**4. Numerical parameters – numerical solvers**

The governing equations along with the complementary equations are solved using a pressure based solution algorithm provided by FLUENT 6.3. This algorithm solves for solution parameters using a segregated method in such a manner that the equations are solved sequentially and in a separate fashion. Briefly stated, the solution parameters are initially updated. The *x*-, *y*-, and *z*-components of velocity are then solved sequentially. The mass conservation is then enforced using the pressure correction equation (SIMPLE algorithm) to ensure consistency and convergence of solution equations. The governing equations are spatially discretized using second-order upwind scheme for greater accuracy and a first-order implicit for time. This allows for the calculation of quantities at cell faces using a Taylor series expansion of the cell-centered solution about the cell centroid. More details related to this can be found in Patankar[29], or FLUENT 6.3 User Guide (2006)[23].

SAND AND PVC MODELS: A modified *k*-*ε* turbulence model is used along with the standard wall function for both phases in the vicinity of the wall. To avoid solution divergence, small time steps on the order of 1 × 10-4 to 1 × 10-6 are adopted. Solution convergence is set to occur for cases where scaled residuals for all variables fall below 1 × 10- 3, except for the continuity equation (1 × 10-4) and the energy equation (1 × 10-6).

SLUDGE MODEL: For this model, a RNG *k* turbulence model is used along with the standard wall function for both phases in the vicinity of the wall. Bunyawanichakul et al.[28] validated their numerical predictions with experimental data by adopting tetrahedral mesh

Numerical Simulation of Pneumatic and Cyclonic Dryers Using Computational Fluid Dynamics 103

the gas inlet; (ii) the turbulent intensity is 10% at the mixture inlet; (iii) the turbulent viscosity ratio was between 5-10%; (iv) particles were assumed to slip at the wall with specularity coefficient of 0.01; and (v) inelastic particle-wall collision with restitution

Fig. 6. Prediction of axial gas humidity (top) and particle moisture distribution (bottom)

along the length of the sand dryer

coefficient of 0.6.

with Reynolds Stress Turbulence Model (RSTM), and hexahedral mesh with standard and RNG *k* turbulence models. It was found that the hexahedral mesh with the RNG *k* turbulence model predicted the pressure drop across the dryer chambers as well as the velocity distribution in the chambers reasonably well when used with the second-order advection scheme. In addition, RNG *k* turbulence model was successfully applied by Huang et al. (2004)[30,31] for modeling of spray dryers with different designs of atomizer. In order to avoid solution divergence in the current model, small time steps on the order of 1 x 10-3 - 1 x 10-4 are adopted. Solution convergence is set to occur for cases where scaled residuals far all variables fall below 1 x 10-3, except for the continuity equation (1 x 10-4) and the energy equation 1 x 10-6. The maximum number of iterations per time step is set to 60. It took roughly 40 days for the solution to converge on Windows XP operating system with Core 2 Quad processor.

For all models, User Defined Functions subroutines (UDFs) are introduced to enhance the performance of the code. Accordingly, all UDFs are implemented directly from a source file written in a C programming language subsequently after the case file is read. This feature enables the macro functions to be visible or rather accessible by the user for them to be included in the solution where they should be applied. Equations implemented in UDFs are the following: a) properties pertaining to the drag force between the phases in Equations; b) the radial distribution function; c) the heat transfer coefficient; d) the mass transfer coefficient; and e) the particle density.

### **5. Results and discussion**

In this section, some of the numerical predictions obtained from the CFD simulation for all cases considered in this chapter are shown. For case I, the numerical results agreed well with the experimental data with the following conditions: (i) the turbulent intensity is 5% at

Fig. 5. Prediction of axial gas and particle temperatures along the length of the sand dryer (top lines, gas temperature; bottom lines, particle temperature)

with Reynolds Stress Turbulence Model (RSTM), and hexahedral mesh with standard and

turbulence model predicted the pressure drop across the dryer chambers as well as the velocity distribution in the chambers reasonably well when used with the second-order

Huang et al. (2004)[30,31] for modeling of spray dryers with different designs of atomizer. In order to avoid solution divergence in the current model, small time steps on the order of 1 x 10-3 - 1 x 10-4 are adopted. Solution convergence is set to occur for cases where scaled residuals far all variables fall below 1 x 10-3, except for the continuity equation (1 x 10-4) and the energy equation 1 x 10-6. The maximum number of iterations per time step is set to 60. It took roughly 40 days for the solution to converge on Windows XP operating system with

For all models, User Defined Functions subroutines (UDFs) are introduced to enhance the performance of the code. Accordingly, all UDFs are implemented directly from a source file written in a C programming language subsequently after the case file is read. This feature enables the macro functions to be visible or rather accessible by the user for them to be included in the solution where they should be applied. Equations implemented in UDFs are the following: a) properties pertaining to the drag force between the phases in Equations; b) the radial distribution function; c) the heat transfer coefficient; d) the mass transfer

In this section, some of the numerical predictions obtained from the CFD simulation for all cases considered in this chapter are shown. For case I, the numerical results agreed well with the experimental data with the following conditions: (i) the turbulent intensity is 5% at

Fig. 5. Prediction of axial gas and particle temperatures along the length of the sand dryer

(top lines, gas temperature; bottom lines, particle temperature)

turbulence models. It was found that the hexahedral mesh with the RNG *k*

turbulence model was successfully applied by

RNG *k*

Core 2 Quad processor.

advection scheme. In addition, RNG *k*

coefficient; and e) the particle density.

**5. Results and discussion** 

the gas inlet; (ii) the turbulent intensity is 10% at the mixture inlet; (iii) the turbulent viscosity ratio was between 5-10%; (iv) particles were assumed to slip at the wall with specularity coefficient of 0.01; and (v) inelastic particle-wall collision with restitution coefficient of 0.6.

Fig. 6. Prediction of axial gas humidity (top) and particle moisture distribution (bottom) along the length of the sand dryer

Numerical Simulation of Pneumatic and Cyclonic Dryers Using Computational Fluid Dynamics 105

 Fig. 9. Contour plot of particulate volume fraction (left) at selected view planes (right)

 Fig. 10. Contour plot of gas (left) and particle (right) temperatures at selected view planes

For case II, in absence of experimental data we relied more on the qualitative gas and solid velocity patterns in the cyclone dryer. In this case, the UDF capability in FLUENT/ANSYS R12.0 was enhanced by incorporating output data from a pneumatic dryer upstream of the

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

cyclone dryer without facing any divergence or instability issues.

(Figure 9, right)

**6. Concluding remarks** 

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

Fig. 9. Contour plot of particulate volume fraction (left) at selected view planes (right)

Fig. 10. Contour plot of gas (left) and particle (right) temperatures at selected view planes (Figure 9, right)

For case II, in absence of experimental data we relied more on the qualitative gas and solid velocity patterns in the cyclone dryer. In this case, the UDF capability in FLUENT/ANSYS R12.0 was enhanced by incorporating output data from a pneumatic dryer upstream of the cyclone dryer without facing any divergence or instability issues.
