Model Of Momentum Transfer Research Articles

Flow factor for molecularly thin fluid films in one-dimensional flow due to fluid discontinuity

This article studies the flow of molecularly thin fluid films confined between and entrained by two contact surfaces in one dimension problem based on a simplified momentum transfer model between fluid molecules. The fluid discontinuity across the fluid film thickness is taken into account. The total fluid mass flow through the contact is directly derived based on this model. According to this obtained flow, the flow factor is introduced into the conventional calculation of this flow, which ignores the fluid discontinuity across the fluid film thickness, to make the flow correction. The calculation of this flow by using the present flow factor would be more accurate. It is also found that in the present molecularly thin film hydrodynamic lubrication, the influence of the fluid discontinuity across the fluid film thickness on the total fluid mass flow through the contact is determined by the operational parameter K which is defined as K = ∂ p / ∂ x h 2 / [ 6 η bulk ( 1 − ξ ) ( u a + u b ) ] . Here, the value of the operational parameter K depends on the fluid film pressure gradient ∂ p/∂ x, the fluid film thickness h, the bulk viscosity η bulk of the fluid, the contact–fluid interfacial slip rate ξ and the speeds u a and u b of the upper and lower contact surfaces. In the present molecularly thin film hydrodynamic lubrication, when the value of the operational parameter K is high, i.e., over 0.1, the influence of the fluid discontinuity across the fluid film thickness on the total fluid mass flow through the contact is significant. When the value of the operational parameter K is low, i.e., close to zero, this influence is negligible. It is found that the fluid film shear stresses at both the upper and lower contact surfaces are reduced by the effect of the fluid discontinuity across the fluid film thickness in the present molecularly thin film hydrodynamic lubrication and this reduction can be significant.

Boundary Shear Distribution in Straight Ducts and Open Channels

A semianalytical model was developed to predict boundary shear distribution in straight, noncircular ducts and open channels. The model was developed using a simplified streamwise vorticity equation, which involves only secondary Reynolds stress terms. These terms are representative of transverse turbulence anisotropy and nonhomogeneity. Transverse anisotropy is modeled using a universal function. Shear stresses are incorporated into the model by applying the momentum transfer model. An empirical model was employed to calculate the effect of the channel boundary on shear stresses. The final equation was applied to calculate boundary shear distribution in triangular ducts and trapezoidal open channels. The model predictions were well correlated with experimental data.

Three-dimensional modelling of radial segregation due to weak convection

A comprehensive three-dimensional, time-dependent model of heat, momentum and solute transfer during solidification is carried out to illustrate the influence of weak convection, caused by surface tension forces, on radial dopant segregation occurring in crystal growth under micro-gravity conditions. 3D adaptive finite element method is used in order to simulate the motion and deformation of the solidification interface. The geometry studied is a Bridgman configuration with a partly coated surface. The small slots in the coating gives a free surface in a controlled way, and is varied in order to alter the Marangoni flow. In this study, A comparison is made between the numerical results and the experimental results. A good agreement has been observed for the effective distribution coefficient k eff and for the radial segregation Δ c′. The radial dopant segregation is affected by weak convection.

Comments on “critical view on new results in micro-fluid mechanics”

In two recent papers [1,2], Drs. H. Herwig and O. Hausner dismiss ‘‘almost all’’ recent studies that claim special effects for flow and heat transfer through microdevices. They find the approach in those studies misleading and argue that existing observations in microdevices can be explained by merely rescaling the traditional models routinely used for macrodevices. Herwig and Hausner suggest that the same equations, properly non-dimensionalized, should be used for both micro and macrosystems. In Ref. [2], Professor Herwig states emphatically and in capital letters, ‘‘IN A NONDIMENSIONAL FORM ALL SPECIAL ‘‘MICRO-EFFECTS’’ WILL TURN OUT TO BE SCALING EFFECTS WITHIN A CONTINUUM THEORY EQUALLY VALID FOR MACRO AND MICRO PROBLEMS.’’ In this Technical Note, we argue that traditional treatments of transport phenomena may not be appropriate for certain situations involving microdevices. The simplistic dimensional analysis approach advocated in [1,2], though not incorrect, does miss important physics and is therefore misleading. We first start by defining microdevices and what we mean by traditional modeling of mass, momentum and heat transfer in or around conventional devices. We then describe the conditions under which non-traditional modeling of transport phenomena may be needed. Finally, we list the available alternative modeling tools. The focus here will be on fluid transport, but similar arguments can be made for solid transport, for example heat conduction through solid media. Microelectromechanical systems (MEMS) refer to devices that have characteristic length of less than 1 mm but more than 1 lm, that combine electrical and me-

Semiclassical theory of spin transport in magnetic multilayers

A semiclassical model of the spin momentum transfer in ferromagnetic film (FM)/normal metal (NM) structures is presented. It is based on the Landau–Lifshitz equation of motion and the exchange interaction in FM, and on the spin diffusion equation in NM. The internal magnetic field is treated by employing Maxwell’s equations. A precessing magnetization in FM creates a spin current which is described by spin pumping proposed by Tserkovnyak et al. The back flow of spins from NM into FM is assumed to be proportional to the spin accumulation in NM as proposed by Silsbee et al. These theoretical calculations are tested against the experimental results obtained by different groups. A good agreement was found for Py/Cu samples, but spin pumping is significantly enhanced in Py/Pt systems.

Reduced bias synthesis of cubic boron nitride thin films by magnetically enhanced inductively coupled radio frequency plasma chemical vapor deposition

Thin films of cubic boron nitride (cBN) were deposited from a mixture of diborane (B 2H 6), nitrogen and argon gas by inductively coupled radio frequency (RF) plasma chemical vapor deposition. Ion bombardment is a necessary condition for the growth of cubic phase. A series of samples were grown by changing the substrate bias voltage and the input RF power. The films were characterized by studying Fourier transformed infrared spectroscopy (FTIR) and the glancing angle X-ray diffraction pattern. XRD spectra showed clear reflection from the cubic phase up to (311). Lattice distortion was observed due to the presence of compressive stress in the films. The threshold of the window of bias voltage for the synthesis of cubic phase was found to decrease when an axial magnetic field of 500 G was applied to the plasma. This red shift of the substrate bias, when the plasma was enhanced magnetically, supported the momentum transfer model for the growth of cubic phase.

Momentum Transfer By A Mountain Meadow Canopy: A Simulation Analysis Based On Massman's (1997) Model

Using a mountain meadow as a case study it is the objective of the present paper todevelop a simple parameterisation for the within-canopy variation of the phytoelementdrag (Cd) and sheltering (Pm) coefficients required for Massman's model of momentum transfer by vegetation. A constant ratio between Cd and Pm is found to overestimate wind speed in the upper canopy and underestimate it in the lower canopy.Two simple parameterisations of Cd/Pm as a function of the plant area density and the cumulative plant area index are developed, using values optimised by least-squares regression between measured and predicted within-canopy wind speeds. A validation with independently measured data indicates that both parameterisations work reliably for simulating wind speed in the investigated meadow. Model predictions of the normalised zero-plane displacement height and the momentum roughness length fall only partly within the range of values given in literature, which may be explained by the accumulation of plantmatter close to the soil surface specific for the investigated canopies. The seasonal course of the normalised zero-plane displacement height and the momentum roughness length are discussed in terms of the seasonal variation of the amount and density of plant matter.

Two-Phase Eulerian/Lagrangian Model for Nucleating Steam Flow

This paper describes an Eulerian/Lagrangian two-phase model for nucleating steam based on classical nucleation theory. The model provides an approach for including spontaneous homogeneous nucleation within a full Navier-Stokes solution scheme where the interaction between the liquid and gas phases for a pure fluid is through appropriately modeled source terms. The method allows for the straightforward inclusion of droplet heat, mass, and momentum transfer models along with nucleation within complex flow systems as found, for example, in low pressure steam turbines. The present paper describes the solution method, emphasizing that the important features of nucleating steam flow are retained through comparison with well-established 1-D solutions for Laval nozzle flows. Results for a two-dimensional cascade blade and three-dimensional low pressure turbine stage are also described.

Physical and mathematical models of gas-liquid fluid dynamics in LD converters

Fluid dynamics of gas-liquid interactions in a LD converter to refine steel was physically and mathematically simulated. Using a water model three cases of gas supply were considered, top blowing, bottom injection and combined process top blowing-bottom injection. Mixing time in top blowing increases with bath height and the distance between the lance of the gaseous jet and the bath surface. The jet penetration was found to be dependent on the modified Froude number. The unstable and unsteady behaviour of the bath topography, as affected by the gaseous jet, was well simulated through a multiphase momentum transfer model. In top blowing, three zones of liquid splashing were found, penetration with low splash, heavy splash and dimpling with low splash intensity. These zones depend on the gas flow rate and the distance from the lance to the bath surface. During bottom injection mixing times decrease with the number of tuyères, increases of bath height and gas flow rate. In a combined process mixing time decreases considerably due to the recirculating flow formed by the action of the top jet and the submerged jets. When a submerged jet is located just below the top jet the mixing time does not decrease as compared with the separated processes either top blowing or bottom stirring. Physikalische und mathematische Modelle zur Strömung von Gas und Schmelze im LD-Konverter. Das Strömungsverhalten in einem LD-Konverter wurde besonders im Hinblick auf die Wechselwirkungen zwischen Gas und Schmelze physikalisch und mathematisch simuliert. Mit einem Wassermodell wurden drei Varianten des Gaseinleitens betrachtet: Aufblasen, Bodenblasen und kombiniertes Blasen. Beim Aufblasen nimmt die Zeit zur Durchmischung mit der Badhöhe als auch mit dem Abstand der Lanze vom Gasstrahl und der Badoberfläche zu. Es zeigte sich, daß die Eindringtiefe des Strahls von der modifizierten Froude-Nummer abhängt. Das instabile und unstetige Verhalten der Badtopographie, soweit vom Gasstrahl betroffen, ließ sich gut mit einem mehrphasigen Momententransfermodell simulieren. Beim Aufblasen läßt sich das Spritzen in drei Zonen unterteilen: geringes Spritzen beim Eindringen des Gasstrahls in die Schmelze, starkes Spritzen und Dimplebildung mit geringer Spritzintensität. Diese Bereiche hängen von den beiden Parametern Strömungsgeschwindigkeit des Gases und Abstand der Lanze von der Badoberfläche ab. Beim Bodenblasen verkürzt sich die Mischzeit mit der Anzahl der Düsen, steigender Badhöhe und Gasströmungsgeschwindigkeit. Beim kombinierten Blasen fällt die Mischzeit infolge der gegenläufigen Strömung, die sich aus den Gasstrahlen der oberen Düse und der Bodendüsen zusammensetzt, beträchtlich. Wenn die Position des aus dem Tauchrohr austretenden Strahls gleich unterhalb des oberen Strahls liegt, nimmt die Mischzeit im Vergleich zum reinen Auf- oder Bodenblasen nicht ab.

Modeling of Dendritic Growth with Convection Using a Modified Cellular Automaton Model with a Diffuse Interface.

A modified cellular automaton model with a diffuse interface has been developed in order to investigate the effects of convection on dendritic growth morphology in an undercooled melt. The present model is based on the coupling of the dendritic growth algorithm generally used in cellular automaton models and the continuum model of phase field models. A diffuse interface is adopted in order to solve the continuum model for species and momentum transfer with convection. The asymmetrical growth of dendrite arms and the deflection behavior have been investigated with various parameters, such as the preferred orientation of crystal growth, the inlet flow velocity, the initial liquid concentration, and the initial supercooling of the melt. It was found that convection induces an asymmetric dendritic growth in the upstream direction, caused by the asymmetry of solute distribution in the liquid ahead of the solid/liquid interface. The asymmetry in dendritic growth is amplified with the increase of both the initial concentration and the flow velocity, and the asymmetry decreases with the increase of the initial supercooling. It can be concluded that the present model can be successfully applied to simulate dendritic growth morphology with convection.

Calculations of the pulse combustion drying system

The paper describes modelling of spray drying system where valved and valveless pulse combustors were applied as a source of drying agent. Experimental analysis of pulse combustors operation was carried out in order to optimize their performance to achieve low emission of toxic substances, stable operation and high and smooth pressure oscillations. Optimized valved and valveless units were applied in the drying system. Extensive drying and evaporation tests were carried out to establish basic data required for modelling of the system. Laser techniques were applied to determine flow field in the drying chamber (LDA) as well as to analyse the structure of disperse phase (PDA). A modified mathematical model of heat, mass and momentum transfer in spray drying, developed earlier, was used to describe the pulse combustion drying system. The model enables to obtain temperatures of continuous and disperse phases, percent of evaporation and positions of particular fractions in the dryer. Air velocity profiles in the axial and radial directions in the drying chamber determined experimentally were substituted to the main programme calculating the spray drying process. A comparison of theoretical and experimental results shows good agreement also for complex hydrodynamics of pulsating flow in the drying chamber. Experimental investigations and mathematical modelling proved that the pulse combustion spray drying system could be effectively applied in dewatering of solutions with low content of solids, which could be important for waste disposal.

<I>Quo Vadis</I> Thermal Spraying?

This paper is devoted to thermal spraying and presents the state of our current knowledge, as well as the following research or development needs: spraying heat sources, i.e., flame, high-velocity oxifuel flame (HVOF), detonation gun (D-Gun), and plasma torches; particle heat and momentum transfer (measurements and modeling), process on-line control, powder morphologies, and injection within the hot jet and reactions with environment; coating formation, i.e., particle flattening and solidification, splat layering, residual stresses, coating microstructure, and properties; and reliability and reproducibility of coatings.

The plasma-sheath transition with a constant mean free path model and the applicability of the Bohm criterion

The fluid model for positive ions is used together with the assumption of a constant ion mean free path to examine the structure of the plasma-wall sheath at low and medium pressures in plasmas where ionization is by electron impact and the ion temperature is set to zero. It is shown that in the near collisionless regime there is the same structure as was found with the constant collision frequency for momentum transfer model with the Bohm speed playing the same role and similar scaling of the transitional layer. At higher pressures there is again no transitional layer, only plasma joining smoothly to a collisional sheath, thus the Bohm criterion has no significance, but the scaling is with a different exponent than for the mobility case. No fundamental differences are found between the two models. An expression is derived to describe the boundary between the parameter region where the Bohm criterion applies and that where it does not.

Thermomechanical theories for swelling porous media with microstructure

Thermomechanical microstructural dual porosity models for swelling porous media incorporating coupled effects of hydration, heat transfer and mechanical deformation are proposed. These models are obtained by generalizing the three-scale system of Murad and Cushman [56,57] to accommodate heat transfer effects and their influence on swelling. The microscale consists of macromolecular structures (clay platelets, polymers, shales, biological tissues, gels) in a solvent (adsorbed water), both of which are considered as distinct nonoverlaying continua. These continua are homogenized to the meso (intermediate scale) in the spirit of hybrid mixture theory (HMT), so that at the mesoscale they may be thought of as two overlaying continua. Application of HMT leads to a two-scale model which incorporates coupled thermal and physico-chemical effects between the macromolecules and adsorbed solvent. Further, a three-scale model is obtained by homogenizing the particles (clusters consisting of macromolecules and adsorbed solvent) with the bulk solvent (solvent not within but next to the swelling particles). This yields a macroscopic microstructural model of dual porosity type. In the macroscopic swelling medium the mesoscale particles act as distributed sources/sinks of mass, momentum and energy to the macroscale bulk phase system. A modified Green's function method is used to reduce the dual porosity system to a single-porosity system with memory. The resultant theory provides a rigorous derivation of creep phenomena which are due to delayed intra-particle drainage (e.g. secondary consolidation of clay soils). In addition, the model reproduces a class of lumped-parameter models for fluid flow, heat conduction and momentum transfer where the distributed source/sink transfer function is a classical exchange term assumed proportional to the difference between the potentials in the bulk phase and swelling particles.

Steady Flow of Newtonian and Dilatant Fluids over an Array of Long Circular Cylinders.

Field equations for the steady flow of power-law dilatant fluids normal to an array of long circular cylinders have been solved numerically using the finite difference method. The cylinder-cylinder interactions have been simulated using the two widely used concentric cylindrical cell models, namely, the Free surface and Zero vorticity cell models. Extensive theoretical results on the individual components of flow resistance arising from pressure and shear forces are presented for a range of physical and kinematic conditions. Furthermore, information on the variation of vorticity and power-law viscosity is also presented to provide some physical insights into the nature of the flow field. The results presented herein encompass the following ranges of physical and kinematic conditions: e = 0.5 and 0.9; Re = 0.1, 1 and 10 and 1 ≤ n ≤ 1.8. An excellent match between theory and experiments for Newtonian fluids demonstrates the utility of this simple approach to the modeling of momentum transfer in fibrous beds and tubular heat exchangers. However, no suitable experimental results are available for dilatant fluids in these systems.

A computational study of transient plane front solidification of alloys in a Bridgman apparatus under microgravity conditions

A mathematical model of heat, momentum and solute transfer during directional solidification of binary alloys in a Bridgman furnace has been developed. A fixed grid single domain approach (enthalpy method) is used. The effects of coupling with the phase diagram (a concentration-dependent melting temperature) and of thermal and solutal convection on segregation of solute, shape and position of the solid/liquid interface are investigated. A vorticity–stream function formulation is used for calculation of the velocity fields. The results presented include calculations at 1 and 10 μ g, both neglecting and including the dependence of melting temperature on concentration.

99/01812 Pressurised steam drying of Australian low-rank coals. Part 1. Equilibrium moisture contents: Bongers, G. D. et al. Fuel Process. Technol., 1998, 57, (1), 41–54

A mathematical model for mass, momentum and heat transfer in a one-dimensional two-phase flow is presented. This model was applied to the drying process of wet coal particles in a gas flow. The coal particles were assumed to have a wet core and a dry oute crust. The evaporation process of liquid from a particle was assumed to be governed by diffusion through the particle crust and convection into the gas medium. As evaporation proceeds, the wet core shrinks as the particle dries. The drying process is assumed to stop when: the moisture content of a particle falls to a predefined value; or the crust temperature reaches the ignition temperature: or break-up of the particle, caused by a pressure rise in the wet core, has occurred. The model was based on the one-dimensional balance equations for mass, momentum and energy of the gas and the dispersed phases. The system of the governing equations was represented by first-order differential equations and solved simultaneously by a numerical method. The model permitted calculation of the mass transfer ratio, change of the core diameter, and change of the average temperatures of the core and the crust. Four operating conditions were simulated using the model: isothermal: adiabatic: fixed wall temperature: and known heat flux. The model is also capable of simulating a dispersed gas-solids flow, without mass or heat transfer, in a one-dimensional transport system. The prediction of the numerical simulation, for the last case, was compared with experimental results of coal-nitrogen conveying in high pressure systems.

An Analytical one-Dimensional Second-Order Closure Model of Turbulence Statistics and the Lagrangian Time Scale Within and Above Plant Canopies of Arbitrary Structure

An analytical one-dimensional second-order closure model is developed to describe the within canopy velocity variances, turbulent intensities, dissipation rates, Lagrangian time scale and Lagrangian far field diffusivities for vegetation canopies of arbitrary structure and density. The model incorporates and extends the model of momentum transfer developed by Massman (1997) and the model of within canopy velocity variances developed by Weil (unpublished) from the second-order closure model of Wilson and Shaw (1977). Model predictions of within and above canopy velocity variances, turbulent intensities, dissipation rates and the Lagrangian time scale are in reasonable agreement with previously measured or estimated values for these parameters. The present model suggests that the Lagrangian time scale and the far field diffusivity could be strongly dependent upon foliage structure and density through the foliage effects on the velocity variances. A simple formulation for the Lagrangian time scale at canopy height is derived from model results. Taken as a whole, the present model may provide a relatively simple way to incorporate turbulence parameters into models of soil/canopy/atmosphere mass transfer.

A coupled phasic exchange algorithm for three-dimensional multi-field analysis of heated flows with mass transfer

A three-dimensional multi-field coupled phasic exchange (CPE) algorithm, for the prediction of general two-phase flows is presented. The algorithm is applicable to an arbitrary number of fields, a four-field construct is adopted here. Ensemble averaged transport equations for mass, momentum, energy and turbulence transport are solved for each field (continuous liquid, continuous vapor, disperse liquid, disperse vapor). This four field structure allows for analysis of adiabatic and boiling systems which contain flow regimes from bubbly through annular. Interfacial mass, momentum, turbulence and heat transfer models provide coupling between fields. The CPE algorithm is a semi-coupled implicit method to solve the set of 25 equations which arise in the formulation. In this paper, the CPE algorithm is summarized, with emphasis on six component numerical strategies employed in the method. These are: (1) incorporation of interfacial momentum force terms in the control volume face flux reconstruction, (2) coupled solution of the discrete linearized system of four constituent field equations for each transport scalar, (3) a consistent pressure-velocity correction scheme which properly accounts for drag and mass transfer, (4) an additive correction strategy for efficient solution of the mixture continuity and coupled field continuity equations, (5) an implicit source term treatment for volume fraction equations which ensures realizability of volume fraction fields during the course of iteration, (6) coupling of the phasic continuity and compatibility equations within the framework of a pressure–volume fraction-velocity correction scheme. The necessity/effectiveness of these strategies is demonstrated in applications to several test cases. The effectiveness and accuracy of the overall method is demonstrated using results of a three-dimensional analysis of boiling SUVA flow in a vertical coolant passage element.

Investigation of the Premixing Phase of a Steam Explosion with Hot Spheres

The multiphase, transient, and three-dimensional interaction of molten corium with water during the premixing phase of a steam explosion is simulated in the QUEOS facility using a large number of small solid spheres at temperatures up to 2300 K. The objective of the experiments is to establish a database for testing the models of heat and momentum transfer in multifluid codes as well as the codes’ capability to correctly describe multiphase flows. Three experiments with up to 10 kg of spheres made of molybdenum are discussed. Results from calculations with the IVA-KA code are compared with experimental data. The agreement obtained is encouraging, and the calculations show that the intense multiphase interactions obtained in QUEOS constitute very critical and thus valuable test cases.