Non-dimensional Number Research Articles

Theoretical Analysis of Type-I Flow Instability of Natural Circulation

Fukuda and Kobori proposed three types of Leginegg instabilities and five types of density wave instabilities, according to different mechanisms of density wave instabilities. The instability dominated by gravity pressure drop is classified as Type-I flow instability. The instability dominated by friction pressure drop is classified as Type-II flow instability. And the instability dominated by accelerated pressure drop is classified as Type-III flow instability.In present work, the Type-I flow instability between rectangular parallel channels of natural circulation was studied theoretically. Models including two-phase flow instability, natural circulation system components were established in combination based on the homogenous model. A computational program was written. The program was validated with experiments, and the results matched well with the experiment data. The marginal stability boundary (MSB) maps under different parameters were obtained by using nondimensional numbers Nsub and Npch. The influence of different kinds of pressure drop, inlet subcooling temperature of heating channels of type-I flow instability were analyzed separately. And the phenomena were explained from mechanism and the change of void fraction. The results show that the induce of inlet subcooling temperature enhances the stability of system. With the increase in system pressure, the system stability of natural circulation is enhanced.

Effect of the density ratio variation on the dynamics of a liquid jet injected into a gaseous cross-flow

In this paper, we investigate the effect of the density ratio on the primary atomization characteristics of a liquid jet injected into a gaseous crossflow. Jets into crossflow with a high density ratio can be challenging for some multiphase models with an interface reconstruction. In this case, it is common practice to artificially reduce the density ratio, keeping constant the dominant non-dimensional parameters, based on the assumption that keeping unaltered the non-dimensional numbers will also maintain the same atomization characteristics. The validity of this assumption is here investigated using large eddy simulations and a stochastic fields transported probability density function (PDF) method (Σ-Y-PDF). A jet into crossflow, with a momentum flux ratio of 6.6 and Weber number of 330, is simulated. Two different density ratios are considered, 10 and 860, corresponding to the ones adopted in previous detailed numerical simulation and experimental investigations, respectively. We find that the liquid column breakup is influenced by the density ratio, with lateral ligaments formation observed only for the lower one. Also, the flow field is affected: decreasing the density ratio, the velocity increases in the wake region with recirculation observed. Furthermore, despite having the same Weber and Reynolds numbers, the two cases show different droplet size distributions. Smaller droplets are produced with the increase in the density ratio. Close to the liquid jet, the shape of the distribution is also affected. For the lower density ratio, a dichotomy is present, related to the presence of two distinct underlying breakup mechanisms, while increasing the density ratio, the dichotomy disappears.

Elasto-inertial microparticle focusing in straight microchannels: A numerical parametric investigation

Elasto-inertial microfluidic particle separation has attracted attention in biotechnological applications due to its passive nature and enhanced versatility compared to inertial systems. Developing a robust elasto-inertial sorting device can be facilitated with numerical simulation. In this study, a numerical parametric investigation was undertaken to study elasto-inertial focusing of microparticles in a straight microchannel. Our goal was to develop an approach that could be both accurate and easily implementable on the commercial solvers. We simulated the flow field using the Carreau model. The resulting elastic lift force was implemented based on an approximation of the Oldroyd-B model. Results were verified and validated against experimental measurements by us and others. A parametric study was conducted to investigate elasto-inertial particle focusing considering the important non-dimensional numbers such as the Reynolds number (Re), the Deborah number (De), dimensionless channel length (L), and blockage ratio (β). Based on this investigation, the commonly used design threshold, that is, De·L·β2=1, for particle focusing was modified and a new threshold was proposed De·Re0.2·L·β2=5. This reduced particle dispersion throughout the width of the channel from ∼20% to ∼3%. Based on this analysis and the new thresholding scheme, an empirical non-dimensional correlation was developed to predict elasto-inertial particle dispersion in straight square cross-sectional microchannels. Using this new correlation, variation in predicted dispersion was reduced from ∼15% to less than ∼5%. Our model can be used to optimize the design of elasto-inertial microfluidic particle sorters to improve experimental outcomes.

Macroscopic and microscopic hydrodynamic mixing of stratified suspensions.

We conducted numerical experiments to investigate the mixing of stratified suspensions containing different types of particles. We used a point-force two-way coupling method. We studied the mixing behavior of stratified suspensions and we discovered two types of mixing: microscopic (individual-particle-level) and macroscopic (vessel-scale) collective mixing. In addition, we examined the vertical mixing speed of the stratified suspension. We used a simple theoretical model to analyze the fingering settling velocity. Then we introduced a nondimensional number representing the difference in collectivities of the upper and lower suspensions while accounting for particle terminal velocities. We discovered that the proposed nondimensional parameter has a negative sign that distinguishes the mixing form of only microscopic individual-particle-level mixing and a positive value that predicts the speed of macroscopic collective mixing of stratified suspensions.

A Combustion Regime-Based Model for Large Eddy Simulation

The aim of this work is to propose a unified (generalized) closure of the chemical source term in the context of Large Eddy Simulation able to cover all the regimes of turbulent premixed combustion. Turbulence/combustion scale interaction is firstly analyzed: a new perspective to look at commonly accepted combustion diagrams is provided based on the evidence that actual turbulent flames can experience locally several combustion regimes although global non-dimensional numbers would locate such flames in a single specific operating point of the standard combustion diagram. The deliverable is a LES subgrid scale model for turbulent premixed flames named Localized Turbulent Scales Model (LTSM). This is founded on the estimation of the local reacting volume fraction of a computational cell that is related to the local turbulent and laminar flame speeds and to the local flame thickness.

Особенности согласованного изменения сопротивления трения и профиля скорости течения в трубах при проявлении эффекта Томса

Object and purpose of research. Relationships between friction resistance coefficient and velocity distributions in the turbulent boundary layer of low-concentrated polymer solutions are investigated. These relationships are different from water because in polymer solutions the friction resistance at constant Reynolds numbers is additionally changed with solution concentrations. Materials and methods. The known experimental data on variations of the friction resistance coefficient and the velocity profiles in turbulent flows in circular tubes at changes in polymer solution concentrations. Main results. The general law of coordinated variations in friction resistance coefficient λ and flow velocity profile in the turbulent boundary layer depending on Reynolds number and polymer solution concentration. The flow models are validated, which describe the laws of velocity variations in all characteristic sections of boundary layer: laminar sublayer, buffer and logarithmic flow areas. A new non-dimensional number is introduced, which characterizes the ability of low concentrated water solutions of polymers to reduce the friction resistance. It is called the Toms effect parameter in the work. Conclusion. Results of the investigation will be useful in developing the theoretical methods for estimation of boundary layer characteristics in polymer solutions.

Vertical Wedge Drop Experiments as a Model for Slamming

_ A deeper comprehension of hydrodynamic slamming can be achieved by revisiting the wedge water entry problem using flexible structures. In this work, two wedge models that are identical, with the exception of different bottom thicknesses, are vertically dropped into calm water. Pressure, full-field out-of-plane deflection, strain, vertical acceleration, and vertical position are measured. Full-field deflections and strains are measured using stereoscopic-digital image correlation (S-DIC) and strain gauges. A nondimensional number, R, quantifying the relative stiffness of the structure with respect to the fluid load is revisited. An experimental parametric study on the effect of R on the nondimensional hydrodynamic pressure and the maximum strain is presented. It was found there is a sharp change in the trend of pressure and strain when R passes through a critical value. It was also discovered that the structural deformation causes a delay in the peak pressure arrival time and a reduction in the peak pressure magnitude during the wedge water entry. Introduction When high-speed planing craft operating in waves becomes airborne and reenters the water surface, a substantial impact or “slam” between the vessel bottom and the water surface will occur (Faltinsen 2005; Lloyd 1989). The bottom slamming events occur frequently and may injure the passengers, compromise the equipment onboard, or even damage the structure. Slamming is a major cause of speed reduction in small craft where slamming loads are important. Current design criteria are primarily based on empirical measurements with little regard for the fluid–structure interaction (FSI) physics of the slamming phenomenon. This study offers a first step toward better understanding of FSI in slamming for optimal structural design in the future. Since the cross sections of most surface effect ships may be approximated by a V-shaped wedge, the slamming characteristics of these sections may be examined by dropping a wedge model into water (Faltinsen 2005; Lloyd 1989). Studying the wedge water entry problem is also helpful in shedding light on the wet deck slamming of catamaran, sloshing under the chamfered roof of a partially filled tank (Faltinsen 2000), seaplane landing (Wagner 1932), water landing of spacecraft and solid rocket boosters, water landing/ditching of aircraft (Abrate 2013), and animal diving behavior (Chang et al. 2016).

CFD validation of condensation heat transfer in scaled-down small modular reactor applications, Part 2: Steam and non-condensable gas

This paper presents the computational fluid dynamics (CFD) validation and scaling assessment of the condensation heat transfer (CHT) models in the presence of non-condensable gas for the passive containment cooling system (PCCS) of the small modular reactor (SMR). The STAR-CCM+ software with 3D scaled-down SMR containment geometries was used in CFD simulations with steam and non-condensable gas (NCG). The limitations and approximations of the previous studies were resolved to avoid scaling distortion and uncertainties. Air was used as the NCG gas with steam. The multi-component gas model was used to define the steam-NCG mixture, and the condensation-seed parameter was used as the source term for the fluid film model. Three different turbulence models were used to check the heat flux performances and temperature distributions on the coolant side. The heat flux was estimated from the axial coolant bulk temperature, which was identical to the test data reduction method. An implicit-unsteady numerical solver was applied to the conjugate heat transfer models between the gas, liquid, and solid regions. Detailed simulations were performed, and simulation results were validated with the measured parameters experimentally. The condensation heat transfer performance was quantified using non-dimensional numbers and compared for different scaled geometries to identify the scaling distortions.

Dynamic crushing of a dedicated buffer during the high-speed vertical water entry process

A composite buffer has been designed to reduce the impact load of high-speed water entry projectile. Rigid Polyurethane (PU) foams of different densities have been used to make the damper of the buffer. A series of compression tests for PU foam specimens are implemented to obtain the stress-strain curves under different loading speeds. The constitutive model used in the simulation for PU foam has been validated by comparing the results with the experimental data. Six different failure modes have been found in the dynamic crushing process of the nose cap. The effects of PU foam density, the length of the nose cap on these failure modes are presented quantitatively by introducing a time-related non-dimensional number that represents the beginning time of each failure mode. The results show, the complete disintegration of the nose cap strongly depends on PU foam density, its effect is more pronounced in the cases when the ratio of the length of the buffer to the diameter of the projectile is greater than 0.92. The dedicated buffer is very efficient in reducing the impact load imposed in the cavitator of the projectile (the highest load-reducing ratio up to 51%).

Parametric modeling of a solid state Ericsson cycle heat engine

The Johnson Thermoelectric Converter (JTEC) operates as an approximation of an Ericsson cycle thermodynamic heat engine with no moving parts. During operation, hydrogen flows from a high-temperature high-pressure region to a low-pressure region by way of a membrane-electrode assembly. In passing through the assembly, the hydrogen is stripped of its electrons which flow through the circuit and reform with protons to the recover hydrogen on the low-pressure side. Some of the electrical power extracted is used to electrochemically “pump” the hydrogen back to the low-temperature high-pressure side and sustain the pressure differential. The objective of the work presented here was to mathematically characterize a JTEC system and to develop the coupled relationships between design goals like efficiency, net power production, and power density; and design parameters like high versus low operating temperatures and pressures, device geometry, and thermophysical properties of the device materials and working fluid. Power production is related to the operating pressure ratio, the ratio of high to low device operating temperatures, the high operating temperature, and the effective heat transfer area of the hot end. The efficiency is related to several non-dimensional and dimensional number groups (especially the recuperator effectiveness). The power density or volume of the device is related to a different recuperator parameter, the high temperature of the heat addition source, the cold temperature of the thermal rejection source, and the internal device geometry. Even with reasonable simplifications and assumptions, the design space contains a large number of variable parameters. The model equations were exercised over the large parametric trade space.

Sea-Spray-Generation Dependence on Wind and Wave Combinations: A Laboratory Study

We investigate the effects of wind–wave interactions on the surface sea-spray-generation flux. To this end, the Marine Aerosol Tunnel Experiment (MATE2019) was conducted at the Pytheas Institute large wave–wind facility in Luminy (Marseille, France) over the period June–July 2019. A unique range of air–sea boundary conditions was generated by configuring the laboratory with four types of wave forcing and five wind speeds spanning 8–20 m s\(^{-1}\). Young and developed waves were included, with wave ages between 1.3 and 9.5 (defined in terms of phase speed and friction velocity). Vertical sea-spray-concentration profiles measured over the 0.1–47.5 \(\upmu \)m radius range and a flux–profile method allowed estimation of the sea-spray-generation flux. Results show that the flux increases for increased wind-induced wave breaking, and is highest for steep and heavily-breaking waves. Scaling analysis shows that the sea-spray generation is best correlated with the wave-slope variance for larger droplets (20 \(\upmu \)m and above, assumed predominantly spume droplets generated by surface tearing). For smaller droplets (7–20 \(\upmu \)m, presumed predominantly jet droplets generated by bubble bursting), the highest correlation is found with a non-dimensional number combining the wave-slope variance with the friction velocity cubed. This is reflected in the formulation of two wave-state-dependent sea-spray-generation functions, each valid for wind speeds 12–20 m s\(^{-1}\) and droplet radii 3–35 \(\upmu \)m, thereby covering jet and spume droplet production.

Stability analysis of a single phase rectangular coupled natural circulation loop system employing a Fourier series based 1-D model

A linear stability analysis of a single-phase Coupled Natural Circulation Loop (CNCL) is carried out, and the stability maps of the CNCL system are obtained. A Fourier series based 1-D model is used to develop the stability maps. A 3-D CFD study is undertaken to assess the ability of the 1-D model to capture the non-periodic oscillatory behaviour exhibited by the CNCL system. After the model verification, the method used to obtain the stability maps is verified, and finally, the stability maps of the system are obtained from the eigenvalues of the steady-state. The steady-state analysis of the 1-D model of the CNCL system indicates that the CNCL has multiple steady states and the stability of a few of the steady states are presented. A thorough parametric study is then conducted to observe the influence of non-dimensional numbers such as the Grashof number, the Stanton number, the Fourier number, flow resistance coefficient and aspect ratio. Increase in Fourier number and flow resistance coefficient lead to an increase in the domain of stability for the range of parameters considered. The linear stability map is then compared with the empirical stability map to demonstrate that the higher-order non-linear terms do not significantly affect the stability boundary.

On simulating the effect of gravity on concurrent flame spread over thin paper through variations in ambient pressure

The environment inside a spacecraft, or a space habitat, can greatly differ from those on earth, affecting the burning behavior of solid fuels. Because in a gravity field there is a flame-induced buoyancy, it is very difficult to reproduce on Earth the environmental conditions of a spacecraft, or a habitat in the Moon or Mars, thus making fire testing and burning predictions harder. A potential alternative approach to overcome this problem is to reduce buoyancy effects by using reduced ambient pressure in normal gravity. The objective of this work is to explore the possibility of simulating the effect of gravity, and in turn buoyancy, through changes in ambient pressure, on upward/concurrent flame spread over a thin combustible solid. Comparisons with available data at different gravity levels are used to determine the extent to which low-pressure can be used to replicate flame spread characteristics at different gravities. Experiments of the upward/concurrent flame spread over thin Kimwipe paper sheets were conducted in normal gravity inside a pressure chamber with ambient pressures ranging between 100 and 30 kPa and a forced flow velocity of 10 cm/s. Results show that reductions of pressure slow down the flame spread over the paper surface, and also reduces flame intensity. Comparison with published partial gravity data shows that as the pressure is reduced, the normal gravity flame spread rate approaches that observed at different gravity levels. The data presented is correlated in terms of a mixed convection non-dimensional number that describes the convective heat transferred from the flame to the solid, and that also describes the primary mechanism controlling the spread of the flame. The correlation provides information about the similitudes of the flame spread process in variable pressure, flow velocity and gravity environments, providing guidance for potential ground-based testing for fire safety design in spacecraft.

Scaling of Droplet Breakup in High-Pressure Homogenizer Orifices. Part II: Visualization of the Turbulent Droplet Breakup

Emulsion formation is of great interest in the chemical and food industry and droplet breakup is the key process. Droplet breakup in a quiet or laminar flow is well understood, however, actual in-dustrial processes are always in the turbulent flow regime, leading to more complex droplet breakup phenomena. Since high resolution optical measurements on microscopic scales are extremely dif-ficult to perform, many aspects of the turbulent droplet breakup are physically unclear. To over-come this problem, scaled experimental setups (with scaling factors of 5 and 50) are used in con-junction with an original scale setup for reference. In addition to the geometric scaling, other non-dimensional numbers such as the Reynolds number, the viscosity ratio and the density ratio were kept constant. The scaling allows observation of the phenomena on macroscopic scales, whereby the objective is to show that the scaling approach makes it possible to directly transfer the findings from the macro- to the micro-/original scale. In this paper, which follows Part I where the flow fields were compared and found to be similar, it is shown by breakup visualizations that the turbulent droplet breakup process is similar on all scales. This makes it possible to transfer the results of detailed parameter variations investigated on the macro scale to the micro scale. The evaluation and analysis of the results imply that the droplet breakup is triggered and strongly influenced by the intensity and scales of the turbulent flow motion.

Cu and Cu-SWCNT Nanoparticles' Suspension in Pulsatile Casson Fluid Flow via Darcy-Forchheimer Porous Channel with Compliant Walls: A Prospective Model for Blood Flow in Stenosed Arteries.

The use of experimental relations to approximate the efficient thermophysical properties of a nanofluid (NF) with Cu nanoparticles (NPs) and hybrid nanofluid (HNF) with Cu-SWCNT NPs and subsequently model the two-dimensional pulsatile Casson fluid flow under the impact of the magnetic field and thermal radiation is a novelty of the current study. Heat and mass transfer analysis of the pulsatile flow of non-Newtonian Casson HNF via a Darcy–Forchheimer porous channel with compliant walls is presented. Such a problem offers a prospective model to study the blood flow via stenosed arteries. A finite-difference flow solver is used to numerically solve the system obtained using the vorticity stream function formulation on the time-dependent governing equations. The behavior of Cu-based NF and Cu-SWCNT-based HNF on the wall shear stress (WSS), velocity, temperature, and concentration profiles are analyzed graphically. The influence of the Casson parameter, radiation parameter, Hartmann number, Darcy number, Soret number, Reynolds number, Strouhal number, and Peclet number on the flow profiles are analyzed. Furthermore, the influence of the flow parameters on the non-dimensional numbers such as the skin friction coefficient, Nusselt number, and Sherwood number is also discussed. These quantities escalate as the Reynolds number is enhanced and reduce by escalating the porosity parameter. The Peclet number shows a high impact on the microorganism’s density in a blood NF. The HNF has been shown to have superior thermal properties to the traditional one. These results could help in devising hydraulic treatments for blood flow in highly stenosed arteries, biomechanical system design, and industrial plants in which flow pulsation is essential.

Capillary and viscous fracturing during drainage in porous media.

Detailed understanding of the couplings between fluid flow and solid deformation in porous media is crucial for the development of novel technologies relating to a wide range of geological and biological processes. A particularly challenging phenomenon that emerges from these couplings is the transition from fluid invasion to fracturing during multiphase flow. Previous studies have shown that this transition is highly sensitive to fluid flow rate, capillarity, and the structural properties of the porous medium. However, a comprehensive characterization of the relevant fluid flow and material failure regimes does not exist. Here, we used our newly developed multiphase Darcy-Brinkman-Biot framework to examine the transition from drainage to material failure during viscously stable multiphase flow in soft porous media in a broad range of flow, wettability, and solid rheology conditions. We demonstrate the existence of three distinct material failure regimes controlled by nondimensional numbers that quantify the balance of viscous, capillary, and structural forces in the porous medium, in agreement with previous experiments and granular simulations. To the best of our knowledge, this study is the first to effectively decouple the effects of viscous and capillary forces on fracturing mechanics. Last, we examine the effects of consolidation or compaction on said dimensional numbers and the system's propensity to fracture.

Thermo-hydraulic and entropy generation analysis for non-Newtonian fluid flow through sinusoidal wavy wall channel

The present investigation deals with numerical simulation of thermo-hydraulic transport characteristics of non-Newtonian fluid flowing through a wavy channel subjected to isothermal condition. The power-law constitutive model is adopted to illustrate the rheological behavior of fluid. The influence of various parameters like index of power-law (n), Reynolds number (Re), amplitude of sinusoidal profile (A), etc. on flow, thermal field, and entropy generation characteristics are delineated in detail. Furthermore, the outcome of the sinusoidal channel is compared with that of conventional straight channel in order to check the performance of wavy-wall channels. Results divulge that reliance of the thermo-hydraulic characteristics on wall geometry is unequivocally affected due to the amplitude of sinusoidal profile. Augmentation in heat transfer rate for lower values of amplitude of sinusoidal profile over the conventional channel is inconsiderable although difference upraises considerably owing to two factors namely: higher amplitude of sinusoidal profile and Re. The heat transfer rate diminishes with increment in power-law index. Consequently, heat transfer rate is progressively conspicuous for shear thinning fluids compared to shear thickening fluids. For comparison of pressure drop in the wavy and equivalent straight channel taking into account heat transfer and corresponding enhancement of pressure drop, we have defined a performance parameter. The comparison of performance parameter illustrates that shear-thickening fluids are more appropriate for engineering applications. Two nondimensional numbers are defined to elucidate the behavior of entropy generation with various parameters like Reynolds number, amplitude of sinusoidal profile, and power-law index. The entropy generation increases as the amplitude of waviness increases. Furthermore, entropy generation also intensify with increment in index of power-law for a distinct Reynolds number and amplitude of waviness. Results obtained from present study can be used as a tool to select wall geometry for design of compact and economical energy exchange devices dealing with non-Newtonian power-law fluids.

Gravity currents interacting with a bottom triangular obstacle and implications on entrainment

Laboratory experiments investigating the interaction of a lock-exchange dense gravity current and a submerged obstacle with a triangular section have been conducted to determine the influence of the relative obstacle height, i.e. the ratio between the heights of the current and the obstacle, on the dynamics of the overflowing dense current. Experimental measurements were aimed to obtain detailed instantaneous density fields through an image analysis technique based on light attenuation. The dense current is deeply affected by the interaction, depending on the relative obstacle height. When the height of the current approaching the obstacle is small, a lower percentage of overflow propagates downstream and a large reduction in the gravity current velocity is observed. The analysis of the density fields highlights that the formation of a macro vortex downstream of the obstacle is the mechanism responsible for the enhanced dilution of the overflow. Nevertheless, the bulk entrainment parameter is slightly affected by the presence of a bottom obstacle. Results deepen our understanding of the entrainment processes related to the interaction with the obstacle and confirm the role of relevant non-dimensional numbers.

Dynamics-based classification of semienclosed basins

This study is guided by other classifications of estuaries that are based on specified physical constraints. Previous classifications have been relevant and revealing of diagnostic functioning of estuaries in terms of their stratification and their baroclinically induced residual circulation. Those classifications, however, have disregarded residual circulations driven by tides, not only in estuaries, but in semienclosed basins in general. The classification proposed here uses tidally averaged, or residual, dynamics. Residual dynamics are explored via drivers, or forcing agents, of residual flow. Drivers are tides or density gradients and are counteracted by ‘modifiers,’ i.e., Earth’s rotation or friction. The relative influence between forcing agents is characterized by a scaled non-dimensional densimetric tidal Froude number, Fr02, which hinges on tidal current amplitude, water depth and reduced gravity. The competition between modifiers is determined by a non-dimensional Ekman number, Ek, which depends on the kinematic eddy viscosity, the latitude and the depth of the basin. The classification suggested identifies all types of estuaries, whose dynamics is influenced by density gradients, but also recognizes frictionless tidal basins, tidal rivers, coastal lagoons, and basins that switch their dynamics from being baroclinically forced to being tidally forced. This classification can also be interpreted as an assessment of the strength of mixing (in Ek) versus the strength of baroclinicity (in Fr02), which determines the residual flows in semienclosed basins. Additionally, the classification incorporates basins forced by wind stress and/or baroclinicity, and basins forced by wind stress and/or tides.

On the fluidization/sedimentation velocity of a homogeneous suspension in a low-inertia fluid

The modeling of the fluidization or sedimentation velocity of a suspension of solid particles is revisited by examining experiments conducted in either a liquid or a gas. A general expression is found in the case of negligible fluid inertia, i.e. at low Reynolds or Archimedes number. It is built as the product of the velocity of an isolated particle by three non-dimensional corrections that each takes into account a specific physical mechanism. The first correction reflects the variation of the buoyancy with the particle concentration. The second correction describes how the drag force increases with the concentration in case of negligible particle inertia. The third one accounts for the further increase of the drag when the particle inertia is increased. Remarkably, each correction only relies on a single of the three independent non-dimensional groups that control the problem: (1) the particle volume fraction Φs; (2) the ratio Φs/Φpack where Φpack is the bed packing concentration; (3) the Stokes number St0, which characterizes the inertia of the particles and controls their agitation. Moreover, the onset of the instability that separates the homogeneous regime from the heterogeneous one is found to be controlled similarly by the Stokes number. Empirical expressions of the corrections are given, which provide a reliable tool to predict fluidization and sedimentation velocities for all values of the three non-dimensional numbers. The present results emphasize the crucial role of particle inertia, which is often disregarded in previous modeling approaches, such as that of Richardson and Zaki.