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Plasma wind tunnels are extensively used for characterization and validation of the materials suitable for thermal protection systems (TPS) for spacecrafts. TPS are single points of failure for spacecrafts involving in atmospheric entry or re-entry which include manned, sample return and interplanetary rover landing missions. Spacecrafts encounter high thermal and high velocity ablative plasma flows due to combined effects of atmospheric drag and aerodynamic heating. It is utmost importance to test and validate the behaviour of TPS-candidate materials in the test flows which stimulate the extreme conditions expected during atmospheric entry or re-entry regime.

Plasma wind tunnel facility at Chonbuk National University’s High Enthalpy Plasma Research Center is designed and equipped for rigorous characterization and validation of TPS-candidate materials[1, 2]. This facility houses a high enthalpy supersonic arc-heated plasma wind tunnel of 0.4 MW class (hereafter PWT) capable of stimulating ablative conditions encountered during atmospheric re-entries.

One of the prerequisites for proper optimization of PWT is to understand the plasma test flow generated in the plasma wind tunnel. In other words, the high efficient validation of TPS-candidate materials by using the PWT depends on the effective characterisation of the plasma test flow. In order to operate and generate high enthalpy supersonic plasma flow in the PWT, a very high pressure is maintained in plasma generating torch and a very low pressure is maintained in test chamber. The torch acts as a high pressure reservoir while the test chamber acts as a low pressure ambience. When the generated plasma flow extrudes from plasma generating section of the torch into the test chamber through a convergent-divergent nozzle, by nature the resultant flow obtained in test chamber is supersonic underexpanded flow. Based on the structure, underexpanded flow can be categorized into i) very highly underexpanded jet ii) highly underexpanded jet and iii) moderately underexpanded jet. This depends on the overall pressure ratio (P_reservoir/P_ambient), a very high difference between reservior and ambient pressure results in a highly underexpanded flow, while low overall pressure ratios result in moderately underexpanded flows. Generally, in case of very highly and highly underexpanded jets, as the flow exits the nozzle into very low pressure ambience, expansion waves are formed and expand upto jet boundary where they get reflected towards axis of the jet in form of weak compression waves. These compression waves then merge into an oblique shock called as intercepting shock. The Mach disk, a shock normal to the jet axis is formed. The intercepting shock interacts with Mach disk and reflected into an another oblique shock. The Mach number profile of the flow across the shocks[3, 4] is shown in Fig. 1.

Fig. 1 
Schematics of Mach disk formation.

It is important to note that Mach disk is not formed in the moderately underexpanded flows which are characterized by formation of diamond shape structures. (For more clarity, refer Figs. 7, 8 and 9 in section 3.)

Even though underexpanded flows are comprehensively studies in researches related aircraft and rockets exhaust plumes and also in fields involving accidental leakage of highly pressurized gases, the studies of underexpanded flow in a plasma wind tunnel with respect to material testing are limited. The broad knowledge of underexpanded flow in the PWT is vital for better characterization of TPS-candidate material, especially the location of Mach disk. As the nature of flow changes abruptly from supersonic to subsonic across the Mach disk, the Mach disk characterization will help in determining better exposure location for material specimen in the plasma test flow. The aim of this study is to measure the position and the diameter of the Mach disk with respect to variations in η_o, where η_o is the overall pressure ratio of the convergent-divergent nozzle. In case of the PWT, η_o is the ratio of the pressure in plasma generating torch to the test chamber pressure. The another main purpose of this study is to understand the aerodynamics of high temperature plasma flow. Apart from testing the materials related to space applications, there are some fascinating future applications for plasma in field of aerospace[5-7]. The aerodynamic applications of plasma include plasma-based flow control and plasma-assisted ignition and combustion technology. Plasma has been found very useful to control boundary layer and flow separation, to initiate combustion and stabilize flame in the combustion chamber. Adamovich et al.[8] have discussed effects of plasma in shock wave propagation. The four effects discussed in their work are 1. shock acceleration, 2. nonmonotonic variation of flow parameters behind the shock front, 3. shock weakening, and 4. shock splitting and spreading. They have discussed various reasons for these effects to occur and emphasized the need for more experiments to understand the plasma shock phenomena. The experimental works of Merriman et al.[9] and Palm et al.[10] of Ohio state university have proved that shock weakening effect observed in supersonic plasma flow is mainly due to thermal effects caused by interaction between heated boundary layer and shock wave and is not solely due to plasma effects. The above mentioned research works are focused on weakly ionized non equilibrium plasma (cold plasma).

The research works related to shockwaves in underexpanded high temperature plasma flows with strong ionization are very limited. The thermal non-equilibrium characteristics of plasma also defines how plasma behave aerodynamically. But throughout literature, many researches have assumed plasma to be in locally thermodynamic equilibrium (LTE) conditions to derive thermodynamic properties of the plasma[11-13]. A similar approach has been adopted in this study to obtain thermodynamic properties of the generated plasma flow. The boundary layer formed by the plasma flow on the nozzle wall is not only an aerodynamic problem but also should treated as a surface electro-chemistry problem. The effects of Debye sheath[14] and effects of free electrons on the heat transfer across the plasma-nozzle wall boundary layer[15] are some of the characteristics which are unique only to plasma flow and have to be carefully considered while investigating the aerodynamics properties of the plasma flow. In this experimental research work, the diameter and position of Mach disk formed in high enthalpy plasma flow is measured and compared with other similar previously conducted research works. This help us to understand plasma-aerodynamics of flow generated in a high enthalpy supersonic arc-heated plasma wind tunnel.

The photographs of very highly, highly and moderately underexpanded flow obtained during the experiment are shown as Fig. 7, 8 and 9.

Fig. 7 
Case 1 data (η_o ≈ 170).

Fig. 8 
Case 2 data (η_o ≈ 30).

Fig. 9 
Case 3 data (η_o< 30).

At η_o<30, the nature of the flow develops into a moderately undexpanded flow instantly with disappearance of Mach disk and appearance of diamond shaped structures. The variation in the structure of the flow temporally is shown as Fig. 10. In Fig. 10, transition of flow from very highly underexpanded flow to moderately underexpanded flow is clearly visible.

Fig. 10 
Underexpanded flow transition.

The Mach disk position (L_M) from the nozzle exit is non-dimensionalized using nozzle exit diameter (D_e) and it’s variation with η_o is shown as Fig. 11.

Fig. 11 
Mach disk position vs η_o.

The position of the Mach disk moves away from the nozzle exit as the η_o increases. From the experimental data, following empirical correlation has been derived.

The above experimental results agrees well with the results of Crist et al.[3], who have developed a similar empirical correlation for their data as below.

Crist et al. used a hot-shot wind tunnel facility for stagnation temperature ranges from 300 K to 4200 K. Their empirical correlation is based on data obtained for their entire temperature range (300 K-4200 K), while the empirical correlation (Eq. 1) obtained in this study corresponds to the thermodynamic properties given in Table 2.

The correspondence between LMDe ratios measured from experimental data and LMDe ratios calculated from the empirical correlation (Eq. 1) shown as Fig. 11. From the Fig. 12, it is very clear that the empirical correlation obtained for LMDe is in good agreement with experimental results.

Fig. 12 
Correspondence between experimental data and empirical correlation (Eq. 1).

Relationship between the Mach disk diameter and η_o is presented as Fig. 13.

Fig. 13 
Mach disk diameter vs η_o.

Fig. 13 also trends similarly to Fig. 11, the diameter of the Mach disk (D_M) increases with η_o. The corresponding empirical correlation is derived as below.

DMDe ratios calculated from above the correlation are plotted along with DMDe ratios measured from the experiment and shown in Fig. 14. The Fig. 14 reveals that empirical correlation for DMDe imitates the experimental results with a considerable accuracy. The above results also corresponds fairly with a similar empirical correlation found in research work of Antsupov[22] for cold air jets. Antsupov’s empirical correlation for DMDe has been modified in terms of overall pressure ratio (η_o) and can be written as,

Fig. 14 
Correspondence between experimental data and empirical correlation (Eq. 3).

Based on observation and experimental results, it is evident that overall pressure ratio is one of the critical factors influencing the diameter and position of the Mach disk in the underexpanded flow. The comparison of results with the previous research work conducted in general cases reveal the Mach disk position and diameter follow a similar tread with respect to overall pressure ratio. A decrease in Mach disk position and diameter has been observed in the current results. The reasons for this observed phenomenon maybe 1) shock weakening by plasma properties. 2) Thermal effects caused by high temperature nature of flow. Although an earlier research work[10] have observed that shock weakening in plasma flow only due to thermal effect, but the flow they have considered is weakly ionized cold plasma, where as the flow generated in this study is considered to be strongly ionized because of high enthalpy and arc-generated. The strong ionization effects on the Mach disk formation has to be considered. More exclusive studies needed to be done for determining thermal and ionization effects on the Mack disk formation in high enthalpy plasma flow. This will lead to better understanding of Mach disk and underexpanded test flows for more accurate TPS material testing and evaluation which is the main purpose of this PWT. Also more experimental work has to be accomplished to determine dependency of Mach disk diameter and position on other factors like specific heats ratio, nozzle geometry, flow rate and input power of PWT.

Experiment to measure the positions and diameter of Mach disk in high enthalpy arc-heated plasma flow is described. The results also show that the nature of underexpanded flow extensively depends on the overall pressure ratio. The empirical correlations for determining Mach disk diameter and position are given as a function of overall pressure ratio which will help to determine better testing position during TPS-material evaluation experiments. Even though variation of Mach disk position and diameter trend similarly with previous studies, there is decrease in Mach disk position and diameter which may be due to thermal and strong ionization effects of the high enthalpy plasma flow.