Large-Eddy simulation of a reactive shear coaxial injector configuration

Abstract

Acquiring experimental data on hydrogen/oxygen coaxial elements under realistic conditions (super-critical pressure, liquid oxygen, high momentum flux ratios) is di cult and the injection of hydrogen at cryogenic temperature makes it even more complex. Not only are there additional cooling requirements but the same injector that provides realistic momentum/velocity ratios with room-temperature hydrogen will produce very small momentum/velocity ratios with a cryogenic hydrogen injection at the same flow rate. The reduced fuel injection temperature has been shown to change the combustion characteristics of the chamber, a phenomenon that is not fully understood yet. Here, a single-element liquid-oxygen gaseous-hydrogen shear-coaxial injector is studied with hydrogen injected at 50 K. Performing three-dimensional simulations of these type of configurations is very costly due to the dimensions of the chamber, the range of scales and also to the diversity of physical phenomena involved, such as complex thermodynamics at elevated pressure. This work investigates the use of two-dimensional models of the real three-dimensional configuration to perform parametric studies. The main advantage of the two-dimensional simulations compared to the full chamber is the reduction in computational cost. Although the flow features observed with the 2D model are not identical to the ones found in the three-dimensional case, some common characteristics can be reproduced. This paper highlights the similarity and di↵erences between two-dimensional and three-dimensional cases and identifies which issues can be studied using two-dimensional simulations. Nomenclature D= mass di↵usivity, m 2 · s 1 DLOX = diameter of the oxygen injector e T = total energy (internal + kinetic) per unit mass, J · kg 1 H sgs = subgrid enthalpy flux, J · m 2 h k = partial mass enthalpy of species k, J · kg 1 J k = mass di↵usion flux, kg · m 2 k sgs = turbulent kinetic energy, m 2 · s 2 NS = total number of species p = pressure, P a QIK = heat flux in the Irving-Kirkwood form, J · m 2 Q sgs k = subgrid enthalpy flux due to di↵usion of species k, J · m 2 QV = volumetric heat release, J/s/m 3 R = gas constant, J · kg 1 · K 1 T = temperature, K t = time, s u = velocity, m · s 1 V k = di↵usion velocity of species k, m · s 1 xi = Cartesian coordinate, m Y k = mass fraction of species k ⌦ sgs k = subgrid di↵usive flux of species k, kg · m 2 ⇢ = density, kg · m 3 sgs = subgrid heat flux, J · m 2 ⌧ij = stress tensor ⌧res = flow residence time, ṡ ! k = reaction rate of species k ⇤ Research engineer † Professor and AIAA Associate Fellow