Abstract
The influence of complicated interaction between the flow field and heat transfer in cooled turbines becomes more and more significant with the increasing turbine inlet temperature. However, classical through-flow methods did not take into account the influence of the interaction caused by air cooling. The aerodynamic design and cooling design of cooled turbines were carried out separately, and the iterations between the aerodynamic design and cooling design led to a long design period and raised the design cost. To shorten the design period and decrease the design cost, this paper proposes a concise aero-thermal coupled through-flow method for the design of cooled turbines, taking into account the influence of the complicated interaction between the flow field and heat transfer in cooled turbines. The governing equations, such as energy equation and continuity equation in classical through-flow method are re-derived theoretically by considering the historical influence of cooling with the same method that deals with viscous losses in this paper. A cooling model is developed in this method. The cooled blade is split into a number of heat transfer elements, and the heat transfer is studied element by element along both the span and the chord in detail. This paper applies the method in the design of a two-stage axial turbine, of which the first stator is cooled with convective cooling. With the prescribed blade temperature limitation and the knowledge of the flow variables of the mainstream at the turbine inlet, such as the total pressure, total temperature and mass flow rate, the convergence of the calculation is then obtained and the properties of the flow field, velocity triangles and coolant requirement are well predicted. The calculated results prove that the aero-thermal coupled through-flow method is a reliable tool for flow analysis and coolant requirement prediction in the design of cooled turbines.
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References
Wu C H. A general theory of three-dimensional flow in subsonic and supersonic turbomachines of axial-, radial-and mixed-flow types. NACA Technical Note, 2604, 1952: 1–96
Novak R A. Steamline curvature computing procedures for fluid-flow problems. J Eng Power, 1967, 89: 478–490
Denton J D. Through flow calculations for transonic axial flow turbines. J Eng Power, 1978, 100: 212–218
Li B, Gu C W, Song Y. Aerodynamic analysis of a highly loaded compressor in semi-closed cycles using a throughflow method. Greenhouse Gases: Sci Tech, 2015, 5: 545–557
Mildner F, Gallus H E. An analysis method for multistage transonic turbines with coolant mass flow addition. ASME J Turbomach, 1998, 120: 744–752
Gehring S, Riess W. Analysis of the mixing process in a 1.5 stage turbine with coolant ejection. In: Proceedings of ASME Turbo Expo 2000, Munich, Germany, 2000, No. 2000-GT-669: 1–8
Petrovic M V, Wiedermann A. Through-flow analysis of air-cooled gas turbines. J Turbomachinery, 2013, 135: 1–8
Hao Z R, Gu C W, Ren X D. The application of discontinuous Galerkin methods in conjugate heat transfer simulations of gas turbines. Energies, 2014, 7: 7857–7877
Li H B, Gu C W, Song Y. Through-flow calculation with a cooling model for cooled turbines. P I Mech Eng A-J Pow, 2015, doi: 10.1177/0957650915594294
Papa M, Goldstein R J, Gori F. Numerical heat transfer predictions and mass/heat transfer measurements in a linear turbine cascade. Appl Therm Eng, 2007, 27: 771–778
Holland M J, Thake T F. Rotor blade cooling in high pressure turbines. J Aircraft, 1989, 17: 412–418
Ainley D G. Internal air cooling for turbine blades: A general design survey. A.R.C. Technical Report, 1957, 3013: 1–42
Consonni S. Performance prediction of gas/steam cycles for power generation. Dissertation of Doctor Degree. Princeton: MAE Dept. Princeton University, 1992
Torbidoni L, Horlock J H. A new method to calculate the coolant requirements of a high temperature gas turbine blade. ASME J Turbomach, 2005, 127: 191–199
Li H B, Gu C W. Through-flow calculations for convective cooled turbines. In: Proceedings of ASME Turbo Expo 2014, Dusseldorf, Germany, 2014, No. 2014-GT-26504. 1–10
Ainley D G, Mathieson G C R. A method of performance estimation for axial-flow turbine. ARC Technical Report, 1957, R&M 2974. 1–32
Dunham J, Came P M. Improvements to the Ainley-Mathieson method of turbine performance prediction. J Eng Power, 1970, 92: 252–256
Kacker S C, Okapuu U. A mean line prediction method for axial flow turbine efficiency. J Eng Power, 1982, 104: 111–119
Li Y S, Lu G L. Centripetal Turbine and Centrifugal Compressor. Beijing: China Machine Press, 1987. 94–108
Holman J P. Heat Transfer. 6th ed. New York: McGraw-Hill, 1986. 254–255
El-Masri M A, Pourkey F. Prediction of cooling flow requirements for advanced utility gas turbines Part 1: Analysis and scaling of the effectiveness curve. In: American Society of Mechanical Engineers winter meeting, Anaheim, CA, USA, 1986, Technical Paper 86-WA/HT-43
Gong R Z, Wang H J, Chen L X, et al. Application of entropy production theory to hydro-turbine hydraulic analysis. Sci China Tech Sci, 2013, 56: 1636–1643
Hartsel J E. Prediction of effects of mass-transfer cooling on the blade-row efficiency of turbine airfoils. In: AIAA, 10th Aerospace Sciences Meeting, San Diego, 1972. AIAA-72-11
Shapiro A. The Dynamics and Thermodynamics of Compressible Fluid Flow: Volume I. New York: Ronald Press, 1953. 219–231
Ji X X, Gu C W, Song Y, et al. Performance prediction and analysis of a three-shaft gas turbine supported by turbine cooling model. In: Proceedings of ASME Turbo Expo 2014, Dusseldorf, Germany, 2014. No. 2014-GT-25312. 1–9
Yan P G, Shi L, Wang X F, et al. Retrofit design of composite cooling structure of a turbine blade by fluid networks and conjugate heat transfer methods. Sci China Tech Sci, 2013, 56: 3104–3114
Shrivastava K D, Maccallum N R L. The effect of a transversely injected stream on the flow through turbine cascades—Part II: Performance changes. In: Proceedings of ASME Turbo Expo 2014, Dusseldorf, Germany, New York, USA, 1987. No. 87-GT-88: 1–10
Day C R B, Oldfield M L G, Lock G D. Aerodynamic performance of an annular cascade of film cooled nozzle guide vanes under engine representative conditions. Exp Fluids, 2000, 29: 117–129
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Gu, C., Li, H. & Song, Y. Development of an aero-thermal coupled through-flow method for cooled turbines. Sci. China Technol. Sci. 58, 2060–2071 (2015). https://doi.org/10.1007/s11431-015-5941-x
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DOI: https://doi.org/10.1007/s11431-015-5941-x