In this paper we report on a direct numerical simulation (DNS) of turbulent heat transfer in a T-junction. In particular, we study the interaction between two liquid streams, a hot horizontal cross-flow and a cold vertical liquid jet coming from above, in a T-junction of rectangular cross-section. We discuss in detail the instantaneous flow structures and present results for the first- and second-order statistics of the flow quantities, and for the budget of the turbulent kinetic energy. Further, we present results of the power spectral density of the velocity and temperature signals at selected locations of the flow field. Our analysis elucidates the properties of the important features of the flow such as the large recirculation bubble and the secondary separation zones that are formed in the vicinity of the entry of the jet. According to our simulations, thermal mixing is mainly driven by the shear layer between the two streams and, to a lesser extent, by the shear layer between the incoming jet and the large recirculation bubble. Thermal mixing is further enhanced by turbulence generation in the regions of adverse pressure gradients downstream of the large recirculation bubble. Within the framework of our study, we have also conducted a wall-resolved large-eddy simulation (LES) of the flow of interest so as to assess its predictive capacity. Overall, the LES predictions agree satisfactorily with our DNS data; the most noticeable discrepancy is that the LES produces mildly diffused profiles for the second-order statistics in the regions of intense turbulence production.

Riming, the process whereby ice crystals get coated by impacting supercooled liquid droplets, is one of the dominant processes leading to precipitation in mixed-phase clouds. How a settling crystal collides with very small water droplets has been mostly studied in laminar conditions. The present numerical study aims at providing further insight on how turbulent flow motion affects the riming of ice crystals. We model the crystals as narrow oblate ellipsoids, smaller than the Kolmogorov elementary scale. By neglecting the effect of fluid inertia on the motion of the crystals and droplets, and using direct numerical simulations of the Navier–Stokes equations in a moderately turbulent regime, over a range of kinetic energy dissipation $1~\text{cm}^{2}~\text{s}^{-3}\lesssim \unicode[STIX]{x1D700}\lesssim 256~\text{cm}^{2}~\text{s}^{-3}$ , we determine the collision rate between disk-shaped ice crystals and very small liquid water droplets. Whereas differential settling plays the dominant role in determining the collision rate at small turbulence intensity, the role of turbulence becomes more important at the large values of $\unicode[STIX]{x1D700}$ simulated, an effect that can be partly attributed to the increased role of inertia. We always find that collisions occur with a large probability on the rim of the ellipsoids, a phenomenon that can be explained to a large extent by kinematic considerations. The difference in the settling velocity of crystals and droplets induces a strong asymmetry in the probability of collision between the faces of the ellipsoids. Our results shed light on the physical mechanisms involved in the riming of ice crystals in clouds.

A uniform nanometric thin liquid film on a solid substrate can become unstable due to the action of van der Waals (vdW) forces. The instability leads to dewetting of the uniform film and the formation of drops. To minimize the total free energy of the system, these drops coarsen over time until one single drop remains. Here, using a thermodynamically consistent framework, we derive a new model for thin films in partial wetting with a free energy that resembles the Cahn–Hilliard form with a height-dependent surface tension that leads to a generalized disjoining pressure, and revisit the dewetting problem. Using both linear stability analysis and nonlinear simulations we show that the new model predicts a slightly smaller critical instability wavelength and a significantly (up to six-fold) faster growth rate than the classical model in the spinodal regime; this faster growth rate brings the theoretical predictions closer to published experimental observations. During coarsening at intermediate times, the dynamics become self-similar and model-independent; we therefore observe the same scalings in both the classical (with and without thermal noise) and new models. Both models also lead to a mean-field Lifshitz–Slyozov–Wagner (LSW)-type droplet-size distribution at intermediate times for small drop sizes. We, however, observe a skewed drop-size distribution for larger drops in the new model; while the tail of the distribution follows a Smoluchowski equation, it is not associated with a coalescence-dominated coarsening, calling into question the association made in some earlier experiments. Our observations point to the importance of the height dependence of surface tension in the early and late stages of dewetting of nanometric films and motivate new high-resolution experimental observations to guide the development of improved models of interfacial flows at the nanoscale.

Wave radiation and diffraction by a circular cylinder submerged below an ice sheet with a crack are considered based on the linearized velocity potential theory together with multipole expansion. The solution starts from the potential due to a single source, or the Green function satisfying both the ice sheet condition and the crack condition, as well as all other conditions apart from that on the body surface. This is obtained in an integral form through Fourier transform, in contrast to what has been obtained previously in which the Green function is in the series form based on the method of matched eigenfunction expansion in each domain on both sides of the crack. The multipole expansion is then constructed through direct differentiation of the Green function with respect to the source position, rather than treating each multipole as a separate problem. The use of the Green function enables the problem of wave diffraction by the crack in the absence of the body to be solved directly. For the circular cylinder, wave radiation and diffraction problems are solved by applying the body surface boundary condition to the multipole expansion, through which the unknown coefficients are obtained. Extensive results are provided for the added mass and damping coefficient as well as the exciting force. When the cylinder is away from the crack, a wide spacing approximation method is used, which is found to provide accurate results apart from when the cylinder is quite close to the crack.

The neutral curves of the boundary layer Görtler-vortex flow generated by free-stream disturbances, i.e., curves that distinguish the perturbation flow conditions of growth and decay, are computed through a receptivity study for different Görtler numbers, wavelengths, and low frequencies of the free-stream disturbance. The perturbations are defined as Klebanoff modes or strong and weak Görtler vortices, depending on their growth rate. The critical Görtler number below which the inviscid instability due to the curvature never occurs is obtained and the conditions for which only Klebanoff modes exist are thus revealed. A streamwise-dependent receptivity coefficient is defined and we discuss the impact of the receptivity on the $N$-factor approach for transition prediction.

Second-mode wave growth within the hypersonic boundary layer of a slender cone is investigated experimentally using high-speed schlieren visualizations. Experiments were performed in AEDC Tunnel 9 over a range of unit Reynolds number conditions at a Mach number of approximately 14. A thin lens with a known density profile placed within the field of view enables calibration of the schlieren set-up, and the relatively high camera frame rates employed allow for the reconstruction of time-resolved pixel intensities at discrete streamwise locations. The calibration in conjunction with the reconstructed signals enables integrated spatial amplification rates ($N$ factors) to be calculated for each unit Reynolds number condition and compared to $N$ factors computed from both pressure transducer measurements and linear parabolized stability equation (PSE) solutions. Good agreement is observed between $N$ factors computed from the schlieren measurements and those computed from the PSE solutions for the most-amplified second-mode frequencies. The streamwise development of $N$ factors calculated from the schlieren measurements compares favourably to that calculated from the pressure measurements with slight variations in the $N$ factor magnitudes calculated for harmonic frequencies. Finally, a bispectral analysis is carried out to identify nonlinear phase-coupled quadratic interactions present within the boundary layer. Multiple interactions are identified and revealed to be associated with the growth of disturbances at higher harmonic frequencies.

This paper presents a novel analytical model that predicts the two-way coupled aeroelastic response of a linear elastic plate in axial potential flow, including the effects of plate curvature. The plate deforms in dynamic balance of the inertia, elastic, and aerodynamic forces. Analytical solutions are obtained by deriving the generalized aerodynamic force with respect to the beam eigenfunctions, which are expressed in a Chebyshev polynomial expansion. Exact expressions are derived for the generated lift, thrust and required input power. The derived solution agrees well with the results reported in the literature for plate flutter and flapping wings.

We consider the propagation of water waves in a waveguide with a surface-piercing circular cylinder. A plane wave interacting with the cylinder leads to a Fano resonance resulting in strong scattering with a large reflection coefficient. Using a smoothly varying bathymetry whose shape is optimized, we show both numerically and experimentally that broadband and robust backscattering reduction can be obtained below the first cutoff frequency.