Currently, no engine by itself is capable of providing both a high Thrust to Weight Ratio (TWR) and a large specific impulse across the entire Mach range (Murthy and Curran, 1991; Daines and Segal, 1998). As shown in Figure 1 (Zhangtian et al., 2019), air-breathing motors have a good specific impulse but are only functional over a limited Mach range. In contrast, rocket engines have the best TWR but a very low specific impulse over the entire Mach range. However, the RBCC engine has the potential to bridge this performance gap by combining air-breathing and rocket engines. It behaves as an augmented rocket from take-off to supersonic speed, a ramjet/scramjet in supersonic/hypersonic flight, and a pure rocket when the density of air becomes too low. This makes it possible to obtain an engine with both good TWR and specific impulse across the entire Mach range, all sharing roughly the same system hardware. Thus, the RBCC engine has the potential to propel single-stage launchers (SSTOs) and hypersonic vehicles.

RBCC engines offer a significant advantage for hypersonic missiles. They allow for increased efficiency, leading to longer ranges and the ability to strike targets that would otherwise be out of reach. They can also achieve even higher speeds than traditional rocket engines, making them more difficult to intercept and giving them a greater advantage in combat.

Even if the realization of single-stage launchers (SSTO) has always been a very attractive idea and the dream of many engineers, its propulsion by rocket engines alone makes its use very inefficient. According to (Escher, Hyde, Anderson), the propellant carried by an SSTO using rocket propulsion alone can represent up to 90% of the initial mass of the vehicle, leaving only 10% of the total mass for the rocket structure, electronics, and payload. However, RBCC engines, with their higher specific impulse, can reduce the propellant mass ratio from 90% to 70%. Thus, this type of engine could be a starting point for SSTO propulsion. However, as explained by Dorrington and Tec (1990), the mass of propellant on board is not the only figure of merit to consider, or even the most appropriate. The use of RBCC engines involves several drawbacks. Indeed, these engines are much heavier than rocket engines, they require larger volumes of propellant (structural stresses), and are subject to more severe conditions at the exit of the atmosphere (stresses on thermal protection).

Typically, RBCC engines rely on liquid rocket engines. Due to their ability to achieve the highest achievable specific impulses, their on-off and throttled operation and as a well-known technology, these engines appear to be the most natural solution for RBCC engines. However, liquid rocket engines are highly complex and subject to operational, safety, and environmental concerns. As an alternative to liquid rocket engines, hybrid propulsion is presented here. While hybrid propulsion was once known for its technological barriers, it is currently experiencing a strong revival due to its several advantages.

To determine the suitability of HRBCC engines for various missile types, a comparison of the performance of solid and HRBCC engines was conducted. Three categories of missiles, based on their weight (light, medium, and heavy), were examined. Their characteristics are summarized in Table 1. These characteristics were used to calculate the missile’s performance assuming both engine types had the same features (diameter, mass, and thrust) and were launched under identical conditions (launch angle and initial velocity).

The propulsive performance of the missiles is defined by simply specifying the following two parameters.

• The propellant mass fraction, noted ξ . This parameter indicates the ratio of the useful propellant mass to the initial mass and is defined as:

Where t b is the burn time of the missile, F is the thrust, M p is the propellant mass and g the gravity constant. A specific impulse of approximately 245s was calculated for each missile, which is consistent with the typical specific impulse of solid rocket engines that use hydroxyl-terminated polybutadiene (HTPB) fuel. Given HTPB’s high regression rate and safety profile, it is the most commonly utilized fuel in hybrid rocket engines, and thus was selected for use in this study.

In order to give a first estimation of the performance achievable by the RBCC engine, an in-house code has been implemented to determine the trajectory of a missile powered by an RBCC engine. For the determination of the trajectory, several assumptions were taken into account.

• The Earth is flat and motionless.

Figure 3A Yang et al. (2015) shows the classical configuration of an RBCC engine which consist of a rocket, inlet, mixing duct, combustor and nozzle. Here, the rocket is embedded in the duct. In Figure 3A, the RBCC engine is represented in an ejector mode. In this mode, the inlet is open and the primary flow generated by the rocket engine entrain the airflow into the mixing duct. The fuel is injected in the combustor chamber, where it is mixed and burned with the primary and secondary flux. Figure 3B shows the schematic of the new design proposed for an HRBCC engine. The propulsion subsystems are integrated into a single engine with only one flow path: the air inlet, combustion chamber, and nozzle. The air intake is axisymmetric, and a duct connects it to the combustion chamber. Because the air-breathing and rocket engines share the same combustion chamber, this engine is smaller than a classical RBCC engine. The combustion chamber has two solid fuel grains, and the oxidizer tank is placed at the center, to simulate the configuration of HyPrSpace’s technology. Furthermore, the engine’s configuration allows for an easy integration of an aerospike nozzle, which offers attractive features like altitude compensation or a lighter and simpler design. However, these nozzles are not widely used principally due to the difficulty of cooling down their larger base aera.

To determine certain characteristics of the combustion products specific to the chosen propellant pair, the Chemical Equilibrium Application (CEA) software developed by NASA (McBride SG, 1996) was used. This software enables to calculate key parameters such as the molecular mass (MW), the temperature of the combustion chamber T c and the ratio of thermal capacities γ of the combustion products. A code was developed to plot these parameters as functions of the O/F mixture ratio. With these parameters, the characteristic velocity c * and thrust coefficient C F , defined by Eq. 4.1, have been calculated. c * = γ R M W T c γ 2 γ + 1 γ + 1 γ − 1 C F = 2 γ 2 γ − 1 2 γ + 1 γ + 1 γ − 1 1 − P e P c γ − 1 γ (4.1)

Where R is the gas constant, P e is the exit pressure and P c the pressure in the combustion chamber. The specific impulse was then plotted as a function of the O/F mixture ratio. The flowchart of the numerical estimation is shown in Figure 4.

For military missions, the performance parameter used was the volumetric specific impulse define by Eq. 4.2. This implies that, at equal specific impulse, a larger volumetric specific impulse would require a smaller volume of fuel. This is a significant advantage for missiles where having a compact design is critical. I s p v o l u m e t r i c = I s p × ρ o (4.2)

The ramjet is one of the simplest engines since it consists only of an inlet, a diffuser, a combustion chamber and a nozzle [See Figure 5 (Zhang et al., 2015)]. It is considered to be the engine of choice for supersonic flights. Since it uses ambient atmospheric air, the ramjet does not require to carry an oxidizer tank on board. It thus offers a saving of weight and space to carry heavier payloads. However, despite their theoretical simplicity, this engine is not capable of propelling a stationary vehicle on its own. Thus, its application is limited and generally reserved to a military use. Unlike the ramjet from Figure 5, where the fuel is injected in the combustor in a liquid form (Liquid Fuel Ramjet or LFRJ), the ramjet studied here uses a solid fuel and operates as a Solid Fuel Ramjet or SFRJ, which is simpler than LFRJ as it avoids fuel-control, fuel-storage and the feed system (Krishnan and George, 1998). The thermodynamic study presented in the next parts relied on the stations described in Figure 5.

In this section, the results of the performance analysis of both pure rocket and ramjet modes are presented. First, the performance of two oxidants, H 2 O 2 and O 2 , for the pure rocket mode is discussed. Then, the design of the air intake using the Oswatitsch method is represented, giving insight into the limitations of supersonic inlets. The results of the thermodynamic study for the ramjet mode are then presented. Finally, the trajectories of both RBCC and solid engines are plotted according to the missile class presented in Section 3.

As it is illustrated in Figure 9, liquid oxygen O 2 performs better with H T P B than H 2 O 2 . However, it is usually more important to consider volumetric specific impulse due to the necessity of reducing weight in military applications. Figure 10 displays the volumetric specific impulse at sea level for both H 2 O 2 / H T P B and O 2 / H T P B couples at a pressure of 34.5 bar as function of the mixture ratio O/F. As a result, H 2 O 2 appears to possess the highest volumetric specific impulse. Furthermore, this propellant offers several advantages over liquid oxygen as it can be stored at ambient temperature, is non-toxic and easy to handle (Tacca and Lentini, 2010).

From Figure 10, the optimal mixing ratio was chosen by selecting the maximum volumetric specific impulse, which was found at O/F = 5.5. For this specific mixture ratio, the specific impulse was determined and represented (green points) in Figure 9. Therefore, the specific impulse at sea level for the H 2 O 2 / H T P B mixture is approximatively equal to 260s for a mixture ratio of 5.5. In comparison to the specific impulse of the solid engines previously found in Section 3, which was about 240s, the H 2 O 2 / H T P B couple provides a slightly better specific impulse. As hybrid engine are known to have better performances than solid rocket engine, this result was expected.

Figure 11 shows the specific impulse as function of the altitude for both H 2 O 2 / H T P B and O 2 / H T P B couples at their optimal mixing ratio. As the density of air decreases with altitude, fewer losses occur and the performance of the engine improve. These data were used for the calculation of the trajectory of the HRBCC engine during the operation of the pure rocket mode.

Based on the method described Section 4.3.1.1, an in-house code was developed to model the geometry of the inlet according to the number of shock waves and Mach number and represent their impact on the geometry design and performance. Figure 12 and Figure 13 display the results for three oblique shockwaves and one final normal shock ( n = 4 ) at, respectively, Mach 3 and 6. The ramp angles for both inlets were selected as equal to [12°, 16°, and 20°].

As the Mach number increases, it is important to notice that the length and height of the inlet have to increase in order for the flow to be “started”. The flow is said to be started when the shockwaves are absorbed by the inlet. As explained by Heiser et al. (1994), this phenomenon is desirable since the inlet can capture as much air as possible, and because any normal shock waves that occur can be managed within the internal path flow. It is reminded here that a perfect gas model was used to determine the properties of the air over the system shockwave. However, this is not accurate especially at high speed and low altitudes where various physical phenomena (boundary layer-shockwave interaction, air dissociation) occur.

Figure 14 displays the variation of the compression ratio with the Mach number. The purple curve represents the ideal compression (isentropic compression) that would occur without any pressure losses. As the number of shockwaves increases, it is possible to reduce pressure losses. While increasing the number of shockwaves can help reduce pressure losses, this also requires a more complex inlet geometry. Additionally, generating a high number of shockwaves at low Mach numbers is not possible. To achieve very good compression ratios over the entire Mach range, the geometry of the inlet has to be variable. For the purposes of the study, it was considered that the air intake had a variable geometry and that only one oblique shock wave and one normal shock wave were generated. Thus, it is possible to determine the compression ratio π using the equation system from Eq 4.4 to Eq 4.6. However, by choosing to generate only one oblique shock wave at the air intake, the compression ratio will be very low, which will impact the performance of the engine.

The various characteristics calculated in the previous sections for the pure rocket mode gave the following results for a pressure in the chamber of combustion of 34.5 Bar.

• A temperature of combustion of 2984 K

In Figure 21; Figure 22; Figure 23, the trajectories for the solid-propulsion missile and the combined cycle missile have been represented. For the HRBCC missile, the trajectory is depicted in orange when in rocket mode and in green when using the ramjet mode. In that way, from take-off until reaching Mach 2, the missile is in pure rocket mode. Once Mach 2 is reached, the inlet is opened, the missile enters the ramjet mode and relies totally on the oxygen in the atmosphere. Once all the propellant is consumed, the engine is turned-off and the missile continues its course until impact. For the same characteristics, it appears that the range reachable for the HRBCC engine is greater than the solid’s ones. If the HRBCC engine seems particularly advantageous for medium missiles, it reached a smaller altitude for the heavy missile, due to the difficulty for the hybrid rocket to accelerate efficiently the missile.

The results of this study must be interpreted with caution. The analysis assumes that both missiles shared identical characteristics, which could not be the case in reality. As it was explained previously, the HRBCC engine is expected to be heavier than the solid one. In the same way, the configuration of the HyPrSpace’s engine would make the diameter of the missile larger, impacting its drag and, hence, its performance. In future studies, it would be more appropriate to compare missiles with specific missions and investigate how the resulting performance impacts the engine design. Furthermore, the trajectory model used is highly questionable as several hypotheses were made to simplify its complexity. The purpose was to provide a first approximation of the achievable performance by the HRBCC system with no intention of achieving precision. It was assumed that using the same model for both engines would suffice to gain insight into the differing behaviors of each engine during flight.

The variation of the propellant mass fraction during the flight has been analyzed for each missile propelled by an RBCC engine and presented in Table 2. The purpose was to determine the impact of the different modes (pure rocket and ramjet) on the propellant consumption. As expected, the pure rocket mode resulted in a high propellant consumption. For the light missile, the pure rocket mode consumed 93% of the total mass propellant, while it was 46% for the medium missile and 30% for the heavy one. These numbers depend on the ability of the rocket engine to efficiently accelerate the vehicle to the Mach of activation of the ramjet mode. In addition, by requiring an oxidizer tank and all the elements that go with it, the pure rocket mode increases the engine’s weight, impacting its performance. Therefore, the RBCC engine usually uses an ejector mode from take-off to supersonic speeds in order to reduce both the weight and propellant consumption. According to Amar and Reddy (2012), that mode is able to boost the performances of the rocket by 15%. However, it is one of the technical barriers that slows down the development of RBCC engines. The major difficulty of this mode comes from the relatively low thrust produced. Several studies have been carried out those past years to improve the overall understanding of the ejector mode and its possible enhancements (Lehman et al., 2000; Han et al., 2002; Heiser, 2010; Lin et al., 2017). In our future work, a study of the ejector-mode consumption and its performances will be investigated to define its suitability for military missions.