A Novel Numerical Approach for Low Mach Number: Application to Supercritical Fluids

2013 ◽  
Author(s):  
Jalil Ouazzani ◽  
Yves Garrabos
Keyword(s):  
Carbon Dioxide ◽  
Equation Of State ◽  
Supercritical Fluid ◽  
Supercritical Fluids ◽  
Energy Equation ◽  
Fluid Flows ◽  
Ideal Gas ◽  
Gas Flows ◽  
Low Mach Number ◽  
Critical Carbon Dioxide

A new numerical algorithm has been developed to compute low Mach number fluids using the cV-formulation of the energy equation. cV is the specific heat at constant volume. It has been applied to both supercritical fluid flows (using a nonlinear equation of state like the van der Waals cubic equation of state) and gas flows (using an ideal gas law). The algorithm is introduced successfully in a finite volume code using the SIMPLE and SIMPLER methods. Its main advantage lies in the decoupling of the energy equation and equation of state from the momentum and continuity equations, leading to decrease significantly the CPU time in the case of supercritical fluids simulations. Moreover it allows for supercritical fluid flow simulations the use of other discretization methods (such as spectral methods and/or finite differences) and any other nonlinear form of the equation of state. The new algorithm is presented after a brief description of the previously existing algorithm to solve supercritical fluid flows. Then three published Benchmark problems for steady and unsteady ideal gas flows are treated, as well as the side heated cavity problem for a near critical carbon dioxide filling. The results are then compared to those obtained from the previous algorithm as well as to those obtained from a spectral code using the new algorithm. This comparative investigation is extended to the Rayleigh-Bénard problem for a near critical carbon dioxide filled square cavity with the use of the Van der Waals and the Peng-Robinson equations of state.

Vaneless Diffuser Performance in a Super-Critical Carbon Dioxide Centrifugal Compressor With Real Gas Effects

2021 ◽  
Author(s):  
Lakshminarayanan Seshadri ◽  
Pramod Kumar
Keyword(s):  
Carbon Dioxide ◽  
Centrifugal Compressor ◽  
Ideal Gas ◽  
Single Step ◽  
Gas Flows ◽  
Vaneless Diffuser ◽  
Strong Function ◽  
Real Gas ◽  
Real Gas Effects ◽  
Critical Carbon Dioxide

Abstract Super-critical Carbon dioxide (s-CO2) flows are neither incompressible nor ideal gas flows. Unlike perfect gases, the enthalpy of s-CO2 near the critical point is a strong function of pressure. Incorporation of these effects is necessary for accurate modeling of flows in centrifugal compressor vaneless diffusers. This study reviews the existing vaneless diffuser modeling technique, and modifications are made to incorporate real gas effects. Like the existing procedure, the proposed formulation does not require multiple iterations for convergence. The results are obtained in a single step using a marching technique. Hence, this model can be incorporated in standard centrifugal compressor design and analysis tools, especially for super-critical carbon dioxide flows, subject to experimental validation.

Generation and Propagation of Thermally Induced Acoustic Waves in Supercritical Fluids: Numerical and Experimental Results

2010 ◽  
Author(s):  
Bakhtier Farouk ◽  
Zhieheng Lei
Keyword(s):  
Carbon Dioxide ◽  
Supercritical Carbon Dioxide ◽  
Supercritical Fluid ◽  
Supercritical Fluids ◽  
Acoustic Waves ◽  
Rapid Heating ◽  
Time Dependent ◽  
Cylindrical Chamber ◽  
Thermally Induced ◽  
Supercritical Carbon

The behavior of thermally induced acoustic waves generated by the rapid heating of a bounding solid wall in a closed cylindrical chamber filled with supercritical carbon dioxide is investigated numerically and experimentally. A time-dependent one-dimensional problem is considered for the numerical simulations where the supercritical fluid is contained between two parallel plates. The NIST Reference Database 12 is used to obtain the property relations for supercritical carbon dioxide. The thermally induced pressure (acoustic) waves undergo repeated reflections at the two confining walls and gradually dissipate. The numerically predicted temperature of the bulk supercritical fluid is found to increase homogeneously (the so called piston effect) within the domain. The details of generation, propagation and dissipation of thermally induced acoustic waves in supercritical fluids are presented under different heating rates. In the experiments, a resistance-capacitance circuit is used to generate a rapid temperature increase in a thin metal foil located at one end of a closed cylindrical chamber. The time-dependent pressure variation in the chamber and the temperature history at the foil are recorded by a fast response measurement system. Both the experimental and numerical studies predict similar pressure wave shapes and profiles due to rapid heating of a wall.

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.

III. On symmetric compressible fluid flows around a flat plate

1965 ◽  
Vol 285 (1402) ◽  
pp. 413-422 ◽  
Keyword(s):  
Equation Of State ◽  
Flat Plate ◽  
Compressible Fluid ◽  
Singular Integrals ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Fluid Flows ◽  
State Equation ◽  
Ideal Gas ◽  
Compressible Fluid Flows

The Navier-Stokes equations for compressible fluid flows around a semi-infinite flat plate under symmetric attack are investigated. It is shown that regular locally subsonic motions, which are defined by bounded pressures and temperature gradients at the edge, exist without placing any restrictions on, for instance, analytic fluid characteristics as equation of state, equation of viscosity, and so forth. Those regular motions are locally incompressible and, hence, display the same flow patterns around the leading or trailing edge of a plate as incompressible fluid motions. In contrast to the existence of regular solutions the equations of motion exclude any singular integrals for which the pressure is infinite at the edge of the plate, provided the equation of state and the equations for viscosity, conductivity and specific heat are sufficiently regular. In particular, no singular solution exists if, for instance, the ideal gas law, Sutherland’s formula of viscosity, etc., are prescribed.

Supercritical Fluid of Carbon Dioxide and Carbon Nanotubes

2013 ◽  
pp. 198-201
Keyword(s):  
Carbon Dioxide ◽  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Gas Phase ◽  
Supercritical Fluid ◽  
Van Der Waals ◽  
Ideal Gas ◽  
Test Tube ◽  
Van Der Waals Equation ◽  
Ideal Gas Law

In this exercise students will learn to use a carbon nanotube as gas phase test tube, to study the transition from a gas to a supercritical fluid for CO2. They will also learn to compare the Ideal Gas Law to the van der Waals equation.

scholarly journals Some Advances in Supercritical Fluid Extraction for Fuels, Bio-Materials and Purification

Processes ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 156 ◽  
Author(s):  
Yizhak Marcus
Keyword(s):  
Carbon Dioxide ◽  
Supercritical Fluid Extraction ◽  
Supercritical Fluid ◽  
Supercritical Fluids ◽  
Chemical Properties ◽  
Physical And Chemical Properties ◽  
Nanosized Particles ◽  
Fluid Extraction ◽  
Physical And Chemical ◽  
And Chemical Properties

Supercritical fluids are used for the extraction of desired ingredients from natural materials, but also for the removal of undesired and harmful ingredients. In this paper, the pertinent physical and chemical properties of supercritical water, methanol, ethanol, carbon dioxide, and their mixtures are provided. The methodologies used with supercritical fluid extraction are briefly dealt with. Advances in the application of supercritical extraction to fuels, the gaining of antioxidants and other useful items from biomass, the removal of undesired ingredients or contaminants, and the preparation of nanosized particles of drugs are described.

A New Correlation for the Turbulent Prandtl Number in Upward Rounded Tubes in Supercritical Fluid Flows

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Mahdi Mohseni ◽  
Majid Bazargan
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Supercritical Fluid ◽  
Supercritical Fluids ◽  
Fluid Pressure ◽  
Fluid Flows ◽  
Numerical Code ◽  
Turbulent Prandtl Number ◽  
New Correlation ◽  
Model Predictions

Numerical results show that at supercritical pressures, once the buoyancy force increases, the effect of the turbulent Prandtl number, Prt, on convective heat transfer becomes considerable. This phenomenon has not been adequately addressed in the literature. In this study, the effect of the turbulent Prandtl number on the rate of heat transfer in both enhanced and deteriorated regimes of heat transfer to supercritical fluid flows has been extensively investigated. Having realized that variations of the turbulent Prandtl number can affect the model predictions so greatly, a new correlation to express the changes of Prt with respect to flow conditions in a supercritical environment is developed. Effects of various important parameters such as heat flux, mass flux, and fluid pressure are included in the proposed correlation. This correlation has been modified to be applicable for different supercritical fluids. The comparison with various experimental data shows that by implementing the new correlation of Prt in the numerical code, it is possible to significantly improve the simulation results. Such a correlation seems to be the first one introduced in the literature for a supercritical fluid flow.

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