AERODYNAMIC PERFORMANCE OF A TRANSONIC TURBINE GUIDE VANE WITH TRAILING EDGE COOLANT EJECTION PART II: NUMERICAL APPROACH

The effect of coolant ejection from the trailing edge of a turbine blade is studied by means of numerical simulation codes. Two solvers based on explicit and implicit algorithms with and without multigridding are used in connection with H, HOH and HC grid types. A simple procedure to model the coolant jet at the trailing edge of the blade is presented which does not require excessive grid refinement. The features of the different approaches are discussed in terms of isentropic Mach number distribution on the blade, base pressures and wake profiles at various exit Mach numbers and coolant flow rates which match the experimental conditions. The coolant ejection effect on the shock pattern is discussed. The trailing edge ejection is found to have a marginal effect on the wake shape and on the measured and computed base pressures. t time uk k-component of the velocity vector Xk k-component of the coordinate frame At time step y specific heat ratio ,u dynamic molecular viscosity turbulent viscosity ,ueff effective viscosity 4,tl curvilinear coordinate frame B implicit-explicit weight for implicit code S central difference operator p fluid density A, A" convective and diffusive eigenvalues NOMENCLATURE a speed of sound A, Av convective and diffusive jacobian e total specific internal energy Fk k-component of the convective flux vector (k=1,2) F k-component of the viscous flux vector klam thermal diffusion coefficient k,b turbulent thermal diffusion coefficient ke ff effective thermal diffusion coefficient I identity matrix p static pressure Po total pressure Q vector or unknowns gjet coolant mass flow rate Re Reynolds number TD total temperature T convective eigenvector matrices INTRODUCTION Proper cooling systems must be designed to prevent serious thermal and mechanical damages to turbine blades operating in wide temperature ranges. Turbine blades are normally cooled by pumping a cool fluid inside the blade and injecting the coolant from the blade surface in proximity of the hot spots. The coolant jet can be simulated numerically and most of the calculation of jet flows in turbomachinery blades are performed by extending the grid inside the jet pipe. This technique necessitates some adhoc modifications to both the grid (patched grids) and the solver (Jourdren et al., 1992). Dorsey and Davies (1993) recently studied numerically the film cooling effect on the turbine first stage focusing their attention to the pressure side coolant ejection. Still, one of the problems of turbine blades located immediately downstream of the combustion chamber is the quite thick trailing edge (TE) which is intended to avoid mechanical problems. Unfortunately, while'a thick TE is necessary to make the blade stand very high stagnation temperatures, it also has a negative effect in terns of aerodynamic efficiency of the blade insofar it produces wide wakes. Presented at the International Gas Turbine and Aeroengine Congress and Exposition The Hague, Netherlands June 13-16, 1994 Copyright © 1994 by ASME Downloaded From: http://proceedings.asmedigitalcollection. asme.org/ on 09/10/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use The deep knowledge of the aerodynamics of the wake mixing and the coolant jet wake interference is a major task in designing turbine blades. The correct prediction of the decay of the total pressure and temperature gradients downstream of turbine blade rows is an important information for optimising a turbine stage. Although the coolant ejection should have a positive effect, at least on a theoretical basis, it is not entirely clear how and how much coolant should be ejected and, last but not least, where it should be ejected. Theoretically, a mechanically resistant TE and a thin wake could be both attained by ejecting the cooling fluid from inside the blade into the wake from the TE. A research project on this subject has been carried out in the frame of the BRITE-Euram Program (1992) which intends to study the effect of the coolant trailing edge ejection on the blade performances and wake evolution both experimentally and numerically. The cooling fluid ejection is in fact expected to energise the wake in its very low speed region thereby reducing the local mean velocity strains. Aim of this work is the development of a numerical simulation program to study the flow field around the cooled blade cascade and provide a convenient interaction with experiments in the understanding of the complex phenomena occurring in the region of wake mixing. GOVERNING EQUATIONS The two dimensional steady compressible viscous flow is governed by the well-known set of Navier Stokes (N-S) equations. The transported and related quantities are made non dimensional with respect to the inlet total pressure P0 and inlet total temperature T0. Viscosity and diffusion coefficients are made non dimensional with respect to the inlet laminar viscosity. The equations can be written in a compact vector form as: CQ+OTk = I d7k =12 (1) a &k Re &k The vectors are defined as follows: 0 P Puk 1 1 Z1k _ 1'1 F —_ /I1 uk + PSl k F'= Q PU2 k PU2Uk + P82k k— ^Ke f 2 e L (e+p)uk TV u1+1Y-1) ak