Film Cooling With Compound Angle Holes: Heat Transfer Heat transfer coefficients have been measured for film cooling injection from a single row of holes laterally directed with a compound angle of 60 deg. Two hole configurations were tested, round holes and holes with a diffusing expansion at the exit. Streamwise-directed round holes were also tested as a basis for comparison. All the holes were inclined at 35 deg with respect to the surface. The density ratio was 1.0, momentum flux ratios ranged from I = 0.16 to 3.9, and mass flux ratios ranged from M = 0.4 to 2.0. Results are presented in terms ofhf/h0, the ratio of film cooling heat transfer coefficient to the heat transfer coefficient for the undisturbed turbulent boundary layer at the same location. Results indicate that for the streamwise directed holes, the heat transfer rates are close to the levels that exist without injection. Similarly, at low momentum flux ratio, holes with a large compound angle had little effect on heat transfer rates. However, at high momentum flux ratios, holes with a large compound angle had significantly increased heat transfer levels. The results were combined with adiabatic effectiveness results to evaluate the overall performance of the three geometries. It is shown that for evaluation of film cooling performance with compound angle injection, especially at high momentum flux ratios, it is critical to know the heat transfer coefficient, as the adiabatic effectiveness alone does not determine the performance. Compound angle injection at high momentum flux ratios gives higher effectiveness values than streamwise-directed holes, but the higher heat transfer levels result in poorer overall performance.

B. Sen D. L Schmidt D. G. Bogard Mechanical Engineering Department, University of Texas at Austin, Austin, TX 78712

Introduction Film cooling is a technique for cooling gas turbine blades to protect them from the high-temperature mainstream. The benefits of film cooling are that it prolongs the life of the blade, and makes higher combustor temperatures (and hence higher efficiency) attainable. Film cooling may be done by injection of a film of cooling air onto the blade surface through discrete holes. These holes are typically inclined at approximately 30 to 40 deg with respect to the surface, and are generally aligned with the direction of the free-stream flow. However, in many cases the holes are aligned at a large angle inclined from the mainstream direction, which is called a compound angle. In this study we have investigated the effect on film cooling heat transfer of using holes with a large compound angle, with and without expansion of the hole exit. Heat transfer to a film cooled blade may be defined as (Goldstein, 1971): q" = hf(Taw -

TJ

(1)

The adiabatic wall temperature is typically expressed in dimensionless form as the adiabatic effectiveness rj. For injection at the free-stream temperature, the adiabatic wall temperature becomes the same as the free-stream (and jet) temperature and hence the heat transfer coefficient can be found from the difference between the wall and free-stream temperatures (Eckert, 1984). It is clear that distributions of both the heat transfer coefficient and the adiabatic wall temperature are required to predict film cooling heat transfer. The net benefit from film cooling can be quantified as a Net Heat Flux Reduction (NHFR) due to film cooling, or the ratio of reduction in heat transfer to the blade with film cooling to heat transfer without film cooling. This is similar to Contributed by the International Gas Turbine Institute and presented at the 39th International Gas Turbine and Aeroengine Congress and Exposition, The Hague, The Netherlands, June 13-16, 1994. Manuscript received by the International Gas Turbine Institute February 9, 1994. Paper No. 94-GT-311. Associate Technical Editor: M. G. Dunn.

the Stanton number reduction described by Luckey et al. (1977): NHFR = 1 - q"lql = 1 - hf(Tm - Tw)/ho(T„ - T„)

(2)

where the subscript 0 denotes conditions with no film cooling. The objective of film cooling is to increase NHFR by reducing hflhQ and lowering Ta„ (and hence increasing rj). If we define the dimensionless temperature ratio 9 by:

(r. - rc)/(T. - Tw)

(3)

it can be readily shown that: NHFR = 1 - hf/h0(\ - T]9)

(4)

Thus, both the adiabatic effectiveness and the heat transfer coefficient are required to evaluate film cooling performance. Note that application of Eq. (4) with an arbitrary value of Q presumes that hf is not dependent on temperature. Film cooling performance is affected by a number of flow and geometric parameters. Injection geometry parameters that affect film cooling include the injection angle, pitch-to-diameter ratio, length-to-diameter ratio, hole exit shape, and orientation of hole with respect to mainstream. Flow parameters include the ratios of density, velocity, mass flux and momentum flux between injectant and mainstream, pressure gradient, and freestream turbulence. (Note that the ratios of jet to mainstream variables, DR, VR, M, and /, are not all independent; specifying any two of them fixes the other two.) Although there have been many studies of adiabatic effectiveness for discrete hole film cooling, there have been relatively few studies of the associated heat transfer. Studies of isothermal heat transfer with film cooling (using jets at the same temperature as the free stream) using a single row of inclined, streamwise directed holes on a flat plate have been completed by Eriksen and Goldstein (1974); Liess (1975); Goldstein and Yoshida (1982); Hay et al. (1985); and Ammari et al. (1990). Similar studies using heated or cooled jets have been done by Forth et al. (1985), Makki and Jakubowski (1986), and Ligrani et al. (1988). The only previous study of heat transfer associ-

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ated with compound angle holes was by Ligrani et al. (1992). A brief summary of the major results from these studies relevant to the work presented in this paper is given below. The consistent trend among all the studies of inclined, streamwise-directed holes is that there is only a slight effect on heat transfer relative to the flow without film cooling. The only significant deviation from htlh0 = 1 . 0 occurs near the hole within xlD = 10. All the studies are consistent in showing increases in hflhQ for higher blowing ratios, 1 s M == 2, with centerline values increasing as much as 40 to 50 percent very near the hole. For moderate blowing ratio, M = 0.5, Eriksen and Goldstein (1974) showed a slight (10 percent) decrease in hflh0, but Liess (1975), Hay et al. (1985), and Ammari et al. (1990) showed slight increases of 10 to 20 percent. With the exception of Makki and Jakubowski (1986), Forth et al. (1985), and Ammari et al. (1990), all the studies listed above used low density ratios ranging from DR = 0.85 to 1.0. Ammari et al. (1990) studied the effect of density ratio on film cooling heat transfer for the same geometries as Hay et al. (1985). They found that increasing the density ratio from DR = 1.0 to DR = 1.52 at a moderate mass flux ratio of M = 0.5 had essentially no effect on the heat transfer. For larger mass flux ratios the laterally averaged heat transfer rate was consistently higher for the lower density ratio. They attributed this to the greater momentum flux ratio of the unit density ratio jet at the same M. Forth et al. (1985) obtained similar results for jets with different density ratios. Film cooling using compound angle holes was studied by Ligrani et al. (1992). Using one and two rows of round holes, they compared results for CA = 0 deg and CA = 50.5 deg. However, the injection angles and hole pitch for the CA = 50.5 deg and CA = 0 deg holes were different (35 and 24 deg, and PID = 6.0 and 7.8 for CA = 0 and 50.5 deg, respectively). Their laterally averaged isothermal heat transfer data show negligible differences between the CA = 0 deg and CA = 50.5 deg holes for the three mass flux ratios, M = 0.5, 1.0, and 1.5, they studied. In each case the laterally averaged isothermal heat transfer ranged from hf/h0 = 1.0 to hf/h0 = 1.15, with slightly increasing heat transfer with increase in M. An important part of this study was determining the net heat transfer reduction by combining the heat transfer results with adiabatic effectiveness results presented in the companion paper (Schmidt et al., 1995). To maximize the accuracy of the heat transfer measurements, heat transfer tests were done with DR = 1.0 (coolant at the same temperature as the free stream). The poor accuracy for high density ratio tests was due to the difficulty of maintaining a steady coolant temperature in our facility for very low coolant temperatures (for further details, see Sen,

1995). Heat transfer measurements were related to effectiveness measurements, which were done at DR = 1.6, by matching the momentum flux ratio, /. Matching in terms of / rather than M was done based on the adiabatic effectiveness results of Sinha et al. (1991) and the thermal field results of Thole et al. (1992), which showed that / is the appropriate scaling parameter for variable density ratio film cooling at moderate to high blowing ratios. The results of Ammari et al. (1990) also showed that / is a more appropriate scaling parameter. Although Ammari et al. showed a significant variation in heat transfer rates when comparing different density ratios at the same M, when compared at approximately the same / the differences are negligible. For example, comparing the laterally averaged heat transfer results of Ammari et al. at M = 2.0 and DR = 1 . 5 with results at M = 1.5 and DR = 1.0, which are at similar / (/ = 2.6 and 2.3, respectively), a maximum difference of less than 4 percent was found. These results support use of the momentum flux ratio to match the heat transfer and adiabatic effectiveness results, which were obtained at different density ratios. Facilities and Instrumentation Measurements were made in a closed-loop wind tunnel with a 0.61-m-high X 0.61-m-wide X 2.4-m-long test section, and a secondary flow loop for the film cooling jets. Figure 1 shows a schematic of the test section in the facility. For a detailed description of this facility see Pietrzyk et al. (1990). The film cooling jet flow and leading edge suction were provided by a secondary flow loop. The static pressure drop across the contraction upstream of the test section was used to measure the freestream velocity, and a sharp-edged orifice flow meter was used to measure the flow rate of the coolant jets. Pietrzyk et al. verified uniform distribution of injectant between the film cooling jets. The leading edge suction was adjusted to provide uniform flow without separation at the leading edge. The test plate consisted of three sections, a 12.7-cm-long leading edge plate, a 14-cm-long injection plate with film cooling holes, and a constant heat flux plate described in detail later. This modular construction made it possible to test different hole geometries using the same constant heat flux surface. A 2.4-mm-dia trip wire was installed 9.5 cm downstream of the leading edge. Results are presented in terms of x (streamwise) and z (spanwise) coordinates, where the origin of x is the trailing edge of the film cooling hole and the origin of z is the centerline of the central hole. All distances are nondimensionalized using the hole diameter of D = 1.11 cm. Figure 2 shows the test plate arrangement and the coordinate system. The film cooling holes had a compound angle of CA = 60 deg. One set of holes had a round hole, and the other set of

Nomenclature A CA D DR

= = = =

surface area compound angle film cooling hole diameter density ratio of coolant to mainstream = pc/poo I = momentum flux ratio of coolant to mainstream = pcU2c/p„Ui L = hole length M = mass flux ratio of coolant to mainstream = pcUJ pJJ„ NHFR = Net Heat Flux Reduction, or ratio of reduction in heat transfer with film cooling to heat transfer without film cooling P = hole spacing Re = Reynolds number T = temperature Tu = free-stream turbulence intensity Journal of Turbomachinery

U = velocity Uc = bulk cooling jet velocity through metering length (inlet) of the hole hf = heat transfer coefficient = q"l (T - T ) \ * aw

•* w J

q" = heat flux x = streamwise coordinate originating at downstream edge of film cooling holes z = spanwise coordinate originating at centerline of central hole