The reactive Navier–Stokes equations with adaptive mesh refinement and a detailed chemical reactive mechanism (11 species, 27 steps) were adopted to investigate a detonation engine considering the injection and supersonic mixing processes. Flame acceleration and deflagration-to-detonation transition (DDT) in a premixed/inhomogeneous supersonic hydrogen–air mixture with and without transverse jet obstacles were addressed. Results demonstrate the difficulty in undergoing DDT in the premixed/inhomogeneous supersonic mixture within a smooth chamber. By contrast, multiple transverse jets injected into the chamber aid detonation transition by introducing perturbed vortices, shock waves and a suitable blockage ratio. Increasing distance between the leading shock and the flame tip impedes detonation transition due to an insufficient blockage ratio. The extremely perturbed distributions of fuel-lean and fuel-rich mixtures lead to more complicated flame structures. Also, a larger flame thickness appears in the inhomogeneous mixture compared with the premixed mixture, resulting in a lower combustion temperature. The key findings are that the DDT, detonation quenching and reinitiation are generated in the inhomogeneous supersonic mixture, but both DDT mechanisms are ascribed to a strong Mach stem with the Zel'dovich gradient mechanism. Additionally, the obtained results demonstrate that an intensely fuel-lean mixture (equivalence ratio = 0.15) results in a partially decoupled flame front. However, detonation reinitiation and subsequent self-sustained detonation occur when a fierce shock wave propagates through a highly sensitive mixture, even within a smaller and elongated area. Moreover, the inhomogeneous mixture also augments the propagation speed and detonation cell structure instabilities and delays the sonic point resulting from the extending non-equilibrium reaction.

Direct numerical simulations are performed to explore the evolution behaviour of the turbulent/non-turbulent interface (TNTI) in a temporally evolving turbulent plane jet, using the evolution equation for the TNTI surface area. A novel algorithm is used to calculate the surface area of the TNTI and entrainment flux. It is shown that the surface area remains relatively constant, which leads to the mean entrainment velocity being inversely proportional to the square root of time. On average, the effects of the stretching and curvature/viscous terms on the TNTI area roughly counterbalance each other, while the curvature/inviscid term associated with vortex stretching is virtually zero. More specifically, the stretching term contributes to the production of the surface area, while the curvature/viscous term is associated with a destruction in the surface area. The local effect of the curvature/viscous term exhibits high spatial intermittency with small-scale extreme/intense events, whereas the effect of the large-scale stretching term is more continuous. To shed light on the contribution of curvature/viscous term to the evolution of the surface area, we decompose it into three components. The effect of the curvature/normal diffusion term (the curvature/viscous dissipation term) in the bulging regions (the valley regions) mainly contributes to the production of the area. The continuous decrease of the average mean curvature is associated with the production of the bulging regions and the destruction of the valley regions. Finally, although the entrainment velocity is mainly dominated by the normal diffusion effect, all three components related to the viscous effect are indispensable to the production and destruction of the TNTI area. This numerical study contributes to a better understanding of the evolution of the TNTI area.

Prandtl's secondary flows of the second kind generated by laterally varying roughness are studied using the linearised Reynolds-averaged Navier–Stokes approach proposed by Zampino et al. (J. Fluid Mech., vol. 944, 2022, p. A4). The momentum equations are coupled to the Spalart–Allmaras model while the roughness is captured by adapting established strategies for homogeneous roughness to heterogeneous surfaces. Linearisation of the governing equations yields a framework that enables a rapid exploration of the parameter space associated with heterogeneous surfaces, in the limiting case of small spanwise variations of the roughness properties. Channel flow is considered, with longitudinal high- and low-roughness strips arranged symmetrically. By varying the strip width, it is found that linear mechanisms play a dominant role in determining the size and intensity of secondary flows. In this setting, secondary flows may be interpreted as the time-averaged output response of the turbulent mean flow subjected to a steady forcing produced by the wall heterogeneity. In fact, the linear model predicts that secondary flows are most intense when the strip width is about 0.7 times the half-channel height, in excellent agreement with available data. Furthermore, a unified framework to analyse combinations of heterogeneous roughness properties and laterally varying topographies, common in applications, is discussed. Noting that the framework assumes small spanwise variations of the surface properties, two separate secondary-flow-inducing source mechanisms are identified, i.e. the lateral variation of the virtual origin from which the turbulent structure develops and the lateral variation of the streamwise velocity slip, capturing the acceleration/deceleration perceived by the bulk flow over troughs and crests of non-planar topographies.

Since 1979, plastic companies have significantly expanded their markets. Evidence suggests that excessive plastic use in Ethiopia has exacerbated environmental pollution, contributing to a “quadruple crisis” involving climate change, biodiversity loss, pollution and public health and economic impacts. To address this, the Ethiopian government needs to establish effective plastic waste management strategies. Key future direction and recommendation include (1) Developing and enforcing national strategies, including a ban on many single-use plastics, for sustainable plastic waste management; (2) adopting international best practices and policies to move toward a zero-waste approach; (3) investing in a circular economy and plastic waste management systems; (4) strengthening policies through comprehensive legislation and extended producer responsibility frameworks; (5) establishing a council to integrate scientific research into policymaking; (6) promoting green technologies and innovations, such as plastic waste-to-energy and smart waste management; (7) engaging in global efforts to monitor hazardous chemicals in plastics and support transparency in a toxic-free circular economy to ensure the public’s right to information.

In this work, the shape of a bluff body is optimized to mitigate velocity fluctuations of turbulent wake flows based on large-eddy simulations (LES). The Reynolds-averaged Navier–Stokes method fails to capture velocity fluctuations, while direct numerical simulations are computationally prohibitive. This necessitates using the LES method for shape optimization given its scale-resolving capability and relatively affordable computational cost. However, using LES for optimization faces challenges in sensitivity estimation as the chaotic nature of turbulent flows can lead to the blowup of the conventional adjoint-based gradient. Here, we propose using the regularized ensemble Kalman method for the LES-based optimization. The method is a statistical optimization approach that uses the sample covariance between geometric parameters and LES predictions to estimate the model gradient, circumventing the blowup issue of the adjoint method for chaotic systems. Moreover, the method allows for the imposition of smoothness constraints with one additional regularization step. The ensemble-based gradient is first evaluated for the Lorenz system, demonstrating its accuracy in the gradient calculation of the chaotic problem. Further, with the proposed method, the cylinder is optimized to be an asymmetric oval, which significantly reduces turbulent kinetic energy and meander amplitudes in the wake flows. The spectral analysis methods are used to characterize the flow field around the optimized shape, identifying large-scale flow structures responsible for the reduction in velocity fluctuations. Furthermore, it is found that the velocity difference in the shear layer is decreased with the shape change, which alleviates the Kelvin–Helmholtz instability and the wake meandering.

Pore-resolved direct numerical simulations have been performed to investigate the turbulent open-channel flow over a rough and permeable sediment bed, represented by a mono-disperse random sphere pack. After a careful validation, eleven cases were simulated to systemically sample a parameter space spanned by a friction Reynolds number $Re_\tau \in [150, 500]$ and a permeability Reynolds number $Re_K \in [0, 2.8]$. By varying the ratio of flow depth to sphere diameter within a range of $h/D \in \{ 3,5,10,\infty \}$, the influence of both Reynolds numbers on the flow field and the turbulence structure could be investigated independently. The simulation results are analysed within a time–space double-averaging framework, whereas flow visualizations provide insight into instantaneous fields. Based on the drag distribution, we propose a consistent interface description, which can be used to define both near-interface and outer-flow coordinates. In these near-interface coordinates, the profiles of the mean velocity and the total shear stress collapse. Furthermore, the proposed interface definition yields outer-layer coordinates, in which the flow and turbulence statistics over a rough and permeable bed reveal similarity to a smooth-wall flow at a similar $Re_\tau$. Within the parameter space, $Re_\tau$ has a strong influence on the wake region of the velocity profile. In contrast, $Re_K$ changes the wall-blocking effect and the shear intensity, which is reflected by the turbulence structure and vortex orientation in the near-interface region. As streamwise velocity streaks disappear and the vortex inclination increases with higher $Re_K$, differences between near-interface and outer-layer turbulence structure are reduced.

Settling velocity statistics for dilute, non-Brownian homogeneous suspensions of polydisperse spheres having a log-normal size distribution are generated from Stokesian dynamics simulations, as a function of the total volume fraction $\phi$ and normalised width $\alpha$ of the particle size distribution. Several hundred instantaneous configurations are averaged to obtain reliable statistics. The paper reports data for the average and fluctuating settling velocity of each particle class in a suspension that is widely polydisperse – previous work was limited to only two or three classes, and the average settling velocity of each particle class was in most cases not reported – and provides an assessment of the accuracy of the analytical models proposed by Batchelor, Richardson & Zaki, Davis & Gecol and Masliyah–Lockett–Bassoon in predicting the simulation data. A limited comparison with dynamic simulations in which the particle microstructure is allowed to evolve in time is also included.

Modern machine-learning techniques are generally considered data-hungry. However, this may not be the case for turbulence as each of its snapshots can hold more information than a single data file in general machine-learning settings. This study asks the question of whether nonlinear machine-learning techniques can effectively extract physical insights even from as little as a single snapshot of turbulent flow. As an example, we consider machine-learning-based super-resolution analysis that reconstructs a high-resolution field from low-resolution data for two examples of two-dimensional isotropic turbulence and three-dimensional turbulent channel flow. First, we reveal that a carefully designed machine-learning model trained with flow tiles sampled from only a single snapshot can reconstruct vortical structures across a range of Reynolds numbers for two-dimensional decaying turbulence. Successful flow reconstruction indicates that nonlinear machine-learning techniques can leverage scale-invariance properties to learn turbulent flows. We also show that training data of turbulent flows can be cleverly collected from a single snapshot by considering characteristics of rotation and shear tensors. Second, we perform the single-snapshot super-resolution analysis for turbulent channel flow, showing that it is possible to extract physical insights from a single flow snapshot even with inhomogeneity. The present findings suggest that embedding prior knowledge in designing a model and collecting data is important for a range of data-driven analyses for turbulent flows. More broadly, this work hopes to stop machine-learning practitioners from being wasteful with turbulent flow data.

When a less-viscous solution of a reactant $A$ displaces a more-viscous solution of another reactant $B$, a fast bimolecular $A + B \rightarrow C$ reaction decreasing locally the viscosity can influence the viscous fingering (VF) instability taking place between the two miscible solutions. We show both experimentally and numerically that, for monotonic viscosity profiles, this decrease in viscosity has opposite effects on the fingering pattern depending on the injection flow rate. For high flow rates, the reaction enhances the shielding effect, creating VF patterns with a lower surface density, i.e. thinner fingers covering a smaller area. In contrast, for lower flow rates, the reaction stabilises the VF dynamics, i.e. delays the instability and gives a less-deformed displacement, reaching in some cases an almost-stable displacement. Nonlinear simulations of reactive VF show that these opposite effects at low or high flow rates can only be reproduced if the diffusivity of $A$ is larger than that of $B$, which favours a larger production of the product $C$ and, hence, a larger viscosity decrease. The analysis of one-dimensional viscosity profiles reconstructed on the basis of a one-dimensional reaction–diffusion–advection model confirms that the VF stabilisation at low Péclet number and in the presence of differential diffusion of reactants originates from an optimum reaction-driven decrease in the gradient of the monotonic viscosity profile.

In this study we consider a freely decaying, stably stratified homogeneous magnetohydrodynamic turbulent plasma with a weak vertical background magnetic field ($\boldsymbol {B}_0=B_0\hat {\boldsymbol {z}}),$ aligned with the density gradient of strength $N$ (i.e. Brunt–Väisälä frequency). Both linear theory and direct numerical simulations (DNS) are used to analyse the flow dynamics for a Boussinesq fluid with unitary magnetic and thermal Prandtl numbers. We implemented a normal mode decomposition emphasizing different types of motions depending on whether both the Froude $F_r$ and Alfvén–Mach $M$ numbers are small or only $F_r$ is small but $M$ is finite. In the former case, there is a non-propagating (NP) mode and fast modes: Alfvén waves with frequency $\omega _a$ and magnetogravity waves with frequency $\omega _{ag}$. In the latter case, there are fast gravity waves with frequency $\omega _g$ and slow modes: NP mode and slow Alfvén waves. The numerical simulations carried out are started from initial isotropic conditions with zero initial magnetic and density fluctuations, so that the initial energy of the NP mode is strictly zero, for $0< B_0/(L_iN)\leqslant 0.12$ and a weak mean magnetic field ($B_0=0.2$ or $B_0=0.4),$ where $L_i$ denotes the isotropic integral length scale. The DNS results indicate a weak turbulence regime for which $F_r$ is small and $M$ is finite. It is found that the vertical magnetic energy as well as the energy of the NP mode are drastically reduced as $N$ increases, while there is instead a forward cascade even for the magnetic field. The contribution coming from the energy of fast (gravity) waves does not exceed $50\,\%,$ while that coming from the energy of the NP mode does not exceed $10\,\%.$ Vertical motions are more affected by the effect of stratification than by the effect of the mean magnetic field, while it is the opposite for horizontal motions. We show that the spectrum of slow (Alfvén) waves and fast (gravity) waves tends to follow the power law $k_\perp ^{-3}$ for a wide range of time, $3< t<20$. At high vertical (or horizontal) wavenumbers, the main contribution to total energy comes from the energy of slow Alfvén waves. At large and intermediate horizontal (or vertical) scales, the spectra of the energy of NP mode exhibit a flat shape.