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

Journal Article · · Journal of Computational Physics
 [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)
+ Show Author Affiliations

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. 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

Research Organization:
California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP)
Grant/Contract Number:
NA0002382
OSTI ID:
1343123
Alternate ID(s):
OSTI ID: 1352895; OSTI ID: 1411835
Journal Information:
Journal of Computational Physics, Vol. 335, Issue C; ISSN 0021-9991
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 21 works
Citation information provided by
Web of Science

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Cited By (7)

Characterization of pseudo-boiling in a transcritical nitrogen jet journal July 2018
Real-fluid effects on standing-wave thermoacoustic instability journal November 2019
Development of a nonconservative discontinuous Galerkin formulation for simulations of unsteady and turbulent flows journal May 2020
A multicomponent real-fluid fully compressible four-equation model for two-phase flow with phase change journal February 2019
An adaptive ALE scheme for non-ideal compressible fluid dynamics over dynamic unstructured meshes journal July 2018
An Adaptive ALE Scheme for Non-Ideal Compressible-Fluid Dynamics over Dynamic Unstructured Meshes text January 2019
Numerical analysis on mixing processes for transcritical real-fluid simulations conference January 2018

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Related Subjects

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