This paper presents an analytical method for modelling the acoustic field radiation from a semi-infinite elliptic duct in the presence of uniform subsonic flow. In contemporary aircraft design, elliptic ducts play crucial roles as inlets for advanced blended wing body configurations owing to their capacity to maximise the pre-compression effect of the fuselage and enhance the stealth performance of aircraft. The method uses Mathieu functions to describe the incident and scattered sound in the elliptic cylindrical coordinates. An analytical Wiener–Hopf technique is developed in this work to derive near- and far-field solutions. Numerical simulations based on a finite element method are conducted to validate the accuracy of the analytical method, revealing a strong correspondence with analytical predictions. A parametric study is conducted to explore the influence of the elliptic cross-section shape on noise directivity. Moreover, we investigate reflections within the duct via an extended derivation of the analytical model. The proposed method can be used to examine the acoustic characteristics of elliptic ducts with inflow mean flows, which holds relevance for noise control and optimisation of turbofan engine inlets and blended wing body applications.

Secondary fragmentation of an impulsively accelerated drop depends on fluid properties and velocity of the ambient flow. The critical Weber number $(\mathit{We}_{cr})$, the minimum Weber number at which a drop undergoes non-vibrational breakup, depends on the density ratio $(\rho )$, the drop $(\mathit{Oh}_d)$ and the ambient $(\mathit{Oh}_o)$ Ohnesorge numbers. The current study uses volume-of-fluid based interface-tracking multiphase flow simulations to quantify the effect of different non-dimensional groups on the threshold at which secondary fragmentation occurs. For $\mathit{Oh}_d \leqslant 0.1$, a decrease in $\mathit{Oh}_d$ was found to significantly influence the breakup morphology, plume formation and $\mathit{We}_{cr}$. The balance between the pressure difference between the poles and the periphery, and the shear stresses on the upstream surface, was found to be controlled by $\rho$ and $\mathit{Oh}_o$. These forces induce flow inside the initially spherical drop, resulting in deformation into pancakes and eventually the breakup morphology of a forward/backward bag. The evolution pathways of the drop morphology based on their non-dimensional groups have been charted. With inclusion of the data from the expanded parameter space, the traditional $\mathit{We}_{cr}-\mathit{Oh}_d$ diagram used to illustrate the dependence of the critical Weber number on $\mathit{Oh}_d$ was found to be inadequate in predicting the minimum initial $\mathit{We}$ required to undergo fragmentation. A new non-dimensional parameter $C_{\textit{breakup}}$ is derived based on the competition between the forces driving the drop deformation and the forces resisting the drop deformation. Tested using available experimental data and current simulations, $C_{\textit{breakup}}$ is found to be a robust predictor for the threshold of drop fragmentation.

While flow confinement effects on a shear layer of an one-sided or submerged vegetation array’s interface have been widely studied, turbulent interactions between shear layers in channels with vegetation on both sides remain unclear. This study presents laboratory experiments investigating flow adjustments and turbulent interaction within a symmetrical vegetation–channel–vegetation system, considering varying array widths and densities. In the outer shear layer, the shear stress is primarily balanced by the pressure gradient. As the array extends laterally, the outer penetration of the shear layer reduces from a fully developed thickness to the half-width of the open region, resulting in flow confinement. Flow confinement enhances the pressure gradient, which increases the interior velocity and shear stress at the interface. Despite the time-averaged shear stress being zero at the centreline when the shear layer is confined, the shear instabilities from both sides interact, producing significant turbulent events at the centreline with equal contributions from each side. Furthermore, the two parallel vortex streets self-organised and created a wave response with a $\pi$-radian phase shift , where alternating vortex cores amplify the pressure gradient, intensifying coherent structures and facilitating momentum exchange across the channel centreline. Although the turbulent intensity is enhanced, the decreased residence time for turbulent flow events may limit transport distance. Overall, the shear layer that develops on one interface acts as an additional resistance to shear turbulence on the other interface, leading to a more rapid decline of shear stress in the open region, despite a higher peak at the interface.

In compressible turbulent boundary layers (CTBLs), the strong Reynolds analogy (SRA) refers to a set of quantitative relationships between temperature and velocity fluctuations. The essence of the SRA is the linear relationship between these fluctuations in large-scale motions. We investigate the transport processes of the second-order statistical moments associated with temperature and velocity fluctuations to reveal the physical mechanisms underlying this linear correlation. An important finding is that there exists a strong linear mechanism between the turbulent production of velocity and temperature fluctuations. Nonlinear mechanisms, such as the viscous-thermal dissipation, the work contribution, and particularly the pressure term, lead to the failure of the existing SRAs in the outer layer. Based on the above findings, a refined SRA (RSRA) is proposed, which better describes the quantitative relation between the temperature and velocity fluctuation intensities. An approximate expression for the turbulent Prandtl number under different Mach numbers and wall-cooling conditions is derived with the newly proposed RSRA. The relations proposed in this paper are validated through the direct numerical simulation data of flat-plate zero-pressure-gradient CTBLs at different Mach numbers and wall temperatures.