2 Discretization schemes

Discretization is the process of converting the continuous governing equations of the fluid flow into discrete algebraic equations, which can be solved by numerical methods. For bubble flows, discretization should account for the coupling between the gas and liquid phases, as well as the transport of mass, momentum, and energy. Depending on the flow regime and the bubble behavior, different types of discretization schemes may be suitable, such as finite volume, finite element, finite difference, or spectral methods. Discretization should also ensure the stability and accuracy of the solution, by using appropriate schemes for the time integration, the spatial interpolation, and the pressure-velocity coupling.

3 Multiphase models

Multiphase models are the mathematical formulations that describe the interaction and exchange between the gas and liquid phases in bubble flows. For CFD simulations, multiphase models should be consistent with the meshing and discretization strategies, as well as the physics and objectives of the problem. Depending on the flow regime and the bubble behavior, different types of multiphase models may be suitable, such as Eulerian-Eulerian, Eulerian-Lagrangian, volume of fluid, level set, or front tracking methods. Multiphase models should also account for the subgrid effects, such as the bubble breakup and coalescence, the interfacial tension, and the turbulence modulation.

4 Boundary and initial conditions

Boundary and initial conditions are the values or functions that specify the state of the fluid flow at the boundaries and at the beginning of the simulation. For bubble flows, boundary and initial conditions should reflect the realistic or experimental conditions of the problem, such as the inlet velocity, pressure, and volume fraction of the gas phase, the outlet pressure or mass flow rate, and the wall shear stress or heat flux. Boundary and initial conditions should also be compatible with the meshing, discretization, and multiphase models, by using appropriate boundary types, such as fixed value, zero gradient, or inlet-outlet conditions.

5 Validation and verification

Validation and verification are the processes of assessing the quality and reliability of the CFD simulation results, by comparing them with experimental data or analytical solutions. For bubble flows, validation and verification should be performed for each case and model, by using appropriate metrics and criteria, such as the bubble size distribution, the interfacial area concentration, the void fraction, and the pressure drop. Validation and verification should also be used to identify and correct the sources of error and uncertainty, such as the mesh dependency, the numerical convergence, and the model limitations.

6 Optimization and sensitivity analysis

Optimization and sensitivity analysis are the processes of finding the optimal or desired values or functions of the input parameters or design variables that affect the performance or outcome of the CFD simulation. For bubble flows, optimization and sensitivity analysis can be used to improve the efficiency or effectiveness of the process or system, such as the mass transfer rate, the heat transfer coefficient, or the bubble coalescence rate. Optimization and sensitivity analysis can also be used to explore the effects of uncertainty or variability in the input parameters or design variables, such as the inlet velocity, pressure, or volume fraction of the gas phase.