Experimental and machine learning-driven assessment of IS 2062 steel under double-base propellant combustion conditions

Static firing characterization of rocket propulsion system

Static firing tests of the rocket motor were imperative to validate the ballistic characteristics of the propellant and the mechanical robustness of the motor’s steel structure under extreme thermal and pressure loads. These tests recreated operational conditions to capture pressure-time histories, propellant regression rates, and the coupled thermal-mechanical response of the steel casing. The principal objectives here are to report the findings from seven static motor firings and assess their alignment with theoretical performance predictions. Furthermore, the section examines patterns in combustion behavior, including any erosive burning phenomena, and establishes a correlation between combustion-driven thermal exposure and steel degradation mechanisms, through comparative analysis of pre- and post-test specimens utilizing multiple advanced characterization methodologies.

Static ballistic test campaign results (Tests 01–07)

A sequence of seven static ballistic qualification tests (designated Tests 01 through 07) was executed, wherein each trial incorporated a systematically varied nozzle throat diameter (Dt) to induce distinct internal ballistic regimes and corresponding chamber pressure environments. For every test iteration, target chamber pressure profiles were established a priori based on ballistic simulation models and historical propellant characterization datasets. To ensure experimental reproducibility and statistical validity, dual firings were performed for each configuration (Tests 1 and 2 per condition).

The comprehensive datasets presented in Tables 4, 5, 6, 7, 8, 9 and 10 encapsulate critical performance indicators for each test scenario, including the time-averaged chamber pressure (P_avg), characteristic velocity (C*), propellant regression rate evaluated at P_avg, and the empirical determination of the pressure exponent (n), indicative of the propellant’s pressure sensitivity in the burning law correlation. Comparative analytics juxtapose the computationally predicted values derived from legacy models and propellant-specific empirical formulations against the empirically acquired metrics from the dual-shot test series, enabling the validation of design assumptions and refinement of propulsion system models.

Static Test-01 (Dt = 15.26 mm)

Static Test-01 employed the maximum nozzle throat diameter of 15.26 mm, designed to establish a nominal average chamber pressure of approximately 82 ksc. As summarized in Table 4, the two independent firings registered mean chamber pressures of ~ 76 ksc and 82 ksc, exhibiting reasonable concordance with the pre-test ballistic forecast of 86.9 ksc. The characteristic velocity (C*) conformed to theoretical expectations (~ 1450 m/s), with empirical values recorded at 1477 m/s and 1412 m/s, respectively. The propellant regression rate, measured under ~ 80 ksc operating conditions, ranged from 20.5 mm/s to 22.4 mm/s, in close agreement with the projected value of 21.8 mm/s. The calculated pressure exponent (n) for this configuration was determined to be 0.34, marginally under the predicted 0.36, suggesting a slightly reduced sensitivity of burn rate to chamber pressure relative to initial design assumptions.

As illustrated in Fig. 2(a), the chamber pressure exhibits a rapid rise immediately following ignition, reaching a peak in the range of 80–85 ksc, followed by a short stabilization phase and a gradual decay as the propellant mass is depleted. During this initial low-pressure test, the pressure-time history displayed minor oscillatory behavior within the pressurization and quasi-steady phases. The subsequent firing, depicted in Fig. 2(b), demonstrated a comparable pressure evolution profile, with a marginally elevated plateau pressure consistent with the higher average chamber pressure attained in Test-2. Both firings confirmed nominal combustion behavior, characterized by stable burning without evidence of flameout or early termination. The total burn duration was consistent with design expectations, occurring over several hundred milliseconds, in accordance with the specified grain geometry and the experimentally determined burn rates.

Static Test-02 (Dt = 13.26 mm)

In Static Test-02, the nozzle throat diameter was decreased to 13.26 mm, targeting an anticipated average chamber pressure of approximately 134 ksc. The dual firings produced mean pressures of 120 ksc and 136 ksc, effectively straddling the predicted value of 134.5 ksc and indicative of typical experimental variability. The characteristic velocities (C*) measured at 1336 m/s and 1430 m/s were within reasonable proximity to the predicted 1452 m/s. Propellant regression rates at the ~ 130 ksc operating regime were measured at 26.2 mm/s and 27.7 mm/s, closely aligning with the forecasted 25.5 mm/s. The pressure exponent (n) was derived as 0.33 for the first shot and 0.36 for the second, with the latter matching the theoretical prediction of 0.36. These results demonstrate overall concordance with the modeled ballistic behavior, with the second test exhibiting near-exact agreement with both the expected burn rate and pressure sensitivity, as detailed in Table 5.

Figures 3(a) and 3(b) present the chamber pressure profiles recorded during the two firings of Static Test-02. The reduction in throat diameter resulted in elevated chamber pressures within the ~ 120–136 ksc range, accompanied by marginally reduced burn duration relative to Static Test-01, attributable to the pressure-accelerated burn rate. The pressure-time trajectories exhibit a steeper pressurization slope when compared to Test-01, reflecting the increased mass flow constraint. Notably, the second firing’s trace closely achieved the predicted pressure regime, sustaining a relatively flat plateau at approximately 130 + ksc before transitioning into the tail-off phase. Conversely, the first firing’s profile displayed a slightly lower peak pressure and a more distinct initial transient characterized by an ignition-induced pressure overshoot prior to stabilization. Both firings demonstrated complete and stable combustion without anomalies, confirming the structural adequacy of the motor hardware and grain design under elevated pressure loading.

Static Test-03 (Dt = 12.20 mm)

For Static Test-03, the nozzle throat was further constricted to 12.20 mm, targeting an average chamber pressure of approximately 174 ksc. The measured average pressures were 163 ksc and 155 ksc, both marginally under the ballistic prediction of 174.5 ksc. The characteristic velocity (C*) stabilized within the range of 1425–1426 m/s, in proximity to the anticipated 1452 m/s. Corresponding burn rates at ~ 160 ksc were recorded at 28.0 mm/s and 25.98 mm/s, aligning closely with the theoretical value of 28.04 mm/s. The pressure exponent (n) derived from the two firings was 0.36 and 0.33, respectively, remaining consistent with the predicted 0.36. These results indicate that the propellant’s ballistic behavior largely adhered to the expected trend, though the second firing exhibited a slight deviation in both pressure and burn rate, as detailed in Table 6.

The pressure-time profiles for Static Test-03, shown in Figs. 4(a) and 4(b), demonstrate the continuation of the trend toward elevated chamber pressures and reduced burn durations as throat diameter decreases. Both firings exhibited rapid pressurization, reaching approximately 160 + ksc before stabilizing. Notably, the plateau regions in both traces lie slightly below the predicted pressure threshold, indicating a modest underperformance relative to the expected pressure levels. The pressure decay phase shows a mildly regressive burn behavior, characterized by a gradual decline as the propellant is depleted. The combustion process remained stable throughout, with no evidence of anomalous pressure oscillations. Additionally, the ignition transients appeared more subdued and temporally compressed, consistent with the accelerated pressurization dynamics associated with the higher chamber pressure regime.

Static Test-04 (Dt = 11.33 mm)

Static Test-04, conducted with a reduced throat diameter of 11.33 mm, was designed to achieve an average chamber pressure of approximately 220 ksc. The recorded average pressures were 210 ksc and 203 ksc, exhibiting close correlation with the predicted 219.9 ksc. The characteristic velocity (C*) values of 1467 m/s and 1420 m/s bracketed the forecasted 1452 m/s. At operating pressures of ~ 205–210 ksc, the propellant burn rates were measured at 30.4 mm/s and 29.7 mm/s, aligning closely with the theoretical estimate of 30.47 mm/s. The pressure exponent (n) values were calculated as 0.36 and 0.34, consistent with the anticipated 0.36 within the margin of experimental uncertainty. These results confirm strong conformity to ballistic predictions within this mid-to-high pressure regime, as summarized in Table 7.

The pressure-time traces for Static Test-04, presented in Figs. 5(a) and 5(b), further emphasize the trend of stable and controlled combustion at elevated chamber pressures. Both firings exhibit a sharp pressure rise, followed by a well-defined and sustained plateau in the 200 + ksc range. The plateau phase is notably flat and uniform, suggesting consistent propellant regression and efficient chamber pressurization during steady-state burning. Any ignition-induced pressure overshoot is minimal, with the system rapidly stabilizing near the target pressure before entering a sharp tail-off phase as propellant depletion occurs. The close agreement in peak pressures between the two tests (210 ksc vs. 203 ksc) is clearly reflected in the near-identical shape and slope of their respective pressure-time signatures, underscoring excellent shot-to-shot repeatability under high-pressure conditions.

Static Test-05 (Dt = 10.74 mm)

Static Test-05, utilizing a nozzle throat diameter of 10.74 mm, was designed for an average chamber pressure target of approximately 259 ksc. The actual measured pressures were 243 ksc and 246 ksc, representing a minor deviation of about 5–6% below the predicted 259.4 ksc. The characteristic velocity (C*) remained within the 1420–1431 m/s range, in reasonable proximity to the theoretical value of 1452 m/s. The propellant burn rates at ~ 245 ksc were recorded at approximately 31.3 mm/s and 32.1 mm/s, closely matching the predicted 32.36 mm/s. The pressure exponent (n) for the two firings was determined to be 0.34 and 0.36, the latter aligning precisely with expectations. Overall, the results confirm that propellant performance remains consistent with ballistic projections, with a slight underperformance in chamber pressure likely attributable to the marginally lower n value observed in one of the tests, as detailed in Table 8.

Figures 6(a) and 6(b) depict the pressure-time profiles for Static Test-05, illustrating the motor’s performance under elevated chamber pressures approaching ~ 250 ksc. The pressure traces exhibit an almost instantaneous rise to the high-pressure plateau with minimal ignition delay, characteristic of rapid pressurization at this throat configuration. The plateau region, spanning approximately 240–250 ksc, is maintained briefly before a sharp pressure decay as propellant depletion occurs. Variations between the two firings are minimal, though a marginally higher initial peak is observable in the early milliseconds of the Test-2 firing (246 ksc vs. 243 ksc). The overall response indicates highly efficient and stable combustion, with negligible pressure oscillations, thereby validating the motor’s capability to sustain reliable performance near the upper bounds of its design pressure envelope.

Static Test-06 (Dt = 10.16 mm)

Static Test-06, configured with a 10.16 mm throat, was designed to achieve an average chamber pressure of approximately 309 ksc. The test outcomes revealed chamber pressures of 321 ksc and 305 ksc, closely aligning with predictions, with one firing marginally exceeding the target. The measured characteristic velocities were 1463 m/s and 1423 m/s, in proximity to the anticipated 1452 m/s. At ~ 313 ksc, propellant burn rates were observed at 37.2 mm/s and 35.8 mm/s, slightly above the predicted 34.45 mm/s. Importantly, the derived pressure exponent (n) for both runs was 0.38, exceeding the expected 0.36, suggesting the onset of a steeper burn rate-pressure dependency at elevated pressures. Despite this trend, both average pressures and burn rates remain within acceptable bounds of the design envelope, exhibiting only a slight upward deviation, as summarized in Table 9.

The pressure-time curves for Static Test-06, shown in Figs. 7(a) and 7(b), exhibit a markedly sharper initial pressurization, with one firing surpassing 320 ksc during the early transient. At this elevated pressure regime, the plateau duration is significantly abbreviated due to the rapid consumption of the propellant at ~ 300 + ksc, resulting in a compressed peak and tail-off sequence. The pressure traces remain smooth and free of instability, signifying stable combustion throughout. The elevated pressure exponent (n ≈ 0.38) correlates with a steeper burn rate-pressure response, as evidenced by the more abrupt pressure rise and higher peak relative to baseline predictions. Despite the observed intensification in burn rate sensitivity, the motor exhibited no structural compromise, demonstrating the system’s capacity to operate reliably under these high-pressure, fast-burning conditions.

Static Test-07 (Dt = 9.82 mm)

Static Test-07, conducted with the smallest nozzle throat of 9.82 mm, targeted an expected average chamber pressure of approximately 344 ksc. However, both firings surpassed this prediction, registering average pressures of ~ 355 ksc and 372 ksc, indicative of more aggressive propellant combustion behavior under this extreme condition. The characteristic velocities measured were 1412 m/s and 1440 m/s, slightly trailing the predicted 1452 m/s, potentially attributable to enhanced thermal losses or two-phase flow effects at elevated pressures. The propellant burn rate at an average pressure of ~ 364 ksc surged to 40.95–41.05 mm/s, significantly exceeding the extrapolated ballistic forecast of 35.8 mm/s. In parallel, the pressure exponent (n) escalated to ~ 0.42 for both tests, marking a substantial deviation from the nominal 0.36 baseline. This sharp increase in n underscores a heightened pressure sensitivity of the propellant burn rate in this ultra-high-pressure regime, as detailed in Table 10.

Figures 8(a) and 8(b) present the pressure-time responses for Static Test-07, characterized by an immediate and steep rise in chamber pressure, peaking well above 350 ksc. The ignition transient in this test registers the highest initial spike across all firings, surpassing the plateau pressure itself. Following this sharp pressurization, the chamber pressure briefly stabilizes in the 360–370 ksc range before undergoing a rapid decay as the propellant is consumed within an extremely short timeframe. The burn duration is notably compressed, driven by the exceptionally high burn rate at this pressure regime. Both pressure traces exhibit smooth, consistent profiles with minimal divergence, aside from the second firing displaying a marginally elevated plateau. The absence of pressure oscillations or instability, even under these extreme conditions, strongly indicates robust combustion stability. Nevertheless, the higher-than-predicted pressures and accelerated burn rates observed in Test-07 are indicative of erosive burning phenomena, as corroborated by the elevated pressure exponent (n ≈ 0.42) and the amplified head-end pressures relative to nominal projections.

The key findings are consolidated in, Table 11 from the seven ballistic static firing tests conducted to evaluate the performance of IS 2062 structural steel under high-temperature double-base propellant combustion. The table outlines the progressive variation in chamber pressure and burn rate as a function of decreasing nozzle throat diameter, revealing a clear trend of increasing thermal-mechanical load on the steel specimens. Starting from Test-01, which demonstrated stable combustion at 255 ksc with negligible surface erosion, a steady rise in chamber pressure is observed across subsequent tests. Notably, Test-06 achieved the most desirable balance with a chamber pressure of 313 ksc and burn rate of 36.9 mm/s, producing minimal surface degradation while maintaining combustion stability. This test is identified as the optimal configuration for maximizing performance without compromising material integrity.The evaluation of performance for each test configuration included combustion stability, pressure-burn rate agreement, and extent of observed surface degradation. Tests with excessive erosion or unstable pressure profiles were categorized as non-optimal.

In contrast, Test-07, with the smallest nozzle throat diameter (7.5 mm), exhibited excessively high chamber pressure (372 ksc) and rapid burn rate (41.2 mm/s), resulting in unstable combustion and severe erosion of the steel surface. The surface observations, including oxidation, pitting, and structural spalling, validate the threshold beyond which the material fails under thermal stress. This comparative summary not only emphasizes the sensitivity of steel degradation to combustion dynamics but also validates the utility of integrated test planning in identifying optimal propulsion configurations. The inclusion of combustion stability, surface condition, and microstructural observations within the table allows for a holistic understanding of steel behavior under transient high-temperature rocket motor conditions.

Graphical analysis and interpretation

The series of pressure-time profiles obtained from Static Test-01 through Static Test-07 Figs. 2, 3, 4, 5, 6, 7 and 8 collectively illustrate distinct trends in the combustion dynamics of the rocket motor across varying chamber pressure regimes. Each plot depicts chamber pressure (ordinate) as a function of time (abscissa), annotated with the corresponding test designation and nozzle throat diameter. Consistently across all tests, the traces exhibit the characteristic ballistic profile an initial rapid pressurization phase culminating in either a sharp peak or a well-defined plateau, followed by a decay phase corresponding to propellant depletion. The morphology of these curves is strongly influenced by internal ballistic phenomena, including nozzle throat area effects, propellant regression kinetics, and pressure-dependent burning behavior. Notable variations in the curve shapes, such as plateau duration, peak overshoots, and slopes of the pressurization ramp, correlate with throat diameter reductions and the associated increase in chamber pressure. The onset of higher-pressure exponents (n) at elevated pressures, as well as erosive burning tendencies in the latter tests, are reflected in the increasingly steep rise rates and shortened burn durations observed. These graphical trends provide valuable insight into the interplay between combustion chamber geometry, propellant behavior, and internal flow dynamics.

• Rise to Peak Pressure: In all tests, ignition is followed by a steep rise in pressure. For the lower-pressure cases (Tests 01–03), this rise is slightly slower and sometimes shows small oscillations or overshoot as the flame establishes itself. In consideration, Static Test-01 the pressure trace has a modest overshoot before settling around 80 ksc, indicating a brief ignition transient where the burn rate spiked then normalized. As the throat gets smaller (Tests 04–07), the pressurization becomes more rapid and overshoot is reduced relative to the ultimate plateau – the system “locks in” to a stable high pressure almost immediately. By Test-07, the pressure rise is almost vertical on the graph, reaching > 350 ksc in a few milliseconds with minimal wavering.

• Plateau (Steady Burn Phase): Once peak pressure is reached, many tests exhibit a plateau region where pressure stays roughly constant for a short duration. This plateau corresponds to the period of balanced grain regression and gas expansionessentially, the propellant burning surface area and gas exhaust through the nozzle are in equilibrium. In the mid-range tests (around Test-04 and 05), this plateau is very flat and steady, indicating a very neutral burn (propellant grain design likely aimed for neutral behaviour). At lower pressures (Test-01/02), the plateau is not as flat and may slope downward immediately, which suggests a slightly regressive behaviour or the propellant initially burning a bit slower until the chamber pressure builds fully. At the highest pressure (Test-07), the “plateau” is extremely short – the burn rate is so high that the propellant mass is depleted almost as soon as peak pressure is achieved, so the pressure starts dropping off sooner.

• Pressure Drop and Tail-off: In all cases, after the main burn the chamber pressure falls rapidly as the fuel is exhausted. The tail of each curve tends to drop sharply, showing that once significant propellant surface area is consumed, pressure cannot be sustained. One noteworthy aspect is the smoothness of the decline in the high-pressure tests. For Tests 06–07, the pressure drop is nearly a clean exponential-like decay with no bumps, implying very stable end-of-burn behavior (no secondary ignitions or chuffing). In contrast, the lower-pressure tests had a longer tail (since the burn lasted longer) and potentially small bumps, possibly due to after-burning of remaining gases or slight unsteady flame extinction.

• Burn Duration: The graphs clearly show that burn duration decreased as the throat diameter decreased (as in case the pressure increased). Static Test-01’s pressure trace lasts on the order of 0.4–0.5 s, whereas Static Test-07’s trace is essentially over by ~ 0.25 s. This is expected from the increase in burn rate with pressure – the propellant burns roughly twice as fast at 350 + ksc as it does at ~ 80 ksc, so the total burn time is roughly halved. All curves end near zero pressure at roughly the times predicted by integrating the burn rate, confirming that the entire propellant grain was consumed in each test.

• Stability and Oscillations: A critical observation from the graphs is the trend in pressure stability. The early, lower-pressure tests showed minor pressure oscillations or irregularities during ignition and early burn (for instance, slight dips or spikes around the time of peak pressure in Test-01 and 02). These could be due to flame spreading dynamics or pressure wave reflections in the chamber when the pressure is lower (less damping). However, as chamber pressure increased (Tests 03 and above), the pressure-time curves became progressively smoother. By ~ 200 ksc (Test-04) and above, the curves are almost perfectly smooth with no visible oscillations. This indicates improved combustion stability at higher pressure, likely because the combustion regime is more robust (higher pressure generally suppresses combustion instabilities and the higher mass flow damps pressure waves). The well-annotated graphs for each test highlight this difference, with annotations pointing out any small oscillation in Test-01 vs. the smooth plateau in Test-05+, etc. No high-frequency oscillatory combustion (a dangerous instability) was observed in any test, which is an important positive outcome.

• Key Trends and Anomalies: The most significant trend, visible across the sequence of pressure vs. time graphs, is the increase in peak pressure and the steepness of the curve as throat diameter decreases. There is also a subtle trend in the shape: lower-pressure tests have a more gradually sloping plateau (slight regression), whereas high-pressure tests have a flatter or even slightly progressive plateau early on (due to erosive burning causing a higher initial burn rate). An anomaly to note is in Static Test-07’s graph: the peak pressure overshoots the expected value considerably (reaching ~ 420 ksc transiently, whereas ~ 344 ksc was the design target). This overshoot and the higher sustained pressure in Test-07’s graph is annotated as evidence of erosive burning – the high gas flow in the narrow port enhanced the burn rate beyond the base prediction. Another observable anomaly is that the measured characteristic velocity (C*) in some high-pressure cases (e.g., Test-07) was slightly lower than predicted, which might be inferred from the graph as a marginally lower area under the pressure curve than expected. This could be due to increased heat losses or incomplete combustion at the extreme pressure, but the effect is small. Overall, the graphical results did not show any alarming anomalies like abrupt extinguishments or pressure spikes beyond expectation – the motor performance was consistent, and trends were logical.

In addition to the pressure-time graphs for each individual test, a composite graphical analysis was performed to correlate burn rate vs. pressure across all tests. Figure 9 presents a log-log plot of average burn rate (ṙ) against average chamber pressure (P_c) for the propellant, compiled from the static ballistic test data.

Each data point on this graph corresponds to one static firing’s outcome (P_avg on the x-axis and the burn rate on the y-axis), and the slope of the trend line represents the pressure exponent n. The graph is annotated to show two distinct regimes: from about 70 ksc to ~ 320 ksc, the points lie roughly on a line with slope ~ 0.36, whereas above ~ 320 ksc, the last few points (from Tests 06–07) deviate to a steeper slope near 0.40–0.42. This break in slope is subtle but significant. It confirms that up to a certain pressure, the propellant’s burning follows the original burn rate law (n ≈ 0.36) closely, but beyond that threshold, combustion accelerates more than expected with pressure (n increases to ~ 0.40). The log-log burn rate vs. pressure plot thus visually captures the erosive burning effect: at very high pressures (and high gas flow velocities), the burning rate is enhanced (the data points for Test-07 sit above the extrapolated line of lower-pressure data). The plotted data from the static tests align well with the propellant’s reported baseline burn rate (e.g., ~ 20 mm/s at ~ 70 ksc) and clearly illustrates the upward deviation for the highest pressure points. Such graphical interpretation is crucial for adjusting the ballistic model – the annotated break-point on the graph suggests that different n values should be used in different pressure regimes for more accurate predictions.

By examining the results of all seven static tests, several important trends and insights can be discerned regarding the propellant’s behaviour and the motor’s performance starting from,

1. 1.

   Burn Rate and Pressure Exponent Trends, The static tests confirmed that the propellant’s burn rate increases with chamber pressure following a power-law trend ṙ = a·P^n. For the majority of the range approximately 70–300 ksc, the pressure exponent n was around 0.34–0.36, in good agreement with the design value of 0.36. However, at the extreme upper end of the pressure range above ~ 320 ksc, the effective n increased to ~ 0.40–0.42. This indicates a transition to erosive burning conditions: the high gas flow velocity in the narrow port increases the propellant’s burning rate beyond the base level^14,15. In essence, the propellant shows a stable burn rate index up to a threshold, beyond which the flame propagation and combustion kinetics are enhanced likely due to increased convective heat feedback to the burning surface. This two-regime behaviour was a key finding – it means the propellant combustion is more pressure-sensitive at very high pressures. The implication for theoretical modeling is that a single pressure exponent may not suffice across the entire range; a piecewise model n ≈ 0.36 for moderate pressures, rising to ~ 0.40 at the extreme end would yield more accurate performance predictions¹⁶.

2. 2.

   Comparison with Predictions: Overall, the observed static test results closely matched the theoretical predictions in terms of average pressure, burn rates, and C* values for each throat diameter. Minor deviations were observed – for instance, Static Test-01 produced a slightly lower pressure than predicted, whereas Static Test-07 produced higher. These differences can be traced to the aforementioned shift in burn rate behaviour: the original prediction assumed n = 0.36 throughout, hence itsover-predicted pressure for the largest throat where actual n was ~ 0.34 and under-predicted for the smallest throat where actual n ~ 0.42. Once the burn rate law was adjusted using the measured data, the revised predictions of chamber pressure aligned very closely with the test results. The characteristic velocity C* remained very close to the expected ~ 1450 m/s in all cases within a few percent, indicating that the combustion efficiency was as expected, and that the propellant’s energy release was consistent. The small drop in C* at the highest pressures might suggest increased losses thermal or due to heterogeneous combustion products but is not dramatic. The consistency of C* also implies that the propellant formulation behaved reliably and there were no issues like significant slag accumulation or unburnt residues affecting the gas expansion^17,18.

3. 3.

   Erosive Burning and Flow Dynamics:The fact that the head-end (HE) pressure was observed to be higher than the nozzle-end (NE) pressure in the motor during high-pressure tests as noted in test logs is a clear sign of erosive burning. In a purely equilibrium situation, pressure would be uniform in a small chamber; here, a pressure gradient along the grain higher at the head where gases first form indicates that the burning rate at the head-end was enhanced by the fast-moving flow of combustion gases this is consistent with classical erosive burning phenomena. The high flow velocity through the grain’s port effectively augmented convective heat transfer to the upstream propellant surfaces, causing them to burn faster¹⁹. This led to a self-feeding cycle: faster burn -> more gas -> sustained higher pressure at head-end. The static tests empirically captured this: Test-07, with the most extreme flow, showed the largest discrepancy in burn rate (and n). This erosive effect is important when extrapolating motor performance – it can give extra thrust or pressure early in the burn as seen by the pressure “blip” or overshoot in the highest-pressure test curves, but also means higher thermal and mechanical stress on the motor’s materials at the head-end^20,21.

4. 4.

   Structural Performance and Steel Degradation: All seven static tests were conducted using an IS 2062 structural steel motor chamber (with alloy steel throat inserts) subjected to flame temperatures ~ 2580 K and pressures up to ~ 370 ksc. Impressively, the steel motor hardware survived all tests without structural failure, owing to the fact to a design safety factor of 3 on yield strength. However, the extreme conditions inevitably caused some surface degradation of the steel. Post-test inspections with in detail characterization indicate and showed signs of oxidation and thermal erosion on the steel surfaces directly exposed to the combustion gases. This is consistent with high-temperature combustion gases as it can oxidize and ablate steel surfaces as propellant flames cause severe steel erosion whereas double-base propellants cause moderate mass loss, this in correlation with RDX rich propellant²². In our tests, the double-base propellant’s combustion products likely caused the formation of iron oxide scales on the IS 2062 steel interior. At the highest pressures, nitride formation may also occur due to the nitrogen in double-base exhaust^23,24. The presence of erosive flow can strip away protective oxide layers as they form, exacerbating material loss^25,26. Although each test was of short duration ~ 0.2–0.5 s burn), the peak temperature (> 2500 K) and high convective flux caused measurable changes such as discoloration, scaling, and slight roughening of the steel surfaces especially near the throat region where thermal flux is highest²⁷.

5. 5.

   Thermodynamic and Material Considerations: The agreement of test results with theory also validates the thermodynamic assumptions made e.g., propellant flame temperature and gas properties. The fact that C* stayed ~ 1400–1450 m/s suggests the propellant delivered near-ideal performance in terms of combustion efficiency. At very high pressures, the slight drop in C* could hint at more energy being lost to heating the chamber and nozzle since thermal conduction rises with pressure and gas density²⁸. This means the steel chamber had to absorb large heat fluxes, causingrapid heating. IS 2062’s bulk temperature during the burn likely rose significantly though the short burn time limited penetration depth of heat. Still, the surface could easily reach several hundred degrees Celsius. The steel’s yield strength would drop at these temperatures, but the safety factor ensured no yielding occurred^29,30. However, if the burn time were longer, more severe heating and possibly plastic deformation is expected. The static tests thus also served to prove the thermal resilience of the structure for short-duration burns. In the context of material behavior, these tests underline that high-temperature exposure even for fractions of a second can alter material surfaces, and repeated exposures accumulate damage through oxidation, phase changes, etc. This is directly relevant to the broader aim of investigating steel degradation under propellant combustion, as it provides realistic data on how quickly and in what manner structural steel degrades when subjected to actual rocket motor conditions³¹.

Comparative analysis of AIML methods for test selection

With limitations to only two static firing tests, the study leveraged AI/ML techniques to extract crucial insights from combustion performance data, helping to determine the most effective test conditions. AIML models, Linear Regression³², Random Forest Regression³³, Support Vector Machines (SVM)³⁴, K-Means Clustering³⁵, and Artificial Neural Networks (ANN) were employed to extract combustion performance insights and rank the tests based on measurable trends such as pressure, burn rate, and erosion indicators. These models helped confirm the optimality of Test-06 from various analytical standpoints. These techniques provided a robust comparison of test performances. By considering key factors such as chamber pressure, burn rate, and thermal erosion effects, AI-driven predictions not only optimized test selection but also reinforced experimental findings, ensuring the best test was chosen while maintaining optimal structural and combustion conditions, as indicated.

• Linear Regression: This model captured the fundamental linear trends between key parameters, most notably the relationship between chamber pressure and burn rate, as indicated in Fig. 10.

Linear regression revealed a consistent proportional increase in burn rate with chamber pressure, flagging Test-07 as a deviation from trend and confirming Test-06’s strong linearity with performance expectations. This strong linear trend helped flag any tests that deviated from expected behaviour. In particular, it predicted how burn rate should increase with pressure across the tests; any test with an actual burn rate far off the linear trend would stand out. Thus, Linear Regression provided a reference against which to judge each test’s performance and stability³⁶.

• Random Forest Regression:Random Forest identified chamber pressure and burn rate as the most influential parameters affecting combustion stability. The feature importance plot as indicated in Fig. 11 supported the experimental selection of Test-06, while showing Test-07 exhibited metrics beyond ideal stability conditions.

Although the limited number of tests made overfitting a concern reflected in a relatively high prediction error and a low or even negative R² in this small dataset, the Random Forest yielded valuable insights into which factors most strongly influence performance³⁷. The model’s feature importance analysis indicated that chamber pressure and burn rate were the dominant predictors of a test’s outcome e.g., throat diameter or performance category, while other parameters like characteristic velocity (C*) and pressure exponent (n) were of secondary influence. This suggests that controlling chamber pressure through throat size or propellant geometry is critical for performance. In terms of selecting the best test, the Random Forest’s ability to model complex patterns helped confirm that there were no hidden non-linear effects causing an unexpected test to be superior the best test would be one excelling in the primary metrics high pressure and burn rate without aberrant side-effects³⁸.

• Support Vector Machine (SVM) Regression: The SVM model (specifically SVR) was used to find an optimal fit with a different approach, effectively trying to model the relationship between inputs and outputs while emphasizing boundary conditions as indicated in Fig. 12.

SVM identified Test-07 as an outlier in the performance envelope due to its significantly higher pressure and burn rate, affirming that Test-06 lay closer to the stable, optimal boundary. In this analysis, SVM did not outperform Linear Regression in terms of overall fit (its predictions had higher error), indicating that the relationship between variables was not complex enough to require the SVM’s piecewise approach. However, SVM was insightful in highlighting the “boundary” cases for example, the highest-pressure tests³⁹. It effectively underscored that Static Test-07 was at the extreme boundary of the data distribution very high pressure and burn rate, whereas Static Test-06 lay closer to the mainstream trend. This distinction supported the selection of Test-06 as a safer optimal point, as SVM showed Test-07 as a potential outlier in the performance space.

• K-Means Clustering: This unsupervised learning method grouped the seven tests into clusters based on similarity in performance metrics (primarily chamber pressure and burn rate), as indicated in Fig. 13.

K-Means clustered Test-06 and Test-07 as part of the high-performance group, but further analysis showed Test-06 was centrally located within this group, indicating optimized performance without instability, unlike Test-07 which lay at the extremity. This clustering provided a clear visualization of how each static test related to the others⁴⁰. Static Test-06 and Test-07 clustered together in the high-performance group (characterized by high chamber pressures ~ 300 + ksc and high burn rates ~ 35–40 + mm/s), whereas tests with lower pressures (Test-01 and Test-02) fell into a distinct low-performance cluster, and the mid-range tests (Test-03, 04, 05) formed a middle cluster. The clustering result was especially helpful in highlighting that Test-06 belonged to the high-performance regime without being an outlier it sat near the centre of the high-performance cluster whereas Test-07, although in the same cluster, was near the edge of the performance envelope. In essence, K-Means categorized Static Test-06 as representative of an optimal high-performance category, while isolating Test-07’s more extreme behaviour⁴¹.

• Artificial Neural Network (ANN): A feed-forward neural network was trained on the dataset to capture any complex, non-linear dependencies among multiple parameters simultaneously as indicated in Fig. 14.

ANN models, though less accurate in this small dataset, confirmed that no hidden nonlinear interactions improved performance in mid-range tests. The model’s failure to outperform simpler methods validated that the combustion metrics behaved in largely linear fashion⁴². In other words, if some subtle interaction e.g. between throat size, burn rate, and pressure exponent had made a mid-range test unexpectedly superior, an ANN might have picked up on it. Instead, the ANN’s failure reinforced the conclusion that the best test would be one excelling in the straightforward metrics high pressure and burn rate without requiring complex parameter interplay^43,44,45. Thus, the ANN analysis supported the choice of Static Test-06 by confirming that no other test had a secretly superior combination of features.

In summary, each AIML method reinforced the selection of the optimal static firing test from a different angle. Linear Regression established the expected trend and identified deviations, Random Forest emphasized the key drivers of performance, SVM highlighted extreme boundary cases, K-Means clustered performance regimes placing Static Test-06 in the ideal regime, and ANN confirmed the absence of any hidden superior outlier. Together, these methods converged on Static Test-06 as the best overall performer.

Static test performance and AIML predictions for Best-Test identification

All seven static firing tests (Static Test-01 through Static Test-07) were analyzed against the AIML model predictions to pinpoint the best candidate for further study. Tables 4, 5, 6, 7, 8, 9 and 10 documented each test’s measured outcomes alongside model predictions, and the AI/ML algorithms processed these results to rank test performance. A clear pattern emerged: as the nozzle throat diameter decreased across the tests, chamber pressure and burn rate increased, pushing the motor into more extreme operating conditions. The AIML models tracked this progression and helped determine which test struck the best balance of high performance and stability. Across all ML models, Static Test-06 consistently ranked as the most efficient and stable configuration, providing near-maximum performance without significant instability or material degradation. In contrast, Test-07, while showing peak performance, was flagged as a potential outlier in multiple models due to abrupt increases in burn rate and pressure exponent, indicating risks of erosive burning. Also, from Fig. 15, which presents, a scatter plot of chamber pressure vs. burn rate, confirming the expected increasing trend taking in consideration of low pressure, mid range and high range tests.

Low-Pressure tests (Static Test-01 and 02)

These early tests, with the largest throats (e.g. 15.26 mm for Test-01), achieved the lowest pressures (~ 80–130 ksc) and correspondingly lower burn rates (~ 20–27 mm/s). The Linear Regression model adequately predicted their performance, and K-Means clustering grouped them into a low-performance cluster⁴⁶. All models agreed that while these tests were stable (pressure exponent n ≈ 0.33–0.36, close to design), their performance was intentionally limited and not optimal for pushing the motor’s capabilities. The AI analysis treated them as baseline cases useful for model training and validation but not contenders for “best” test due to their lower thrust output⁴⁷.

Mid-Range Tests (Static Test-03, 04, 05): In the mid-range throat sizes (~ 12.2–11.0 mm), the average chamber pressures rose to ~ 155–210 ksc and burn rates to ~ 26–30 mm/s, moving closer to the desired high-performance regime. These tests still closely followed the linear trends predicted by the models; for instance, the measured burn rates matched linear regression predictions within a few percent, and the pressure exponents remained around n ≈ 0.33–0.36, indicating consistent combustion behaviour. The Random Forest model, although not very accurate in absolute prediction, identified that no unusual interactions were present – the performance increase from Test-03 to Test-05 was as expected from simply raising the pressure. K-Means clustering placed these tests in an intermediate cluster between the extremes. In terms of AIML analysis, the mid-range tests confirmed the trends: each incremental decrease in throat diameter yielded higher pressure and burn rate, with no anomalies. However, none of these mid-range tests reached the combination of maximum stable pressure and burn rate that would identify the single best test; they were stepping stones toward that goal.

High-Pressure tests (Static Test-06 and 07)

The final two tests in the series had the smallest throats and thus targeted the highest pressures. According to predictions, this high-pressure regime is where the optimal test would lie but also where deviation from predictions could occur due to extreme conditions (e.g. erosive burning, material limits). Static Test-06, with a 10.16 mm throat, was predicted to reach ~ 309 ksc. In practice it achieved ~ 313 ksc (averaging 321 and 305 ksc in two firings) with burn rates around 36–37 mm/s, very close to the linear regression’s extrapolated expectation. The slight overshoot in pressure and burn rate (and a marginally higher pressure exponent n = 0.38 vs. the nominal 0.36) indicated a robust performance without dramatically breaking the trend – exactly what the AIML models flagged as an optimal outcome. Both firings of Test-06 were consistent with each other and with predictions, reflecting stable combustionbehavior. The SVM and clustering analyses placed Test-06 solidly within the high-performance group but not at an extreme boundary, reinforcing it as a balanced choice.

In contrast, Static Test-07 (9.82 mm throat) pushed the motor to the very limit, with pressures measured at ~ 355 and 372 ksc (well above the ~ 344 ksc prediction) and an extremely high burn rate (~ 41 mm/s at ~ 364 ksc). While this was the absolute performance peak (highest thrust output), all prediction indicators suggested it came with trade-offs. The linear regression trend was exceeded significantly – Test-07’s burn rate was much higher than the model’s extrapolation (by ~ 15%), making it a clear outlier. The pressure exponent jumped to n ≈ 0.42, a notable deviation that implied erosive burning or a fundamentally accelerated combustion regime at these pressures. Such a steep exponent means the burn rate became far more sensitive to pressure, a warning sign for stability and material stress. Indeed, the Random Forest model would regard this data point as having unusual characteristics since pressure was high but C* efficiency slightly dropped and variance between firings increased. K-Means still grouped Test-07 with Test-06 in the high-performance cluster, but within that cluster Test-07 was at the extreme end. In practical terms, the prediction analysis highlighted that Static Test-07, despite its record-high output, showed symptoms of being beyond the optimal operating window for example, larger pressure fluctuations and potential onset of motor material degradation as evidenced by signs of throat erosion or thermal damage⁴⁸.

By processing all tests through these algorithms, the consensus emerged that Static Test-06 was the best candidate for further characterization. It achieved near-maximal performance (second-highest pressure and burn rate) while maintaining stability and predictable behaviour. The slight increase in burn rate and pressure in Test-06 was manageable and consistent, indicating the motor was operating efficiently but not over-stressed. In contrast, Test-07’s data, as interpreted by the ML models, served as a cautionary tale of diminishing returns: pushing for the last few percent of performance led to disproportionate increases in combustion aggressiveness and possible reliability issues. The AI/ML-driven examination of trends, outliers, and clusters therefore decisively pointed to Static Test-06 as the optimal static firing test balancing performance and safety margins. This is the test selected for detailed post-combustion material analysis.

Material characterization before and after static tests

Following the identification of Static Test-06 as the optimal firing, a comprehensive material characterization was performed on the motor’s steel components (IS 2026 steel) before and after the combustion test. This analysis aimed to reveal any microstructural or chemical changes in the steel due to the high-pressure, high-temperature (T ≈ 2580 K) environment of Test-06, thereby assessing the steel’s performance in terms of oxidation resistance, thermal stability, structural resistance and durability. Figures 16, 17, 18, 19, 20 and 21 present the results from various characterization techniques, comparing the pristine steel sample with the sample retrieved after the Static Test-06 firing.

Baseline (Pre-Combustion) material properties

The pristine steel was first analyzed to establish a reference. Figure 16 shows the spectral analysis of the unused steel: X-ray Diffraction (XRD) patterns, Fourier Transform Infrared (FTIR) spectra, and Raman spectra of the material before exposure to combustion.

X-ray diffraction (XRD) is indeed a powerful and widely used technique for analyzing crystalline materials, offering a wealth of information about the sample’s structure^{49,50,51,52,53}. The XRD pattern in Fig. 16(a) exhibits the characteristic peaks of the steel’s primary phases, confirming the expected crystal structure of IS 2026 steel a predominantly ferritic/martensitic phase composition with no unusual secondary phases^{54,55,56,57,58}. The absence of additional peaks indicates no oxides or contaminants on the fresh surface. Similarly, the FTIR spectrum of the pristine steel Fig. 16(b) is essentially featureless in terms of organic functional groups, as expected for a metal, but serves as a baseline showing no significant oxide-related absorption bands for instance, no strong Fe–O vibrational peaks, which typically appear in the far-infrared^57,58. The Raman analysis Fig. 16(c) of the pristine steel did not show prominent peaks either – metals usually give weak Raman signalsbut it was conducted to potentially detect any carbonaceous or oxide species. In the pristine state, as expected, no carbon residue or oxide-related Raman bands are present^59,60. Collectively, Fig. 16 confirms that prior to firing, the steel sample is in a clean, unoxidized state with its original microstructure intact and no surface corrosion products.The microstructure and surface morphology of the pristine steel are illustrated in Figs. 17 and 18.

Figure 17 presents FESEM images of the steel surface before firing, alongside EDS (Energy Dispersive Spectroscopy) spectra for elemental composition. The FESEM micrographs Fig. 17 reveal a smooth, machined surface with typical grinding marks and no visible pitting or coating. The grain structure is not directly visible on the as-prepared surface, but the overall appearance is that of a uniform, dense metal. Correspondingly, the EDS analysis Fig. 17 detects mainly iron (Fe) as the primary element, with smaller peaks for alloying elements (such as carbon (C), manganese (Mn), etc., depending on the exact steel grade). Notably, there is little to no oxygen detected in the pristine sample’s EDS spectrum, confirming the lack of an oxide layer initially⁶¹. Figure 18 shows an AFM (Atomic Force Microscopy) surface topography map of the pristine steel. The AFM analysis quantifies the nanoscale surface roughness, which was found to be relatively low (a low average roughness Ra on the order of a few tens of nanometers)^62,63. The smooth topography Fig. 18 indicates that before combustion the steel’s surface is in good condition, which is crucial for establishing how much it degrades after the test.

Post-Combustion material changes (Static Test-06 Exposure)

After the Static Test-06 firing, the steel (specifically the sections directly exposed to the combustion gases and heat, such as the nozzle throat insert or chamber wall) was extracted for the same analyses.The most immediate changes were observed in the surface morphology and composition, as shown in Figs. 19 and 20.

The FESEM images in Fig. 19 display a stark contrast to the pristine surface. The post-combustion steel surface is rougher and covered with a layer of scale/deposits. One can see areas of flaky or granular oxide scale that formed during the high-temperature exposure^58,59. There are also small pits and uneven features, suggesting that material erosion or melting may have occurred in localized spots under the intense heat flux. The accompanying EDS spectrum in Fig. 19 confirms a significant increase in oxygen content on the surface of the steel after firing a strong oxygen peak is now present, which was absent before. This indicates the formation of iron oxide layers likely mixtures of FeO/Fe₃O₄ near the metal interface and Fe₂O₃ at the outer surface as the steel reacted with oxidizing combustion products⁶⁴. In addition to oxygen, the EDS might also show traces of other elements deposited from the combustion environment. For instance, if the propellant or insulation released species like aluminium or chlorine, small amounts of Al or Cl might appear in the spectrum. In our case, any such traces are minor; the primary change is oxidation of the iron⁶⁵. The formation of this oxide scale in Static Test-06 suggests that the steel was heated to temperatures where oxidation kinetics are non-negligible (likely several hundred degrees Celsius), but the fact that the motor remained intact implies the oxide layer did not catastrophically spall during the short burn duration. This thin oxide layer can act as a protective barrier, though its presence also signals that the material was pushed close to its thermal limits for oxidation resistance^33,45.

The AFM analysis of the post-combustion surface in Fig. 20 further quantifies the increased roughness qualitatively observed in FESEM. The AFM topographical map after combustion shows a much rougher profile with higher peaks and deeper valleys compared to Fig. 18. The average roughness Ra may have increased by an order of magnitude into the hundreds of nanometers range, reflecting the development of oxide scales and possible micro-cracks. Such an increase in roughness has implications for material performance: a rougher surface has more surface area and potentially more initiation sites for corrosion or crack formation if the component were to be reused or subjected to cyclic thermal stresses. It also indicates some material loss in certain areas (erosion), consistent with the idea of erosive burning at high pressure hot gas and particle flow can physically wear away the steel surface. Despite these changes, no through-thickness cracks or structural failures were observed on the sample, which is an encouraging sign that Static Test-06 conditions, while aggressive, did not irreparably damage the steel component.

To complement the microscopy, Fig. 21 compares TGA (Thermogravimetric Analysis) and DTA (Differential Thermal Analysis) curves for the pristine steel versus the combustion-exposed steel. These thermal analyses were conducted to assess how the prior high-temperature exposure altered the steel’s oxidation behaviour and thermal stability. In Fig. 21(a), the TGA curves show the weight change of each sample as it is heated in an oxidative environment. The pristine steel sample exhibits a certain weight gain starting at high temperatures for example, above ~ 400 °C due to the onset of oxidation formation of iron oxides on fresh metal⁵². In contrast, the steel sample from Static Test-06, which already has an oxide layer from the firing, shows a different TGA profile: the initial weight gain is delayed or reduced, since a thin protective oxide existed and must first be penetrated before fresh metal oxidizes. Essentially, the combustion-exposed steel has a slight “head start” on oxidation – it might even show a small weight loss at first if any loosely adhered scale spalls off, followed by a more gradual weight gain compared to the pristine steel. By the end of the TGA run (e.g., at ~ 1000 °C), both samples tend toward a similar total weight gain, indicating that eventually both form a comparable amount of oxide, but the kinetics differ in the early stages⁵⁸.

The DTA curves in Fig. 21(b) provide insight into the thermal events corresponding to these weight changes. The pristine steel shows an exothermic peak when oxidation kicks in vigorously as the formation of iron oxide is exothermic. The combustion-exposed steel shows a tempered response – the exothermic peak is smaller or shifted, reflecting that part of the steel surface was already oxidized during Static Test-06, and thus the exothermic oxidation reaction upon heating is less intense. No additional phase transformation peaks like steel phase changes differ significantly between the samples, implying that the bulk microstructure of the steel e.g., phase composition like martensite vs. tempered sorbite remained largely unchanged by the brief high-temperature exposure. This is consistent with the short duration of the static firing on the order of seconds, which is not enough to fully reheat-treat the bulk steel, though the surface did get very hot^53,57.

Implications for steel performance in High-Temperature environments

The before-and-after characterization of the Static Test-06 sample provides critical insights into how this steel behaves under extreme rocket motor conditions, and the same is summarized in Table 12.

The observations can be summarized as follows: prior to combustion the material was clean and sound; after combustion it developed an oxide scale, increased surface roughness, and minor surface erosion, but retained overall structural integrity. For high-temperature applications like rocket motors, this suggests that IS 2026 steel can withstand short-term exposure to ~ 300 ksc combustion conditions, forming a protective oxide in the process. The presence of a stable oxide layer is a double-edged sword: on one hand, it protects the underlying metal from further rapid oxidation (as seen by the altered TGA behaviour, the pre-formed scale slowed additional weight gain); on the other hand, that oxide is brittle and can crack or spall under thermal cycling or vibration, which could expose fresh metal. Therefore, while Static Test-06 did not cause immediate failure, repeated firings or longer-duration burns might require either allowing this scale to form and then remain undisturbed or using a steel alloy that forms a more adherent, heat-resistant oxide (such as a chromium-rich stainless steel). The increased roughness and signs of erosion on the post-test surface highlight the mechanical wear the steel experienced.