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NASA Technical Paper 1679
NASA TP 16 79 c . 1
Comparison of Elastic and Elastic J
Plastic Structural Analyses for Cooled Turbine Blade Airfoils
Albert Kaufman
JULY 1980
NASA
https://ntrs.nasa.gov/search.jsp?R=19800019218 20180509T19:55:00+00:00Z
TECH LIBRARY KAFB, NM
00b774b  4 3 y
NASA Technjcal ,Paper 1679
Comparison of Elastic and Elastic Plastic Structural Analyses for Cooled Turbine Blade Airfoils
Albert Kaufman Lewis Research Ce rz ter Cleveland, Ohio
P
NASA National Aeronautics and Space Administration
Scientific and Technical Information Office
1980
Summary Von Mises effective stress and total and plastic
strain states in cooled turbine blade airfoils were calculated for the initial takeoff transient of an advanced technology engine (1990 time frame) with a blade relative effective gas temperature of 1400O C and a gas inlet total pressure of 2860 kilopascals at maximum takeoff. Three analytical approaches were considered: a threedimensional elasticplastic analysis using the MARC nonlinear finiteelement structural computer code, a threedimensional elastic analysis using MARC with the identical finite element model, and a onedimensional elasticplastic beamtheory analysis. Eight cases involving different combinations of thermal and mechanical loads and two cooling configurations were analyzed. One of the cooling configurations was an allimpingement cooled system in which air flowed through holes in an internal sheet metal insert to impinge on the inner surface of the airfoil shell. The second cooling configuration also utilized impingement cooling with the addition of angled leadingedge filmcooling holes.
The results at maximum takeoff showed agreement in terms of effective total strains between the MARC elasticplastic and elastic analyses within 9 percent for rotating airfoils and 28 percent for stationary airfoils with the elastic results on the conservative side. Poor agreement was shown between stress distributions computed from the threedimensional finiteelement and onedimensional beamtheory elasticplastic analyses, particularly at the hot gas side airfoil surfaces.
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i
? Introduction The trend toward increased turbine blade tip
speeds and gas temperatures in advanced aircraft engines has resulted in turbine blade airfoil stresses at critical locations that exceed the yield strength of the material. The computation of stressstrain states in a complex geometry such as a cooled turbine blade undergoing plastic flow is a formidable problem requiring the use of nonlinear finiteelement codes such as MARC (ref. 1). These nonlinear codes are not currently used as blade design tools because of the extensive demands they make on computer
(I
resources. Nonlinear structural analyses also require cyclic material properties and transient metal temperatures which are frequently too unreliable to justify the cost of this type of analysis.
Current practice in turbine blade structural design is to use simplified analytical methods and approximations as design tools. One approach which has found widespread use is to calculate the total strains at the maximum load condition of the engine cycle from an elastic finiteelement analysis and to apply these as total strain ranges for cyclic life calculations. This method is based on the assumption that the total strain in a structure undergoing plastic flow can be predicted from an elastic stress analysis. Although the calculated stresses from an elastic analysis will be incorrect, more accurate stresses and the plastic strains can be estimated from the total strains and the known stressstrain behavior of the material. A further refinement of this approach is the method of elastic strain invariance (ref. 2) wherein the total strain ranges are calculated from elastic analyses of both the maximum and minimum load conditions.
Another common approach in turbine blade design has been the use of onedimensional elasticplastic analyses based on the beam theory assumption that plane sections remain plane (ref. 3). The relative simplicity and rapid solution time of beam theory computer programs in comparison to finiteelement programs makes them attractive for turbine blade design. However, the beam theory approach is of questionable validity for airfoils with small aspect ratios and nonlinear spanwise temperature gradients (ref. 4).
The purpose of this study was to compare stress and strain states derived from elastic finiteelement and elasticplastic beamtheory methods to results from an elasticplastic finiteelement analysis for the complex geometries and thermomechanical loading conditions of cooled turbine blade airfoils. This is one of a series of studies of cooled gas turbine blades; the results of previous studies are reported in references 5 and 6.
Threedimensional elastic and elasticplastic finite element analyses of cooled turbine blade airfoils were performed for an initial engine takeoff transient using the MARC nonlinear structural analysis computer program. The analyses were based on the takeoff conditions of an advanced technology
I 1 1 1 1 II I
RFH
RI RF
SI SF
S M
SFH
1111 II 1111111.11 111111111 111111 1111 I IIIIII.11111 I 1111111111IIII.11.1.1 ,,,,,,, ,11111 I I I., 11..1.11. . 
Impingement, leading edge film cooled
All impingement Impingement,
leading edge film cooled
All impingement Impingement,
leading edge film cooled
All impingement
Impingement, leading edge film cooled
aircraft engine with a blade relative effective gas temperature of 1400 C and a gas inlet total pressure of 2860 kilopascals at maximum takeoff. The eight cases studied involved different combinations of thermal and mechanical loads for each of two impingement cooling configurationsone with and one without leadingedge filmcooling holes. One dimensional beamtheory analyses were also performed for some cases. Comparisons were made of the von Mises effective stressstrain states at maximum takeoff computed from the simpler analytical approaches to the results of the elastic plastic finiteelement analyses. Creep effects were not considered in this study.
Analytical Procedure Stressstrain states in cooled turbine blade airfoils
were calculated for an assumed takeoff transient of an advanced technology aircraft engine.
Conditions of Analyses
The analyses were based on the estimated operating conditions during takeoff of a firststage turbine blade in an advanced highbypassratio turbofan engine being studied for use in commercial passenger aircraft in the 1990s.
Figure 1 illustrates the airfoil cooling system. Air flows radially up the cavity formed by an internal sheet metal insert and then flows through an array of holes in the insert to impingement cool the inside surface of the airfoil shell. Two versions of this cooling system were considered: an allimpingement cooled configuration and a similar impingement cooled configuration with the addition of a row of leadingedge filmcooling holes.
A 5second takeoff transient was assumed from a midspan blade relative effective gas temperature of 670 C at idle to 1400O C at maximum takeoff. The gas inlet total pressure was 2860 kilopascals and the coolant to gas flow ratio was 0.117 at maximum takeoff.
Eight analytical cases were studied (table I). The cases designated with R were for rotating airfoils and those designated with S were for stationary airfoils. Cases designated with an I involved allimpingement cooled airfoils, while those with an F involved impingementcooled airfoils with leadingedge film cooling holes. In cases RIH and RFH, the centrifugal loading included the mass of the impingement insert. In cases RI and RF, only the centrifugal loading of the airfoil shell was considered. Cases RIH, RI, and SI had identical thermal loading, as did cases RFH, RF, and SF. The metal temperatures for cases SIH
TABLE I.  ANALYTICAL CASES Centrifugal
loading
Airfoil, impinge ment insert
Airfoil, impinge ment insert

Airfoil Airfoil
Thermal loading
Figure 2(a)
Figure Z ( b )
 .
Figure 2(a) Figure 2(b)
Figure Z(a) Figure 26)
Figure 2(a) +28O C
Figure Z ( b ) +28O C
r Blade shell I
Impingement I , Coolant channel insert ,& I , (fed by impingement)
w Detail of leading edge film coding holes for cases RFH, RF, SF, and SFH
Figure 1. Air foi l cooling configurations, i
and SFH were increased 2 8 O C over the comparable metal temperatures for cases SI and SF, respectively: this was done to simulate the higher temperatures that a stator vane would be exposed to, compared to a rotor blade for the same turbine stage. Hence, the designation H for the rotating cases signifies higher centrifugal load while for the stationary cases, H signifies higher temperatures.
L
Input for Analyses
The airfoil geometry, transient temperatures, and mechanical loads which were used as input to the structural analysis computer programs were based on the turbine blade design and operating conditions of the candidate aircraft gas turbine engine.
Geometry.The blade airfoil had a span length of 3.8 centimeters, an aspect ratio of 1, a wall thickness
i taper from 0.13 centimeter at the hub to 0.08 centimeter at the tip (outside surface contour constant from hub to tip), and a hub to tip radius ratio of 0.85. The holes in the leadingedge film cooled configuration were 0.05 centimeter in diameter with a spacing of 10 diameters and
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