Abstract
In this paper, the influence of incidence angle on the aerodynamics of the steam flow field around a rotor tip section is investigated. An Eulerian–Eulerian method, based on a non-equilibrium thermodynamics model for simulating the wet flow is employed. In this study, the effects of incidence angle on different design parameters such as: outflow Mach number, outflow gas phase mass fraction, loss coefficient and deviation angle are studied.
Similar content being viewed by others
Notes
International Association of Properties of Water and Steam.
Abbreviations
- A :
-
Area (m2)
- C :
-
Chord (mm)
- h :
-
Static enthalpy (J/kg)
- H :
-
Total enthalpy (J/kg)
- i :
-
Incidence angle (=β in − χ in ) (°)
- J :
-
Nucleation rate [(Droplet #’s)/(m3 s)]
- k :
-
Conduction coefficient (W/m K)
- m :
-
Mass (kg)
- M :
-
Mach number
- N :
-
Number of droplets per unit mass of vapor [(Droplet #’s)/kgg]
- P :
-
Pressure (N/m2)
- S :
-
Blade pitch (mm)
- S w+d , S h :
-
Source term for energy equation (W/m3)
- S F , S u :
-
Source term for momentum equation (N/m3)
- S m :
-
Source term representing the evaporation rate of vapor [kg/(m3 s)]
- t :
-
Time (s)
- T :
-
Temperature (K)
- ΔT :
-
Super cooling degree (=Tsat − Tg) (K)
- U :
-
Velocity (m/s)
- X :
-
Spatial dimension (m)
- y + :
-
Dimensionless wall distance
- Α :
-
Mass fraction of liquid water to water vapor (kgf/kgg)
- Γ :
-
Specific heat ratio
- Β :
-
Flow direction (°)
- Ω :
-
Specific dissipation rate (1/s)
- Κ :
-
Turbulent kinetic energy (m2/s2)
- Μ :
-
Dynamic viscosity [kg/(m s)]
- Π :
-
Pressure loss coefficient
- Ρ :
-
Density (kg/m3)
- χ :
-
Blade metal angle (°)
- out :
-
Outlet condition
- eff :
-
Effective (laminar + turbulent)
- f :
-
Liquid
- g :
-
Gas
- i, j :
-
Tensor notation
- in :
-
Inlet condition
- 0 :
-
Stagnation condition
- Sat :
-
Saturation
References
Moore MJ, Walters PT, Crane RI, Davidson BJ (1973) Predicting the fog-drop size in wet steam turbines. In: Institute of mechanical engineering conference, Warwick, pp. 37–73
Skilings SA, Jackson R (1987) A robust time-marching solver for one-dimensional nucleating steam flows. Int J Heat Fluid Flow 8:138–144
McCallum M, Hunt R (1999) The flow of wet steam in a one-dimensional nozzle. Int J Numer Meth Eng 44:1807–1821
White AJ, Young JB (1993) Time-marching method for the prediction of two-dimensional, unsteady flows of condensing steam. J Propulsion Power 9:579–587
White AJ, Hounslow MJ (2000) Modeling droplet size distributions in polydispersed wet-steam flows. Int J Heat Mass Transfer 43:1873–1884
Moheban M, Young JB (1985) A study of thermal nonequilibrium effects in low-pressure wet-steam turbines using a blade-to-blade time-marching technique. Int J Heat Fluid Flow 6:269–278
Yang Y, Shen S (2009) Numerical simulation on non-equilibrium spontaneous condensation in supersonic steam flow. Int Commun Heat Mass Transfer 36:902–907
Sun L, Zheng Q, Liu S (2007) 2D-simulation of wet steam flow in a steam turbine with spontaneous condensation. J Marine Sci Appl 6:36–59
Gerber AG (2002) Two-phase Eulerian/Lagrangian model for nucleating steam flow. ASME J Fluids Eng 124:465–475
Gerber AG, Kermani MJ (2003) A pressure based Eulerian–Eulerian multi-phase model for non-equilibrium condensation in transonic steam flow. Int J Heat Mass Transfer 47:2217–2231
Dykas S, Wroblewki W, Lukovicz H (2007) Prediction of losses in the flow through the last stage of low-pressure steam turbine. Int J Numer Meth Fluids 53:933–945
Gerber AG, Sigg R, Volker L, Casey MV, Surken N (2007) Predictions of non-equilibrium phase transition in a model low-pressure steam turbine. J Power Energy 221:825–834
Wroblewski W, Dykas S, Gepert A (2009) Steam condensing flow modeling in turbine channels. Int J Multiphase Flow 35:498–506
Bakhtar F, Mahpeykar MR (1996) On the performance of a cascade of turbine rotor tip section blading in nucleating steam, Part 3: theoretical treatment. Proc Inst Mech Eng Part C 211:195–211
White AJ, Young JB, Walters PT (1996) Experimental validation of condensing flow theory for a stationary cascade of steam turbine blades. Philos Trans R Soc Landon A 354:59–68
Li SM, Chu TL, Yoo YS, Ng WF (2002) Transonic and low supersonic flow losses of two steam turbine blades at large incidences. ASME J Fluids Eng 126:966–975
Chibli HA, Abdelfattah SA, Schobeiri MT (2009) An experimental and numerical study of the effects of flow incidence angles on the performance of a stator blade cascade of a high pressure steam turbine. In: Proceedings of ASME TURBO EXPO, Orlando, Florida, GT, pp 821–830
Herzog N, Binner M, Seume JR, Rothe K (2007) Verification of low-flow conditions in a multistage turbine. In: Proceedings of ASME, pp 563–574
Roland S, Casey V, Mayer F (2008) The influence of lean and sweep in a low pressure steam turbine: analysis of three stages with a 3D CFD model. In: Proceedings of ASME, pp 969–978
Chibli A, Abdelfattah A, Schobeiri MT, Kang C (2009) An experimental and numerical study of the effects of flow incidence angles on the performance of a stator blade cascade of a high pressure steam turbine. In: Proceedings of ASME, pp 821–830
Stein A, Hofer DC, Filippenko V, Slepski J (2010) Aerodynamic design of transonic tip sections. In: Proceedings of ASME, pp 2109–2118
Equations of IAPWS-IF97, A summary by Bernhard Spang, Hamburg, Germany, at The Chemical Engineers’ Resource Page
IAPWS Equations for Transport Properties and, Surface Tension of Water and Steam, A summary by Bernhard Spang, Hamburg, Germany, at The Chemical Engineers’ Resource Page
Bakhtar F, Ebrahimi M, Webb RA (1995) On the performance of a cascade of turbine rotor tip section blading in nucleating steam, Part 1: surface pressure distributions. Proc Inst Mech Eng Part C 209:115–124
Bakhtar F, Zidi K (1989) Nucleation phenomena in flowing high-pressure steam, experimental results. Proc Inst Mech Eng 203:195–200
ANSYS CFX 11-Solver Theory Guide (2006) Discretization and solution theory, pp. 277–280
Beheshti Amiri H, Kermani MJ (2015) The effect of inlet stagnation supercooling degree on the aerodynamics of the steam flow field around a rotor tip section. J Heat Mass Transfer 51:117–128
Beheshti Amiri H, Kermani MJ, Piroozi AA (2015) Parametric studies influencing condensation evolution in compressible steam flow. J Heat Mass Transfer 51:1075–1084
Lichtfuss H-J, Starken H (1974) Supersonic cascade flow, DFVLR Sonderdruck Number 376. Prog Aerosp Sci 15:37–149
Bakhtar F, Yousif FH (1974) The behavior of wet steam after disruption by a shock wave. In: Symposium on multi-phase flow systems, Univ of Strathclyde, Institution of Chemical Engineering, G3
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Beheshti Amiri, H., Salmaniyeh, F. & Izadi, A. The influence of incidence angle on the aerodynamics of condensing flow around a rotor tip section of steam turbine. Heat Mass Transfer 52, 2423–2436 (2016). https://doi.org/10.1007/s00231-015-1736-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00231-015-1736-7