The eigenvalues and eigenvectors of the Jacobian matrix of the homogeneously condensing two-phase flow equations are derived. These are useful for all upwind schemes. Details of the implementation in the Roe scheme are described. Example calculations for condensing wet steam flow are provided, which compare well with the experimental results.
RoeP.Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys., 1981, 43, 357–372.
2.
OsherS.SalomonF.Upwind difference schemes for hyperbolic systems of conservation laws. Math. Comput., 1982, 28, 339–374.
3.
van LeerB.Towards the ultimate conservative scheme, monotony and conservation combined in a scheme. J. Comput. Phys., 1974, 14, 361–370.
4.
GuhaA.YoungJ. B.Time-marching prediction of unsteady condensation phenomena due to supercritical heat addition. Turbomachinery: latest developments in a changing scene1991, pp. 167–177 (IMechE, London), ISBN 0852987617.
5.
GuhaA.A unified theory of aerodynamic and condensation shock waves in vapour-droplet flows with or without a carrier gas. Phys. Fluids, 1994, 6 (5), 1893–1913.
6.
GuhaA.Two-phase flows with phase transition. VKI lecture series 1995–06, 1995, pp. 1–110 (von Karman Institute for Fluid Dynamics, Belgium), ISSN 0377–8312.
7.
SchnerrG. H.DohrmannU.Transonic flow around airfoils with relaxation and energy supply by homogeneous condensation. AIAA J., 1990, 28 (7), 1187–1193.
8.
BarschdorffD.FillipovG. A.Analysis of certain special operating modes of laval nozzles with local heat supply. Heat Transf. Soviet Res., 1970, 2 (5), 76–87.
9.
LiouM. S.The years in the making AUSM-family. AIAA paper 2001–2521, 2001.
10.
MeiY.GuhaA.Implicit numerical simulation of transonic flow through turbine cascades on unstructured grids. Proc. IMechE, Part A: J. Power and Energy, 2005, 219, 35–47.
