Calculations of the condensing water steam flows in turbine blade cascades

• Autorzy: Wróblewski W.
• Języki publikacji: EN

Abstrakty

EN

This paper describes modelling of two- and three-dimensional flows with homogeneous condensation. It needs a simultaneous solution of a differential governing equations (continuity, momentum and energy- equations) and differential equation of condensate formation. It was assumed that flow is inviscid, the velocity slip between the vapour and liquid droplets is neglected. The formation of the liquid phase is calculated using classical nucleation theory. Superheated and subcooled steam parameters are computed from a virial non-linear equation of state. The influence of correction methods and droplet growth models is discussed. The finite volume cell centred calculation method is used. The solution procedure is based on the upwind Godunov-type scheme adapted to the real gas problems. Presented algorithm is capable to investigate unsteady condensation phenomena in the flow. The computational results of the two-phase flow modelling with condensation through a turbine cascade are presented. For the turbine stator of the steam turbine the 3-D flow structure is described.

Słowa kluczowe

EN

turbine blade cascade; condensing water steam flow; two-dimensional flow; three-dimensional flow; modelling

PL

łopatka turbiny; przepływ dwuwymiarowy; przepływ trójwymiarowy; para wodna; kondensacja; modelowanie

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Turbulence : international journal
• Rocznik: 2000
• Tom: Vol. 6-7
• Strony: 209--223
• Opis fizyczny: Bibliogr. 27 poz.

Twórcy

autor

Wróblewski W.

• Institute of Power Machinery, Silesian University of Technology, Gliwice, ul. Konarskiego 18, 44-100 Gliwice

Bibliografia

• [1] Adam S., Schnerr G., Instabilities and bifurcation of non-equilibrium two-phase flows, J. Fluid Mech. 1997, 348, 1-28.
• [2] Bakhtar F., Mahpeykar M.R., Abbas K.K., An investigation of nucleating flows of steam in cascade of turbine blading-theoretical treatment, Transaction of ASME, Journal of Fluids Engineering 1995, 117, March, 138-144
• [3] Bakhtar F., Mohammadi Tochai M.T., An investigation of two-dimensional flows of nucleating and wet steam by the time-marching method, Int. J. Heat & Fluid Flow 1980, 2, 1.
• [4] Braem S., Laali A.R., Dorey J.M., Kleitz A., Modelling of unsteady condensing steam flows: two-dimensional approach using exact thermodynamic formulations, 2nd European Conference on Turbomachinery-Fluid Dynamics and Thermodynamics, Antwerpen 1997.
• [5] Chmielniak T.J., Wróblewski W., Dykas S., Calculation of water vapour 1kw with condensation, Archives of Thermodynamics 1997, 18, 1-2, 99-l 14.
• [6] Dejc M.E., Filippow G.A., Gasdynamics of Two-Phase Flow, Energia, Moscow 1981 (in Russian).
• [7] Frenkel J., Kinetic Theory of Liquids, Dover Publ., New York 1955.
• [8] Hill P.G., Condensation of water vapour during supersonic expansion in nozzles, J. Fluid Mech. 1966, 25, 3, 593-620.
• [9] Godunov S.K., A difference scheme for numerical computation of discontinuous solution of hydrodynamic equations, Math. Sbornik 1959, 47, 271-306 (in Russian).
• [10] Gyarmathy G., Grundlagen einer Theorie der Nassdampfturbine, Dissertation, Juris Verlag, Züirich 1960.
• [11] Kantrowitz A., Nucleation in very rapid vapour expansions, Journal Chem. Phys. 1951, 19, 1097-1100.
• [12] Krzyżanowski J., Erozja łopatek turbin parowych, Ossolineum, Warszawa 1991.
• [13] Moheban M., Young J.B., A time-marching method for the calculation of blade-to blade non equilibrium wet steam flows in turbine cascades, IMechE, Conference on Computational Methods in Turbomachinery 1984, Paper C76/84, 89-99,
• [14] Puzyrewski R., Król T., Numerical analysis of Hertz-Knudsen model of condensation upon small droplets in water vapour, Prace IMP PAN, Gdańsk 1976, nr 70-72.
• [15] Rivkin C.L., Kremenevskaya E.A., Equations of state of water and water vapour for the computation of the processes in power plants, Teploenergetika 1967, 3, 69-73 (in Russian).
• [16] Schnerr G., Heiłer M., Two-phase flow instabilities in channels and turbine cascades, Modelling and Design in Fluid-Flow Machinery, ed. J. Badur, J. Mikielewicz, Z. Bilicki, E. Śliwicki, Gdańsk 1997.
• [17] Sejna M., Lam J., Numerical modelling of wet steam flow with homogenous condensation on unstructured trianguiar meshes, ZAMM 1994, 74, 5.
• [18] Singh U., Method for nucleating steam flow in low-pressure turbine stages, IMechE 1999, C557 827-836.
• [19] Stastny M., Sejna M., Jonas O., Modelling the flow with condensation and chemical impurities in steam turbine cascades, 2nd European Conference on Turbomachinery-Fluid Dynamics and Thermodynamics, Antwerpen 1997.
• [20] Stastny M., Sejna M., Numerical analysis of hetero-homogeneous condensation of the steam fiowing in turbine cascade, IMechE 1999, C557 815-826.
• [21] van Albada G.D., van Leer B., Roberts W.W., A comparative study of computational methods in cosmic gas dynamics, Astron. Astrophysics 1982, 108, 76-84.
• [22] van Leer B., Towards the ultimate conservative difference scheme, V. A second order sequel to Godunov’s Method, Journal of Computational Physics 1979, 32, 101-136.
• [23] White A.J., Young J.B., A time-marching method for the prediction of two-dimensional un steady flows of condensing steam, J. of Propulsion and Power 1993,9, 579-587.
• [24] White A.J., Young J.B., Walters P.T., Experimental validation of condensing flow theory for a stationary cascade of steam turbine blades, Phil. Trans. R. Soc. Lond. A. 1996, 3 54-59.
• [25] Wróblewski W., Numeryczna symulacja zjawisk przepływowych w turbinach cieplnych, ZN Politechniki Śląskiej 2000, s. Energetyka 132.
• [26] Wukalowicz M.P., Riykin C.L., Equations of state of the superheated water vapour, Teploenergetika 1969, 3, 60-66 (in Russian).
• [27] Young J.B., Two-dimensional, non-equilibrium wet-steam calculations for nozzles and turbine cascades, J. of Turbomachinery 1992, 114, 569-579.