# Mathematical Modeling on Gas Turbine Blades/Vanes Under Variable Convective and Radiative Heat Flux with Tentative Different Laws of Cooling

Mathematical Modeling on Gas Turbine Blades/Vanes Under Variable Convective and Radiative Heat Flux with Tentative Different Laws of Cooling

F. Floris G. Viglialoro

Department of Mechanical, Chemical and Material Engineering. University of Cagliari (Italy)

Department of Mathematics and Computer Science. University of Cagliari (Italy)

Page:
55-65
|
DOI:
ttps://doi.org/10.2495/CMEM-V5-N1-55-65
N/A
| |
Accepted:
N/A
| | Citation

OPEN ACCESS

Abstract:

In the last twenty years the modeling of heat transfer on gas turbine cascades has been based on computational fluid dynamic and turbulence modeling at sonic transition. The method is called Conjugate Flow and Heat Transfer (CHT). The quest for higher Turbine Inlet Temperature (TIT) to increase electrical efficiency makes radiative transfer the more and more effective in the leading edge and suction/ pressure sides. Calculation of its amount and transfer towards surface are therefore needed. In this paper we decouple convection and radiation load, the first assumed from convective heat transfer data and the second by means of emissivity charts and analytical fits of heteropolar species as CO2 and H2O. Then we propose to solve the temperature profile in the blade through a quasi-two-dimensional power balance in the form of a second order partial differential equation which includes radiation and convection.

Real cascades are cooled internally trough cool compressed air, so that we include in the power balance the effect of a heat sink or law of cooling that is up to the designer to test in order to reduce the thermal gradients and material temperature. The problem is numerically solved by means of the Finite Element Method (FEM) and, subsequently, some numerical simulations are also presented.

Keywords:

finite element method, gas turbines, heat balance equation, mathematical simulations, radiative/convective heat transfer

References

[1] Chiesa, P., Lozza, G., Macchi, E. & Consonni, S., An assessment of the thermodynamic performance of mixed gas-steam cycles: part b: water-injected and HAT cycles. Journal of Engineering for Gas Turbines and Power, 117(3), pp. 499–508, 1995. http://dx.doi.org/10.1115/1.2814123

[2] Eckardt, D. & Rufli, P., Advanced gas turbine technology - ABB/BBC historical firsts. Journal of Engineering Gas Turbines and Power, 124(3), pp. 542–549, 2002. http://dx.doi.org/10.1115/1.1470484

[3] Gaul, G.R., Diakunchak, I.S. & Dodd, A.M., The W5b1G testing and validation in the Siemens Westinghouse advanced turbine systems program. ASME Proceedings Electric Power, Paper 2001-GT-0399, 2011.

[4] Macchi, E., Consonni, S., Lozza, G. & Chiesa, P., An assessment of the thermodynamic performance of mixed gas-steam cycles: part a-intercooled and steam-injected cycles. Journal of Engineering for Gas Turbines and Power, 117(3), pp. 489–498, 1995.

[5] Bunker, R.S., Gas turbine heat transfer: ten remaining hot gas path challenges. Journal of Turbomachinery, 129(2), pp. 193–201, 2006. http://dx.doi.org/10.1115/1.2464142

[6] Han, J.C. & Wright, L.M., Enhanced Internal Cooling of Turbine Blades and Vanes. The Gas Turbine Handbook, U.S., National Energy technology Laboratory, Morgantown. Section 4.2.2.2. 2007.

[7] Alhajeri, M. & Alhamad Alhajeri, H., Heat and fluid flow analysis in gas turbine cooling passages with semicircular turbulators. International Journal of Physical Science. 4(12), pp. 835–845, 2009.

[8] Akhter, M.N. & Funakazi, K., Development of prediction method of boundary layer bypass transition using intermittency transport equation. International Journal of Gas Turbine, Propulsion and Power Systems (JGPP), 1(1), pp. 30–37, 2007.

[9] Bhaskaran, R. & Lele, S.K., Heat transfer prediction in high pressure turbine cascade with free-stream turbulence using LES. 41st AIAA Fluid Dynamics Conference and Exhibit, 27–30 June 2011, Honolulu, Hawaii. http://dx.doi.org/10.2514/6.2011-3266

[10] Floris, F., Ilemin, B. & Orrii, P.F., Quasi 1-D analysis of heat equation with exact solutions and comparison with numerical simulation in liquid/vapour pressure tanks, waterwalls and hot drawing machines. 31st UITHeat Transfer Conference, 25–27 June 2013, Como, Italy.

[11] McAdams, W.H., Heat Transmission, 3 edn., McGraw-Hill, 1954.

[12] Rohsenow, W.R. & Choi, H., Heat, Mass, and Momentum Transfer, Prentice-Hall, Inc, 1961.

[13] Bueters, K.A., Cogoli, J.C. & Habelt, W.W., Performance prediction of tangentially fired utility furnaces by computer model. Symposium International on Combustion, 15, pp. 1245–1260, 1975. http://dx.doi.org/10.1016/s0082-0784(75)80387-0

[14] Incropera, F.P. & De Witt, D.P., Fundamentals of Heat and Mass Transfer, 5 edn, John Wiley & Sons: New York, 2001.

[15] Mehrotra, A.K., Karan, K. & Behie, L.A., Estimate gas emissivities for equipment and process design. Chemical Engineering Progress, 91, pp. 70–77, 1995.

[16] Gao, Z., Narzary, D.P. & Han, J.C., Film-cooling on a gas turbine blade pressure side or suction side with compound angle shaped holes. Journal of Turbomachinery, 131(1), p. 11, 2008.

[17] McElroy, M.W., Lawrie, A. & Bond, I.P., Optimisation of an air film cooled CFRP panel with an embedded vascular network. International Journal of Heat Mass Transfer. 88, pp. 284–296, 2015. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.04.071

[18] Wright, L.M., McClain, S.T. & Clemenson, M.D., Effect of density ratio on flat plate film cooling with shaped holes using PSP. Journal of Turbomachinery, 133(4), p. 11, 2011.

[19] Zienkiewicz, O.C. & Taylor, R.L., The Finite Element Method, Butterworth-Heinemann, 2000.

[20] Hecht, F., Pironneau, O., Le Hyaric, A. & Ohtsuda, K., FreeFem++ (Third Edition, Version 3.19). Laboratoire Jacques-Louis Lions, Universite Pierre et Marie Curie, Paris, available at: http://www.freefem. org/ff++/

[21] Díaz Moreno, J.M., García Vazquez, C., Gonzalez Montesinos, M.T., Ortegon Gallego, F. & Viglialoro, G., Mathematical modeling of heat treatment for a steering rack including mechanical effects. Journal Numerical Mathematics, 20(3–4), pp. 215–232, 2012.

[22] Viglialoro, G., Gonzalez, A. & Murcia, J., A mixed finite-element finite-difference method to solve the equilibrium equations of a prestressed membrane. International Journal of Computer Mathematics, available at: http://www.tandfonline.com/doi/pdf/10.1080/00207160.2016.1154950, 2016.

[23] Viglialoro, G. & Murcia, J., Á singular elliptic problem related to the membrane equilibrium equations. International Journal of Computer Mathematics, 90(10), pp. 2185–2196, 2013. http://dx.doi.org/10.1080/00207160.2013.793317