Secondary flows in vane passages sweep off the endwall and onto the suction surface at a location typically close to the throat. These endwall/vane junction flows often have an immediate impact on heat transfer in this region and also move any film cooling off the affected region of the vane. The present paper documents the impact of secondary flows on suction surface heat transfer acquired over a range of turbulence levels (0.7–17.4%) and a range of exit chord Reynolds numbers (500,000–2,000,000). Heat transfer data are acquired with both an unheated endwall boundary condition and a heated endwall boundary condition. The vane design includes an aft loaded suction surface and a large leading edge diameter. The unheated endwall boundary condition produces initially very high heat transfer levels due to the thin thermal boundary layer starting at the edge of heating. This unheated starting length effect quickly falls off with the thermal boundary layer growth as the secondary flow sweeps up onto the vane suction surface. The heat transfer visualization for the heated endwall condition shows no initial high heat transfer level near the edge of heating on the vane. The heat transfer level in the region affected by the secondary flows is largely uniform, except for a notable depression in the affected region. This heat transfer depression is believed due to an upwash region generated above the separation line of the passage vortex, likely in conjunction with the counter rotating suction leg of the horseshoe vortex. The extent and definition of the secondary flow-affected region on the suction surface are clearly evident at lower Reynolds numbers and lower turbulence levels when the suction surface flow is largely laminar. The heat transfer in the plateau region has a magnitude similar to a turbulent boundary layer. However, the location and extent of this secondary flow-affected region are less perceptible at higher turbulence levels where transitional or turbulent flow is present. Also, aggressive mixing at higher turbulence levels serves to smooth out discernable differences in the heat transfer due to the secondary flows.

## Introduction

The National Energy Technology Laboratory recently announced goals to develop technologies, which will allow the achievement of greater than 65% combined cycle efficiency. The stated path toward these goals includes developing technologies to achieve turbine entry temperatures of 3100 °F. The challenge includes maintaining low emission requirements of NOx while managing cooling requirements. The resulting cooling challenges require improved knowledge of gas path heat transfer distributions. Heat transfer rates on the pressure surface of first vanes are often close to two-dimensional (2D). However, on the suction surface, the passage vortex together with the suction surface leg of the horseshoe vortex moves off the endwall onto the suction surface and has a significant influence on heat transfer and film cooling. The present research on suction surface heat transfer has been conducted to provide a better understanding of the influence of these secondary flows on suction surface heat transfer at elevated turbulence levels and over a range of Reynolds numbers. Elevated turbulence levels have been associated with dry low NOx combustion systems commonly used in large land-based gas turbines. The database presented in this paper is expected to be useful in grounding computational methods used to predict full surface heat loads in turbine nozzles.

## Background

Secondary flows and their impact on vane and endwall heat transfer have been subject to a substantial level of investigation by the turbomachinery community. Sieverding [1] discusses some of the early work of investigators including Langston et al. [2]. Langston's model identifies both the pressure and suction side legs of the leading edge horseshoe vortex and the passage vortex. He suggests that the pressure side of the horseshoe vortex merges with the passage vortex. Sieverding's own work suggests that the suction surface leg of the horseshoe vortex continues on the midspan side of the passage vortex and rotates counter to it. Graziani et al. [3] measured blade and endwall heat transfer in a blade cascade similar to Langston's using both a thin and thicker inlet boundary layer. They found that increasing inlet boundary layer thickness extended the region on the suction surface influenced by the passage vortex. They also found the highest levels of heat transfer near the endwall where the passage vortex is reattached onto the suction surface.

Chen and Goldstein [4] investigated convective transport on the suction surface of a turbine blade using a naphthalene sublimation technique. They present Goldstein and Spores [5] turbine passage secondary flow model and suggest that heat transfer on the suction surface is influenced by the passage vortex and suction surface leg of the horseshoe vortex, which is positioned on the midspan side of the passage vortex. However, they suggest that there are two suction surface corner vortices present near the endwall, which also produce noticeably high levels of heat transfer. They note a lower heat transfer valley between the passage vortex separation line and the suction leg of the horseshoe vortex separation line. The area below these lines on the suction surface is important because based on Goldstein and Chen [6], this region will be not protected by film cooling due to the action of the passage vortex. Goldstein et al. [7] conducted extended mass transfer investigations of blade surface convection due to secondary flows near the endwall to provide a more complete picture. Also, Wang et al. [8] studied flow visualization in the same cascade at low Reynolds number using smoke wire visualization to present a more definitive picture of secondary flow structures.

Chen and Goldstein [4] and Goldstein et al. [7] reported very high levels of heat transfer on the suction surface near the endwall, which they attributed to the action of the corner vortices. Chen and Goldstein acquired their data in a blade cascade at low Reynolds numbers (120,000–170,000). Blair [9] and Giel et al. [10] also reported similar high levels of heat transfer in the near endwall region of the suction surface while again their research investigated turbine rotor passages. Conversely, Harasgama and Wedlake [11] investigated transient heat transfer in an annular vane cascade and found midspan heat transfer levels were consistently higher than values near the endwall. They conducted these experiments with an inlet turbulence level of 6.5% using a grid at chord exit Reynolds numbers ranging from 1,700,000 to 5,200,000. They attributed the lower heat transfer levels near the endwalls to the thick endwall boundary layers migrating onto the suction surface. They noted an asymmetry in the secondary flows on the suction surface due to the radial pressure variation. Martinez-Botas et al. [12] also noted a similar region of lower heat transfer on the aft suction surface due to the action of the passage vortex. The inlet turbulence level was around 13% with an exit chord Reynolds number of 2,000,000. They also noted a region of higher heat transfer where the suction surface vortex was passed onto the suction surface. Based on the work of Ames et al. [13,14], as turbulence levels rise, the ability to see the influence of discrete vorticity on heat transfer will diminish due to turbulent mixing and unsteadiness.

The current data exhibit no similar high level of heat transfer near the endwall as noted in the blade studies except, to a lesser extent, at the low Reynolds number. However, the current data were acquired in a linear vane cascade at moderate Reynolds numbers (500,000–2,000,000). The current data provide an enhanced physical understanding of the combined role of turbulence level and secondary flows on the convective heat transfer in the near endwall region of a vane suction surface. They also provide an indication of the extent that upstream film cooling will be influenced by these secondary flows. However, due to the annular nature of actual turbine passages, we can expect the extent of the secondary flows on both the suction surface and the endwall regions to be influenced by the flow geometry. Consequently, the present data will serve to provide a well-resolved database for grounding computational methods for the prediction of heat load in turbine vane passages.

## Experimental Approach

The present cascade experiment has been developed to investigate thermal boundary conditions related to a double wall cooling design [15] to enable the grounding of computational predictive tools. The computational predictive tools are expected to be used to refine the thermal boundary conditions for an eventual cooled vane design scheduled for experimental evaluation. Consequently, the current study has been designed to evaluate the combined effects of secondary flows, turbulence levels, and Reynolds number on vane suction surface heat transfer. The pressure surface of a vane is known to be largely two-dimensional. The ability to determine the effects of secondary flows on suction surface heat transfer is critical as levels can be higher or lower than midspan levels depending on the turbulence level, the Reynolds number, the inlet boundary layer thickness, and the turning. Also, the secondary flows are known to move film cooling protection away from the region below the passage vortex separation line.

The suction surface heat transfer measurements were acquired on a vane in the linear cascade test section shown schematically in Fig. 2. The cascade was designed in a four-vane three-passage arrangement with 15% bleed flow adjustments above the top vane and below the bottom vane in the cascade. The bleed flows together with a row of inlet static taps located one-quarter axial chord upstream from the leading edge plan of the vane were used to adjust the inlet uniformity of the flow. Tailboards were integrated into the trailing edge of the bottom and top vanes in the cascade to help control exit periodicity. A row of exit static taps were placed one-quarter axial chord downstream from the trailing edge plane of the vanes and were used to sense exit periodicity. Both the bleed flow geometry and the tailboard placement were set closely to streamlines from a periodic flow analysis around the vane design. The cascade has a window to enable the third vane from the bottom to be replaced and to provide access for instrumentation. Individual vanes for acquiring surface pressure distributions and heat transfer distributions were used in the current study. The endwall has two constant heat flux 0.023 mm Inconel foils covering its surface to provide a consistent constant heat flux boundary condition with the vane. The substrate under the endwall foils includes a 2.54 cm thick layer of isocyanurate foam covered using a 0.38 mm thick sheet of fiberglass epoxy board (G10), which has 48 fine wire thermocouple integrated into its surface. University of North Dakota's infrared camera has visual access to the far suction surface through two inserts in the lower tailboard. The polycarbonate inserts are designed to be replaced with a 7.62 cm diameter zinc selenide window to provide infrared access for the camera as shown in the schematic.

### Inlet Turbulence Conditions.

Five inlet turbulence conditions were chosen to investigate the impact of turbulence on the extent and discrete nature of the secondary flows affecting the suction surface in terms of the resulting influence on heat transfer. The five inlet turbulence conditions chosen ranged in turbulence intensity from 0.7% to 17.4% and included the low turbulence (LT) condition (Tu = 0.7%), the small grid far (SGF) condition (Tu = 3.5%), the large grid (LG) condition (Tu = 8.0%), the aero-combustor (AC) condition (Tu = 12.6%), and the new high turbulence aero-combustor (HT) condition (Tu = 17.4%). The low turbulence condition is generated using the tunnel arrangement described in the cascade wind tunnel section. The grid turbulence conditions are generated by attaching a 0.914 m long rectangular section between the 3.6 and 1 contraction nozzle and the cascade to accommodate the grids. The small grid far condition was generated by placing a square bar (b = 0.635 cm) square mesh (M = 3.175 cm) grid 32 mesh lengths upstream from the leading edge plane of the vanes in the cascade test section. The large grid condition was generated by placing a larger square bar (b = 1.27 cm) square mesh (M = 6.35 cm) grid 10 mesh lengths upstream from the leading edge plane in the cascade. The aero-combustor condition was created by replacing the nozzle with the mock aero-combustor turbulence generator, which in turn was connected directly to the cascade. The high turbulence aero-combustor turbulence condition was developed by replacing the nozzle with the high turbulence mock aero-combustor turbulence generator. These inlet turbulence conditions are presented in Table 1 and include the nominal inlet velocity. The measurements were acquired at the turbulence intensity (Tu), the integral (Lx) and the energy (Lu) scales as well as the dissipation for the reported velocity. All the reported values of turbulence, length scale, and dissipation are based on the streamwise component of turbulence and the one-dimensional energy spectrum. The turbulence characteristics reported in Table 1 were acquired in previous studies and the reported inlet velocities vary somewhat from the values used in the present investigation.

### Heat Transfer Measurements.

Surface heat transfer measurements were acquired on a vane instrumented with 55 fine wire thermocouples and wrapped with a constant heat flux Inconel foil. The interior of the heat transfer vane was fabricated from isocyanurate foam. The external surface was cast from a low thermal conductivity epoxy, which formed the outer 1.6 mm of the vane. The 55 fine wire thermocouples were cast into the epoxy and the junctions were located near the surface of the vane at midspan. The 0.023 mm Inconel foil was later wrapped around the exterior of the vane to generate the constant heat flux boundary condition. The large Inconel foil is backed with a 0.05 mm thick sheet of Kapton and adhered using a high temperature acrylic adhesive. The foil has a copper bus bars soldered to its ends, which fit into grooves near the trailing edge to minimize their influence on boundary layer development. Adiabatic wall temperatures and heated wall temperatures are acquired at the steady-state conditions. Any small differences between the inlet conditions are adjusted using the inlet total temperatures, which are acquired for each run. The DC power to the foil was determined from the voltage across and the current through the heater. The current was calculated using the voltage across a precision shut resistor. The heat transfer coefficient is determined from the dissipated heat flux less the calculated local radiation loss (εFOIL = 0.21) divided by the local heated to adiabatic temperature difference. The exit chord Reynolds number for a particular case was determined from the inlet total temperature and pressure and a representative exit static pressure downstream from the instrumented vane along with the true chord. An example of the experimental midspan Stanton number distributions for the unpainted foil are presented in Fig. 4 at an exit chord Reynolds number of 1,000,000 for the five turbulence cases. These data were previously reported by Varty and Ames [16].

The present full-surface heat transfer distributions were taken on the vane suction surface using a FLIR SC500 infrared camera. Surface thermography images were acquired through the two view locations in the lower tailboard as shown in Fig. 2. Prior to the infrared measurements, the vane was painted black using a water-based paint by Hallcrest to increase the emissivity (εPAINT = 0.96) for the infrared temperature measurements. Heat transfer measurements based on the fine wire thermocouples were acquired on the vane at the same time as the infrared temperature measurements to provide an in situ temperature for calibration. These heat transfer measurements also verified the influence of the paint on the radiation loss calculation. Midspan Stanton number distributions are compared for the unpainted and painted vane in Fig. 5 and show good agreement suggesting that the radiation loss model is accurate. Reflective dots were also painted on the vane at locations of 1.27 cm, 6.35 cm, and 11.42 cm from the endwall and at locations starting 1.1 cm from the start of heating. The reflective dots were applied to provide a visible spatial reference point on the image, which can be used to help map the temperature distribution image. A raw image of the heated suction surface is presented in Fig. 6 based on an excel visualization. The reflective dots on the image are clearly visible showing the distortion of the wide angle lens, which is located approximately 20.3 cm from the vane suction surface at the upper camera location. The image shown is approximately 19.6 cm by 14.4 cm. However, the image can be transformed to physical coordinates with reasonable accuracy. A comparison between the aft suction surface midspan temperatures and the raw IR camera midspan temperature distribution, before applying the in situ calibration, is presented in Fig. 7. The FLIR SC500 camera, which is based on microbolometer technology, is reported to be accurate within 2 °C. Figure 7 shows variations between thermocouple temperatures in symbols and the raw SC500 temperatures with a continuous line, which are consistent with the 2 °C accuracy for both the heated and unheated conditions. The correction to the SC500 temperatures is based on a linear regression that reduces this error to about 0.7 °C or about one-third of the raw error. The correction is consequently believed to improve the accuracy of the full-surface heat transfer distribution substantially.

### Uncertainty Estimation.

The experimental uncertainties were estimated using the root sum square method described by Moffat [22]. The uncertainty in the reported Stanton number is as high as ±12% with the largest component due to the uncertainty in the in situ temperature calibration. The uncertainty in the heat flux (±3%) and the uncertainty in the adiabatic wall temperature (±2%) are also significant components. The reported pressure distribution has an uncertainty as large as ±2% due to an uncertainty in the exit static pressure distribution and due to a slight uncertainty in the location in high pressure gradients. The uncertainty in the reporting of Reynolds number is estimated to be ±1.5%. The turbulence intensity was determined using hot wire anemometry, and the uncertainty in the reported value was estimated to ±3% due to both calibration drift and precision error. The uncertainty in reporting the turbulent energy scale (Lu) and the longitudinal integral scale (Lx) was estimated to be ±13%. All values were reported based on a 95% confidence interval.

## Experimental Results

The infrared camera is positioned normal to the tail board with its centerline 6.35 cm off the far endwall. The camera was able to view from slightly below the endwall to slightly above midspan, which includes a view along the midspan row of thermocouples. The top position included a view, which began slightly above the trailing edge. The bottom position has a slight overlap with the top position. Infrared images were acquired over five varying turbulence levels and three Reynolds numbers for a consistent endwall heating condition and for the unheated endwall condition.

A full-surface Stanton number visualization is presented at the LT condition for the 1,000,000 Reynolds number case in Fig. 8 for the consistent heated endwall condition. The magnitude of the Stanton number is portrayed as height above the streamwise and spanwise surface. The image indicates that the influence of the passage vortex begins just upstream of the bottom of the lower camera position. The laminar flow over the suction surface at the low turbulence condition is evident over the majority of the suction surface as shown. The Stanton numbers in this laminar region vary from around 0.0009 in the upstream region of the suction surface shown to around 0.0004 downstream. The influence of the secondary flows paints a sharp contrast in the visualization showing peak values above Stanton numbers of 0.0018 near the endwall. These values drop below 0.0015 in the minimum region near the location of the passage vortex separation line then rising again in the region above the passage vortex before dropping quickly to the laminar levels. Near the trailing edge, an asymmetry is seen in the heat transfer data, which may be due to stronger secondary flows generated on the near endwall. By the trailing edge, the secondary flow affects cover about 25% of the span while the passage vortex reaches a point about 17% of the span off the endwall. The combination of a thin inlet boundary layer and an aft loaded suction surface is likely to reduce the strength of the secondary flows.

The small grid far condition for the 1,000,000 Reynolds number case initially shows similar behavior to the low turbulence condition in the upstream region as shown in Fig. 9. However, the small grid far condition begins transitioning over the surface shown in the view and has significantly higher heat transfer by the trailing edge of the vane. The region on the suction surface affected by the secondary flows has grown slightly perhaps due to a thicker endwall boundary layer or the mixing due to the turbulence. The location of the passage vortex separation line has moved slightly upward onto the suction surface and the secondary peak above the separation line, due to a counter rotating vortex, has spread more due to turbulence or unsteadiness. Additionally, transition has produced rising Stanton numbers at the end of the suction surface, which result in less contrast with the effects of the secondary flows. Generally, in the streamwise direction, the Stanton number increases and in the region of the secondary flows, the contrast between and peaks and valleys also increases.

The region of the suction surface visualized in the Stanton number surface in Fig. 10 for the large grid condition at a Reynolds number of 1,000,000 presents a contrasting view to the previous distributions. The flow is initially transitional as the passage vortex moves onto the suction surface and this affected region begins to show as a region of higher heat transfer. However, the thin aggressive turbulent boundary layer that is forming on the suction surface quickly rises to a Stanton number, which is well above the value on the region affected by the secondary flows. This endwall flow-affected region shows heat transfer levels, which are consistent with a turbulent boundary layer. However, the levels are not as high as the recently transitioned boundary layer augmented by grid turbulence. The secondary flows show as a region of lower Stanton number. The minimum region is likely the mean location of the separation line of the passage vortex. Any film cooling protection, which might have been discharged on the suction surface, would likely be largely swept away up to this line. This reduced heat transfer in the region of secondary flows is consistent with the heat transfer studies of Harasgama and Wedlake [11] and Martinez-Botas et al. [12].

The aero-combustor condition is similar to the large grid condition at a Reynolds number of 1,000,000 as shown in Fig. 11. The flow visualized on the suction surface is transitional but further along as compared to the large grid. The region affected by the secondary flows is initially presented as an increase in heat transfer over the remainder of the suction surface but quickly becomes a region of lower Stanton number. The Stanton number visualization does show a minimum region, which may correlate with the separation line of the passage vortex but this region is now much smoother due to the mixing action of the turbulence in addition to the accompanying unsteadiness. Similar to the large grid, the region affected by the endwall flow appears to grow to about one-quarter span by the trailing edge.

The high turbulence (HT) condition is presented for the 1,000,000 Reynolds number in Fig. 12. This figure looks very similar to the aero-combustor case. However, transition has proceeded earlier for the high turbulence condition, and the level of Stanton numbers is slightly higher in the fully turbulent region.

The influence of Reynolds number also has an important contribution to suction surface heat transfer. The surface Stanton number visualization for the 500,000 Reynolds number case is shown in Fig. 13 for the small grid far condition. The flow developing on the suction surface remains laminar for the entire downstream surface. The emergence of the passage vortex onto the suction surface is quite prominent in the initial region of the visualization as shown in the figure. This passage vortex-affected region has very high levels of Stanton number and remains high in this region as the region affected by the passage vortex grows. The Stanton surface indicates that the secondary flows have reached a bit past 1/4th span as shown in the figure. The minimum in the secondary flow region represents the approximate separation line for the passage vortex rising up onto the suction surface. The effect of the counter rotating vortex above the separation line of the passage vortex is notable but much lower than the heat transfer in the region below the passage vortex separation line.

The 2,000,000 Reynolds number case for the large grid shows an interesting contrast to the lower Reynolds number cases. The visualization shown in Fig. 14 shows that heat transfer on the suction surface has nearly completed transition at the beginning of the visualization. The two higher peaks at the beginning indicate regions where transition has proceeded earlier. The location closer to midspan appears to be due to the roughness resulting from painting the reflective spots on the black surface. After transition is complete, the region on the suction surface affected by the secondary flows is seen as an area where heat transfer is reduced. The recently transitioned boundary layer on the suction surface is thin and aggressive in terms of the heat transfer level. The passage vortex moves the secondary loss core onto the region off the suction surface, and it is reasonable that the level of heat transfer under this loss core is less aggressive than a recently transitioned thin turbulent boundary layer augmented to a degree by grid turbulence.

The endwall in the previous Stanton number visualizations was heated at a consistent heat flux compared to the vane surface heat flux. The boundary condition shown in Fig. 15 for the large grid condition has no endwall heating. The resulting Stanton number visualization is presented at the 1,000,000 Reynolds number. The Stanton number level on the vane near the endwall junction is very high due to the unheated starting length effect caused by the unheated flow moving up onto the vane from the endwall. This near endwall region on the suction surface stays consistently high. The level of Stanton number is seen to quickly decrease as this unheated fluid moves up over the suction surface and the final levels are reasonably consistent with the heated endwall data. A comparison with Fig. 10 for the same condition (LG) but with a heated endwall provides an excellent method to assess the influence of the unheated endwall on heat transfer. This Stanton number visualization shows the importance of a consistent boundary condition in experiments as well as the thermal history effects.

Comparing the surface visualizations is difficult in their present state. However, the relative extent of the secondary flows and their level as compared to the midspan Stanton number is shown in Fig. 16. The figure compares spanwise distributions of suction surface Stanton numbers near the trailing edge. The LT and small grid far conditions show the extent of the secondary flows and their influence on heat transfer. The region influenced on the suction surface is larger for the small grid far condition, which may be due a thicker endwall boundary layer. The flow has transitioned for the large grid, aero-combustor and the high turbulence conditions. However, the extent of the secondary flows is generally indicated by the reduced level of heat transfer in the new wall region. The variation in the Stanton number is significantly diminished by the rising turbulence levels due no doubt to the resulting enhanced mixing and increased unsteadiness. Additionally, the Stanton number in the near endwall region decreases at the two highest turbulence levels. First, the endwall boundary layer is expected to be notably thicker due to the action of the turbulence, and this effect could help to reduce Stanton number levels. The high turbulence is also known to break up and mix away discrete vorticity, and the absence of strong discrete vorticity in this region may also influence the level of the near endwall heat transfer in this region.

## Conclusions

Suction surface Stanton number distributions were acquired on the surface of an aft loaded vane at five turbulence conditions ranging from low turbulence (0.7%) to very high turbulence (17.4%) at three Reynolds numbers ranging from 500,000 to 2,000,000. The data generally show the extent of the region affected by secondary flows on the suction surface as well has their relative level compared with the midspan heat transfer.

The region of the suction surface influenced by the secondary flows generally shows Stanton number levels consistent with turbulent boundary layer levels. The visualizations show evidence of the influence of the passage vortex on suction surface heat transfer, the location of the passage vortex separation line, and the evidence of a counter rotating vortex above the passage vortex, which results in a ridge of higher Stanton number levels.

The passage vortex separation line is clearly evident by a minimum Stanton number line in the region affected by the secondary flows. However, at higher turbulence levels, it is difficult to conclude where mixing has washed out and obscured this line or if the influence of turbulence on the endwall boundary layer has had an influence on its location.

The Stanton number distributions at higher turbulence levels and at higher Reynolds numbers, where flow has transitioned, show the influence of secondary flows by the reduced levels of Stanton number. The newly transitioned and aggressive turbulent boundary layers on the suction surface generate high and uniform Stanton numbers, and the region affected by the secondary flows is evident by the depression of values in this region.

Reynolds number had an influence in the results due to the state of the suction surface boundary layer and due to the extent of the secondary flows. Generally, the movement of the passage vortex was slightly higher with decreasing Reynolds number.

## Acknowledgment

The views and opinions expressed in this paper are those of the authors and they do not reflect the official position or policy of the Department of Energy or the U.S. Government.

## Funding Data

• University Turbine System Research Program of the Department of Energy's National Energy Technology Laboratory, Office of Fossil Energy (Grant No. DE-FE0011875).

## Nomenclature

• C =

true chord length, m

•
• CP =

specific heat at constant pressure, J/kg K

•
• h =

heat transfer coefficient, W/m2 K

•
• Lu =

energy scale, Lu = 1.5 |u′|3/ε, m

•
• Lx =

longitudinal integral scale of turbulence, m

•
• P =

pressure, Pa

•
• ReC =

chord Reynolds number based on exit conditions

•
• St =

Stanton number, St = h/ρUEXITCp

•
• T =

temperature, K

•
• Tu =

local turbulence intensity, u′/U

•
• U =

free-stream velocity, m/s

•
• $u′,|u′|$ =

streamwise component rms fluctuation velocity, m/s

### Greek Symbols

Greek Symbols

• ε =

turbulent dissipation rate, m2/s3

•
• ε =

surface emissivity

•
• ρ =

density, kg/m3

### Subscripts

Subscripts

• EXIT =

referenced to vane exit conditions

•
• S =

static condition

•
• T =

total condition

## References

References
1.
Sieverding
,
C. H.
,
1985
, “
Recent Progress in the Understanding of Basic Aspects of Secondary Flows in Turbine Blade Passages
,”
ASME J. Eng. Gas Turbines Power
,
107
(2), pp.
248
257
.
2.
Langston
,
L. S.
,
Nice
,
M. L.
, and
Hooper
,
R. M.
,
1977
, “
Three-Dimensional Flow Within a Turbine Cascade Passage
,”
ASME J. Eng. Power
,
99
(1), pp.
21
28
.
3.
Graziani
,
R. A.
,
Blair
,
M. F.
,
Taylor
,
J. R.
, and
Mayle
,
R. E.
,
1980
, “
An Experimental Study of Endwall and Airfoil Surface Heat Transfer in a Large Scale Turbine Blade Cascade
,”
ASME J. Eng. Power
,
102
(2), pp.
257
267
.
4.
Chen
,
P. H.
, and
Goldstein
,
R. J.
,
1992
, “
Convective Transport Phenomena on the Suction Surface of a Turbine Blade Including the Influence of Secondary Flows Near the Endwall
,”
ASME J. Turbomach.
,
114
(4), pp.
776
787
.
5.
Goldstein
,
R. J.
, and
Spores
,
R. A.
,
1988
, “
Turbulent Transport on the Endwall in the Region Between Adjacent Turbine Blades
,”
ASME J. Heat Transfer
,
110
(4a), pp.
862
869
.
6.
Goldstein
,
R. J.
, and
Chen
,
P.-H.
,
1987
, “
Film Cooling of a Turbine Blade With Injection Through Two Rows of Holes in the Near-Endwall Region
,”
ASME J. Turbomach.
,
109
(4), pp.
588
593
.
7.
Goldstein
,
R.
,
Wang
,
H.
, and
Jabbari
,
M.
,
1995
, “
The Influence of Secondary Flows Near the Endwall and Boundary Layer Disturbance on Convective Transport From a Turbine Blade
,”
ASME J. Turbomach.
,
117
(4), pp.
657
665
.
8.
Wang
,
H. P.
,
Olson
,
S. J.
,
Goldstein
,
R. J.
, and
Eckert
,
E. R. G.
,
1997
, “
Flow Visualization in a Linear Turbine Cascade of High Performance Turbine Blades
,”
ASME J. Turbomach.
,
119
(1), pp.
1
8
.
9.
Blair
,
M. F.
,
1992
, “
An Experimental Study of Heat Transfer in a Large-Scale Turbine Rotor Passage
,”
ASME
Paper No. 92-GT-195.
10.
Giel
,
P. W.
,
Van Fossen
,
G. J.
,
Boyle
,
R. J.
,
Thurman
,
D. R.
, and
Civinskas
,
K. C.
,
1999
, “
,”
ASME
Paper No. 99-GT-125.
11.
Harasgama
,
S. P.
, and
Wedlake
,
E. T.
,
1991
, “
Heat Transfer and Aerodynamics of a High Rim Speed Turbine Nozzle Guide Vane Tested in the RAE Isentropic Light Piston Cascade (ILPC)
,”
ASME J. Turbomach.
,
113
(3), pp.
384
391
.
12.
Martinez-Botas
,
R. F.
,
Lock
,
G. D.
, and
Jones
,
T. V.
,
1995
, “
Heat Transfer Measurements in an Annular Cascade of Transonic Gas Turbine Blades Using the Transient Liquid Crystal Technique
,”
ASME J. Turbomach.
,
117
(3), pp.
425
431
.
13.
Ames
,
F. E.
,
Barbot
,
P. A.
, and
Wang
,
C.
,
2005
, “
Effects of Catalytic and Dry Low NOx Combustor Turbulence on Endwall Heat Transfer Distributions
,”
ASME J. Heat Transfer
,
127
(4), pp.
414
424
.
14.
Ames
,
F. E.
,
Barbot
,
P. A.
, and
Wang
,
C.
,
2003
, “
Effects of Aeroderivative Combustor Turbulence on Endwall Heat Transfer Distributions Acquired in a Linear Vane Cascade
,”
ASME J. Turbomach.
,
125
(2), pp.
221
231
.
15.
Kingery
,
J. A.
,
Ames
,
F. E.
,
Downs
,
J.
,
Acharya
,
S.
, and
Barker
,
B. J.
,
2015
, “
An Analysis of a Deposition Tolerant Cooling Approach for Nozzle Guide Vanes
,”
ASME
Paper No. GT2015-42419.
16.
Varty
,
J.
, and
Ames
,
F. E.
,
2016
, “
Experimental Heat Transfer Distributions Over an Aft Loaded Vane With a Large Leading Edge at Very High Turbulence Levels
,”
ASME
Paper No. IMECE2016-67029.
17.
Busche
,
M. L.
,
Moualeu
,
L. P.
,
Tang
,
C.
, and
Ames
,
F. E.
,
2013
, “
Heat Transfer and Pressure Drop Measurements in High Solidity Pin Fin Cooling Arrays With Incremental Replenishment
,”
ASME J. Turbomach.
,
135
(4), p.
041011
.
18.
Busche
,
M. L.
,
Kingery
,
J. E.
, and
Ames
,
F. E.
,
2014
, “
Slot Film Cooling in an Accelerating Boundary Layer With High Free-Stream Turbulence
,”
ASME
Paper No. GT2014-25360.
19.
Kingery
,
J.
, and
Ames
,
F.
,
2016
, “
Full Coverage Shaped Hole Film Cooling in an Accelerating Boundary Layer With High Free-Stream Turbulence
,”
ASME J. Turbomach.
,
138
(
7
), p.
071002
.
20.
ANSYS, 2015, “
ANSYS Fluent Release 16.0 Copyright 2014
,” ANSYS Inc., Canonsburg, PA.
21.
Shih
,
T.-H.
,
Liou
,
W. W.
,
Shabbir
,
A.
, and
Zhu
,
J.
,
1995
, “
A New k–ε Eddy-Viscosity Model for High Reynolds Number Turbulent Flows—Model Development and Validation
,”
Comput. Fluids
,
24
(3), pp.
227
238
.
22.
Moffat
,
R. J.
,
1988
, “
Describing the Uncertainties in Experimental Results
,”
Exp. Therm. Fluid Sci.
,
1
(1), pp.
3
17
.