Numerical simulations for non conservative hyperbolic system. Application to transient two-phase flow with cavitation phenomenon
Abstract
A numerical method for simulating transient flows of gas-liquid mixtures is proposed. The mathematical model, established for a suspension of gas bubbles in liquid, includes an equation taking into account the relative velocity between the gas and liquid. A numerical technique based on the MacCormack scheme combined with the method of characteristics is presented. Theoretical results for transients initiated by a rapid closing valves are compared with measurements. A good agreement is found particularly for large values of initial dissolved gas concentration.
Keyword : non conservative system, MacCormack scheme, hyperbolic system, two phase flow, cavitation
How to Cite
Achchab, B., Agouzal, A., & El Idrissi, A. Q. (2019). Numerical simulations for non conservative hyperbolic system. Application to transient two-phase flow with cavitation phenomenon. Mathematical Modelling and Analysis, 24(2), 218-235. https://doi.org/10.3846/mma.2019.015
This work is licensed under a Creative Commons Attribution 4.0 International License.
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46(2):411–442, 2012.
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A. Qadi El Idrissi. Ecoulement Transitoire en Conduite avec Prise en Compte de Ph´enom`enes Diphasiques. Thesis, Institut National des Sciences Appliques de Lyon (France), 1996.
A. Jafarian and A. Pisheva. An exact multiphase Riemann solver for compressible cavitating flows. Multiphase Flow, 88:152–166, 2017. https://doi.org/10.1016/j.ijmultiphaseflow.2016.08.001
D. Liuzzi. Two-Phase Cavitation Modelling. Thesis, University of Rome - La Sapienza, 2012.
S. T. Munkejord, S. Evje and T. Flåtten. A Musta scheme for a nonconservative two-fluid model. SIAM J. Sci. Comput., 31(4):2587–2622, 2009. https://doi.org/10.1137/080719273
M. L. Munoz-Ruiz and C. Parés. Godunov method for nonconservative hyperbolic systems. Math. Model. Numer. Anal, 41(1):169–185, 2007. https://doi.org/10.1051/m2an:2007011
C. Parés. Numerical methods for nonconservative hyperbolic systems: A theoretical framework. SIAM J. Numer. Anal., 44(1):300–321, 2006. https://doi.org/10.1137/050628052
A. Prosperetti and L. V. Wijngaarden. On the characteristics of the equations of motion for a bubbly flow and the related problem of critical flow. Eng. Math., 10(2):153–162, 1976. https://doi.org/10.1007/BF01535658
O. V. Vasilyev R. S. Lagumbay and A. Haselbacher. Homogeneous equilibrium mixture model for simulation of multiphase/multicomponent flows. Numer. Meth. Fluids, 00:1–6, 2007.
N. D. Tam. Fluid Transients in Complex Systems with Air Entrainment. Thesis, National University of Singapore, 2009.
H. S. Tang and D. Huang. A second-order accurate capturing scheme for 1D inviscid flows of gas and water with vacuum zones. Comput. Phys., 128:301–318, 1996. https://doi.org/10.1006/jcph.1996.0212
D. C. Wiggert and M. J. Sundquist. The effect of gaseous cavitation on fluid transients. Fluids Eng., 101(1):79–86, 1979. https://doi.org/10.1115/1.3448739