In scramjet engines, burning in the supersonic stream must always cause relatively higher heat addition losses. It has been always a major concern to seek the ideal heat release of supersonic combustion to the smallest entropy increase, which corresponds to the performance limit of supersonic combustion. Many of the efforts to date have centered on parameterizing the heat release and then performing parameter optimizations. Inevitably, the parameterization will introduce high-dimensional problems due to the infinite degree of freedom of heat addition. In the present study, the problem of optimizing heat release is viewed from a perspective of the functional and calculus of variations. Different from the previous studies devoted to finding the optimal parameters in the finite-dimensional parameter space, the present study attempts to seek the ideal heat release of supersonic combustion in the infinite-dimensional function space. Mathematically, the optimization problem is a constrained maximization of the functional with differential equation constraints and fixed endpoints. Correspondingly, the method of optimal control and Lagrange multipliers is applied to solving the optimal solution of the functional, subject to the physical constraints. Solutions of the ideal heat release of supersonic combustion in both constant-area combustors and diverging combustors are provided.
Ideal Heat Release of Supersonic Combustion
Journal of Propulsion and Power ; 29 , 3 ; 621-627
2013-05-01
Article (Journal)
Electronic Resource
English
Ideal Heat Release of Supersonic Combustion
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