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The slurry pump, which forms the core equipment of the deep-sea mining (DSM) system, provides lifting power for the ore from the seabed to the sea level, which is crucial for the safety of coarse ore particle transportation. Velocity slip plays a significant role in revealing the migration of the pump particles. Therefore, this study analyzes the velocity slip in a slurry pump using the computational fluid dynamics–discrete element method (CFD-DEM) for the first time. The relationship between the pump head and velocity slip was proposed and verified in this study based on the velocity triangle and Euler equation of the solid-liquid two-phase flow in the impeller. The effects of different particle sizes on the velocity slip are compared in detail. According to the computational results, the head depends on the larger velocity slip of the impeller outlet and lower velocity slip at the inlet. The peak value of the velocity slip was significantly reduced, and the peak position of the velocity slip and zero-point position moved backward for particle sizes ranging between 5-15 mm. This study provides a reference for the problems of particle migration and velocity slip in slurry pumps.

Experiments and numerical simulations of inertial particles in underexpanded jets are performed. The structure of the jet is controlled by varying the nozzle pressure ratio, while the influence of particles on emerging shocks and rarefaction patterns is controlled by varying the particle size and mass loading. Ultra-high-speed schlieren and Lagrangian particle tracking are used to experimentally determine the two-phase flow quantities. Three-dimensional simulations are performed using a high-order, low-dissipative discretization of the gas phase while particles are tracked individually in a Lagrangian manner. A simple two-way coupling strategy is proposed to handle interphase exchange in the vicinity of shocks. Velocity statistics of each phase are reported for a wide range of pressure ratios, particle sizes and volume fractions. An upstream shift of the Mach disk in the presence of particles reveals significant two-way coupling even at low mass loading. A semi-analytic model that predicts the extent of the Mach disk shift is presented based on a one-dimensional Fanno flow that takes into account volume displacement by particles and interphase exchange due to drag and heat transfer. The per cent shift in Mach disk is found to scale with the mass loading, nozzle pressure ratio and interphase slip velocity and inversely with the particle diameter.

Point-particle direct numerical simulations have been employed to quantify the turbulence modulation and particle responses in a turbulent particle-laden jet in the two-way coupled regime with an inlet Reynolds number based on bulk velocity and jet diameter $({D_j})$ of ~10 000. The investigation focuses on three cases with inlet bulk Stokes numbers of 0.3, 1.4 and 11.2. Special care is taken to account for the particle–gas slip velocity and non-uniform particle concentrations at the nozzle outlet, enabling a reasonable prediction of particle velocity and concentration fields. Turbulence modulation is quantified by the variation of the gas-phase turbulent kinetic energy (TKE). The presence of the particle phase is found to damp the gas-phase TKE in the near-field region within $5{D_j}$ from the inlet but subsequently increases the TKE in the intermediate region of (5–20)Dj. An analysis of the gas-phase TKE transport equation reveals that the direct impact of the particle phase is to dissipate TKE via the particle-induced source term. However, the finite inertia of the particle phase affects the gas-phase velocity gradients, which indirectly affects the TKE production and dissipation, leading to the observed TKE attenuation and enhancement. Particle response to the gas-phase flow is quantified. Particles are found to exhibit notably stronger response to the gas-phase axial velocity than to the radial velocity. A new dimensionless figure is presented that collapses both the axial and radial components of the particle response as a function of the local Stokes number based on their respective integral length scales.

This study proposes a method for simultaneous measurements of time-resolved three-dimensional velocity fields of the dispersed and continuous phases of a turbulent bubbly jet at a low void fraction using Lagrangian particle tracking (LPT) velocimetry with the Shake-The-Box algorithm. Four high-speed cameras are used to acquire time series of images that include both bubbles and fluid tracer particles. Bubbles are firstly tracked using intensity differences between tracer particles and bubbles, then the bubble images are removed from the camera images and all tracer particles are tracked using the residual images. Subsequently, FlowFit interpolation is applied to the LPT results obtained by phase separation to investigate flow characteristics of a bubbly jet. The bubbly jet was divided into two regions along the vertical direction: jet-like and plume-like regions. Streamwise vortex structures of continuous phase were generated mainly by the rising bubbles. The Gaussian and top-hat velocity profiles matched well with the ensemble-averaged fluid and bubble velocities, respectively. The measured slip velocity in the radial direction was not constant but linearly increased. The classical assumption of self-similarity with Gaussian profiles for fluid velocity and bubble concentration is experimentally verified. The fluid volume flux and entrainment coefficient are obtained as a function of the slip velocity, void fraction, plume and bubble width based on three-dimensional measurements. We found that the classical integral theory agrees well with experiments in the plume region.

We investigate the transport of size-selected particles suspended in turbulent boundary layers at friction Reynolds numbers up to $Re_\\tau = 19\\,000$. We use microscopic glass spheres in air, spanning a wide range of viscous Stokes numbers, $St^+ = 18\\text {--}870$. These are imaged simultaneously with the flow tracers, and particle image and tracking velocimetry are used to measure the two-phase flow along a wall-normal plane in the logarithmic region. The air flow statistics are not altered by the particles at the present mass loading. In comparison to the classic equilibrium solution, the particle concentration profiles display weaker wall-normal gradients. This is shown to be an effect of particle inertia: this manifests itself through different mechanisms in different strata of the flow, and the effects on the concentration are captured by a three-layer parameterization of the profile. The particles lag the fluid across the boundary layer, with a mean slip velocity of the order of the friction velocity and increasing with particle inertia. Near the wall this lag is mainly due to the instantaneous slip of the particles relative to the surrounding fluid, while away from the wall the leading cause is the preferential sampling of low-speed fluid regions. Larger particles (in the size range of sand, as opposed to dust) display a qualitatively different behaviour, likely because of nonlinear drag effects. All considered particles oversample specific regions of the fluid flow: they favour regions of negative streamwise fluctuations, especially ejection events, and are likely to be found about the centre of strain cells with backward-leaning compressive axis and forward-leaning extensive axis. This pattern is visible for a wide range of Stokes numbers, underscoring the multi-scale nature of preferential concentration. The present findings highlight how high-Reynolds-number features of turbulent boundary layers impact the transport of suspended inertial particles, and thus are especially relevant to environmental and geophysical flows.

The purpose of this research elaborates the behaviour of the two-phase hybrid nano-fluid flow of viscous fluid through the stretching sheet. Impacts of heat transfer, for MHD two-dimensional steady flow over stretching surface with Cattaneo-Christov (CC) model are discussed. Bio-convective, thermal radiation and convective conditions are considered. Porous surface and velocity slip effects are also considered. Darcy-Forchheimer relation characterizes porous medium. The governing equations are solved through MATLAB. Plots of temperature and velocity fields are discussed via various estimations of emerging variables. Results findings shows the velocity profile decreases in case of both simple and hybrid nano-fluids for higher estimations of magnetic parameter and local inertia coefficient parameter. Fluid temperature reduces for maximum thermal relaxation parameter and possess higher values against radiation parameter. Microorganism profile reduces bio-convection Lewis number but increases for the magnetic parameter. Prominent results from this study include determining the effective parameters to enhance heat transfer efficiency and defining the circumstances in which the nano-fluid performs better than traditional fluids. These discoveries offer significant perspectives on the utilization of Cattaneo-Christov model with hybrid nano-fluid flow in comprehensive thermal management systems and establish a basis for subsequent practical and theoretical investigations within the domain.

It is significant to explore the slip velocity characteristics of two-phase in blade tip clearance (BTC) of multiphase pump for improving semi-open mixed-flow pump performance. On the ground of the Euler-Euler inhomogeneous model, a gas-liquid mixed-flow pump was taken as the research object. Using CFX software to simulate the flow field in the multiphase pump with conditions of the inlet gas void fraction (IGVF) are 10%, 20% and 30%. The slip velocity characteristics of gas-liquid two-phase in mixed-flow multiphase pump with different blade tip clearance sizes (BTCS) were analyzed. The results show that there is obvious slip velocity on blade leading edge (L.E.), trailing edge (T.E.) and pressure side (PS) of BTC of mixed-flow pump impeller. When BTCS is small, the slip velocity on the tip pressure side has little change along flow direction, but with the increase of BTCS, slip velocity on the tip pressure side will gradually increase. There is a positive correlation between slip velocity and the pressure gradient. The research results can provide significant guidance for optimization design of semi-open mixed-flow multiphase pump.

We study the turbulent square duct flow of dense suspensions of neutrally buoyant spherical particles. Direct numerical simulations (DNS) are performed in the range of volume fractions $\\unicode[STIX]{x1D719}=0{-}0.2$ , using the immersed boundary method (IBM) to account for the dispersed phase. Based on the hydraulic diameter a Reynolds number of 5600 is considered. We observe that for $\\unicode[STIX]{x1D719}=0.05$ and 0.1, particles preferentially accumulate on the corner bisectors, close to the corners, as also observed for laminar square duct flows of the same duct-to-particle size ratio. At the highest volume fraction, particles preferentially accumulate in the core region. For plane channel flows, in the absence of lateral confinement, particles are found instead to be uniformly distributed across the channel. The intensity of the cross-stream secondary flows increases (with respect to the unladen case) with the volume fraction up to $\\unicode[STIX]{x1D719}=0.1$ , as a consequence of the high concentration of particles along the corner bisector. For $\\unicode[STIX]{x1D719}=0.2$ the turbulence activity is reduced and the intensity of the secondary flows reduces to below that of the unladen case. The friction Reynolds number increases with $\\unicode[STIX]{x1D719}$ in dilute conditions, as observed for channel flows. However, for $\\unicode[STIX]{x1D719}=0.2$ the mean friction Reynolds number is similar to that for $\\unicode[STIX]{x1D719}=0.1$ . By performing the turbulent kinetic energy budget, we see that the turbulence production is enhanced up to $\\unicode[STIX]{x1D719}=0.1$ , while for $\\unicode[STIX]{x1D719}=0.2$ the production decreases below the values for $\\unicode[STIX]{x1D719}=0.05$ . On the other hand, the dissipation and the transport monotonically increase with $\\unicode[STIX]{x1D719}$ . The interphase interaction term also contributes positively to the turbulent kinetic energy budget and increases monotonically with $\\unicode[STIX]{x1D719}$ , in a similar way as the mean transport. Finally, we show that particles move on average faster than the fluid. However, there are regions close to the walls and at the corners where they lag behind it. In particular, for $\\unicode[STIX]{x1D719}=0.05,0.1$ , the slip velocity distribution at the corner bisectors seems correlated to the locations of maximum concentration: the concentration is higher where the slip velocity vanishes. The wall-normal hydrodynamic and collision forces acting on the particles push them away from the corners. The combination of these forces vanishes around the locations of maximum concentration. The total mean forces are generally low along the corner bisectors and at the core, also explaining the concentration distribution for $\\unicode[STIX]{x1D719}=0.2$ .

In this study, we conducted interface-capturing high-resolution simulations of a bubbly upflow in a vertical channel to investigate the bubble distribution and its interaction with surrounding turbulence, focusing on the effects of the density ratio. A bulk Reynolds number $Re_b=2300$ was used for all simulations. The influence of density ratio on vortex structures and turbulence statistics differed between the near-wall and core regions of the channel. Adding 5.43 $\\%$ gas caused an increase in wall friction. By applying a generalised FIK identity to analyse wall friction, it was determined that the drag rise in the bubbly channel was mostly due to the near-wall region. Visualisation of the bubble and vortex structures showed that small bubbles near the wall induced larger magnitude of Reynolds shear stress and increased wall friction. Bubble behaviour near the wall region was similar for density ratios above 30, leading to wall friction saturation. In the core region, large deformable bubbles created wake vortices due to slip velocity between liquid and gas phases. Wake vortices help large bubbles absorb smaller bubbles and maintain their sizes. As the density ratio increased, the slip velocity increased owing to greater difference in the gravitational acceleration between liquid and gas phases, resulting in corresponding increase in wake intensity and velocity fluctuations. However, quadrant analysis showed that Q1 and Q3 events increased together with Q2 and Q4 events in the core region, cancelling out any net effect of wake vortices on Reynolds shear stress or wall friction.

Abstract Motivated by the temporal relaxation feature of the Jeffrey model and its practical uses in the rheological modeling of several vital liquids, this study aimed to present a theoretical analysis of three-dimensional MHD Jeffrey nanofluid flows over a dual stretching surface with velocity slip conditions. By adopting the nonhomogeneous nanofluid model along with the passive control approach of nanoparticles, the current flow problem is solved semi-analytically via the homotopy analysis method for convective heating and multiple slip conditions. Dynamically, the magnetic and viscoelastic parameters have a declining effect on the velocity distributions in both directions in the existence and absence of slip effects, while the Deborah number has generally an escalating influence on the flow distributions. On the other hand, the variations of the velocity profiles in both directions are always greater in the presence of slip effect as compared to the nonslip case. Besides, the velocity stretching factor rises the velocity profiles in both directions. Furthermore, this increasing impact is dominant for the velocity distribution along the $y{\\rm{-}}$direction as compared to the velocity field along the $x{\\rm{-}}$direction. Thermally, the greater Biot number increases the temperature distribution. However, the bigger Schmidt number reduces the concentration distribution. Graphical Abstract Graphical Abstract