HLLC-type methods for compressible two-phase flow in ducts with discontinuous area changes

•We develop HLLC-type schemes for flow in ducts of variable cross-sectional area.•The schemes are developed for general equations of state.•For two-phase flow simulations, the homogeneous equilibrium model is employed.•The schemes are tested on Riemann problems for ideal gas and two-phase CO2.•Inclu...

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Bibliographic Details
Published in:Computers & fluids 2021-09, Vol.227, p.105023, Article 105023
Main Authors: Log, Alexandra Metallinou, Munkejord, Svend Tollak, Hammer, Morten
Format: Article
Language:English
Subjects:
Compressibility
Compressible flow
Ducts
Equations of state
Equilibrium flow
Finite-volume method
HLLC solver
Non-conservative system
Nozzle flow
Numerical methods
Riemann solver
Robustness (mathematics)
Subsonic flow
Thermodynamic equilibrium
Thermodynamic properties
Two phase flow
Variable cross-section
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Summary:•We develop HLLC-type schemes for flow in ducts of variable cross-sectional area.•The schemes are developed for general equations of state.•For two-phase flow simulations, the homogeneous equilibrium model is employed.•The schemes are tested on Riemann problems for ideal gas and two-phase CO2.•Including the non-conservative term in the solver wave structure is the most robust. In this work, the Harten-Lax-van Leer Contact (HLLC) approximate Riemann solver is extended to two-phase flow through ducts with discontinuous cross-sections. Two main strategies are explored regarding the treatment of the non-conservative term arising in the governing equations. In the first, labelled HLLC+S, the non-conservative term is discretized separately. In the second, labelled HLLCS, the non-conservative term is incorporated in the Riemann solver. The methods are assessed by numerical tests for single and two-phase flow of CO2, the latter employing a homogeneous equilibrium model where the thermodynamic properties are calculated using the Peng–Robinson equation of state. The methods have different strengths, but in general, HLLCS is found to work best. In particular, it is demonstrated to be equally accurate and more robust than existing methods for non-resonant flow. It is also well-balanced for subsonic flow in the sense that it conserves steady-state flow.
ISSN:0045-7930
1879-0747
DOI:10.1016/j.compfluid.2021.105023