Analysis of Different Approaches to Modeling of the Nozzle Flows in the Near Continuum Regime

For investigating the steady irrotational isentropic flow of a perfect gas in two dimensions, the hodograph method is to determine in the first instance the position coordinates x, y and the stream function ψ as functions of velocity compoments, conveniently taken as q (the speed) and θ (direction angle). Inversion then gives ψ, q, θ as functions of x, y. The method has the great advantage that its field equations are linear, so that it is practicable to obtain exact solutions, and from any two solutions an infinity of others are obtainable by superposition. For problems of flow past fixed boundaries the linearity of the field equations is usually offset by non-linearity in the boundary conditions, but this objection does not arise in problems of transsonic nozzle design, where the rigid boundary is the end-point of the investigation.

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Thermoacoustic Shape Optimization of a Subsonic Nozzle

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.4025038 ◽

2013 ◽

Vol 135 (10) ◽

Cited By ~ 6

Author(s):

Alexis Giauque ◽

Maxime Huet ◽

Franck Clero ◽

Sébastien Ducruix ◽

Franck Richecoeur

Keyword(s):

Acoustic Emission ◽

Cross Section ◽

Source Term ◽

Combustion Noise ◽

Noise Emission ◽

Cross Section Area ◽

Section Area ◽

The Cross ◽

Nozzle Flows ◽

Subsonic Nozzle

Indirect combustion noise originates from the acceleration of nonuniform temperature or high vorticity regions when convected through a nozzle or a turbine. In a recent contribution (Giauque et al., 2012, “Analytical Analysis of Indirect Combustion Noise in Subcritical Nozzles,” ASME J. Eng. Gas Turbies Power, 134(11), p. 111202) the authors have presented an analytical thermoacoustic model providing the indirect combustion noise generated by a subcritical nozzle when forced with entropy waves. This model explicitly takes into account the effect of the local changes in the cross-section area along the configuration of interest. In this article, the authors introduce this model into an optimization procedure in order to minimize or maximize the thermoacoustic noise emitted by arbitrarily shaped nozzles operating under subsonic conditions. Each component of the complete algorithm is described in detail. The evolution of the cross-section changes are introduced using Bezier's splines, which provide the necessary freedom to actually achieve arbitrary shapes. Bezier's polar coordinates constitute the parameters defining the geometry of a given individual nozzle. Starting from a population of nozzles of random shapes, it is shown that a specifically designed genetic optimization algorithm coupled with the analytical model converges at will toward a quieter or noisier population. As already described by Bloy (Bloy, 1979, “The Pressure Waves Produced by the Convection of Temperature Disturbances in High Subsonic Nozzle Flows,” J. Fluid Mech., 94(3), pp. 465–475), the results therefore confirm the significant dependence of the indirect combustion noise with respect to the shape of the nozzle, even when the operating regime is kept constant. It appears that the quietest nozzle profile evolves almost linearly along its converging and diverging sections, leading to a square evolution of the cross-section area. Providing insight into the underlying physical reason leading to the difference in the noise emission between two extreme individuals, the integral value of the source term of the equation describing the behavior of the acoustic pressure of the nozzle is considered. It is shown that its evolution with the frequency can be related to the global acoustic emission. Strong evidence suggest that the noise emission increases as the source term in the converging and diverging parts less compensate each other. The main result of this article is the definition and proposition of an acoustic emission factor, which can be used as a surrogate to the complex determination of the exact acoustic levels in the nozzle for the thermoacoustic shape optimization of nozzle flows. This acoustic emission factor, which is much faster to compute, only involves the knowledge of the evolution of the cross-section area and the inlet thermodynamic and velocity characteristics to be computed.

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