1 Introduction

Simple shock tubes are employed as a research tool for producing shock waves since a century, followed by the invention of the first free piston driven shock tube (FPST) to generate high enthalpy shock waves [1]. From the past one decade, our Shock Induced Materials Chemistry Laboratory (SIMCL), Bengaluru, India, is involved in developing unique shock tube facilities to study the interaction of strong shock wave with different forms of materials. Shock tubes are used as ground test facilities for various applications like aerospace, chemical kinetics, materials research, etc. In recent years shock tubes are used in materials research to study homogenous (gas-gas) and heterogeneous (gas-solid) interactions in millisecond timescales. The reaction time, pressure, and temperature of the shock-heated test gases play a major role to understand the aerothermodynamic reactions occurring on the surface of reentry space vehicles. To overcome the effects of non-ideal pressure and temperature in shock tubes, additional techniques such as driver inserts, driver extensions, etc. are also used [2, 3]. Some researchers also tried to increase the shock strength by focusing the shock waves using a convergent nozzle at the diaphragm station [4] and parabolic reflectors [5, 6] and also by focusing shock waves in water [7].

In this paper we present different configurations of shock tubes to increase the test time, reflected shock pressure, and temperature to study the material interaction with the shock-heated test gases. A novel idea of focusing shock wave using a convergent nozzle at the end of the driven section of shock tube is done for the first time to increase the reflected shock temperature and pressure.

2 Experimental Setup

The simple MST consisting of 2.1 m driver and 5.1 m long driven section with 80 mm inner diameter and 115 mm outer diameter available at SIMCL is used for materials research, which is capable of handling samples in the form of thin films, pellets, and fine powders [8]. Significant modifications of MST are done in the recent years, which include increasing the length of driver section of MST to twice its length (4.4 m) by connecting a U-shaped tube of radius 11.5 mm which is named as MST-E. The driver extension technique to increase the test time is reported in the literature [9]. The shock focusing technique is implemented in MST by connecting a 0.2 m long convergent nozzle with an area ratio of 8.8 and attaching a 1.2 m long extension tube having an inner diameter similar to the nozzle exit, named as MST-R. The MST-R is capable of increasing the shock strength thereby augmenting the T 5 and P 5.

In all the three configurations, it is essential to evacuate the driver section to low vacuum (10−3 mbar) using a rotary pump and the driven section to high vacuum (2 × 10−5 mbar) using a turbomolecular pumping system before filling the respective ultrahigh pure (UHP) gases for a high-quality materials research using shock tubes. In this paper all the experiments are performed by filling helium as a driver gas and 1 bar air as a test gas. The schematic diagrams of the different shock tube configurations are shown Fig. 1. The schematic of the simple MST with a driver and driven section, MST-E, and MST-R is shown in Fig. 1a–c. Typical pressure signals recorded using PCB pressure sensors for different configurations of shock tubes are shown in Fig. 2.

Fig. 1
figure 1

Schematic diagram of the various configurations of shock tubes used for their performance evaluation: (a) Simple MST, (b) MST-E, (c) MST-R

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Fig. 2
figure 2

Typical pressure profiles of various configurations of shock tubes used for their performance evaluation: (a) simple MST, (b) MST-E, (c) MST-R

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2.1 Performance Evaluation Using Different Methods

Experiments are performed on all the three configurations of MST. The shock parameters such as shock Mach number (Ms), P 5, and test time are recorded using PCB pressure transducers. The pressure transducers mounted at the wall of shock tubes are used to acquire data by using high-frequency multichannel Tektronix digital oscilloscopes.

The KASIMIR program is used to simulate the various shock parameters and to compare it with the experimental values. The copyright of this shock tube simulation program was obtained from Stoßwellenlabor, RWTH Aachen/Shock Wave Laboratory, RWTH Aachen University, Germany. The program is based on a 1-D code which takes into account high temperature effects such as real gas effects and strong changes in the internal degrees of freedom due to chemical and thermal non-equilibrium conditions.

The time taken (Δt) for the shock to travel distance between the two pressure transducers (ΔL = 0.5 and 0.25 m) was calculated from the acquired data. Another pressure sensor at the end of the shock tube records the reflected shock pressure (P 5). The time taken by the shock wave (∆t) to cross the two given sensor locations and the distance between sensors (∆L) are used to find out the shock speed (V S) and M S. The M S is then used to calculate the reflected shock temperature (T 5) at the end flange of the shock tube using 1-D normal shock relation (NSR) [10].

3 Results and Discussions

The augmentation of test time (t IE), shock temperature, and pressure are the major goals of this work. It is evident that using MST-E and MST-R shock tubes, the t IE has extended and P 5 and T 5 have augmented to a certain extent compared to the simple MST configuration.

The shock parameters for the present study using experiments are estimated from the plot of time versus pressure history as shown in Fig. 2. It is understood from the Fig. 2 that there is a significant difference in the constant pressure region between various configurations of shock tubes. The constant pressure region is more in the MST-E (Fig. 2b) shock tube compared to other configurations. In MST-R the immediate follow-up of contact surface and an expansion fan behind the P 5 and T 5 is considerably more as shown in Fig. 2c.

Due to the area change, the P 2 should be increased to a certain extent according to the 1-D normal shock relations for a given Ms, but in the experiments the P 2 remains the same before and after the reduction of MST-R. Additionally, due to the Mach number increase in the driven section after the reduction, P 2 rise before and after the area reduction has negligible difference.

In the experiments concerned with material interaction and combustion experiments in shock tubes, the reaction usually occurs at the stagnation region of the shock tube where the shock reflection causes T 5 and P 5 to increase. So behind reflected shock waves, the shock tube test time, t, is defined as the time between the reflected shock wave from the endwall (I) to the time the next wave (compression or expansion) arrives at the endwall (E) [3]. A standard plot of x-t diagram with the thermodynamic regions for a tIE is shown in Fig. 3.

Fig. 3
figure 3

Standard x-t plot of simple shock tubes for chemical kinetic studies [3]

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Comparing the experimental results, there is a slight increase in test time of 10% in MST-E than simple MST as shown in Fig. 4. The test time obtained using KASIMIR is overpredicted, and the solution has a discrepancy of about 15–60% for MST and MST-E as shown in Fig. 4. Test time calculation using experiments and prediction using KASIMIR was tedious for MST-R as there was lot of shock-shock interaction as the shock moves forward and also during the reflections. These reflections are most prominent for MST-R configuration. Due to the contact surface interference with the incident shock wave and the interactions later with the upcoming expansion waves, the test time vary with Ms. The Ms versus t IE plot shown in Fig. 4a, b clearly indicates that the test time changes according to the Ms.

Fig. 4
figure 4

Plot of test time (t IE) versus shock Mach number (Ms) of (a) Simple MST, (b) MST-E shock tube

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In order to validate the various shock parameters of different configurations of shock tubes, various tools are described in Sect. 2.1. Figure 5 shows the comparison of P 5/P 1 and T 5/T 1 of simple MST configuration. Figure 5a shows a good agreement of P 5/P 1 between 1-D NSR and KASIMIR, but there is a discrepancy of about 3–20% (avg.) in comparison with the experimental values. The absolute shock temperature measurement techniques are not available at present, so the temperatures (T 5/T 1) are estimated only by theoretical method. The plot of Ms versus T 5/T 1 for MST shows a similar trend in comparison with 1-D NSR and KASIMIR as shown in Fig. 5b. The discrepancy of Ms estimation between experiment and KASIMIR ranges about 5–15% in average for all configurations of shock tubes.

Fig. 5
figure 5

Comparison of shock parameters between experiment and KASIMIR for simple MST: (a) Reflected shock pressure (P 5/P 1), (b) Reflected shock temperature (T 5/T 1)

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Similarly the MST-E and MST-R are also compared with various tools to validate the results. Figures 6 and 7 show the comparison of P 5/P 1 and T 5/T 1 of MST-E and MST-R, respectively. The discrepancy of P 5/P 1 and T 5/T 1 maintains its range of about 4–20% (avg.) as shown in Figs. 6a and 7a. On the other hand, T 5/T 1 has a good agreement for MST-E and MST-R as shown in Figs. 6b and 7b.

Fig. 6
figure 6

Comparison of shock parameters between experiment and KASIMIR for MST-E: (a) Reflected shock pressure (P 5/P 1), (b) Reflected shock temperature (T 5/T 1)

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Fig. 7
figure 7

Comparison of shock parameters between experiment and 1-D NSR for MST-R: (a) Reflected shock pressure (P 5/P 1), (b) Reflected shock temperature (T 5/T 1)

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To achieve an extreme value of T 5 and P 5 of about 12000 K and 60 bar, experiments in MST-R were performed at different partial pressures of Ar test gas, and the results obtained are not presented here in this paper due to space constraints. Such thermodynamic conditions are essential to study the interaction of UHTC materials with the shock-heated test gases.

4 Conclusion and Future Prospects

The experimental results show that the T 5 has been increased by approximately 15% in the MST-R setup and there is a 10% difference in t IE between the simple MST and MST-E shock tubes. In all the different shock tube configurations, discrepancy in P 5/P 1 shows a variation of about 4–30%, but the variation of T 5/T 1 shows a similar trend. All the experiments are performed with air as a test gas. The plot of Mach number versus test time shows that the test time is inversely proportional to Mach number. In the MST-E configuration, the test time has a 10% increase compared to MST. The test time measured using KASIMIR is overpredicted, and the solution has a discrepancy of about 15–60% in all configurations.

So we conclude that our high vacuum shock tube facilities of different configurations are specially fabricated and calibrated to perform shock-induced materials research. The thermal and chemical non-equilibrium conditions prevailing in our shock tubes are suitable to disassociate the gas species and to interact with high temperature ceramic materials to study the catalytic and non-catalytic surface reactions.

Some issues like exploring the tailored mode condition of the shock tubes in various configurations are in progress, and this stands one of our interests to perform experiments for a longer test time at a constant and augmented P 5 and T 5.