scholarly journals One-dimensional refraction properties of compression shocks in non-ideal gases

2017 ◽  
Vol 814 ◽  
pp. 185-221 ◽  
Author(s):  
Nicolas Alferez ◽  
Emile Touber
Keyword(s):  
Critical Point ◽  
Equations Of State ◽  
Organic Rankine Cycle ◽  
Ideal Gas ◽  
Acoustic Properties ◽  
Compressible Turbulence ◽  
Isentropic Compression ◽  
Volume Expansivity ◽  
Ideal Gases ◽  
Mach Numbers

Non-ideal gases refer to deformable substances in which the speed of sound can decrease following an isentropic compression. This may occur near a phase transition such as the liquid–vapour critical point due to long-range molecular interactions. Isentropes can then become locally concave in the pressure/specific-volume phase diagram (e.g. Bethe–Zel’dovich–Thompson (BZT) gases). Following the pioneering work of Bethe (Tech. Rep. 545, Office of Scientific Research and Development, 1942) on shocks in non-ideal gases, this paper explores the refraction properties of stable compression shocks in non-reacting but arbitrary substances featuring a positive isobaric volume expansivity. A small-perturbation analysis is carried out to obtain analytical expressions for the thermo-acoustic properties of the refracted field normal to the shock front. Three new regimes are discovered: (i) an extensive but selective (in upstream Mach numbers) amplification of the entropy mode (hundreds of times larger than those of a corresponding ideal gas); (ii) discontinuous (in upstream Mach numbers) refraction properties following the appearance of non-admissible portions of the shock adiabats; (iii) the emergence of a phase shift for the generated acoustic modes and therefore the existence of conditions for which the perturbed shock does not produce any acoustic field (i.e. ‘quiet’ shocks, to contrast with the spontaneous D’yakov–Kontorovich acoustic emission expected in 2D or 3D). In the context of multidimensional flows, and compressible turbulence in particular, these results demonstrate a variety of pathways by which a supplied amount of energy (in the form of an entropy, vortical or acoustic mode) can be redistributed in the form of other entropy, acoustic and vortical modes in a manner that is simply not achievable in ideal gases. These findings are relevant for turbines and compressors operating close to the liquid–vapour critical point (e.g. organic Rankine cycle expanders, supercritical $\text{CO}_{2}$ compressors), astrophysical flows modelled as continuum media with exotic equations of state (e.g. the early Universe) or Bose–Einstein condensates with small but finite temperature effects.

Uncertainty Analysis of a Polytropic Compression Process and Application to Centrifugal Compressor Performance Testing

2005 ◽  
Author(s):  
Jose´ L. Gilarranz
Keyword(s):  
Uncertainty Analysis ◽  
Centrifugal Compressor ◽  
Equations Of State ◽  
Pressure Ratio ◽  
Ideal Gas ◽  
Isentropic Compression ◽  
Real Gas ◽  
Compression Model ◽  
Test Loop ◽  
Real Gas Equations

In recent years, several papers have been written concerning the application of uncertainty analyses for isentropic compression processes under the assumption of ideal gas behavior. However, for high-pressure ratio machines, the ideal gas model fails to capture the physics of the process. Still, the estimation of test uncertainty for polytropic processes is hindered by the complexity of the equations used to calculate the performance parameters and by the incorporation of real gas equations into the models. This paper presents an uncertainty analysis developed to estimate the error levels in data gathered during factory aero-performance tests of single- or multi-stage centrifugal compressors. The analysis incorporates the effects of the variation and uncertainty levels of every parameter used to calculate centrifugal compressor aero-thermal performance. Included are the variables used to define the thermodynamic states of the fluid inside the compressor, as well as geometric and operational parameters associated with the machine and test loop. Two different methods have been utilized and the results compared to evaluate the advantages and drawbacks of each. The first method is based on the direct use of the Monte Carlo simulation technique combined with real gas equations of state. The second method employs uncertainty propagation equations and the methodology included in the ASME PTC-19.1 (1998) Test Code. Both approaches utilize the polytropic compression model and equations for performance evaluation that are included in the ASME PTC 10 (1997) Power Test Code for compressors and exhausters. The methods and results from this work may be easily extended to the isentropic compression model as well. The use of real gas equations of state make the methods applicable to virtually any gas composition. Although the analysis was intended to be applied to ASME PTC 10 Type 2 tests, the method can be extended to evaluate Type 1 and/or on-site field tests, as long as certain considerations are addressed. The uncertainty analysis presented is then used to evaluate data from several machines, ranging from a low-pressure ratio gas pipeline compressor to an eight-stage machine used for natural gas processing. Comments are offered concerning the effects of machine pressure ratio on the levels of uncertainty, as well as the importance of proper selection of instrumentation to minimize the error level of the test data. Special emphasis is placed on the benefits of using this analysis during the planning phase of the test program, to determine the optimal combination of instruments, to guarantee acceptable levels of uncertainty.

scholarly journals Large Eddy Simulations of Strongly Non-Ideal Compressible Flows through a Transonic Cascade

Energies ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 772
Author(s):  
Jean-Christophe Hoarau ◽  
Paola Cinnella ◽  
Xavier Gloerfelt
Keyword(s):  
Compressible Flows ◽  
Flow Behavior ◽  
Pressure Ratio ◽  
Organic Rankine Cycle ◽  
Ideal Gas ◽  
Operating Conditions ◽  
Large Eddy Simulations ◽  
Working Fluid ◽  
Viscous Effects ◽  
Large Eddy

Transonic flows of a molecularly complex organic fluid through a stator cascade were investigated by means of large eddy simulations (LESs). The selected configuration was considered as representative of the high-pressure stages of high-temperature Organic Rankine Cycle (ORC) axial turbines, which may exhibit significant non-ideal gas effects. A heavy fluorocarbon, perhydrophenanthrene (PP11), was selected as the working fluid to exacerbate deviations from the ideal flow behavior. The LESs were carried out at various operating conditions (pressure ratio and total conditions at inlet), and their influence on compressibility and viscous effects is discussed. The complex thermodynamic behavior of the fluid generates highly non-ideal shock systems at the blade trailing edge. These are shown to undergo complex interactions with the transitional viscous boundary layers and wakes, with an impact on the loss mechanisms and predicted loss coefficients compared to lower-fidelity models relying on the Reynolds-averaged Navier–Stokes (RANS) equations.

Wake-Induced Unsteady Stagnation-Region Heat Transfer Measurements

1994 ◽  
Vol 116 (1) ◽  
pp. 29-38 ◽  
Author(s):  
P. J. Magari ◽  
L. E. LaGraff
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Edge Region ◽  
Isentropic Compression ◽  
Stagnation Region ◽  
Stagnation Line ◽  
Wide Range ◽  
Mach Numbers

An experimental investigation of wake-induced unsteady heat transfer in the stagnation region of a cylinder was conducted. The objective of the study was to create a quasi-steady representation of the stator/rotor interaction in a gas turbine using two stationary cylinders in crossflow. In this simulation, a larger cylinder, representing the leading-edge region of a rotor blade, was immersed in the wake of a smaller cylinder, representing the trailing-edge region of a stator vane. Time-averaged and time-resolved heat transfer results were obtained over a wide range of Reynolds number at two Mach numbers: one incompressible and one transonic. The tests were conducted at Reynolds numbers, Mach numbers, and gas-to-wall temperature ratios characteristic of turbine engine conditions in an isentropic compression-heated transient wind tunnel (LICH tube). The augmentation of the heat transfer in the stagnation region due to wake unsteadiness was documented by comparison with isolated cylinder tests. It was found that the time-averaged heat transfer rate at the stagnation line, expressed in terms of the Frossling number (Nu/Re), reached a maximum independent of the Reynolds number. The power spectra and cross-correlation of the heat transfer signals in the stagnation region revealed the importance of large vortical structures shed from the upstream wake generator. These structures caused large positive and negative excursions about the mean heat transfer rate in the stagnation region.

Implications of Phase Change on the Aerodynamics of Centrifugal Compressors for Supercritical Carbon Dioxide Applications

2020 ◽  
Author(s):  
Giacomo Persico ◽  
Lorenzo Toni ◽  
Paolo Gaetani ◽  
Ernani Fulvio Bellobuono ◽  
Alessandro Romei ◽  
...  
Keyword(s):  
Carbon Dioxide ◽  
Power Systems ◽  
Phase Change ◽  
Critical Point ◽  
Fluid Dynamic ◽  
Flow Analysis ◽  
Design Strategy ◽  
Ideal Gas ◽  
New Challenges ◽  
Line Design

Abstract Closed Joule-Bryton cycles operating with carbon dioxide in supercritical conditions (sCO2) are nowadays collecting a significant scientific interest, due to their high potential efficiency, the compactness of their components, and the flexibility that makes them suitable to exploit diverse energy sources. However, the technical implementation of sCO2 power systems introduces new challenges related to the design and operation of the components. The compressor, in particular, operates in a thermodynamic condition close to the critical point, whereby the fluid exhibits significant non-ideal gas effects and is prone to phase change in the intake region of the machine. These new challenges require novel design concepts and strategies, as well as proper tools to achieve reliable predictions. In the present study, we consider an exemplary sCO2 power cycle with main compressor operating in proximity to the critical point, with an intake entropy level of the fluid lower than the critical value. In this condition, the phase change occurs as evaporation/flashing, thus resembling cavitation phenomena observed in liquid pumps, even though with specific issues associated to compressibility effects occurring in both the phases. The flow configuration is therefore highly nonconventional and demands the development of proper tools for fluid and flow modeling, which are instrumental for the compressor design. The paper discusses the modeling issues from the thermodynamic perspective and then highlighting the implications on the compressor aerodynamics. We propose tailored models to account for the effect of the phase change in 0D mean-line design tools as well as in fully 3D computational fluid-dynamic (CFD) simulations. In this way, a design strategy is build-up as a combination of mean-line tools, industrial design experience, and CFD for detailed flow analysis. The application of the design strategy reveals that the potential onset of the phase change might alter significantly the performance and operation of the compressor, both in design and in off-design conditions.

Gaseous Solutions

1993 ◽  
Author(s):  
Greg M. Anderson ◽  
David A. Crerar
Keyword(s):  
Equations Of State ◽  
Intermolecular Forces ◽  
Point Of View ◽  
Alternative Methods ◽  
Gaseous Species ◽  
Fugacity Coefficient ◽  
Ideal Gases ◽  
Component Systems ◽  
Liquid Solutions ◽  
History Of

The procedures described in Chapter 15 are well suited to solid and liquid solutions and could also be applied to gases, but in fact, other approaches are generally used. The main reason for this is partly historical; much work was done early in the history of physical chemistry on the behavior of gases, and these methods have continued to evolve to the present day. We have also just seen that the Margules equations become very unwieldy with multi-component systems. Because true gases are completely miscible, natural gases often contain many different components, so the Margules approach is not very suitable. Unfortunately, the most successful alternative methods described in this section are also quite unwieldy; however, they do not become much more complicated for multi-component gases than they are for the pure gases themselves, and this is a definite advantage. We have seen that with real, non-ideal gases, all the thermodynamic properties are described if we know the T, P, and the fugacity coefficient. For gaseous solutions, the fugacity coefficient for each component generally depends on the concentrations and types of other gaseous species in the same mixture. All gases, whether pure or multi-component, should approach ideality at higher T and lower P; conversely, non-ideality is most pronounced in dense, low-temperature gases where intermolecular forces are strongest. The challenge here is to find an equation of state that can adequately cover this range of conditions for gases of many different constituents. In the following discussion we first briefly outline some of the equations of state used to describe pure gases. We will introduce these from the molecular point of view since this helps understand the physical basis (and limitations) of each model. Each of these equations of state can then be applied to mixtures of gases using a set of rules which we describe at the end of this section.

Phase Transitions

2019 ◽  
pp. 205-222
Author(s):  
Robert H. Swendsen
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
Phase Transitions ◽  
Helmholtz Free Energy ◽  
Equations Of State ◽  
Van Der Waals ◽  
Ideal Gas ◽  
Phase Rule ◽  
Clapeyron Equation ◽  
Maxwell Construction

Phase transitions are introduced using the van der Waals gas as an example. The equations of state are derived from the Helmholtz free energy of the ideal gas. The behavior of this model is analyzed, and an instability leads to a liquid-gas phase transition. The Maxwell construction for the pressure at which a phase transition occurs is derived. The effect of phase transition on the Gibbs free energy and Helmholtz free energy is shown. Latent heat is defined, and the Clausius–Clapeyron equation is derived. Gibbs' phase rule is derived and illustrated.

scholarly journals Modification of the Electron Entropy Production in a Plasma

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 935
Author(s):  
Juan F. García-Camacho ◽  
Gonzalo Ares de Parga ◽  
Karen Arango-Reyes ◽  
Encarnación Salinas-Hernández ◽  
Samuel Domínguez-Hernández
Keyword(s):  
Entropy Production ◽  
Equations Of State ◽  
Hermite Polynomials ◽  
Ideal Gas ◽  
Modified Equations ◽  
Modified Entropy ◽  
The Ideal

A modified expression of the electron entropy production in a plasma is deduced by means of the Kelly equations of state instead of the ideal gas equations of state. From the Debye–Hückel model which considers the interaction between the charges, such equations of state are derived for a plasma and the entropy is deduced. The technique to obtain the modified entropy production is based on usual developments but including the modified equations of state giving the regular result plus some extra terms. We derive an expression of the modified entropy production in terms of the tensorial Hermitian moments hr1…rm(m) by means of the irreducible tensorial Hermite polynomials.

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