Influence of Wave Rotor Thermal Decomposition on Alternative Nuclear Rocket Propellant Performance ^†

Abstract

The proposed wave rotor enhanced nuclear propulsion (WREN) system is a potential technology candidate for timely and efficient manned missions to Mars. Using Hydrogen (H₂), conventional nuclear thermal propulsion (NTP) can attain an ${\mathrm{I}}_{sp}$ of 800–1000 s as it reaches the thermal limits of its solid core reactor material. A four-port wave rotor turbomachine coupled to a closed Brayton cycle can go beyond this limitation, further heating the H₂ to attain an ${\mathrm{I}}_{sp}$ of 1400–1500 s. Despite this improvement, liquid H₂ currently poses significant storage problems that limit transit performance. This work explores the use of denser propellants that use the full launch mass of a rocket compared to liquid H₂. This includes ammonia (NH₃), water (H₂O), and methane (CH₄). Using NERVA-class NTP technology, the ${\mathrm{I}}_{sp}$ of these alternatives is comparable to chemical rockets. The WREN fluid and subsystem cycle was modeled using an object-oriented hardware sizing program equipped with NASA CEA thermochemistry and coupled to an optimization framework. Given a specific set of constraints, a 25-klb_f (111.2 kN) class WREN engine produced $I_{sp}$ values of 663.6 s for NH₃, 469.6 s for H₂O, and 360.1 s for CH₄. NH₃ and H₂O achieved density-impulse values comparable to vacuum-rated hydrolox engines, making them competitive with in-space chemical rockets on a volumetric basis. NH₃ provided the strongest overall balance of $I_{sp}$, storage density, and $\mathrm{\Delta }V$ favorability compared with H₂ NTP, whereas H₂O produced a small radiator that enabled a higher thrust-to-weight regime. At a representative $\mathrm{\Delta }V$ of 12 km/s, the propellant savings of NH₃ WREN reduced the combined propellant-tank and radiator launch elements from 27 launches for conventional NH₃ NTP to 13 launches, of which only nine were propellant-tank launches.

1. Introduction

1.1. Context

Solid nuclear thermal propulsion (NTP) is identified by NASA as a preferred propulsion method for human missions throughout the solar system. In an NTP engine, a solid fissile fuel embedded in a ceramic or carbide lattice heats pressurized liquid hydrogen (LH₂) propellant, which expands through a nozzle to generate thrust [1,2].

The performance advantage of NTP relative to chemical combustion propulsion (CCP) arises primarily from the low molecular weight ($M_W$) of its hydrogen exhaust (H₂). The ideal rocket specific impulse ($I_{sp}$) is

$$I_{sp}={\displaystyle \frac{1}{g}}\sqrt{{\displaystyle \frac{2\gamma }{(\gamma -1)}}{\displaystyle \frac{R_u{T}_{ch}}{M_W}}\left(1-{\left({\displaystyle \frac{p_{ex}}{p_{ch}}}\right)}^{\left({\displaystyle \frac{\gamma -1}{\gamma }}\right)}\right)}$$

(1)

where $R_u$ is the universal gas constant, $\gamma$ is the ratio of specific heats, and g is Earth’s gravitational acceleration. $I_{sp}$ is the measure of time, in seconds, in which 1 kg of propellant can produce a force equal to its own weight. The equation provides a qualitative basis for understanding the fundamental performance trade between CCP and NTP. That is, as $M_W$ decreases or chamber temperature ($T_{ch}$) increases, the engine becomes more effective at using its onboard propellant to generate thrust. With one of the smallest $M_W$ values of any propellant (≤2.016 g/mol), H₂ NTP can achieve a much higher $I_{sp}$ ceiling than CCP.

The fundamental contrast between the two systems is that CCP is primarily energy limited, whereas NTP is power limited by the thermal and structural constraints of the reactor. This power limitation more directly constrains the achievable thrust of NTP systems. The highest thrust engine of the US Nuclear Engine for Rocket Vehicle Applications (NERVA) program, the XE Prime, and its USSR counterpart, the RD-0410 of the Chemical Automatics Design Bureau (KBKhA), achieved 55.4 klb_f (246.6 kN) and 7 klb_f (35.3 kN), respectively [3,4]. NTP, nevertheless, offers additional potential advantages over CCP, including the use of a single working fluid without the need to store a separate oxidizer and the absence of a combustion process, which may simplify propellant management and facilitate reliable multiple engine restarts. For this work, the primary motivation is to assess the potential propellant-mass savings of different NTP propellants and engine configurations relative to CCP for mission profiles with comparable $\mathrm{\Delta }$V requirements.

The SpaceX Raptor engine is capable of up to ∼380 s of $I_{sp}$ using a methalox ($M_W$ of 21–23 g/mol) propellant in a vacuum [5]. The highest $I_{sp}$ CCP engine is the RL-10: a hydrolox ($M_W$ of 10–14 g/mol) engine capable of ∼465.5 s [6]. By contrast, the NERVA program and Soviet RD-0410 NTP engines demonstrated 811–910 s of vacuum $I_{sp}$ using purely H₂ propellant [3,4]. More recent system-level concept studies, such as the ESA’s ALUMNI project [7], ISRO’s small nuclear rocket designs [8], and KAIST’s Korea Advanced Nuclear Thermal Engine Rocket (KANUTER) concept [9], reported $I_{sp}$ performance estimates of 865–944.5 s. This doubling of $I_{sp}$ eases the burden of required mass fractions for a given mission profile $\mathrm{\Delta }$V, as shown by the ideal rocket equation

$$\mathrm{\Delta }V=-I_{sp}glnR,$$

(2)

with the stage mass fraction

$$R={\displaystyle \frac{m_v+m_{p,t}}{m_v+m_{p,t}+m_p}},$$

(3)

where $m_v$ is the mass of the vehicle, including engine and payload, $m_{p,t}$ is the final mass of the propellant tanks, and $m_p$ is the mass of the propellant used during the burn.

Despite its high $I_{sp}$, LH₂ presents significant storage challenges due to its low density. To evaluate performance under volume constraints, the density-impulse metric ($I_{\rho }$) is defined as the product of propellant storage density and respective engine $I_{sp}$ [10]. A higher $I_{\rho }$ indicates greater total impulse for a given tank volume.

Table 1. Storage density of propellants and the required ${\mathrm{I}}_{sp}$ to be comparable with the RL-10 and Raptor $I_{\rho }$ in a vacuum.

Propellant	Storage Density	Required ${\mathrm{I}}_{\mathit{sp}}$ (RL-10)	Required ${\mathrm{I}}_{\mathit{sp}}$ (Raptor)
Hydrogen (LH2)	70.8 kg/m3	6356 s	5226 s
Methane (LCH4)	423 kg/m3	1064 s	875 s
Ammonia (LNH3)	680 kg/m3	661 s	544 s
Water (LH2O)	1000 kg/m3	450 s	370 s
Oxygen (LO2)	1140 kg/m3	-	-

lists storage densities for several candidate NTP alternative propellants and other liquids.

Based on Table 1, NERVA NTP has an $I_{\rho }$ of ∼$63.7\times {10}^3$ $\mathrm{kg}·\mathrm{s}{\mathrm{m}}^{-3}$. For comparison, the RL-10 Hydrolox and Raptor Methalox have an $I_{\rho }$ of approximately $450\times {10}^3$ and $370\times {10}^3$ $\mathrm{kg}·\mathrm{s}{\mathrm{m}}^{-3}$, respectively. It can be assumed then that CCP is potentially more advantageous to NTP based on packaging constraint. This was one of the motivations for the development of the now canceled SLS Block II cargo shroud to alleviate the volume constraint of launching LH₂ to orbit and enable a more favorable mass fraction.

Table 1 also includes the approximate $I_{sp}$ required to match the $I_{\rho }$ of the RL-10 and Raptor engines. Compared to LH₂, the other candidate NTP propellant $I_{sp}$ are far less demanding for equivalent packaging performance to CCP. However, the temperatures required to achieve these $I_{sp}$ values exceed the material limits of solid-core NTP fuel elements [11,12], where structural materials experience an unacceptable loss of strength. This work demonstrates how wave rotor technology could enable an unsteady energy-exchange process that circumvents reactor core material limitations, making alternative NTP propellant systems (NTP-A) a viable and cost-effective architecture for a cislunar tug or Mars transit vehicle.

1.2. Propellant Limitations and Alternatives

LH₂ is a “hard” cryogen that is one of the most difficult propellants to store long-term. In order to reach its maximum liquid density of 70.8 kg/m³ at 1–2 bar, LH₂ must be maintained at or below 25 K. It is an inherent issue of leakage [13] and vapor pressure curve [14], shown in Figure 1, that prevents the use of higher pressure storage which may circumvent temperature requirements. Due to it is low density, LH₂ can be volume limited depending on the launch vehicle. In the case of the SLS Block 2 Cargo system, the large shroud mitigates this issue by accommodating a 988 m³ payload volume for a >46 t payload to trans-lunar injection (TLI). Commercial vehicles, on the other hand, tend to have much smaller fairings, limiting the volume of LH₂ that can be sent to orbit.

In practicality, tank size must conform to the aspect ratio of the available launch vehicle fairing size to maximize packing density. The mass penalties of a cylindrical tank of an aspect ratio of 2:1 compared to a spherical tank of equivalent volume increase by 20% based on geometry alone [15]. Additionally, the increased surface area necessitates more insulation and thermo-optical cabling to attain reduced boil-off (RBO) of the LH₂, further exacerbating mass penalty and volume limitations.

Unless given excessive insulation through foam or complex and heavy annular cryogenic fluid jackets, gaseous LH₂ must be continuously vented [16,17]. Zero boil-off (ZBO) tanking has been demonstrated to store large quantities of LH₂ with zero loss for durations ≥13 months, but mass fractions and other system-level penalties become mission-limiting, especially for shorter loiter times [17,18]. RBO NTP vehicles are the best in terms of maximized mass fractions [15] but are impractical for long mission times. Current RBO cryostat technology designs are intended to store LH₂ for a few weeks. Consequently, proposed NTP Mars architectures often require on-orbit construction of numerous propellant drop tanks and extensive launch campaigns to account for propellant losses and to optimize stage mass fractions. Figure 2 is a conceived Mars vehicle architecture with a multitude of RBO drop tanks and inline (mission permanent) ZBO tanks, requiring no less than 8 HLV/SLS launches for construction and refueling operations [19]. This particular system is intended for a 3-year conjunction-class mission with a 100-day transit to and from Mars and a required Mars surface stay time of roughly 660 days. A faster alternative proposed by Aerojet Rocketdyne is a 2-year opposition-class mission with a surface stay of ∼30 days but would require on the order of 4 SLS and 16 HLV launches [20]. Reducing this time as much as possible while enabling reasonable surface-stay times is in the interest of manned missions, as it minimizes risks that could jeopardize astronaut safety and mission success.

To assemble the spacecraft, repeated transits within cislunar space may require flexibility, where the immediate need of a lunar tug will limit the time frame of orbital refueling. Thereby ZBO becomes cost-effective in limiting launch number and is open to rapid CONOPS. For these reasons there has been a large investment into the research of LH₂ ZBO [18]. This work is then motivated to explore other alternative propellants that may be easier to use for long-duration missions.

Higher-density liquids including water (LH₂O), ammonia (LNH₃), and methane (LCH₄) have been identified as high-potential NTP-A propellant candidates [12,15]. With storage densities of approximately 1000 kg/m³ (277 K), 680 kg/m³ (239.8 K), and 423 kg/m³ (111.7 K) at 1 atm (1.01325 bar), respectively, these fluids reduce volume and insulation requirements. This leads to potentially better vehicle mass fractions and lower tank launch count for specific $\mathrm{\Delta }$V regimes. Moreover, storage technologies for these liquids are mature or less demanding. For example, ammonia may achieve passive ZBO using high-reflectivity coatings [15], and long-duration methane storage has already been demonstrated by SpaceX [21]. Water requires only modest pressures to remain liquid at temperatures above the background of space, suggesting potential dual-use as a thermal heat sink.

These propellants are also compatible with in situ resource utilization (ISRU) strategies emphasized by the Artemis program [22,23,24]. Near-term architectures; however, primarily focus on minimizing launch mass to low Earth orbit (LEO) before ISRU becomes operational. Thus the scope of this research only extends to tank launches to LEO which can utilize a space-tug delivery system to various orbits. This allows the stage propellant mass fraction to be maximized and the NTP/NTP-A vehicle to be fully fueled for an injection burn.

Despite these advantages, the performance of these heavy NTP-A propellants is limited by the maximum operating temperature (MOT) of the fuel elements. For reference, Figure 3 shows the projected NTP core endurance versus the exit temperature of H₂ [25]. Using the NASA Chemical Equilibrium with Applications (CEA) program [26,27], Figure 4 presents the average $M_W$ of propellants as a function of temperature at their corresponding critical pressures. The purpose of this pressure convention is to demonstrate how the NTP-A propellant $M_W$ compares within a physical reactor, which requires the propellant to be at a critical state, at a minimum, during core heating. Note that a pronounced reduction in $M_W$ occurs above approximately 3000 K, indicating increased hydrogen species concentrations above long-endurance MOT of existing solid NTP core materials.

Under NERVA conditions of 2400–2850 K and at critical pressure, ammonia NTP-A can theoretically achieve ∼450 s $I_{sp}$ [12], assuming the ideal Equation (2) with no losses. This is comparable to hydrolox CCP but still half of hydrogen NTP. Nevertheless, its resultant $I_{\rho }$ is $\sim 306,000$ $\mathrm{kg}·\mathrm{s}{\mathrm{m}}^{-3}$, roughly five times that of LH₂. Whether this implies a larger payload capacity or range depends on the mass fraction favored by Equation (2).

Because high $I_{sp}$ remains the dominant factor for maximizing $\mathrm{\Delta }V$, hydrogen still offers the highest performance ceiling. Overcoming reactor MOT limits is therefore essential for enabling competitive NTP-A systems.

1.3. Solutions to Challenges

One solution to the power limitations of NTP-A is a liquid- or gas-phase nuclear core [28,29,30,31,32]. These engines allow their fuel to change state to enable exceptionally high temperatures, up to ∼5200 K for liquid and >10,000 K for gas cores. A liquid-phase core has been suggested by Houts et al. [29] to enable the use of any passively storable volatile, with a performance of 700–900 s $I_{sp}$ for propellants heavier than H₂ [30]. However, material and fuel element containment still requires significant maturation as a fully integrated system. To mitigate fuel erosion, one proposed concept is the Centrifugal Nuclear Thermal Rocket (CNTR) [29,31], in which the fuel elements are rotated at high speed using turbines that are turned by the propellant flowing from the nozzle regenerative cooling cycle. The centrifugal force generated can hold the liquid fissile material to the walls while bubbles of propellant are pumped through it, heated, and subsequently exhausted for high efficiency burns. Apart from the low technological maturity compared with solid core reactors, the rate at which extremely high $M_w$ reactor fuel is vaporized will cause efficiency to drop at high power. Work by Santana and Hollingsworth [33] estimated an upper limit of 1400 s for liquid-phase-core $I_{sp}$ using $H_2$ at a chamber temperature and pressure of 4500 K and 100 atm (101.2 bar). Beyond this temperature or below this pressure, the reactor fuel material is entrained in the flow at significant concentrations. Above this pressure and the $H_2$ dissociation rate diminishes.

The present authors explore the use of wave rotor (WR) technology to facilitate the superheating of a propellant by an unsteady, shock-driven energy exchange with a closed Brayton cycle (CBC) [25,34]. The wave rotor enhanced nuclear (WREN) propulsion concept, which has been further developed in [35,36], integrates a WR between the NTP reactor core outlet and the nozzle inlet. This configuration enables propellant superheating outside the core, thereby circumventing MOT constraints inherent to the reactor. A CBC, analogous to architectures proposed for Prometheus systems, supplies the required compression work via a high-sound-speed driver fluid. Assuming a full hydrogen WREN cycle, where both the propellant and CBC driver fluids are H₂, results indicate that the $I_{sp}$ of conventional solid-core NTP systems could be boosted by approximately 50–60% at NERVA-class thrust with the addition of large radiators for power generation.

Historical experiments and propulsion studies support this capability of compressive heating. For example, the Cornell Aeronautical Laboratory “Wave Superheater” was a 2 m wide WR device capable of producing compressed air as high as 4000 K and 120 bar, starting from ambient [37,38]. The Superheater featured a nozzle extension following the compressed gas exit port for flow exhaustion to a test chamber to emulate hypersonic conditions [38], demonstrating its potential rocket-like application. This potential was first noted by Squire and Saad in the early 1960s [39,40]. For in-space propulsion, they considered a Rankine cycle using steam for the driver in order to provide a low cycle bottom temperature. To the author’s knowledge, this is the only instance where a WR was considered in this application. Unfortunately, Squire and Saad’s method was found to be relatively ineffective at increasing H₂ $I_{sp}$ despite greater system complexity, owing to the low sound speed of the driver relative to that of the compressed gas, with a maximum $I_{sp}$ of ∼1000 s [39]. In order for the Wave Superheater to attain such effective compression, the system used hot helium as the low $M_W$ driver gas to attain the desired sound speeds [38].

CBC power generation in spaceflight is limited by the power cycle’s ability to reject waste heat generated by its energy conversion process. NASA’s Prometheus program had determined that a nuclear electric propulsion (NEP) spacecraft should use a helium, helium-xenon, or other high sound-speed working fluid within a CBC in order to minimize the radiator area [41,42,43]. This is a coincidental overlap noted by the authors’ past work [34,35,36], where WR compression and Brayton-based NEP architecture may enable improved NTP performance.

A major component of the WRs’ benefit is not only the ability to heat a flow via shock-driven compression but also the ability to decompose a fluid into its constituent particles to a greater extent than thermal equilibrium alone, known aptly as “cracking” in an unsteady process [44]. These considerations motivate the use of the WREN architecture proposed by Gosse et al. [34] as a pathway for high-performance NTP-A systems using high-TRL components and more practical propellant storage strategies. In this framework, WREN offers the potential to achieve $I_{sp}$ equivalent to or exceeding those of traditional CCP while simultaneously alleviating NTP requirements of high in-orbit tank delivery count and poor mass fractions. From an $I_{\rho }$ perspective, however, competitiveness with the CCP requires that the WREN system attain the target $I_{sp}$ values for each candidate propellant listed in Table 1. Consequently, this work seeks to quantify the extent to which WR-driven heating can enable these performance thresholds, thereby assessing the viability of WREN-enabled NTP-A architectures for future in-space propulsion applications.

1.4. Work Overview

This article is a revised and expanded version of a conference paper entitled “Propellant Alternatives of Nuclear Thermal Propulsion using Wave Rotor Pressure Exchanges”, which was published in the Proceedings of the 2025 AIAA SciTech Forum, Orlando, FL, USA, 6–10 January 2025, as AIAA-2025-0150 [36].

The present study incorporates corrections to the constraints and operation of the system, which were ignored in the previous work. This includes: (i) NTP-A propellants are held at or above supercritical state during heating; (ii) WREN H₂ cycle uses an H₂ driver gas (identical configuration to Gosse et al. [34]), while the other NTP-A propellants use a helium (He) driver in the CBC; (iii) the propellant turbopump receives power from the main CBC drive shaft rather than assuming losses via a bleed cycle configuration [1]; and (iv) the heat exchanger (recuperator) model, which provides some additional cooling to the CBC to enable reduced radiator sizing, has been updated to align with current in-space heat exchanger technology [45].

No particular trajectories or burn times are analyzed in this work. Instead, general analyses of comparative performance and implications of the WREN NTP-A propellants are addressed. Many of the same parametric and sensitivity studies previously disseminated during the conference proceedings [36] are included and updated here. This includes baseline design performance estimates in Section 3.1, sensitivity to thrust, $I_{sp}$, and core temperatures in Section 3.2, and trade analysis in fuel savings to required launcher campaigns followed by $\mathrm{\Delta }$V favorability compared with other architectures in Section 3.3. A new optimization framework to the zero-dimensional systems-level performance model has been developed to broaden the search of feasible designs and is described in Section 2.3. Additionally, the potential for WREN to enable the more challenging propellants is explored in more detail in Section 2.5.1.

2. Materials and Methods

2.1. Wave Rotor Technology

The wave rotor (WR), or dynamic pressure exchanger, is a turbomachinery device that transfers energy between fluids through shock waves and expansion fans. WRs have been applied in combustion systems, refrigeration cycles, and high-enthalpy test gas generation [37]. A four-port, through-flow WR, illustrated in Figure 5, consists of an array of equally sized axisymmetric channels that rotate about a central, motorized drum within a housing. This rotation periodically exposes the channels to ducted pressure reservoir ports, enabling controlled sequences of shocks and expansions.

The associated wave pattern for compression and expansion processes is shown in Figure 6. When high-pressure driver gas (HPDG) enters a channel, it initiates a compression shock that raises the pressure and temperature of the low-pressure compressed gas (LPCG). The reflected hammer shock further increases the state to a high-pressure compressed gas (HPCG) prior to exhaustion. Subsequent expansion waves remove the driver gas and reset the channel for the next cycle. The outflow of HPCG and the now low pressure driver gas (LPDG) is homogeneous through the correct timing of port openings and wave reflection.

The WR has been studied at length in the context of jet Brayton cycles, where the WR receives LPCG from the compressor and HPDG from the combustion chamber; this generates HPCG to extract more power from the combustion chamber and expands the HPDG to LPDG where it is below or at the MOT of a turbine upon exhaustion. This process has been shown by the likes of Paxson [46], Wilson [47], and Welch [48] to improve the specific power and thermal efficiency of engines. This is due to the high isentropic efficiency afforded by shock-driven wave compressors [37], which increase pressure on the turbine by >20% compared to the compressor outlet [47]. Their research also found that macroscopic balances of volume-averaged thermodynamic properties within the rotor passage control volume provide a simple, system-level method for analyzing performance.

The WR can be configured to operate as a type of compressor by directly exhausting the HPCG. Instead of topping a Brayton cycle, the WR utilizes a separate heated driver flow or closed Brayton cycle (CBC) for a desired compressive heating of a fluid, such as the Wave Superheater [38].

It should be noted that since the WR is an unsteady inertial fluid device, the rapid alternation between hot and cold flows will exist within the channels in approximately equal times and below the heat transfer rate of the channel walls [48]. Therefore, the WR is tolerant to transient peak fluid temperatures and pressures that exceed continuous exposure limits, making it an ideal option for superheating propellants.

2.2. Wave Rotor Topping Cycle

A schematic of the Wave Rotor Enhanced Nuclear (WREN) propulsion concept NTP cycle is shown in Figure 7. Station 4 corresponds to LPCG, station 5 to the HPCG, station 5c to the HPDG, and station 6c to the LPDG. The working (CBC) fluid flowing from stations 5c to 6c (driver gas) provides the energy required to compress the propellant, or motive gas, from stations 4 to 5.

Assuming equal compression and expansion work within the wave rotor control volume, infinitesimally thin channels for continuity, and negligible viscous effects, an ideal characteristic equation can be derived based on the work of Wilson and Paxson [47]. If the compression and expansion processes are further assumed to be polytropic, the pressure ratio from station 4 to station 6c is

$$P{R}_{4-6c}=P{R}_{5-6c}{\left[{\displaystyle \frac{1-\frac{(1-{\eta }_{5c-6c})}{{\eta }_{5c-6c}{\eta }_{5-4}}\frac{T_1}{T_{6c}}\left[P{R}_{5-4}^{\frac{\gamma -1}{\gamma }}-1\right]}{1+\frac{1}{{\eta }_{5-4}}\frac{T_1}{T_{6c}}\left[P{R}_{5-4}^{\frac{\gamma -1}{\gamma }}-1\right]}}\right]}^{{\displaystyle \frac{\gamma }{\gamma -1}}}$$

(4)

This quantity is also referred to as the total pressure ratio (TPR), defined as $p_{6c}/p_4$. The expression is useful for estimating boundary conditions in systems-level modeling. Experimental results indicate that excessively high TPR values reduce confidence in achievable polytropic efficiencies at minimum exhaust gas recirculation (EGR), which provides practical constraints for the macro-model. Work by Tuchler and Copeland [49] identified a maximum TPR of ∼$1.63$ for an isentropic efficiency (${\eta }_{4-5}$ and ${\eta }_{5c-6c}$) of 80%. EGR is an inherent characteristic of WRs, arising from the incongruity between rotor rotation and diffusion across gas discontinuities, shock-wave propagation speeds, and viscous wall boundary-layer effects [50].

The mass flow rates of the expansion and compression process for Equation (4) are also assumed equal; however, this is not the case for the NTP WR, which couples the NTP and CBC cycles. During a systems analysis, where the temperature and pressure ratios of the ports satisfy Equation (4), the necessary mass flow rates that yield the intended compression ratio of the motive gas can be determined. This is done by calculating the work of the compression process:

$${\dot{W}}_{WR-comp}={\dot{m}}_{4-5}|h_5-h_4|$$

(5)

where ${\dot{m}}_{4-5}$ is given by the intended thrust, and enthalpy (h) is based on the CEA results of the fluid states solved by Equation (4). Since the work of expansion is assumed equivalent to compression, the mass flow rate of the driver gas can be calculated by:

$${\dot{m}}_{5c-6c}={\displaystyle \frac{{\dot{W}}_{WR-comp}}{|h_{5c}-h_{6c}|}}$$

(6)

2.3. Systems-Level Fluid Equilibrium and Optimization Model

In order to model the system as a whole, an object-oriented program (OOP) algorithm was developed. Each subsystem is modeled as an independent object, allowing the application of different constraints on the propulsion system for robust iteration and optimization. These object classes were established as either inheriting or being composed of other classes. For example, all the engine sub-components that contain some sort of gas flow are given the thermochemical qualities of a “gas class” to determine work processes. Adjacent components were interfaced through shared up- or down-stream values of fluid stations, and thermodynamic properties were calculated using the NASA chemical equilibrium and applications (CEA).

CEA is a thermodynamic database program developed at NASA Glenn that uses ideal gas thermodynamic properties of individual species and minimizes the Gibbs energy of thermodynamic states specified by the user [26,27]. Minimization occurs through the iteration of species quantities using a Newton–Raphson method based on an original guess of molar ratios for the given fluid(s). This program was incorporated into the OOP WREN model through a MATLAB R2024a wrapper module (CEAM 1.3) [51]. Inputs and outputs from system components were processed through a code object that called upon the module while keeping track of the current species and thermodynamic states. These states were saved as individual properties within the objects to track the progression of states throughout the NTP and CBC subsystems.

An optimization framework is introduced, which iterates and refines on input arguments to the OOP framework. This is done through a hybrid global search and local refinement approach, in which an initial population of candidate designs is sampled randomly using Monte-Carlo sampling across the allowable design space. Random sampling was performed using a Mersenne Twister pseudorandom-number generator, with a nominal seed of 1 to ensure reproducibility. The highest-performing candidates are then selected as starting points for local refinement using a Nelder–Mead simplex method [52]. Bounds on the design variables are enforced through a logistic variable transformation, while constraint violations are incorporated into the objective through quadratic penalty terms. This allows the optimizer to explore a broad range of feasible and near-feasible designs before converging toward configurations that satisfy the encoded constraints. Apart from constraint violations, the model scored the systems on a schedule of minimum mass and/or maximum ${\mathrm{I}}_{sp}$, depending on parametric analysis, and a balanced drive train. For this work, an initial population of 15,000 designs was sampled, of which the top 50 were chosen for refinement.

2.4. Model Assumptions and Constraints

2.4.1. Full Engine Architecture

The generalized concept of the full WREN NTP-only system is illustrated in Figure 8. In order to provide the NTP WR with the required supply of pressurized driver gas needed to compress the motive gas, a closed Brayton cycle (CBC) coupled to a second WR was proposed [34]. The Brayton-topping wave rotor (BWR) is intended to both constrain turbomachinery size and improve CBC thermal efficiency. WREN also incorporates large radiators to reject the CBC waste heat. Accordingly, a key objective of this work is to justify radiator sizing by quantifying the extent to which CBC coupling enhances NTP and NTP-A performance.

Through diversion piping of the working fluids and alternator actuation via the drive shaft, the CBC can also provide substantial electrical power for an NEP mode after completion of the NTP burn. This bimodal architecture increases the average mission profile ${\mathrm{I}}_{sp}$ and enables faster translunar trajectories. The novelty of this approach is twofold: (i) CBC power conversion has not previously been considered for NTP superheating through WR coupling, and (ii) both NTP and NEP capabilities are enabled through a shared, localized power-conversion engine. This contrasts with prior hybrid transit concepts such as the NEP-CP Hybrid concept vehicle 1.2 [2], which employs separate, dedicated engines and power systems. This work focuses on the implications of alternative propellants for WREN operating in NTP mode only; therefore, engine sizing estimates exclude NEP-specific hardware.

A conservative design approach for component masses and WR performance is assumed to ensure the system remains feasible under worst-case conditions, avoids performance shortfalls caused by underestimated weight, prevents cascading redesigns, and provides safety margins that can be reduced later as the system becomes better understood. This includes the decision to model two separate solid cores instead of a unified core that heats both the motive and driver gases simultaneously. The second Brayton reactor core, apart from the NTP reactor core, supports CBC power generation.

Aside from what is discussed here, the reader is referred to the authors past work [25,34,35,36] for additional model details.

2.4.2. Subsystem Sizing

Subsystem masses are estimated using a specific-mass framework described in the authors’ previous WREN modeling work, where specific mass ($\alpha$) represents the mass required to convert, exchange, or process a unit of power. For example, the turbine and compressors are sized to an $\alpha$ of 0.10 and 0.15 kg/kW, respectively, based on the average $\alpha$ of space nuclear power systems as reported by Walter [53]. This work was written in 1987; therefore, it is assumed to be an overestimation of turbomachinery mass by modern material standards.

The reactor radiation shielding must be sized in such a way to limit dosage to the crew and payload. Past work done by Sager [54] details the requirements of scaling parameters ($\alpha$), which are based on the maximum power output of the reactor cores to the minimum core radiation dosage to astronauts. Sager’s model assumes a maximum dosage of 0.05 Sv for a mission; instead, this shield model assumes no greater than 0.02 Sv to cover a broad range of possible missions ($\alpha \approx 8$ kg/MW). For the reactor cores, the $\alpha$ of low power NTP designs was assumed in order to attain a similarly conservative mass estimate ($\alpha \approx 4.5$ kg/MW) [55,56].

Exceptions to this mass framework include the radiators and WRs. The WRs are assumed to be constructed of a high-temperature carbon-carbon composite with a density of $\rho \approx 1800$ kg/m³ to handle the large thermal loads during operation. Due to the WR’s simple design, it would add little additional mass to a power conversion system. The power requirements to operate the rotor are negligible as it does not play a direct role in driving the working fluid like a compressor [37,48] and would then require a relatively small electric motor or coupling to the main drive shaft. A cylinder of length and diameter comparable to the Cornell Wave Superheater was modeled [38], and thus it is assumed to be an overestimate in mass. Future computational work in port timing will be necessary to determine the exact dimensions of the rotor and rotational power requirements.

The radiator designs are derived from the NASA Compass study [2] thermal-control methodology and informed by multiple radiator concepts, including a study by Morrison [57] and a carbon-fiber fabric heat-pipe radiator concept reported by Tomboulian [58]. The design uses a pump loop cooling system of NaK due to the high heat loads. A range of expected heat-rejection loads ($P{W}_{reject}$) for NTP operation was approximated and used to generate three representative radiator designs. For each design, radiator area was calculated over the expected range of effective average radiator temperatures ($T_{\mathrm{avg}}$) using a NASA Compass-style radiative balance, and radiator mass was estimated from area-based scaling terms for the panels, structural components, valves, and deployment mechanism. The resulting radiator mass ($m_{\mathrm{rad}}$) and area ($A_{\mathrm{rad}}$) were found to fit well with power-law regression, where

$$m_{rad}=8.26815·{10}^{19}·T_{avg}^{-4.025}·P{W}_{reject}$$

(7)

$$A_{rad}=2.756·{10}^{19}·T_{avg}^{-4.024}·P{W}_{reject}$$

(8)

2.4.3. Engine Cycle

A single WREN engine with an individual nozzle is assumed for all thrust classes, with baseline and comparative results based on the 25-klb_f (111.21 kN) class. Although a dual-CBC WREN cycle could improve thermal efficiency and redundancy [59], only one engine cycle is modeled for simplicity. Nozzle and skirt-extension masses are assumed negligible, although future models may need to account for them based on outlet-flow conditions and cooling requirements.

Helium (He) is used as the CBC driver fluid for WREN NTP-A because of its high sound speed, chemical inertness, and established use in space reactors, as discussed in Section 1.3. While H₂ has a slightly higher sound speed compared to He at the range of conditions considered, He will produce minimal erosion of the Brayton reactor. The only exception to this is the H₂ propellant WREN system, which will continue to use an H₂ driver so that the sound speed is equal to or above that of the propellant to facilitate useful compression.

The radiator model Equations (7) and (8) retain the previous H₂–NaK heat-exchange model of the authors’ previous work. Future work will compare radiator performance using H₂, He, and their mixtures. An He–Xe mixture may be preferable for radiator operation because a 0.75:1 He molar ratio can produce an exceptionally low Prandtl number [60], but its lower sound speed would be detrimental to the WR driver gas.

The separate Brayton and NTP cores are assigned outlet temperatures of 2850 K ($T_{5c}$ and $T_4$), corresponding to the conventional LH₂ NTP target of 900 s specific impulse [61]. The LH₂O and LCH₄ NTP-A cores are exceptions [62], as described in Section 2.5.1. The CBC turbine inlet temperature ($T_{8c}$) is limited to 1650 K. This is the projected maximum turbine MOT from NASA Glenn based on the current state of SiC/SiC ceramic matrix composite material used in their HyTec turbines [63].

Cycle pressures are set from the respective propellant critical pressures after recuperative preheating and regenerative cooling. Referring to Figure 8, the NTP WR and Brayton WR total-pressure ratios ($p_{6c}/p_4$ and $p_{8c}/p_{1c}$) are limited to 1.63 [49]. Meanwhile, their compression ratios ($p_5/p_4$ and $p_{2c}/p_{1c}$) are constrained to 1.01–3.6. The upper bound represents an achievable “advanced” WR [47], while the lower bound is an arbitrary minimum that ensures compression. Turbomachinery pressure ratios are solved automatically to balance the cycle but are restricted to 1.01–10 to avoid poor convergence. All non-turbomachine components are assigned a 2% pressure loss, based on the results of other Brayton space reactor studies [42].

The nominal radiator-area limit is 2500 m², as specified for NASA Compass NEP-CCP concept vehicle 1.2 [2]. This conservative area can fit within the SLS 8.4 m fairing with minimal folding and actuator mass. It is assumed that a larger radiator, up to a factor of 4 (≤10,000 m²), is justified if the transit time and other system masses, including propellant needs, could be significantly reduced. Effective radiator-equivalent temperature is limited to 600 °C (873.15 K), following Tomboulian’s carbon-fiber-fin radiator work [58].

For the optimization model, ${\mathrm{I}}_{sp}$ is maximized while mass is minimized. Net driveshaft power is minimized but kept slightly positive to retain a power-loss margin. A recuperator transfers heat from the NTP motive-gas line downstream of the tank turbopump, reducing the Brayton-cycle minimum temperature and constraining radiator size, as shown in Figure 8. Recuperator power exchange must approach zero within a few Watts, consistent with the current model fidelity.

2.5. Propellant Strategies

2.5.1. Delayed Decomposition

H₂O and CH₄ pose the greatest challenge for applicability to NTP-A [11,12,22,62]. Water at high temperatures will oxidize engine materials, and hydroxyl-assisted recession will exasperate erosion rates of the fuel elements. Methane thermally decomposes and nucleates into graphite, which can coat subsystem components and fuel element walls; note that CH₄ $M_W$ in Figure 4 has an inflection point between 3000 K and 4000 K, corresponding to the appearance and breakdown of graphite with increasing temperature.

The strategy of lower core temperature has already been studied at length for H₂O NTP-A [62], where the core temperature is commonly assigned to a maximum temperature of 2400 K to minimize erosion. Figure 4 demonstrates insignificant decomposition of H₂O at this temperature. CH₄, however, experiences pyrolosis at temperatures as low as 1100–1200 K without a catalyst [64]; below these temperatures, and the reaction rate is potentially low enough to facilitate its use in NTP-A over a constrained burn duration at a high flow rate. Considering a maximum reactor core of 1000 K, this would only supply a potential ∼320 s of ${\mathrm{I}}_{sp}$; this is below the ${\mathrm{I}}_{\rho }$ of Methalox CCP.

Shockwaves propagating through a fluid cause a nearly instantaneous rise in pressure, density, and temperature. This often triggers further decomposition beyond what is possible with thermochemical equilibrium. Heating from the NTP WR through unsteady energy exchange with a CBC could enable these alternatives to reach Table 1 ${\mathrm{I}}_{sp}$ targets without conductive heating that could drastically affect core life. This configuration, where ${\mathrm{H}}_2$ is produced through WR cracking of a high hydrogen molarity fluid, is also referred to as a Wave Reformer [44].

Furthermore, the presence of H₂ within the NTP reactor core prior to shock initiation may further enhance propellant cracking. Historical shock-tube experiments by Johnson [65] demonstrated that the addition of H₂ approximately doubled ammonia decomposition rates, increasing the equilibrium hydrogen fraction by ∼11% near 3000 K. This effect is consistent with the lower-enthalpy reaction pathway

$${\mathrm{NH}}_3+\mathrm{H}\to {\mathrm{NH}}_2+{\mathrm{H}}_2$$

(9)

which has an enthalpy of formation of 4.45 kcal/mol, significantly lower than the 108.52 kcal/mol required for the initial ammonia decomposition step [66]. Consequently, the WR may enhance $I_{sp}$ not only through compressive heating but also via non-equilibrium chemical decomposition. Equilibrium-based predictions from CEA are therefore likely to provide conservative estimates of H₂ species formation under shock-heating conditions. Future work is required to quantify the extent of propellant decomposition and subsequent recombination during expansion through the WR, nozzle, and into the exhaust plume.

For this model, the NTP core outlet is set to a maximum of 2400 K and 1000 K for H₂O and CH₄, respectively. Propellants with substantial improvements to their ${\mathrm{I}}_{sp}$ are modeled at lower core temperatures to assess the potential for longer NTP core life with WREN.

2.5.2. Storage Tanks

The storage state of each propellant will be based on the liquid density noted in Table 1 corresponding to their cryogenic temperatures at 1 atm (1.01325 bar) of pressure.

To calculate tank number to orbit for a given $\mathrm{\Delta }$V, or vice versa, an object was developed which takes into account propellant species, launcher vehicle, and published extraneous masses. In order to calculate the overall volume of propellant possible for a launcher vehicle fairing, the following equations for baseline tank mass by Akin [67] were used:

$$m_{L{H}_2,t}=9.09V+2.88{\left({\displaystyle \frac{V}{4\pi /3}}\right)}^{1/3}$$

(10)

$$m_{L{O}_2,t}=12.16V+1.123{\left({\displaystyle \frac{V}{4\pi /3}}\right)}^{1/3}$$

(11)

$$m_{A,t}=12.16V$$

(12)

where V is liquid volume. Equation (12) is the assumed tank mass for all other NTP-A propellants which do not incorporate any substantial thermal insulation. These equations were based on propellant tank regression data of various ground and spaceflight storage units of LH₂, LO₂, and RP-1, respectively. Insulation requirements of RP-1 are assumed equivalent to the NTP-A propellants. LO₂ is included to compare performance of the WREN to Hydrolox CP.

These equations are rewritten for the total mass to LEO. In the OOP model, the equations used are as follows:

$$\begin{array}{cc}\hfill m_{{\mathrm{LH}}_2,\mathrm{full}}=& \left(70.8+9.09\right)V+2.88{\left({\displaystyle \frac{3V}{4\pi }}\right)}^{1/3}+m_{\mathrm{ext}.}\hfill \end{array}$$

(13)

$$\begin{array}{cc}\hfill m_{{\mathrm{LH}}_2/{\mathrm{LO}}_2,\mathrm{full}}=& {\left[\left(70.8+9.09\right)V+2.88{\left({\displaystyle \frac{3V}{4\pi }}\right)}^{1/3}\right]}_{{\mathrm{LH}}_2}+\hfill \\ \hfill & {\left[\left(1141+12.16\right)V+1.123{\left({\displaystyle \frac{3V}{4\pi }}\right)}^{1/3}\right]}_{{\mathrm{LO}}_2}+m_{\mathrm{ext}.}\hfill \end{array}$$

(14)

$$m_{\mathrm{A},\mathrm{full}}=\rho V+12.16V+m_{\mathrm{ext}.}$$

(15)

where $\rho$ is the assigned storage density of the NTP-A propellant and $m_{\mathrm{ext}.}$ is the extraneous mass. Equation (14) combines Equations (10) and (11) for Hydrolox CP engines, assuming that the proper proportions of each propellant are launched in a single vehicle. For simplicity of calculation, it is assumed that the volumetric proportions of LH₂ to LOX is similar to the Space Shuttle; around 2.68:1 [68].

The extraneous mass, $m_{\mathrm{ext}.}$, includes the reaction control system (RCS) propulsion for rendezvous and docking, power systems, elements of navigation and control systems, cryogenic insulation, and structural hardware. For inline and drop tanks, $m_{\mathrm{ext}.}$ was estimated to be ∼13.5 t (metric tons) and ∼5.5 t, respectively. These values were extrapolated from the work of Joyner and Kokan [20] and Reynolds et al. [69] using LH₂ propellant. Inline mass includes ZBO insulation and heavy structural hardware, since those tanks are mission permanent, but both include some amount of insulation meant for LH₂. Additionally, recent progress in on-orbit satellite servicing will reduce launch mass requirements for future navigation and control systems [70,71]. This implies $m_{\mathrm{ext}.}$ may be oversized, particularly for NTP-A and CP propellants.

In contrast to LH₂, LH₂O tanks may require heat-exchange piping in order to deliver heat from the system so that the water remains liquid in space while stored at maximum $\rho$ vapor pressures. For now it is assumed that the LH₂O will be maintained at liquid temperature without additional plumbing, possibly by absorbing the heat that comes from the radiators. To the author’s knowledge, this aspect of LH₂O storage as an NTP-A propellant has not been explored.

2.5.3. Launch Vehicles

Two superheavy lift vehicles are used in the analysis of this work: the Blue Origin New Glenn 9 × 4 (NG) and the SpaceX Starship (SS). StarShip has the highest maximum payload of any commercial vehicle [15,72] and is intended to become fully reusable, thus it will carry all propellants within drop tanks for improved mass fractions and cost. The New Glenn 9 × 4 is used for inline tanks since it is only partially reusable, but it intends to provide a large shroud with a ∼8.7 m wide meter fairing [73], which can accommodate the added hardware and relieve the mass difficulties of large aspect ratio tank capsules.

Besides LH₂, the other NTP-A propellants do not require excessive measures for ZBO. However, for vehicle structure and long-term storage purposes, all launch schedules will include two inline tanks leading, similar to Figure 2 Copernicus reference vehicle. This then allows the assumption of insignificant losses to LH₂. The model will not include a dedicted vehicle core stage, as it is not known what percent of the fairing volume the WREN engine will fill, especially taking into consideration the Brayton power conversion subsystem. By extension the traditional LH₂ NTP systems will only use the inline and drop tanks as well to compare performance with WREN.

Using what is known about the extraneous tank masses [20,69], the mass and volume limits of the Starship and New Glenn fairing shroud, and implementing Equations (10)–(15),

Table 2. Approximate launcher vehicle mass and stage main propellant mass fraction.

Propellant	Tank-Launcher	Mass to LEO (t)	Mass Fraction	Tank Shape
LH2	Inline-NG	61.4	0.692	Capsule
	Drop-SS	77.4	0.824	Capsule
LNH3	Inline-NG	70	0.793	Sphere
	Drop-SS	100	0.929	Sphere
LCH4	Inline-NG	70	0.785	Sphere
	Drop-SS	100	0.919	Sphere
LH2O	Inline-NG	70	0.794	Sphere
	Drop-SS	100	0.934	Sphere
Hydrolox	Inline-NG	70	0.787	Capsule
	Drop-SS	100	0.921	Capsule

outlines the approximate mass to LEO for each launcher and the calculated stage propellant mass ratio for each launcher by propellant type.

2.6. Performance Comparison

The WREN system performance will be compared to traditional NTP and NTP-A engines derived from the 25-klb_f (111.21 kN) “Peewee” class engines of the Rover program [19]. These engines were considered sufficient unit sizes by NASA for the Mars Design Reference Architecture (DRA) 5.0 study. For CCP, a 25-klb_f RL-10 Hydrolox engine with active nozzle extension was used for comparison [74].

At high reactor core power, the mass for an NTP-A engine may be substantially larger than NTP for equivalent power output and thrust. Modeling efforts by Nikitaeva and Thomas [12,22] have substantially matured NTP-A technology. Their work has produced refined and validated model estimates of engine size and performance for NH₃ and H₂O base systems, which includes various forms of pressure and momentum loss effects along with direct losses due to the nozzle efficiency and associated expansion model. They however do not explicitly model propellant dissociation; instead, a weighted average of $\gamma$ is used during the nozzle expansion process to approximate changes in the thermodynamic state. Their NTP-A modeling work was chosen for comparison to WREN due to the availability of validated engine mass data at equivalent operating conditions as those assumed in this work, while the resultant $I_{sp}$ of WREN will not assume some of the same performance effects as Nikitaeva and Thomas (particularly nozzle efficiency losses and associated expansion model), the WREN cycle assumes an equilibrium model that is frozen at the nozzle throat, and which has already been established to be conservative relative to the nonequilbrium of WR shock heating. Again, future work discussed in Section 2.5.1 will be required, along with a coupled finite-rate chemistry CFD as part of a detailed nozzle design to optimize $I_{sp}$ performance.

The comparison engine specifications are shown in

Table 3. Specifications of engines being compared to WREN.

Class	NTP H2	NTP-A NH3	NTP-A H2O	CP RL-10
Engine Cycle	Expander	Expander	Expander	Closed Expander
Core Exit Temp., K	2850	2850	2400	3350
${\mathrm{I}}_{sp}$, s	900	371.0	316.9	465.5
$I_{\rho }$, $\times {10}^3$$\mathrm{kg}·\mathrm{s}{\mathrm{m}}^{-3}$	63.7	252	317	450
Engine mass (t)	2.55	4.94	4.98	0.301
Source	[3]	[22]	[22]	[74]

, including their resultant maximum $I_{sp}$ for 25 klb_f of thrust. There is no existing model for CH₄ NTP-A.

To provide a baseline for performance, every vehicle is equipped with a 45 t payload. This is the approximate mass of a manned deep space habitat which can support a crew of 6 with supplies for 1000 days [34]. Based on mission analysis and radiation requirements of the NASA Compass report [2], this mass represents items such as emergency supplies, ground infrastructure, and scientific payloads, and is designed for both deep space radiation and the expected additional shielding required above the main reactor shield. For this analysis, it is treated as a generic and static payload.

Using the values in Table 2, $\mathrm{\Delta }$V can be approximated as a function of tank launch count to LEO by modifying Equation (1). For every launch of an inline tank (n) of full mass $m_i$ and mass fraction $R_i$, and drop tank (k) of full mass $m_d$ and mass fraction $R_d$,

$$\begin{array}{c}\hfill \mathrm{\Delta }V=-I_{sp}·g\left[ln{\displaystyle \frac{m_v+n·m_i(1-R_i)}{m_v+n·m_i}}+{\displaystyle \sum _{i=1}^k}ln{\displaystyle \frac{m_v+n·m_i+m_d(k-R_d)}{m_v+n·m_i+k·m_d}}\right]\end{array}$$

(16)

where $m_v$ is the mass of the engine and payload. This will be the primary function which compares these systems.

3. Results

3.1. Baseline Vehicle Performance

To assess sensitivity to the stochastic initialization and substantiate that results are not accidental outputs of the model, the optimization conducted for spacecraft model design closure was repeated using five independent pseudo-random number seeds (Mersenne Twister seeds 1–5) for each propellant. All optimization parameters, bounds, and constraints were held constant for a given propellant model. Although some optimized design variables exhibited seed-dependent variation, the primary performance metric remained highly consistent across independent optimizations. The propellant model with the largest variability, NH₃, exhibited a coefficient of variation of 0.15% and a relative range of 0.32% for ${\mathrm{I}}_{sp}$, while engine mass exhibited a coefficient of variation of 3.15%. The variation in individual design variables suggests the presence of multiple near-equivalent configurations within the design space rather than strong sensitivity of system-level performance to the initial Monte Carlo population. The optimized NH₃ design variables and subsequent objective results are shown in

Table 4. Optimized design variable and objective results of 25-klb_f (111.21 kN) class NH₃ WREN model across five independent pseudo-random number seeds. Please refer to Figure 8 for station number variables.

Design Variable/Objective	Seed 1	Seed 2	Seed 3	Seed 4	Seed 5
NTP WR, $p_5/p_4$	3.54	3.58	3.52	3.59	3.52
Brayton WR, $p_{2c}/p_{1c}$	3.55	1.73	3.40	3.50	3.56
Compressor 1, $p_{1c}/p_{0c}$	1.21	1.81	1.86	1.53	1.31
Radiator 2.1, $T_{10c}$, K	450.8	541.1	612.7	514.2	448.3
Radiator 2.2, $T_{3c}$, K	646.7	373.0	488.7	579.5	653.3
Vacuum ${\mathrm{I}}_{sp}$, s	663.6	664.7	663.0	665.0	662.9
Engine Mass, t	46.2	48.7	49.3	47.3	45.9

.

Table 5. Theoretical performance of 25-klb_f (111.21 kN) class WREN NTP and NTP-A systems.

Parameter	NH3	H2O	CH4	H2
Exit Temperature, K	3845	2978	1192	3561
Vacuum ${\mathrm{I}}_{sp}$, s	663.6	469.6	360.1	1424
$I_{\rho }$, $\times {10}^3$$\mathrm{kg}·\mathrm{s}{\mathrm{m}}^{-3}$	451.2	469.6	152.3	100.8
Engine Mass, t	46.2	28.6	28.4	90.9
Engine T/W	0.25	0.40	0.40	0.12
Radiator Area, m2	8333	2901	7239	9989
Effective Equivalent Radiator Temp., K	791.2	844.0	686.1	737.4
Motive gas $\dot{m},\mathrm{kg}/\mathrm{s}$	17.1	24.1	31.5	7.96
Driver gas $\dot{m},\mathrm{kg}/\mathrm{s}$	26.4	13.8	12.0	13.3
Flow Rate Ratio	1.55	0.57	0.38	1.67
NTP WR Compression Ratio	3.54	3.59	3.04	2.93
NTP Core Power, ${\mathrm{MW}}_{th}$	222.6	135.6	72.5	324.3
Brayton Core Power ${\mathrm{MW}}_{th}$	368.9	177.4	203.6	583.8
Thrust Power, MW	361.9	256.1	196.3	776.6

shows the resultant nominal performance parameters of interest for each WREN propellant based on system constraints and assumptions. What is immediately apparent is the ${\mathrm{I}}_{sp}$ of the WREN NH₃ and H₂O systems have surpassed the necessary value to compete with RL-10 Hydrolox ${\mathrm{I}}_{\rho }$ (see Table 1). H₂ is nearly 5× lower than what would be necessary to compete volumetrically with hydrolox, but it has surpassed the 1400 s maximum limit estimate of liquid-phase reactors.

Despite an optimized NTP WR compression ratio above 3, CH₄ is still substantially below Methalox ${\mathrm{I}}_{\rho }$. In addition to this relatively poor performance, losses from graphite-coated surfaces in and around the WR is beyond the modeling scope of this work. Thus this alternative will not be investigated further beyond the baseline.

Of the propellants considered, NH₃ and H₂ approach their maximum radiator area limit. Since the radiators compose such a significant portion of the WRENs mass, up to ∼30% [34], this produces the lowest dry engine T/W, with H₂ being considerably heavier as a result of its H₂ driver fluid and large driver to motive fluid flow ratio across the NTP WR. However, NH₃ is capable of utilizing the near maximum WR compression ratio limit to attain an ${\mathrm{I}}_{sp}$ of ∼664 s. Meanwhile, H₂O attains the hottest effective equivalent radiator temperature, enabling a considerably significant improvement in T/W compared with the other propellants. Due to preferences in performance as a WREN propellant alternative, NH₃ is given more focus across results. However, some important considerations are made for H₂O due to its higher thrust margin.

3.2. Parametric Analysis

Figure 9, Figure 10, Figure 11 and Figure 12 show the results of the parametric analysis using the optimization program of the WREN cycle OOP model for NH₃ and H₂O. This includes changes to thrust in Figure 9 and Figure 10, ${\mathrm{I}}_{sp}$ in Figure 11, and NTP core exit temperature in Figure 12. For the two latter analyses, the thrust remains fixed at the 25-klb_f (111.21 kN) reference thrust. Figures which show the average optimized performance results also feature 5th to 95th percentile interval bars which show the distribution of converged results.

Figure 9 is the ideal equilibrium-theory based ${\mathrm{I}}_{sp}$ found by the optimizer for the NH₃ WREN at 2850 K NTP core exit temperature, thus it does not include the 5th to 95th percentile interval bars. Since an objective of the optimizer is to maximize ${\mathrm{I}}_{sp}$, this figure serves to demonstrate model behavior and the upper bounds of ${\mathrm{I}}_{sp}$ without significant bias to other factors such as total mass.

A fifth-order polynomial trendline is overlaid with Figure 9 results. The ${\mathrm{I}}_{sp}$ plateaus around a value of 663–665 s below ∼23 klb_f (102.31 kN). Above this thrust and ${\mathrm{I}}_{sp}$ diminishes continuously until the optimizer was unable to find a solution; stopping at a maximum of 40 klb_f (177.93 kN). Hence, this range was limited to between 15 klb_f (66.72 kN), to check if the values remain constant below 23 klb_f at reasonable computational cost, and 40 klb_f.

Figure 10 shows the dry mass of the WREN NH₃ and H₂O engines, in metric tons, as it relates to thrust. Please note to convert klb_f of thrust to kN, the value is simply multiplied by ∼4.448 kN/klb_f. The range of optimal solutions for NH₃ decreases with increasing thrust, coinciding with the lack of convergent solutions at these higher regimes. While the H₂O WREN design points could be further extended to higher levels of thrust, it is clear that the H₂O WREN has a much larger potential thrust ceiling. In their dissertation, Nikitaeva [62] determined that a conventional H₂O NTP-A expander cycle architecture operating at a core exit temperature of 2400 K limited thrust to ∼48 klb_f (213.5 kN) due to a combination of factors including designed reactor power limit, core cladding erosion rates, fixed nozzle design, and turbopump complexity. For this reason, the H₂O WREN model was modeled up to a thrust of 50 klb_f (222.4 kN). Results of NH₃ WREN thrust; however, fall below the maximum potential thrust of NTP-A NH₃ (∼42.5 klb_f or 189.0 kN). Future work is required to understand the factors which will limit the H₂O WREN, and whether it may be optimized for higher values.

Setting the optimizer to solve WREN with a fixed ${\mathrm{I}}_{sp}$ and thrust, the radiator area, which is effectively the main driver of system mass, is calculated in Figure 11 as a function of ${\mathrm{I}}_{sp}$. Due to the thermodynamic qualities of H₂O in CEA, the WR compression ratio was constrained to a high value (≳3). Numbers lower than 3 tended to fail, with cycle balance producing pressures and temperatures that would cause a gas to liquid phase change, thus the H₂O nuclear core outlet temperature was allowed to float for this case, but was maximized up to 2400 K if possible. NH₃ ${\mathrm{I}}_{sp}$ tended to vary with WR compression ratio alone, where the lower ${\mathrm{I}}_{sp}$ bound for WREN NH₃ correlated with the minimum allowed 1.01 compression ratio. Note the limited design variation of radiator area at this compression and at the upper bound of radiator area.

As mentioned previously, core life can be drastically extended by decreasing the core exit temperature. Figure 12 shows the resultant ${\mathrm{I}}_{sp}$ of the H₂O and NH₃ WREN system as the nuclear core exit temperature is decreased from its maximum down to 2000 K. Thrust was constrained at 25 klb_f. System mass and radiator size were found to not correlate strongly with reactor outlet temperature when maximizing ${\mathrm{I}}_{sp}$ is sought, as is demonstrated by the extremely wide result intervals shown in Figure 13.

Even after decreasing the core to 2000 K, the ${\mathrm{I}}_{sp}$ of either propellant is still 50–150 s higher than their respective NTP-A counterparts. This has considerable implications to the use of WREN as a high efficiency, long-term space tug system that may be supported by ISRU architecutre.

3.3. System Performance Comparison

Figure 14 shows the resultant Equation (16) $\mathrm{\Delta }$V of each tank-engine system from Table 2, Table 3 and Table 5 as a function of tank launches up to 15. Please note the first two propellant launches are of inline tanks and the rest are drop tanks.

Among these systems, the H₂ WREN, H₂ NTP, and NH₃ WREN vehicles were the only three to exceed a $\mathrm{\Delta }$V of 15 km/s within 15 launches. These are also the only systems which surpass hydrolox across $\mathrm{\Delta }$V performance. After about 5 tank launches, WREN LNH₃ maintains a gap of ∼3.75 km/s below LH₂ NTP for every tank to orbit.

An important question regarding the use of WREN is whether the savings in propellant is worth the number of launches required to construct the radiators, assuming the 2500 m² radiator limitation and combined inline and drop tank strategy. To demonstrate this, the NH₃ WREN ${\mathrm{I}}_{sp}$ variation analysis is revisited. Using resultant ${\mathrm{I}}_{sp}$ of 535, 600, 625, and 664 s, of which the minimum and maximum of the set represent the approximate smallest and largest convergent models, the WREN NH₃ vehicle is compared with the conventional NH₃ NTP-A of Table 3. This comparison is made in terms of required tank and radiator launch count to orbit to achieve a specified $\mathrm{\Delta }$V.

Figure 15 shows the results of this analysis. Clearly, a large radiator acreage heavily constrains the tank launch count at high $\mathrm{\Delta }$V. Excluding the WREN engine and payload, the total number of launches to attain 12 km/s is reduced from 27 to only 13 total at the maximum WREN LNH₃ ${\mathrm{I}}_{sp}$ and 625 s system, of which only 9 launches are for propellant tanks; a third of the propellant required for NTP-A. This increases to an 80% reduction at 16 km/s, where NTP-A requires a total of 86 tanks not shown in Figure 15.

Opportunities for use of alternative propellant systems can be generalized by the mass fractions in which the rocket equation begins to favor the respective propellant over traditional NTP. LNH₃ can be stored at the same internal pressure as LH₂, thus both tanks will be constructed of the same strength to weight material. Assuming the engine and payload mass are negligible, that is to say the $\mathrm{\Delta }$V becomes so large that the system mass fraction approaches the mass fraction of the storage tanks to the propellant, i.e.,

$$R={\displaystyle \frac{m_v+m_{p,t}}{m_v+m_p+m_{p,t}}}\approx {\displaystyle \frac{m_{p,t}}{m_p+m_{p,t}}}$$

(17)

and each tank is at the same internal pressure, then there will be a notional crossover point in the rocket equation in which each propellant-engine system will have a higher $\mathrm{\Delta }$V ceiling without consideration to a particular arrangement of inline tanks, drop tanks, or payload.

Extending results of Figure 14 to an arbitrarily large number of tanks satisfies Equation (17) approximation, where H₂ NTP, NH₃ NTP-A, and NH₃ WREN approach an R of 0.177, 0.071, and 0.071, respectively; corresponding to their propellant types. The “cross-over” in terms of $\mathrm{\Delta }$V preference will then occur at the same R for both NH₃ systems with reference to H₂ NTP. However, due to the WREN NH₃ systems larger ${\mathrm{I}}_{sp}$, it will have a separate H₂ NTP R value for a greater $\mathrm{\Delta }$V ceiling.

Figure 16a provides the $\mathrm{\Delta }$V of the 25-klb_f H₂ NTP, NH₃ NTP-A, and WREN NH₃ systems simply as a function of R.

Traditional H₂ NTP ${\mathrm{I}}_{sp}$ is about 900 s, or 2.43 and 1.36 times the NH₃ NTP-A and NH₃ WREN, respectively. Therefore, the cross over for the respective systems occurs when the natural logarithm of their LNH₃ tank mass fractions is less than 2.43 and 1.36 times that of the LH₂ tank mass fraction, respectively [15]. Taking into account the solved mass fraction of each system, the two NH₃ system lines in Figure 16a can be shifted to correlate with the new cross-over R values, as shown in Figure 16b.

Here, the rocket equation favors both NH₃ vehicles at an H₂ NTP R value ≳ 0.34, corresponding to a $\mathrm{\Delta }$V favorability of ≲9.6 km/s. The improved ${\mathrm{I}}_{sp}$ of the WREN shifts this favorability to H₂ NTP R ≳ 0.14. This implies that the WREN NH₃ vehicle $\mathrm{\Delta }$V ceiling is favorable up to ∼17.2 km/s compared to traditional H₂ NTP for design conditions where the tank wet mass is the dominant mass on the vehicle.

4. Discussion

4.1. Interpretation

Within the assumptions of the present model, NH₃ and H₂O emerge as the most promising alternative WREN propellants, although they favor different applications. At the 25-klb_f (111.21 kN) reference thrust, NH₃ WREN attains an $I_{sp}$ of approximately 664 s, compared with approximately 470 s for H₂O WREN. The higher NH₃ performance is obtained at a near-maximum NTP WR compression ratio and requires a comparatively large driver-gas flow rate and radiator area. The H₂O system, in contrast, requires a similarly high WR compression ratio but operates with a lower driver-to-motive-gas flow-rate ratio and a smaller Brayton core thermal power. Consequently, its modeled engine mass is approximately 28.6 t, compared with 46.2 t for NH₃, and its radiator area is approximately 2901 m², compared with 8333 m² for NH₃. These results suggest that NH₃ is more attractive for long-duration, high-energy transit missions, while H₂O may be more appropriate for higher-thrust applications in which engine dry mass and radiator deployment are dominant constraints.

The thrust parametric results in Figure 9 and Figure 10 reinforce this distinction. The NH₃ WREN $I_{sp}$ plateaus near 663–665 s below approximately 23 klb_f (102.31 kN) and decreases steadily as thrust increases toward 40 klb_f (177.93 kN), beyond which the present optimizer did not identify feasible solutions. H₂O WREN exhibited a broader range of converged designs, enabling a higher thrust ceiling, which is consistent with current H₂O NTP-A studies [22].

These model behaviors are a result of the energy exchange requirements within the NTP WR and the constraints of radiator area. As motive gas flow rate (${\dot{m}}_{4-5}$) increases to match a higher NTP thrust, the CBC driver fluid mass flow rate (${\dot{m}}_{5c-6c}$) must also increase to ensure the work of compression and expansion are equal. This implies a larger required $P{W}_{reject}$, which is directly correlated with radiator size. More importantly, the specific heat capacity of NH₃ tends to be much higher than H₂O at NTP-A conditions [62], thus the compression work produced from expansion of the drive gas is much higher for a given thrust. This indicates the radiator needs to operate at an impractically low temperature compared with its available area to maintain CBC powertrain balance at sufficiently high thrust. Hence, the larger thrust availability of H₂O WREN in Figure 10 and the diminishing maximum $I_{sp}$ in Figure 9. At low thrust, by contrast, the NTP WR can use the full NTP compression ratio ($p_5/p_4$) since the radiators are below there area limit, resulting in the $I_{sp}$ plateau.

A principal advantage of the WREN architecture is that the maximum propellant temperature is produced downstream of the NTP core. Therefore, the reactor outlet temperature can be reduced without an equivalent reduction in nozzle-inlet temperature or $I_{sp}$. The parametric results in Figure 12 show that, even when the NH₃ and H₂O core outlet temperatures are reduced to 2000 K, the predicted $I_{sp}$ remains approximately 50–150 s higher than that of the corresponding conventional NTP-A systems [12]. This decoupling of reactor temperature from final propellant temperature provides performance benefits in both propellant utilization and potential core endurance. If the endurance trend shown in Figure 3 is considered qualitatively, reducing the core outlet temperature could potentially increase cumulative burn duration into the tens-ofhours regime. This would be particularly important for reusable space-tugs, vehicles requiring multiple departure burns, and bimodal systems expected to remain operational over several mission legs.

The $I\rho$ results provide a second important interpretation. Of the WREN alternative propellants, NH₃ and H₂O improve upon their respective conventional NTP-A counterparts sufficiently to become competitive with both methalox and hydrolox CCP on a volumetric basis. Optimization within the established cycle constraints and assumed WR limits produced $I\rho$ values of approximately $451.2\times {10}^3$ and $469.6\times {10}^3$ $\mathrm{kg}·\mathrm{s}{\mathrm{m}}^{-3}$ for NH₃ and H₂O, respectively. These values are nearly identical to that of the RL-10 hydrolox reference system. At a first-order level, this indicates that NH₃ and H₂O WREN can provide a similar total impulse per unit stored-fluid volume to hydrolox. Accordingly, the WREN systems can mitigate the large launch-fairing volume required to deliver a given quantity of impulse to orbit for conventional LH₂ NTP.

Equivalent $I_{\rho }$ does not; however, imply equivalent mission $\mathrm{\Delta }V$. The vehicle mass fraction must also account for tank structure, engine dry mass, and payload. Once the modeled tank mass fractions are included, H₂ WREN, H₂ NTP, and NH₃ WREN are the only systems considered that surpass hydrolox. The other systems require considerably more drop-tank launches to achieve a $\mathrm{\Delta }V$ of 15 km/s, making them comparatively poor candidates under the assumed launch architecture.

The launch-count comparison also shows that the large dry mass of the WREN engine does not necessarily eliminate its mission-level advantage. For an NH₃ mission requiring 12 km/s, the modeled launch count decreases from 27 tank launches for conventional NH₃ NTP-A to 9 launches for the highest-performing NH₃ WREN cases. At 16 km/s, the calculated reduction in tank launches approaches 80%. Thus, although the WREN radiator and power-conversion system impose a major initial dry-mass and launch penalty (2–6 launches), that penalty is quickly amortized as mission $\mathrm{\Delta }V$ and required propellant mass increase. At this fidelity of analysis; however, the maximum performing NH₃ WREN requires a similar number of total launches of tanks and radiators to its lower $I_{sp}$ variations at a moderate $\mathrm{\Delta }V$. Thus, careful consideration must be given to the size of the NTP WR compression ratio in terms of mass fraction.

For lower-$\mathrm{\Delta }V$ missions, the benefits are not nearly as clear. The present results do not establish that WREN is preferable to conventional NTP-A for routine cislunar transport, where the radiator and engine dry mass may dominate the relatively modest propellant requirement. This may apply best to H₂O WREN, where an apparent high T/W ceiling with a CCP-comparable $I_{sp}$ on a semi-permanent cislunar transport architecture can rapidly out-compete H₂O NTP-A. Addressing this gap in applications will require a higher-fidelity analysis within the lower-$\mathrm{\Delta }V$ design space, including repeated use, specific orbital maneuvers, payload delivery cadence, and the potential value of the CBC in an NEP or power-generation mode. A reusable tug completing many missions could distribute its initial dry-mass penalty across a large cumulative delivered mass, even if WREN is not optimal for a single isolated maneuver.

Translunar and interplanetary targets such as Mars appear more favorable for NTP-A propellants used through WREN propulsion because the reduced tankage and initial packaged volume become increasingly important as $\mathrm{\Delta }V$ rises. The NH₃ WREN system is especially promising in this regime. Water WREN may also retain value for missions in which water is already carried for life support, radiation shielding, thermal control, or ISRU feedstock. Such multifunctional use could improve its effective system-level mass fraction beyond that represented by the propulsion-only comparison in this work.

The generalized mass-fraction analysis further clarifies when NH₃ WREN becomes competitive with H₂ NTP. It is estimated that a combined RBO and ZBO H₂ tank vehicle will have an asymptotic mass fraction of approximately $R\gtrsim 0.177$. Under this assumption, the LNH₃ WREN vehicle has a comparatively higher $\mathrm{\Delta }V$ ceiling because it combines improved $I_{sp}$ with a lower limiting tank mass fraction at equivalent internal pressure. It is therefore a credible alternative to H₂ NTP for vehicles in which tank wet mass composes the majority of the initial vehicle mass. If only RBO storage is assumed; however, and the H₂ tank is constructed from the same class of material and operated at the same internal pressure as the LNH₃ tank, the H₂ mass fraction may be as low as $R\approx 0.035$ for a 7000-series aluminum design, according to Foulds et al. [15]. Under that optimistic short-duration storage assumption, a multi-launch, high-$\mathrm{\Delta }V$ mission becomes preferential to LH₂ NTP.

A realistic multi-launch, high-$\mathrm{\Delta }V$, long-duration mission would likely employ a combination of RBO and ZBO tanks. The effective LH₂ mass fraction would therefore lie somewhere between 0.035 and 0.177, depending on mission CONOPS and payload. The 25-klb_f NH₃ WREN shifts the crossover with H₂ NTP to an LH₂-vehicle mass fraction of approximately $R\gtrsim 0.14$, which lies within this realistic RBO–ZBO range. The corresponding idealized $\mathrm{\Delta }V$ ceiling is approximately 17.2 km/s under tank-dominated conditions. It can therefore be inferred that NH₃ WREN may provide a higher $\mathrm{\Delta }V$ ceiling than H₂ NTP for some long-duration missions whose H2 storage system approaches the heavier end of the RBO–ZBO mass-fraction range. This is not a universal advantage over LH₂; rather, it identifies the storage system penalty at which the density and storability of LNH₃ overcome the higher $I_{sp}$ of LH₂ NTP.

Additionally, the LNH₃ mass fraction at which the crossover occurs is equivalent for NH₃ WREN and conventional NH₃ NTP-A because both systems use the same propellant and nominal tank technology. The higher $I_{sp}$ of WREN instead changes the corresponding crossover mass fraction of the competing H₂ NTP vehicle. This distinction indicates that there is a margin of permissible WREN dry mass within the region favored by the rocket equation. Therefore, the larger WREN engine dry mass is not necessarily detrimental when competing with H₂. Nevertheless, this conclusion becomes weaker as payload and engine dry mass represent a larger fraction of the initial vehicle mass, as is the case for low-$\mathrm{\Delta }V$ missions.

4.2. Limitations and Future Research

The optimization program considered in this work, while capable of converging to reasonably consistent solutions, requires a larger number of independently obtained solutions to establish statistical confidence in the reported optima and feasibility boundaries. The present framework samples 15,000 initial designs and locally refines the 50 highest-performing candidates. Although this approach identifies repeated clusters of feasible solutions, it does not guarantee discovery of the global optimum in a highly constrained and potentially discontinuous design space. The average parametric results are noticeably variant from a trendline, particularly for propellants whose results are near the radiator constraints of the CBC powertrain. Future analyses should repeat the stochastic search with a larger number of random seeds, increase the initial population and number of refined candidates, and quantify the probability that additional sampling produces a materially better solution. Alternative global methods should also be compared with the present Monte-Carlo/Nelder–Mead method. A formal multi-objective treatment would better expose the Pareto trade among $I_{sp}$, thrust, radiator area, engine mass, core temperature, and WR compression ratio. Reporting a Pareto frontier would also avoid implying that one optimized design is universally preferred when different missions may assign substantially different value to different performance parameters.

The present study was conducted at a NASA Pre-Phase A, concept studies level [75]. A subsequent Phase A study should additionally propagate uncertainties in component performance, mass models, structural and thermal limits, and mission-level requirements through the OOP design space rather than treating these quantities solely as deterministic constraints. Sensitivity and uncertainty analyses will be used to identify which assumptions most strongly affect feasibility boundaries and whether the preferred design region remains robust as higher-fidelity WR, structural, radiator, and mission models are introduced.

The WREN model does not resolve the time-dependent shock and expansion-wave structure within the WR channels, finite channel width, leakage, boundary layers, EGR, or gas mixing. The assumed WR pressure ratios and efficiencies are informed by prior experiments, but their simultaneous realization at the temperatures, pressures, molecular weights, and mass-flow ratios required by WREN has not been demonstrated. The assumption of equivalent compression and expansion work within the WR control volume also requires validation for systems with unequal motive- and driver-gas mass-flow rates. Detailed one-dimensional wave-diagram calculations followed by multidimensional CFD are needed to determine WR dimensions, operation, thermal loading, and achievable compression efficiency for each propellant.

Thermochemical properties are presently calculated using CEA equilibrium states. This approach does not capture finite-rate shock chemistry, non-equilibrium cracking, species freezing during nozzle expansion, or recombination as the fluid exits the WR. The true performance could be higher than predicted if rapid shock heating increases the production of low-molecular-weight hydrogen species beyond equilibrium values. It could also be lower if dissociated species recombine before useful expansion or if chemical energy remains frozen in non-propulsive internal modes. Time-resolved chemical-kinetics calculations and shock-tube experiments are therefore required for NH₃, H₂O, and CH₄ at representative WREN pressure, temperature, and residence-time conditions.

Dynamic loading within and around the WR represents an additional structural and life-limiting consideration. Repeated pressure waves generate cyclic loads, while WR rotation introduces additional inertial loading; at the elevated operating temperatures considered here, the resulting alternating stresses may interact with thermally activated creep and fatigue mechanisms. The magnitude and frequency content of these loads, and their relationship to the natural frequencies of the rotor and surrounding spacecraft architecture must therefore be established before structural feasibility can be assessed. Future work should use time-resolved CFD to determine pressure-wave timing and amplitudes followed by coupled thermal and structural FEA to evaluate alternating stresses, material constraints, and additional rotor cooling requirements. WR geometry and rotational speed may also provide design freedom to separate dominant excitation frequencies from structural resonances, but this must be demonstrated for the WREN operating regime rather than assumed from existing WR applications. At the vehicle level, biological shielding requirements and the associated separation between the reactor and crewed elements can produce long trusses with low-frequency bending modes. Consequently, as a generic call-to-action for most NTP and NEP architectures, future vehicle-level analyses should include the coupled effects of reactor shielding, truss and radiator flexibility, turbomachinery excitation, and spacecraft maneuvering when establishing structural mass and feasibility.

Radiator mass and area represent a major fraction of WREN dry mass, but the present radiator model is based on fitted specific-mass relationships and an assumed NaK heat-transport loop. The model retains the authors earlier H₂–NaK heat-exchange treatment even though He is used as the CBC fluid for the alternative-propellant cases. Future work should compare He, H₂, He–Xe, and other mixtures. It was found that radiators approximately 4 times larger than current NASA designs provide a significant advantage in total mission architecture mass savings and launch elements. The feasibility of mass, deployment, thermal control, and structural behavior of radiator areas approaching 10,000 m² should be evaluated within the coupled vehicle-level structural and dynamic analyses described above.

Several engine component masses are estimated using historical specific-mass ($\alpha$) relationships. Although conservative assumptions were intentionally selected, the resulting masses remain uncertain because the WREN architecture combines power levels and operating temperatures outside the range of many reference systems. The nozzle, skirt extension, some plumbing, and electrical hardware are excluded or simplified. Conversely, use of two separate reactor cores and historical turbomachinery scaling may overestimate mass relative to an integrated modern design. A component-by-component mass model with explicit geometry is therefore needed to establish credible uncertainty bounds.

The tank and launch-count analysis also contains simplifying assumptions. This model applies fixed launcher payload and fairing limits, fixed inline and drop-tank extraneous masses, idealized tank shapes, negligible propellant losses, and a constant 45 t payload. It also assumes that the engine and payload can be assembled independently of the tank launches and that all launch vehicles achieve their nominal payload capability. Because a campaign containing tens of launches would be strongly affected by launch and assembly operational considerations, the reported launch counts should be interpreted as comparative indicators rather than complete mission plans.

The ideal rocket equation neglects gravity losses, steering losses, residual propellant, and the timing of drop-tank disposal. These effects may be especially important for the relatively low T/W of the H₂ and NH₃ WREN configurations. Alternatively, the higher T/W of H₂O WREN has the potential of circumventing non-impulsive maneuver losses. Future trajectory optimization should consider cislunar tugs, conjunction- and opposition-class Mars missions, abort requirements, drop-tank staging, and the possible combined use of NTP and NEP modes. This analysis is necessary to determine whether the higher ideal $\mathrm{\Delta }V$ translates into shorter trip time, greater payload, or fewer launches.

5. Conclusions

This study has demonstrated that wave-rotor-enhanced nuclear (WREN) propulsion could provide a viable pathway for using higher-density alternative propellants in solid-core NTP systems while overcoming much of the $I_{sp}$ penalties associated with their greater molecular weights. Incorporating NASA CEA thermochemistry into the WREN object-oriented systems model enabled the chemical decomposition and thermodynamic behavior of H₂, NH₃, H₂O, and CH₄ to be evaluated throughout the coupled NTP and closed Brayton cycles. For the 25-klb_f (111.21 kN) baseline systems, WREN produced vacuum $I_{sp}$ values of approximately 664 s for NH₃, 470 s for H₂O, 360 s for CH₄, and 1424 s for H₂. The corresponding density-impulse ($I\rho$) values for NH₃ and H₂O, respectively, were comparable to hydrolox chemical propulsion. Parametric analysis further showed that reducing the NH₃ and H₂O reactor-core outlet temperatures to 2000 K still produced an $I_{sp}$ approximately 50–150 s greater than their conventional NTP-A counterparts, indicating that WREN may simultaneously improve propellant efficiency and extend reactor-core life. When the engine results were incorporated into a simplified tank-launch and rocket-equation analysis, WREN NH₃ was one of only three systems considered to exceed 15 km/s within 15 tank launches. For a representative 12 km/s requirement, the highest-performing NH₃ WREN designs reduced the combined tank and radiator campaign from 27 launches for conventional NH₃ NTP-A to 13 launches, demonstrating that the fixed mass and deployment penalty of the WREN power-conversion system can be offset by propellant savings at sufficiently high mission $\mathrm{\Delta }V$.

Within model limitations, the present work demonstrates that WR superheating can fundamentally alter the trade between propellant performance and storage density. The results do not establish that WREN is preferable for every mission, but they identify a physically meaningful design region in which the fixed mass of the power-conversion and radiator system can be offset by reduced propellant tankage, improved core endurance, and potentially reusable bimodal capability. This region is sufficiently promising to justify continued component-level development and mission-specific evaluation.

The systems analysis and parametric studies identified radiator performance, WR thermal-fluid behavior, and preferred $\mathrm{\Delta }V$ regime as the principal areas requiring higher-fidelity investigation. Future research should include multidimensional CFD, finite-rate chemical-kinetics modeling, and conjugate heat-transfer analysis of the WR, nozzle, and radiators under representative NH₃ and H₂O operating conditions. Experimental studies are also required to assess fluid-surface interactions under repeated dynamic loading from shock-heated alternative propellants. At the system level, the optimization framework should be expanded through repeated global searches and multi-objective methods, while the comparative vehicle model should incorporate detailed tank geometry, boil-off and cryocooling requirements, finite-burn trajectories, radiator deployment, reusable operations, and mission-specific payload and CONOPS assumptions.

Overall, the present results identify NH₃ WREN as the most balanced alternative-propellant architecture considered. H₂O WREN provides a complementary design point with lower engine mass, smaller radiator area, and potentially greater thrust scalability, although its lower $I_{sp}$ limits its ultimate $\mathrm{\Delta }V$ ceiling. H₂ WREN retains the greatest specific impulse but incurs a substantial engine and radiator mass penalty, whereas CH₄ WREN does not achieve competitive density impulse and introduces unresolved graphite-deposition concerns. These findings emphasize that the preferred WREN propellant must be selected at the mission-architecture level rather than through isolated engine performance. By connecting WR pressure exchange, CBC power conversion, equilibrium thermochemistry, alternative-propellant storage, and launch-campaign analysis within a common systems framework, this work establishes a foundation for evaluating WREN-enabled NTP-A vehicles for reusable space-tugs, long-duration transportation systems, and high-$\mathrm{\Delta }V$ interplanetary missions.