Development and testing of a diamond calorimeter heat transfer gauge
Keywords: aerodynamics
heat flux transducers
hypersonics
heat transfer
thermofluids

Surface heat flux measurements in hypersonic pulse-flow facilities, such as Reflected Shock Tunnels and Expansion Tunnels, provide vital information for the design of hypersonic and hypervelocity vehicles and for the understanding of these complex flow environments. However, test-times in these facilities are on the order of microseconds to milliseconds, and by nature of their operation, the flow contains particles of metal diaphragms, resulting in damage to instrumentation. Additionally, at high flow enthalpies, ionised species and free electrons are present in the gas. Given these significant challenges, this thesis describes the design and manufacture of a new surface heat flux gauge, called the Diamond Heat Transfer Gauge (DHTG), and presents new data reduction methods, the results of calibration experiments, and two experimental campaigns in pulse-flow facilities. The DHTG is shown to overcome limitations of current instrumentation by increasing robustness, and improving response time, electrical isolation, and accuracy.
Four types of DHTG have been manufactured, consisting of a 2.5 mm diameter disk of synthetic diamond, either 75 µm, 150 µm, 220 µm or 325 µm thick, mounted into a cylindrical steel housing, with a platinum thin-film resistance temperature detector sputtered on the rear surface of the diamond to measure its temperature rise. An analysis of the gauge as a calorimeter showed that the rise-time of the four types of DHTG are 2.4 µs, 11.6 µs, 36.3 µs, and 54.4 µs respectively, and that the measurement error due to the data reduction method grows with time, limiting measurements to 500 µs for a 1 % drop in accuracy. While the rise-time is sufficiently fast for use in pulse-flow facilities, in order to extend the useful test-time and enable accurate measurements in a wider range of facilities, a non-linear implementation of the Sequential Function Specification Method (SFSM) was developed as an alternative data reduction method. This method deconvolves the impulse response of the gauge from a measured temperature rise to estimate the surface heat flux, and using a numerical study is shown to be accurate to within 0.5 % over a typical 2.5 ms Reflected Shock Tunnel test-time. Additionally, for high signal-to-noise ratio measurements, the SFSM method can improve the rise-time of the DHTG.
The typical experimental measurement uncertainty of the DHTG was calculated to be 7.5 % and is primarily driven by uncertainty in the specific heat capacity of diamond. This is comparable to or better than values of uncertainty for existing techniques, such as thin-film gauges and coaxial thermocouples. An experiment to measure the impulse response of the DHTG to reduce measurement uncertainty further was performed using a laser to provide a short-duration pulse of heat flux. Issues stemming from spatial non-uniformity of the laser intensity and measurement uncertainty meant that the measured response was unsuitable for direct use in the SFSM data reduction method. No significant difference was found between the specific heat capacity of diamond estimated from this experiment and values given in the literature.
Experimental measurements in the X2 expansion tunnel on blunt- and sharpnosed wedge models showed that the DHTG is a viable method for measuring heat fluxes in an expansion tunnel, but is more susceptible to damage from diaphragm fragments than surface junction thermocouples. The five flow conditions used had total enthalpies ranging from 25 MJ·kg−1 to 70 MJ·kg−1 , resulting in DHTG heat flux measurements of up to 129 MW·m−2 . Agreement better than 12 % was seen between the heat fluxes measured by the two types of gauge for the majority of the conditions. Across the set of tests, DHTGs were mounted on surfaces at angles of attack from 0° to 90°. No DHTGs were damaged at 0°, whereas those mounted at higher angles of attack survived between 1 and 17 shots, with half still operational at the end of the experimental campaign, but with significant signs of surface damage.
In a second experimental campaign, a DHTG, a coaxial thermocouple, and a thinfilm heat transfer gauge were used to make stagnation point heat flux measurements in the T6 Reflected Shock Tunnel at a flow total enthalpy of 2.5 MJ·kg−1 . The DHTG and the thermocouple were undamaged after three shots, while the thin-film gauge was damaged beyond use after one shot. The DHTG measurements agree with the Fay and Riddell correlation, but are 20 % lower than the thermocouple measurement. The difference is believed to be a result of error in the effective thermal effusivity used in the data reduction of the thermocouples: the junctions were formed by abrasion using sandpaper, whereas for the experiments in X2 the junctions were created by making two larger-scale scratches. For stagnation point measurements in a Reflected Shock Tunnel, the DHTG is shown to be the preferred measurement technique, demonstrating significant improvements in robustness versus thin-film gauges, and in measurement uncertainty versus surface junction thermocouples.