Efficient high‐pressure state equations

Harstad, K.; Miller, Richard S.; Bellan, Josette

doi:10.1002/aic.690430624

Cited by 158 publications

(93 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…(8) and (9) have to be determined using an appropriate EOS. As the PR equation [29] is known to be not very accurate in predicting the density in transcritical regions, an additional volume-correction method established by Harstad et al [30] has been applied within the present work:…”

Section: Thermodynamic Properties and Equation Of Statementioning

confidence: 99%

Real gas CFD simulations of hydrogen/oxygen supercritical combustion

Pohl

Jarczyk

Pfitzner

et al. 2013

Progress in Propulsion Physics

View full text Add to dashboard Cite

A comprehensive numerical framework has been established to simulate reacting §ows under conditions typically encountered in rocket combustion chambers. The model implemented into the commercial CFD Code ANSYS CFX includes appropriate real gas relations based on the volume-corrected PengRobinson (PR) equation of state (EOS) for the §ow ¦eld and a real gas extension of the laminar §amelet combustion model. The results indicate that the real gas relations have a considerably larger impact on the §ow ¦eld than on the detailed §ame structure. Generally, a realistic §ame shape could be achieved for the real gas approach compared to experimental data from the Mascotte test rig V03 operated at ONERA when the di¨erential di¨usion processes were only considered within the §ame zone.

show abstract

Section: Thermodynamic Properties and Equation Of Statementioning

confidence: 99%

Real gas CFD simulations of hydrogen/oxygen supercritical combustion

Pohl

Jarczyk

Pfitzner

et al. 2013

Progress in Propulsion Physics

View full text Add to dashboard Cite

show abstract

“…Furthermore, the molar volume v is related to the density by v = m/ρ. The components of the PR parameters are provided by an appropriate set of mixing rules which vary for different state equations and may even have variations for the same state equation; in the present model we follow the mixing rules given in Harstad et al (1997), and the exact set of mixing rules is provided in Appendix A. These mixing rules are a synthesis of those in Reid, Prausnitz & Polling (1987) and Prausnitz et al (1986).…”

Section: Equation Of Statementioning

confidence: 99%

“…We therefore limit the range of thermodynamic state space which will be considered to the range 600 6 T 6 1100 K, 40 6 p 6 80 atm, and of course 0 6 Y h 6 1. This particular region is chosen for two primary reasons: (1) The PR EOS was found to be highly accurate within this region when compared to the more accurate model of Harstad et al (1997) with the relative error being in no case greater than approximately 1% for both the entropy and enthalpy predictions (this error can be larger than 25% at p = 6 MPa and T = 350 K). (2) Contour plots (not shown) of the viscosity, and of the Schmidt (Sc) and Prandtl (P r) numbers based on accurate species transport properties calculated as in Harstad & Bellan (1998), revealed that the viscosity is predominantly a function of T alone, whereas Sc and P r are predominantly functions of the mass fraction.…”

Section: Equation Of Statementioning

confidence: 99%

Direct numerical simulations of supercritical fluid mixing layers applied to heptane–nitrogen

2001

Self Cite

View full text Add to dashboard Cite

Direct numerical simulations (DNS) are conducted of a model hydrocarbon-nitrogen mixing layer under supercritical conditions. The temporally developing mixing layer configuration is studied using heptane and nitrogen supercritical fluid streams at a pressure of 60 atm as a model system related to practical hydrocarbon-fuel/air systems. An entirely self-consistent cubic Peng-Robinson equation of state is used to describe all thermodynamic mixture variables, including the pressure, internal energy, enthalpy, heat capacity, and speed of sound along with additional terms associated with the generalized heat and mass transport vectors. The Peng-Robinson formulation is based on pure-species reference states accurate to better than 1% relative error through comparisons with highly accurate state equations over the range of variables used in this study (600 6 T 6 1100 K, 40 6 p 6 80 atm) and is augmented by an accurate curve fit to the internal energy so as not to require iterative solutions. The DNS results of two-dimensional and three-dimensional layers elucidate the unique thermodynamic and mixing features associated with supercritical conditions. Departures from the perfect gas and ideal mixture conditions are quantified by the compression factor and by the mass diffusion factor, both of which show reductions from the unity value. It is found that the qualitative aspects of the mixing layer may be different according to the specification of the thermal diffusion factors whose value is generally unknown, and the reason for this difference is identified by examining the second-order statistics: the constant Bearman-Kirkwood (BK) thermal diffusion factor excites fluctuations that the constant Irwing-Kirkwood (IK) one does not, and thus enhances overall mixing. Combined with the effect of the mass diffusion factor, constant positive large BK thermal diffusion factors retard diffusional mixing, whereas constant moderate IK factors tend to promote diffusional mixing. Constant positive BK thermal diffusion factors also tend to maintain density gradients, with resulting greater shear and vorticity. These conclusions about IK and BK thermal diffusion factors are speciespair dependent, and therefore are not necessarily universal. Increasing the temperature of the lower stream to approach that of the higher stream results in increased layer growth as measured by the momentum thickness. The three-dimensional mixing layer exhibits slow formation of turbulent small scales, and transition to turbulence does not occur even for a relatively long non-dimensional time when compared to a previous, atmospheric conditions study. The primary reason for this delay is the initial density stratification of the flow, while the formation of strong density gradient regions both in the braid and between-the-braid planes may constitute a secondary reason for the hindering of transition through damping of emerging turbulent eddies. † Present address:

show abstract

“…By translating the thermodynamic state of the §uid along its volume axis, the density prediction is considerably improved. An example is the empirical method of Harstad et al [24], which has been implemented in both codes. This volume correction method will henceforth be referred to as PR-VC.…”

Section: Thermophysical Modelingmentioning

confidence: 99%

Large-eddy simulation of trans- and supercritical injection

Müller

Niedermeier

Jarczyk

et al. 2016

Progress in Propulsion Physics

View full text Add to dashboard Cite

In a joint e¨ort to develop a robust numerical tool for the simulation of injection, mixing, and combustion in liquid rocket engines at high pressure, a real-gas thermodynamics model has been implemented into two computational §uid dynamics (CFD) codes, the density-based INCA and a pressure-based version of OpenFOAM. As a part of the validation process, both codes have been used to perform large-eddy simulations (LES) of trans-and supercritical nitrogen injection. Despite the di¨erent code architecture and the di¨erent subgrid scale turbulence modeling strategy, both codes yield similar results. The agreement with the available experimental data is good.

show abstract

Efficient high‐pressure state equations

Cited by 158 publications

References 4 publications

Real gas CFD simulations of hydrogen/oxygen supercritical combustion

Real gas CFD simulations of hydrogen/oxygen supercritical combustion

Direct numerical simulations of supercritical fluid mixing layers applied to heptane–nitrogen

Large-eddy simulation of trans- and supercritical injection

Contact Info

Product

Resources

About