Handbook of Turbomachinery Second Edition Revised - Ventech!

component. Use of a hot cascade for steady-state experiments or shortduration
facilities for transient experiments becomes a necessity for
obtaining reliable data and validation of the airfoil cooling systems.
Realistically simulated steady-state hot cascade experiments using actual
engine hardware with proper external/internal cooling arrangements can be
extremely beneficial for turbine airfoil local temperature prediction in the
early stage of turbine development. A few of the experiments using actual
engine configuration were reported [12–16]. However, heat-transfer experiments
including evaluation and comparison of the cooling effectiveness in
both engine and hot cascade environments are rarely discussed in the open
literature.
The solutions of the Navier–Stokes and energy equations for
compressible flow depend on a number of dimensionless groups. These
equations suggest that the similarity of fluid streamlines and the isotherms in
forced convection heat transfer can be enforced by using the same
magnitudes of these nondimensional groups for both the actual phenomenon
and the simulation experiment. When the momentum and energy
equations are nondimensionalized, the solution strongly depends on four
nondimensional parameters: Re, Gr/Re 2 , 1/(Pr Re), and Ec.
For most of the forced convection problems of interest to us such as
external heat transfer on a gas turbine blade, buoyancy forces are considered
negligible compared to inertial forces. The Eckert number Ec can be
expressed in terms of free-stream Mach number, Ma, wall-to-free-stream
total temperature ratio, and the specific heat ratio: Ec ¼ðg 1ÞMa 2
ðT?=T?0Þ=ð1 Tw=T?0Þ
The static to total temperature ratio can be replaced by using the
isentropic relation, to obtain
Ec ¼ðg 1ÞMa 2 1= 1 þðg 1ÞMa 2 =2 =ð1 Tw=T?0 Þ
STEADY-STATE AND TRANSIENT HEAT-TRANSFER ISSUES
IN THE ENGINE HOT SECTION
Over the past three decades, turbine heat-transfer calculations and
experimental data have been reported in the open literature by numerous
industry, government, and university authors. The detail reported for a
particular calculation generally depends on the competition sensitive nature
of the data. Understandably, the company design codes distinguish the
manufacturers, and detail about these codes will be kept proprietary.
Copyright © 2003 Marcel Dekker, Inc.