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.

On some smooth symmetric transonic flows with nonzero angular velocity and vorticity

This paper concerns the structural stability of smooth cylindrically symmetric transonic flows in a concentric cylinder. Both cylindrical and axi-symmetric perturbations are considered. The governing system here is of mixed elliptic–hyperbolic and changes type and the suitable formulation of boundary conditions at the boundaries is of great importance. First, we establish the existence and uniqueness of smooth cylindrical transonic spiral solutions with nonzero angular velocity and vorticity which are close to the background transonic flow with small perturbations of the Bernoulli’s function and the entropy at the outer cylinder and the flow angles at both the inner and outer cylinders independent of the symmetric axis, and it is shown that in this case, the sonic points of the flow are nonexceptional and noncharacteristically degenerate, and form a cylindrical surface. Second, we also prove the existence and uniqueness of axi-symmetric smooth transonic rotational flows which are adjacent to the background transonic flow, whose sonic points form an axi-symmetric surface. The key elements in our analysis are to utilize the deformation-curl decomposition for the steady Euler system to deal with the hyperbolicity in subsonic regions and to find an appropriate multiplier for the linearized second-order mixed type equations which are crucial to identify the suitable boundary conditions and to yield the important basic energy estimates.