Similarity Solutions of Radially Symmetric Two-Phase Flow
Author(s)
Weeks, Scott
Sander, G.
Lisle, I.
Parlange, J.
Griffith University Author(s)
Year published
1994
Metadata
Show full item recordAbstract
When both the diffusivityD and fractional flow functionf have a power law dependence on the water content θ, i.e.D=Doθα andf=θα+1, the nonlinear transport equation for radially symmetric two phase flow can, in certain circumstances, be reduced to a weakly coupled system of two first order nonlinear ordinary differential equations. Numerical solutions of these equations for a constant flux boundary conditionVwo and comparison with experimental data are given. In particular, when the fluxVwo and a are related byVwo(α + 1)/Do=2, a new fully explicit analytical solution is found as θ(r, t)=(1 − αr2/4Dot)1/α forr2 < 4Dot/α and ...
View more >When both the diffusivityD and fractional flow functionf have a power law dependence on the water content θ, i.e.D=Doθα andf=θα+1, the nonlinear transport equation for radially symmetric two phase flow can, in certain circumstances, be reduced to a weakly coupled system of two first order nonlinear ordinary differential equations. Numerical solutions of these equations for a constant flux boundary conditionVwo and comparison with experimental data are given. In particular, when the fluxVwo and a are related byVwo(α + 1)/Do=2, a new fully explicit analytical solution is found as θ(r, t)=(1 − αr2/4Dot)1/α forr2 < 4Dot/α and θ(r, t)=0 forr2 ≥ 4Dot/α We show that the existence of this exact soution is due to the presence of a Lagrangian symmetry.
View less >
View more >When both the diffusivityD and fractional flow functionf have a power law dependence on the water content θ, i.e.D=Doθα andf=θα+1, the nonlinear transport equation for radially symmetric two phase flow can, in certain circumstances, be reduced to a weakly coupled system of two first order nonlinear ordinary differential equations. Numerical solutions of these equations for a constant flux boundary conditionVwo and comparison with experimental data are given. In particular, when the fluxVwo and a are related byVwo(α + 1)/Do=2, a new fully explicit analytical solution is found as θ(r, t)=(1 − αr2/4Dot)1/α forr2 < 4Dot/α and θ(r, t)=0 forr2 ≥ 4Dot/α We show that the existence of this exact soution is due to the presence of a Lagrangian symmetry.
View less >
Journal Title
Journal of Applied Mathematics and Physics
Volume
45
Issue
6
Publisher URI
Subject
Mathematical Sciences
Applied Mathematics
Mathematical Physics