Determination of thrust specific impulse losses occurring due to chemical non-equilibrium in aircraft power plant

Аuthors

Biruykov V. I.^*, Kochetkov Y. M.^**, Zenin E. S.

Keldysh Research Centre, 8, Onezhskaya str., Moscow, 125438, Russia

*e-mail: aviatex@mail.ru
**e-mail: swgeorgy@gmail.com

Abstract

As usual, thermodynamics and statistical mechanics deal with the problems, which suppose a system to be in equilibrium. Thus, the implemented mathematical tools could be rather conditional in cases of the systems with irreversible chemical reactions, as well as gas flows with thermodynamic non-equilibrium. Depending on how the system differs fr om equilibrium state, the great majority of practical solutions of combustion problems referenced in classical literature this condition is observed. In contrary cases, i. e. significant non-equilibrium in combustion in high-speed flows problems, and detonation in particular, the variation fr om stationary proliferation of chemical reaction fronts is unreasonably neglected. The traditional combustion in gas flows problem statement is unidimensional and based on consumption, momentum and energy conservation laws. Effects of viscosity force and thermal conduction are accounted for herewith. The basic difference of idealization consists in supposition of consistency and averaging of thermal capacitance value under constant pressure and volume. However, these values are dependent from chemical components composition and temperature in particular. Viscosity factor and other factors, characterizing transition are also functions of gas mixtures composition and temperature. As a consequence, gas constant and constitutive equation differ significantly from the idealized form. For complete analytical description of combustion gas dynamics, accounting for mutual diffusion of chemical components, regularities of components vanishing and occurring of new ones, as well as evaluation of total heat emission due to the completion of chemical reactions are required.

Systematic numerical studies of homogeneous and heterogeneous chemically non-equilibrium gas flows in aircraft power station nozzles are already conducted for many years. Various authors obtained results for combustion products of a number of fuels employed in aviation and rocketry. However, calculations of such flows do not satisfy modern practical requirements in all respects. Their main disadvantage consists in orientation on strictly defined set of substances and chemical reactions. To other shortcomings are neglecting the small concentrations of the reacting components, which compels to coarsen recombination mechanism. The variety of propulsion installations designs predetermines the presence of various units with non-equilibrium combustion in the area of lean and reach mixtures, such as gas generators; liquid rocket engines combustion chambers with complex mixture-formation systems; a number of pressurization systems and gas passages with gas flows; combustion chambers and afterburners of air-jet engines.

To a certain extent, determination of specific impulse losses in rocket solid engines due to chemical non-equilibrium with allowance for its effect on formation of Al₂O₃ and ALN condensed particles presents practical interest. The nowadays reality is the study of combustion detonation mode, wherein flows idealization is unjustified due to high conversion rates, and chemical reactions are principally non-equilibrium. The paper presents gas flows with non-equilibrium chemical reactions modeling in the form of conservation equations: uniformity of energy and impulses, wh ere impulses are presented as a product of gas mixtures density scalar and their velocity vector. As a result, in addition to the equation in Navier-Stokes form the authors obtained one more member, accounting for relaxation processes in thermodynamic system. Based on carried out analysis of the law of mass action the authors obtained interrelation between Gibbs thermodynamic potential with the equation member, accounting for non-equilibrium in gas flows with specified content in the form of normalized function. Based on it, the authors offer an engineering design procedure of a rocket engine specific thrust losses (aircraft power plant) caused by chemical non-equilibrium. The values of combustion products equilibrium and frozen compositions for the specified fuels are used for computation of adiabatic coefficients for lim it cases and normalized function. The paper presents graphs illustrating the computations for a wide spectrum of combustion products compositions. The examples of computation results of specific impulse for various cross sections of rocket engines nozzles.

The engineering method for calculation of the thrust specific impulse losses occurring due to chemical non-equilibrium allows estimate adequately their contribution to the common share of losses.

Keywords:

chemical non-equilibrium, specific impulse, thermodynamics basics, Gibbs potential

References

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