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Flow electrification constitutes a significant hazard to operational safety in industry and for this reason it has been studied in detail over the years. It is generally accepted that the impact of turbulence on the electrification of liquids is of paramount importance. More specifically, at sufficiently high Reynolds numbers and for low-conductivity liquids such as hydrocarbons, the thickness of the hydrodynamic boundary layer can become comparable to that of the electrical double layer. This can lead to increased charge diffusion towards the bulk of the flow and, subsequently, flow electrification. However, quantitative information of the underpinning mechanisms of this phenomenon is still lacking. In this paper we present a computational framework for the study of electrification of liquid flows via numerical simulations. In the first part of the paper, we present the governing equations and describe the proposed algorithm and its implementation in pafiX, which is a computational tool for the simulation of fluid flows related to explosion protection. In the second part, we present results from numerical tests that we performed in order to access the efficiency of the proposed computational framework.

Preferential concentration of inertial particles in wall-bounded turbulent flows is of paramount importance and, thus, subject of fundamental research. In practical applications of confined particle-laden flows the particles experience frequent collisions with the piping system which may result in an unwanted electric charge separation through triboelectric effects. The consequential occurrence of electrostatic forces alters the particle trajectories and their distribution. In this work the influence of charges on the averaged concentration of inertial particles in a fully developed turbulent duct flow was investigated by means of a combined numerical and experimental approach. The order of magnitude of the potential charge accumulation was estimated and imposed in a parametric study to the particulate phase in the simulations. Also, a new numerical approach based on the stochastic parcel method is introduced that allows to handle a large number of charged particles in a Lagrangian framework. This new approach extends standard formulations by including the effect of electrostatic forces on each parcel. The simulations demonstrate that the concentration profiles are for the most part independent of the prescribed charge except in the region close to the walls. The peaks of the particle number density at the walls caused by turbophoresis are strongly reduced through the local increase of repelling electrostatic forces. The comparison of numerical with experimental data indicates that the particles in the experimental setup could be affected by a surface charge density of the order of 100 C/m2. The presented results aim to elucidate the impact of electrostatic forces in the particle distribution in wall-bounded particle-laden flows.

Stokes’ hypothesis states that the bulk viscosity of a Newtonian fluid can be set to zero. Although not valid for many fluids, it is common practice to invoke this hypothesis in the study of low-Mach-number, variable-density flows. Based on scaling arguments, we provide a necessary condition for neglecting the bulk viscous pressure from the governing equations. More specifically, we show that the Reynolds number defined with respect to the bulk viscosity must be very large. We further show that even when this condition is not satisfied, the bulk viscous pressure does not need to be taken explicitly into account in the computation of the velocity field because it can be combined with the hydrodynamic pressure.

International audience; In this paper, we present simulations of turbulent thermal convection driven by free-surface evaporation above and by a heated wall below. A novel algorithm is proposed for predicting evaporation rates at a free surface, which we then validate against experimental data. At the top of a cuboidal domain, a shear-free boundary condition acts as an approximation of the free surface. We first focus on a domain of aspect ratio Γ = 1, where a fully resolved direct numerical simulation is carried out at a moderate Rayleigh number, Ra = 1.2 × 107, and we compare flow statistics with a Large-Eddy Simulation (LES) on a coarse grid. Both the fully resolved simulation and the LES predict well the time- and area-averaged evaporation rate and free surface temperature when compared with the experimental data. Next, we carry out a series of LES with an increasing lower wall temperature and, consequently, Ra. We then validate the evaporation model by comparing LES predictions of the time- and area-averaged mass flux and temperature at the upper boundary against the experimental measurements. The aspect ratio of the domain is then reduced, and we show, for the first time, the transition to a dual-roll state of the large-scale circulation (LSC) at the aspect ratio of Γ = 1/4 in a cuboidal domain. The temperature and velocity distributions at the free surface are impacted by the state of the LSC. However, we find that the water-side turbulence and aspect ratio play a negligible role on the evaporation rate above, in accordance with experimental observations.

This article reports on numerical simulations of detonation propagation in channels that contain one or more porous obstructions. The porous media considered herein have high porosity and are of fine microstructure, i.e. the diameter of the fibres of the solid matrix is smaller than the characteristic chemical length scale. Our study is based on a thermo-mechanical model for flows in superposed porous and pure-fluid regions. According to it, the solid matrix is represented as a rigid continuum and its porosity is introduced as a distribution that varies in space. With regard to chemical kinetics, two different three-step chain-branching schemes are considered; their difference being in the termination reaction. Our simulations predict that, even at high porosity, the porous obstructions act as a highly efficient momentum sink, thereby causing the detonation to attenuate significantly. In the case of a single porous section, the detonation re-initiates downstream via chain-branching explosion. However, arrays of porous zones that span the entire cross section of the domain produce a decoupling of the reaction zone from the leading shock, thereby effectively suppressing the detonation. Also, our study reveals that in domains with arrays of porous blocks that only partially cover the cross section of the channel, the detonations do not quench. Instead, they propagate as low-velocity detonations, the properties of which are elaborated herein as well.

We report on direct numerical simulations of the effect of electrostatic charges on particle-laden duct flows. The corresponding electrostatic forces are known to affect particle dynamics at small scales and the associated turbophoretic drift. Our simulations, however, predicted that electrostatic forces also dominate the vortical motion of the particles, induced by the secondary flows of Prandtl's second kind of the carrier fluid. Herein we treated flows at two frictional Reynolds numbers ($Re_\mathrm{\tau}=$ 300 and~600), two particle-to-gas density ratios ($\rho_\mathrm{p}/\rho=$ 1000 and 7500), and three Coulombic-to-gravitational force ratios ($F_\mathrm{el}/F_\mathrm{g}=$ 0, 0.004, and 0.026). In flows with a high density ratio at $Re_\mathrm{\tau}=$ 600 and $F_\mathrm{el}/F_\mathrm{g}=$ 0.004, the particles tend to accumulate at the walls. On the other hand, at a lower density ratio, respectively a higher $F_\mathrm{el}/F_\mathrm{g}$ of 0.026, the charged particles still follow the secondary flow structures that are developed in the duct. However, even in this case, the electrostatic forces counteract the particles' inward flux from the wall and, as a result, their vortical motion in these secondary structures is significantly attenuated. This change in the flow pattern results in an increase of the particle number density at the bisectors of the walls by a factor of five compared to the corresponding flow with uncharged particles. Finally, at $Re_\mathrm{\tau}=$ 300, $\rho_\mathrm{p}/\rho=$ 1000, and $F_\mathrm{el}/F_\mathrm{g}=$ 0.026 the electrostatic forces dominate over the aerodynamic forces and gravity and, consequently the particles no longer follow the streamlines of the carrier gas.

In this paper we study turbulent thermal convection driven by free-surface evaporation at the top and a uniformly heated wall at the bottom. More specifically, we report on direct numerical simulations over 1.25 decades of Rayleigh number, Ra. At the top of the cubic domain, a shear-free boundary condition acts as an approximation of a free surface, and different evaporation rates form the basis of a temperature gradient assigned as a non-zero Neumann boundary condition. The corresponding lower wall temperature is fixed and we assess the thermal mixing on the water side of the air–water interface. The set-up is considered a simplified model of the turbulent natural convection in the upper volumes of spent-fuel pools of nuclear power plants. Surface temperatures are investigated over a range of 40 K, resulting in a sixteenfold increase in evaporation rates. Our work allows, for the first time, analysis of the features and mean flow statistics of this particular thermal convection configuration. Results show that a shear-free surface increases heat transfer within the domain; however, the exponent in the diagnosed power-law relation between the Nusselt and Rayleigh numbers, Nu = 0.178Ra 0.301 , is similar to that of classical turbulent Rayleigh–Bénard convection. Further, the free slip accelerates the fluid after impingement on the upper boundary, significantly affecting the structure of the large-scale circulation in the container. Analysis of the flow statistics then shows how the shear-free surface introduces inhomogeneities in thermal boundary layer heights. Overall, the investigated turbulent convection configuration shows unique traits, borrowing from both turbulent Rayleigh–Bénard convection and evaporative cooling.

In this paper we propose a time-accurate algorithm for the calculation of two-phase granular flows via two-velocity, two-pressure Eulerian models. Such flows exhibit a number of important characteristics that make their computation particularly challenging. For example, even at constant-density flows the suspended granular phase can compact or expand so that the velocity fields of the two phases are not solenoidal. Also, the granular material typically exhibits a complex and highly nonlinear rheological behaviour. Moreover, the governing equation for the granular volume fraction (often referred to in the literature as “compaction equation” or “particle migration model”) involves stresses as source terms and, therefore it is strongly coupled to the momentum balance laws. Herein we show that this coupling can be a strong destabilising factor in the computations if it is not treated properly. Our algorithm is based on a predictor–corrector time-integration scheme. Further, it employs a generalized double projection method for non-solenoidal velocity fields that results in second-order elliptic equations for the phasial pressures. The efficiency of the proposed algorithm is illustrated via a series of simulations of transient flows with strong concentration gradients, namely, sedimentation of a granular suspension, compaction of a dense sediment bed, and collapse of a submerged granular column. Numerical grid-convergence studies further show that the algorithm exhibits satisfactory convergence rates. Overall, these numerical results indicate that the proposed algorithm is well suited for the simulation of flows of dense suspensions, flows with high volume-fraction variations or material interfaces, as well as for unsteady fluid–solid interaction problems.

In this paper we report on a direct numerical simulation (DNS) of turbulent heat transfer in a T-junction. In particular, we study the interaction between two liquid streams, a hot horizontal cross-flow and a cold vertical liquid jet coming from above, in a T-junction of rectangular cross-section. We discuss in detail the instantaneous flow structures and present results for the first- and second-order statistics of the flow quantities, and for the budget of the turbulent kinetic energy. Further, we present results of the power spectral density of the velocity and temperature signals at selected locations of the flow field. Our analysis elucidates the properties of the important features of the flow such as the large recirculation bubble and the secondary separation zones that are formed in the vicinity of the entry of the jet. According to our simulations, thermal mixing is mainly driven by the shear layer between the two streams and, to a lesser extent, by the shear layer between the incoming jet and the large recirculation bubble. Thermal mixing is further enhanced by turbulence generation in the regions of adverse pressure gradients downstream of the large recirculation bubble. Within the framework of our study, we have also conducted a wall-resolved large-eddy simulation (LES) of the flow of interest so as to assess its predictive capacity. Overall, the LES predictions agree satisfactorily with our DNS data; the most noticeable discrepancy is that the LES produces mildly diffused profiles for the second-order statistics in the regions of intense turbulence production.

In this paper we present a numerical study of the dynamics of the Large-Scale Circulation (LSC) in turbulent convection with a free surface. Our study is based on Large-Eddy Simulations of thermal convection in a cube with a heated bottom wall and a cooled free-slip upper boundary which approximates the free surface. With water as the working fluid, simulations are performed at two different Rayleigh numbers, R a = 2 × 10 7 and R a = 1 × 10 8 . The LSC is the principal convective structure and is driven by plume formation at the top and bottom boundaries. In cuboidal domains, the LSC orientates itself along one of the diagonal planes. However, neither the orientation plane nor the direction of circulation remain fixed with time and reorientation events occur. Herein we first present the basic features of the LSC and then examine the frequency of reorientations and their role in turbulence statistics. According to our simulations, the most frequent event is the change of orientation plane, whereas changes in the direction of circulation are scarce. Also, the frequency of reorientations reduces significantly as the Rayleigh number increases. Finally, our analysis shows that reorientation events have an impact on the root-mean-square of the fluctuating component of the horizontal velocity. Therefore, statistics should be taken over long time periods so as to account for a sufficiently large number of events.

A helicopter flying through an atmosphere containing particulates may accumulate high electrostatic charges that can challenge its operational safety. In this paper the influence of the helicopter ...

In this paper we present a detailed study of turbulent mixing between a cold crossflow and a hot incoming jet in a T-junction. Our study is based on wall-resolved and experimentally validated Large Eddy Simulations (LES) without invoking the Boussinesq approximation regarding density variations. Emphasis is placed on the role of the temperature as an active scalar and the impact of thermal stratification on the emerging structures in the flow field. Herein we discuss in detail the main features of the flow, such as the shear layer between the two streams, the regions of flow acceleration due to the Venturi effect, the recirculation regions, and the thermal mixing downstream the reattachment point of the flow. We also elaborate on the first and second-order statistics of flow quantities, including the turbulent heat fluxes, and on the near-wall behaviour of the streamwise velocity component. Our numerical predictions compare favourably with existing experimental measurements, as regards both the temperature field and the turbulent heat fluxes. Our study also includes a spectral analysis of the temperature signal at selected locations near the solid boundaries, which is helpful for assessing the risk of thermal fatigue at the walls of the T-junction.

The accurate calculation of the electrostatic forces between charged particles requires a reliable representation of the emerging electric field. To this end, two principle formulations are available, namely Coulomb's and Gauss' laws. While both approaches are in this specific case mathematically equivalent, the numerical solution of Gauss' law on a grid is contaminated by a spatial discretization error. In this paper, we explore under which conditions this error depreciates the computed results of the particle dynamics. More specifically, we introduce a length-scale of the electrostatic interaction which serves as a base to evaluate the required grid resolution. Also, according to our numerical study, this error reduces in case the particle dynamics is contact dominated. Furthermore, we introduce a computationally efficient hybrid scheme which combines the advantages of both formulations and examine in which situations its accuracy is superior to schemes based on the numerical solution of Gauss' law.

In this paper we report on a computational study for the plane Poiseuille flow of a dense non-colloidal suspension at low Reynolds numbers. Our study is based on a recently developed two-phase model that appropriately accommodates constitutive relations for the suspension rheology and a migration model in the form of an advection-diffusion equation for the volume fraction of the granular phase [1]. Our numerical predictions accord well to experimental data and to previously reported numerical results based on a particle resolved method, especially as regards the particle distribution in the bulk of the channel. Further, we delineate the impact of the nonlocal stresses due to particle interactions on the structure of the flow and assess their effect on particle migration. Finally, we examine the role of these stresses in suspensions close to the jamming transition.

The accumulation of static electricity during powder transport is a possible ignition source for explosions and, thus, a hazard for operation safety in process industry. However, due to its high sensitivity to initial and boundary conditions, the process of charge build-up is challenging to study experimentally and many of the underlying mechanisms are still not well understood. Aiming at bridging this gap, in this paper we present the results of our experimental study on the influence of a range of parameters on the triboelectric charging of powders and transport pipes. The experiments were conducted in a recently assembled test-rig that facilitates the control of the ambient conditions to a high degree. According to our measurements, the powder charge increases if the conveying air velocity is increased. However, at a certain velocity the powder experiences a maximum charge whereas for higher velocities the charge subsequently drops. The air velocity that maximized the powder charge depends on the pipe material, diameter and powder loading. Further, a larger pipe diameter showed to enhance the charging process significantly. The results were highly repeatable and in good comparison with theoretical predictions.

During pneumatic transport, powders often experience the build-up of electrostatic charge due to collisions of the particles with the pipe. Since this can lead to hazardous spark discharges with unwanted implications, such as accidental explosions, there is a strong interest in exploring various options to limit this electrification process. In this paper we present the results of numerical simulations that we performed in order to evaluate the influence of the material properties of the powder and pipe, respectively, on this process. In our study, the turbulent flow of the carrier gaseous phase was treated numerically via Large Eddy Simulations while the particles were tracked individually in Lagrangian framework. Four-way coupling between the powder and the gaseous phase was also assumed. Our numerical simulations predicted that the particle Poisson ratio and Young's modulus, its electrical resistivity, as well as the permittivity represent promising measures to control the charge of the powder. More specifically, an increase of each of these quantities by 50% may lead to a decrease of the powder charge of up to 40%.

A helicopter flying through an atmosphere containing particulates may accumulate high electrostatic charges which can challenge its operational safety. In this paper we elaborate and validate a triboelectric charging model to predict the electrification experienced by a helicopter while hovering in dusty air. We employed Large Eddy simulations to describe the turbulent structures inherent in the flow around the rotorcraft. The dust particles were tracked individually in a Lagrangian framework. A model accounting for the triboelectric charge transfer when a particle hits the helicopter was introduced. The results demonstrate the accuracy of the proposed approach and allow a detailed analysis of the location of the charge accumulation.

The electrification of particles embedded in a turbulent flow may cause hazards such as spark discharges but is also exploited in several industrial applications. Nonetheless, due to its complexity and sensitivity to the initial conditions, the process of build-up of particle charge is currently not well understood. In order to gain a deeper understanding of this phenomenon, we performed fully resolved numerical simulations of particle charging. More specifically, our study concerned the charging process of particles dispersed in a turbulent channel flow at a friction Reynolds number of $Re_{\unicode[STIX]{x1D70F}}=180$. Emphasis was placed on the analysis of the interplay between the different physical mechanisms underlying particle electrification, such as fluid turbulence, particle dynamics and particle collisions. Further, we investigated the influence of some important physical parameters. According to our simulations the charge build-up depends strongly on the particle Stokes number, $Stk$. In particular, at small Stokes numbers, $Stk=0.2$, the turbopheretic drift inhibits particle charging. By contrast, at moderate Stokes numbers, $Stk=2$, and low particle number densities, the electric charge builds up but cannot escape the viscous sublayer due to limited particle migration. However, in the case of high particle number densities, the charge is transported away from the wall via inter-particle charge diffusion. A further increase to $Stk=20$ leads to strong charging and particle-bound charge transport towards the bulk of the channel.

In this paper we examine droplet behavior and macroscopic atomization characteristics of a non-reactive liquid spray via a series of large-eddy simulations. In our numerical study we examine three popular models for spray atomization, namely, the Taylor analogy breakup (TAB), Reitz–Diwakar and Pilch–Erdman models, and compare their predictions against available experimental data. According to our simulations, and for the flow conditions considered herein, the TAB model exhibits a slightly better performance than the other two models do. Further, since the TAB model is known to underestimate the effect of disruptive drag forces, we present a modification to it and assess its predictive capacity. More specifically, according to the numerical test presented herein, our modification has the potential to improve the accuracy in the numerical computation of important global quantities of the spray, such as the liquid and vapor penetration distances.

In this paper, we present an existence and uniqueness theory for the Darcy–Brinkman–Forchheimer equations that govern the stationary flow of a porous medium and a clear fluid occupying both bounded and unbounded domains. By extending Ladyzhenskaya's functional method to the equations at hand, we establish the existence of at least one weak solution. For the case of bounded domains, we additionally show that this solution is unique provided that a suitable smallness assumption, involving the Reynolds number, the porosity of the porous medium and the first eigenvalue of the Laplacian, is satisfied.

If a particle is in contact with another solid electric charge may be exchanged. Previous experimental observations clearly prove that the amount of exchanged charge does not only depend on the charge carried by the particle prior to the contact but also on its local distribution on the particles surface. However, most existing modeling approaches utilize the assumption of a uniformly charged particle. In the present paper we propose a new model which accurately accounts for the charge distribution on the particles surface during particle-wall and inter-particle collisions. Further, the results obtained with the new model are compared to data of single particle charging experiments. Moreover, we implemented the model in a Computational Fluid Dynamics (CFD) simulation of powder pneumatically transported in a pipe. We show that the charging behavior of the powder is quantitatively and qualitatively different if a non-uniform charge distribution is taken into account.

In this paper, a two-phase thermomechanical theory for granular suspensions is presented. Our approach is based on a mixture-theoretic formalism and is coupled with a nonlinear representation for the granular viscous stresses so as to capture the complex non-Newtonian behaviour of the suspensions of interest. This representation has a number of interesting properties: it is thermodynamically consistent, it is non-singular and vanishes at equilibrium and it predicts non-zero granular bulk viscosity and shear-rate-dependent normal viscous stresses. Another feature of the theory is that the resulting model incorporates a rate equation for the evolution of the volume fraction of the granular phase. As a result, the velocity fields of both the granular material and the carrier fluid are divergent even for constant-density flows. Further, in this article we present the incompressible limit of our model which is derived via low-Mach-number asymptotics. The reduced equations for the important special case of constant-density flows are also presented and discussed. Finally, we apply the proposed model to two test cases, namely, steady shear flow of a homogeneous suspension and fully developed pressure-driven channel flow, and compare its predictions with available experimental and numerical results.

The triboelectric charging of powders and hoses during pneumatic transport can cause hazardous spark discharges. In this work we employ numerical simulations to gain a deeper understanding in the physical processes involved in the build-up of electrostatic charge. To this end, Large Eddy Simulations are performed to simulate the turbulent flow of the gaseous phase while the particulate phase is described in Lagrangian framework. Dynamic models accounting for the particle-wall and particle-particle charge exchange are implemented and a model describing the charge distribution in an insulating hose is also developed. Our numerical results are in good agreement with available experimental data, while our simulations provide additional physical insight and information about the charging process. The results presented herein can be used to improve the safety of operation of many pneumatic components in process engineering.

Triboelectric charging of powders during pneumatic transport can lead to hazardous spark discharges. In this study, the charging process was studied numerically by means of large eddy simulations. A range of design parameters was then analyzed statistically applying the Design of Experiments methodology. It is shown that the electric charge of the powder can be significantly decreased by reducing the conveying air velocity. Furthermore, the usage of pipes of a larger diameter and the application of higher solid mass flow rates also reduce the powder charge.

In this paper we report on numerical simulations of temporally evolving, thermally stratified shear flows in superposed porous and pure-fluid domains. In particular, we study two different types of flows, namely, pressure-driven channel flows and unforced shear layers. Our study is based on a recently developed thermo-mechanical model for flows in the domains of interest. This model follows a mixture-theoretic approach, according to which the medium’s porosity is introduced as a concentration parameter, thus allowing the derivation of a single set of equations that is valid simultaneously in both domains. For the types of flows examined herein, our simulations predict the formation of spanwise vortical structures (rollers) at the porous–pure fluid interface. These rollers grow in time thereby inducing fluid circulation inside the porous medium. For the case of pressure-driven channel flows, our simulations further predict the development of plumes of hot and cold fluid due to convective instabilities that interact with the rollers. In the case of unforced shear layers, unstable stratification accelerates the growth of the rollers, which soon start to merge, and enhances fluid mixing. By contrast, the effect of stable stratification is exactly the opposite. Herein we discuss in detail the temporal evolution of the predicted flow structures and the interactions between them, as well as the mechanisms that induce thermal non-equilibrium inside the porous medium.

In this paper, we report on direct numerical and large-eddy simulations of turbulent thermal convection without invoking the Oberbeck–Boussinesq approximation. The working medium is liquid water and we employ a free-slip upper boundary condition. This flow is a simplified model of thermal convection of water in a cavity heated from below with heat loss at its free surface. Analysis of the flow statistics suggests similarities in spatial structures to classical turbulent Rayleigh–Bénard convection but with turbulent fluctuations near the free-slip boundary. One important observation is the asymmetry in the thermal boundary layer heights at the lower and upper boundaries. Similarly, the budget of the turbulent kinetic energy shows different behaviour at the free-slip and at the lower wall. Interestingly, the work of the mean pressure is dominant due to the hydrostatic component of the mean-pressure gradient but also depends on the density fluctuations which are small but, critically, non-zero. As expected the boundary-layer heights decrease with the Rayleigh number, due to increased turbulence intensity. However, independent of the Rayleigh number, the height of the thermal boundary layer at the upper boundary is always smaller than that on the lower wall.

In this paper, the stability of a plane, unidirectional Couette flow of a dense granular material is investigated via the means of a normal mode stability analysis. Our studies are based on a continuum mechanical model for the flows of interest coupled with the constitutive expressions for the normal and the shear stresses of the granular material induced by the ${\it\mu}(I)$-rheology. According to our analysis, both the Couette gap and the wall velocity play a destabilizing role in the flows of interest as opposed to the initial concentration that acts as stabilizer. For sufficiently high Couette gaps and wall velocities, unstable modes are recovered. The predicted instability manifests itself through shear-induced dilatancy that, in turn, engenders particle migration and the formation of bulbs, similar to the ones that have been acquired through molecular dynamics simulations.

In this paper, we develop a thermo-mechanical model for flows in superposed porous and fluid layers with interphasial heat and mass exchange. This model is based on a mixture-theoretic formalism, according to which, the fluid and the solid phases are treated as two coexisting but open thermodynamic continua that interact with each other. As such, each phase is endowed with its own set of thermodynamic variables and conservation laws. In particular, each phase is assigned with its own temperature field, thereby allowing for thermal non-equilibrium between the two phases. Constitutive equations for all dissipative and relaxation phenomena occurring in both phases are derived by exploiting the constraints imposed by the entropy axiom when applied to the entire mixture. This model is valid for both compressible and incompressible flows. Herein we also derive its low-Mach number approximation, which is substantially simpler and, therefore, more convenient for flows where compressibility effects are negligible. The efficacy of the proposed model and the effect of thermal non-equilibrium between the two phases are examined via direct numerical simulations of natural convection in a horizontal channel consisting of a porous layer and a superposed pure-fluid domain.

In this paper, a numerical analysis of two velocity-two pressure models for flows of solid particles and fluids is presented. First, a formal exploitation of the weak formulation of such models asserts that they are amenable to integration via projection methods. The challenging issues in the algorithm development for these models are then documented and suitable numerical methodologies for their remedy are devised. Subsequently, an algorithm for the integration of the models of interest is proposed. This is a two-phase projection method on collocated grids that utilizes a fractional-step time-marching scheme. It is further endowed with an interface detection-and-treatment methodology to properly account for the stiffness induced by the presence of moving and deforming material interfaces. The efficiency and robustness of the proposed numerical method are assessed in a series of numerical experiments that are delineated in the last part of this paper.

A helicopter flying through an atmosphere containing particulates may accumulate high electrostatic charges which can challenge its operational safety. In this paper we report on the in uence of the helicopter configuration on its electrification. Our study is based on a recently developed numerical approach according to which the turbulent air flow around the rotorcraft is estimated via large eddy simulations while the particulate flow is computed via Lagrangian particle tracking. Also, this approach incorporates a model for the triboelectric charge transfer during particle-helicopter collisions that is brie y described herein. The configurations that we examined in our study include rotor systems of two different sizes equipped with two, three or four blades. Our results reveal that a helicopter with fewer blades accumulates less electric current even though the charge on each individual blade is higher. Further, the location of the charge build-up on the rotor disk depends strongly on the number of blades. Also, according to our computations, a reduction of the rotor size leads to a reduction of its electrification, if all other parameters are kept constant. (Less)

The present study establishes the link between the well-known Nielsen model for the calculation of tortuosity in polymer-filled systems and the Darcy-Brinkman equation for flows in porous media. Based on the fact that the polymer-filled system is a porous medium, with properties fixed by the volume fraction and the geometry of the fillers, we employ the Darcy-Brinkman equations to compute an expression for tortuosity. This expression is then directly linked to the interphasial drag coefficient. Finally, we prove that the Nielsen model constitutes a special case of our derived formula.

In this letter, we establish an existence theory for an overdetermined system of nonlinear PDEs describing hydrostatics of fluid-saturated granular materials. Our proof consists of three steps: (i) the conduction of an integrability analysis, (ii) the reduction of the governing system to a singular elliptic PDE, for which the existence of solutions can be obtained via weak-convergence methods, and (iii) the development of an existence theory for the original system.

In this paper, a novel algorithm for incompressible flows of two-phase granular mixtures is proposed. The algorithm constitutes a generalization of projection-type methods to multi-phase flows and employs a predictor-corrector time-marching scheme. For the computation of the phasial pressures, a Poisson equation and a second-order elliptic PDE with variable coefficients are solved at both the prediction and the correction stage. Further, the algorithm is combined with a regularization scheme for the numerical treatment of material interfaces which are a common characteristic of the flows of interest. The efficiency and robustness of the proposed algorithm are illustrated via numerical simulations of unsteady two-dimensional shear flows for a reference mixture of beach sand and water.

Turbulent heat transfer in circular pipe flow with constant heat flux on the wall is investigated numerically via Large Eddy Simulations for frictional Reynolds number Re τ = 180 and for Prandtl numbers in the range 0.1 ≤ Pr ≤ 1.0. In our simulations we employ a second-order finite difference scheme, combined with a projection method for the pressure, on a collocated grid in cylindrical coordinates. The predicted statistical properties of the velocity and temperature fields show good agreement with available data from direct numerical simulations. Further, we study the local thermal flow structures for different Prandtl numbers. As expected, our simulations predict that by reducing the Prandtl number, the range of variations in the local heat transfer and the Nusselt number decrease. Moreover, the thermal flow structures smear in the flow and become larger in size with less sharpness, especially in the vicinity of the wall. In order to characterize the local instantaneous heat transfer, probability density functions (PDFs) for the instantaneous Nusselt number are derived for different Prandtl number. Also, it is shown that these PDFs are actually scaled by the square root of the Prandtl number, so that a single PDF can be employed for all Prandtl numbers. The curve fits of the PDFs are presented in two forms of log-normal and skewed Gaussian distributions.

A conundrum in non-equilibrium thermodynamics of heterogeneous mixtures with microstructure concerns the selection of thermodynamic currents and forces in the entropy production rate from the multitude of available options. The objective of this article is to demonstrate that the low-Mach-number approximation can narrow down this ambiguity. More specifically, by postulating that the post-constitutive equations are well behaved with respect to this perturbation analysis we assert that thermal non-equilibrium should be chosen as an independent force even if this requires the explicit manipulation of the entropy inequality. According to our analysis, alternative choices result in post-constitutive equations; the incompressible limit of which gives rise to questionable predictions.

In this paper, we generalize the concept of low-Mach-number approximation to multi-phase flows and apply it to the two-phase flow model of Papalexandris (J. Fluid Mech., vol. 517, 2004, p. 103) for granular materials. In our approach, the governing system of equations is first non-dimensionalized with values that correspond to a reference thermodynamic state of the phase with the smaller speed of sound. By doing so, the Mach number based on this reference state emerges as a perturbation parameter of the equations in hand. Subsequently, we expand each variable in power series of this parameter and apply singular perturbation techniques to derive the low-Mach-number equations. As expected, the resulting equations are considerably simpler than the unperturbed compressible equations. Our methodology is quite general and can be directly applied for the systematic reduction of continuum models for granular materials and for many different types of multi-phase flows. The structure of the low-Mach-number equations for two special cases of particular interest, namely, constant-density flows and the equilibrium limit is also discussed and analysed. The paper concludes with some proposals for experimental validation of the equations.

In this paper we analyze the equilibrium limit of the constitutive model for two-phase granular mixtures introduced in Papalexandris (2004) [13], and develop an algorithm for its numerical approximation. At, equilibrium, the constitutive model reduces to a strongly coupled, overdetermined system of quasilinear elliptic partial differential equations with respect to the pressure and the volume fraction of the solid granular phase. First we carry a perturbation analysis based on standard hydrostatic-type scaling arguments which reduces the complexity of the coupling of the equations. The perturbed system is then supplemented by an appropriate compatibility condition which arises from the properties of the gradient operator. Further, based on the Helmholtz decomposition and Ladyzhenskaya's decomposition theorem, we develop a projection-type, Successive-Over-Relaxation numerical method. This method is general enough and can be applied to a variety of continuum models of complex mixtures and mixtures with micro-structure. We also prove that this method is both stable and consistent hence, under standard assumptions, convergent. The paper concludes with the presentation of representative numerical results.

Dispersed solid particles in wall-bounded flows may get electrified during particle-wall collisions due to triboelectric effects. Subsequently, the electrostatic charge migrates from the near-wall regions to the bulk of the flow through the dynamics of the particles (particle-bound charge transport) and charge transfer during collisions between particles (inter-particle charge diffusion). In this paper, we explore the physics underlying the mechanism of inter-particle charge diffusion, which remains not well understood, by means of numerical simulations. We investigated the efficiency of the charge transport within the particulate phase via this mechanism and propose a time-scale for its characterization for particular systems. The considered parameters of these systems included the particle number density and charge as well as their mechanical and electrical properties. It was found that both an increase of the material density of the particles or of their number density results in an enhanced inter-particle charge diffusion and, thus, a reduction of its time scale. Moreover, if only the number density is high but the material density is kept low, then inter-particle charge diffusion may even become the dominant wall-normal charge transport mechanism. Further, in case some particles carry a high charge they are accelerated towards uncharged particles through electrostatic forces which leads to an efficient charge redistribution.

In this paper, we present some experimental and analytical model results of two-component fuel mixtures of methane, propane and hydrogen. Experimentally obtained turbulent burning velocity S-T for outwardly propagating spherical lean turbulent premixed flames is examined with an algebraic flame surface wrinkling reaction model using 1) mean local burning velocity, and 2) the critical chemical time scale from the leading edge model by Zel'dovich and Frank-Kamenetskii. Based on the latter approach, the time scale that characterizes the effects of preferential diffusion phenomenon in critically curved spherical flames is incorporated into the reaction model. For this, a proposed simple linear model is used for estimating the effective Lewis number of the two-component fuel (CH4H2 and C3H8-H-2)/Air mixtures. in general, both approaches are effective ways in achieving qualitatively consistent ST trends for both mixtures. However, in the second approach, model predictions show large S-T deviation especially at high turbulence. This I may be attributed to the use of approximate values of activation temperature and for the use of the effective Lewis number of both mixtures based on the simple linear model. (C) 2009 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.

In this article, we present and analyze a conservative approximation to reduced one-pressure one-velocity models for compressible two-phase flows that contain non-conservative products. This approximation is valid when certain material properties of the two phases are considerably different from each other. Although it cannot be applied to arbitrary mixtures, it is applicable to many heterogeneous mixtures of technological interest. Herein, we derive the Rankine-Hugoniot relations and Riemann invariants for the homogeneous part of the proposed model and develop an exact Riemann solver for it. Further, we investigate the structure of the steady two-phase detonation waves, with inert or reactive solid particles, admitted by the proposed model. Comparisons with the corresponding gaseous detonations are also made. Moreover, we derive a lower limit for the propagation speed of steady two-phase detonations in the case of reactive particles. At the limiting case of very dilute mixtures, this minimum speed tends to the Chapman-Jouguet velocity of gaseous detonations. Finally, we report on numerical simulations of the transmission of a purely gaseous detonation to heterogeneous mixtures containing inert or reactive solid particles. The effect of the solid particles on the structure of the resulting two-phase detonation is discussed in detail.

A new hydrodynamical algorithm to study astrophysical detonations is presented. A prime motivation of this development is the description of a carbon detonation in conditions relevant to superbursts, which are thought to result from the propagation of a detonation front around the surface of a neutron star in the carbon layer underlying the atmosphere. The one-dimensional calculations we have performed demonstrate that the carbon detonation at the surface of a neutron star is a multiscale phenomenon. We show that a multi-resolution approach can be used to solve all the reaction lengths. For mixed H/He accreting systems, we have introduced a new reduced network to study the impact of the photodesintegration of the heavy elements on the detonation.

PurposeThis paper sets out to perform a detailed numerical study of turbulent channel flow with strong temperature gradients using large‐eddy simulations.Design/methodology/approachA recently developed time‐accurate algorithm based on a predictor‐corrector time integration scheme is used in the simulations. Spatial discretization is performed on a collocated grid system using a flux interpolation technique. This interpolation technique avoids the pressure odd‐even decoupling problem that is typically encountered in collocated grids. The eddy viscosity is calculated with the extension of the dynamic Smagorinsky model to variable‐density flows.FindingsThe mean velocity profile at the cold side deviates from the classical isothermal logarithmic law of the wall. Nonetheless, at the hot side, there is a better agreement between the present results and the isothermal law of the wall. Further, the numerical study predicts that the turbulence kinetic energy near the cold wall is higher than near the hot one. In other words heat addition tends to laminarize the channel flow. The temperature fluctuations were also higher in the vicinity of the cold wall, even though the peak of these fluctuations occurs at the side of the hot wall.Practical implicationsThe findings of the paper have applications in the design and analysis of convective heat transfer equipment such as heat exchangers and cooling systems of nuclear reactors.Originality/valueThe paper presents the first numerical results for non‐isothermal turbulent channel flow with high wall‐temperature ratios (up to 9). These findings can be of interest to scientists carrying out research in turbulent flows.

Aims. This work presents a new hydrodynamical algorithm to study astrophysical detonations. A prime motivation of this development is the description of a carbon detonation in conditions relevant to superbursts, which are thought to result from the propagation of a detonation front around the surface of a neutron star in the carbon layer underlying the atmosphere. Methods. The algorithm we have developed is a finite-volume method inspired by the original MUSCL scheme of van Leer (1979). The algorithm is of second-order in the smooth part of the flow and avoids dimensional splitting. It is applied to some test cases, and the time-dependent results are compared to the corresponding steady state solution. Results. Our algorithm proves to be robust to test cases, and is considered to be reliably applicable to astrophysical detonations. The preliminary one-dimensional calculations we have performed demonstrate that the carbon detonation at the surface of a neutron star is a multiscale phenomenon. The length scale of liberation of energy is $10^6$ times smaller than the total reaction length. We show that a multi-resolution approach can be used to solve all the reaction lengths. This result will be very useful in future multi-dimensional simulations. We present also thermodynamical and composition profiles after the passage of a detonation in a pure carbon or mixed carbon-iron layer, in thermodynamical conditions relevant to superbursts in pure helium accretor systems., Comment: 7 pages, 7 figures, Astronomy and Astrophysics in press, a version of the paper with higher figures resolution can be found on http://www.astro.ulb.ac.be/Html/ps.html#Hydro

In this article we present a new numerical procedure for solving exactly the Riemann problem of compressible two-phase flow models containing non-conservative products. These products appear in the expressions for the interactions between the two phases. Thus, in the compressible limit, the governing equations are hyperbolic but can not be written as conservation laws, i.e. in divergence form. In general, the solution to the Riemann problem of these models contains six distinct centered waves. According to the relative position of these waves in the x-t plane, the possible solutions can be classified into four principal configurations. The Riemann solver we propose herein investigates sequentially each of these configurations until an admissible solution is calculated. Special configurations, corresponding to coalescence of waves, are also analyzed and included in the solver. Further, we examine the accuracy and robustness of three known methods for the integration of the non-conservative products, via a series of numerical tests. Finally, the issue of existence and uniqueness of solutions to the Riemann problem is discussed.

We report on numerical simulations of the evolution of two-dimensional detonation waves that are expanded from a small channel to a larger one. In accordance with experimental data, the simulations predict three different types of evolution, namely, supercritical, critical and subcritical detonations. In a supercritical detonation, the reaction zone remains always attached to the precursor shock, whereas in a critical one it temporarily detaches and then re-attaches to the front. In the subcritical type, the extinction is permanent, i.e., the detonation quenches. The effects of the fuel's activation energy and the channel-width ratio are studied via a parametric study. It is found that sufficiently large values of these two parameters can result to flows of the critical and even the subcritical type. Finally, three-dimensional simulations have also been performed and are briefly discussed herein. (c) 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

In this article we present a detailed numerical study of three-dimensional structures in gaseous detonations, using a parallelized, unsplit, shock-capturing algorithm. The computational domain consisted of a rectangular tube with periodic conditions on its lateral boundaries. A slightly perturbed ZND profile has been used as initial condition. Previous experimental studies in rectangular shock tubes suggest that there are two basic types of detonation structures: rectangular and diagonal ones. Rectangular structures are characterized by triple lines along the front that are parallel to the walls of the flow domain and by the presence of slapping waves on the walls. On the other hand, diagonal structures are characterized by diagonal triple lines and the absence of slapping waves on the walls. Both structures have been numerically reproduced in our study by suitably perturbing the initial conditions. All the important features of the flow fields that have been experimentally observed are reproduced in our simulations. Finally, an analysis of the geometric similarities between the two types of structures is also presented herein. (c) 2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

A time-accurate algorithm is proposed for low Mach number, variable density flows with or without chemical reactions. The algorithm is based on a predictor-corrector time integration scheme that employs a projection method for the momentum equation. A constant-coefficient Poisson equation is solved for the pressure following both the predictor and corrector steps to fully satisfy the continuity equation at each time step. Spatial discretization is performed on a collocated grid system that offers computational simplicity and straightforward extension to curvilinear coordinate systems. To avoid the pressure odd-even decoupling that is typically encountered in such grids, a flux interpolation technique is introduced for the equations governing variable density flows. An important characteristic of the proposed algorithm is that it can be applied to flows in both open and closed domains. Its robustness and accuracy are illustrated with a series of numerical experiments. In particular, we present simulations of non-isothermal, turbulent channel flow as well as simulations of a premixed flame-vortex interaction.

In this article we examine numerically the multidimensional Structure of detonation waves propagating in a mixture consisting of a combustible gas and inert solid particles. First, we provide a brief description of the two-phase flow model that is employed in our study. Subsequently, we present and analyze the results from numerical simulations of three representative cases. These results show in detail the flow structures that are developed behind the leading shock due to the momentum and energy exchanges between the two phases. The article also includes a parametric study on the effect of the particle volume fraction of the Mixture and the particle diameter. It is predicted that the detonation wave speed decreases monotonically as the particle volume fraction increases. In particular, sufficiently high volume fractions can cause detonation quenching. Finally it is predicted that, under constant volume fraction, the decrease in detonation speed is slightly more important for large particles than for small ones. C 2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

In this article we introduce a new two-phase model for compressible viscous flows of saturated mixtures consisting of a carrier fluid and a granular material. The mixture is treated as a multicomponent fluid, with a set of thermodynamic variables assigned to each of its constituents. The volume fraction occupied by the granular phase and its spatial gradient are introduced as additional degrees of freedom. Then, by applying the classical theory of irreversible processes we derive algebraic expressions for the viscous stresses and heat flux vectors, the momentum and energy exchanges between the two phases, as well as a parabolic partial differential equation for the volume fraction. In our model, thermal non-equilibrium between the two phases emerges as a source term of the evolution equation for the volume fraction, in contrast with earlier models.