Granular Continuum-Transition Regime

粒状连续体转变机制

• 批准号: 188876449
• 负责人: Professor Dr. Thorsten Pöschel
• 金额: --
• 依托单位: Lehrstuhl für Multiscale Simulation of Particulate Systems (MSS)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2011
• 资助国家: 德国
• 起止时间: 2010-12-31 至 2015-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/188876449?language=en
• 关键词: Granular; Continuum; Transition; Regime

Granular materials are ubiquitous and Nature and central in industry and agriculture. The proposed project will focus on their fluidized phase, known as the "granular gas". Powerful methods of kinetic theory have been employed to produce highly successful hydrodynamic descriptions of granular gases. Hydrodynamics is restricted to low Knudsen numbers (ratio of the mean free path to the pertinent macroscopic scales), and it therefore does; not apply to e.g., the interior of shocks or rarefied (granular) gases. When the Knudsen number is much larger than unity the collisionless limit of the Boltzmann equation applies, however, when is it of the order of unity a detailed study of the kinetics is called for. This defines the "continuum transition regime", which has parallels in e.g., molecular shocks and systems that involve rarefied gases as encountered e.g., in high altitude flights and chip-producing reactors. The goal of the proposed project is to produce continuum descriptions of the granular continuum transition regime and apply these to specific systems, the paradigm being vertically vibrated granular gases. This is planned to be achieved by harnessing recently developed powerful computer-aided analytic tools for the study of the pertinent Boltzmann equation (using the Grad moment expansion as one of the methods) in conjunction with efficient numerical simulations.

颗粒状物质在工业和农业中是普遍存在和重要的.拟议的项目将侧重于其流化阶段，称为“颗粒气”。动力学理论的强有力的方法已经被用来产生非常成功的颗粒气体的流体动力学描述。流体动力学仅限于低努森数（平均自由程与相关宏观尺度的比值），因此不适用于例如，冲击波或稀薄（颗粒状）气体的内部。当克努森数远大于1时，玻尔兹曼方程的无碰撞极限适用，然而，当它是1的数量级时，需要详细研究动力学。这就定义了“连续过渡制度”，它与例如，分子冲击和涉及遇到的稀薄气体的系统例如，在高空飞行和生产芯片的反应堆中。拟议项目的目标是产生连续描述的颗粒连续过渡制度，并将其应用到特定的系统，垂直振动的颗粒气体的范例。计划通过利用最近开发的强大的计算机辅助分析工具来研究相关的玻尔兹曼方程（使用格拉德矩展开作为方法之一），并结合有效的数值模拟来实现这一目标。