The effect of inertia and vertical confinement on the flow past a circular cylinder in a Hele-Shaw configuration

The Poiseuille flow (centreline velocity $U_c$ ) of a fluid (kinematic viscosity $\nu$ ) past a circular cylinder (radius $R$ ) in a Hele-Shaw cell (height $2h$ ) is traditionally characterised by a Stokes flow ( $\varLambda =(U_cR/\nu )(h/R)^2 \ll 1$ ) through a thin gap ( $\epsilon =h/R \ll 1$ ). In this work we use asymptotic methods and direct numerical simulations to explore the parameter space $\varLambda$ – $\epsilon$ when these conditions are not met. Starting with the Navier–Stokes equations and increasing $\varLambda$ (which corresponds to increasing inertial effects), four successive regimes are identified, namely the linear regime, nonlinear regimes I and II in the boundary layer (the ‘ inner’ region) and a nonlinear regime III in both the inner and outer region. Flow phenomena are studied with extensive comparisons made between reduced calculations, direct numerical simulations and previous analytical work. For $\epsilon =0.01$ , the limiting condition for a steady flow as $\varLambda$ is increased is the instability of the Poiseuille flow. However, for larger $\epsilon$ , this limit is at a much higher $\varLambda$ , resulting in a laminar separation bubble, of size ${O}(h)$ , forming for a certain range of $\epsilon$ at the back of the cylinder, where the azimuthal location was dependent on $\epsilon$ . As $\epsilon$ is increased to approximately 0.5, the secondary flow becomes increasingly confined adjacent to the sidewalls. The results of the analysis and numerical simulations are summarised in a plot of the parameter space $\varLambda$ – $\epsilon$ .

Predicting evaporation rates of droplet arrays

The evaporation of multiple sessile droplets is both scientifically interesting and practically important, occurring in many natural and industrial applications. Although there are simple analytic expressions to predict evaporation rates of single droplets, there are no such frameworks for general configurations of droplets of arbitrary size, contact angle or spacing. However, a recent theoretical contribution by Masoud, Howell & Stone (J. Fluid Mech., vol. 927, 2021, R4) shows how considerable insight can be gained into the evaporation of arbitrary configurations of droplets without having either to obtain the solution for the concentration of vapour in the atmosphere or to perform direct numerical simulations of the full problem. The theoretical predictions show excellent agreement with simulations for all configurations, only deviating by 25 % for the most confined droplets.

Scalar Forcing Methodology for Direct Numerical Simulations of Turbulent Stratified Mixture Combustion

Scalar forcing in the context of turbulent stratified flame simulations aims to maintain the fuel-air inhomogeneity in the unburned gas. With scalar forcing, stratified flame simulations have the potential to reach a statistically stationary state with a prescribed mixture fraction distribution and root-mean-square value in the unburned gas, irrespective of the turbulence intensity. The applicability of scalar forcing for Direct Numerical Simulations of stratified mixture combustion is assessed by considering a recently developed scalar forcing scheme, known as the reaction analogy method, applied to both passive scalar mixing and the imperfectly mixed unburned reactants of statistically planar stratified flames under low Mach number conditions. The newly developed method enables statistically symmetric scalar distributions between bell-shaped and bimodal to be maintained without any significant departure from the specified bounds of the scalar. Moreover, the performance of the newly proposed scalar forcing methodology has been assessed for a range of different velocity forcing schemes (Lundgren forcing and modified bandwidth forcing) and also without any velocity forcing. It has been found that the scalar forcing scheme has no adverse impact on flame-turbulence interaction and it only maintains the prescribed root-mean-square value of the scalar fluctuation, and its distribution. The scalar integral length scale evolution is shown to be unaffected by the scalar forcing scheme studied in this paper. Thus, the scalar forcing scheme has a high potential to provide a valuable computational tool to enable analysis of the effects of unburned mixture stratification on turbulent flame dynamics.

Three-dimensional geometry and topology effects in viscous streaming

Recent studies on viscous streaming flows in two dimensions have elucidated the impact of body curvature variations on resulting flow topology and dynamics, with opportunities for microfluidic applications. Following that, we present here a three-dimensional characterization of streaming flows as functions of changes in body geometry and topology, starting from the well-known case of a sphere to progressively arrive at toroidal shapes. We leverage direct numerical simulations and dynamical systems theory to systematically analyse the reorganization of streaming flows into a dynamically rich set of regimes, the origins of which are explained using bifurcation theory.