1. Introduction
2. Solid fuel materials and composition for enhanced ramjet performance
3. Theoretical analysis of ramjet performance
3.1 Adiabatic flame temperature
3.2 Oxygen/fuel ratio
3.3 Characteristic velocity
3.4 Specific impulse
3.5 Density impulse
3.6 Exhaust mole fraction
4. Conclusion
Nomenclature
C* : characteristic velocity (m･s-1)
F : thrust (N)
Isp : specific impulse (s)
It : total impulse (N.s)
Ispd : density impulse (N･s･m-3)
mF : mass of fuel (kg)
Mflight : mach number at fight condition of the ramjet
Ra : gas constant for air (kg･m2･s-2･K-1･mol-1)
Rv : ratio of fuel volume with and without additives
Ta : temperature at ramjet flight conditions (K)
t : total flight time (s)
V : volume (m3)
: ratio of specific heat
ρ : density (kg･m-3)
g0 : acceleration due to gravity (m･s-2)
Φ : fuel-air equivalence ratio
Abbreviations
CuO : copper oxide
HTPB : hydroxyl-terminated polybutadiene
L/D : ratio of lift to drag
O/F : oxidizer/Fuel ratio
PMMA : polymethyl methacrylate
PTFE : polytetrafluoroethylene
PE : polyethylene
SFRJ : solid fuel ramjet
WO3 : tungsten trioxide
Fe2O3 : ferric oxide
Vol : volume
1. Introduction
Solid Fuel Ramjet (SFRJ) propulsion systems offer a promising combination of simplicity, reliability, and cost-effectiveness, making them highly suitable for applications in surveillance, search and rescue, and environmental monitoring. Unlike traditional propulsion systems, SFRJs provide high specific impulse without requiring complex fuel control, storage, or feed systems. This simplicity is achieved by utilizing air-breathing, subsonic combustion with minimal moving parts, resulting in a low-cost, highly reliable design [1]. The SFRJ structure typically consists of a cylindrical body containing solid fuel and a diffuser to compress incoming air, which then reacts with the solid fuel to produce a diffuse flame [2-3]. This efficient combustion process enables SFRJs to achieve specific impulse values 3-4 times greater than those of conventional rocket engines, making them suitable for various applications, including long-range tactical missiles and supersonic flight [4].
The solid fuels most commonly used in SFRJs are polymeric hydrocarbons, such as hydroxyl-terminated polybutadiene (HTPB), polymethyl methacrylate (PMMA), and polyethylene (PE). These materials are preferred for their high mechanical stability, favorable regression rates, and effective combustion characteristics. Recent studies have also highlighted paraffin as a promising alternative due to its superior performance in ramjet applications [5,6]. The incorporation of high-energy additives—such as aluminum (Al), boron (B), and magnesium (Mg)—into these fuels can significantly enhance their gravimetric and volumetric heat release, optimizing both specific impulse and density-specific impulse for ramjet propulsion.
This study focuses on analyzing the theoretical performance characteristics of SFRJs utilizing HTPB-based fuels with various metal additives to improve specific impulse and density-specific impulse. An altitude of 12 km was selected for this analysis, which aligns well with the operational needs of missions like fire detection, search and rescue, and locating missing persons. At this altitude, a surveillance or emergency response vehicle can monitor large areas efficiently, capture high-resolution imagery and thermal data, and remain safely below the typical cruising altitude of commercial air traffic. Additionally, 12 km offers an optimal atmospheric density for ramjet operation, ensuring efficient combustion and extended flight endurance. Insights from this theoretical analysis can inform future experimental studies and real-world applications where high fuel efficiency, endurance, and observational capabilities are critical.
Among commonly used high-energy metals, aluminum has historically been the preferred additive due to its favorable combustion properties and compatibility with polymeric fuels [7,8]. However, boron presents an attractive alternative with a volumetric heat of combustion approximately 61% higher and a gravimetric heat value about 86% greater than aluminum [9,10,21]. Despite these advantages, boron’s application has been limited by challenges such as poor ignition characteristics and low combustion efficiency [11,12]. Recent studies, however, have shown that coating boron particles with materials like nickel oxide (NiO) or titanium oxide (TiO2) can lower its ignition temperature and enhance combustion efficiency by reducing the oxidation temperature and ignition delay time [13,14,15,16,17,18].
To enhance combustion further, researchers have explored addition of various as high-density energetic particles and polymers. For example, Liu et al. [7] observed the boron added with nano-CuO improved its thermochemical behavior, reducing the reaction temperature by approximately 117°C. Similarly, Huang et al. [17] demonstrated that CuO is among the most effective combustion enhancers for boron, significantly improving ignition and combustion properties. This study investigates the theoretical performance of SFRJs using HTPB-based fuels with aluminum, boron, and magnesium additives, as well as CuO as high-density energetic particles and PTFE as a polymer. Our goal is to identify the most effective fuel compositions for SFRJ applications, laying the groundwork for future experimental validations.
2. Solid fuel materials and composition for enhanced ramjet performance
In this study, hydroxyl-terminated polybutadiene (HTPB) (density: 0.916 g/cm3) was used as the base fuel matrix, supplemented with various energetic metal additives including magnesium, boron, and aluminum. Additionally, copper oxide (CuO) and polytetrafluoroethylene (PTFE) were employed as high-density energetic particles to further enhance fuel performance. Tables 1 and 2 outline the properties of the metal additives and high-density energetic particles used in this investigation and Table 3 shows the corresponding fuel-additives composition.
Table 1.
Properties of fuel matrix and metal additives.
| Fuel Matrix | Chemical Formula | Density (g/cm3) |
| HTPB-R45 | 0.916 | |
| Aluminum | Al | 2.7 |
| Boron | B | 2.34 |
| Magnesium | Mg | 1.738 |
Table 2.
Properties of high-density energetic particles.
| Properties | Copper oxide | PTFE |
| Chemical formula | CuO | (C2F4)n |
| Density (g/cm3) | 6.31 | 2.32 |
| Melting Point (°C) | 1326 | 327 |
| Molecular weight (g/mol) | 79.545 | 100.01 |
Table 3.
Theoretical sample composition.
3. Theoretical analysis of ramjet performance
The performance of HTPB (C10H15.4O0.07) loaded with aluminum, boron, or magnesium as metal additives, along with CuO or PTFE as energetic particles, has been investigated under flight conditions at an altitude of 12 km for various equivalence ratios, ϕ, varying between 0.6 and 1.1. Considering the flight altitude of 12 km of interest for the future experimental activities, the corresponding incoming air temperature and pressure into the combustor were found to be 511.13 K and 1 MPa. The influence of these metal additives and energetic particles on key ramjet performance metrics such as adiabatic flame temperature, specific impulse, density-specific impulse, and characteristic velocity was theoretically estimated using NASA’s chemical equilibrium application (CEA) software [19].
3.1 Adiabatic flame temperature
The adiabatic flame temperatures for different fuel grain compositions and fuel-air equivalence ratios (ϕ) are shown in Fig. 1. These calculations were conducted assuming a combustion chamber pressure of 1 MPa and a temperature of 511.13 K, with ϕ values ranging from 0.6 to 1.1, corresponding to flight conditions at an altitude of 12 km. The results indicate that as the fuel-air equivalence ratio increases, the combustion chamber temperature also rises, reaching its maximum at the stoichiometric point. This allows for predicting the stoichiometric fuel/air ratio for various fuel compositions.
Fig. 1 also shows a significant rise in peak flame temperature as the concentration of metal additives increases from 20% to 40% in 10% increments. This increase occurs because the addition of metal additives enriches the fuel mixture. This enrichment plays an important role in engine design, as it affects the mass flow rate of air relative to the fuel; a lower oxygen-to-fuel ratio (O/F) reduces the required frontal area of the engine.
Among the different configurations, HTPB with aluminum shows the highest combustion chamber temperature at a fuel-air equivalence ratio of 1.1. Specifically, HTPB with 40% aluminum achieves a flame temperature of 2676.1 K, which increases to 2697.6 K with the addition of 5% PTFE. Magnesium and boron, both at 40% concentration with 5% PTFE, result in adiabatic flame temperatures of 2671.4 K and 2562.2 K, respectively. In contrast, pure HTPB reaches a temperature of 2337.5 K at the same equivalence ratio.
The rise in the temperature is due to the high hear of combustion provided by the metal additives. These additives increase the gas-phase temperature of the fuel, resulting in the higher adiabatic flame temperatures and improved combustion efficiency [20].
3.2 Oxygen/fuel ratio
The O/F ratio is a critical parameter in solid fuel performance, as it influences the combustion efficiency and engine design (Fig. 2). By varying the concentration of metal additives such as aluminum, boron, and magnesium, the figure demonstrates how these additives affect the O/F ratio for each fuel mixture. A lower O/F ratio typically indicates a more fuel-rich mixture, which can lead to higher combustion temperatures and more efficient energy release, depending on the additive concentration and composition. This relationship is essential for optimizing fuel formulations in solid fuel ramjet applications. It is noteworthy that the stoichiometric ratio is achieved at lower O/F ratios due to the effects of the additives (Fig. 2(c)). At an equivalence ratio of 1, HTPB with magnesium and 5% CuO exhibits a notably low O/F ratio of 9.8, which is lower compared to other HTPB-based fuel formulations. In contrast, pure HTPB at the same equivalence ratio has an O/F ratio of 15.54. The inclusion of CuO and PTFE in the fuel formulations consistently reduces the O/F ratio across all compositions, highlighting their role in optimizing combustion efficiency for a lower oxidizer mass flow rate.
3.3 Characteristic velocity
Characteristic velocity is a key parameter in evaluating the combustion performance of solid propellants, as it directly relates to the efficiency of energy conversion during combustion. Fig. 3 presents the characteristic velocity (C*) for various HTPB-based solid fuels containing different metal additives.
The performance of solid fuels can be predicted by evaluating the C* as a function of the O/F ratio (Davis and Yilmaz 2014). The HTPB loaded with 40% B formulation shows a maximum value of C* of 1231 m/s. The addition of B to HTPB improves the C* compared to that of Al and magnesium formulation where their effects in the decrease of the C*. It is interesting to note that the C* for HTPB with 40% B is initially high. However, as the O/F increases, the C* value decreases. In contrast, for HTPB with 20% B, the C* value increases slightly with an increasing O/F ratio. The HTPB/Mg-based composition has a lower value of C* compared to other HTPB based formulations. It is important to note that the characteristic velocity is a function of the propellent and independent of the rocket geometry, hence, with the improvement in characteristic velocity, higher performance can be achieved due to the improved combustion temperature at a lower O/F ratio allowing for a smaller, lighter oxidizer tank.
3.4 Specific impulse
The specific impulse (Isp) is a key performance metric in propulsion systems, representing the efficiency with which fuel mass is converted into thrust. It is defined as the amount of thrust produced per unit of propellant flow rate and is commonly expressed in seconds. For ramjet engines, the specific impulse depends on various factors, including the composition of the fuel, the fuel-air equivalence ratio, and the operating conditions such as altitude and pressure. In this study, the Isp of the ramjet is calculated using NASA’s CEA code, taking into account the different additives incorporated into HTPB-based solid fuels.
Fig. 4, shows the theoretical specific impulse (Isp) for different equivalence ratios. The Isp of the ramjet is calculated by using the specific impulse of the rocket calculated with NASA CEA code and there by subtracting the corresponding flight mach number (at which the ramjet flies) multiplied with O/F ratio and speed of sound at the corresponding altitude as in Eq. (1).
Among the various fuel combinations examined, HTPB loaded with boron (B), along with CuO and PTFE as additives, shows a noticeable increase in specific impulse. On the other hand, HTPB formulations with aluminum (Al) and magnesium (Mg) additives demonstrate a decrease in specific impulse, performing below pure HTPB. This indicates that, despite the increase in flame temperature with these metal additives, the higher molecular weight of Al and Mg offsets the performance gains.
In contrast, boron’s lower molecular weight—1.6 and 1.4 times lower than aluminum and magnesium, respectively—contributes to its higher performance compared to pure HTPB across all equivalence ratios. Notably, HTPB with 40% boron achieves the highest specific impulse at 2032.58 s. Pure HTPB follows, with a specific impulse of 1841.7 s at an equivalence ratio of 0.6, showing a decreasing trend as the equivalence ratio increases.
3.5 Density impulse
Another key performance factor, particularly relevant in scenarios with volume constraints, is the density impulse. The density impulse of a propellant is defined as the total impulse (thrust generated over time) that can be produced per unit volume of the propellant. Higher fuel density can lead to a reduction in tank volume, making it crucial for applications where space is limited. A preliminary analysis can be conducted by considering that for a given mission time (flight duration), one of the most important parameters is the total impulse (It)
The total impulse is defined by Eq. (2).
Being the mass of the fuel given by Eq. (3).
The total impulse can be written as Eq. (4).
This equation highlights that total impulse depends on density impulse. Assuming a constant total impulse, the ratio (Rv) of the required volume with additives to the volume without additives can be defined as in Eq. (5).
A real advantage in additives addition is achieved if R<1, indicating that the fuel with additives provides a higher density impulse, enabling smaller tank sizes. This can be seen from the Fig. 5.
As shown in Fig. 5, the density impulse for each propellant system is calculated at its respective Isp values. The addition of metal additives enhances the density impulse across all fuel formulations. At an equivalence ratio of 0.6, the boron-based fuel formulation with 5% CuO achieves a density impulse of 3436.86 s, which is twice that of pure HTPB. For the same equivalence ratio, aluminum- and magnesium-based fuels show improvements of 1.73 and 1.29 times, respectively. This demonstrates that metal additives can significantly enhance the density impulse, making these formulations advantageous for reducing tank volume while maintaining or improving performance.
3.6 Exhaust mole fraction
Fig. 6(a)-(j) shows the species mole fractions for HTPB-based solid fuels loaded with boron, aluminum, and magnesium, along with CuO and PTFE as additives, combusting in atmospheric air at a pressure of 1 MPa and a temperature of 511.3 K, simulating flight conditions at an altitude of 12 km. Only species with mole fractions higher than 0.01 are considered in these plots, which are presented as a function of the O/F ratio.
For pure HTPB, Fig. 6(a), the main combustion products are CO, CO2, H2O, and O2. A notable improvement in boron combustion is observed with the addition of CuO and PTFE. Among all the fuel compositions, the boron-based mixture produces a lower concentration of H2O and forms HBO isomers, which are more stable during combustion [10-11].
This behavior can be attributed to the high flame temperature, which discourages the formation of stable products like H2O. However, the presence of HBO isomers suggests that further recombination may occur during gas expansion in the nozzle, which could further increase the specific impulse, as demonstrated in Fig. 2. This stability in combustion products, combined with the additives’ effect on flame temperature, makes boron-based fuels particularly effective in improving performance.
Fig. 6.
Mole fractions of HTPB-based fuel loaded with (a) Pure HTPB (b) 40% Aluminium; (c) 40% Aluminium; and 5% CUO; (d) 40% Aluminium and 5% PTFE (e) 40% Boron; (f) 40% Boron and 5% CUO; (g) 40% Boron and 5% PTFE; (h) 40% magnesium; (i) 40% magnesium and 5% CUO; (j) 40% magnesium and 5% PTFE; additives burning in gaseous oxygen (O2).
4. Conclusion
This study evaluated the feasibility and performance enhancements achievable through the incorporation of aluminum (Al), boron (B), and magnesium (Mg) as metal additives in HTPB-based solid fuels for solid fuel ramjet (SFRJ) applications, with a specific focus on improving key metrics such as specific impulse, density-specific impulse, and flame temperature. Ramjet propulsion systems that utilize solid fuels offer distinct advantages, including structural simplicity, reliability, and reduced operational complexity compared to liquid and hybrid propulsion systems. However, they also face limitations in adaptability and control. By examining the impact of various metal additives, this research provides insights into addressing these limitations and advancing the performance of SFRJs.
The theoretical analysis demonstrated that the addition of high-energy particles like Al, B, and Mg can enhance ramjet performance significantly, especially in applications where volumetric constraints and aerodynamic efficiency are prioritized. Boron-based formulations, in particular, displayed the highest specific impulse values, achieving up to 2032.58 s at optimal equivalence ratios. This is a substantial improvement over pure HTPB, which showed a specific impulse of 1841.7 s under similar conditions, indicating that boron offers a significant advantage for high-performance applications. In addition, boron formulations exhibited the lowest oxygen/fuel (O/F) ratios, around 9.8 at an equivalence ratio of 1, compared to pure HTPB’s O/F ratio of 15.54. This lower O/F ratio reflects an increased fuel efficiency, reducing the oxidizer mass flow requirement, which is crucial in fuel-dense applications.
The addition of CuO and PTFE to these metal-loaded fuels proved beneficial in enhancing combustion temperature, with boron and aluminum formulations reaching peak adiabatic flame temperatures of approximately 2697.6 K with the inclusion of 5% PTFE. This increase in flame temperature directly correlates to higher thermal energy release, supporting increased specific impulse and better combustion efficiency. This is particularly beneficial in applications where compact tank sizes are needed, as the density-specific impulse improved markedly with the addition of metal additives. For example, the boron-based fuel formulation with 5% CuO achieved a density impulse of 3436.86 s at an equivalence ratio of 0.6, effectively doubling that of pure HTPB. Aluminum- and magnesium-based formulations also showed significant improvements, with density impulse values enhanced by 1.73 and 1.29 times, respectively, compared to pure HTPB.
An additional focus of this study was the effect of these metal additives on exhaust species. The boron-based formulation, for instance, demonstrated reduced water vapor (H2O) production, forming more stable HBO isomers during combustion. This reduced H2O production, coupled with the presence of HBO isomers, suggests enhanced stability in combustion products, which could lead to further recombination during nozzle expansion and potentially increase the overall specific impulse. Such stability in exhaust products, combined with the high flame temperature achieved, positions boron-based fuels as highly effective in boosting overall SFRJ performance.
The results of this study underscore the potential of solid fuels, particularly those containing boron, to meet the stringent performance requirements of SFRJ systems. Specifically, boron-based fuels with CuO or PTFE offer significant benefits in high-density impulse and fuel efficiency, making them suitable for dual-mode ramjet applications where reduced aerodynamic drag and optimized volumetric fuel density are paramount. These findings suggest that solid fuel ramjets with optimized fuel compositions could be advantageous for future small launch vehicles and tactical systems, where simplicity, high performance, and reduced volume requirements are critical.
For future research, experimental validation of these theoretical results under various flight conditions would provide valuable real-world insights. Additionally, investigating the combustion mechanisms and two-phase flow dynamics within the combustion chamber could offer further optimization possibilities for solid fuel compositions. Continued research in this area could drive the development of advanced dual-mode ramjet technologies, expanding the applications and effectiveness of solid fuel ramjets in modern aerospace propulsion.
