Stagnation heat flux measurement in the shock tube .1 Signal Processing

1.2) Considering the substrate to be a semi-infinite solid maintained at an initial temperature T i and is

6.4 Calibration of Shock Tube

6.4.3 Stagnation heat flux measurement in the shock tube .1 Signal Processing

6.4.3 Stagnation heat flux measurement in the shock tube

interactions. Further, the occurrence of any interaction between different waves depends upon the shock tube driving conditions, which is accounted for the change in the pattern of the temperature signals. The interpretation of such phenomena through temperature signals from surface junction thermocouples is one of the strong outcomes of this experimental investigation.

Once the installed shock tube is benchmarked for calibration of the thermal probe, the fabricated thermal sensors as described in Chapter 4 namely, E, T and J-types respectively are utilized to measure stagnation point heat flux using hemispherical model having a radius of 10 mm fitted at the end-flange of the shock tube as seen in Fig. 6.10 (b). Through the experiment, an attempt has been made to measure transient heat flux in the highly transient environment of the shock tube (Fig. 6.16). Attainment of thermal equilibrium between the test object and the fluid flow is not possible due to small test duration. The performance of the fabricated sensors are tested by measuring the stagnation point heat flux inside the shock-tube facility. The thermal sensor is flush mounted one by one on the hemispherical model fitted at the end-flange. The schematic of the mounting assembly is shown in Figs. 6.9(a-b) and Fig. 6.10-b. A hot shock layer is formed due to convective heat transfer on the supersonic model resulting in transient temperature rise at the model surface. An isothermal ambience was maintained during the test time by wrapping the connecting leads of the sensor and the cold junction of the thermal sensor in the hemisphere. An op-amp instrumentation amplifier (TEXAS make, INA 128) was used to amplify the output of the CSJT. The amplifier has a gain factor of 500 with an operating bandwidth frequency in the range of 1-40 kHz, which was sufficient for the familiarizing with the shock tube environment. The experiments are conducted using both nitrogen and helium as driver gas for all the thermal sensors (E, T and J-type); the typical voltage signal and rise in temperature signals (computed using sensitivity value) obtained for all the sensors are plotted in Fig. 6.19. The coaxial thermal sensor always gives the signal in the form of voltage as it works on the principle of Seebeck effect. A typical parabolic trend has been observed from the obtained signals, which signifies the typical case of constant heat flux of the semi-infinite theory of slab heat conduction (Figs. 6.20(a-b)). The experiments are conducted for three number of runs for all the thermal sensors, in order to check the repeatability of the thermal sensor.

(a) (b)

Fig. 6.17: Typical voltage histories captured from E-type CSJT mounted on the end flange of the shock tube obtained using nitrogen and helium as driver gas

(a) (b)

Fig. 6.18: Typical voltage histories captured from E-type CSJT mounted on the end flange of the shock tube obtained using nitrogen and helium as driver gas

(a) (b)

(a) (b)

Fig. 6.20: Typical rise in transient surface temperature from CSJT mounted on the end flange of the shock tube

6.4.3.2 Heat Flux Estimation

The obtained temperature signals are then used for evaluating the respective stagnation heat flux.

Here, thermal properties of the substrate are treated as constant and the surface heat flux qS

 

t is calculated using Duhamel's superposition integral as explained in detailed in chapter 3. The surface heat flux computed by using Eq. (3.4). For the present case, the thermal product is chosen from an experiment conducted as depicted in chapter 5. The obtained heat flux for all the tests (nitrogen and helium driver) which includes CSJT mounted as flush on the end flange as well as on the hemispherical model are plotted in Figs. 6.21(a-b) and Figs. 6.22(a-b).

(a) (b)

Fig. 6.21: Surface heat flux histories from E-type CSJT mounted on the end flange of the shock tube

Considering Figs. 6.21(a-b), similar trends of surface heat flux are seen with different peak heat flux values as, 160 W/cm² and 434 W/cm², with nitrogen and helium driver gas, respectively.

This “similarity nature” in the heat flux signal can be marked as the property of the sensor since the maximum rate of temperature rise is same for both driving conditions. Further, different interactions may be responsible for the change in heat flux signal after the test time such as interaction between reflected shock and contact surface, reflected shock and expansion fan etc.

Thus, present studies are found essential in evaluating the maximum rate of temperature rise for a given thermal sensor, thus considered as the property of sensing surface. In this case, the CSJT fabricated in-house has a potential of capturing highly transient phenomena of temperature rise in a shock tube. With another viewpoint, current investigations also recommend the use of shock tube as calibrating facility of any transient thermal sensors for evaluating the maximum rate of temperature rise. From the flow as captured from the hemispherical model, it is expected to form a bow shock over the model for the free stream flow. It has been observed that E and T-type thermal sensors predict the value of heat flux in close agreement with each other (Figs. 6.22(a-b)).

Table 6.4 gives the comparative assessment of the heat flux predicted for three number of repeated shots for all the thermal sensors. However, the J-type thermal probe slightly overpredicts the values as compared with the other two types considering both the gases (Table 6.4). The thermal product value of J-type CSJT could be one such reasons for the over-prediction in heat flux value. In addition, the purity in the construction process, purity of the thermocouple material etc. may also lead to the uncertainty in the heat flux values as compared to its counterparts. In continuation, a

(a) (b)

Fig. 6.22: Heat flux signal obtained from the temperature history of CSJTs flush mounted on the

similarity in heat flux value with the steady region can be observed from the flow containing helium as the driver gas for all the thermal sensors. However, it is difficult to observe a similar phenomenon in case of nitrogen as driver gas. Besides to validate the obtained CSJTs results, an experiment has been conducted using Silver thin-film gauge (STFG), fabricated in-house. The brief details of the study is mentioned in Appendix F. The experiments using the CSJTs is justified from the heat flux value as estimated using the STFG.

Table 6.4: Comparative Chart showing the heat flux obtained using hemispherical model

Sl.

No.

Types of CSJT

Experimental Incident Shock

Mach Number

 

^M_S

Average Heat Flux



^{W cm2}



Average Heat Flux



^{W cm2}



Helium Nitrogen Helium Nitrogen STFG 1. E 3.56 2.04 465 ± 1.8% 179 ± 3.75%

449.8 2. J 3.55 2.38 582 ± 4.6% 232 ± 4.15%

3. T 3.77 2.42 445 ± 3.5% 100 ± 5%

Further, the uncertainty analysis has been performed (based on Appendix E) for the calculations of shock Mach number and subsequently its effect on reflected shock Mach number, pressure and temperature ratios across primary and reflected shocks. Similarly, uncertainties for temperature measurements and heat flux calculation are also estimated during shock tube calibration. The average values of overall uncertainties for each of the parameters are given in Table 6.5.

Table 6.5: Uncertainty values for shock tube parameters during calibration Shock tube

parameters

Average value of uncertainty

Nitrogen Helium

Ms ±0.1% ±0.11%

p2 p1 ±0.19% ±0.22%

p5 p1 ±1.6% ±9.17%

T T2 1 ±1.97% ±2.99%

T T5 1 ±2.68% ±9.23%

 

T ts ±0.16% ±0.24%

 

qS t ^{±0.55% ±0.2%}