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DOI: 10.1615/ICHMT.2000.TherSieProcVol2.730
157 pages

Zvonimir Guzovic
Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lucica 5, Zagreb, Croatia

Branimir Matijasevic
Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lucica 5, Zagreb, Croatia

Miroslav Rusevljan
Department for Termotechniqe and Process Engineering, Faculty of Mechanical Engineering and Naval Architecture, Ivana Lucica 5, 10 000 Zagreb, Croatia


In developing new designs of steam and gas turbines, and when defining their flow part, it is necessary to perform a large number of various calculations. Among others, these include also the calculation of heat transfer between working fluid and blades of stator and rotor cascades (e.g. due to determining the efficiency of energy conversion i.e. losses in turbine stage, efficiency of the cooling systems of cooled stator and rotor blades, temperature fields i.e. state of temperature stresses and deformations of flow part elements, etc.). For these calculations it is necessary to know either the local or the average values of the convective heat transfer coefficients, depending on the accuracy of calculations.
In general, the convective heat transfer coefficients can be determined on the basis of experimentally obtained dependencies (correlations), then by analytical methods and at present by numerical methods as well. At subsonic flow of the working fluid the system of differential equations which describes the flow of working fluid in channels between blades allows separate calculation of real flow in cascade which provides the fields of velocity and pressure round the profile contour, and then determination of the heat transfer and losses based on calculation of the thermal and hydraulic boundary layers. However, even in this simple case of gradient flow around surface the calculation of boundary layer is accompanied by a series of difficulties and complexities. As the result of the present intensive progress in computers and information technology series commercial users' software for heat transfer calculation on turbine blades have been developed. It needs to be mentioned that with the aim of validating the accuracy of calculation results, these programs also require experimental checking. For these reasons the tendency is still that in the engineering practice the average convective heat transfer coefficients are calculated by using simple exponential equations obtained on the basis of experimental investigations, often without checking the possibility of their application in the individual case. Particularly, when high accuracy of calculations is not a requirement. Concretely, in calculating heat transfer in the flow part of steam and gas turbines this is indicated by the tendency to use the average value of convective heat transfer coefficients hav in calculations, which can be determined by experimental dependencies of type Nuav = cRen.
These correlations obtained under different conditions of experiments with various profiles cascades and in different ranges of Reynolds number change, are mutually distinguished by values of factor c and exponent n, so that calculations often give essentially different values. The differences in values of the exponent above Reynolds number indicate different lengths of the laminar, turbulent and transient boundary layers on the investigated blades, or the separation of the flow. Evidently, the character of the Nusselt number dependence is first of all determined by the flow characteristics around profiles. The variability of the factor c is caused by selection of characteristic quantities (dimension, temperature, velocity of the flow around profiles). Sometimes, the additional factors are introduced in correlations, which estimate the influence on the heat transfer of the cascade geometry and the flow conditions.
All the mentioned facts complicate practical usage of numerous correlations obtained on the basis of single experiments, and therefore in the work [Guzovic, 1998] they have been first systematized and then the systematized correlations have been statistically analyzed. The obtained original generalized statistics correlations allow simpler and faster determination of the average convective heat transfer coefficients in turbo-machinery cascades, with accuracy acceptable for engineering applications. This paper presents both the results of the mentioned systematization and the original generalized statistics correlations.

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