As node-wise non-structural superstructure model is applied to heat exchanger network optimization, heat exchanger crossover may appear. It is found that crossover structure causes an increase of total heat transfer area for heat exchange unit with same heat loads. At the same time, it reduces obviously computational efficiency of the algorithm. A vertical node-wise non-structural superstructure model is established. Compared with node-wise non-structural superstructure, the vertical node-wise non-structural superstructure model reduces computational complexity in the optimization process and eliminates adverse effects of crossover structure, which improves efficiency and accuracy of optimization. Finally, optimization performance of RWCE algorithm based on vertical non-structural superstructure model is analyzed in two examples. The results are superior to those in literature.

Dynamics characteristics of two bubbles in a quiescent fluid were simulated with three-dimensional lattice Boltzmann model. Eight-point and eighteen-point difference schemes were used to calculate the first and the second order derivative ▽ φ and ▽²φ in order to avoid numerical instability caused by large density ratios. It shows that for two rising bubbles with same size, the leading bubble rises like an isolated bubble, and the trailing bubble is influenced by the wake of the leading bubble. For two rising bubbles with different sizes, however, the larger bubble always strongly affects the smaller one in any initial sizes and locations.

Dynamics behavior of a vapor bubble such as rising, growth and deformation in superheated liquid was simulated with three-dimensional lattice Boltzmann phase-change model. To study effect of heat and mass transfer on vapor bubble, process of bubble rising in isothermal system was simulated. It shows that deformation extent of vapor bubble is small in superheated liquid. It is suggested that the effect of phase-change on vapor bubble is similar to surface tension force, which makes vapor bubble tend to keep its initial shape. Rising velocity of vapor bubble in superheated liquid was smaller. It implied that the effect of drag force on vapor bubble was dominant in superheated situation. In addition, growth rate of vapor bubble reaches the maximum at initial stage; Then it tended to nearly a constant. As vapor bubble volume and velocity increase, influence of disturbance on flow field is more and more intense. Meanwhile, growth of vapor bubble and convection induced by bubble rising have great impact on evolution of temperature field.