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Direct numerical simulations (DNS) are performed in a triply periodic unit cell of a face-centred cubic (FCC) lattice covering the unsteady inertial, to fully turbulent, flow regimes. The DNS data are used to quantify the flow topology, integral scales, turbulent kinetic energy (TKE) transport and anisotropy distribution in the tortuous geometry. Several unique flow features are observed within this low porosity configuration, where the mean flow undergoes strong acceleration and deceleration regions with presence of three-dimensional helical motions, weak wake-like structures behind spheres, stagnation and jet-impingement-like flows together with merging and spreading jets in the main pore space. The jet-impingement and weak wake-like flow structures give rise to regions with negative total TKE production. Unlike flows in complex shaped ducts, the turbulence intensity levels in the cross-stream directions are found to be larger than those in the streamwise direction. Furthermore, due to the compact nature and confined geometry of the FCC packing, the turbulent integral length scales are estimated to be less than 10 % of the bead diameter even for the lowest Reynolds number studied, indicating the absence of macroscale turbulence structures for this configuration. This finding suggests that even for the highly anisotropic flow within the pore, the upscaled flow statistics are captured well by the representative volumes defined by the unit cell.

A numerical investigation of unsteady hydrodynamic forces on the particle bed in an oscillatory flow environment is performed by means of direct numerical simulations. Statistical descriptions of drag and lift forces for two particle sizes of diameter 372 and 125 in wall units in a very rough turbulent flow regime are reported. Characterization of unsteady forces in terms of spatial distribution, temporal autocorrelation, force spectrum as well as cross-correlations with measurable flow variables is carried out. Based on the concept of impulse, intermittency in the drag and lift forces is also investigated. Temporal correlations show drag and lift to be positively correlated with a time delay that is approximately equal to the Taylor micro-scale related to the drag/lift fluctuations. The force spectra for drag and lift reveal roughly two scaling regions,$-11/3$and$-7/3$; the former typically represents turbulence–mean-shear interactions, whereas the latter indicates dominance of turbulence–turbulence interactions. Particle forces are strongly correlated with streamwise velocity and pressure fluctuations in the near-bed region for both flow cases. In comparison to the large-diameter particle case, the spatial extent of these correlations is 2–3 times larger in homogeneous directions for the small sized particle, a feature that is reminiscent of longer near-bed structures. For both large- and small-particle cases, it is shown that the distributions of drag (lift) fluctuations, in particular, peakedness and long tails, match remarkably well with fourth-order Gram–Charlier distributions of velocity (pressure) fluctuations. Furthermore, it is demonstrated that the intermittency is larger in the case of the lift force compared to that for the drag in both flow cases. Distributions of impulse events are heavily and positively skewed and are well described by a generalized extreme value distribution.

Particle-resolved direct numerical simulations (DNS) are performed to investigate the behaviour of an oscillatory flow field over a rough bed, corresponding to the experimental set-up of Keiller & Sleath (J. Fluid Mech., vol. 73 (04), 1976, pp. 673–691) for transitional and turbulent flows over a range of Reynolds numbers (95–400) based on the Stokes-layer thickness. It is shown that the roughness modulates the near-bed turbulence, produces streamwise horseshoe structures which then undergo distortion and breaking, and therefore reduces the large-scale anisotropy. A fully developed equilibrium turbulence is observed in the central part of the oscillation cycle, with two-component turbulence in the near-bed region and cigar-shaped turbulence in the outer region. A double averaging of the flow field reveals spatial inhomogeneities at the roughness scale and alternate paths of energy transport in the turbulent kinetic energy (TKE) budget. Contrary to the unidirectional, steady flow over rough beds, bed-induced production terms are important and comparable to the shear production term. It is shown that the near-bed velocity and pressure fluctuations are non-Gaussian, a result of critical importance for the modelling of incipient motion of sediment grains.

When a few bubbles are entrained in a travelling vortex ring, it has been shown that, even at extremely low volume loadings, their presence can significantly affect the structure of the vortex core (Sridhar & Katz, J. Fluid Mech., vol. 397, 1999, pp. 171–202). A typical Euler–Lagrange point-particle model with two-way coupling for this dilute system, wherein the bubbles are assumed subgrid and momentum point sources are used to model their effect on the flow, is shown to be unable to capture accurately the experimental trends of bubble settling location, bubble escape and vortex distortion for a range of bubble parameters and vortex strengths. The bubbles experience significant amounts of drag, lift, added mass, pressure and gravity forces. However, these forces are in balance with each other as the bubbles reach a mean settling location away from the vortex core. The reaction force on the fluid due to the net summation of these forces alone is thus very small and is unable to affect the vortex core. By accounting for fluid volume displacement due to bubble motion, experimental trends on vortex distortion and bubble settling location are captured accurately. The fluid displacement effects are studied by computing various contributions to an effective volume displacement force and are found to be important even at low volume loadings. As the bubble size and hence bubble Reynolds number increase, the bubbles settle further away from the vortex centre and have strong potential for vortex distortion. The net volume displacement force depends on the radial pressure force, the radial settling location of the bubble, as well as the vortex Reynolds number. The resultant of the volume displacement force is found to be roughly at $4{5}^{\circ } $ with the vortex travel direction, resulting in wakes directed towards the vortex centre. Finally, a simple modification to the standard point-particle two-way coupling approach is developed wherein the interphase reaction source terms are consistently altered to account for the fluid displacement effects and reactions due to bubble accelerations.

The unsteady flow evolution in a porous chamber with surface mass injection simulating propellant burning in a nozzleless solid rocket motor has been investigated by means of a large-eddy simulation (LES) technique. Of particular importance is the turbulence-transition mechanism in injection-driven compressible flows with high injection rates in a chamber closed at one end and connected to a divergent nozzle at the exit. The spatially filtered and Favre-averaged conservation equations of mass, momentum and energy are solved for resolved scales. The effect of unresolved subgrid scales is treated by using a dynamic Smagorinsky model extended to compressible flows. Three successive regimes of flow development are observed: laminar, transitional, and fully developed turbulent flow. Surface transpiration facilitates the formation of roller-like vortical structures close to the injection surface. The flow is essentially two-dimensional up to the mid-section of the chamber, with the dominant frequencies of vortex shedding governed by two-dimensional hydrodynamic instability waves. These two-dimensional structures are convected downstream and break into complex three-dimensional eddies. Transition to turbulence occurs further away from the wall than in standard channel flows without mass injection. The peak in turbulence intensity moves closer to the wall in the downstream direction until the surface injection prohibits further penetration of turbulence. The temporal and spatial evolution of the vorticity field obtained herein is significantly different from that of channel flow without transpiration.