Range Of Dimensionless Numbers Research Articles

Impact of gravity and inertia on stable displacements of DNAPL in highly permeable porous media

The flow of Dense Non-Aqueous Phase Liquid (DNAPL) in highly permeable porous media is characterized by a complex interplay between surface tension, viscous, gravity, and inertia forces. Gravitational effects in these systems have been particularly studied in the context of displacement instability, but little work has focused on the impact of gravitational and inertia forces on the stable displacement of DNAPL in highly permeable but non-fractured porous media. Here, we study the impact of the gravity and Forchheimer numbers on the stable displacement of DNAPL fronts in porous media. We first performed DNAPL injection experiments in bead packings of different sizes for different inlet flow rates and initial saturation. These experiments were accurately modeled using a Darcy–Forchheimer model combined with an Arbitrary Lagrangian–Eulerian tracking of the DNAPL front. Once validated against stable injections in glass beads, the model was then used to perform a broader parametric study than available with our experimental setup. We explored different injection and pumping scenarios over a range of dimensionless numbers. We found that gravity can significantly alter the fluid front in flows commonly found in contaminant hydrology. We estimate, however, that inertia will have a non-negligible impact upon the displacement of DNAPL only during active remediation techniques (e.g., free product pumping method) or pipe rupture events involving low-viscous DNAPL in highly-permeable porous media.

Effects of surrounding pressure on cone–jet formation in electrospray process

A numerical approach has been employed to investigate the role of surrounding gas pressure in the electrospray cone–jet status as the most desired and practical mode in various applications. The simulations carried out based on heptane as the working liquid and air as the surrounding gas, over an extent of absolute pressures lying in 10 kPa to 1000 kPa for the liquid flow rate 6.2 mLh−1 and the electric potential 4 kV. The simulating cases fall in the range of dimensionless numbers 82.2 < $${\text{Re}}_{j}$$ < 112.3, 17.3 < $${\text{We}}_{j}$$ < 44.0, 0.2 < $${\text{Ca}}_{j}$$ < 0.4 and $${\chi }_{j}$$ < 4 × 10–4, confirming the formation of a stable cone–jet pattern in compliance with the convective instability limits. Despite the preservation of cone–jet geometry, the results clarify that the surrounding pressure could obviously contribute a dual effect through the length and surface undulations of the jet owing to change in the drag force. The jet tip disintegration into droplets remarkably demonstrates a transition from a prolate to an oblate mode at the upper bound pressures. The surrounding medium also influences flow pattern within the cone zone by means of contracting and relocating vortices further downstream as the pressure rises up. The droplet mean size shows 7.9% variation all over the pressure extent, however, the droplet number size appears to earn more weight as the size spectrum broadens while the surrounding pressure increases.

Simulation of droplet detachment from hydrophobic and hydrophilic solid surfaces under the electric field using Lattice Boltzmann Method (LBM)

In this work, the dynamic behaviour of the droplet formation, deformation, breakup, and fragmentation is studied under the influence of the electric field using a potential model and leaky dielectric assumption via the lattice Boltzmann method (LBM). Through a lattice dependency analysis, the size ratio between the droplet and the channel conduit, as well as the lattice dimensions is optimized, by quantifying the changes in the pressure difference and surface tension at the droplet boundary, and variations of instantaneous and terminal Reynolds numbers. Effects of gravitational, surface tension, viscous and electric field forces are also studied in a range of dimensionless numbers: Eotvos number (6 ≤ Eo ≤ 24), capillary number (0 ≤ CaE ≤ 4) and at constant values of Ohnesorge number, conductivity and dielectric constant ratios respectively set to Ohd = 0.07, Rσ = 2 and Sε = 0.5. Hydrophobicity (θd > 90) and hydrophilicity (θd < 90) of the surface versus the positive and negative distinction functions are also taken into consideration. The morphology changes of the droplet into an oblate or prolate shapes under different dielectric constant ratios (0.5 < Sε < 2), and resulting streamlines and velocity vector fields are also investigated. It was shown that the electric field behaves differently under positive or negative distinction functions in terms of preventing or promoting the droplet detachment from the ceiling. Moreover, the balance between Eotvos and capillary numbers at different hydrophobicity and hydrophilicity conditions is discussed on the quality of droplet detachment, deformation, breakup and morphology change. It is also shown that droplet deforms to an oblate or prolate shape at various dielectric ratios. Simulation results also showed an acceptable agreement with the analytical and numerical solutions.

Evaporation effect on spreading time of a droplet in fluidized bed wet granulation

The spreading rate of fine droplets on solid particles is an effective parameter in the probability of particles aggregation in fluidized bed wet granulation. In this paper, evaporation effect on spreading time of a binder droplet on a solid substrate is investigated. Employing force balance between the surface tension force and the binder viscous force and considering the droplet volume change due to evaporation, a mechanistic model is developed. Based on mass conservation equation, evaporation process is modeled by considering diffusion and convection. Also, the local dependence of physico-chemical properties of gas on its temperature is considered. The effect of evaporation rate on droplet spreading time is evaluated for air-ethanol and air-water systems at different conditions of temperature, vapor pressure, contact angle, and droplet diameter by the presented model. The results show that evaporation plays a significant role in spreading of ethanol droplet in comparison with water droplet because of more volatility and smaller contact angle. Moreover, the dimensional analysis is utilized to obtain effective dimensionless numbers (Ohnesorge number, tanθ, humidity, and Schmidt number), and finally, the range of dimensionless numbers in which the binder evaporation plays a significant role in the droplet spreading time is specified for two systems.

Generalization of the Total Current–Voltage Characteristics for Transferred Arc Plasma Torch With Steam and Air Plasmas Based on the Analytical Anisotropic Model

Total current–voltage characteristics (CVCs) of a transferred arc plasma torch were determined for the case of oxidative plasma type, steam and air, by the application of the anisotropic analytical model to dc electric arc. The model takes into account the arc radiation reabsorption in the approximation of radiant thermal conductivity and is based on the power function approximation of temperature dependence on plasma electrical conductivity with different exponents along the longitudinal and transversal coordinates. The experimental data generalization for a 50-kW plasma torch was obtained in a simple form of dimensionless expression with a high statistically acceptable level. The electric resistance of arc as a generalized function ${\pi _{\rm dep}}$ is mainly affected by convection number of the energy transfer ${\pi _{\rm conv}}$ . This generalized characteristic can be used with subsequent application in the design of steam- and air-transferred arc plasma torches at a wide range of dimensionless numbers: ${\pi _{\rm dep}}$ between 90 and 932, ${\pi _{\rm conv}}$ from $5.16 \times {10^{ - 5}}$ to $1.76 \times {10^{ - 3}}$ , and the Reynolds number from 526 to 2212.

Combined buoyancy and viscous effects in liquid–liquid flows in a vertical pipe

This paper presents experimental and numerical results of interfacial dynamics of liquid-liquid flows when an immiscible core liquid is introduced into a continuous liquid flow. The fully developed flow model predicts multiple solutions of the jet diameter over a range of dimensionless numbers: flow rate ratio, viscosity ratio, Bond and Capillary numbers. Experiments have been carried out using Polyethylene Glycol (PEG) and Canola oil to investigate the realizability of the three possible solutions predicted by the fully developed flow model. The measured values of inner fluid radii agree very well with the lower branch of the three branched solution while deviating from the top branch beyond a critical flow ratio value. This deviation is attributed to the fact that the flow develops a non-axisymmetric solution at this critical point. Computational fluid dynamics simulations have also been performed to examine the developing core annular flow and to compare the analytical solution results of liquid jet radius. The results predicted by numerical simulations agree very well with both the lower and upper branches of solution predicted by the analytical theory.