Influence of turbulence modelling on non-equilibrium condensing flows in nozzle and turbine cascade

Abstract The accurate analysis of a condensing flow plays an important role in the development of high-efficiency steam turbines. This paper presents an investigation of turbulence modelling influence on non-equilibrium condensing steam flows in a Laval nozzle and in a stationary cascade of turbine blades using a commercial computational fluid dynamics (CFD) code. The calculations were conducted by employing 2D compressible Reynolds-averaged Navier–Stokes (RANS) equations coupled with a two equation turbulence model. The condensation phenomena were modelled on the basis of the classical nucleation theory. The standard k – e turbulence model was modified, and the modifications were implemented in the CFD code. The influence of inlet flow turbulence on condensing process was discussed. The impact of turbulence modelling on wet-steam flow was examined based on the experimental data available in the literature. The cascade loss coefficients were calculated numerically as well. The presented study of losses that occur due to the irreversible heat and mass transfer during the condensation process emphasised the importance of turbulence modelling for wet-steam flows in turbines. The paper demonstrates that the accurate computational prediction of condensing steam flow requires the turbulence to be modelled accurately.

[1]  G Gyarmathy,et al.  Nucleation of steam in high-pressure nozzle experiments , 2005 .

[2]  D. J. Ryley,et al.  Nucleation studies in flowing high pressure steam , 1975 .

[3]  Mohammad Reza Mahpeykar,et al.  An Investigation of nucleating flows of steam in a cascade of turbine blading-theoretical treatment , 1995 .

[4]  J. Young.  Spontaneous condensation of steam in supersonic nozzles , 1982 .

[5]  Teemu Turunen-Saaresti,et al.  The Effect of Turbulence and Real Gas Models on the Two Phase Spontaneously Condensing Flows in Nozzle , 2013 .

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

[7]  C. G. Speziale.  On nonlinear K-l and K-ε models of turbulence , 1987, Journal of Fluid Mechanics.

[8]  P. Roache.  Perspective: A Method for Uniform Reporting of Grid Refinement Studies , 1994 .

[9]  Leonid I. Zaichik,et al.  The effect of turbulence on spontaneously condensing wet-steam flow , 2005 .

[10]  J. D. Denton,et al.  An Improved Time-Marching Method for Turbomachinery Flow Calculation , 1983 .

[11]  T. Gatski,et al.  On explicit algebraic stress models for complex turbulent flows , 1992, Journal of Fluid Mechanics.

[12]  Kentaro Sano,et al.  Parallel-Implicit Computation of Three-dimensional Multistage Stator-Rotor Cascade Flows with Condensation , 2007 .

[13]  Leonid I. Zaichik,et al.  Effects of turbulence and inlet moisture on two-phase spontaneously condensing flows in transonic nozzles , 2008 .

[14]  Alexander J. White,et al.  Viscous and unsteady flow calculations of condensing steam in nozzles , 2005 .

[15]  Alexander J. White,et al.  Numerical investigation of condensing steam flow in boundary layers , 2000 .

[16]  L. Richardson,et al.  The Deferred Approach to the Limit. Part I. Single Lattice. Part II. Interpenetrating Lattices , 1927 .

[17]  M. Kermani,et al.  A pressure based Eulerian–Eulerian multi-phase model for non-equilibrium condensation in transonic steam flow , 2004 .

[18]  Andrew G. Gerber,et al.  Two-Phase Eulerian/Lagrangian Model for Nucleating Steam Flow , 2002 .

[19]  J. Young,et al.  Critical Conditions and the Choking Mass Flow Rate in Nonequilibrium Wet Steam Flows , 1984 .

[20]  J. Young,et al.  An Equation of State for Steam for Turbomachinery and Other Flow Calculations , 1988 .

[21]  Sławomir Dykas,et al.  Steam condensing flow modeling in turbine channels , 2009 .

[22]  L. Richardson.  The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations, with an Application to the Stresses in a Masonry Dam , 1911 .

[23]  W. Reynolds,et al.  Thermodynamic properties in SI: Graphs, tables, and computational equations for forty substances , 1979 .

[24]  E. Eckert,et al.  Analysis of heat and mass transfer , 1971 .

[25]  F. Bakhtar,et al.  On the Performance of a Cascade of Turbine Rotor Tip Section Blading in Nucleating Steam: Part 2: Wake Traverses , 1995 .

[26]  Michael Casey,et al.  Modelling and Validation of Wet Steam Flow in a Low Pressure Steam Turbine , 2011 .

[27]  Dieter Barschdorff,et al.  Verlauf der Zustandsgrößen und gasdynamische Zusammenhänge bei der spontanen Kondensation reinen Wasserdampfes in Lavaldüsen , 1971 .

[28]  P. T. Walters,et al.  Experimental validation of condensing flow theory for a stationary cascade of steam turbine blades , 1996, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[29]  F Bakhtar,et al.  On the Performance of a Cascade of Turbine Rotor Tip Section Blading in Nucleating Steam: Part 1: Surface Pressure Distributions , 1995 .

[30]  P. Wegener,et al.  Nonequilibrium flow with condensation , 1975 .

[31]  T. J. Praisner,et al.  Measurements of Losses and Reynolds Stresses in the Secondary Flow Downstream of a Low-Speed Linear Turbine Cascade , 2010 .

[32]  Sławomir Dykas,et al.  Two-fluid model for prediction of wet steam transonic flow , 2013 .

[33]  F. Bakhtar,et al.  Nucleation Phenomena in Flowing High-Pressure Steam Part 2: Theoretical Analysis , 1990 .

[34]  F. Bakhtar,et al.  Nucleation Phenomena in Flowing High-Pressure Steam: Experimental Results , 1989 .

[35]  Shigeki Senoo,et al.  Numerical Simulations of Unsteady Wet Steam Flows With Non-Equilibrium Condensation in the Nozzle and the Steam Turbine , 2006 .

[36]  Aki Grönman,et al.  Numerical Investigation of Turbulence Modelling on Condensing Steam Flows in Turbine Cascade , 2014 .

[37]  G. Stein,et al.  On the Growth of Steam Droplets Formed in a Laval Nozzle Using both Static Pressure and Light Scattering Measurements , 1978 .

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

[39]  J. B. Young,et al.  Time-marching method for the prediction of two-dimensional, unsteady flows of condensing steam , 1993 .

[40]  P. G. Hill,et al.  Condensation of water vapour during supersonic expansion in nozzles , 1966, Journal of Fluid Mechanics.

[41]  Olivier Simonin,et al.  Two statistical models for predicting collision rates of inertial particles in homogeneous isotropic turbulence , 2003 .

[42]  Satoshi Miyake,et al.  Simulation of Unsteady 3-D Wet-Steam Flows Through Three-Stage Stator-Rotor Blade Rows With Equilibrium and Nonequilibrium Condensations , 2012 .

[43]  B. Launder,et al.  The numerical computation of turbulent flows , 1990 .

[44]  D. G. Gregory-Smith,et al.  Turbulence Measurements and Secondary Flows in a Turbine Rotor Cascade , 1988 .

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

[46]  Sławomir Dykas,et al.  Single- and two-fluid models for steam condensing flow modeling , 2011 .

[47]  P. Roe.  CHARACTERISTIC-BASED SCHEMES FOR THE EULER EQUATIONS , 1986 .

[48]  John D. Denton,et al.  The 1993 IGTI Scholar Lecture: Loss Mechanisms in Turbomachines , 1993 .