Steady-State, Overall Average Heat Transfer Measurement Technique

As the name suggests, this technique gives the overall, average heat transfer over the entire test surface. This technique gives a representative idea of the overall heat transfer from a test surface and was frequently used about one to two decades ago. The technique’s inability to get the local heat transfer coefficient is a major drawback. A modified version of this technique gives the regionally averaged heat transfer over the test surface and will be described in the next section.

Single Copper Plate with Heater and Thermocouples

A single metal plate with high thermal conductivity is used as the test wall for which heat transfer is to be studied. Copper, which has a very high thermal conductivity of -400 W/mK, is frequently used. Aluminum, which has a thermal conductivity of -177 W/mK, can also be used. By using a material which has a high conductivity, the entire test surface attains the same temperature at steady-state conditions. If the Biot number is less than 0.1, the entire test surface will give the same wall temperature. The Biot number is given in Equation (5.8)

where h is the heat transfer coefficient on the surface, к is the thermal conductivity of the metal, and Lc is a characteristic length equal to the ratio of the volume of the plate, V, and the surface area, A„ available for convection. If aluminum is used as the test wall material, the researchers should ensure the convective heat transfer coefficients are sufficiently low enough to ensure the Biot number remains less than 0.1. The test wall is instrumented with thermocouples for temperature measurement and fitted with a heater on the underside to provide a uniform heat flux.

Experiment Example

Internal cooling passages likely to be found in the trailing region of gas turbine blades were experimentally investigated by Lau et al. [2]. Trailing edge cooling passages are generally relatively narrow channels, as required by the tapered shape of the turbine airfoils. To increase the structural rigidity within these narrow passages and increase the convective surface area, these channels are commonly lined with pin-fins. These pin-fins are most often an array of short cylinders spanning from the pressure side to the suction side of the channel.

Lau et al. [2] acquired “overall” heat transfer coefficient under a variety of flow conditions typically found in trailing edge cooling channels. In addition to varying the Reynolds number of the coolant through the channels, they also considered multiple pin-fin arrays, and they quantified the effect of trailing edge ejection (the lateral expulsion of coolant from the channel for trailing edge film cooling).

While two separate test sections were used by Lau et al., only one of those channels is described in this example. Figure 5.2 shows the experimental setup for measurement of overall heat transfer coefficients [2]. As explained previously, for the measurement of “overall” heat transfer coefficients, it is necessary to construct the cooling channel from a material with a high thermal conductivity. For the present example, all walls of the channel (as well as the circular pin-fins) were fabricated from copper. For their baseline case (referred to a “Configuration A” in the referenced paper), the rectangular channel had a cross-sectional area of 95.3 x 6.4 mm, and the length of the channel was 95.3 mm. A staggered array of pin-fins was used in the channel, and the pins were arranged such that streamwise and spanwise spacings of the pins were 2.5 times the pin diameter (D = 6.4 mm).

The copper walls of the channel were constructed of 6.4 mm thick copper, and strip heaters were placed on the backside of the copper to heat the walls of the channel. As shown in Figure 5.2, nine thermocouples were imbedded in the top wall of the channel and four thermocouples were used on the bottom wall. The thermocouple outputs were recorded by a thermocouple data logger, and the power supplied to the strip heaters was measured using a digital multimeter (the power to the heaters was varied using a variable autotransformer). For this stationary, rectangular channel, the power to the heaters was adjusted so the wall temperatures were approximately 19.4°C greater than the inlet air temperature.

For the current experiment, the following raw data were recorded for each cooling configuration: (a) ambient room temperature (needed for heat loss calculation), (b) inlet bulk temperature, (c) wall temperature from each thermocouple, and (d) the power supplied to the heater. In addition, a separate heat loss calibration was

Experimental setup for measurement of overall heat transfer coefficients

FIGURE 5.2 Experimental setup for measurement of overall heat transfer coefficients.

required to determine the magnitude of the energy that was lost through the support structure of the test section (not convection away from the wall by the cooling air). For this heat loss calibration, two sets of data (wall temperatures and heater powers) were obtained, so the heat loss during the actual test could be approximated using linear interpolation.

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