Experimental Investigations on the Impact of Hydrogen Injection Apertures in Pulsed Detonation Combustor

Abstract

Combustion through detonation marks an important leap in efficiency over standard deflagration methods. This research introduces a Pulsed Detonation Combustor (PDC) model that uses Hydrogen as fuel and Oxygen as an oxidizer, specifically targeting carbon-free combustion efforts. The PDC aerodynamic features boost operating cycle frequency and facilitate Deflagration-to-Detonation Transition (DDT) within distances less than 200 mm by means of Hartmann–Sprenger resonators and cross-flow fuel/oxidizer injection. The achievement of quality mixing in a short-time filling process represents not only higher cycle operation but also enhanced performances. The scope of this paper is to assess the impact of different fuel injectors with different opening areas on the performances of the PDC. This assessment, expressed as a function of the Equivalence Ratio (ER), is conducted using two primary methods. Instantaneous static pressures are recorded and processed to extract the maximum and average cycle pressure and characterize the pressure augmentation. Thrust measurements obtained using a load cell are averaged over the detonation cycle to calculate the time-averaged thrust. The specific impulse is subsequently determined based on these thrust measurements and the corresponding mass flow data.

1. Introduction

A new approach in developing propulsion architectures involves the use of pressure gain combustion (PGC). Compared to its counterpart, where fuel burns gradually (deflagration combustion), detonation combustion triggers supersonic waves paired with supersonic combustion fronts. This coupling represents the detonation wave, which results in nearly instantaneous heat release, significantly higher pressures, and elevated temperatures. The anticipated results include higher thermodynamic efficiency and reduced heat losses, which translate into greater thrust output and increased specific impulse. The advantages offered by detonation engines make them a compelling option for propulsion systems across a range of aerospace applications, such as launch vehicles, high-speed atmospheric flights, and hypersonic systems [1].

There are three main types of detonation combustors that are considered for aerospace applications: Pulsed Detonation Combustors (PDCs), Rotating Detonation Combustors (RDCs), and Oblique Detonation Wave Combustors (ODWCs), the first two being the most promising. All three concepts have proven their feasibility through experimental and flight tests, but challenges and limitations remain to be addressed before they can be fully developed for practical use. In 2021, JAXA tested both a PDE [2] and an RDE [3] in space as part of the S-520-31 sounding rocket mission. Despite these advancements, significant concerns related to ODWE stability in real-life applications are limiting their practical implementation to date. The primary challenge continues to be the control of detonation wave initiation and propagation [4]. Another crucial factor is the compactness of the combustor, which leads to a lighter engine, which is an important consideration, particularly in space propulsion technologies.

To date, both experimental and numerical studies on PDCs show their advantage over traditional combustors; however, experimental operational and performance maps are still not available. Extensive experimental validation is needed to be able to reach practical applications of PDCs. Significant research efforts have been directed toward exploring applications for pulse detonation engine technology.

The PDC [4,5] involves a reactive mixture in a tube where a detonation wave is generated at one end and travels to the other. The cycle starts by filling the chamber with a fuel/oxidizer mixture via a valve and then igniting the mixture with a high-frequency device. Thrust is generated through the exhaust of combustion products. The cycle includes filling, detonation, propagation, and blowout/purging stages. After purging completion, a new cycle is initiated. To surpass the performances of traditional deflagration combustion, a minimum frequency of 75 Hz is required, with current devices achieving between 100 and 400 Hz [6,7].

In contrast to RDCs, PDCs face the challenge of requiring extended channels to facilitate the deflagration-to-detonation transition (DDT). At the component level, traditional methods to reduce DDT length and time are Schelkin spirals [8], perforated plates [9], and solid or fluid obstacles [10,11,12]. Alternative methods to achieve shorter and faster DDT are Hartmann–Sprenger resonators to enhance shock wave strength or jet injection in cross flow [13,14].

The Jet in Cross-Flow (JICF) refers to the injection of a fluid jet perpendicular to a cross-flow created by another jet stream. This technique has been extensively studied and demonstrated to be an effective approach for detonation due to several advantages, such as the combustor’s design simplicity, flame acceleration, and the ability to propagate detonation in supersonic flow [15]. The modification of the flow structure, including various wave configurations, caused by JICF generates vortices that enhance turbulence and promote mixing [16,17]. In addition, JICF serves as a control and stabilization technique for the detonation process by adjusting critical parameters that influence flow characteristics. Key parameters include but are not limited to injection pressure and temperature, as well as the size and location of the injection aperture [15].

Experimental studies have demonstrated that applying the JICF technique to PDEs after the formation of premixed gases results in a nearly 45% reduction in ignition time for Hydrogen/Air mixtures. This improvement enhances operational frequencies due to increased turbulence (up to 240%) and a shorter deflagration-to-detonation transition (DDT) [13]. Lowe et al. [18] explored the injection location of JICF and showed that it can result in peak pressure increases ranging from 13% to 120%, although without affecting the velocity. Frolov et al. [14] found that high-pressure supersonic jets of fuel (natural gas) and oxidizer (oxygen) in cross-flow achieve effective mixing within a 74 mm smooth detonation tube. This setup facilitates a swift deflagration-to-detonation transition (DDT) over distances up to four tube diameters, occurring in less than a millisecond. However, there are relatively few studies that examine the application of JICF for the premixing of gases in PDEs.

Lowe and Wylie [19] conducted a numerical investigation into parallel and serial injection schemes in a PDE across various flow rates. Their findings indicated that each scheme could be optimal depending on the flow range, and in some cases, a combination of both schemes proved to be most effective. Yan et al. [20] conducted experimental investigations into the impact of fuel injector sizes on a Pulse Detonation Rocket Engine (PDRE) using liquid fuels across various frequencies. Their findings indicated that each injector size performed optimally at specific frequencies, except for the injector with the smallest throat diameter. The largest average peak pressure was achieved with the injector featuring the largest throat diameter, although this was observed at lower frequencies. All experiments were conducted at high equivalence ratios (ER). Braun et al. [21] explored various orifice sizes for fuel injection in a colliding jet configuration with the oxidizer. Their pressure trend analysis revealed that the peak detonation pressure is influenced by both the injection pressure and the size of the fuel orifice.

Research indicates that detonation waves triggered by supersonic jet interactions generate high-frequency oscillations [22,23]. Hinkey et al. [24] performed experiments using wall pressure sensors, thrust measurements, and detonation wave velocity data to evaluate the deflagration-to-detonation transition (DDT). Their results highlight that DDT depends on the tube length, initial mixture thermodynamics, and residual turbulence. These methods offer significant benefits, including enhanced mixing, simpler ignition, flashback prevention, better detonation control, reduced size, increased stability, and lower emissions [25]. Lacaralle et al. [26] have reported that the spatial oscillations of a jet in cross-flow lead to enhanced scalar mixing. Additionally, it has been demonstrated that higher oscillation frequencies accelerate the mixing process [27].

This paper aims to fill the existing gap in experimental investigations of JICF during the premixing phase of a PDC. The PDC prototype discussed in this paper, specifically designed for aerospace applications, has been thoroughly investigated, achieving a Technology Readiness Level (TRL) of 5. In our earlier studies [28,29], the PDC’s performances were mapped, including key data such as maximum pressure, pressure gain, thrust, and specific impulse. With the operational envelope and performance characteristics well defined, our current objective is to further optimize the combustor. This paper extends our previous research by experimentally analyzing how size variations in fuel injector openings, a critical parameter of JICF, influence the PDC’s performance when using Hydrogen/Oxygen mixtures. These advancements bring us closer to making this technology viable for practical applications.

2. Materials and Methods

2.1. Experimental Design

The PDC breadboard discussed in this paper is based on passive control methods to increase mixing efficiency. The JICF technique applied to premix the injected Hydrogen and Oxygen improves aerodynamic characteristics by generating vortices. Furthermore, Hartmann–Sprenger wave generators regulate the frequency of the counter-rotating vortex structures formed by the JICF, facilitating high-frequency oscillations that support the propagation of high-frequency detonation waves.

The main components of the PDC prototype (Figure 1 (a) PDC Section [28], (b) Premixing Section, (c) Mixing Diagram, (d) Fuel Injection Section are I—Premixing Section, where injection and mixing occur; II—Ignition Section (9); and III—Detonation Channel (10), where the detonation wave is forced to exhaust into the atmosphere. Gaseous Hydrogen is injected axially into the premixing chamber (3—fuel inlet), while Oxygen is injected tangentially through channels (1—oxidizer inlet), creating the JICF technique. The incoming flow passes through Hartmann–Sprenger resonators (8), which enhance the frequency of the generated pressure waves through reflections (2—end wall, 4—air passage window, 5—perforated plate) and collisions. Collision occurs between the oxidant jets generating the counter-rotating vortices (6—vortex generation chamber), effectively increasing mixing properties.

Figure 1b illustrates the process of vortex generation and alternation within the premixing section. In addition to enhancing the mixing quality, the vortex also functions as an aerodynamic valve, regulating the fuel admission into the premixing chamber. High vortex intensity means low static pressure, which is favorable for fuel injection and mixing. As the rotation velocity of the vortex decreases, a stagnation zone with high static pressure forms, effectively closing the aerodynamic valve and halting fuel entry. The cycle then repeats with the formation of a new vortex rotating in the opposite direction.

The interaction between the aerodynamic valve and the flow in the premixing chamber dictates the overall process. When the valve is open, vortex generation occurs, resulting in primarily tangential flow within the premixing chamber. Conversely, when the valve is closed, the elevated pressure in the premixing chamber drives the fresh mixture supersonically into the detonation chamber, leading to a shock wave. Additionally, the diaphragm (7), situated between the premixing and ignition sections, ensures that the flow accelerates to supersonic speeds.

Within the detonation chamber, a spark plug ignites the fuel–oxidizer mixture, generating the combustion wave. Another function of the diaphragm (7) is to halt the wave from upstream propagation. The diameter jump at the entrance of the Detonation Channel is intended to decelerate the faster-moving shock wave, enabling the slower combustion wave to catch up and merge, forming the detonation wave, which then travels towards the outlet of the PDE [29].

This paper builds on our previous research [28,29] by focusing on optimizing the fuel inlet size to evaluate its impact on the performance of the PDC. The schematics of the fuel injection plate are shown in Figure 1d, while the size variations are presented in

Table 1. Fuel Injection Aperture Design.

Fuel Injection Type	Injection Diameter	Injection Length
A	0.7 mm	3 mm
B	0.8 mm	3 mm
C	0.9 mm	3 mm

. By adjusting the fuel injection sizes, we aim to determine how these variations influence key parameters such as pressure, pressure gain, thrust, and specific impulse during the detonation process. Additionally, by examining injector size, we aim to address a critical aspect of the JICF technique, evaluating how it affects both fuel–air mixing and detonation performance.

2.2. Experimental Setup

Figure 2 displays both the experimental facility and the setup used for the experiments. The detailed instrumentation for the Hydrogen and Oxygen supply lines, along with the command-and-control panel and the data acquisition system, is thoroughly described in [29]. The Oxygen line provides up to 20 bar at ambient temperature with a flow rate of 0.2 kg/s. The Hydrogen line offers up to 20 bar at ambient temperature with a flow rate of 0.05 kg/s. A variable-frequency spark plug is used for ignition. The Hydrogen and Oxygen supply lines are equipped with ALICAT MQ-250SLPM-D (from ALICAT Scientific Inc., Tucson, AZ, USA) and ALICAT MQ-2000SLPM-D (from ALICAT Scientific Inc., Tucson, AZ, USA) flow meters, respectively. These devices measure pressure, flow rate, and temperature, enabling the calculation of the equivalence ratio.

For thrust measurements, a STA-3-100 load cell sensor from LCM Systems (Newport, UK) with 20 gF accuracy is used. The PDC breadboard slides on a test bed using vertical ball sliders. The sensor is mounted vertically beneath the model, aligned with its axis to reduce measurement errors. Calibration involved using 10 identical 5 lbs weights and was performed with multiple loading/unloading cycles to address sensor hysteresis, achieving an R² value over 0.99. Data are acquired through a Strain Gauge Amplifier—SGA (from Micron Meters, Tucker, GA, USA) [30], connected to a computer via an acquisition board. Thrust values are time-averaged for accuracy and combined with ER calculations based on flow meters data, the specific impulse is determined.

Figure 2b illustrates the placement of two Kulite ETM-HT-375 (M) sensors within the detonation channel, used for rapid static pressure measurements, along with the schematics of the instrumentation ports. The operating pressure capacity of each sensor is up to 35 bara. Both have a 3 kHz bandwidth, a typical non-linearity, hysteresis, and repeatability of ±0.5% FSO. Their natural frequency exceeds 400 kHz and has an acceleration sensitivity of $1.1\times {10}^4$% FS/g. The sensors were calibrated from 1 to 20 bar in 0.5 bar increments. The transfer function, based on linear regression, achieved R² values of 0.99990 for K1 and 0.99999 for K2. Data were sampled at 20 kHz, with the averaged results presented in the next section.

The experimental campaign was structured to evaluate the impact of JICF upon the parameters that characterize the operation of the PDC by varying the fed gases’ pressure for each fuel injector opening size. The ignition frequency of the spark plug was set at 100 Hz, consistent with the aerodynamic system’s design frequency, and the detonation channel length was maintained at 200 mm. The test matrix is composed of 16 cases, based on the combination of fed gases’ pressure (given in

Table 2. Explicit values of fed gases’ pressure.

Factor	Level 0	Level 1	Level 2	Level 3
$p_{H_2}^{set}$ [bar]	5.5	7.0	8.5	10.0
$p_{O_2}^{set}$ [bar]	9.0	7.5	6.0	4.5

) repeated for each fuel injector opening size (see Table 1).

3. Results and Discussion

The key performance metrics of the PDC presented in this section include maximum cycle pressure, mean cycle pressure, and thrust, all of which were measured experimentally. Cycle-averaged values were calculated over a minimum of 500 detonation cycles post-ignition. Based on previous research [31], it was determined that increasing the number of cycles beyond 30 reduces the change in the average to less than 0.01%, suggesting that further averaging would not significantly affect the results presented.

The pressure gain was evaluated as the difference between peak cycle pressure and the mean pressure during the refilling of the fresh mixture. Total specific impulse (1), a metric typically applied in launcher and in-space propulsion systems where both fuel and oxidizer are onboard, was also calculated.

$$I_{sp}={\displaystyle \frac{T}{{g(\dot{M}}_{H_2}+{\dot{M}}_{O_2})}}$$

(1)

In addition, fuel-specific impulse (2) is reported to facilitate comparisons with air-breathing propulsion technologies. This parameter, which provides a direct assessment of the combustor’s efficiency, reflects both the quality of mixing and the ability to harness the available chemical energy for propulsion.

$$I_{sp}={\displaystyle \frac{T}{{g\dot{M}}_{H_2}}}$$

(2)

The data are presented as their variation with the equivalence ratio—$\varphi$ (3), which is determined by using the values recorded from the mass flow meters from each supply line [29].

$$\varphi ={\displaystyle \frac{{\dot{M}}_{H_2}/{\dot{M}}_{O_2}}{{{(\dot{M}}_{H_2}/{\dot{M}}_{O_2})}_{st}}}$$

(3)

The tests yielding sustained pulsed detonation were recorded only for ERs ranging between 0.05 and 0.18.

3.1. Maximum Pressure

Figure 3 presents the correlation between maximum cycle pressure and ER. At a low oxidizer pressure of 4.5 bar (Figure 3a), the Type C fuel injection opening does not exhibit any sustained detonation, as the mixture is too fuel-rich, and only deflagration regimes occur. The Type C fuel injector opening fails to sustain detonation, leading to overly rich mixtures that only result in deflagration regimes. This is attributed to the aerodynamic valve’s (cross-flow) inability to close the fuel intake during the vortex generation and vortex shedding phases into the ignition chamber.

Similarly, at a high oxidizer pressure of 9 bar (Figure 3d), the Type A injector opening is too small to achieve ignition, as the fuel jet cannot sufficiently penetrate the cross-flow-generated vortex. Even when directional changes in the vortex occur, the limited fuel injection prevents proper mixing formation, which is necessary for successful detonation.

At lower oxidizer pressures of 4.5 (Figure 3a) and 6 bar (Figure 3b), the smallest fuel opening, Type A, yields the highest maximum cycle pressure, suggesting an optimal correlation between fuel injection and vortex intensity at these conditions. As the oxidizer pressure increases to 7.5 (Figure 3c) and 9 bar (Figure 3d), the intensified vortex generated in the premixing chamber by the more energetic Oxygen cross-flow and Hartmann–Sprenger resonators requires a greater fuel mass flow to penetrate the vortex and enable proper mixing for detonation. Consequently, the Type C fuel opening, with its larger size, produces the highest maximum pressure. The peak pressure of approximately 3.75 bar is reached when the highest feed gas pressures (see Table 2) are used.

3.2. Mean Pressure

Figure 4 illustrates the variation in average cycle pressure as a function of the ER. The average cycle pressure was calculated without considering the peak detonation pressure. This approach was chosen to specifically evaluate the influence of JICF on the non-detonation phases of the pulsed detonation cycle.

At lower oxidizer pressure (Figure 4a), injector Type A consistently shows lower mean cycle pressure values compared to Type B, which shows a more consistent increase as the ER rises. The smaller fuel opening limits the fuel flow, resulting in less efficient mixing with the oxidizer during the non-detonation phases of the cycle, such as the filling and mixing stages. However, Type B seems to provide a better balance between fuel flow and oxidizer, resulting in a relatively higher mean cycle pressure during these phases. This indicates that JICF improves the mixing dynamics more effectively for injector Type B under these conditions.

At oxidizer pressures of 6 and 7.5 bar, injector Type B consistently achieves the highest mean cycle pressure at intermediate ER values. Under these conditions, Type B appears to be the optimal choice for mixing efficiency during the non-detonation phases due to its balanced interaction between the fuel jet and the cross-flow. This balance allows Type B to effectively penetrate the vortex generated by the cross-flow, leading to higher pressures during the pre-detonation phases. In contrast, injectors Type A and Type C either under-supply or over-supply fuel negatively impact mixing efficiency.

At high oxidizer pressures (Figure 4d), Injector Types B and C exhibit very similar performance, suggesting that with increasing pressure, the non-detonation phases of the cycle, such as the filling and mixing phases, are less dependent on injector size. Instead, the increased oxidizer pressure dominates the mixing process, leading to similar outcomes across different injector sizes.

Taking into account that injector Type A fails to achieve detonation at an oxidizer feed pressure of 9 bar, it becomes evident that larger injectors are more effective at higher oxidizer pressures. This suggests that for JICF-driven mixing to be successful at elevated pressures, larger injector sizes are necessary to optimize performance during the pre-detonation phases.

3.3. Pressure Gain

The pressure gain of the cycle is computed as the difference between the maximum pressure (peak pressure) and the mean pressure during the refilling phase of fresh reactants. Figure 5 depicts the pressure gain variation with ER for different oxidizer pressures.

At low oxidizer pressure (4.5 bar), injector Type A maintains a relatively stable pressure gain. Although injector Type B shows lower values initially, it demonstrates an upward trend as the ER increases. This indicates that as more fuel becomes available, the performance of Type B improves, likely due to better fuel–oxidant mixing at higher ERs.

At a slightly higher oxidizer pressure (6 bar), injector Type A exhibits a noticeable dip in pressure gain around ER = 0.1, indicating suboptimal mixing and the influence of its smaller opening on fuel injection effectiveness. In contrast, injector Type B shows less variation in pressure gain across the range of ERs, suggesting that its fuel penetration is more consistent, allowing for better blending with the vortex created by the cross-flow, even across different ER levels.

At an oxidizer pressure of 7.5 bar, both injector Types B and C demonstrate an upward trend in pressure gain with increasing ER. This indicates that at higher oxidizer pressures, which correlate with greater vortex intensity, larger fuel injection openings enhance mixing and improve the detonation potential of the mixture.

At the highest oxidizer pressure (9 bar), the data highlight that as oxidizer injection pressure increases, larger injectors (Type C) give better output. The significant jump in pressure gain around ER = 0.1 emphasizes that the fuel injector opening must be large enough to provide the necessary mass flow and velocity for the fuel to effectively penetrate and be entrained in the vortex, ensuring proper mixing and detonation performance.

3.4. Time-Averaged Thrust

Figure 6 depicts the variation in time-averaged thrust with ER for different oxidizer pressures. While thrust values are expected to correlate with the pressure data, certain test cases in this experimental campaign show discrepancies due to the occurrence of misfires. These misfires lead to inconsistencies in thrust measurements, causing deviations from the expected correlation between pressure and thrust output.

At low oxidizer pressures (4.5 bar), thrust values exhibit minimal variation with ER. Injector Type A emerges as the optimal choice across ERs, with values around 5 N, except for the lowest tested ER. Injector Type B displays smaller but stable values, around 1.5 N. This suggests that, for lower oxidizer pressures, a smaller fuel injector opening is more effective at being entrained in the vortex and generates better mixing.

As the oxidizer pressure increases, Figure 6b and Figure 6c reveal that Injector Type C achieves the highest thrust values of 9.2 N and 10 N, respectively. This is due to the larger injector opening facilitating better mixing, which enhances the overall performance at elevated pressures. Injector Type A, on the other hand, exhibits a more stable but lower thrust profile, reflecting poorer mixing due to its smaller opening size, which limits the fuel’s ability to penetrate and properly mix with the oxidizer. For Injector Type B, however, the thrust trends begin to deviate from the pressure profiles. This suggests that under these conditions, the JICF technique is not as effective, leading to a higher number of missfires. Missfires play a crucial role in these deviations, as they directly impact the time-averaged thrust. Since thrust is directly tied to the momentum change from combustion events, an increased number of missfires results in a decrease in overall thrust over time, even though peak pressures during successful cycles may still be high.

Notably, at an oxidizer pressure of 9 bar (Figure 6d), Injector Type C achieves a significant thrust level of 19.2 N, which is substantially higher than the thrust values produced by other injectors. This highlights the effectiveness of the larger injector opening at high oxidizer pressures, enabling better mixing and more efficient combustion. The superior thrust generated by Injector Type C under these conditions reinforces the importance of sufficient fuel mass flow and proper entrainment into the cross-flow vortex for maximizing performance at elevated pressures.

3.5. Time-Averaged Total Specific Impulse

The total specific impulse (Figure 7) is a key metric for determining how effectively the system converts propellant mass into thrust, as it directly impacts the vehicle’s operational range and fuel requirements during space missions.

In Figure 7a, Injector Type A maintains relatively stable total specific impulse values, peaking at around 75 s, indicating decent mixing efficiency even at low ERs. Injector Type B, however, shows significantly lower values throughout the range of ERs.

As shown in Figure 7b and Figure 7c, Injector Type C produces the highest total specific impulse (around 90 s and 75 s, respectively), outperforming the other injectors. This emphasizes that at intermediate oxidizer pressures, a larger injector opening aids better fuel entrainment in the cross-flow vortex, improving mixing efficiency. Injector Type A outperforms the medium opening injector, likely due to optimized fuel delivery within the vortex, which reduces the number of missfires, providing higher time-averaged thrust values (Figure 6b,c).

In Figure 7d, injector Type C continues to yield the highest values of total specific impulse, surpassing 90 s. This emphasizes the necessity of larger injector sizes at high oxidizer pressures to match the increased vortex intensity created by the cross-flow. At these elevated pressures, the fuel jet requires both sufficient mass flow and velocity to effectively penetrate the vortex and ensure thorough mixing, a condition that Type C manages to fulfill.

However, despite Injector Type C achieving the highest thrust values at an oxidizer pressure of 9 bar (Figure 6d), the total specific impulse is not as high as one might expect. This discrepancy arises from the significantly increased oxidizer mass flow rate, which offsets the benefit of higher thrust. Since total specific impulse is a ratio of thrust to the combined mass flow of fuel and oxidizer, the increase in oxidizer consumption lowers the total specific impulse, even though the thrust is maximized. This demonstrates the delicate balance between injector size, oxidizer pressure, and overall system efficiency.

3.6. Time-Averaged Fuel-Specific Impulse

The fuel-specific impulse plots (Figure 8) offer a direct assessment of the combustor’s performance in terms of mixing efficiency and energy conversion from the available fuel’s chemical energy. These plots highlight how well the injected fuel interacts with the oxidizer, optimizing the energy release during combustion.

At 4.5 bar oxidizer pressure (Figure 8a), Injector Type A shows a distinct peak, 6803 s, in fuel-specific impulse at an ER of around 0.1. This indicates that at this ER, the fuel is more efficiently mixed with the oxidizer, resulting in better energy harvesting. As the ER increases further, the fuel-specific impulse declines, implying that Injector Type A loses mixing efficiency. Injector Type B, on the other hand, remains relatively flat with significantly lower values, indicating poor fuel utilization and weaker energy conversion. This suggests that a smaller injector opening (Type A) at lower oxidizer pressures performs better in terms of fuel mixing and energy harvesting.

At 6.0 bar (Figure 8b), Injector Type A exhibits a similar trend, with a peak at 5984 s, around ER = 0.1, followed by a decline. However, Injector Type C shows better performance than both A and B in terms of fuel-specific impulse, peaking at 7055 s. This implies that Type C’s larger fuel injector size starts to capitalize on the increased vortex intensity at this higher pressure, allowing more effective mixing and better energy extraction. Meanwhile, Injector Type B continues to show low and consistent values, indicating suboptimal performance in fuel mixing under these conditions.

In Figure 8c, Injector Type C achieves the highest value of 7990 s, around ER = 0.1. Injector Type A continues to display higher values than Type B, which shows hindered effectiveness in fuel energy conversion.

At the highest oxidizer pressure of 9.0 bar (Figure 8d), Injector Type C achieves its highest value, 8237 s, while Injector Type B continues to lag significantly behind. The plots clearly demonstrate that at higher oxidizer pressures, larger injectors (like Type C) are crucial for effective energy harvesting from the fuel, as they ensure sufficient penetration and mixing with the oxidizer, especially in highly turbulent conditions.

A summary of the results for each injector type is given in

Table 3. Injector Type A Results Summary.

Fuel Pressure [bar]	Oxidizer Pressure [bar]	ER [-]	Thrust [N]	Total Isp [s]	Fuel Isp [s]	Max Pressure [bar]	Mean Pressure [bar]	Pressure Gain [%]
5.5	9	X	X	X	X	X	X	X
5.5	7.5	X	X	X	X	X	X	X
5.5	6	X	X	X	X	X	X	X
5.5	4.5	0.08728	5.062	74.345	6888.079	1.767	1.194	148.0053
7	9	X	X	X	X	X	X	X
7	7.5	X	X	X	X	X	X	X
7	6	0.11608	5.13	80.981	5662.006	1.978	1.286	153.7597
7	4.5	0.11109	5.027	77.713	5673.829	1.986	1.203	165.0893
8.5	9	X	X	X	X	X	X	X
8.5	7.5	X	X	X	X	X	X	X
8.5	6	0.08153	7.012	60.480	5994.566	2.233	1.178	189.4520
8.5	4.5	0.05659	4.005	63.529	2546.602	2.066	1.227	168.3775
10	9	X	X	X	X	X	X	X
10	7.5	0.06413	9.107	54.091	6801.183	1.870	1.184	157.9327
10	6	0.12011	7.083	66.711	4509.852	2.341	1.194	195.9283
10	4.5	0.17221	5.014	73.865	3505.130	2.032	1.263	160.8370

,

Table 4. Injector Type B Results Summary.

Fuel Pressure [bar]	Oxidizer Pressure [bar]	ER [-]	Thrust [N]	Total Isp [s]	Fuel Isp [s]	Max Pressure [bar]	Mean Pressure [bar]	Pressure Gain [%]
5.5	9	X	X	X	X	X	X	X
5.5	7.5	X	X	X	X	X	X	X
5.5	6	X	X	X	X	X	X	X
5.5	4.5	0.14090	1.3890	17.162	991.591	1.840	1.307	140.775
7	9	X	X	X	X	X	X	X
7	7.5	0.08378	2.4307	15.425	1488.324	2.051	1.182	173.595
7	6	0.10379	4.0280	32.364	2526.990	2.249	1.361	165.225
7	4.5	0.18455	0.5556	7.088	314.323	2.156	1.366	157.787
8.5	9	X	X	X	X	X	X	X
8.5	7.5	0.10072	3.9817	23.756	1910.640	2.227	1.294	172.098
8.5	6	0.14520	2.9632	23.927	1342.176	2.030	1.276	159.075
8.5	4.5	X	X	X	X	X	X	X
10	9	0.09508	4.4447	21.615	1840.324	2.239	1.239	180.660
10	7.5	0.13035	4.9077	29.801	1858.855	2.353	1.216	193.610
10	6	0.17792	3.3336	26.841	1233.740	1.990	1.159	171.719
10	4.5	X	X	X	X	X	X	X

and

Table 5. Injector Type C Results Summary.

Fuel Pressure [bar]	Oxidizer Pressure [bar]	ER [-]	Thrust [N]	Total Isp [s]	Fuel Isp [s]	Max Pressure [bar]	Mean Pressure [bar]	Pressure Gain [%]
5.5	9	X	X	X	X	X	X	X
5.5	7.5	0.07823	10.102	78.168	8072.072	1.889	1.162	162.518
5.5	6	0.10067	9.003	87.716	7058.267	2.138	1.267	168.726
5.5	4.5	X	X	X	X	X	X	X
7	9	X	X	X	X	X	X	X
7	7.5	0.12154	7.997	61.081	4081.617	2.372	1.193	198.868
7	6	X	X	X	X	X	X	X
7	4.5	X	X	X	X	X	X	X
8.5	9	0.08365	19.105	85.717	8282.903	2.444	1.240	197.113
8.5	7.5	0.12251	8.02	52.212	3461.695	2.686	1.278	210.112
8.5	6	X	X	X	X	X	X	X
8.5	4.5	X	X	X	X	X	X	X
10	9	0.10126	16.067	71.629	5730.731	3.633	1.174	309.412
10	7.5	X	X	X	X	X	X	X
10	6	X	X	X	X	X	X	X
10	4.5	X	X	X	X	X	X	X

. The X value in these tables marks the tests that yielded no detonation regimes.

4. Conclusions

The present study examined how the size of the fuel injection opening, a critical parameter in JICF, affects the performance of our Hydrogen-fueled PDC. Performance was evaluated using maximum and average pressure values, including pressure gain and time-averaged thrust values. The latter, combined with mass flow calculations, were used to determine the total specific impulse and the fuel-specific impulse.

The fuel injector size opening significantly affects the maximum pressure achieved during detonation. At lower oxidizer pressures, smaller injector openings—Type A produce higher maximum pressures due to better fuel entrainment into the vortex, optimizing the mixing process. Larger injectors struggle in these conditions, leading to deflagration rather than detonation due to excessively rich mixtures. As oxidizer pressure increases, the JICF intensifies, and larger injectors become necessary to provide sufficient fuel penetration and mixing. At higher pressures (7.5 and 9 bar), the increased vortex strength requires a greater fuel mass flow for successful detonation, which Type C achieves, leading to the highest maximum pressures. The JICF’s role in fuel-oxidant mixing becomes increasingly critical with rising oxidizer pressure, dictating the effectiveness of the fuel injection and determining maximum pressure performance.

The chosen approach of excluding detonation peaks and focusing on mean cycle pressure reveals how JICF significantly impacts the non-detonation phases of the pulsed detonation cycle, especially the mixing and filling processes. At lower pressures, injector size is more critical in achieving efficient mixing, but as oxidizer pressure increases, the JICF effect becomes strong enough that injector size plays a lesser role.

Pressure gain increases with ER, particularly when larger injectors are used at higher oxidizer pressures. This suggests that a larger fuel supply is necessary to achieve optimal mixing and detonation performance when oxidizer pressure is increased. Injectors Type A and B follow a similar trend with a slight rise in pressure gain, but they lag behind Injector Type C, confirming that smaller injectors struggle to optimize mixing as oxidizer pressure increases. Injector Type C consistently outperforms the smaller injectors at higher oxidizer pressures, indicating that larger fuel injectors improve mixing efficiency and detonation success during the JICF process, especially at elevated oxidizer pressures.

The difference between time-averaged thrust and pressure values could explain why thrust does not always follow the pressure trends. Missfires (failed detonation cycles) introduce significant variability, as these non-detonation events contribute to thrust inconsistencies, reducing the overall time-averaged thrust even when pressure data seems promising. These inconsistencies are particularly noticeable at higher oxidizer pressures, where injector performance becomes more critical for proper mixing and detonation.

Since thrust is directly related to the momentum change from combustion events, a higher number of missfires leads to a reduction in total thrust over time, even if peak pressures during successful cycles are high. The time-averaged thrust thus reflects the accumulation of these missfires, which explains why thrust does not always correlate directly with pressure augmentation.

The correlation between the total specific impulse and the JICF behavior is clear. At lower pressures, where the cross-flow vortex is less intense, smaller injectors—Type A—can penetrate effectively and achieve higher total specific impulse values. As the oxidizer pressure increases, the vortex becomes stronger, necessitating larger injector openings—Type C—to maintain efficient fuel entrainment, mixing, and combustion. Injectors that cannot match the vortex intensity at higher pressures show a decline in total specific impulse, as the poor mixing results in inefficient fuel utilization and reduced thrust production relative to the mass flow.

The fuel-specific impulse results underline the importance of proper injector size in relation to the oxidizer pressure. As the pressure increases, the need for larger injectors becomes evident, as they enable more effective mixing of fuel with the oxidizer, which directly influences the combustor’s ability to extract and convert the fuel’s chemical energy. Conversely, smaller injectors struggle to maintain mixing efficiency at higher pressures, leading to a significant drop in fuel-specific impulse and overall performance.

A trade-off has been identified when evaluating the impact of JICF on the performance of the PDC. At low oxidizer pressures, the fuel injector with the smallest opening (Type A) delivers good values in terms of pressure gain and thrust. This is advantageous because it requires a lower mass flow rate, which is beneficial for space applications where carrying less fuel and oxidizer reduces overall mass and costs. Conversely, at high oxidizer pressures, the fuel injector with the largest opening (Type C) provides superior performance in terms of pressure gain and thrust. However, this comes with the need for higher mass flow rates, meaning more fuel and oxidizer must be stored on board, increasing the overall mass and potentially the costs.

Future work on the PDC prototype will focus on reducing missfires, as they significantly affect the consistency of thrust and pressure data. This could involve exploring advanced ignition methods or optimizing the fuel–oxidizer ratio to improve combustion stability. Additionally, further investigation into the length of Hartman resonators and their interaction with different fuel injector openings is necessary. Understanding the combined effects of the resonators with JICF dynamics could lead to better vortex formation and more efficient detonation. Finally, scalability issues must be addressed to understand the implications of increasing or decreasing the combustor’s size. This will be crucial in adapting the combustor design for various applications, whether for larger propulsion systems or smaller, more compact devices. By tackling these challenges, the combustor’s performance, efficiency, and versatility can be significantly enhanced.