The processes involved in the transmission of radiation in rocket engine exhaust plumes—such as thermo-chemical reactions, propellant combustion, turbulent flow, and gas molecule vibrational transitions—are extremely complex. These processes are characterized by high dimensionality, strong nonlinear behaviors, and intricate propagation mechanisms. The infrared radiation characteristics of the rocket engine plume are influenced by various parameters, including engine parameters (propellant type, propellant formulation, nozzle geometry, engine thrust), flight parameters (flight altitude, flight velocity), and detection parameters (detection angle, detection wavelength). It is crucial to perform a sensitivity analysis of these parameters to the infrared radiation signals emitted by rocket engines. Such an analysis will help classify and identify radiation signal layers from the plume and reverse-engineer of the engine formulation.

The sensitivity analysis is performed using a combination of polynomial chaos expansions (PCE) and Sobol' indices. The process begins by defining the input variables’ probability space, including their distribution types and sampling range. The sparse grid method is then employed to sample the input variables, with the resulting samples fed into the numerical simulation or experiment to generate the response values. These values, along with the input parameters, are used to solve for the PCE coefficients for variance decomposition. Finally, the main and total Sobol' indices are calculated using the total variance and local variance. The infrared radiation model for the rocket plume consists of three parts: 1) A CEA code calculates the engine nozzle exit parameters such as pressure, temperature, velocity, and gas components. 2) A k-ε two-equation turbulence model is used to compute the engine plume’s flow field, while a finite-rate chemical kinetic model with 10 reactions and 9 components describes the chemical nonequilibrium effects. 3) A single-line group (SLG) model with the Curtis-Godson approximation combined with the line-of-sight (LOS) method is applied to solve the radiative transfer equations.

The oxygen-fuel ratio primarily affects the nozzle exit temperature and gas components, while the combustion chamber pressure and nozzle expansion ratio significantly influence the nozzle exit pressure, velocity, density, and specific impulse (Fig. 6). The nozzle diameter solely affects the thrust. The combustion chamber pressure dominates the spectral radiation intensity in the 2?20 μm range at altitudes below 31 km (Fig. 8). In contrast, the oxygen-fuel ratio significantly influences spectral radiation intensity in the 1?2 μm shortwave and 8?15 μm ranges. As altitude increases, the main Sobol' indices S_i for the oxygen-fuel ratio progressively grow. The relationship between integrated radiation intensity and flight altitude (Fig. 9) is examined across four different bands: 2.7?3.0 μm, 4.2?4.5 μm, 3.7?4.8 μm, and 7.7?9.5 μm. At altitudes up to 35 km, the effects of the oxygen-fuel ratio and flight velocity on radiation are minimal, with combustion chamber pressure being the dominant factor. However, at altitudes above 55 km, the influence of the oxygen-fuel ratio and flight velocity increases significantly, surpassing the influence of the combustion chamber pressure. At low and medium altitudes, the mutual coupling between flight velocity, oxygen-fuel ratio, and combustion chamber pressure has a more significant effect on plume radiation intensity (Fig. 11). As altitude increases, the coupling strength of these input parameters approaches a value slightly above 1. At higher altitudes, the total and main Sobol' indices for the three parameters converge, indicating that individual parameter variations dominate the effect on plume radiation intensity.

We use the RD-180 liquid-oxygen/kerosene rocket engine exhaust plume as a reference to conduct a sensitivity analysis of the nozzle flow parameters and the plume’s infrared radiation signal. The analysis employs the polynomial chaos expansion method combined with Sobol' indices, using a sparse grid algorithm to minimize the number of samples required. Key conclusions are as follows: 1) The oxygen-fuel ratio primarily affects gas temperature and composition at the nozzle exit, while combustion chamber pressure influences the exit pressure and density. The nozzle expansion ratio affects the exit velocity and specific impulse, and the nozzle diameter only influences thrust. 2) A quantitative analysis of how operational parameters like oxygen-fuel ratio, combustion chamber pressure, and flight velocity affect spectral radiation intensity in the 1?20 μm wavelength range was conducted across altitudes of 11?61 km. Below 31 km, combustion chamber pressure is the dominant factor for radiation intensity in the 2?20 μm range. The oxygen-fuel ratio affects the spectral radiation intensity at a shorter wavelength range of 1?2 μm and affects the intensity more significantly as altitude increases, particularly in the 8?15 μm range. 3) The integral radiation intensity analysis across bands (2.7?3.0 μm, 4.2?4.5 μm, 3.7?4.8 μm, and 7.7?9.5 μm) shows that the effects of oxygen-fuel ratio and flight velocity are minimal below 35 km, where combustion chamber pressure dominates. Above 55 km, the influence of the oxygen-fuel ratio and flight velocity surpasses that of the combustion chamber pressure. Coupling effects between input parameters diminish with altitude, with individual variations becoming the dominant factor affecting plume radiation intensity.