Experiment Example

Background and Introduction to Experiment

Han et al. in 1993 [13] investigated local heat transfer distributions on a turbine blade airfoil using a linear cascade. The linear cascade consisted of five blades, and each blade was a two-dimensional representation of a traditional high-pressure turbine blade. With the selected blade profile, the air turns 107° while accelerating 2.5 times from the inlet of the cascade to the exit. Heat transfer coefficient (Nusselt number) distributions were obtained with varying flow conditions (Re = 100,000-300,000) and wake conditions. A spoked wheel was used to simulate the presence of the upstream stator, and the wheel was rotated to accurately model the passing of the rotating blade relative to the stationary vane.

As indicated by Han et al. [13], the center blade was instrumented with thin foil heater strips and thermocouples to provide a local Nusselt number distribution on the blade from the leading edge to the trailing edge. A total of 26 heaters strips were used on the blade surface (as shown in Figure 5.8), and the heater strips were connected in series. Each heater strip was 25.4 cm long, 2 cm wide, and 0.00378 cm thick. Thermocouples were attached to the backside of the foils to provide a local wall temperature distribution. The instrumented blade was manufactured from wood to minimize heat loss by conduction through the blade substrate.

While many cases were considered in the experimental study, only one case will be considered in the present example. The baseline case of “no wake” will be considered at the inlet velocity of 21 m/s (corresponding to Reynolds number of 300,000). The characteristic length in both the Reynolds number and Nusselt number calculation is the chord length of the airfoil, which is given as C = 22.68 cm.

FIGURE 5.8 Overview of experimental facilities for measurement of local heat transfer coefficients using thin foil heaters and thermocouples.

Freestream Velocity Calculation

With wind tunnel studies of this nature, the freestream velocity is often monitored using a Pitot tube. As Pitot tubes measure both the static and dynamic pressures, the velocity inside the wind tunnel can easily be calculated from Bernoulli’s equation. Therefore, it is necessary to determine the flow velocity (and differential pressure) that is needed to provide the desired Reynolds number. In the current example, the desired Reynolds number is Re = 300,000. For the given experimental setup, the Reynolds number can be calculated in Equation (5.39).

Equation (5.39) can be rearranged to solve for the required freestream velocity at a desired Reynolds number.

For the given geometry and flow through the open loop wind tunnel, the required velocity can be calculated as shown in Equation (5.41).

As a Pitot tube is a logical choice to monitor the freestream velocity, it is necessary to use Bernoulli’s equation to determine the differential pressure that corresponds to the desired velocity of 21.0 m/s. A simplified form of Bernoulli’s equation is provided in Equation (5.42).

With pressures of this low magnitude it is often desired to convert the pressure into a column of water or mercury. For the present experiment, the Pitot tube is attached to a digital manometer with the pressure is given in inches of water. Therefore, the differential pressure reading can be converted to inches of water as shown in Equations (5.43) and (5.44).

Acquired Experimental Data (Heat Loss and Convective Heat Transfer Data)

As with other steady-state heat transfer experiments, the bulk of the test section should be composed of a low conductivity material to minimize the conduction of heat through the material (and maximize the heat convected away from the surface). However, even with the use of low conductivity materials, stray heat losses exist, and they must be taken into account.

To calculate the heat lost during the actual experiments, two sets of calibration data were obtained. In a “no flow” scenario, the instrumented blade was heated to a “low” temperature (lower wall temperature than expected during actual experiment) and to a “high” temperature. The wall temperature distributions were obtained at both of these conditions (low and high temperature) under a steady-state condition. In addition, the room temperature and the power supplied to the heaters were recorded. Under this no flow condition, the power supplied to the heaters is equivalent to the heat lost during the actual test (which is dominated by forced convection). Table 5.21 presents the wall temperature distributions obtained during the heat loss calibration.

The origin (x = 0) corresponds to the leading edge of the airfoil. The .v-direction is defined in the streamline direction, with the positive direction being along the suction surface, and the negative direction along the pressure surface.

TABLE 5.21

Temperature Distributions Acquired through the Heat Loss Calibration

TABLE 5.22

Voltage and Resistance Measurements from Heat Loss Calibration

The input power to the heater (comprised of multiple foil strips connected in series) was measured for each test, and the voltages and resistances are shown in Table 5.22.

The temperature distribution and the heater input power measured during the selected case are shown in Tables 5.23 and 5.24, respectively.

TABLE 5.23

Wall Temperature Distribution Acquired at Re = 300,000

TABLE 5.24

Voltage and Resistance Measurements at Re = 300,000

Airfoil Heat Transfer Coefficient Distributions

The objective of this experimental study was to obtain local heat transfer coefficient (Nusselt number) distributions on a blade surface under a variety of freestream turbulence conditions. Therefore, it is necessary to utilize the measured quantities (wall temperatures and heater power) to obtain heat transfer coefficient distributions. Rearranging the traditional convective heat transfer equation, equation (5.45) can be used to calculate the local heat transfer coefficient.

As indicated in the work by Han et al. [13], the adiabatic wall temperature (T_m) is taken as room temperature and is approximately 25°C.

Similar to the regional heat transfer enhancement example (from Han et al. [13]), linear interpolation can be used to determine the “net” rate of heat transfer for the heater. Using the “high” and “low” heat loss data along with the actual test data (both temperature and power input), the local distribution for the rate of heat transfer can be determined. The heat transfer rates are summarized in Table 5.25.

Given the physical size of each heater strip (25.4 cm long x 2 cm wide) and the total number of heater strips (26), the total heater area is known (A = 0.132 m²).

TABLE 5.25

Heat Generation, Heat Loss, and Net Power Distribution

TABLE 5.26

Local Heat Transfer Coefficient Distribution

With the known surface area, the net heat flux (G«,/a) can be determined, and from Equation 5.45, the local heat transfer coefficient can be calculated. Table 5.26 shows the heat transfer coefficient distribution from the selected case.

Finally, both the length scale (x) and the heat transfer coefficients (h) can be non- dimensionalized. The x-coordinate is normalized by the chord length of the blade (22.68 cm), and the Nusselt number is calculated from the heat transfer coefficient (as shown in Equation (5.46)).

Table 5.27 shows the Nusselt number distributions, and the values are plotted in Figure 5.9. The data calculated in the example and showrn in Figure 5.9 represent the “No Wake” case shown in Figure 9 from the work of Han et al. [13].

With the thin foil heater technique, the local Nusselt number distribution clearly captures the separation of the boundary layer near the trailing edge of the suction surface (x/C = 0.9) as indicated in the sudden increase in the local Nusselt numbers. The ability to capture both transition and separation points, is a marked advantage of the thin foil technique.

TABLE 5.27

Local Nusselt Number Distribution

FIGURE 5.9 Local Nusselt number distributions for “No Wake” case at Re = 300,000.

Additional References

The aforementioned foil-heater-thermocouple measurements have been applied to determine the local heat transfer coefficient distributions for many film cooling and internal enhanced channel flow applications. Several selected papers have been published using this methodology for flat-plate film cooling by Eriksen and Goldstein [14] and for turbine blade film cooling by Mehendale et al. [15]. This local heat transfer measurement technique has also been applied to determine the local heat transfer coefficient distributions for rectangular cooling channels with various turbulence promoters by Han and Park [16]. Interested readers can read these papers for their detailed flow loop design, test geometry, experimental procedure, and data analysis and results presentation.