By Nikolay I. Kolev PhD., DrSc (auth.)

ISBN-10: 3540698345

ISBN-13: 9783540698340

ISBN-10: 3540698353

ISBN-13: 9783540698357

Multi-phase flows are a part of our average atmosphere comparable to tornadoes, typhoons, air and water pollutants and volcanic actions in addition to a part of commercial expertise corresponding to strength vegetation, combustion engines, propulsion structures, or chemical and organic undefined. the economic use of multi-phase platforms calls for analytical and numerical thoughts for predicting their habit. In its 3rd prolonged variation this ebook comprises idea, equipment and functional adventure for describing advanced brief multi-phase techniques in arbitrary geometrical configurations. This e-book presents a scientific presentation of the speculation and perform of numerical multi-phase fluid dynamics. within the current moment quantity the mechanical and thermal interactions in multiphase dynamics are supplied. This 3rd variation contains numerous updates, extensions, advancements and corrections.

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**Example text**

Regime parameter: air-water, atmospheric conditions. 85m / s Pqogpencvwtg" Latin Cli mass concentration of species i inside the field l, dimensionless C0 drift flux distribution coefficient, dimensionless Dd particle diameter (bubble, droplet, particle), m D1,solid like bubbles with size less then this behave as a solid sphere, m Dh DFR hydraulic diameter, m/s rod diameter, m Fr = ( ρ w) 2 gDh vh , Froude number, dimensionless 26 1 Flow regime transition criteria G , Froude number, dimensionless gDh ρ 22 Fr20 = G = ∑ α l ρl wl , mass flow rate, kg/(m²s) g H hl h ′′ h′ j gravitational acceleration, m/s² distance between two parallel plates, m specific enthalpy of the velocity field l, J/kg saturated vapor specific enthalpy, J/kg saturated liquid specific enthalpy, J/kg = α1V1 + (1 − α1 )V2 , mixture volumetric flux, m/s A FR pitch diameter, m 3 l =1 t d A TB Ma Nη 2 mean free path length of oscillating particles, m length of the Taylor bubble, m local Mach number, dimensionless = η2 / ρ 2σ 2 λRT n1 p q w′′ number of bubbles per unit mixture volume,1/m³ pressure, Pa heat flux from the wall into the flow, W/m² Re20 Volcell = GDh / η2 , Reynolds number, dimensionless cell volume, m3 V1Ku = 2 ⎡⎣ gσ 2 ( ρ 2 − ρ1 ) / ρ 22 ⎤⎦ A 1/ 4 , Kutateladze bubble rise velocity in a pool, m/s VTB = ρ 2 − ρ1 gDh slug (Taylor bubble) raising velocity, m/s ρ2 V1 gas velocity, m/s V2 liquid velocity, m/s V1,stratified gas velocity dividing the non-stratified from the stratified flow, m/s V2,stratified liquid velocity dividing the non-stratified from the stratified flow, m/s V1,annular gas velocity dividing the non-annular from the annular flow, m/s V1,wavy velocity: for gas velocity larger than this velocity the surface of the liquid is wavy (stratified wavy flow), m/s V2,bubble critical liquid velocity for transition into bubble flow, m/s We20 = G 2 Dh ρ 2σ 2 , Weber number, dimensionless Nomenclature X 1,eq X1 z = 27 ∑ X h − h′ , equilibrium mass flow concentration of the vapor velocl l h′′ − h ′ ity field, dimensionless mass flow concentration of the vapor velocity field 1, dimensionless axial coordinate, m Greek αl local volume fractions of the fields l, dimensionless αd local volume fractions of the dispersed field d, dimensionless α1,B −Ch gas volume fraction that divides bubble and churn turbulent flow, dimensionless α1,bubble to slug gas volume fraction that divides bubble and slug flow, dimensionless α1, slug to churn gas volume fraction that divides slug and churn turbulent flow, dimen- δ 2F λ fr sionless = X 1v1 / vh , homogeneous gas mass fraction, dimensionless volume porosity – volume occupied by the flow divided by the total cell volume, dimensionless averaged distance between the centers of two adjacent particles, m average distance between two adjacent particles if they are assumed to be rhomboid arrays, m liquid thickness, m friction coefficient, dimensionless λRT ρ1 ρ2 ρw σ2 ε2 η1 η2 Rayleigh-Taylor wavelength, m gas density, kg/m³ liquid density, kg/m³ mixture mass flow rate, kg/(m²s) viscous tension, N/m dissipation rate of the turbulent kinetic energy of the liquid, W/m3 dynamic gas viscosity, kg/(ms) dynamic liquid viscosity, kg/(ms) β γv ΔA d ΔA 3 vh = X 1v1 + (1 − X 1 ) v2 , homogeneous specific volume, m³/kg θ angle with origin the pipe axis defined between the upwards oriented vertical and the liquid-gas-wall triple point, rad angle between the upwards oriented vertical and the pipe axis, rad ϕ 28 1 Flow regime transition criteria Tghgtgpegu" Anoda Y, Kukita Y, Nakamura N, Tasaka K (1989) Flow regime transition in high-pressure large diameter horizontal two-phase flow, ANS Proc.

Integrating the pressure distribution over the surface one obtains a resulting force that is different from zero. As shown in Vol. 2, the different spatial components of the integral correspond to different forces: drag-, lift and virtual mass forces. The averaging procedure over a family of particles gives some averaged forces which can be used in the computational analysis based on coarse meshes in the space. The purpose of this section is to summarize the empirical information for computation of the drag-, lift and virtual mass forces in multi-phase flow analysis.

38 × 105 , 373 < T3 < 973 K. 8% lower than the value for the non-boiling case under atmospheric conditions and free falling. More complicated is the case if the free particles are part of a solid/liquid/gas mixture. Consider first the bubble three-phase flow. 75) the bubble three-phase flow is defined. 52. In any case if three-phase bubble flow is identified we distinguish two sub cases. 76) the theoretical possibility exists that the particles are carried only by a liquid. This hypotheses is supported if one considers the ratio of the free setting velocity in gas and liquid 44 2 Drag, lift and virtual mass forces w31∞ = w32 ∞ ρ3 − ρ1 ρ 2 >> 1 .

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