Direct-quadrature generalized moment based methods were analysed in terms of accuracy, computational cost and robustness for the solution of the population balance problems in the [0,∞) and [0,1] domains. The minimum condition number of the coefficient matrix of their linear system of equations was obtained by global optimization. An heuristic scaling rule from the literature was also evaluated. The results indicate that the methods based on Legendre generalized moments are the most robust for the finite domain problems, while the DQMoM formulation that solves for the abscissas and weights using the heuristic scaling rule is the best for the infinite domain problems.

Riemann-solver based schemes are difficult and sometimes impossible to be applied for complex flows due to the required average state. Other methods that do not use Riemann-solvers are best suited for such cases. Among them, AUSM+, AUSMDV and the recently proposed Hybrid Lax-Friedrichs-Lax-Wendroff (HLFW) have been extended to two-phase flows. The eigenstructure of the two-fluid model is complex due to the phase interactions, leading to numerous numerical difficulties. One of them is the well-posedness of the equation system because it may lose hyperbolicity. Therefore, the methods that are not based on the wave structure and that are not TVNI could lead to strong oscillations. The common strategy to handle this problem is the adoption of a pressure correction due to interfacial effects. In this work, this procedure was applied to HLFW and AUSM-type methods and their results analyzed. The AUSM+ and AUSMDV were extended to achieve second-order using the MUSCL strategy for which a conservative and a non-conservative formulation were tested. Additionally, several AUSMDV weighting functions were compared. The first and second-order AUSM-type and HLFW methods were compared for the solution of the water faucet and the shock tube benchmark problems. The pressure correction strategy was efficient to ensure hyperbolicity, but numerical diffusion increased. The MUSCL AUSMDV and HLFW methods with pressure correction strategy were, on average, the best of the analyzed methods for these test problems. The HLFW was more stable than the other methods when the pressure correction was considered.

Classical and recent numerical schemes for solving hyperbolic conservation laws were analyzed for computational efficiency and application to nonideal gas flows. The Roe-Pike approximate Riemann solver with entropy correction, the Harten second-order scheme and the extension of the Roe-Pike method to second-order by the MUSCL strategy were compared for one-dimensional flows of an ideal gas. These methods require the so-called Roe's average state, which is frequently difficult and sometimes impossible to obtain. Other methods that do not require the average state are best suited for complex equations of state. Of these, the VFRoe, AUSM+ and Hybrid Lax-Friedrich-Lax-Wendroff methods were compared for one-dimensional compressible flows of a Van der Waals gas. All methods were evaluated regarding their accuracy for given mesh sizes and their computational cost for a given solution accuracy. It was shown that, even though they require more floating points and indirect addressing operations per time step, for a given time interval for integration the second-order methods are less-time consuming than the first-order methods for a required accuracy. It was also shown that AUSM+ and VFRoe are the most accurate methods and that AUSM+ is much faster than the others, and is thus recommended for nonideal one-phase gas flows.

The modeling and simulation of mold filling must include a method to capture the interface formed between the inlet fluid and the fluid that was initially in the mold. A commonly used front-capturing method in a Eulerian mesh is the volume-of-fluid (VOF) method. The VOF advection equation solution may show numerical diffusion and/or dispersion and high-order numerical schemes, such as the TVD schemes with dimensional splitting, have to be employed to discretize the convective terms. The present contribution explores the use of RCM for solution of the VOF color-function equation during mold filling with recirculating flows. The Navier-Stokes equations are solved by a finite-volume method using the SIMPLER algorithm. Filling simulations using the TVD and RCM methods are compared. RCM was able to generate diffusion-free results, sharply defining the interface, even when topological changes (generation of droplets) occur.

Experimental bubble size distributions and bubble mean diameters were obtained by means of a photographic technique for a direct-contact evaporator operating in the quasi-steady-state regime. Four gas superficial velocities and three different spargers were analysed for the air-water system. In order to assure the statistical significance of the determined size distributions, a minimum number of 450 bubbles was analysed for each experimental condition. Some runs were also conducted with an aqueous solution of sucrose to study the solute effect on bubble size distribution. For the lowest gas superficial velocity considered, at which the homogeneous bubbling regime is observed, the size distribution was log-normal and depended on the orifice diameter in the sparger. As the gas superficial velocity was increased, the size distribution progressively acquired a bimodal shape, regardless of the sparger employed. The presence of sucrose in the continuous phase led to coalescence hindrance.