Abstract
We propose an approach for the design of the subsonic part of plane and axisymmetric Laval nozzles for real gases. The proposed approach is based on the hodograph method and allows one to solve the inverse design problem directly. Real gas effects are taken into consideration using the chemical equilibrium model. We present nozzle contours computed with the proposed method for a stoichiometric methane-air mixture. Results confirm that real gas effects have a strong influence on the nozzle shape. The described method can be used in the design of nozzles for rocket engines and for high-enthalpy wind tunnels.
Highlights
Supersonic nozzles are used in jet engines and in high-enthalpy wind tunnels for acceleration of a hot gas mixture in order to generate uniform supersonic flow
In the particular case of a simple reaction, this estimate is reduced to τchem ≈ 1/kr ( T, p), where kr is the reaction rate constant. Τchem depends both on the reaction rate constants of all individual backward and forward reactions and the concentrations of each component. If this time is very small compared to characteristic time τV associated with gas motion, we can assume that at each point, the mixture is in local chemical equilibrium
The approach is based on the hodograph method, developed earlier for the potential flow of perfect gases, and the chemical equilibrium model
Summary
Supersonic nozzles are used in jet engines and in high-enthalpy wind tunnels for acceleration of a hot gas mixture in order to generate uniform supersonic flow. In contrast with the inverse problem, the direct problem is well posed and in most cases can be solved numerically In such optimization methods, the nozzle shape is parameterized using any convenient form (splines, Bezier curves), and the problem is formulated as a functional minimization problem for some objective function, for instance the norm of the deviation of output flow parameters from the desired ones [1,4,5]. In accordance with boundary layer theory, this property guarantees the separation of the free wall [8,9], which in turn justifies the applicability of the inviscid model Another advantage of this method is that it provides the opportunity to design nozzles with a plane sonic surface.
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