Parallel-Implicit Computation of Three-dimensional Multistage Stator-Rotor Cascade Flows with Condensation

This paper presents the recent progress in our research group for developing a parallel computational code which can simulate three-dimensional multistage stator-rotor cascade flows in gas and steam turbines. This code can calculate not only those air flows, but also those flows of moist air and of wet steam. We named this code “Numerical Turbine”. The fundamental equations consist of conservation laws of the total density, the momentums, the total energy, the density of water vapor, the density of water liquid, and the number density of water droplets and they are coupled with SST turbulence model in general curvilinear coordinates. The high-order high-resolution finite-difference method based on the fourth-order compact MUSCL TVD(Compact MUSCL) scheme and Roe's approximate Riemann solver is used for the space discretization of convection terms. A parallelized LU-SGS method based on the pipelining method is newly employed for the parallel-implicit time-integration. As numerical examples, 2-D and 3-D flows of wet steam through two-stage stator-rotor cascade channels in a steam turbine are computed.

[1]  Seokkwan Yoon,et al.  Parallelization of Gauss-Seidel Relaxation for Real Gas Flow , 2005 .

[2]  Onset of Condensation in Vortical Flow over Sharp-Edged Delta Wing , 2001 .

[3]  F. Bakhtar,et al.  An investigation of two-dimensional flows of nucleating and wet steam by the time-marching method , 1980 .

[4]  Y. Sasao,et al.  Numerical Simulation of Wet-steam Flows Through Turbine Cascades in Multiple Stage , 2007 .

[5]  W. J. Moran,et al.  Computerized aircraft synthesis. , 1967 .

[6]  F. Menter.  Two-equation eddy-viscosity turbulence models for engineering applications , 1994 .

[7]  J. Frankel.  Kinetic theory of liquids , 1946 .

[8]  I︠A︡kov Ilʹich Frenkelʹ.  Kinetic Theory of Liquids , 1955 .

[9]  Satoru Yamamoto,et al.  Numerical Prediction of Humid Effect to Transonic Flows in Turbomachinery , 2003 .

[10]  J. Young,et al.  Two-Dimensional, Nonequilibrium, Wet-Steam Calculations for Nozzles and Turbine Cascades , 1992 .

[11]  H. Daiguji,et al.  A High-Resolution Finite Difference Scheme for Supersonic Wet-Stream Flows. , 1994 .

[12]  Günter H. Schnerr,et al.  Instabilities and bifurcation of non-equilibrium two-phase flows , 1997, Journal of Fluid Mechanics.

[13]  A. Jameson,et al.  Lower-upper Symmetric-Gauss-Seidel method for the Euler and Navier-Stokes equations , 1988 .

[14]  P. Roe.  Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[15]  Satoru Yamamoto,et al.  Numerical Prediction of Unsteady Flows Through Turbine Stator-Rotor Channels With Condensation , 2005 .

[16]  Satoru Yamamoto,et al.  Higher-order-accurate upwind schemes for solving the compressible Euler and Navier-Stokes equations , 1993 .