Hybrid rocket engine simulations reviewed as commercial spaceflight demand grows

Hybrid rocket engines, which burn a solid fuel against a liquid or gaseous oxidizer, have moved from curiosity to commercial reality, with more than 40 launches over the past two decades by companies and agencies including Virgin Galactic, HyImpulse, Gilmour Space Technologies and TiSPACE. A new systematic review published in Advances in Aerodynamics argues that the computational models used to design these engines remain far less mature than the flight hardware, and it maps out why reacting flow simulations of hybrid rockets are among the most intricate analyses in computational fluid dynamics. The review, led by Arvind Pallela and colleagues, examines the experimental configurations reported to date, compares them with their numerical counterparts, and identifies where the two diverge.

The core problem is structural. In a hybrid rocket engine, fuel and oxidizer sit in different states of matter and meet only during combustion. Heat from a pyrotechnic or torch igniter starts a surface reaction, and the resulting exothermic combustion sublimates the next layer of solid fuel, which then reacts with the gaseous or liquid oxidizer flowing in from the injectors. This layered regression means the fuel supply rate is not a controlled input, as it is in a liquid engine, but an emergent outcome of the flame’s heat feedback to the grain surface. Any interruption in oxidizer flow can extinguish the reaction entirely. Simulating that coupled gas-solid process, with turbulence, finite-rate chemistry and a receding boundary, pushes standard computational tools well beyond their comfort zone.

The review finds that existing numerical models have limited applicability to a complete hybrid rocket engine configuration. Most published simulations rely on the Reynolds-averaged Navier-Stokes framework, which filters out small-scale fluctuations to focus on mean flow. Within that family, the authors assess the trade-offs of the common closures. The Spalart-Allmaras one-equation model, originally developed for external aerodynamics, yields large errors in confined reacting flows and is not recommended for hybrid rocket combustion. The widely used k-epsilon and k-omega two-equation models are cheap and useful for preliminary two-dimensional analysis, but they omit many relevant mechanisms and are unreliable for full combustion predictions. The shear stress transport hybrid performs better near walls, while large eddy simulation and detached eddy simulation resolve more of the three-dimensional turbulence at a steep computational price.

Chemistry is the second bottleneck. Detailed reaction mechanisms covering hundreds of species are prohibitively expensive in three-dimensional simulations, so researchers use skeletal mechanisms with tens of species. The review highlights work in which a 94-species detailed mechanism for butadiene, a proxy for hydroxyl-terminated polybutadiene pyrolysis, was reduced to roughly 20 to 27 species while preserving key flame characteristics. A separate reduction of a 561-species n-heptane mechanism produced skeletal schemes with fewer than 20 species across various pressures. But the simplification carries a measurable cost: in one comparison, a 17-species model carried an error margin of around 10 percent, which fell to less than 1 percent when the mechanism was expanded to 39 species. Smaller schemes can underestimate radical concentrations such as H, OH and CH, mispredict ignition delays and alter flame temperature, radiative heat feedback and, ultimately, the fuel regression rate.

The experimental side of the review documents how researchers have tried to raise that regression rate, the defining performance metric of a hybrid engine. Paraffin wax decomposes roughly three to four times faster than HTPB but loses structural stability above 60 degrees Celsius, so no single fuel emerges as ideal. Composite grains attempt to combine strengths: a paraffin fuel embedded in an ABS substrate improved performance by 20 percent over plain paraffin, and doping HTPB with aluminium nanoparticles gave the best results among metallic additives in several studies. Grain geometry matters too. Multiport designs increase burning surface area without sacrificing fuel volume, a wagon-wheel port tested by NASA outperformed a star-shaped port while needing less oxidizer, and a helical fore section combined with a circular aft port improved regression rate by 40 percent.

Injector selection shows equally large effects. In comparative tests with paraffin and nitrous oxide, a vortex injector improved regression rate by 58 percent over a pressure swirl injector and 23 percent over a showerhead design, while a regular swirl injector achieved up to 2.4 times the regression rate of a plain axial injector. These differences arise because injectors do more than meter oxidizer; they induce the turbulence that homogenizes mixing in a system where fuel enters the port through its entire surface while oxidizer arrives through small injector orifices of one to two millimeters. The review notes that boundary conditions at the fuel inlet must be tuned to minimize particle diffusion and match experimental mass flow, a persistent source of error in two-dimensional models where conversion parameters are frequently mishandled.

On the numerical craft itself, the authors offer concrete guidance. Mesh density is critical because combustion flow patterns change on time scales as short as one hundred-thousandth of a second; for a second-order numerical scheme, roughly 24 mesh points per wavelength are recommended to keep phase error acceptable. Second-order schemes are the best compromise between accuracy and cost and are the most widely used for hybrid rocket combustion, while third-order schemes are more accurate but computationally expensive. Coupled solvers are preferred over segregated approaches that solve each variable independently. For ignition, the review explains that pyrotechnic ignition cannot currently be modeled with a chemical kinetic solver, since only one reaction set can be active at a time, so modelers instead patch an ideal fuel-oxidizer composition and ignite it with a 50 to 100 millijoule charge to emulate the igniter’s energy.

The dimensional trade-off is quantified in the review’s own demonstration simulations. Comparing ethylene fuel burned with nitrous oxide against 80 percent oxygen, the oxygen case produced a chamber pressure of 3.111 megapascals versus 3.001 megapascals for nitrous oxide, and a maximum exit velocity of 6680 meters per second versus 5397 meters per second. Fuel regression was more uniform with nitrous oxide, while the oxygen case showed sharper spatial variation in fuel mass fraction along the port, a three-dimensional instability signature that a two-dimensional model cannot reproduce. Yet the accuracy penalty of going two-dimensional is modest: in one validated comparison using large eddy simulation with finite-rate chemistry, the two-dimensional model deviated from experiment by less than 2.25 percent and the three-dimensional model by 1.8 percent, while costing roughly 10 to 15 times less computation.

Thermoacoustic instability receives its own treatment. Unlike liquid engines, where injector defects drive chugging and screeching, and solid motors, where cavity growth drives chuffing, hybrid engines have not shown disruptive pressure oscillations, but the review catalogs three instability mechanisms: latency in fuel vaporization and combustion, periodic accumulation and dissociation of char or melted surface layers, and acoustic coupling through pressure-sensitive regression rates. It proposes that boundary-condition choices, such as raising fuel-inlet turbulence intensity from 5 to 10 percent, can recreate these instabilities closer to experimental observations.

The review’s central recommendation is a staged workflow: begin with a cheap axisymmetric two-dimensional model to eliminate preliminary errors, refine the mesh in the areas it flags, compensate input factors such as hydraulic diameter, then evolve the validated setup into a three-dimensional large eddy simulation with boundary conditions matched to experiment. It also calls for customized chemical kinetic files stripped of unnecessary reactions, user-defined functions to capture solid-fuel decomposition and entrainment, and a two-scale validation protocol running from zero-dimensional ignition-delay checks through grid and time-step convergence against measured chamber pressure, regression rate and pressure spectra. With the space-tourism market valued at about 1.2 billion dollars in 2024 and projected to reach roughly 5.3 billion dollars by 2034, the authors argue that closing the gap between simulation and firing test is now an economic necessity as much as a scientific one.

Subject of Research: Computational modelling and reacting flow simulation of hybrid rocket engines

Article Title: A systematic review on computational modelling and reacting flow simulations of a hybrid rocket engine

Article References: Pallela, A., Thakur, A. K., Gupta, L. R., Kumar, R., & Singh, R. (2026). A systematic review on computational modelling and reacting flow simulations of a hybrid rocket engine. Advances in Aerodynamics, 8(1), Article 29. https://doi.org/10.1186/s42774-025-00237-0

Image Credits: AI Generated

DOI: 10.1186/s42774-025-00237-0

Keywords: hybrid rocket engine, computational fluid dynamics, reacting flow simulation, turbulence models, chemical kinetics, regression rate, large eddy simulation, combustion instability, space propulsion, mesh refinement, fuel grain geometry, space tourism