Comparative Study on Several Criteria for Non-equilibrium Phase Separation

Several different kinds of criteria for non-equilibrium phase separation to discriminate the two stages, the spinnodal decompostion (SD) and domain growth (DG), are compared and further investigated. The characteristic domain size and morphological function present two geometric criteria. Both of them can only provide rough estimations for the crossover from SD to DG. The reason for domain size is that the crossover in this description covers a process, instead of a specific time. The reason for the morphological function is that the result may rely on chosen threshold value. However, both the non-equilibrium strength and the entropy production rate are physical criteria and are more convenient to provide critical times. In fact, not only the non-equilibrium strength defined in the moment space opened by all the independent components of the used non-equilibrium quantities but also those defined in its subspaces can be used as criteria. Each of those criteria characterizes the phase separation process from its own perspective. Consequently, the obtained critical times may show slight differences. It should be pointed out that these slight differences are not contradictive, but consistent with each other and complementary in describing the complex phenomena.Comment: arXiv admin note: text overlap with arXiv:1808.0769

Multiple-Relaxation-Time Lattice Boltzmann Approach to Compressible Flows with Flexible Specific-Heat Ratio and Prandtl Number

A new multiple-relaxation-time lattice Boltzmann scheme for compressible flows with arbitrary specific heat ratio and Prandtl number is presented. In the new scheme, which is based on a two-dimensional 16-discrete-velocity model, the moment space and the corresponding transformation matrix are constructed according to the seven-moment relations associated with the local equilibrium distribution function. In the continuum limit, the model recovers the compressible Navier-Stokes equations with flexible specific-heat ratio and Prandtl number. Numerical experiments show that compressible flows with strong shocks can be simulated by the present model up to Mach numbers $Ma \sim 5$.Comment: Accepted for publication in EP

Prandtl number effects in MRT Lattice Boltzmann models for shocked and unshocked compressible fluids

For compressible fluids under shock wave reaction, we have proposed two Multiple-Relaxation-Time (MRT) Lattice Boltzmann (LB) models [F. Chen, et al, EPL \textbf{90} (2010) 54003; Phys. Lett. A \textbf{375} (2011) 2129.]. In this paper, we construct a new MRT Lattice Boltzmann model which is not only for the shocked compressible fluids, but also for the unshocked compressible fluids. To make the model work for unshocked compressible fluids, a key step is to modify the collision operators of energy flux so that the viscous coefficient in momentum equation is consistent with that in energy equation even in the unshocked system. The unnecessity of the modification for systems under strong shock is analyzed. The model is validated by some well-known benchmark tests, including (i) thermal Couette flow, (ii) Riemann problem, (iii) Richtmyer-Meshkov instability. The first system is unshocked and the latter two are shocked. In all the three systems, the Prandtl numbers effects are checked. Satisfying agreements are obtained between new model results and analytical ones or other numerical results.Comment: 17 pages, 8 figure

Forest biomass resources and utilization in China

Under the context of climate change, persistent high oil prices and rapidly growing dependence on imported oil prompt China to pay much more attention to biofuels that provide environmental benefits besides fuel. China has rich biodiversity with 30 thousand high plant species and 154 kinds of energy trees could produce seeds containing more than 40% of oil, with total production of the seeds totaling 5 million t, and 200 x109 t of biomass production per year, which is equal to 2 x 109 t of petroleum. There are over 2000 types of wild and cultivated firewood plants in the country. So far there is 4 million ha raising oil-bearing trees planted on some land in different regions. Another 57 million ha of waste land are available and suitable for planting trees for the production of forest bioenergy. On part of these lands, the central government plans to cultivate a total of 13 million ha of high-grade bioenergy forests by 2020. This will yield 6 million tons of diesel that would be enough to fuel power plants with a combined capacity of 11 GW each year. Moreover, forest biomass plantations potentially offer many direct and indirect environmental benefits. In view of climate change their globally significant environmental benefits may result from using forest biomass for energy rather than fossil fuels.Key words: Biomass energy, China, forest biomass resources