myhill
Keyword(s):  
Equation Of State ◽  
Equations Of State ◽  
Deformation Gradient ◽  
Seismic Velocities ◽  
San Carlos Olivine ◽  
High Pressure High Temperature ◽  
Wide Range ◽  
Anisotropic Equation ◽  
Scalar Properties ◽  
San Carlos

This paper presents a strategy for consistently extending isotropic equations of state to model anisotropic materials over a wide range of pressures and temperatures under nearly hydrostatic conditions. The method can be applied to materials of arbitrary symmetry. The paper provides expressions for the deformation gradient tensor, the lattice parameters, the isothermal elastic compliance tensor and thermal expansivity tensor. Scalar properties including the Gibbs energy, volume and heat capacities are inherited from the isotropic equation of state. Other physical properties including the isothermal and isentropic stiffness tensors, the Grueneisen tensor and anisotropic seismic velocities can be derived from these properties.The equation of state is demonstrated using periclase (cubic) and San Carlos olivine (orthorhombic) as examples.

scholarly journals AQUA: a collection of H2O equations of state for planetary models

2020 ◽  
Vol 643 ◽  
pp. A105 ◽  
Author(s):  
Jonas Haldemann ◽  
Yann Alibert ◽  
Christoph Mordasini ◽  
Willy Benz
Keyword(s):  
Equation Of State ◽  
Internal Energy ◽  
High Pressures ◽  
Equations Of State ◽  
Chemical Elements ◽  
Thermodynamic Quantities ◽  
Calculated Density ◽  
Temperature Range ◽  
Wide Range ◽  
The Impact

Context. Water is one of the key chemical elements in planetary structure modelling. Due to its complex phase diagram, equations of state often only cover parts of the pressure-temperature space needed in planetary modelling. Aims. We aim to construct an equation of state of H2O spanning a very wide range, from 0.1 Pa to 400 TPa and 150 to 105 K, which can be used to model the interior of planets. Methods. We combined equations of state valid in localised regions to form a continuous equation of state spanning over the above-mentioned pressure and temperature range. Results. We provide tabulated values for the most important thermodynamic quantities: the density, adiabatic temperature gradient, entropy, internal energy, and bulk speed of sound of water over this pressure and temperature range. For better usability we also calculated density-temperature and density-internal energy grids. We discuss further the impact of this equation of state on the mass radius relation of planets compared to other popular equations of state like ANEOS and QEOS. Conclusions. AQUA is a combination of existing equations of state useful for planetary models. We show that, in most regions, AQUA is a thermodynamic consistent description of water. At pressures above 10 GPa, AQUA predicts systematic larger densities than ANEOS or QEOS. This is a feature that was already present in a previously proposed equation of state, which is the main underlying equation of this work. We show that the choice of the equation of state can have a large impact on the mass-radius relation, which highlights the importance of future developments in the field of equations of state and regarding experimental data of water at high pressures.

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