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Title: An oscillation free shock-capturing method for compressible van der Waals supercritical fluid flows

Abstract

Numerical solutions of the Euler equations using real gas equations of state (EOS) often exhibit serious inaccuracies. The focus here is the van der Waals EOS and its variants (often used in supercritical fluid computations). The problems are not related to a lack of convexity of the EOS since the EOS are considered in their domain of convexity at any mesh point and at any time. The difficulties appear as soon as a density discontinuity is present with the rest of the fluid in mechanical equilibrium and typically result in spurious pressure and velocity oscillations. This is reminiscent of well-known pressure oscillations occurring with ideal gas mixtures when a mass fraction discontinuity is present, which can be interpreted as a discontinuity in the EOS parameters. We are concerned with pressure oscillations that appear just for a single fluid each time a density discontinuity is present. As a result, the combination of density in a nonlinear fashion in the EOS with diffusion by the numerical method results in violation of mechanical equilibrium conditions which are not easy to eliminate, even under grid refinement.

Authors:
 [1];  [2];  [3]
  1. Univ. of Illinois at Urbana-Champaign, Urbana, IL (United States)
  2. Aix Marseille Univ. and Univ. Institute of France, Marseille Cedex (France); RS2N SAS, Saint Zacharie (France)
  3. Ecole Centrale Paris, Chatenay-Malabry (France); Lab. d'Energetique Moleculaire et Macroscopique, Chatenay-Malabry (France)
Publication Date:
Research Org.:
California Inst. of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP) (NA-10)
OSTI Identifier:
1343123
Alternate Identifier(s):
OSTI ID: 1352895; OSTI ID: 1411835
Grant/Contract Number:
NA0002382
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 335; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; shock-capturing methods; real equation of state; Van der Waals; nonconservative equations; pressure oscillations; 97 MATHEMATICS AND COMPUTING

Citation Formats

Pantano, C., Saurel, R., and Schmitt, T.. An oscillation free shock-capturing method for compressible van der Waals supercritical fluid flows. United States: N. p., 2017. Web. doi:10.1016/j.jcp.2017.01.057.
Pantano, C., Saurel, R., & Schmitt, T.. An oscillation free shock-capturing method for compressible van der Waals supercritical fluid flows. United States. doi:10.1016/j.jcp.2017.01.057.
Pantano, C., Saurel, R., and Schmitt, T.. Wed . "An oscillation free shock-capturing method for compressible van der Waals supercritical fluid flows". United States. doi:10.1016/j.jcp.2017.01.057. https://www.osti.gov/servlets/purl/1343123.
@article{osti_1343123,
title = {An oscillation free shock-capturing method for compressible van der Waals supercritical fluid flows},
author = {Pantano, C. and Saurel, R. and Schmitt, T.},
abstractNote = {Numerical solutions of the Euler equations using real gas equations of state (EOS) often exhibit serious inaccuracies. The focus here is the van der Waals EOS and its variants (often used in supercritical fluid computations). The problems are not related to a lack of convexity of the EOS since the EOS are considered in their domain of convexity at any mesh point and at any time. The difficulties appear as soon as a density discontinuity is present with the rest of the fluid in mechanical equilibrium and typically result in spurious pressure and velocity oscillations. This is reminiscent of well-known pressure oscillations occurring with ideal gas mixtures when a mass fraction discontinuity is present, which can be interpreted as a discontinuity in the EOS parameters. We are concerned with pressure oscillations that appear just for a single fluid each time a density discontinuity is present. As a result, the combination of density in a nonlinear fashion in the EOS with diffusion by the numerical method results in violation of mechanical equilibrium conditions which are not easy to eliminate, even under grid refinement.},
doi = {10.1016/j.jcp.2017.01.057},
journal = {Journal of Computational Physics},
number = C,
volume = 335,
place = {United States},
year = {Wed Feb 01 00:00:00 EST 2017},
month = {Wed Feb 01 00:00:00 EST 2017}
}

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  • Numerical solutions of the Euler equations using real gas equations of state (EOS) often exhibit serious inaccuracies. The focus here is the van der Waals EOS and its variants (often used in supercritical fluid computations). The problems are not related to a lack of convexity of the EOS since the EOS are considered in their domain of convexity at any mesh point and at any time. The difficulties appear as soon as a density discontinuity is present with the rest of the fluid in mechanical equilibrium and typically result in spurious pressure and velocity oscillations. This is reminiscent of well-knownmore » pressure oscillations occurring with ideal gas mixtures when a mass fraction discontinuity is present, which can be interpreted as a discontinuity in the EOS parameters. We are concerned with pressure oscillations that appear just for a single fluid each time a density discontinuity is present. The combination of density in a nonlinear fashion in the EOS with diffusion by the numerical method results in violation of mechanical equilibrium conditions which are not easy to eliminate, even under grid refinement. A cure to this problem is developed in the present paper for the van der Waals EOS based on previous ideas. A special extra field and its corresponding evolution equation is added to the flow model. This new field separates the evolution of the nonlinear part of the density in the EOS and produce oscillation free solutions. The extra equation being nonconservative the behavior of two established numerical schemes on shocks computation is studied and compared to exact reference solutions that are available in the present context. The analysis shows that shock conditions of the nonconservative equation have important consequence on the results. Last, multidimensional computations of a supercritical gas jet is performed to illustrate the benefits of the present method, compared to conventional flow solvers« less
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  • Supercritical fluids near the critical point are characterized by liquid-like densities and gas-like transport properties. These features are purposely exploited in different contexts ranging from natural products extraction/fractionation to aerospace propulsion. Large part of studies concerns this last context, focusing on the dynamics of supercritical fluids at high Mach number where compressibility and thermodynamics strictly interact. Despite the widespread use also at low Mach number, the turbulent mixing properties of slightly supercritical fluids have still not investigated in detail in this regime. This topic is addressed here by dealing with Direct Numerical Simulations of a coaxial jet of a slightlymore » supercritical van der Waals fluid. Since acoustic effects are irrelevant in the low Mach number conditions found in many industrial applications, the numerical model is based on a suitable low-Mach number expansion of the governing equation. According to experimental observations, the weakly supercritical regime is characterized by the formation of finger-like structures – the so-called ligaments – in the shear layers separating the two streams. The mechanism of ligament formation at vanishing Mach number is extracted from the simulations and a detailed statistical characterization is provided. Ligaments always form whenever a high density contrast occurs, independently of real or perfect gas behaviors. The difference between real and perfect gas conditions is found in the ligament small-scale structure. More intense density gradients and thinner interfaces characterize the near critical fluid in comparison with the smoother behavior of the perfect gas. A phenomenological interpretation is here provided on the basis of the real gas thermodynamics properties.« less
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