## 7 Process Optimization Through CFD Simulations
### Sensitivity Analysis and Parameter Estimation  
In computational modeling of food processes, sensitivity analysis (SA) and parameter estimation (PE) are essential tools for understanding the influence of uncertain input variables and for calibrating models to experimental or industrial data. Their integration with CFD enhances model robustness, reduces uncertainty, and improves predictive reliability across applications such as process optimization, scale-up, and real-time control. These techniques are especially important in food systems, where thermophysical and rheological properties--such as viscosity, diffusivity, or heat transfer coefficients--are often variable and difficult to measure directly, and where multiple coupled phenomena such as phase change or biochemical reactions occur [135]. SA: Scope and Methods  
SA quantifies how variations in input parameters influence model outputs. In CFD applications, this can help prioritize critical inputs, guide model simplification, and improve experimental planning. Two main categories of SA are commonly used:  
* Local SA, which evaluates small perturbations of individual parameters using partial derivatives or finite difference methods. It is best suited for smooth, deterministic models but is limited in nonlinear or interactive systems. * Global SA, which assesses variability across the entire parameter space using statistical techniques such as:* Morris screening (qualitative ranking), Sobol' indices (variance-based decomposition), Fourier amplitude sensitivity testing (FAST), LHS with regression or surrogate modeling. * Global SA is particularly useful in complex CFD scenarios such as extrusion, spray drying, or fluidized bed systems, where nonlinear interactions between inputs are common [136]. PE in CFD Models  
PE involves identifying unknown model parameters by minimizing the difference between simulated and observed outcomes. In CFD-based food process models, PE is used to calibrate:  
* Rheological laws (e.g., power-law, Herschel-Bulkley),
* Kinetic expressions (e.g., reaction rate constants, activation energy),
* Transport coefficients (e.g., diffusivity, evaporation rates),
* Boundary conditions (e.g., convective heat transfer coefficients). PE problems are often formulated as optimization tasks, where the goal is to minimize an objective function, typically the sum of squared errors between experimental and simulated data:  
\[minimize\sum_{i=1}^{n}\left(y_{i}^{exp}-y_{i}^{sim}(\theta)\right)^{2}\]  
Here, \(\theta\) represents the parameter set to be estimated. Estimation methods include gradient-based algorithms (e.g., Levenberg-Marquardt), metaheuristics (e.g., genetic algorithms, particle swarm optimization), and Bayesian approaches such as Markov Chain Monte Carlo (MCMC), which also provide uncertainty bounds [137; 138]. Integrated SA-PE Workflows  
Combining SA with PE enhances computational efficiency and model reliability. SA helps prioritize parameters for estimation and reduce problem dimensionality, while PE refines parameter values based on experimental alignment. This integrated approach improves model validation and uncertainty quantification [139]. For instance, in spray drying of probiotic formulations, SA identified inlet air temperature and droplet size as key variables affecting survival and moisture content, which were subsequently estimated from drying curves. In extrusion modeling, calibrated shear-thinning parameters (flow index, consistency) allowed accurate prediction of pressure and expansion across varying moisture levels [140]. Challenges and Best Practices  
* Despite their value, SA and PE in CFD face notable challenges:
* High computational cost: Repeated simulations across parameter sets are resource-intensive; surrogate models (e.g., Kriging, neural networks) can help alleviate this burden. * Identifiability issues: Multiple parameter combinations may yield similar outputs, requiring regularization and sensitivity-based filtering.