Modern Modelling Methods in Drying

Abstract

Several modern modelling techniques are presented as tools for drying science and technology, namely pore networks, discrete element method and population balances. After first presenting results from their own research, the authors indicate what future contributions to a better understanding of the drying process at different levels-single porous particles, agitated and fluidised beds-may be expected. NomenclatureA Pore throat cross section [m 2 ] c p Heat capacity [kJ kg −1 K −1 ] f Number density [m −3 kg −1 ] G Rate of drying/wetting [kg s −1 ] L Capillary or pore throat length [m] l Amount of liquid [kg] M Mass flow rate [kg s −1 ] M Molar mass [kg kmol −1 ] m l Liquid mass density [kg −3 ] N mix Mixing number [-] n Rotational frequency [s −1 ] n Number density [s −1 ] or [m −3 ] n Number flow rate [s −2 ] T. 104 Thomas Metzger et al. R Ideal gas constant [kJ kmol −1 K −1 ] p Pressure [Pa] r Radius [m] r 0 Mean radius [m] s Meniscus position [m] T Absolute temperature [K] t Time [s] t mix Revolution time [s] t R Mixing time [s] v Particle volume [m 3 ] z Space coordinate [m] Greek symbols α Heat transfer coefficient [W m −2 K −1 ] β Mass transfer coefficient [m s −1 ] β Agglomeration kernel [s −1 ] δ Binary diffusion coefficient [m 2 s −1 ] ζ Dimensionless position [-] η Dynamic viscosity [Pa s] λ Thermal conductivity [Wm −1 K −1 ] ν Dimensionless drying rate [-] ρ Density [kg m −3 ] σ Surface tension [N m −1 ] σ 0 Radius standard deviation [m] τ Age of particle [s] ψ Porosity [-]

Novel CFD-DEM Model for Spouted Bed Drying Incorporating Intraparticle Heat and Mass Diffusion

“…Then the heat flux is calculated by the particle surface area A i and the temperature difference between the solid surface and air as (13) The energy source term in eq 6 is calculated by (14) The evaporation rate of the water is determined by (15) where Y e is the water concentration required to maintain equilibrium with the surrounding atmosphere. β i is the mass transfer coefficient and is calculated by (16) The relationship between Y and the relative humidity (RH) of the air is 34 (17) where p sat is the saturation pressure and is estimated based on the liquid temperature in the saturated state (T sat ) 35 (18) As mentioned in refs 20 and 36, T sat is the adiabatic saturation temperature, which is calculated by (19) where L is the latent heat of vaporization and C v , C w , and C f are the specific heat capacities of vapor, water, and air, respectively. The source term in eq 5 is obtained based on q Y,i by ( 20)…”

A Framework and Numerical Solution of the Drying Process in Porous Media by Using a Continuous Model

“…At the microscopic scale, the drying of porous media can be modelled as a network of pores, and the motion of the liquid-gas interface is modelled at the pore level, for example, in the work of Laurindo and Prat [7], Prat [8], Segura and Toledo [9], Metzger et al [10], and Hirschmann and Tsotsas [11]. By using this approach [12], which we will refer to as the discrete approach, the microscopic structure and therefore the transport properties of the porous medium can be modelled with better accuracy. However, the problem becomes very large, and solving the system of equations of coupled heat-mass transfer becomes in many cases impractical, in particular when dealing with systems of large geometrical dimension.…”

Grey-box modelling of a viscose-fibre drying process

“…In [13] a drying model for acetate fibre is presented, but since the fibre is a filament, the drying process is quite different than for a fibre sheet. A general paper about modelling methods is given by [14], with specific details concerning pore networks and population balances in fluidized bed drying.…”