Influences of key parameters on flow features in the curved ducts with equal area

Curved ducts are widely used in aircraft engines to improve some capability of aero-engines. Complex internal flow characteristics would be induced by the curvature in such components. In this study, the influence of parameters, including the arc angle α, the curvature radius R i, and the height H, on the local accelerating and transonic flow in the curved ducts with equal area were studied numerically and theoretically under different nozzle pressure ratios (NPRs). The range of the Re number based on the height of the duct and the velocity at the inlet was [Formula: see text] ∼ [Formula: see text]. The shear stress transport κ-ω turbulent model was proved by the test data to suitably simulate the flow field in curved ducts because it could accurately predict the flow separations under adverse pressure gradients. The uncertainty of the pressure scan value to obtain the test data was ±0.05%. Numerical results showed that the effect of α on the flow characteristics of the curved ducts is little. The maximum Ma number in the curved section reduces with the increase of R i, and that grows with the increase of H. The range of the maximum Ma number was 1.20∼1.80. The critical NPRs, which decided the special flow features, were found in the curved ducts. The critical NPR rises with the increase of R i; however, the effect of H on the critical NPR is irregular due to the flow separations located near the lower wall induced by the large adverse pressure gradient. The theoretical results based on the small perturbation theory of transonic flow in the polar coordinate system proved that the distribution of sonic line was just dependent on the inner diameter R1, the outer diameter R2, and the arc angle θmax of the curved section. The critical mass flow and the critical NPR2 are only related to R1 and R2.

Nonlinear sound propagation in two-dimensional curved ducts: a multimodal approach

A method for studying weakly nonlinear acoustic propagation in two-dimensional ducts of general shape – including curvature and variable width – is presented. The method is based on a local modal decomposition of the pressure and velocity in the duct. A pair of nonlinear ordinary differential equations for the modal amplitudes of the pressure and velocity modes is derived. To overcome the inherent instability of these equations, a nonlinear admittance relation between the pressure and velocity modes is presented, introducing a novel ‘nonlinear admittance’ term. Appropriate equations for the admittance are derived which are to be solved through the duct, with a radiation condition applied at the duct exit. The pressure and velocity are subsequently found by integrating an equation involving the admittance through the duct. The method is compared, both analytically and numerically, against published results and the importance of nonlinearity is demonstrated in ducts of complex geometry. Comparisons between ducts of differing geometry are also performed to illustrate the effect of geometry on nonlinear sound propagation. A new ‘nonlinear reflectance’ term is introduced, providing a more complete description of acoustic reflection that also takes into account the amplitude of the incident wave.