Locally variable turbulent Prandtl number considerations on the modeling of liquid rocket engines operating above the critical point
Leandro Magalhães  1, 2@  , Jorge Barata  1, 2@  , André Silva  1, 2, *@  
1 : LAETA\UBI_AEROG-Aeronautics and Astronautics Research Center
Edifício II das Engenharias, 6201-001 Covilhã -  Portugal
2 : University of Beira Interior [Portugal]
Rua Marquês D'Ávila e Bolama, 6201-001 Covilhã -  Portugal
* : Corresponding author

The general idea behind the present work is to study numerically the injection phenomena into a cryogenic liquid rocket engine, where injectant conditions are above the thermodynamic critical point, for a non-reactive case.

The singular behavior of thermodynamic and transport properties at and around the critical point makes this a most challenging task. While mass diffusivity, surface tension, and latent heat are zero at the critical point, isentropic compressibility, specific heat, and thermal conductivity tend to infinity. As a result, the distinction between liquid and solid phases disappears. Ultimately, the fluid has liquid-like density and gas-like properties, mass diffusion replaces vaporization as a governing parameter and it dominates over jet atomization. Henceforth, any model used incorporates as close as possible to reality, the variation of thermodynamic and transport properties.

An incompressible flow with density variations is simulated using Favre averages (FANS) with a locally variable turbulent Prandtl number, taking into account potential core, transition, and self-similar region. The use of a turbulence model with a variable turbulent Prandtl number arises from the ineffectiveness in predicting observed anisotropies in the thermal eddy diffusivity fields when this value is taken as a constant

Favre averaged conservation equations for mass, momentum, and energy are coupled with the k-ε two equation turbulent model and discretized following the third order upwind QUICK scheme. Stability and accuracy of the results are maintained through a careful selection of the parameters involved in the models. The use of the conservation equation for energy is justified as an indirect means to evaluate the thermal field.

Results are compared with experimental cases for validation purposes as well as LES computations for performance comparison and evaluation of the degree of model complexity needed to achieve satisfactory results.

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