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. 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.more » 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

Authors:

Pantano, C. ^[1]; Saurel, R. ^[2]; Schmitt, T. ^[3]

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+ Show Author Affiliations

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:

Wed Feb 01 00:00:00 EST 2017

Research Org.:

California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Org.:

USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP)

OSTI Identifier:

1343123

Alternate Identifier(s):

OSTI ID: 1352895; OSTI ID: 1411835

Grant/Contract Number:  

NA0002382

Resource Type:

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