In view of the complex nature of the flowfield in the hot section of gas turbine engines, the need to predict heat transfer and flow losses, the possible appearance of separation and strong secondary flows, etc., the present effort is focusing upon a Navier-Stokes approach to the three dimensional turbine stator problem. The advantages of a full Navier-Stokes approach are clear since when combined with a suitable turbulence model these equations represent the flow and heat transfer physics. In particular, the Navier-Stokes equations accurately represent possible separated regions and regions of significant secondary flow. In addition, the Navier-Stokes approach allows representation of the entire flow field by a single set of equations, thus avoiding problems associated with representing different regions of the flow by different equations and then matching flow regions

Briley, W. R.

Buggeln, R. C.

Shamroth, S. J.

English

NASA Technical Reports Server

N88- 11163
FLOW IN A MODEL TURBINE STATOR _
R.C. Buggeln, S.J. Shamroth and W.R. Briley
Scientific Research Associates, P.O. Box 498, Glastonbury, CT 06033
INTRODUCTION
A major problem area associated with the successful design and operation of
modern gas turbine engines is the engine hot section. Of particular interest in the
present study is the turbine. The turbine section represents a considerable
challenge as it contains significant regions of complex three-dlmenslonal flow
including both aerodynamic and heat transfer phenomena. In particular, the turbine
flow field contains several features which makes its analysis a formidable problem.
These include complex geometry, multiple length scales, three-dlmenslonal effects,
possible strong secondary flows, possible flow separation at off-deslgn operation,
possible transonic effects, and possibly important unsteady effects.
In considering possible approaches to this problem, three approaches are
evident. These are (i) inviscld analyses, (il) inv_scld analyses with boundary
layer corrections, and (ill) full Navler-Stokes analyses. In view of the complex
nature of the flow, the need to predict heat transfer and flow losses, the possible
appearance of separation and strong secondary flows, etc., the present effort is
focusing upon a Navler-Stokes approach to the three-dimenslonal turbine stator
problem. The advantages of a full Navler-Stokes approach are clear since when
combined with a suitable turbulence model these equations represent the flow and
heat transfer physics discussed previously. In particular, the Navler_Stokes
equations accurately represent possible separated regions and regions of significant
secondary flow. In addition, the Navler-Stokes approach allows representation of
the entire flow field by a single set of equations thus avoiding problems associated
with representing different regions of the flow by different equations and then
matching flow regions. Although turbulence modelling remains a problem, turbulence
modelling presents the same difficulties with alternate approaches, and alternate
approaches cannot necessarily represent the highly complex flow physics to be found
in general turbine stator flow fields.
However, application of the Navier-Stokes equations to the turbine stator
problem is not an easy task. The presence of complex geometries, rapidly varying
flows, strong secondary flows and the need for adequately resolving the various
physical scales are items which all present their own problems. Nevertheless, with
continued improvement of numerical solution techniques the Navler-Stokes approach is
becoming a practical procedure for the three-dlmenslonal turbine stator problem.
APPROACH
The present approach solves the ensemble-averaged Navler-Stokes equations via
the Linearlzed Block Implicit (LBI) of Briley and McDonald (Ref. 1).
Boundary conditions for subsonic inflow and outflow (the usual case) set upstream
stagnation pressure, upstream stagnation temperature, upstream flow angle, and
downstream static pressure. Additional conditions used are density derivative on
the inflow (upstream boundary), and velocity and temperature second derivatives on
*Work done under NASA Contract NAS3-24358.
221 .,.:-c.,,_,_._ PAGE BLANK NOT FILM. ED
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the downstream boundary. On the cascade blade no-slip conditions and a zero
pressure gradient condition are applied along with either a specified temperature or
a specified heat transfer rate. In applying the no-slip wall conditions, proper
wall resolution is mandatory. In general, the first grid point off the wall is
taken so as to place a point in the viscous sublayer. The governing equations are
written in general tensor form and solved in a body-fitted coordinate system.
Details of the governing equations, numerical technique, grid construction,
turbulence model, etc. are given in Refs. 2-4.
Using this approach in a previously described HOST effort (Refs. 3 and 4), two-
and three-dimensional calculations were made for a turbine cascade. The purpose of
the first effort was two-fold; (i) demonstration of the Navier-Stokes current
capability in simulating these complex flow fields, and (ii) demonstration that the
Navier-Stokes approach is a practical procedure with current technology. The first
goal was reached via heat transfer and pressure distribution comparisons with
experimental data for two-dlmensional cases and a demonstration three-dimensional
laminar cascade calculation. The quantitative comparisons for the two-dimensional
cases showed good agreement between calculation and measurement; a comparison
between predicted and measured heat transfer on a C3X airfoil with specified
transition location is shown in Fig. I. In addition, the demonstration
three-dimensional calculation showed many of the expected features such as the
saddle point singularity in the endwall boundary layer as shown in Fig. 2.
In addition to providing accurate simulations, the Navier-Stokes approach, if
it is to be practical, must have reasonable run times to convergence. Long run
times, even if leading to accurate simulations, would severely hamper application of
the Navier-Stokes procedure to practical turbine stator or rotor problems on a
regular basis. Computer run time is based upon run time per time step and number of
time steps to convergence. In regard to the first item the current Navier-Stokes
cascade code, BMINT/CX, requires approximately 1.2 x i0Z4 secs/grid point/time steps
on a CRAY-I computer which for typical two-dimensional cases having 3500 grid points
gives 0.4 secs/time step. A three-dimensional case of 70,000 grid points, due to
additional code overhead, would require approximately 12 secs per time step. In
regard to time steps to convergence selected cases showed essential convergence for
engineering purpose in 70-100 time steps whereas other cases required approximately
150 time steps convergence. Both of these cases are within the constraints required
for the Navier-Stokes approach to be a practical approach to the turbine blade row
problem.
PRESENT EFFORTS
The present turbine cascade program focuses upon three efforts: (i) further
code development with particular emphasis on increasing the number of grid points
which can be run on a given machine, (ii) further convergence studies, and
(iii) calculation of the turbulent flow through a three-dimensional turbine stator.
In regard to the first objective, this will be passive to the user and will simply
allow for a higher resolution calculation by utilizing out-of-core storage.
The second objective would detail the convergence properties of the procedure.
Results obtained in Refs. 3 and 4 indicate rapid convergence insofar as engineering
predictions are concerned. Under the present effort these convergence properties
are considered in more detail for a wider variety of cases.
222
The initial test case chosen for the convergence study was the Turner turbine
cascade (Ref. 5). The convergence study calculation was run with a 'C' grid
containing 113 pseudo-azimuthal grid points, and 30 pseudo-radlal grid points. High
wall resolution was obtained with the first point off the wall being approximately
1.5 x 10-5 chords from the blade surface. In regard to convergence, several
criteria can be considered. These include surface pressure distribution, maximum
normalized residual and pressure coefficient at the stagnation point. In regard to
these factors, it should be noted that in the present calculations it is the
converged steady state flow field which is the item of interest. Therefore,
although the current numerical procedure solves the unsteady flow equations, it is
not necessary and, in fact, is uneconomical to obtain a tlme-accurate solution when
seeking steady state solutions. Instead, matrix preconditioning techniques are used
to obtain a converged solution as rapidly as possible. In these studies, the
calculation was initiated from a very simple flow field in which the velocity
magnitude and static pressure were set constant throughout the flow with the
velocity flow angle a function of axial location. Very simple profiles were used
near the blade surface to bring the velocity to the no-sllp condition.
A plot showing the maximum normalized flow residual is presented in Fig. 3.
As can be seen, the maximum residual drops slightly over 4 orders of magnitude in
150 time step iterations and then levels. In general, based upon previous
experience, three orders of magnitude drop in residual give convergence suitable for
many engineering applications. However, in addition to monitoring the residual
behavior, it is necessary to consider the flow field dependent variable behavior.
Based upon experience one sensitive item is the pressure coefficient at the
stagnation point where Cp is taken as (p - Pref)/i/2 Pref q2ref"
The reference quantities are taken from the inflow boundary and consequently since
only total pressure, total temperature and flow angle are specified, these may vary
with time. The results show the variation of stagnation point Cp with tlme-step
iteration number. The calculation was run with an inflow Mach number of
approximately 0.24; on an invlscld basis this should lead to a stagnation point Cp
of approximately 1.015. The present results converge to a value of approximately
1.005 for the Navier-Stokes simulation. As can be seen in Figs. 4 and 5, the
stagnation point Cp was obstenslbly converged at 100 time steps although some
sllght oscilatlons occurred until 150 time steps. These results clearly indicate
the rapid convergence of the present Navler-Stokes _rocedure and its potential for
use as an engineering tool. It is expected that this type of convergence shall also
be obtained for three-dlmenslonal calculations.
In addition to these results, the present effort is aiming at the
three-dlmenslonal cascade problem for turbulent flow. A calculation shall be done
for a modern turbine cascade design, the convergence properties of the procedure
assessed and if possible, a comparison made between computed flow field values and
values obtained by experimental measurement.
223
i •
•
•
e
e
REFERENCES
Briley, W.R. and McDonald, H.: Solution of the Multidimensional Compressible
Navier-Stokes Equations by a Generalized Implicit Method• Journal of
Computational Physics, Vol. 24, pp. 372-397, 1977.
Shamroth, S.J., McDonald, H. and Briley, W.R.: Prediction of Cascade Flow
Fields Using the Averaged Navier-Stokes Equations. ASME Journal of Engineering
for Gas Turbines and Power, Vol. 196, pp. 383-390, 1984.
Yang, R.-J., Weinberg, B.C., Shamroth, S.J. and McDonald, H.: Numerical
Solutions of the Navier-Stokes Equations for Two- and Three-Dimensional Turbine
Cascades with Heat Transfer• NASA CR-174929. 1985.
Weinberg, B.C., Yang, R.-J., McDonald, H. and Shamroth, S.J.: Calculation of
Two- and Three-Dimensional Transonic Cascade Flow Fields Using the
Navier-Stokes Equations• ASME Paper 85-GT-66, 1985.
Turner, A.B.: Local Heat Transfer Measurements on a Gas Turbine Blade.
Journal of Mechanical Engineering Sciences, Vol. 13, 1971.
224
CASE 144
HEAT TRANSFER COEFFICIENT
Mexlt = 0.90 Reexlt = 2.43 X 106 Tw/Tg = 0.75
1.0
0.8
0.6
H/H o
0.4
0.2
0
1.0
÷÷ + +_
•1" ÷ 4- ÷4.
WITH BLOWING I
W/OUT BLOWING ]
1 1 I I
4-
4. ÷÷ 4-
_÷ +÷ *_"
4.4. ÷
÷÷4. 4. I
J 1 1
0.8 0.6 0,4 0.2
PRESSURE SIDE
0
X/C,X
0.2 0.4 0.6 0.0 1.0
SUCTION SIDE
FIGURE i
/
/ • • • °-.
(a) VECTOR PLOT ON 0.135% SPANWlSE PLANE (b) VECTOR PLOT ON MIDSPAN PLANE
FIGURE 2
225
MAXIMUM
NORMALIZED
RESIDUAL
CONVERGENCE RATE
iO =
10 o
iO -I
iO -z
iO -3
IO -4
iO -s
O
WITH MATRIX CONDITIONING
I 1 I
50 IOO 150
TIME STEP ITERATIONS
FIGURE 3
J
200
CONVERGENCE OF PRESSURE
AT STAGNATION POINT
Cp AT
STAGNAT ION
POINT
3.0
2.0
I.O
WITH MATRIX CONDITIONING
0
I I I J
50 I00 150 200
TIME STEP ITERATIONS
FIGURE 4
CONVERGENCE OF PRESSURE
AT STAGNATION POINT
REDUCED SCALE PLOT
Cp AT
STAGNATION
POINT
I.O5 I
i
1.00
0.95
0
I I I I
50 I00 150
TIME STEP ITERATIONS
200
FIGURE 5
226


Flow in a model turbine stator

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