## 6 CFD Analysis of Drying as a Mechanically Aided Process  
### Fluid-Bed Drying and Spray Drying as Coupled Heat-Mass Transfer and Mechanical Systems  
Drying is a fundamental unit operation in food engineering, essential for improving product shelf life, microbiological stability, and handling characteristics. Among the most widely used drying methods are fluid-bed drying and spray drying, which integrate thermal and mechanical phenomena within inherently multiphase systems. The application of CFD provides valuable insights into these processes by enabling detailed analysis of airflow behavior, particle or droplet motion, temperature and moisture distributions, and mechanical agitation--variables that are often challenging to measure directly (Table 2) [74]. CFD simulations of spray drying processes for dairy emulsions, such as infant formula or milk protein concentrates, enable prediction of droplet trajectories, temperature gradients, and zones susceptible to wall deposition. [PERSON] et al. (2020) applied Lagrangian-Eulerian modeling to a lab-scale spray dryer and identified how airflow asymmetries caused incomplete drying and powder loss [111]. These insights support chamber design modifications that improve hygien performance and powder yield in industrial dairy powder production [111]. Fluid-bed drying is based on suspending food particles in an upward stream of hot air, where the drag force exerted by the gas counterbalances the gravitational force. This creates fluid-like behavior of the solid phase, promoting efficient heat and mass transfer. Mechanical effects, such as vibration or pulsating airflow, are commonly employed to improve particle mobility and prevent agglomeration. Fluid-bed drying is widely applied in the processing of powders, pellets, and coated particles. CFD models typically use EL or EE frameworks to simulate gas-solid interactions, enabling prediction of particle velocities, residence times, temperature profiles, moisture reduction, and zones susceptible to agglomeration. Coupling CFD with the DEM allows for detailed representation of inter-particle collisions and granular bed behavior, especially important in high-throughput or vibration-assisted systems [112]. Spray drying, on the other hand, involves the transformation of liquid feeds into fine droplets, which are then rapidly dried in a hot gas environment. This process is characterized by strong coupling between heat and mass transfer, droplet dynamics, and chamber airflow. It is widely used in the production of dairy powders, flavorings, instant beverages, and encapsulated bioactives. CFD simulations of spray drying focus on droplet atomization, trajectory prediction via Lagrangian particle tracking, and modeling of evaporation kinetics as a function of local temperature, humidity, and vapor pressure. Advanced simulations may also account for phenomena such as droplet shrinkage, crust formation, internal moisture diffusion, and wall deposition, which are critical for ensuring product quality, maximizing yield, and maintaining hygienic operation [113]. Spray drying of dairy emulsions, such as infant formula or coffee creamers, benefits from CFD modeling to ensure uniform droplet drying and minimize wall deposition--critical factors for product safety and consistency [106,114]. A key aspect of both drying methods is the integration of mechanical factors with heat and mass transfer. In fluid-bed systems, mechanical agitation enhances mixing and drying uniformity, and CFD-DEM coupling is often employed to describe particle-particle interactions. In spray dryers, atomizers introduce swirling or turbulent velocity fields that significantly influence droplet dispersion and drying trajectories. Accurate modeling requires simultaneous resolution of Navier-Stokes equations, species transport equations for water vapor, energy equations for temperature fields, and motion equations for dispersed phases [115]. CFD-based modeling has been successfully applied to optimize industrial drying processes.