THREE-DIMENSIONAL NAVIER-STOKES ANALYSISOF TURBINE PASSAGEHEAT TRANSFER Ali A. Ameri Center for Research, .Inc. University of Kansas Lawrence, Kansas and Andrea Arnone Department of Energy Engineering University of Florence Florence, Italy Abstract Thethree-dimensional Reynolds-averaged Navier- Stokes equations are numerically solved to obtain the pressure distribution and heat transferrateson the endwalls and the blades of two linear turbine cascades. TheTRAF3D code which has recently been developed in a joint project between researchers from the Univer- sity of Florence and NASA Lewis Research Center is used.The effect of turbulence is taken into account by using the eddy viscosity hypothesis and the two-layer mixing length model of Baldwin and Lomax. Predic- tions of surface heat transferare made for Langston's cascade and compared with thedata obtained for that cascade by Graziani. The comparison was found to be favorable. Thecode is also applied toa linear transonic rotor cascade to predict thepressure distributions and heattransfer rates. Nomenclature b axialchord C p pressure coefficient, (p - Pin)/(1/2puin2) c p constantpressure specific heat d wall-distance h heattransfer coefficient, Qwl(T w - T lt ) n normalcoordinate direction P pressure Pr Prandtl number Q heatflux Re Reynolds number based on the axial chord St Stanton number, hi puc p T temperature u streamwise velocity Greek Symbols Jl dynamic viscosity p density of fluid Subscripts o totalcondition 1 2 exitcondition bl blade ew endwall aw adiabatic wall b axial chord e conditions at the exit in conditions at the inlet T turbulent t totalconditions w wall I Introduction Continued improvements in cycle efficiency and specific power of gasturbinesgenerally requires in- creased turbine inlet temperature and increased work factors. This resultsin highly loaded gasturbine stages.These loadings give rise to strong secondar , flows and complex heatransferdistributions.For small aspect ratios, a considerable portion of the airfo surface is directly influenced by the horseshoe and p sage vortices. Accurate prediction of theheattransfer ratesis neededto provide efficient cooling schemes. Given the foregoing, a three-dimensional analysis is necessary in order to gain abetterunderstanding of suchflows.Three-dimensional Navier-Stokes analyses enable one to make computations of flowswith sepa- ration,which in turnallows the analysis of off-design conditions. The aim of this work is toexplore the abil- ity of the commonly used Baldwin-Lomax model[l] predicting heat transfer. As two-dimensional grid dependence analysis has shown [2], there is a need for fine grids to correctly pre- dict details in the boundary layer. This requirement is even more stringent forthe calculation of heat trans- fer. For three-dimensional problems the memory and time requirements are large, even for a modern super- computer.In this work, the governing equations are solved using the TRAF3D code developed by Arnon et aI.[3].The code has proved to be reliable in the prediction of pressure and losses and the use of th al- gebraic model reduces the memory and time require