Van Driest's constant

Area of bottom surface of the computational cell attached to top surface Projection of area of the interface between computational cell and impeller blade on a plane normal to the tangential velocity Discretization coefficients Interfacial area per unit volume Empirical constant in Eq. (3.26)

Discretization coefficients corresponding to outflow contributions Blade width

Inertial resistance factors characterizing the porous media

Parameters of k-e model

Drag coefficient


Empirical lift coefficient

Heat capacity virtual mass coefficient


Molecular diffusion coefficient or diameter or impeller diameter Also used as diffusive contributions in discretized equations (Chapter 6)

Thermal mass diffusion coefficient for species 'k'

Empirical constant in wall function, also used as a reciprocal of a characteristic micro-mixing time scale

Turbulent kinetic energy contained in wave number range of k to k+dk

Restitution coefficient

Mixture fraction, Eq. (5.19)

Basset force coefficient

Transversal lift coefficient

Eulerian quantity at node 'n'

virtual mass coefficient

External or inter-phase force or marker function

Also used as convective contributions in discretized equations

(Chapter 6)

Interface coupling terms except pressure Surface force

Generation of turbulent kinetic energy

Extra generation of turbulence in phase 'k' due to presence of other phases

Acceleration due to gravity Radial distribution function Enthalpy

Hydrostatic head above the sparger Unit vector in the f direction Diffusive flux of species k Inter-phase momentum exchange coefficient k Thermal conductivity of fluid or turbulent kinetic energy ka Wave number of dissipative eddies ke Wave number of energy containing eddies ko Frequency factor kL, kT Resistance coefficients of the sparger (laminar and turbulent contributions)

lT Length scale of turbulence

LB, Lp Distance between centers of two moving spheres/bubbles

Ls Segregation length scale m Mass fraction

N Impeller rotational speed in revolutions per unit time n Moles or surface normal, Eq. (4.6) or unit normal vector or number of moles of oxidizer required to burn one mole of fuel p Pressure p' Pressure correction or fluctuating pressure po Total pressure at inlet boundary ps Static pressure in solution domain

P Pee function given by Eq. (3.39)

Pc,sn Pressure due collision between solid phases 's' and 'n'

Ps Solid phase pressure q Flux of enthalpy

Qr Circulatory flow in the reactor

Qpk Energy transfer between pth and kth phase r Radial co-ordinate

R Reaction rate or radius

R' Universal gas constant

Rep Reynolds number of particle

Rz Axial flow resistance

S Source or Surface of a computational cell

Sc Mass source term

Scm Momentum source term

Sk Source term of 'k'

SM Mass imbalance

Spk Rate of mass transfer from pth phase to kth phase t Time, time scale

T Temperature tDS Diffusion time scale tE Characteristic time for engulfment step u Fluctuating velocity uT Characteristic velocity

U Velocity, radial velocity component

Uj Local velocity in xj direction

UT Characteristic wall velocity, ^Jxw/p

V Superficial velocity, tangential velocity component

Vb Effective bubble velocity in a swarm

VblXJ Rise velocity of a single bubble

Vcell Volume of computational cell

Vkj Mean velocity of phase 'k' in direction 'i'

VR Volume of reactor

WBLD Tangential velocity of the blade x, X Mole fraction or co-ordinate direction y Distance from wall yp Distance between wall and nearest node zrk Molar stoichiometric coefficient of component 'r' in reaction 'k'

Greek notation


Volume fraction


Under-relaxation parameter


Permeability of porous media


Kronecker delta function

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