Effect of Evaporation of Liquid Droplets on the Distribution of Parameters in a Two–Species Laminar Flow

A calculation model was developed, and the heat– and mass–transfer characteristics in a laminar air—vapor—droplet flow moving in a round tube were studied numerically. The distributions of parameters of the two–phase flow over the tube radius were obtained for varied initial concentrations of the gas phase. The calculated heat and mass transfer is compared to experimental data and calculations of other authors. It is shown that evaporation of droplets in a vapor—gas flow leads to a more intense heat release as compared to a one–species vapor—droplet flow and one–phase vapor flow     

Sloping Saturated–Unsaturated Flow with Outflow at Seepage Face

Analytic series solutions are constructed for the phreatic free surface problem of two-dimensional steady downslope saturated–unsaturated flow, with water exiting at a seepage face. The region in free parameter space is delineated for which the water table intersects the upper surface, and the steady state with uniform constant irrigation rate, ceases to exist. The flow solution is extended to a case of the domain being more general than a parallelogram, with the upper and lower boundaries being piecewise linear. This geometry resembles that of large-scale rainfall simulators that are designed to test slope stability of wetted soil beds.     

Sediment–Water Interface Flow with the Multiparticle Collision Dynamics

This paper presents an experimental study of particle transport in porous medium using a self-developed sand layer transportation–deposition testing system, aiming at delineating the detachment characteristics of deposited particles in porous medium. Two experimental modes, increase flow velocity and change flow direction, were adopted in this study. The tests were conducted using quartz powder as the particles and quartz sand as the porous media to study the response of detachment characteristics to changes in particle diameter (\(d_{s}\), with median diameter 18 and 41 \(\upmu \)m) and grain diameter (\(d_{p}\), with median diameter 0.36 and 1.25 mm). Breakthrough curves after the second peak were well described by a double exponential model with parameters of weight coefficient and detachment coefficient. This study shows that both modes can change the detach rate of deposited particles observably, and detach rate is affected by the value of flow velocity greatly.     

Joule–Thomson Effects on the Flow of Liquid Water

We present a revised form of the energy balance for the coupled thermodynamics of liquid water flowing in porous media and give examples of situations where a commonly used formulation based on transport of enthalpy leads to erroneous results. Assuming negligible contribution from kinetic energy as well as sources and sinks such as energy from radioactive decay, total energy conservation is reduced to a balance between changes in internal energy, enthalpy, conductive heat flux, and gravitational potential energy. The Joule–Thomson coefficient is defined as the change in temperature with respect to an increase in pressure at constant enthalpy. Because liquid water has a negative Joule–Thomson coefficient at low temperatures, at a constant gravitational potential water cools as it compresses and heats as it expands. If one ignores the gravitational energy, transport of enthalpy alone leads to water heating by 2 \(^\circ \) C per kilometer as it is brought up from depth. The corrected energy balance transports methalpy, which is enthalpy plus gravitational potential energy. Although the simpler form leads to small changes in the temperature profile for typical simulations, there are several instances where this effect may prove to be important. The most important impact of the erroneous form is probably in the field of geothermal energy production, where the creation of a few degrees of heat in a simulation could lead to miscalculation of power plant efficiencies.     

Transport of Polymer Particles in Oil–Water Flow in Porous Media: Enhancing Oil Recovery

Transport in Porous Media - 3D printing with powders offers the most analogous method to the natural way in which clastic reservoir rocks are formed, resulting in pore network textures and...     

Flow Through Super-elliptic Ducts Filled with a Darcy–Brinkman Medium

The fully developed flow and constant flux heat transfer in super-elliptic ducts filled with a porous (Darcy–Brinkman) medium are studied. Super-elliptic ducts resemble rectangular ducts with rounded corners. An efficient Ritz method is used to determine the velocity and temperature fields. Extensive tables for friction factor–Reynolds number product and Nusselt number are given.     

Slip–Brinkman Flow Through Corrugated Microannulus with Stationary Random Roughness

This paper presents a boundary perturbation method of the Brinkman-extended Darcy model to investigate the flow in corrugated microannuli cylindrical tubes with slip surfaces. The stationary random model is used to mimic the surface roughness of the cylindrical walls. The tube is filled with a porous medium. We shall consider the two cases where corrugations are either perpendicular or parallel to the flow, and particular attention is given to the effect of the phase shift. The effects of the corrugations on the flow rate and pressure gradient are investigated as functions of wavelength, the permeability of the medium, the radius ratio and the slip parameter. Particular surface roughnesses are examined as special cases of stationary random surface. It is found that the effect of the partial slip is significant on the corrugation functions. The limiting cases of Stokes and Darcy’s flows and no-slip case are discussed.     

On the Darcy–Brinkman–Boussinesq Flow in a Thin Channel with Irregularities

In this paper, we investigate the effects of a small boundary perturbation on the non-isothermal fluid flow through a thin channel filled with porous medium. Starting from the Darcy–Brinkman–Boussinesq system and employing asymptotic analysis, we derive a higher-order effective model given by the explicit formulae. To observe the effects of the boundary irregularities, we numerically visualize the asymptotic approximation for the temperature, whereas the justification and the order of accuracy of the model is provided by the theoretical error analysis.

     

Effect of Inertial Terms on Fluid–Porous Medium Flow Coupling

The study considers an effect of the nonlinear inertial terms in the Brinkman filtration equation on the characteristics of coupled flows in a pure fluid and porous medium in the frameworks of two independent problems. The first problem is the forced boundary-layer flow overlying the Darcy–Brinkman porous medium. The Prandtl theory is used, and the self-similar equations are built to describe it. It is shown that the inertial terms have a valuable effect on the boundary-layer structure because of the large velocity gradient in the transition zone. The boundary-layer thickness in a porous medium rapidly grows at large Reynolds numbers. The velocity magnitude and gradient at the interface also change. The second independent problem is an analysis of the inertial terms effect on the flow stability. The neutral curves of the full and linearized flow models are built using the shooting method. They have different short-wave asymptotic, but there are no significant changes in the critical Reynolds numbers and corresponding wave numbers.     

Numerical Study of Hydrodynamics and Heat and Mass Transfer of a Ducted Gas–Vapor‐Droplet Flow

A computational model has been developed to predict heat and mass transfer and hydrodynamic characteristics of a turbulent gas–vapor–droplet flow. Turbulent characteristics of the gas phase are computed using the k– model of turbulence. It is shown that, with increasing inlet droplet diameter, the rate of heat transfer between the duct surface and the vapor–gas mixture decreases appreciably, whereas the wall friction increases only insignificantly. The predicted values agree fairly well with available experimental and numerical data     

Mechanical Testing of Solid–Solid Interfaces at the Microscale

In order to determine the influence of internal interfaces on the material’s global mechanical behavior, the strength of single interfaces is of great interest. The experimental framework presented here enables quantitative measurements of the initiation and propagation of interfacial cracks on the microscale. Cantilever beams are fabricated by focused ion beam milling out of a bulk sample, with an interface of interest placed close to the fixed end of the cantilever. Additionally, a U-notch is fabricated at the location of the interface to serve as a stress concentrator for the initiation of the crack. The cantilevers are then mechanically deflected using a nanoindentation system for high resolution load-displacement measurements. In order to determine the onset and propagation of damage, the stiffness of the cantilevers is recorded by partial unloads during the test as well as by making use of a continuous stiffness technique. A finite element model is used to normalize the load and stiffness in order to establish the framework for comparisons between different interfaces.     

New Progress on Fine Particles in China

~~New Progress on Fine Particles in China     

On the Darcy–Brinkman Flow Through a Channel with Slightly Perturbed Boundary

The goal of this paper is to study the effects of a slightly perturbed boundary on the Darcy–Brinkman flow through a porous channel. We start from a rectangular domain and then perturb the upper part of its boundary by the product of the small parameter \(\epsilon \) and arbitrary smooth function h. Using asymptotic analysis with respect to \(\epsilon \), the effective model has been formally derived. Being in the form of the explicit formulae for the velocity and pressure, the asymptotic approximation clearly shows the nonlocal effects of the small boundary perturbation. The error analysis is also conducted providing the order of accuracy of the asymptotic solution.     

Periodic Klein–Gordon Chains with Three Particles in 1:2:2 Resonance

Journal of Dynamics and Differential Equations - In this paper, we deal with the three degrees of freedom Hamiltonian systems describing the Klein–Gordon chains with three particles of equal...     

Response to Comments on the Article Titled ‘The Starting Flow in Ducts Filled with a Darcy–Brinkman Medium’

The fully developed flow and constant flux heat transfer in super-elliptic ducts filled with a porous (Darcy–Brinkman) medium are studied. Super-elliptic ducts resemble rectangular ducts with rounded corners. An efficient Ritz method is used to determine the velocity and temperature fields. Extensive tables for friction factor–Reynolds number product and Nusselt number are given.     

Aluminum Particles–air Detonation at Elevated Pressures

The effect of initial pressure on aluminum particles–air detonation was experimentally investigated in a 13 m long, 80 mm diameter tube for 100 nm and 2 μm spherical particles. While the 100 nm Al–air detonation propagates at 1 atm initial pressure in the tube, transition to the 2 μm aluminum–air detonation occurs only when the initial pressure is increased to 2.5 atm. The detonation wave manifests itself in a spinning wave structure. An increase in initial pressure increases the detonation sensitivity and reduces the detonation transition distance. Global analysis suggests that the tube diameter for single-head spinning detonation or characteristic detonation cell size would be proportional to (d ₀: aluminum particle size, p ₀: initial pressure). Its application to the experimental data results in m ~ O(1) and n ~ O(1) for 1 to 2 μm aluminum–air detonation, thus indicating a strong dependence on initial pressure and gas-phase kinetics for the aluminum reaction mechanism in detonation. Hence, combustion models based on the fuel droplet diffusion theory may not be adequate in describing micrometric aluminum–air detonation initiation, transition and propagation. For 2 μm aluminum–air mixtures at 2 atm initial pressure and below, experiments show a transition to a “dust quasi-detonation” that propagates quasi-steadily with a shock velocity deficit nearly 40% with respect to the theoretical C–J detonation value. The dust quasi- detonation wave can propagate in a tube with a diameter less than 0.4–0.5 times the diameter required for a spinning detonation wave.     

Diffusion–Convection in a Porous Medium with Impervious Inclusions at Low Flow Rates

The aim of this paper is to develop a macroscopic model for the transport of a passive solute, by diffusion and convection, in a heterogeneous medium consisting of impervious solids periodically distributed in a porous matrix. In the porous part, the flow is described by Darcy's law. Attempt is made to derive the macroscopic equation governing the average concentration field in the equivalent macroscopic medium and the macroscopic transport parameters. The analysis is conducted in the case when convection and diffusion are of the same order of magnitude at the macroscopic level, that is, when the Péclet number is of order 1. The proposed macroscopic model is obtained using the homogenization method for periodic structures with a double scale asymptotic expansion, in which the small parameter is the ratio between the two characteristic lengths l (the period scale of the impervious bodies distribution) and L (the scale of the macroscopic sample). The macroscopic parameters, which characterize the multiporous medium, depend solely on the transport parameters in the porous matrix and on the geometry of the impervious inclusions without any phenomenological assumption. Numerical computations are performed using a finite element method for several geometries of the solid inclusions, in two- and three-dimensional cases.     

Instability of Hadley–Prats Flow with Viscous Heating in a Horizontal Porous Layer

The onset of convective rolls instability in a horizontal porous layer subject to a basic temperature gradient inclined with respect to gravity is investigated. The basic velocity has a linear profile with a non-vanishing mass flow rate, i.e., it is the superposition of a Hadley-type flow and a uniform flow. The influence of the viscous heating contribution on the critical conditions for the onset of the instability is assessed. There are four governing parameters: a horizontal Rayleigh number and a vertical Rayleigh number defining the intensity of the inclined temperature gradient, a Péclet number associated with the basic horizontal flow rate, and a Gebhart number associated with the viscous dissipation effect. The critical wave number and the critical vertical Rayleigh number are evaluated for assigned values of the horizontal Rayleigh number, of the Péclet number, and of the Gebhart number. The linear stability analysis is performed with reference either to transverse or to longitudinal roll disturbances. It is shown that generally the longitudinal rolls represent the preferred mode of instability.