## 7 Process Optimization Through CFD Simulations  
### DoE and CFD  
The integration of CFD with DoE methodologies offers a powerful framework for systematic and efficient process optimization in food engineering. While CFD provides detailed insights into transport phenomena--such as flow behavior, heat transfer, and mass diffusion--DoE enables the structured exploration of input variables and their interactions, facilitating the identification of optimal process conditions with a limited number of simulations [126]. By combining CFD and DoE, engineers can leverage high-resolution simulation data to build predictive models that reduce development time and cost while improving process understanding. This synergy is particularly valuable in applications involving nonlinear, multiparametric systems, where conventional trial-and-error approaches are inefficient or impractical [127]. In the context of CFD, DoE is used to efficiently explore the design space, quantify the impact of process parameters, and construct surrogate models or response surfaces that approximate CFD outputs. Typical experimental designs applied include full and fractional factorial designs, central composite and Box-Behnken designs for response surface methodology, Latin hypercube sampling (LHS) for meta-modeling, and Taguchi methods for robustness analysis [128]. A standard CFD-DoE workflow begins with defining the optimization objectives (e.g., maximizing drying uniformity, minimizing energy consumption) and selecting key input parameters such as air velocity, temperature, nozzle geometry, or screw speed. Based on these factors, a design matrix is generated using DoE software platforms. CFD simulations are then performed for each design point, and the resulting data are analyzed using statistical tools such as analysis of variance (ANOVA) and regression modeling. The final step involves building predictive models and validating the identified optimum through high-fidelity simulation or experimental trials. This approach allows for multidimensional optimization while avoiding the computational burden of exhaustive parametric sweeps [129]. Applications of the CFD-DoE approach in food process engineering are diverse. In spray drying, it has been used to optimize inlet air temperature, feed rate, and droplet size to enhance powder quality and minimize wall deposition. In extrusion cooking, CFD-DoE models support the balance between energy efficiency and product texture by analyzing the effects of screw speed and barrel temperature. In mixing processes, this method helps identify the ideal impeller geometry and rotational speed for achieving uniform ingredient distribution in minimal time. In fluid-bed drying, it has been used to tune distributor plate configurations and airflow rates for energy-efficient operation without compromising product quality [130]. An illustrative example is the optimization of spray drying for probiotic powders, where CFD-DoE analysis revealed strong interaction effects between inlet temperature and feed rate on final moisture content and bacterial viability. Using a central composite design, a response surface model was developed with a prediction error below 5%, later validated in pilot-scale experiments [131]. The advantages of integrating DoE with CFD include a substantial reduction in the number of simulations or trials, improved understanding of parameter interactions, and the ability to construct predictive tools for control and scale-up. This integration also supports multi-objective optimization strategies, balancing factors such as quality, efficiency, and environmental impact [132]. Nonetheless, limitations exist. The accuracy of outcomes depends on the quality and resolution of CFD simulations, and computational cost can escalate with high model complexity or numerous factors. Additionally, response surfaces may struggle to capture highly nonlinear or discontinuous behaviors. These issues can be mitigated through adaptive sampling, hybrid DoE-AI strategies, or combining coarse and fine modeling approaches [133].