Direct numerical simulations of spiral Poiseuille flows in a narrow gap geometry are performed with the aim of identifying the mechanisms governing the dynamics of the axial friction coefficient. The investigation has explored a small portion of the Reynolds number–Taylor number phase space ($600 \leq Re \leq 5766$ and $1500 \leq Ta \leq 5000$), for which reference experimental results are available. The study is focused on the mechanism leading to the enhancement of the axial friction coefficient with the Taylor number when the Reynolds number is kept constant. The analysis of the spatial distribution of the Reynolds stress tensor and of the turbulent energy budget has evidenced the key role of the pressure–strain correlation in the energy transfer from the azimuthal to the axial component. The latter eventually determines the increase of the axial friction coefficient through the enhanced radial mixing of axial momentum. Data have also shown that the flow dynamics is heavily dependent on the $Ta/Re$ ratio, and different regimes develop (ranging from laminar to turbulent), each with peculiar behaviours.

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.

Keeping a tube from being plugged by a fluid is an important process in applications. An interesting re-entrant phenomenon for the capillary state with the occluding state sandwiching the non-occluding state from both the high- and low-Bond-number regions can appear by inserting a rod into a horizontal tube at an eccentric position (Tan et al., J. Fluid Mech, vol. 946, 2022, A7). Containers with rounded corners are very common. We theoretically investigate a situation for a horizontal open tube with rounded corner(s). The results show that a re-entrant non-occlusion at a contact angle can also appear without the insertion of any object. The competition between the rounded corner wetting/non-wetting effect and gravity effect can lead to a re-entrant non-occlusion. The re-entrant non-occlusion is affected by the shape and orientation of the rounded corner(s). For a tube with only one rounded corner, the re-entrant non-occlusion exists when the rounded corner has a not-so-large corner radius and is not in a landscape orientation. For a tube with two (or more) rounded corners, the corner(s) with the strongest corner effect will determine the existence or non-existence of the re-entrant non-occlusion. This paper provides an effective scheme for designing a high-performance capillary with corners that are not easily occluded by a fluid and removing fluid blockage from a capillary in optofluidic/microfluidic applications.

Wind tunnel measurements of the incident turbulent velocity fields and axial forces on a horizontal axis turbine and porous disc analogues are reported. The models were tested in both a simulated atmospheric boundary layer (ABL) and in grid turbulence, allowing for a range of turbulence length scale to rotor diameter ratios to be considered. A theoretical framework to account for the combined effect of distortion and potential flow blocking in the induction zone is presented. In the case of very large length-scale turbulence to diameter ratios, where distortion effects are minimal, a quasi-steady approach is adopted for the effect of blocking. For the small length-scale ratio limit, the method is developed from the classical analyses for rapid distortion of turbulence and blockage from flow through a porous sheet of resistance. For general length-scale ratios, an efficient prediction method based on interpolation between the two length-scale ratio extremes is established. For very large length-scale ratios, a quasi-steady theory without distortion is appropriate for a rotor or disc in a simulated ABL. The small length-scale theory is applicable for tests conducted in grid turbulence. The results of the study can inform the prediction and interpretation of typical measurements of turbulence within the induction zone and the fluctuating loads on a rotor, at both prototype and full scale. This is of particular importance to fatigue load assessments.

Particulate flows at moderate particle Reynolds numbers are important in critical engineering and geological applications. This experimental study explores neutrally buoyant suspensions in an outer-rotating coaxial rheometer for solid fractions, $\phi$, from 0.1 to 0.5, and particle Reynolds number, $Re$, from 0.5 to 800, covering laminar, transitional and turbulent regimes; $Re$ is defined in terms of the square of the particle diameter and the shear rate. For $0.1 < \phi < 0.4$ and $0.5 < Re <10$, the direct torque measurements normalised by the laminar flow torque, $M/M_{lam}$, are independent of $Re$, but depend on $\phi$. For the same range of $\phi$ and for $10< Re<100$, the normalised torques depend on both $\phi$ and $Re$, and show an increasing dependence on $Re$. As $Re$ increases, the flow transitions to turbulence. Small particles delay the turbulent transition for $\phi \leqslant 0.3$, while large particles augment the transition. A modified Reynolds number, $Re^\prime$, that depends linearly on the particle diameter and the maximum velocity, $U_{o}$, is introduced for both laminar and turbulent flows and shows a better correlation of the results as compared with $Re$. For $\phi = 50\,\%$, the normalised torque minus the torque at zero rotational speed is nearly independent of $Re^\prime$. Rheological models based on $Re^\prime$ and the Krieger–Dougherty relative viscosity are proposed in the laminar regime for $10< Re^\prime <500$; in the turbulent regime, a correlation is proposed in terms of $Re^\prime$ and $\phi$ for $1000< Re^\prime < 6000$.

Predicting the magnitude of the slip velocity of non-tracer particles with respect to the surrounding fluid is crucial to address both fundamental and practical questions involving dispersed turbulent flows. Here we derive an analytical model to predict the slip velocity of spherical particles in homogeneous isotropic turbulence. We modulate the particle equation of motion according to the inertial filtering framework, and obtain closed-form expressions for the mean slip velocity magnitude as a function of the governing parameters. These are compared against laboratory measurements and direct numerical simulations, demonstrating close agreement for both light and heavy particles, both smaller and larger than the Kolmogorov scales. The predictive value of the model and its implications are discussed, as well as the range of validity of the underlying assumptions.

A linear stability analysis of circular Couette flow of a Bingham fluid subjected to axisymmetric perturbations was presented by Peng & Zhu (J. Fluid Mech., vol. 512, 2004, pp. 21–45) and Landry et al. (J. Fluid Mech., vol. 560, 2006, pp. 321–353). Here, we consider the stability of this flow with respect to a finite amplitude perturbation. We focus particularly on the case where the basic flow has an unyielded fluid layer on outer cylinder. A weakly nonlinear stability analysis is developed for a wide gap and a narrow gap. A third-order Ginzburg–Landau equation is derived, and the influence of the different nonlinearities on bifurcation features is investigated in detail. The results indicate that: (i) the nonlinear inertial terms act in favour of pitchfork supercritical bifurcation and the nonlinear yield stress terms promote a subcritical bifurcation; (ii) for a range of Bingham numbers $B$, the extent of which depends on the radius ratio and outer Reynolds number, the nonlinear yield stress terms are dominant and the primary bifurcation is subcritical. The amplitude analysis indicates that in the supercritical bifurcation regime, near the threshold, when the nonlinear inertial terms are dominant, the amplitude decreases slightly with increasing $B$. Once the nonlinear yield stress terms start to become significant, the equilibrium amplitude increases substantially with increasing $B$. Similar trends are observed for Taylor vortex strength. Finally, the erosion of the static layer is analysed. It is shown that the nonlinear yield stress terms play a significant role.

Analysis of the classic problem of shallow film flow on an inclined plane is revisited for a Brownian suspension. The particle phase, considered in a two-fluid model, is predicted to cause pronounced changes to the instability characteristics of the flow. These are due to an indirect effect of the non-Newtonian rheology, with the normal stresses causing migration and a viscosity stratification which strongly alters the base state from its Newtonian counterpart. Both the short- and long-wavelength inertial stability boundaries are altered, and, more strikingly, an instability at zero Reynolds number is found.

This paper investigates the nonlinear evolution and acoustic radiation of coherent structures (CS) in the near-nozzle region of a subsonic turbulent circular jet. A CS is taken to be a wavepacket consisting of multiple ring/helical modes, which are considered to be inviscid instability waves supported by the mean-flow profile. As the three-dimensionality of helical modes is weak in the near-nozzle region, the ring and helical modes with the same frequency have nearly the same growth rates and critical levels. They coexist and interact with each other in their common critical layer at high Reynolds numbers. The self and mutual quadratic interactions generate a mean-flow distortion and streaks, which act back on the fundamental components through the cubic interaction. The amplitude of the CS is governed by an integro-partial-differential equation, a significant feature of which is that differentiations with respect to the azimuthal coordinate appear in the history-dependent nonlinear terms. The non-parallelism of the mean flow as well as the impact of fine-scale turbulence on CS are taken into account and found to affect the nonlinear terms. By solving the amplitude equation, the development of the constituting modes, streamwise vortices and streaks are described. For CS consisting of frequency sideband, low-frequency components are excited nonlinearly and amplify to reach a considerable level. By analysing the large-distance asymptote of the perturbation, the low-frequency acoustic waves are found to be emitted by the temporally–spatially varying mean-flow distortion and streaks generated by the nonlinear interactions of the CS, and are thereby determined on the basis of first principles. Interestingly, the energetic part of the streaky structure that contributes to the nonlinear dynamics does not radiate directly, and instead the Reynolds stresses driving the subdominant radiating components represent the true physical sources.

This paper presents an experimental study of the interaction of turbulent spots with an initially laminar separation, using schlieren visualisation and dynamic measurements of surface heat transfer and pressure. The separation is generated on a blunt cylinder-flare body, tested at Mach 9, and entropy layer effects result in a boundary layer edge Mach number of 3.43 at separation. A single roughness element is used to produce isolated spots, defined such that separation collapse and re-establishment is completed before arrival of the next spot. On average the spot axial length, at the start of the interaction, is 2.5 times the separation length, growing to 6.8 times as the spot base passes the original reattachment position. As such the spot comprises a large perturbation. The local separation responds almost immediately with passage of the spot, so that the downstream region may be unaffected while the upstream part has already collapsed. Re-establishment of separation is slow, taking up to four times the total transit time of the spot. A basic model is presented to explore the transient wave processes during spot passage.