Thermodynamic and Geometric Optimization of Systems with Flow Irreversibilities

具有流动不可逆性的系统的热力学和几何优化

• 批准号: 0001269
• 负责人: Adrian Bejan
• 金额: $ 20.57万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-06-01 至 2004-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0001269&HistoricalAwards=false
• 关键词: Thermodynamic; Geometric; Optimization; Systems; Flow

This project extends in several new directions the method of optimizing thermodynamically the geometry of tree-shaped flows between points and volumes. The geometric details of the flow structure will be deduced from the maximization of global thermodynamic performance (e.g., overall flow resistance) subject to global constraints. Examples are the tree-shaped networks that collect and distribute water and electric power over a territory. The method will also be extended to economics, where the flow consists of goods, and the global objective is revenue maximization. In the field of bioheat transfer, the method will be applied to the pairs of fluid trees (arteries and veins) that are present in vascularized tissues. Flows that are shaped as trees are found everywhere in natural systems, animate and inanimate (e.g., lungs, rivers, lighting). They are also prevalent in engineering, economics and society. The objective of this project is to deduce the optimal geometric structure of tree-shaped flows from the principle of maximizing the global performance of the system permeated by the flow. For example, in a tree network for the distribution of water and electric power over an urban area the global objective is minimum flow resistance and minimum cost. In economics, in the distribution or collection of goods over a territory, the objective is the maximization of revenue. In vascularized tissues under the skin, where trees of arteries and veins are arranged in pairs and in counterflow, the objective is the minimization of flow resistance and body heat loss. All these flow structures will be generated and studied from the point of view of geometric optimization based on global thermodynamic optimization.

这个项目在几个新的方向上扩展了优化热力学的方法，即点和体积之间的树状流动的几何形状。流动结构的几何细节将从全局约束下的全局热力性能(例如，总体流动阻力)的最大化中推导出来。在一个地区收集和分配水和电力的树状网络就是一个例子。这种方法还将扩展到经济学领域，在经济学中，流动由商品组成，全球目标是收入最大化。在生物热传递领域，该方法将应用于血管组织中存在的流体树对(动脉和静脉)。树木形状的水流在自然系统中随处可见，无论是有生命的还是无生命的(例如，肺、河流、灯光)。它们在工程、经济和社会中也很普遍。本课题的目标是从最大化系统整体性能的原则出发，推导出树形流的最优几何结构。例如，在城市地区供水和电力分配的树形网络中，全局目标是最小的流动阻力和最小的成本。在经济学中，在一个地区内分配或收集货物时，目标是使收入最大化。在皮肤下的血管组织中，动脉和静脉成对排列并逆流排列，目标是将流动阻力和身体热量损失降至最低。所有这些流动结构都将从基于全局热力学优化的几何优化的角度来生成和研究。