Abstract
Flow with a phase transition interface in a horizontally extended porous medium is considered when a heavier phase (water) is located above a lighter phase (air-steam mixture). It is shown that if there exists a steady-state flow with a plane phase interface and this flow is stable with respect to infinitely small harmonic surface perturbations then only a local finite perturbation of the upper or lower boundary of the low-conductivity layer directed upward can lead to disappearance of the steady-state solution. This flow restructuring is possible only in the case of immiscible porous medium. Using a numerical experiment, it is shown that there exists a threshold value of the absolute value of the amplitude above which the steady-state flow ceases to exist. This threshold value decreases with increase in the “effective” width of the localized perturbation and tends asymptotically to a value corresponding to infinitely large effective width of the localized perturbation. An analytic expression for this quantity is found.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A.T. Il’ichev and G.G. Tsypkin, “Instabilities of Homogeneous Flows through a Porous Medium with a Phase Transition,” Zh. Eks. Teor. Fiz. 134, No. 4, 815–830 (2008).
A.T. Il’ichev and G.G. Tsypkin, “Catastrophic Transition to Instability of Evaporation Front in a Porous Medium,” Eur. J. Mech. B. Fluids 27, No. 6, 665–677 (2008).
G.G. Tsypkin and A.T. Il’ichev, “Gravitational Stability of the Interface in Water over Steam Geothermal Reservoirs,” Transp. Porous Media 55, No. 2, 183–199 (2004).
Z.H. Khan and D. Pritchard, “LiquidVapour Fronts in Porous Media: Multiplicity and Stability of Front Positions,” Int. J. of Heat Mass Transfer. 2013. V. 61. P. 1–17.
A.A. Afanas’ev, A.A. Barmin, and O.E. Melnik, “Hydrodynamic Stability of Evaporation Fronts in Porous Media,” Fluid Dynamics 42, No. 5, 773–783 (2007).
A.A. Afanas’ev and A.A. Barmin, “Unsteady One-Dimensional Water and Steam Flows through a Porous Medium with Allowance for Phase Transitions,” Fluid Dynamics 42(4), 627–636 (2007).
A.A. Afanas’ev, “A Representation of the Equations of Multicomponent Multiphase Flow through a Porous Medium,” Prikl. Mat. Mekh. 76, No. 2, 265–274 (2012).
M.P. Vukalovich, Thermodynamic Properties of Water and Steam (Mashgiz, Moscow, 1955).
A.T. Ilichev and V.A. Shargatov, “Dynamics of Water Evaporation Fronts,” Zh. Vychisl. Matematiki Mat. Fiz. 53, No. 9, 1531–1553 (2013).
V.A. Shargatov, V.A. Krivosheev, S.A. Gibun, and N.F. Lozik, “Instability of a Steady-State Solution of Homogeneous Flow through a Porous Medium with a Phase Transition,” Vestnik NIYaU “MIFI” 2, No. 3, 305–313 (2013).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © S.A. Gubin, V.A. Krivosheev, A.V. Shargatov, 2015, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2015, Vol. 50, No. 2, pp. 70–80.
Rights and permissions
About this article
Cite this article
Gubin, S.A., Krivosheev, V.A. & Shargatov, A.V. Existence of a steady-statewater evaporation front in a horizontally extended low-permeability region. Fluid Dyn 50, 240–249 (2015). https://doi.org/10.1134/S0015462815020088
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0015462815020088