Deposition of solid particles in laminar boundary layer on a flat plate

Results are given of experimental and theoretical investigation of deposition of small solid particles on the surface of a flat plate under conditions of vertical laminar boundary layer. The present investigation is aimed at qualitatively and quantitatively estimating the effect made by the parameters of two-phase flow of the “gas—solid particles” type and by the adhesive properties of particles and surface on the deposition of particles on the plate surface. The flow velocity is 1.5 and 3 m/s. In so doing, the value of Reynolds number along the plate does not exceed 10⁵. Synthetic corundum powders with average sizes of 12, 23, and 32 μm are used as the dispersed phase of two-phase flow. The mass concentration of particles in the flow is 0.01 kg/m³. A flat plate of stainless steel is used as the object of investigation. The distributions of gas velocity and concentration of particles within the boundary layer are measured using laser optical diagnostics. The number of particles deposited along the plate surface is measured by the gravimetric method. The adhesive properties of the “particle-surface” pair are studied using the centrifugal method of detachment of particles from the surface. Logarithmic-normal dependences of the number of adhesion of particles on the force of detachment are obtained. The hydrodynamic parameters of two-phase flow in the vicinity of the plate surface are calculated using the model of two-phase laminar boundary layer. The mathematical expression is suggested for the calculation of the magnitude of deposition of solid particles along the surface of a flat plate, which includes the special features of hydrodynamics of flow, the adhesive properties of the particles and surface, and the probabilistic pattern of the process of entrapment of particles by the surface.     

Experimental study of the dynamics of an air-dust jet

This paper presents the results of an experimental study of the development of a two-phase jet containing solid particles with initial concentration H₀ 1.0 kg/kg. The experimental data show that the temperature fields in the jet cross sections in dimensionless coordinates may be correlated by a single universal curve for various sections and various initial concentrations. The effect of solids on the jet boundary layer growth is shown to be greater than expected before. It is found that the increase of the width of the air-dust jet depends not only on the density variation across the mixing zone but also on the effect of the solid particles on the turbulent mixing process. This effect results in slower increase of the width of the jet and, consequently, slower damping of the jet.     

Modelling of a turbulent reacting gas/particle flow

Summary A mathematical model for two-phase turbulent reactive flows is presented which is based on considering both phases in Lagrangian manner. The mechanical and thermodynamical properties of the two-phase mixture are calculated along the trajectories of particles representing the system. Similar to Monte-Carlo methods for solving a high dimensional joint velocity-composition probability density function, the turbulent gas phase is described by means of stochastic calculus. The deterministic equations for individual solid particles can be treated directly. In this approach, the interaction between both phases is not smeared over computational cells but restricted to the vicinity of solid particles by the definition of an action-sphere which is attached to every solid particle. Applications of the method to isotropic, homogeneous turbulence indicate that it is capable of providing information on the local structure of combustion zones with species formation and transport. The results show that the method is applicable independent of the combustion modes in the gas phase, and it provides extensive statistics of various correlations of properties.     

Effects of particle–particle collisions on sudden expansion gas-particle flows via a two-phase kinetic energy-particle temperature model

In the framework of the gas–particle two-fluid mode, an improved gas–particle two-phase kinetic energy incorporating into a particles collision model (k–k_p–θ) is proposed to study the sudden expansion gas–particle turbulent flows in a cylindrical pipe section. Anisotropy of gas–solid two-phase stress and the interaction between two-phase stresses are considered by means of a transport equation of two-phase fluctuation velocity correlation. Xu and Zhou [10] experimental data is used to quantitatively validate k–k_p–θ and k–k_p model for analysis the effects of particle–particle collision. Numerical predicted results show that time-averaged velocity, fluctuation velocity of gas and particle and correlation of two-phase fluctuation velocity considering particles collision are better than those of the without particle temperature model and they are in good agreement with experimental data. Larger particle concentration and particle temperature located at shear layer adjacent to wall surface and re-circulation region. Energy dissipation due to smaller scale particles collision contributes to homogeneous distribution of Reynolds stress and affects the particle transportation behavior together with particle inertia.     

Analysis of the Flow of Rarefied Gas Through a Layer of a Porous Body on the Basis of Direct Numerical Solution of the Kinetic Boltzmann Equation

The problem of the flow of rarefied gas through a layer of a porous body, which is replaced by a homogeneous system of immobile spherical particles, is solved on the basis of the method of direct numerical solution of the kinetic Boltzmann equation. The effect of the spherical particles on the gas molecules is described as a kind of boundary condition distributed in space. Dependences of the density, temperature, and velocity on the coordinate in physical space are obtained; cross sections of the distribution function of the gas molecules by velocities are presented.     

Phase Separation Kinetics of Solid 3He-4He Mixtures

The kinetics of isotopic phase separation in solid mixture of ³ He in ⁴ He with the initial concentration 2.05 % at various molar volumes has been investigated by precise pressure measurements. It has been shown that during both stepped and fast cooldown into the metastable region the equilibrium of coexisting phases is described by the exponential law with a characteristic time constant , The value of is found to decrease as the molar volume increases and the temperature lowers. It confirms that the growth of the ³ He-rich phase is connected with nonthermally activated (quantum) diffusion in the gas of delocalized ³ He quasiparticles. The obtained experimental results can be described only qualitatively by current kinetic theory of binary quantum solid mixtures. The conditions permitting the realization of the isotopic phase separation during the time observed in the experiment are analyzed. The effective quantum diffusion coefficient providing required ³ He atoms transport is about an order of magnitude higher than the corresponding value measured in NMR experiments. These conditions are probably fulfilled at the big concentration gradient which takes place at isotopic phase separation. The corresponding kinetic theory should be developed.     

Development of Magnetic Resonance Imaging Technique for Ultra Low Temperature Physics

We have developed a Magnetic Resonance Imaging (MRI) technique applicable for ultra low temperature physics. In contrast to conventional MRI for general use where a pulsed-field gradient method is commonly used, we used a steady-field gradient method to avoid an eddy current heating due to metallic parts around the sample cell. We applied the MRI for ³ He-⁴ He mixture liquid with a critical concentration below 1 K and visualized the shape of the phase-separated boundary. We obtained two-dimensional space resolution of a few 10 m. We extracted the interfacial tension of the boundary which was in good agreement with reported values. The contact angle of the boundary to the cell wall was small at low temperature and increased toward 90° near the critical temperature.     

Aerodynamic structure of a flat plate laminar boundary layer with diffusion flame

An aerodynamic structure of a laminar boundary layer over a flat plate with uniform fuel injection from the flat plate and with diffusion flame is investigated numerically. Elliptic type conservation equations are used to take into account the pressure variation within the boundary layer. Velocities and the pressure are solved numerically by SIMPLER algorithm. One step irreversible chemical reaction of methane is assumed. An Arrhenius type chemical reaction rate model is assumed and the pre-exponential factor is varied from 1.0 × 10¹² to 1.0 × 10³⁰ m³/(kg s) as a parameter of the reactivity in order to elucidate the effect of the reactivity on the structure of the boundary layer. When the chemical reaction is very fast, the leading edge of the reaction zone reaches the flat plate. As the chemical reaction rate is decreased with a decrease in the pre- exponential factor, the leading edge of the reaction zone parts from the flat plate and it shifts downstream. The fuel is injected in front of the leading edge of the reaction zone, where the air is dominant, and the oxygen penetrates into the fuel dominant zone through the region between the leading edge and the flat plate. As a consequence, a premixed gas is formed around the leading edge of the reaction zone. The premixed gas seems to react in the region apart from the main visible flame.Part of this work was presented at ICCM 86, Tokyo, Japan, May 25–29, 1986     

A Free-Convection Boundary-Layer Model for the Centrifugal Etching of an Axisymmetric Cavity

The etching of an axisymmetric cavity under the influence of an artificial acceleration field generated inside a centrifuge is considered. It is shown that the etching process is governed by a thin convective-diffusive boundary layer along the curved cavity wall. To describe this boundary layer, local coordinates are introduced near the wall, with arc length s being one of these. It is shown that the resulting boundary-layer model can be solved explicitly, whence an exact representation of mass transport from the wall follows. The solution is then substituted in the moving-boundary condition. This results in a highly nonlinear hyperbolic differential equation for the wall position as a function of s and time t. It is further shown that this equation admits a family of similarity solutions in terms of the variable = st ^–4/5. The position variables are now functions of only and a highly nonlinear system of ordinary differential equations results. This system is subjected to a series of transformations, until a system suitable for numerical integration is obtained and a family of similarity curves, i.e. cavity shapes, can be generated. It is remarkable that the integration stops at a finite value of beyond which, apparently, the similarity concept is no longer tenable.     

Stagnation flow and heat transfer in a zonal magnetic field

Summary The problem stated in the title is studied for small values of the diffusivity ratio and the magnetic force coefficient , the magnetic field being of internal origin. Uniformly valid expansions are derived for the velocity and magnetic fields in the fluid. It is found that as 1, the viscous layer is brought to rest and the current in the layer is uniform and normal to the wall.The heat transfer is next calculated at a uniformly heated wall on the assumption of small temperature variations. It is deduced that when log(^–1) approaches a certain value depending on the wall temperature etc., the thermal boundary layer separates at the stagnation point and, if dissipation is neglected, along the whole wall.     

Effects of higher wall roughness on dense particle–laden dispersion behaviors

To analyze the effects of higher wall roughness on dense particle–laden dispersion behaviors under reduced gravity environments, a dense gas–particle two-phase second-order-moment turbulent model are developed. In this model, the wall roughness function and the kinetic theory of granular flows are coupled and closed. Anisotropy of gas–solid two-phase stresses and the interaction between gas–particle are fully considered using two-phase Reynolds stress model and the two-phase correlation transport equation. Numerical simulation test is validated by Sommerfeld and Kussin (2003) experiments data with higher wall roughness 8.32 μm. Predicted results showed that the particle concentration distribution, particle fluctuation velocity, particle temperature and particle collision frequency are greatly affected by higher wall roughness, as well as particle Reynolds stress and interactions between gas and particle turbulent flows are redistributed. Under microgravity conditions, particle temperature and collision frequency are greatly less than those of earth and lunar gravity.     

Qualitative analysis of the processes of aerosol propagation in a containment

Characteristic times of the removal of aerosols are evaluated for different processes of deposition. Gas flows in a containment in the presence of suspended particles of various concentrations have been analyzed. A mathematical model is suggested for describing the propagation and deposition of aerosols under the conditions of large-scale convection.Notation n concentration of a particle - r radius of a particle - U particle velocity - A surface area - p _s density of a solid particle - p _g density of a gas - time - g free fall acceleration - coefficient of molecular diffusion - _d boundary layer dimension - k Boltzmann constant - T surrounding-gas temperature - B particle mobility - v kinematic viscosity - S(r, t) source of aerosols - parameter characterizing the density of a set of particles - Sk Stokes number Institute of Radiative Physicochemical Problems of the Belorussian Academy of Sciences Minsk. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 4, pp. 426–432, April, 1993.     

Parameter-free quasiclassical boundary conditions for superfluid3He at rough walls. B-phase order parameter and density of states

Parameter-free boundary conditions are discussed for the quasiclassical Green's functions at a rough wall. These conditions have a closed form: all information specific to the wall is eliminated under the assumption that the impurity layer covering the wall is much thicker than the mean-free path of quasiparticles. To demonstrate them in action we calculate the³He-B order parameter and the density of states, and compare them with previous work. Our main conclusion is that the new boundary conditions give qualitatively similar density of states as the thin-impurity-layer model, but different from that of the randomly-rippled-wall model. Moreover, our approach, being much simpler, allows us to resolve the fine structure of quasiparticle resonances which has not been reported earlier.     

Determination of wall shear stress from velocity profile measurement in the outer part of the boundary layer

The shear stress on a wall is determined through a comparison of experimental and theoretical determinations of velocity distribution using a family of Thompson or Cole profiles.Notation C_f friction coefficient - u current velocity over the thickness of the boundary layer - u₁ velocity at the outer boundary of the boundary layer - _W wall shear stress - dynamic velocity - u^*=u/v_*; y^*=yv_*/; parameter in Coles' wake law - (u/u₁)_in, (u/v*)_in velocity distribution in the wall region [Eqs. (10), (11), (1)] Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 5, pp. 787–792, May, 1981.     

On a nonlinear stefan problem arising in the continuous casting of steel

Summary The continuous casting process employed in the steel industry is a many faceted big industrial problem which has given rise to many sub-problems. Here, we examine the problem involving the determination of the solid-liquid steel interface and we develop and extend a previously proposed model, which incorporates heat transfer through two layers of solid and liquid mould powder and the interface between the solid powder and the mould wall. The problem simplifies to the classical Stefan problem except that the condition on the boundary is nonlinear. Integral formulation procedures are used to establish the normalized pseudo steady state temperature as an upper bound to the normalized actual temperature. The pseudo steady state approximation yields an upper bound on the interface position, which an independent numerical enthalpy scheme confirms to be an extremely accurate approximation for the parameter values occurring in practice. The present work is important since it provides a simple method for the prediction of the solid-liquid steel interface and a bounding procedure which can be used to validate other estimates.List of symbols D flux thickness atz ^*=0 - H enthalpy - L latent heat of steel - M the half thickness of the cast steel - Q heat flux - R interface thermal contact resistance - S _m ^* melting temperature of steel - T ^* temperature - T normalized temperature - T _m ^* melting temperature of mould powder - T ^* temperature of cooling water - T _w ^* temperature on mould wall - T _u ^* temperature of solid flux on its interface with mould wall - T ₀ ^* temperature on casting surfaceT ^*(0,z ^*) - U casting speed - X ^*(z ^*) physical coordinate of the steel phase change boundary - X(z) non-dimensional coordinate of the steel phase change boundary - c specific heat of steel - h(z ^*) thickness of liquid flux layer - k thermal conductivity of steel - ks thermal conductivity of solid flux layer - k _l thermal conductivity of liquid flux layer - m surface heat transfer coefficient - s(z ^*) thickness of solid flux layer - t time - , , positive constants given by (3.2) - constant given by (3.5) - coefficient of linear thermal expansion of steel - angle shown in Figure 2 - positive constant defined by (M-D)/2 - (z) positive parameter - (z ^*) amount of contraction of steel - density - (z) positive parameter used in (5.7) and (5.8)     

Hydrogen dissociation below 1 K

We report on an investigation of hydrogen dissociation at dilution refrigerator temperatures. The objective of this study is to develop a low-temperature hydrogen atom source for experiments on spin-polarized atomic hydrogen. We find that, in a discharge tube coated with a solid H₂ layer and a superfluid He film, hydrogen dissociation is mediated by a glow discharge supported by He vapor. The He discharge provides the energetic particles needed for removing H atoms from the solid H₂ coating. In order to strike a He discharge, the He vapor pressure has to correspond to a wall temperature of 0.60–0.75 K. The best results are obtained close to the low-temperature threshold for ignition, or at even lower temperatures if the rf discharge pulse is preceded by a heat pulse adjusted to flash-evaporate the required initial He density. Hydrogen atom yields of 10¹³ H/discharge pulse are typical, and scale with the pulsed rf energy as long as the discharge volume is not overheated and remains in good thermal contact with its cooling jacket. In these conditions the H flux from the dissociator is proportional to the average rf power with a dissociation efficiency of 3%. With a dilution refrigerator circulation of 0.3 mmole/sec of³He, H fluxes of 5×10¹³ H/sec are obtained in steady-state discharge conditions.Deceased March 1986.     

Diffusion mechanisms and reactions during reduction of oolitic iron-oxide mineral

Diffusion mechanisms with moving reaction interfaces involved in the reduction process of oolitic iron oxide, containing small goethite particles in a kaolinite matrix, are presented. Reduction was effected by means of CO gas at 950° C, with the oolite already transformed by dehydroxylation into haematite particles and a metakaolinite matrix. The haematite particle under the CO + O CO₂ reaction taking place at its external surface develops concentric layers with unreacted haematite at the core enclosed by magnetite wustite and metallic iron, in that order. In the matrix between particles, bridges of a two-phase mixture of hercynite and fayalite develop by diffusion of iron ions and reactive transport of oxygen (by means of CO₂ molecules), thereby permitting coarsening of the metallic particles. Detailed models are presented for the diffusion mechanisms and reactions involved, and the thermodynamical picture is brought out.Deceased November 1987.     

Strength,hardness and fracture toughness of a complex nickel silicide containing ductile phase particles

Measurements have been made at room temperature of the strength and fracture toughness of a complex nickel silicide containing particles of a ductile phase. The matrix was either a single-phase L1₂ distorted Ni₃Si (₂) or a two-phase Ni₃Si (₁) and Ni₃₁Si₁₂ () mixture. The particles were a solid solution of Ni(Si) encased within a rim of ₁; they contained a dispersion of ₁ precipitates. The principal variable was the particle size, and this had little effect on the properties. The results show that the compressive yield strength ( 1200 MPa), the compressive ductility (2–10%) and the fracture toughness (17 ± 3 MPa m^1/2) are relatively high. The toughness and ductility are attributed to the plastic deformation and ductile fracture of the crack-stopping Ni(Si) particles.     

Embedding Impurities into Solid Helium

We have developed a new technique to imbed impurities in solid ⁴He. It consists in injecting helium gas mixed with the impurity on the top surface of Helium liquid-solid interface, with the solid continuously moving downwards by pumping at the bottom of the cell. Due to the large temperature gradient, sedimentation occurs through the thin (1–2 mm) upper layer of liquid helium. We achieved a guest-particle density of 3 10¹⁹ per cm³ and a doped crystal growth rate of 0.05 mm/s. The possibilities of this novel method for matrix isolation spectroscopy as well as for quantum crystal studies are discussed.     

Joule-Thompson effect in a disperse medium

An expression for the Joule-Thompson coefficient of a polydisperse medium subject to throttling is derived in the relaxation approximation of thermodynamics of irreversible processes, with both temperature and velocity relaxation in the phases taken into account.Notation A_qk, A_fk thermal and momentum interphase exchange affinities - _qk, _fk relaxation parameters - T, w temperature and velocity of a phase relaxation in the mixture - density of the mixture - T_o, T_k temperature of the carrier phase and of the k-th group of solid particles - p pressure of the carrier phase - h enthalpy of the mixture - W _o ² /2 specific kinetic energy of the carrier phase - _o, _k volume concentration of the carrier phase and of the k-th group of solid particles - _o, _k true density of the carrier phase and of the k-th group of solid particles - c_v and c_p constant-volume and constant-pressure specific heats of the mixture - c_k specific heat of the k-th group of solid particles - c_v, c_p constant-volume and constant-pressure specific heats, respectively, of the mixture referred to volume - _qk, _fk temperature and velocity relaxation times, respectively, of the k-th group of solid particles - t times - frequency in the Fourier series expansion - differential Joule-Thompson coefficient (adiabatic throttle effect) - N number of groups of particles in the mixture Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 825–829, November, 1979.