**6. Concluding remarks**

104 Mass Transfer in Chemical Engineering Processes

Fig. 7. Prediction of axial gas temperature along the length of the PVC dryer

Fig. 8. Prediction of axial particle moisture distribution along the length of the PVC dryer

This chapter demonstrated a simple application of CFD for industrial drying processes. With careful consideration, CFD can be used as a tool to predict the hydrodynamic as well as the heat- and mass-transfer mechanisms occurring in the drying units. It can also be used to better understand and design the drying equipment with less cost and effort than laboratory testing. Although considerable growth in the development and application of CFD in the area of drying is obvious, the numerical predictions are by far still considered as qualitative measures of the drying kinetics and should be validated against experimental results. This is due to the fact that model approximations are used in association with CFD

Numerical Simulation of Pneumatic and Cyclonic Dryers Using Computational Fluid Dynamics 107

Mass transfer between phases per unit volume [kg/m3s]

Heat exchange between the phases per unit volume [W/m3]

*kg* Turbulence quantity of the gas phase [m2/s2] *ks* Turbulence quantity of the solid phase [m2/s2] *ksg* Turbulence quantity of the inter-phase [m2/s2]

Number of particles per unit volume [1/m3]

*R* Gas constant [J/kmol K]; Particle radius [m] *Res* Solid Reynolds number [dimensionless] *Sc* Schmidt number [dimensionless] *Sh* Sherwood number [dimensionless]

 Velocity vector of phase *q* [m/s] Velocity vector of gas phase [m/s] Velocity vector of solid phase [m/s]

Drift velocity vector [m/s]

*X* Particle moisture content [%]

 Mean particle moisture content [%] *Yq* Mass fraction of vapor in phase *q* [%] Strain-rate tensor for phase *q* [1/s]

Relative velocity between the phases [m/s]

Particle slip-velocity parallel to the wall [m/s]

*XH2O* Vapor mole fraction in the gas phase [dimensionless]

*<sup>q</sup>* Volume fraction of phase *q* (s = solid; g = gas)

Drag force per unit volume between the phases [N/m3]

*<sup>s</sup>* Collisional dissipation of granular temperature [kg/m3 s]

Turbulent dissipation rate of gas phase [m2/s3]

Turbulent dissipation rate of solid phase [m2/s3]

*s,max* Maximum volume fraction of solid phase

Turbulent dissipation rate [m2/s3]

*Lt,g* Length scale [m] *ms* Solid mass [kg]

*P* Pressure [N/m2] *Ps* Solid pressure [N/m2] *Psat* Saturated vapor pressure [Pa] *Pr* Prandtl number [dimensionless]

*M pq* 

*Nd*

*Qpq*

*U <sup>q</sup> U <sup>g</sup> U <sup>s</sup> U <sup>s</sup> <sup>g</sup> U dr U <sup>s</sup>* ||,

*t* Time [s]

*V* Volume [m3]

**7.2 Greek symbols** 

 

 

 

 

*X*

*Dq*

*sg*

*g*

*s*

*Tg* Gas temperature [K] *Ts* Solid temperature [K]

*M* Molecular weight [kg/kmol]

*Nus* Nusselt number [dimensionless]

methods to facilitate and represent complex geometries and reduce computational time and convergence problems.

Although CFD techniques are widely used, the modeller should bear in mind many of the pitfalls that characterize them. Some of these pitfalls are related to but not limited to the choice of the meshing technique; the numerical formulation; the physical correlations; the coding of meaningful and case specific UDFs; the choice from a spectrum of low and high order schemes for the formulation of the governing equations; and last but not least, the choice of iterative and solution dependent parameters.

In addition, due to the complex nature of the processes occurring in the drying systems, extensive simulations must be carried out to demonstrate that the solution is time- and gridindependent, and that the numerical schemes used have high level of accuracy by validating them with either experimental data or parametric and sensitivity analysis. This is particularly crucial in the approximation of the convective terms, as low order schemes are stable but diffusive, whereas high order schemes are more accurate but harder to converge.
