1 Copyright © 2003 by ASME
Proceedings of ASME Turbo Expo 2003
Power for Land, Sea, and Air
June 16–19, 2003, Atlanta, Georgia, USA
GT-2003-38140
FILM COOLING ANALYSIS USING DES TURBULENCE MODEL
Subrata Roy and Sagar Kapadia
Computational Plasma Dynamics Laboratory
Kettering University, Flint, MI 48504
James D. Heidmann
NASA Glenn Research Center
Cleveland, OH 44135
ABSTRACT
The complex dynamic nature of the spanwise vortices in
film cooling of turbine blades makes it necessary to accurately
model the flow field temporally and spatially using detailed
simulation techniques like direct numerical simulation or large
eddy simulation of turbulence. Although, the later requires less
computational effort and thus can simulate flows at higher
Reynolds number than direct simulation, both these methods
remain very expensive. As a viable alternative, this paper
presents a Spalart-Allamaras based detached eddy simulation
(DES) that is applied to a film cooled flat plate for the first
time. The numerical model uses an unstructured grid system to
resolve the dynamic flow structures on both sides of the plate as
well as inside the hole itself. Detailed computation of a single
row of 35 degree round holes on a flat plate has been obtained
for blowing ratio of 1.0, and a density ratio of 2.0. The DES
solution is also benchmarked with Reynolds averaged Navier-
Stokes formulation for the same blade-hole configuration. The
comparison shows that the DES simulation, which makes no
assumption of isotropy downstream of the hole, greatly
enhances the realistic description of the dynamic mixing
processes.
INTRODUCTION
In a variety of industrial applications the interaction of cool
air jets with hot crossflow becomes important. Examples
include vertical takeoff and landing (V/STOL) engineering and
film cooling of gas turbine blades. Systematic investigation of
such flowfield started in late 50s. Jordison [1], Fearn and
Weston [2], Moussa, et al. [3], Andreopoulos and Rodi [4]
studied isothermal jets into crossflow. For thermal flows, the
resulting temperature downstream of the jet, the trajectory and
physical path of the jet are critical design parameters.
Specifically, the blades/vanes in propulsion gas turbine engines
require film cooling to protect the airfoils from thermal stresses
caused by exposure to hot combustion gases. The problem
becomes aggravated by the growing trend to use higher turbine
inlet temperature for better engine performance. Figure 1 shows
the schematic of a single round jet injected in the crossflow at
an angle. This geometry is very appropriate for the turbine
engine community and has been extensively studied for cooling
performance for a wide range of blowing ratio (i.e., momentum
ratio of injected air to crossflow). These results show details of
the vortex interaction region, and mixing and mean centerline
species concentration decay in the near and far field.
Goldstein [5] summarized early studies in the area of film
cooling. These studies were based on slot flows, and f ilm
cooling effectiveness values were found to correlate well with
the parameter x/Mb, where x is the downstream distance, M is
the blowing ratio, and b is the slot width. This parameter has
also been used for discrete hole cooling, with b defined as the
effective slot width for the row of holes. However, the physics
of discrete hole cooling is quite different from that of a slot. A
row of discrete holes typically has a much lower span averaged
downstream film effectiveness distribution for the same x/Mb
due to the formation of vortices which allow hot gas to
penetrate to the wall. These vortices are of the scale of the hole
size, so if a numerical simulation has a spanwise grid spacing
greater than the film hole spanwise pitch, as is typical for
turbine blade aerodynamic design, their effect is lost. In
essence, any such calculation is two-dimensional on the scale
of the film holes.
Numerical investigations of jets based on integral methods
were done by Vizel and Mostinskii [6], Chen [7] and Adler and
Baron [8] initially. These models were essentially idealized
models. A number of numerical models have also been
proposed that approximated the three-dimensional vortex sheet
by a two-dimensional one to predict details of the flowfield [7].
However, the mixing of a jet in a cross-stream is a fully three-
dimensional phenomenon (Moussa et al. [3], Fric and Roshko
[9], Smith and Mungal [10]), and thus such idealized treatments
lack accuracy. Numerical solutions of the full Navier-Stokes
equations have also been used to obtain detailed solutions in