Uncertainty quantification in RANS of LOX-CH4 pintle injector

This work presents the numerical characterization under uncertainty of a pintle- injector liquid rocket engine thrust chamber, fueled with LOX-CH4, and operated at subcritical pressure. Being the design optimization the ultimate goal of this effort, the numerical characterization is carried out employing a Eulerian- Lagrangian Reynolds-averaged Navier Stokes equations approach within the OpenFOAM CFD toolbox. The numerical model of choice, as well as the rich variety of physical phenomena taking place in such a device, require the knowledge of a large number of model parameters, many of which are challenging to be calibrated under the severe thermophysical conditions of interest. A possible way to overcome this lack of knowledge is to resort to the Uncertainty Quantification (UQ) framework to estimate the effects of model and parameter uncertainties on the solution accuracy. In particular, this research aims at propagating the uncertainty associated with the most probable diameter d0 which characterizes the injection Rosin-Rammler distribution for the liquid droplets, employing a Polynomial Chaos Expansion (PCE) representation of the uncertainty. The pintle configuration consists of a horizontal gaseous methane inflow and a vertical LOX spray injection. A set of RANS are conducted to generate the PCEs surrogate model for the estimation of the probability distribution of the quantities of interest, as well as the visualization of their credibility intervals. Lastly, to assess whether the uncertainty on d0 can overshadow the sensitivity to the pintle design, the same study is performed for two geometries, which differ in the so-called skip length, i.e., the distance between the annulus final section and the fuel-oxidizer impingement location. The results provided by the UQ analysis show how the temperature axial distribution in proximity of the pintle head and the extension of the core recirculation region, although affected by input parametric uncertainty, remain distinct for the two configurations. On the other hand, the confidence intervals associated with the radial temperature distribution in correspondence of the chamber region mainly occupied by evaporated LOX almost overlap. Provided these considerations, the present work still has to be intended as a preliminary feasibility study which paves the way for further investigations, aimed at including parametric uncertainty deriving from different models.