DRAFT GT2003-38118

EXPERIMENTAL AND NUMERICAL INVESTIGATION OF IMPINGEMENT ON A RIB-ROUGHENED LEADING-EDGE WALL

by

M.E. Taslim, K. Bakhtari and H. LiuMechanical, Industrial and Manufacturing Engineering Department

Northeastern UniversityBoston, Massachusetts

USA

ABSTRACT

Leading edge cooling cavities in modern gas turbine airfoils play an important role in maintaining the leading edge temperature at levels consistent with airfoil design life. These cavities often have a complex cross-sectional shape to be compatible with the external contour of the blade at the leading edge. Furthermore, to enhance the heat transfer coefficient in these cavities, they are often roughened on three walls with ribs of different geometries. The cooling flow for these geometries usually enters the cavity from one end of the airfoil flows radially to the other side or, in the most recent designs, enters the leading edge cavity from the adjacent cavity through a series of crossover holes on the partition wall between the two cavities. In the latter case, the crossover jets impinge on a smooth leading-edge wall and exit through the showerhead film holes, gill film holes on the pressure and suction sides, and, in some cases, form a crossflow in the leading-edge cavity and move toward the end of the cavity. It was the main objective of this investigation to measure the heat transfer coefficient on a smooth as well as rib-roughened leading-edge wall. Experimental data for impingement on a leading edge surface roughed with different conical bumps and radial ribs are reported by the same authors, previously. This investigation, however, deals with impingement on different horseshoe ribs and makes a comparison between the experimental and numerical results. Three geometries representing the leading-edge cooling cavity of a modern gas turbine airfoil with crossover jets impinging on 1) a smooth wall, 2) a wall roughened with horseshoe ribs , and 3) a wall roughened with notched-horseshoe ribs were investigated. The tests were run for a range of flow arrangements and jet Reynolds numbers. The major conclusions of this study were : a) Impingement on the smooth target surface produced the highest overall heat transfer coefficients followed by the notched-horseshoe and horse-shoe geometries. b) There is, however, a heat transfer enhancement benefit in roughening the target surface. Amongst the three target surface geometries, the notched-horseshoe ribs produced the highest heat removal from the target surface which was attributed entirely to the area increase of the target surface. c) CFD could be considered as a viable tool for the prediction of impingement heat transfer coefficients on an airfoil leading-edge wall.

NOMENCLATURE

Abase leading-edge base area for the smooth caseAhole crossover holes areaAHT total heat transfer area including the surface roughnessAR cooling channel aspect ratioARrib rib aspect ratiodjet jet diameterDh cooling channel hydraulic diametere roughness heighth average heat transfer coefficient on the leading-edge wall, [(vi/AHT)-qloss]/(Ts-Tjet)i current through the foil heater on the middle brass piecek air thermal conductivitym air mass flow rate through the middle (fourth) crossover holesNujet average Nusselt number based on the jet diameter, hdjet /kPfeed supply channel pressurePLE leading-edge channel pressure qloss heat losses from the middle bronze piece to the ambient by conduction and convection as well as the heat losses by radiation to the unheated wallsRnose channel radius at the leading edgeRejet Reynolds number based on the jet diameter (ρUjetdjet /µ)S Rib pitchTjet air jet temperatureTs surface temperatureUjet jet mean velocity, m/ρAhole

Z jet place distance to the target surface (Fig. 1)v voltage drop across the foil heater on the middle bronze pieceα rib angle of attackµ air dynamic viscosity at jet temperatureρ air density at jet temperature and pressure

INTRODUCTION

Various methods have been developed over the years to keep the turbine airfoils temperatures below critical levels consistent with the required life for each component. Parallel with advances in airfoil material properties, advances in airfoil cooling schemes have also been remarkable. A main objective in turbine airfoil cooling design is to achieve maximum heat removal from the airfoil metal while minimizing the required coolant flow rate. One such method is to route coolant air through serpentine passages within the airfoil and convectively remove heat from the airfoil. The coolant is then ejected either at the tip of the airfoil, through the cooling slots along the trailing edge or the film holes on the airfoil surface at critical locations. To further enhance the heat transfer, the cooling chan-

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nel walls are often roughened with ribs. Extensive research has been conducted on various aspects of the rib-roughened channels and it is concluded that geometric parameters such as passage aspect ratio (AR), rib height to passage hydraulic diameter or blockage ratio (e/Dh), rib angle of attack (α), the manner in which the ribs are positioned relative to one another (in-line, staggered, crisscross, etc.), rib pitch-to-height ratio (S/e) and rib shape (round versus sharp corners, fillets, rib aspect ratio (ARrib), and skewness towards the flow direction) have pronounced effects on both local and overall heat transfer coefficients. The interested reader is referred to the work of investigators such as Burggraf [1], Chandra and Han [2], El-Husayni et al. [3], Han [4], Han et al. [5, 6, 7], Metzger et al. [8, 9, 10], Taslim and Spring [11,12], Taslim et al. [13, 14, 15], Webb et al. [16] and Zhang et al. [17].

Airfoil leading-edge surface, being exposed to very high gas temperatures, is often a life-limiting region and requires more complex cooling schemes especially in modern gas turbines with elevated turbine inlet temperatures. A combination of convective and film cooling is used in conventional de-signs to maintain the leading-edge metal temperature at levels consistent with airfoil design life. This study focuses on the leading-edge jet impingement and effects that roughening of the leading-edge surface has on the impingement heat transfer coefficient. In this flow arrangement, the coolant enters the leading-edge cooling cavity as jets from the adjacent cavity through a series of crossover holes on the partition wall between the two cavities. The cross-over jets impinge on the leading-edge wall and exit through the leading-edge film holes on the pressure and suction sides, or form a crossflow in the leading-edge cavity and move toward the airfoil tip. A survey of many existing gas turbine airfoil geometries show that, for analytical as well as experimental analyses, such cavities can be simplified by simulating the shape as a four-sided polygon with one curved side that simulates the leading edge curvature, a rectangle with one curved side (often the smaller side) or a trapezoid, the smaller base of which is replaced with a curved wall. The available data in open literature is mostly for the jet im-pingement on flat surfaces that are smooth or rib-roughened and a few cases of impingement on concave but smooth surfaces. These studies include the work of Chupp et al. [18], Metzger et al. [19], Kercher and Tabakoff [20], Florschetz, et al. [21, 22, 23], Metzger and Bunker [24], Bunker and Metzger [25], Van Treuren et al. [26], Chang et al. [27], Huang et al. [28], and Akella and Han [29]. Taslim et al [33, 34, 35] reported on impingement cooling of a smooth as well as roughened airfoil leading edge. They examined sandpaper roughness and different conical bump and radial rib geome-tries in a test section with a circular nose, two tapered side walls and a flat fourth wall on which the crossover jets were positioned. Circular and racetrack-shaped crossover jets, at 0o and 45o angles with the channel’s radial axis were compared. Results were also compared for leading-edge geometries with and without showerhead film holes. This paper, however, deals with impingement on an airfoil leading-edge that is roughened with horseshoe ribs that are commonly used on the leading-edge sur-face in the traditional channel flow cooling of the leading-edge cavity. A numerical study was also conducted and the the numerical results for representative cases are compared with the corresponding tests results.

TEST SECTIONS

Figures 1 and 2 show schematically the layout, cross-sectional area, and the target surface geom-etries for the three test sections investigated in this project. A conventional technique of heated walls in conjunction with thermocouples was used to measure the heat transfer coefficient. The test wall, where all measurements were taken, consisted of three removable cast bronze pieces which were heated by foil heaters attached on the back of the pieces. By proper adjustment of the ohmic power to

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the foil heater the desirable surface temperature was obtained. All test sections were 85.5 cm long. The circular wall simulating the leading-edge nose had an inner radius of 1.1 cm and an arc angle of 137o, was made up of fiberglass with a 9.9 cm long recess in the middle to house the three bronze pieces. This circular recess along the inner radius with a depth of 3.2 mm allowed the bronze pieces to be fitted into the fiberglass shell. A flange on each side of the leading-edge piece facilitated the connections of the side walls. The two identical side channels with a cross-sectional area of 38.86 cm2 (5.1 cm by 7.62 cm) and same length as the leading-edge piece were also made of fiberglass. The side channels’ main function was to maintain the dump pressure to consequently control the amount of flow through the "gill" holes on the airfoil suction and pressure sides. Eight angled cylindrical holes with a diameter of 4.88 mm and a center-to-center distance of 3.25 cm were drilled on each side channel wall at an angle of 30o with the sidewall to simulate gill holes on the suction and pressure sides of an airfoil. These holes were staggered along the length of the test section with respect to the crossover jet holes on the jet plate.

Two removable 1 mm thick jet plates corresponding to a Z/djet=3.2 were made of aluminum to produce the impinging jets for the symmetric and asymmetric impingement tests (Figure 2d). Seven cylindrical holes with a diameter of 0.71 cm were drilled at a distance of 3.27 cm from each other (center-to-center) on each jet plate. The only difference between the two jet plates was the manner by which the crossover holes were drilled. For the symmetric impingement, the crossover holes were arranged such that the jets impinged on the horseshoe or notched-horseshoe ribs while for the asym-metric impingement tests, jets impinged in between the horseshoe or notched-horseshoe ribs. For the smooth wall, of course, the symmetric and asymmetric cases were identical. Therefore, for all smooth wall tests, jets impinged in the middle of the bronze pieces. The jet plate was attachedand sealed to the side channel walls to simulate the partition wall between the leading-edge and its adjacent cavities. The cylindrical holes were centered along both the length and width of the jet plate. The removable bronze pieces, installed in the fiberglass outer shell, provided the ability to change the impingement surface geometries in the test rig. Three different target geometries were manufactured and tested(Figure 2) : (1) a smooth wall that served as a baseline, (2) a roughened wall with horseshoe and straight ribs, (3) a roughened wall with notched-horseshoe and straight ribs.

For each geometry, a Unigraphics® model was created for a LOM (Laminated Object Model)

machine. This LOM model was used to mold and create three cast bronze test pieces for each of the three geometries. A 3 cm by 6.1 cm custom-made thin etched-foil heater with a thickness of about 0.2 mm was glued around the outer curved surface of each bronze piece to provide the necessary heat flux. For each geometry, three identical bronze pieces, separated by a 1 mm thick rubber insulator, were mounted next to each other. Heat transfer coefficients were measured on the middle piece while the other two pieces acted as guard heaters to minimize the heat losses to the adjacent walls. In addition, two custom-made thin etched-foil heaters were also mounted on the test section side channel walls next to the middle bronze piece free edges, again acting as guard heaters. The test section wall tem-perature was adjusted to a desirable level by varying the ohmic power to these heaters. Six thermocouples embedded in the middle bronze piece and three thermocouples embedded in each guard bronze piece measured the wall temperatures. The average of the six thermocouple readings in the middle bronze piece which, if different only differed by a fraction of a degree, was used as the surface temperature in the data reduction software for the average heat transfer coefficient. The se-lected nominal surface temperature was 45oC. With a jet temperature of about 20oC, a reasonable 25oC temperature difference between the wall surface and air was attained. Two thermocouples embedded in the wall behind the guard heaters were used to measure the side wall temperature adjacent to the

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middle bronze piece. By proper adjustment of the power to the side heaters, the wall temperature under the side heaters was set to be around 45oC. The conduction heat loss from the test piece to the fiber-glass wall was calculated to be negligible (less than 0.02% of the total heat flux). AC power was supplied to individual heaters through an existing power panel with individual Variacs for each heater. Typical amperage and voltage levels for each heater varied from 0.23 - 0.4 Amps and 20-45 Volts, respectively. Air properties were evaluated at jet temperature. The supply channel was formed by the exterior walls of the side channels, the jet plate and a 1.27 cm thick aluminum back plate. The end caps with throttling valves controlled the flow and pressure in each channel thus simulating many varia-tions that may occur in a real airfoil. Static pressure taps and thermocouples in each channel measured the pressure and temperature at different locations. The test sections were covered on all sides, by 5 cm thick glasswool sheets to minimize heat losses to the environment. The radiational heat loss from the heated wall to the unheated walls as well as losses to ambient air through the fiberglass nose piece were taken into consideration when heat transfer coefficients were reduced. A contact micromanom-eter with an accuracy of 0.025 mm of water as well as a series of oil and mercury manometers measured the pressures and pressure differences between the static pressure taps mounted on bothsides of the target wall for each geometry. For all cases, a critical venturimeter was used to measure the total air mass flow rate entering the supply channel.

COMPUTATIONAL MODELS

The computational models were constructed for a representative repeated domain with two sym-metric planes in each case. Figure 4 shows this representative domain for the horseshoe geometry and details of the mesh distribution on the surface of the domain. The computational domain size for the other two geometries were the same. The CFD analysis was performed using Fluent/UNS solver by Fluent, Inc., a pressure-correction based, multi-block, multigrid, unstructured/adaptive solver. Stan-dard high Reynolds number k-ε turbulence model in conjunction with the generalized wall function was used for turbulence closure. Other available turbulence models in this commercial code, short of two-layer model which required a change in mesh arrangement for each geometry and was beyond the scope of this investigation, were also tested and did not produce results significantly different from those of k-ε model. Mesh independence was achieved at about 400,000 cells for a typical model. Cells in all models were entirely hexagonal, a preferred choice for CFD analyses, and were varied in size biogeometrically from the boundaries to the center of the computational domain in order to have finer mesh close to the boundaries. Figure 5 shows the mesh distribution around the periphery of a typical model.

RESULTS AND DISCUSSION

A total of 31 test setups each for seven jet Reynolds numbers ranging from 10,000 to 50,000 were run in this investigation. All tests had several common features described as follows. There were always seven impinging jets issuing from the jet plate. The middle jet (forth) always impinged on the bronze test piece in the middle of the test section and the reported heat transfer results are always for that middle bronze test piece. The third and fifth jets impinged on the side bronze pieces that acted as guard heaters. The remaining four jets impinged on the fiberglass leading-edge wall to simulatethe flow field in a typical leading-edge cavity. The jet Reynolds number is based on the air mass flow rate through the middle crossover hole. The non-dimensional jet distance to the target surface, Z/djet, re-mained fixed at 3.2 for all target surface geometries. Two inflow arrangements to the supply channel,

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as shown in Figure 3a, where air either entered from one end or both ends, were tested. The outflow arrangement, shown in Figure 3b, was consisted of four different cases. For the "nominal flow" case the air, after impinging on the leading-edge wall, ejected equally through the side channel holes which simulate the gill holes on the pressure and suction sides of an airfoil. For the "one-sided" case the air, after impinging on the leading-edge wall, ejected through the gill holes on one side only. For the "circular flow" case the air, after impinging on the leading-edge wall, ejected from the same side of the test section as it entered while for the "crossflow" case the air, after impinging on the leading-edge wall, ejected from the opposite side of the channel simulating exit flow through an airfoil tip. In the latter two flow arrangements, all side channel holes were plugged and valves were closed so that the only way out for the cooling air after impingement was through one end of the leading-edge channel. The three jets upstream of the middle jet (spent air) formed a crossflow that severely affected the impingement heat transfer coefficient. For a consistent comparison of heat transfer results for all these arrangements, the jet Reynolds number for all cases was calculated based on the air mass flow rate through the fourth crossover hole. To determine the air mass flow rate variation across the crossover holes, a one-dimensional flow circuit of each test setup consisting of appropriate orifices, tubes, mo-mentum and pressure chambers, shown in Figure 3c, was built and analyzed. The results, shown in Figure 6, revealed that the air mass flow rate through the fourth crossover hole for the cases of flow entering the supply channel from one end or both ends and exiting through the side holes (on both sides or on one side) was very close to that of average mass flow through the seven holes i.e. 14.28% each. The maximum difference was calculated to be 0.01%. It is also noted that the mass flow rates through other crossover holes are very close to the average percentage for these cases. For the circular and crossflow arrangements, however, a 1% drop, compared to the average mass flow percentage of 14.28, was calculated for the mass flow rate through the forth crossover hole and the jet Reynolds number was corrected accordingly. Static pressure taps in the middle and at each end of the supply channel did not measure a significant difference (about 1 cm of water column for a supplypressure ranging from 110 to 172 KPa, absolute). Experimental uncertainties in heat transfer coefficient and jet Reynolds number, following the method of Kline and McClintock (1953) were determined to be 6% and 1.5%, respectively.

Geometry 1

Impingement on a smooth leading-edge wall, shown in Figure 2a, was tested in thisbaseline geometry. Heat transfer results of this geometry are shown in Figure 7. Several observations are made. Whether flow was entering the supply channel from one end or both ends, it had no significant effect on the impingement heat transfer coefficient because, as we showed in Figure 6, the air mass flow rate through the forth crossover hole for which the heat transfer results are reported, was nearly identical for both inflow arrangements. Other target surface geometries behaved similarly as we have shown in Figure 12. The maximum calculated difference of 1.9% was for the nominal outflow at the lowest Reynolds number. Similarly, whether the jets, after impinging on the target surface, were exiting the leading-edge channel through one row of side holes or both rows, it had no significant effect on the impingement heat transfer coefficient. The maximum calculated difference of 3.9% was again at the lowest Reynolds number. The cross- and circular flow arrangements, however, produced lower heat transfer coefficients. An explanation for this behavior is the presence of a crossflow (spent air), gen-erated by the fifth, sixth and seventh jets in the circular flow arrangement and by the first, second and third jets for the crossflow arrangement. This crossflow reduces the strength of the fourth jet before it impinges on the target surface which in turn reduces the impingement heat transfer coefficient. The maximum decrease compared with the nominal outflow case was calculated to be about 13% which

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occurred at the lowest jet Reynolds number. This difference decreased with increasing jet Reynolds number to about 2.5% at the highest jet Reynolds number.

Geometry 2

Horseshoe ribs are commonly used on the leading-edge surface of the airfoil cooling cavities in order to enhance the convective heat transfer coefficients on the leading-edge surface when the cool-ant is traveling in the cooling channels radially. Several investigators including the first author have reported experimental data on a variety of leading-edge rib geometries, often a critical area in airfoil life expectancy. Impingement on horseshoe ribs, however, is not reported by any investigator yet. The target wall for this geometry was roughened with two sets of ribs - a horseshoe rib that wrapped around the leading edge and two radial ribs in between the horseshoe ribs and on both sides of the airfoil stagnation line as shown in Figure 2b. Compared to the baseline geometry, the total wetted heat trans-fer area was increased by about 40.5%. The two radial ribs were installed in between the horseshoe ribs because it was speculated that the jets, after impinging on the horseshoe ribs would interact with the radial ribs on their exit way through the gill holes, thereby increase the overall heat transfer coefficient.

To establish the superiority of the impingement cooling over the convective cooling, the heat transfer coefficient results for the two flow arrangements and for the same amount of cooling flow are compared in Figure 8. The Reynolds number represented on the horizontal axis, is based on the jet diameter for the impingement cooling and the channel hydraulic diameter for the channel flow. Each pair of data points correspond to the same amount of cooling flow. Or for a given Reynolds number, the impingement cooling flow rate was about 11% higher than that of the channel flow. The heat transfer coefficient was not non-dimensionalized to the Nusselt number to make the comparison more realistic. The impingement heat transfer coefficient is about 2.6 times that of channel flow at the lowest Reynolds number and about 3.3 times at the highest Reynolds number. It should be noted that these ratios are for the average heat transfer coefficient on the entire leading-edge surface (on the surface of the cast bronze piece). Local heat transfer coefficient ratios around the impingement point could be much higher than these values. This comparison proved that where high heat removal rates are desirable, impingement is a viable solution. Impingement tests for this geometry were conducted for all inflow and outflow arrangements shown in Figure 3. The final results, however, are shown in Figure 9 for one inflow case since, similar to the smooth target surface case, whether flow entered the supply channel form one end or both ends, the impingement heat transfer results did not show a significant change. Symmetric and asymmetric impingement cases, however, produced different results. For asymmetric impingement where jets impinged on the leading-edge area in between the horseshoe ribs, the nominal and one-sided outflow cases produced higher heat transfer coefficients compared with the symmetric impingement cases. The reason for this increase of up to 13% at low Reynolds numbers is the interaction of coolant with both horseshoe and radial ribs on its way to the side holes. The asymmetric impingements for the circular and crossflow cases, however, produced lower heat transfer coefficients compared with the symmetric impingements. With the aid of Figure 6 it can be reasoned that the share of the middle bronze piece from the cooling air in the asymmetric impingement case is two half-jets that, with different amount of crossflow, are less effective than one full jet in the symmetric impingement case.

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Geometry 3

The target wall for this geometry was identical to that of geometry 2 except that the horseshoe ribs had a 60o notch in the middle as shown in Figure 2c. Based on our experience with notched ribs in rib-roughened axial-flow channels, it was expected that vortices shed off the notch in the cross- and circular flow cases could improve the overall impingement heat transfer coefficients. Compared to the baseline geometry, the total wetted heat transfer area on the middle bronze piece was increased by about 40%. This geometry was also tested for all inflow and outflow arrangements the results of which are shown in Figure 10. The asymmetric impingement produced higher heat transfer coefficients than those in the symmetric impingement for the nominal, one-sided and crossflow cases while it did not show a significant difference for the circular flow case. When comparisons are made between the three target surface geometries in Figure 11, we see that in general when crossover jets impinge on the unroughened part of the target surface, they produce higher local heat transfer coefficients around the impingement area and the role of roughnesses is mostly to act as extended areas to increase the total heat pickup. That is why we notice higher heat transfer coefficients in most asymmetric cases.

Comparisons

Figures 11 and 12 compare the results of the three target surface geometries for symmetric impingement. Several observations are made. First, for all three target surface geometries, whether the cooling flow entered the supply channel from one end or both ends, the overall heat transfer coefficient did not change as shown in Figure 12 for selected representative cases. A physical expla-nation based on Figure 6 was given when the results of geometry 1 were discussed above. The same discussion holds for the other two target surface geometries. Second, smooth target surface geometry produced higher impingement heat transfer coefficients than roughened target surface with horseshoe or notched-horseshoe ribs, and notched-horseshoe ribs performed better than horseshoe ribs. Our CFD results showed the same behavior. The presence of horseshoe roughness directly under the impinging jet for the symmetric case seems to have reduced the effectiveness of the impingement for two reasons. One is that when the same jet was impinged on the smooth surface in between the horseshoe ribs, higher heat transfer coefficients were recorded and the other is that, based on the CFD velocity vectors shown in Figure 16, the presence of radial ribs slows down the returning flow and creates recirculating zones that further reduce the overall heat transfer coefficients. Our previous work in this area dealing with impingement on target surfaces roughened with conical bumps of different sizes, sandpaper roughness and radials ribs showed the same results i.e. the target surface roughnesses when they are smaller in size and more in numbers, at best, improve the impingement heat transfer coeffi-cient by a few percent. A maximum reduction of 27% in heat transfer coefficient between the nominal cases of smooth and horseshoe geometries at the lowest Reynolds number was measured. However, what makes these roughnesses desirable is the area increase they introduce on the target surface which results in higher heat removal from the leading-edge surface which is often a critical area in turbine airfoil cooling design. Figure 13 includes the contribution of the increased area in the overall heat transfer from the target surface [Nujet(AHT/Abase)] in the data reported in Figure 11. The lower cluster of data represent the smooth geometry while the notched-horseshoe cases represent the highest area-augmented heat transfer. A maximum increase of about 32% in heat removal for the notched-horseshoe geometry, compared to the smooth target surface, was measured at the lowest Reynolds number which is entirely attributed to the increase in heat transfer area.

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Static pressure ratios across the jet plate for all geometries and representative flow arrange-ments are shown in Figure 14. At the lower Reynolds number range, different geometries and flow arrangements have almost the same pressure ratios across the crossover holes. At higher Reynolds numbers, however, a difference in pressure ratios across the crossover holes for different geometries is observed. Higher pressure ratios which did not go beyond 1.011, in general, correspond to the nominal cases in which there is a flow split after impingement. The small difference between the pressure ratios were mainly due to different inflow and outflow arrangements and not to target surface geometry.

CFD Results

Representative CFD results are compared with the experimental data in Figure 15. CFD models with constant heat flux boundary conditions identical to the tested geometry for each case were run on PC Pentium4, 1.6 GHz machines with 512 MB memory. A typical case took about 1000 iterations and about four to five hours to converge. Very good agreements between the measured and numerically calculated impingement heat transfer coefficients are observed. A small difference of 4%, at the most, for the smooth target wall makes these CFD packages viable tools in predicting the impingement heat transfer coefficient. For the roughened target surface cases, the difference is higher due to the presence of recirculating zones in the flow domain, as seen in Figure 16 and generally more complex flow patterns around the horseshoe and straight ribs. A maximum difference of about 9% between the test and CFD results for the notched-horseshoe geometry is very encouraging. It is worth noticing that the numerical results also confirm that the smooth target surface produced higher impingement heat transfer coefficients followed by the notched-horseshoe and horseshoe geometries. Representative heat transfer coefficient and target surface temperature variations are shown in Figures 17 and 18. As physically expected, the area directly under the jet show the highest heat transfer coefficient and lowest surface temperature with the opposite behavior for the areas that are not directly affected by the jet.

CONCLUSIONS

Three leading-edge surface geometries, consisting of a baseline smooth surface and two surfaces roughened with a combination of horseshoe and straight radial ribs, were tested for impingement cooling. The smooth target surface produced the highest impingement heat transfer coefficients fol-lowed by the notched-horseshoe and horseshoe ribs. However, when the contribution of the increased area in the overall heat transfer is taken into consideration, the target surface roughed with notched-horseshoe ribs, for all inflow and outflow cases, proved to be the most effective geometry. An overall increase of about 27% in heat removal can be accomplished by roughening the leading-edge wall with these ribs. The increase is entirely attributed to the increase in the heat transfer area. A very good agreement between the numerical and experimental results, especially for the smooth target surface geometry, suggests that the CFD analyses are becoming a viable tool for the prediction of impinge-ment heat transfer coefficients in turbine airfoil cooling.

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[16] Webb, R.L., Eckert, E.R.G. and Goldstein, R.J., 1971, ‘‘Heat Transfer and Friction in Tubes with Repeated-Rib- Roughness,’’ Int. J. Heat Mass Transfer, Vol. 14, pp. 601-617.

[17] Zhang, Y.M., Gu, W.Z. and Han, J.C., 1994, ‘‘Heat Transfer and Friction in Rectangular Chan-nels with Ribbed or Ribbed-Grooved Walls,’’ J. Heat Transfer, Vol. 116, No. 1, pp. 58-65.

[18] Chupp, R.E., Helms, H.E., McFadden, P.W., and Brown, T.R., 1969, ‘‘Evaluation of Internal Heat Transfer Coefficients for Impingement Cooled Turbine Blades,’’ J. Aircraft, Vol. 6, No. 1, pp. 203-208.

[19] Metzger, D.E., Yamashita,T. and Jenkins, C.W., 1969, ‘‘ Impingement Cooling of Concave Sur-faces With Lines of Circular Air Jets,’’ J. Engr. for Power, Vol. 93, No. 3, pp. 149-155.

[20] Kercher, D.M. and Tabakoff, W., 1970, ‘‘Heat Transfer by a Square Array of Round Air Jets Impinging Perpendicular to a Flat Surface Including the Effect of Spent Air,’’ J. Engr. for Power, Vol. 92, No. 1, pp. 73-82.

[21] Florschetz, L.W., Berry, R.A., and Metzger, D.E., 1980, ‘‘ Periodic Streamwise Variation of Heat Transfer Coefficients for Inline and Staggered of Circular Jets with Crossflow of Spent Air,’’ J. Heat Transfer, Vol. 102, No. 1, pp. 132-137.

[22] Florschetz, L.W., Truman, C.R., and Metzger, D.E., 1981, ‘‘Streamwise Flow and Heat Transfer Distribution for Jet Impingement with Crossflow ,’’ J. Heat Transfer, Vol. 103, No. 2, pp. 337-342.

[23] Florschetz, L.W., Metzger, D.E., Su, C.C., Isoda, Y., and Tseng,H.H., 1984, ‘‘Heat Transfer Characteristics for Jet Arrays Impingement with Initial Crossflow ,’’ J. Heat Transfer, Vol. 106, No. 1, pp. 34-41.

[24] Metzger, D.E., and Bunker, R.S., 1990, ‘‘Local Heat Transfer in Internally Cooled Turbine Air-foil Leading Edge Regions: Part I - Impingement Cooling Without Film Coolant Extraction,’’ J. Turbomachinery, Vol. 112, No. 3, pp. 451-458.

25] Bunker, R.S., and Metzger, D.E., 1990, ‘‘Local Heat Transfer in Internally Cooled Turbine Airfoil Leading Edge Regions: Part II - Impingement Cooling With Film Coolant Extraction,’’ J. Turboma-chinery, Vol. 112, No. 3, pp. 459-466.

11

[26] Van Treuren, K.W., Wang, Z., Ireland, P.T., and Jones, T.V., 1994, ‘‘Detailed Measurements of Local Heat Transfer Coefficient and Adiabatic Wall Temperature Beneath an Array of Impinging Jets,’’ J. of Turbomachinery, Vol. 116, No. 2, pp. 269-374.

[27] Chang, H., Zhang, D., and Huang, T., 1997, ‘‘Impingement Heat Transfer from Rib Roughened Surface Within Arrays of Circular Jet : The Effect of the Relative Position of the jet Hole to the Ribs,’’ Paper # 97-GT-331.

[28] Huang, Y., Ekkad, S.V., and Han, J.C., 1998, ‘‘Detailed Heat Transfer Distributions Under an Array of Orthogonal Impinging Jets,’’ J. Thermophysics and Heat Transfer, Vol. 12, No. 1, pp. 73-79.

[29] Akella, K.V. and Han, J.C., 1999, ‘‘Impingement Cooling in Rotating Two-pass Rectangular Channels with Ribbed Walls,’’J. Thermophysics and Heat Transfer, Vol. 13, No. 3, pp. 364-371.

[30] Taslim, M.E., Pan, Y. and Spring, S.D., 2001, ‘‘An Experimental Study of Impingement on Roughened Airfoil Leading-Walls with Film Holes,’’ J. of Turbomachinery, Vol. 123, No. 4, pp. 766-773.

[31] Pan, Y., 2000, ‘‘An Experimental Investigation of an Airfoil Leading-Edge Impingement Cool-ing with Showerhead Film Holes’’, MS Thesis, Mechanical, Industrial and Manufacturing Engineer-ing Department, Northeastern University, Boston, MA.

[32] Kline, S.J. and McClintock, F.A., 1953, ‘‘Describing Uncertainty in Single-Sample Experi-ments,’’ Mechanical Engineering, Vol. 75, Jan., pp. 3-8.

[33] Taslim, M.E. and Setayeshgar, L., 2001, ‘‘Experimental Leading-Edge Impingement Cooling Through Racetrack Crossover Holes,’’ Paper # 2001-GT-0153.

[34] Taslim, M.E., Setayeshgar, L. and Spring, S.D., 2001, ‘‘ An Experimental Evaluation of Ad-vanced Leading Edge Impingement Cooling Concepts,’’ J. of Turbomachinery, Vol. 123, No. 2, pp. 147-153.

[35] Taslim, M.E., Pan, Y. and Bakhtari, K., 2002, ‘‘Experimenta Racetrack Shaped Jet Impingement On a Roughened Leading-Edge Wall With Film Holes,’’ Paper # GT-2002-30477.

12

Leading Edge

Geom. 3Notched-Horseshoe Ribs

Leading Edge

Geom. 1Smooth

Geom. 2Horseshoe Ribs

Supply Channel

Side Channel Side ChannelFi

berg

lass

Fiberglas

Fibe

rgla

s

7.62

5.1

φ=0.

488

1.1

2.62

137o

Side

Heater

Bronze

Sectio

n A

-A

10

All Dimensions in cmNot to Scale

8 H

oles

8 Holes

30o

Foil Heater

Back Plate

85.5

Supply Channel

Target Surface

Jet Plate

A

A End CapBack Plate

Test Section

Removable End

Leading-Edge Channel

d gill

3.25

7 Ho

les

2.0

Jet Plate

0.7 d =0.71 jet

1.8

0.1

Z=2.25

7-0.71 cm Holes

Figure 1 Schematic of the test apparatus.

13

d) Jet Plate Geometry

All Dimensions in cmNot to Scale

a) Geometry 1 Smooth

0.292

3.17

Leading-Edge

Channel Axis

1.9

0.68

ϕ=0.

71

1.8

c) Notched horseshoe with small axial ribs

0.2030.28

60o

137o

49.5

3

3.27

b) Horseshoe with small axial ribs

7 H

oles

0.407

0.40

7

0.407

0.40

7

0.813

r=0.122 (all corners)

Symmetric Impingement (on the horseshoe ribs)

Asymmetric Impinge-ment (In between the horseshoe ribs)

Figure 2 Target surface and crossover hole geometries.

14

Inflow from One End

Supply Channel

Target Channel

3a) Inflow Inflow from Both Ends

Nominal Case One-Sided Case

3b) Outflow

Crossflow Case

Circular Flow Case

3 bronze pieces

3c) A typical flow circuit for the crossover holes mass flow rate analysis (circular flow case).

OrificeMomentun Chamber

Tube

Figure 3 Inflow and outflow arrangements.

Pressure Chamber

15

Figure 4 Mesh arrangement on target and outer walls.

16

Figure 5 Typical mesh arrangement around the computational domain periphery..

17

1 2 3 4 5 6 710

11

12

13

14

15

16

17

18

19

20

% o

f to

tal f

low

Inflow from Both endsInflow from One endsCircular flowCrossflow

Jet numberFigure 6 Percentage of air flow rate through each crossover holes for all flow arrangements.

18

100

160

50

60

70

80

90

10000 20000 30000 5000040000

Rejet

Nujet

Smooth Target Wall

Nominal One End Nominal Both Ends One-Sided One End One-Sided Both Ends Circular Crossflow

Outflow Inflow

Figure 7 Nusselt number variation with Reynolds number for the smooth surface (baseline) target geometry.

19

10000

Re

100

h, W

/m2 K

Channel FlowImpingement

20000 30000 40000 500008000

200

300

400

500

600

100

ChannelImpingement

Figure 8 Comparison between the heat transfer results of channel and impingement flows.

20

Nominal SymmetricNominal AsymmetricOne-Sided SymmetricOne-Sided AsymmetricCircular SymmetricCircular AsymmetricCrossflow SymmetricCrossflow Asymmetric

Outflow Impingement

100

150

50

60

70

80

90

10000 20000 30000 5000040000

Rejet

Nujet

SymmetricAsymmetricImpingement

Inflow from one end

Figure 9 Nusselt number variation with Reynolds number for the horseshoe-roughened target surface geometry.

21

Nominal SymmetricNominal AsymmetricOne-Sided SymmetricOne-Sided AsymmetricCircular SymmetricCircular AsymmetricCrossflow SymmetricCrossflow Asymmetric

Outflow Impingement

100

170

50

60

70

80

90

10000 20000 30000 5000040000

Rejet

Nujet

SymmetricAsymmetricImpingement

Figure 10 Nusselt number variation with Reynolds number for the notched-horseshoe target surface geometry.

22

100

Smooth NominalSmooth One-SidedSmooth CircularSmooth Crossflow

Horseshoe NominalHorseshoe One-SidedHorseshoe CircularHorseshoe CrossflowNotched NominalNotched One-SidedNotched CircularNotched Crossflow

180

50

60

70

80

90

10000 20000 30000 5000040000

Rejet

Symmetric Impingement

Geom Outflow

Geom Outflow

Inflow from one end

Nujet

Figure 11 Comparison between the heat transfer results of all target surface geometries.

23

Geom Inflow ArrangementSmooth One EndSmooth Both EndsHorseshoe One EndHorseshoe Both EndsNotched-Horseshoe One EndNotched-Horseshoe Both Ends

100

200

40

50

60

70

80

90

10000 20000 30000 5000040000

Rejet

Nujet

Symmetric ImpingementNominal Outflow

Figure 12 Comparison between the heat transfer results of all target surface geometries for the two inflow arrangements.

24

100

200

60

70

80

90

10000 20000 30000 5000040000

Rejet

Symmetric Impingement

Smooth NominalSmooth One-SidedSmooth CircularSmooth Crossflow

Geom Outflow

Horseshoe NominalHorseshoe One-SidedHorseshoe CircularHorseshoe CrossflowNotched NominalNotched One-SidedNotched CircularNotched Crossflow

Geom Outflow

Inflow from one end

220

Nu

jet(A

HT/A

base

)

Figure 13 Comparison between the area-augmented heat transfer results of all target surface geometries.

25

10000 20000 30000 40000 50000

Rejet

1.00

1.01

1.02

1.03

1.04

1.05

1.06

1.07

1.08

1.09

1.10

1.11

1.12

Pfeed

PLE

Symmetric Impingement

Inflow from one end

Smooth NominalSmooth One-SidedSmooth CircularSmooth Crossflow

Geom Outflow

Horseshoe NominalHorseshoe One-SidedHorseshoe CircularHorseshoe CrossflowNotched NominalNotched One-SidedNotched CircularNotched Crossflow

Figure 14 Comparison between the pressure ratios across the crossover holes for all target surface geometries.

Pfeed

PLE

Pfeed

PLE

Pfeed

PLE

26

27

100

200

40

50

60

70

80

90

10000 20000 30000 5000040000

Rejet

Nujet

Symmetric Impingement

Smooth Nominal TestSmooth Nominal CFDSmooth One-Sided TestSmooth One-Sided CFDHorseshoe Nominal TestHorseshoe Nominal CFDHorseshoe One-Sided TestHorseshoe One-Sided CFD

Geom Outflow

Figure 15 Comparison between the experimental and numerical heat transfer results of all target surface geometries.

28

29

365

359

353

348

342

336

330

324

318

313

307

301

295

Figure 18 Represtative temperature variation on the heated surface.

K

2040

1878

1716

1554

1392

1230

1068

905

743

581

419

257

95

W/m2

Figure 17 Representative heat transfer coefficient variation on the heated surface.