Simulated Acoustics of a Solid Fuel Ramjet

Abstract

In this paper, large eddy simulations (LES) are employed to study the cold flow inside a Solid Fueled Ramjet (SFRJ) using a finite element method with a Discontinuous Galerkin bases in the open-source multi-physics software SU2. The fuel-gas boundary conditions and heat release due to mixing are modeled using novel LES formulations obtained using integration by parts over the discontinuous Galerkin bases. To capture scalar variance, the Smagorisnki and wall-adapted subgrid stress models are implemented and investigated in two-dimensions. Spectral Proper Orthogonal Decomposition is used to analyze CFD results and determine acoustic modes in the ramjet. Numerical and experimental results are compared by examining peak acoustic frequencies. Simulations performed with a 2D axisymmetric domain are compared to those with a full 3D domain/ The large eddy simulation (LES) of cold flow inside a Solid Fueled Ramjet (SFRJ) shows two dominant acoustic modes with Strouhal numbers St\equiv f/f_0=3.18, which appear to be insensitive to the cavity configuration. The first peak corresponds to a longitudinal mode associated with the chamber's fundamental oscillations, characterized by the length scale L_c. The second mode exhibits radial fluctuations in the mixing chamber and is associated with the maximum chamber radius of the ramjet as its scaling length. The intermediate frequency range shows mixed modes with both radial and axial fluctuations, highlighting the impact of a slanted aft wall on the acoustics. Three-dimensional cold flow simulations predict weak non-symmetric (azimuthal) modes. Integration by parts over the discontinuous Galerkin bases is used to obtain novel LES formulations for fuel-gas boundary conditions and heat release due to mixing, with the Smagorinsky and wall-adapted subgrid stress models for scalar variance implemented and investigated in two dimensions. The CFD results are analyzed using Spectral Proper Orthogonal Decomposition to determine acoustic modes in the ramjet, and the peak acoustic frequencies are compared with experimental results. Simulations are performed with both a 2D axisymmetric and full 3D domain, and comparisons are made between them. The hot-flow simulations reveal that the presence of the cavity leads to a significant increase in the mean chamber pressure, which is consistent with the experimental findings and suggests that the cavity improves the flame-holding in solid-fuel ramjets. Analysis of the ramjet's acoustic modes demonstrates that low-frequency modes emerge in the cavity cases, consistent with the experimental data. These low-frequency modes are associated with the breathing of the recirculation region at the nozzle throat through the use of SPOD analysis. The perturbations are localized in the throat region due to Mach number pressure scaling, and they do not appear to have any impact on pressure fluctuations or combustion in the chamber. Additionally, the cavity supports the decrease of high-wave number harmonics of the ramjet chamber acoustic mode, along with the emergence of low-frequency vortical modes. These fluctuations are the result of the nonlinear amplification of the fundamental mode, which is amplified by the thermo-acoustic coupling.