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Parametric Studies on Aerodynamic Performance of Various Types of LP Turbine Airfoils for Aero-Engines

Daichi Murakami1, Ken-ichi Funazaki1 and Juo Furukawa2

1 Iwate University 3-5, Ueda 4, Morioka 020-8551, Japan

Phone: +81-19-621-6422, E-mail: funazaki@iwate-u.ac.jp

2 IHI Corporation

ABSTRACT This study executes parametric investigations of aerodynamic

performance of various types of LP turbine cascades with different flow deceleration rates (DR) on their suction surfaces under a low freestream turbulence condition. The Reynolds numbers examined in this study range from 57,000 to 170, 0000, corresponding to the conditions from cruise to take-off/landing. The freestream turbu-lence are about 1.0%. A Pitot tube is used to measure the total pressure loss of each of the cascades and a single hot-wire probe is employed to make steady and unsteady boundary-layer measure-ments over the rear part of the suction surface in addition to the measurements on the pressure surface near the trailing edge. In the data analysis of the boundary-layer measurements, Denton’s method for loss audit based on the momentum theory is used to estimate the cascade loss by taking advantage of RANS calcula-tions and experimental data. The estimated loss values are com-pared with the directly measured loss data.

NOMENCLATURE , xC C : actual, axial chord length ( )

pC x : static pressure distribution coefficient

: static pressure coefficient

pbC : base pressure coefficient DR : flow deceleration rate

0,p p : static pressure, stagnation pressure

Re : Reynolds number (2

U C )

0S : suction surface length

,max ,,

U U teS S : surface length measured from the trailing edge to the

points where max

U and te

U appeared, respectively t : cascade pitch

maxU : maximum velocity on the suction surface

teU : velocity near the trailing edge (suction side)

2U : mass-averaged exit velocity from the cascade w : throat length

pY : loss coefficient

wZ : Zweifel loading factor

1 2, : inlet and outlet flow angles

: displacement thickness : momentum thickness : density : solidity (=

xC t )

: Denton’s loss coefficient 1, 2 : inlet, outlet PS, SS : pressure surface, suction surface

INTRODUCTION In recent years, bypass ratio of aero engines has been steadily

increasing for the sake of reduction in fuel burn and noise level. Since the most of the engine thrust is produced by fan blades, it is indispensable for achieving higher efficiency of aero engines to improve the efficiency of the low-pressure turbine (LPT) that drives the fan blades. Since the LPT is composed of multiple stages, there exist in the LPT section various flow phenomena such as periodic wakes shed from the upstream airfoils or accumulated mainstream or freestream turbulence, affecting the aerodynamic performance of each of the turbine airfoils. For better understand-ing of the loss mechanism of LPT, it is important to grasp the in-fluence of wakes as well as freestream turbulence on the loss gen-eration. There are a number of previous studies related to high-lift LPT airfoils under the influences of incoming wakes and freestream turbulence, including ones done by Funazaki et al. (2009), Funazaki et al. (2010), Funazaki et al. (2012), Funazaki et al. (2013), Furukawa et al. (2015). In fact, Coull et al. (2008) car-ried out detailed investigations of flat plate boundary layers with various realistic pressure gradient distributions under the influences of periodic wakes and/or freestream turbulence. Based on those experimental data, they derived the correlation to predict the profile loss of high-lift LPT cascade (Coull et al. (2010)). Despite these efforts, there are still other design spaces that were not dealt with in the above-mentioned studies in order to develop high-lift LPT cascades with higher performance under a wide range of operating conditions.

This study, as the first part of the study to develop a method for designing high-lift LPT airfoils with high efficiency under realistic flow conditions, executed parametric investigations of aerody-namic performance of various types LPT cascades with different flow deceleration rates (DR) on their suction surfaces without incoming wake condition. The Reynolds numbers examined in this study ranged from 57,000 to 170, 0000, corresponding to the con-ditions from cruise to take-off/landing. The freestream turbulence was about 1%. A Pitot tube was used to measure the stagnation pressure loss of the cascades and a single hot-wire probe was em-ployed to make steady and unsteady boundary-layer measurements over the rear part of the suction surface in addition to the meas-urements on the pressure surface near the trailing edge. The data obtained from the boundary-layer measurements were used to calculate displacement thickness and momentum thickness for the estimation of cascade profile loss based on the method developed by Denton (1993) with the aid of numerical simulations. The es-timated loss values were then compared with the measured stag-nation pressure loss data.

NUMERICAL METHODS This study employed a commercial flow solver, ANSYS CFX

Proceedings of the Asian Congress on Gas Turbines August 22~24, 2018, Morioka, Japan ACGT 2018-TS16

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Ver.15(ANSYS) to execute RANS simulation for obtaining a static pressure distribution for each airfoil. The computational domain with boundary conditions is displayed in Figure 1. SST (Shear-Stress Transport) turbulence model with a transition model was used, which was vital for achieving a good agreement between the experimental data and the numerical results. A velocity vector and inlet turbulence intensity were specified on the inlet boundary and a constant static pressure was given on the outlet boundary. The spanwise extension of the domain was 15%Cx. Grid generation was made by use of Pointwise Ver.16.04R4 (Pointwise), as shown in Figure 2. The grid system consisted of H-O-H type sub-systems so as to attain a high-quality grid generation around the airfoil. Accordingly the closest point to the surface was located so that y+ of the point was less than unity. The total number of the grid points was about 4.5 million.

Figure 1 Computational domain and boundary conditions

Figure 2 Grid points around the airfoil (Design A)

EXPERIMENTAL METHODS Test Facilities

Figure 3 Test apparatus

Figure 3 shows the test apparatus used in this study, including the wind tunnel and the linear cascade section. As shown in the figure, this test apparatus consisted mainly of the following four parts, i.e., blower, wind tunnel, wake generator and test section. In this test apparatus, the air was discharged from the blower, passing through the settling chamber and the wake generator, entered the linear cascade section. A flow rate was adjusted by the valve at-tached to the intake of the blower. When the blower was continu-ously operating, the air temperature tended to rise, which was particularly noticeable at low flow rates. Therefore, it was im-portant to confirm that the temperature was almost unchanged during the test. The monitored main flow temperature was used to compensate the output from the hot-wire probe in consideration of the temperature deviation from the calibration temperature. The contraction nozzle of the wind tunnel was installed ahead of the rectification section. The size of the contraction nozzle was 1000 × 1000 [mm] at the entrance cross section, 1000 × 300 [mm] at the exit cross section, and the length was 550 [mm]. The duct was attached to the exit of the contraction nozzle, in which a turbulence grid was able to be installed to change mainstream turbulence.

Figure 4 Test linear cascade

Figure 4 depicts the test linear cascade section located at the

most downstream of the test apparatus. The test cascade consisted of 6 or 7 airfoils. All tested airfoils had the same axial chord length (100mm) and the span (254mm). They were made by elec-tric-discharge machining from aluminum and brass ingots, the latter of which were equipped with pressure holes for the static pressure measurement on the suction and pressure surfaces. The airfoil surface was carefully polished using a water-proof sandpa-per so that the surface was hydraulically smooth for the flow with Reynolds number less than 170,000. Each of the cascade airfoils was fixed in the linear cascade by using two end plates with the airfoil shape machined. The airfoils located at the middle of the cascade, which are numbered with 3 and 4 in Figure 4, respectively, were the target airfoils for the stagnation pressure measurements by use of a miniature Pitot tube as well as the boundary-layer meas-urement by use of a single hot-wire probe (Dantec Dynamics Co.). Upstream and downstream guide plates were attached near the cascade airfoils 1 and 7. The positions and angles of those plates were adjusted so as to attain periodicity of the flow field down-stream of each of the test cascades.

Measurements by pneumatic probes

In the cascade loss measurement, several miniature Pitot tubes (Tsukuba Rika Seiki Co.) were employed to measure an inlet stagnation pressure 30% Cx upstream of the cascade leading edge and the outlet total pressure 15% Cx downstream of the cascade trailing edge. The Pitot tube at the cascade downstream was moved in the pitchwise direction by the PC-controlled traversing unit,

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covering more than 2 cascade pitch zone. Since the dynamic pressure of the outlet flow was relatively small, especially for the low Reynolds number condition, three different types of pressure transducers (Setra Systems Co. Model 265) were used, whose maximum pressure ranges were 100 [Pa], 250 [Pa] and from 500 [Pa], with about 0.25% error of each full scale. The selection of the transducer depended on the test Reynolds number. The calibration using a precise pressure calibrator (Setra Micro-Cal 869), which eventually confirmed a good linearity of each transducer. The voltage value from the transducer was acquired and digitized by the AD conversion board (Interface Inc.) and stored in PC. A similar procedure was taken for the static pressure measurement on the airfoil.

Measurements by hot-wire probe

A single hot-wire probe (MODEL 55 P 11, Dantec Dynamics) was used to measure the boundary layer on the airfoil surface with a constant temperature anemometer system (CTA; Kanomax Co.), where the output from the hot-wire probe was compensated by measuring the temperature variation from the temperature at which the probe was calibrated. The probe was moved precisely in the normal direction to the airfoil surface and in the surface-wise di-rection along the surface by use of the two-axis traversing unit. The output from the CTA system was first discretized by a data-logger (Keyence Wave Logger) and stored in the PC. Thereafter, the temperature compensation and linearization were performed in a post-processing manner. Before the boundary layer measurement, the hot-wire probe was calibrated using a calibration wind tunnel to obtain the correlation between the output voltage of the hot wire and the flow velocity, where the data was approximated by a third-order polynomial curve.

In the suction surface measurement, 8 to 12 locations were se-lected over the surface in the streamwise direction from the load peak to the vicinity of the blade trailing edge for the boundary layer measurement, on which the velocity measurement was conducted in the normal direction to the surface by use of the hot-wire probe. For each location, 32 points along the normal line were measured, with 0.1mm increment from 0.2mm to 2.1mm from the surface, 0.25mm increment from 2.1mm to 3.1mm, 0.5mm increment from 3.1mm to 5.1mm and 1mm increment from 5.1mm to 9.1mm. In the case of pressure surface, however, because of the difficulty in probe insertion, the measurement position was restricted to the vicinity of the airfoil trailing edge.

Test airfoils

This study adopted seven different shapes of LPT airfoils with different pitches, pressure distributions and resultant loading indi-ces, which are named Design A, Design B and so on. Table 1 shows the characteristics of each of the test airfoils used in this study. This table contains several important indices related to aerodynamic loading associated with each airfoil, DR and

wZ , both of which

are explained in the following. DR represents a non-dimensional flow deceleration rate over

the suction surface, defined by Eq. (1).

max

,max , 0

( )

( )te te

refU U te

U U UDR DR

S S S

. (1)

The values of flow deceleration rate in Table 1, which were actually normalized by the reference value, were obtained by the meas-urement, as described in the next section. Actually, the static pres-sure distribution around each of the airfoils is also important in-formation. It is because it provides more detailed clues for under-standing the flow situation such as flow acceleration/deceleration or separation/reattachment of separation bubble, in addition to the fact that the pressure distribution directly affects the flow deceler-ation rate along with the peak position of Cp on the suction side. In general, the change in DR can be realized by changing the airfoil load level and the Cp peak position. Regarding the airfoil load

level, lowering the solidity increases the load and accordingly the deceleration rate becomes stronger. As for peak position, by setting the peak position to the blade trailing edge side (aft loading), the surface length required for deceleration becomes short, leading to a strong deceleration.

On the other hand, w

Z is the Zweifel loading factor proposed by Zweifel (1945), which is a non-dimensionalized tangential force exerted on the airfoil, is given for the incompressible flow by Eq. (2),

22

1 2

21 2

1

2 cos(tan tan )

2cossin( )

cos

wZ

. (2)

In general, w

Z >1 means that the airfoil can be regarded as a highly-loaded airfoil. RESULTS AND DISCUSSIONS Static pressure measurement

Figure 5 exhibits static pressure distributions for all test airfoils under three Reynolds number conditions, i.e., (a) Re=57,000, (b) Re=100,000 and (c) Re=170,000, where a free-stream turbulence intensity was about 1%, where the static pressure coefficient Cp was defined by

. (3)

Note that the detailed information on the airfoils, including their shapes are not allowed to be shown here because they are still classified except Design A, which is shown in Figure 6 along with its static pressure distribution. This figure contains a close-up of the pressure distribution around the region where a separation bubble appears on the suction surface. From this data one may make a rough judgment of the position identification of separation and reattachment points. Airfoil categorization

Test airfoils was roughly grouped as shown in Figure 7, which was based on the Zweifel factor and the loading (static pressure) distribution. Design A, which can be regarded as a datum airfoil, was a typical front-loaded high-lift airfoil with Zw = 1.09 and DR = 0.58. It is clear from the static pressure distribution in Figure 3, Design B was an aft-loaded airfoil with almost the same level of loading and cascade pitch as Design A (Zw = 1.09). However, since DR of Design B was larger than that of Design A, there still re-mained a separation bubble on the suction surface of Design B. Design C and Design D were slightly aft-loaded airfoils with higher Zweifel factor than that of Design A (Zw = 1.15 and Zw = 1.25). Due to the high level of the airfoil loading of Design D, its DR became large (DR = 1.05) and the static pressure distributions of Deign D indicate the existence of a large-scale separation bubble even under the highest Reynolds number condition, resulting in large cascade loss in this case, as will be described later. Design E was also an aft-loaded with the Cp peak position at 63%Cx. Since the solidity of Design E was very low, its Zweifel factor and DR were the highest of the all test cases (Zw = 1.26, DR=1.72). Therefore, Design E was inevitably accompanied with a very large separation bubble and its cascade loss was also found to be the largest.

In contrast to Design A – E, Design F and G were moderately loaded airfoils with Zweifel factors less than unity and DR less than that of Design A. The main features of these two cascades were the Cp peak positions (66%Cx and 68%Cx) and longer acceleration before the peaks.

Boundary-layer measurements

Figure 8 demonstrates time-averaged velocity (left column) and RMS (Root-Mean Squared value) (right column) contours obtained

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from the boundary-layer measurements of Design A, D and E at Re = 57,000. In comparison with Design A case, in which a long sep-aration bubble appeared on the suction surface, showing a transi-tional behavior near the trailing edge, the separation bubbles of Design D and E became shorter and grew in the heightwise direc-tion. It was easily imagined that the appearance of these massive separation followed by abrupt reattachment would cause a drastic increase in cascade loss, which will be discussed in the following.

Table 1 Test airfoils with their characteristics

(a) Re =57,000

(b) Re = 100,000

(c) Re = 170,000

Figure 5 Static pressure distributions of all test airfoils with a

low free-stream turbulence intensity

Figure 6 Static pressure distributions of all test airfoils with a

low free-stream turbulence intensity

Figure 7 Grouping of test airfoils

Figure 8 Boundary-layer measurements for Design A (top), Design D (middle) and Design E (bottom) at Re = 57,000

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Figure 9 Relationship between separation bubble charac-

teristics and flow deceleration rate at Re = 57,000

Based on the findings through the boundary-layer measure-ments as shown in Figure 8, an attempt was made to seek out a relationship between separation bubble characteristics such as bubble height or length and the flow deceleration rate. Figure 9 is an example of the attempt obtained from the data at Re=57,000. As DR increased, the separation bubble tended to become shorter in a linear fashion, while the bubble height gradually increased. It may be stated that at least for low Reynolds number condition the sep-aration bubble characteristics was likely to correlate with the value of DR.

Cascade loss

Figure 10 are distributions of cascade loss coefficient Yp over the non-dimensionalized pitchwise region for the three Reynolds conditions. The loss coefficient was defined by Eq. (4),

1 222

( )( )

1 2t t

p

p p yY y

U

, (4)

where the loss values for each Reynolds number condition were normalized by the corresponding mass-averaged loss coefficient of Design A. Integrating these loss distribution along the pitchwise direction over each one-pitch region, the mass-averaged loss coef-ficients were obtained for the three Reynolds number conditions, which were plotted against the flow deceleration rate, as shown in Figure 11. Note that the loss coefficients in Figure 11 were non-dimensionalized by the loss value of Design A obtained at Re=100,000.

It is evident from Figures 10 and 11 that the data were able to be categorized into three distinct groups based on the Reynolds number. The loss coefficients of the group for Re = 57,000 were very large compared to those of the other groups, exhibiting a clear correlation with DR. It seems that this correlation has a connection with the trends of separation bubble characteristics as seen in Fig-ure 9. The data in the group for Re=100,000 were plotted between the groups for Re=57,000 and Re=170,000, also showing a similar trend against DR with the group for Re=57,000. In contrast, the group for Re=170,000 varied quite faintly with DR, which was probably due to the size of separation bubble or growth rate of the boundary layer on the suction surface. It can be mentioned from Figure 10(c), the contribution from the suction surface boundary layer to the cascade loss tended to decrease with the Reynolds number especially for highly loaded airfoils such as Design D or E, while the contribution from the pressure surface boundary layer or other factors does not seem to change drastically, resulting in less dependency on DR.

(a) Re = 57,000

(b) Re = 100,000

(c) Re = 170,000

Figure 10 Cascade loss distributions for the three Reynolds number conditions

Figure 11 Mass-averaged cascade loss coefficients versus

flow deceleration rate

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Denton’s method for loss prediction Denton (1993) proposed a following expression to predict the

cascade loss, based on the momentum theory.

, , , , 22 2

( ) ( ) ( )pb TE TE SS TE PS TE SS TE PS TEC t t

w w w

(5) To calculate this loss coefficient, the following information was needed; displacement and momentum thicknesses of the bounda-ry-layer on the suction and pressure surfaces near the trailing edge, and base pressure coefficient. The boundary-layer thicknesses were directly obtained from the measurement, as shown in Figure 12. As for the displacement thickness, a separation bubble was a major contributor, followed by the growth of a turbulent boundary layer after the reattachment. In contrast, the momentum thickness was mainly governed by the growth of a turbulent boundary layer. It is obvious that the highly loaded airfoils such as Design E, D and C exhibited clear increases in the momentum thickness towards the trailing edge, indicating a possibility that the momentum thickness may be correlated with the loading such as DR. Figure 13 was plotted to confirm this supposition. In fact, as can be seen in this figure, the momentum thickness was properly correlated with DR.

As for the base pressure coefficient, it was quite difficult to obtain an accurate value by the measurement, although an attempt has been made by one of the authors to obtain the value experi-mentally. This study employed RANS simulation to calculate the base pressure coefficient, as illustrated in Figure 14. It should be mentioned that the base region is characterized by very complex flow phenomena with intense unsteadiness, which is beyond the capability of RANS simulation. Therefore, some errors associated with the RANS simulation cannot be avoided.

Figure 12 Non-dimensionalized boundary-layer thicknesses on the suction surface (upper: displacement thickness, lower:

momentum thickness)

Figure 13 Momentum thickness measured near the trailing

edge versus the flow deceleration rate

Figure 14 The numerical approach to obtain the base

pressure

Figure 15 Comparison between the measured cascade loss and the predictions by Denton’s method

Figure 15 shows the comparison between the measured cascade

loss and the predictions obtained by Denton’s method. Each data point in this figure is plotted based on the pneumatic probe meas-urement Yp in the vertical direction and on the Denton’s prediction using the results of the boundary-layer measurement as well as RANS simulation. In the plot, three Reynolds number conditions in the steady condition are shown and the loss values are all normal-ized. If the loss values by the two methods coincide with each other, the plotted point should be on the solid straight line of y = x, oth-erwise the prediction expression is underestimated / overestimated

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and the plotted point deviates from the solid line accordingly. Looking at Figure 15, it was found that the predicted loss values

are within about ± 10 [%] at all Reynolds numbers, and almost all the plots are located near the solid line. Therefore, it can be con-cluded that the loss prediction method can predict the loss value which would be expected to obtain from the pneumatic probe measurement almost to a reasonable level, at least under the steady condition.

Figure 16 provides the results of detailed inspection to clarify how the main loss factors in Eq. (5) contributed to the total cascade loss for various deceleration rates at Re=57,000, In the figure, the cascade loss data from the pneumatic probe measurement Yp are also superimposed. As mentioned above, the cascade losses Yp as well as ζ tended to increase almost monotonically with the increase in DR. It is evident from this figure that the main contributor to the cascade loss was the suction surface boundary layer (SSBL) and it tended to dominate the loss with DR, while the pressure surface boundary layer (PSBL) had a limited impact on the cascade loss, slightly decreasing with DR. The blockage loss due to the dis-placement thicknesses and the trailing edge, which was the second largest contributor to the cascade loss, remained almost constant regardless of DR. Lastly, it was found that the base pressure loss was small in comparison with other loss contributors and decreased with DR. Interestingly, the base pressure loss became negative, meaning that the base pressure worked for loss reduction in this case.

Figure 16 Detailed inspection of the main contributors to the

cascade loss (Re=57,000) CONCLUSIONS

This study executed parametric investigations of aerodynamic performance of various types of LP turbine cascades with different flow deceleration rates (DR) on their suction surfaces under a low freestream turbulence condition. The following findings were obtained. 1. Under the steady condition, it was found that the loss evalu-

ation method proposed by Denton, which is based on the boundary layer thickness, successfully predicted the cascade loss measured by use of the pneumatic probe.

2. The base pressure coefficient depended on the airfoil loading

and positive values of Cpb (negative loss) were obtained in high loading cases.

3. A close relationship was found between the cascade loss and the development of the suction surface boundary layer, where the suction surface boundary layer loss was the most domi-nant contributor to the cascade loss and increased with DR.

4. The increase and decrease in the boundary layer loss were governed by the height of separation bubble and the extent of the turbulent flow area on the suction surface.

5. For high DR airfoils where a separation bubble grew in the height direction, the momentum thickness significantly in-creased due to the abrupt reattachment of separation bubble and the development of the turbulent boundary layer, leading to the drastic increase in cascade loss.

REFERENCES

Coull J. D., Thomas R. L., Hodson H. P., 2008, "Velocity Dis-tributions for Low Pressure Turbines", ASME paper GT 2008-50589.

Coull J. D. and Hodson H. P., 2010, "Predicting the Profile Loss of High-Lift Low Low Pressure Turbines", ASME paper GT 2010-22675.

Denton J. D., 1993, "Loss Mechanism in Turbomachines", ASME Journal of Turbomachinery, Vol. 115 (4), pp. 621 – 656.

Funazaki, K., Yamada, K., Tanaka, N. and Chiba, Y., 2009, “Detailed Studies on Separated Boundary Layers over Low-Pressure Turbine Airfoils under Several High Lift Conditions: Effect of Freesteam Turbulence,” ASME Paper, GT2009-59813.

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Zweifel O., 1945, "Die Frage der Optimalen Schaufelteilung bei Beschaufelungen von Turbomaschinen", Insbesondere bei Grober Umlenkung in den Schaufelreihen, Boveri Report, Vol. 32, No. 12, pp. 436 – 444.