Numerical solution of one-dimensional transient, two-phase flows with temporal fully implicit high order schemes: Subcooled boiling in pipes Articles uri icon


publication date

  • March 2017

start page

  • 319

end page

  • 329


  • 313

International Standard Serial Number (ISSN)

  • 0029-5493

Electronic International Standard Serial Number (EISSN)

  • 1872-759X


  • An extension for 1-D transient two-phase flows of the SIMPLE-ESDIRK method, initially developed for incompressible viscous flows by ljaz is presented. This extension is motivated by the high temporal order of accuracy demanded to cope with fast phase change events. This methodology is suitable for boiling heat exchangers, solar thermal receivers, etc. The methodology of the solution consist in a finite volume staggered grid discretization of the governing equations in which the transient terms are treated with the explicit first stage singly diagonally implicit Runge-Kutta (ESDIRK) method. It is suitable for stiff differential equations, present in instant boiling or condensation processes. It is combined with the semi implicit pressure linked equations algorithm (SIMPLE) for the calculation of the pressure field. The case of study consists of the numerical reproduction of the Bartolomei upward boiling pipe flow experiment. The steady-state validation of the numerical algorithm is made against these experimental results and well known numerical results for that experiment. In addition, a detailed study reveals the benefits over the first order Euler Backward method when applying 3rd and 4th order schemes, making emphasis in the behaviour when the system is subjected to periodic square wave wall heat function disturbances, concluding that the use of the ESDIRK method in two-phase calculations presents remarkable accuracy and computational advantages.


  • 1-d two-phase flows; runge-kutta methods; esdirk method; finite volume method; quasi-homogeneous model; phase change events; runge-kutta methods; 2-fluid model; posedness; equations