The research, conducted by H. R. Alimohammadi and H. Naseh of the Aerospace Research Institute in Tehran and F. Ommi of Tarbiat Modares University, focuses on the design optimization of a thrust chamber for the RD-161 propulsion system. The team set out with two objective functions at the center of the work: specific impulse, which measures how efficiently propellant is converted into thrust, and thrust-to-weight ratio, which captures how much acceleration an engine can deliver for the mass it adds to the vehicle. These two quantities are widely regarded as the defining figures of merit for liquid-propellant engines, and they frequently pull the design in opposite directions. A chamber shaped for maximum exhaust velocity may end up heavy; a lightweight design may sacrifice combustion efficiency.

To formalize the problem, the researchers identified seven input variables that govern the geometry and operating conditions of the chamber: the propellant consumption ratio, the combustion chamber pressure, the contraction area ratio between the chamber cross-section and the throat, the expansion pressure ratio across the nozzle, two geometric ratios describing the convergence of the chamber walls, and the contraction angle itself. Together, these parameters define a vast multidimensional design space in which even a modest number of candidate configurations quickly becomes computationally overwhelming. Evaluating every possible combination with high-fidelity physics simulations would require an impractical amount of time and computing resources, which is precisely the bottleneck the surrogate approach is designed to remove.

A surrogate model, sometimes called a metamodel, is essentially a fast mathematical approximation of a slower, more expensive simulation. Instead of running a full physics-based analysis for every candidate design, engineers run a strategically chosen subset of simulations and then fit a statistical model that interpolates the results across the entire design space. The quality of the surrogate depends critically on how those sample points are selected, which is where the Design of Experiments methodology comes in. In this study, the team carried out 46 different numerical experiments on the RD-161 propulsion system, varying the seven input parameters according to a structured experimental plan. Of those 46 runs, 39 produced results that were approved and found compatible with the problem constraints, forming the data foundation on which the response surfaces were built.

From that approved dataset, the researchers drew response surface curves and derived the corresponding objective function equations that link the seven input variables to the two performance outputs. Response surfaces are a powerful visualization and analysis tool because they reveal not just the optimum point but the entire topology of the design landscape: where performance rises steeply, where it plateaus, and where design variables interact in ways that a one-at-a-time sensitivity study would miss. The team then applied the Analysis of Variance, or ANOVA, to quantify how much of the variation in specific impulse and thrust-to-weight ratio could be attributed to each input factor and their combinations. According to the published results, the ANOVA demonstrated that the model is capable of predicting the responses adequately within the limits of the input parameters, a crucial validation step before any optimization can be trusted.

The precision of the fitted model was assessed against independent checks, and the authors report that the outputs showed high accuracy when interpreted and analyzed. With a validated surrogate in hand, the optimization itself could proceed far more efficiently than a brute-force sweep of the design space. The study notes that classical optimization techniques such as Genetic Algorithms and Sequential Quadratic Programming are commonly paired with surrogate models in this domain, allowing search algorithms to evaluate thousands of candidate configurations on the cheap statistical approximation while reserving full simulations for the most promising regions. This combination is what makes multidisciplinary design optimization of rocket engines practical on realistic engineering timescales.

The headline results are striking for a field where gains are often measured in fractions of a percent. Applying the methodology to optimize the thrust chamber, the researchers achieved a 2.8-second increase in specific impulse and an 8.5 percent increase in thrust-to-weight ratio for the chamber itself. When the objective functions were evaluated at the level of the complete engine, the improvements grew even larger: specific impulse rose by 3 seconds and the thrust-to-weight ratio climbed by 12 percent. In the conservative world of liquid-propellant engine design, where flight-proven hardware changes slowly and every design revision must survive rigorous qualification, improvements of this magnitude are considered considerably large, and they illustrate how much performance may be left on the table when chambers are designed by iteration and experience alone rather than systematic global optimization.

The work also sits within a broader movement in propulsion engineering toward simulation-driven, data-rich design. Earlier studies have applied genetic algorithms, particle swarm methods, and mass-based models to liquid rocket engine design problems, and the same research group has previously developed surrogate-based frameworks for optimizing the cooling systems and multidisciplinary robust design of liquid-propellant engines. Regenerative cooling channels, turbine design, and combustion modeling have all been drawn into multidisciplinary optimization frameworks in recent years, reflecting a recognition that the classical separation of engine components into isolated design silos leaves coupled performance gains undiscovered. The surrogate approach presented here extends that trajectory to one of the most consequential components in the entire engine.

What makes the surrogate methodology especially attractive for engineering practice is that it produces not just a single optimized point but an interpretable map of the design space, complete with objective function equations that other teams can reuse and adapt. The response surfaces can expose trade-off frontiers between specific impulse and mass, guiding engineers toward designs that best serve a particular mission profile rather than a generic ideal. The study also underscores the importance of constraint filtering: of the 46 experiments conducted, 7 fell outside the problem constraints and were excluded, a reminder that raw computational sweeps are only as useful as the feasibility boundaries that frame them. Careful constraint definition, the authors’ results suggest, is as essential to credible optimization as the statistical model itself.

For the wider aerospace community, the implications extend beyond the RD-161. As launch providers pursue reusable boosters and satellite operators demand ever more capable propulsion for orbit-raising and station-keeping, the pressure to extract maximum performance from minimum mass will only intensify. Surrogate-based design optimization offers a path to that performance without the prohibitive cost of exhaustive high-fidelity simulation, and the substantial gains reported in this study provide concrete evidence that the approach is ready to move from academic methodology into the engine design offices where the next generation of liquid-propellant engines will take shape. The datasets generated and analyzed in the study are available from the corresponding author on reasonable request, opening the door for other groups to build on the framework.

Subject of Research: Surrogate model development for the design optimization of a liquid-propellant rocket engine thrust chamber

Article Title: A surrogate model development for design optimization of thrust chamber

Article References: Alimohammadi, H. R., Naseh, H., & Ommi, F. (2026). A surrogate model development for design optimization of thrust chamber. Aerospace Systems. https://doi.org/10.1007/s42401-026-00548-0

Image Credits: AI Generated

DOI: 10.1007/s42401-026-00548-0

Keywords: surrogate model, thrust chamber, liquid-propellant engine, design optimization, specific impulse, thrust-to-weight ratio, response surface methodology, ANOVA, Design of Experiments, rocket propulsion, Aerospace Systems, RD-161