The ambient conditions surrounding liquid droplets determine their growth or shrinkage. However, the precise fate of a liquid droplet expelled from a respiratory puff as dictated by its surroundings and the puff itself has not yet been fully quantified. From the view of airborne disease transmission, such as SARS-CoV-2, knowledge of such dependencies is critical. Here, we employ direct numerical simulations (DNS) of a turbulent respiratory vapor puff and account for the mass and temperature exchange with respiratory droplets and aerosols. In particular, we investigate how droplets respond to different ambient temperatures and relative humidity (RH) by tracking their Lagrangian statistics. We reveal and quantify that in cold and humid environments, as there the respiratory puff is supersaturated, expelled droplets can first experience significant growth, and only later followed by shrinkage, in contrast to the monotonic shrinkage of droplets as expected from the classical view by Wells in 1934. Indeed, cold and humid environments diminish the ability of air to hold water vapor, thus causing the respiratory vapor puff to supersaturate. Consequently, the supersaturated vapor field drives the growth of droplets that are caught and transported within the humid puff. To analytically predict the likelihood for droplet growth, we propose a model for the axial RH based on the assumption of a quasistationary jet. Our model correctly predicts supersaturated RH conditions and is in good quantitative agreement with our DNS. Our results culminate in a temperature-RH map that can be employed as an indicator for droplet growth or shrinkage.

We use the Reynolds-averaged Navier-Stokes (RANS) equations with a full Reynolds stress model (RSM) to study the effect of the corner angle in supersonic corner flow. RANS data are compared to reference direct numerical simulation of fully developed a square duct flow, which support predictive capability of secondary flows from Stress-ω RSM. We then carry out a parametric study by changing the corner angle in the range θ=45°-135°, focusing on the effect on the mean streamwise and secondary flow. The maximum strength of the secondary flows of about 0.015u∞ occurs for θ=90°, which is similar to what is found in fully developed square ducts. Secondary eddies have approximately unit aspect ratio, and they maintain their shape for different corner angles by translating in the direction parallel to the closest wall. As a result, the position of the vortex center can be described by a simple geometrical transformation of the wall-parallel coordinate. We find that small corner angles are responsible for locally relaminarization flow at the corner, but otherwise the mean streamwise velocity profiles transformed according to van Driest following the canonical law-of-the-wall.