基于方向导数法的换热系统性能优化
|
摘要
为了揭示换热系统性能优化的物理概念和规律,提出应用方向导数法来优化换热系统性能的新方法。首先,介绍了方向导数法的概念和数学形式,并阐明了方向导数法与拉格朗日乘子法之间的关系。其次,基于■耗散热阻思想和热阻网络原理,应用方向导数法分别对独立以及串联、并联换热器网络进行了分析。针对两独立换热器网络求其最大换热量问题,性能优化准则为两换热器换热量对热导(或热容量流)的导数相等。这相当于换热器换热量对热导(或热容量流)导数的离散场的协同。最后,应用方向导数法对含串并联单元的换热器网络进行了优化计算,得到了各设计参数最优值。对优化结果分析发现,应用系统分级等效思想可以指导并简化换热系统的优化设计,系统性能的优化取决于资源(热导或热容量流)的优化分配,即遵循大值与大值相匹配的原则。
In order to reveal the physical concepts and the laws of performance optimization of heat exchanging system, directional derivative method is adopted. Firstly, the concept and the mathematical forms of directional derivative method are introduced, and the relationship between directional derivative method and lagrange multiplier method is illustrated. Secondly, based on the concept of entransy-dissipation-based thermal resistance and the principle of thermal resistance network, the paper analyzes the heat exchanger networks in independent, series and parallel composition respectively by directional derivative method. For the network of two independent heat exchangers,when the total heat transfer amount reaches a maximum, the derivatives of heat transfer amount with respect to thermal conductance(or heat capacity rate) of two heat exchangers are equal. It is a kind of discrete field synergy of derivative. Finally, the optimization calculations of heat exchanger network with both series and parallel units are carried out by directional derivative method and the optimal values of design parameters are obtained. Analysis finds that the thought of system classification and equivalence can guide and simplify the optimal design of heat exchanging system. System performance optimization depends on the optimal allocation of resources(like thermal conductance and heat capacity rate). That is, it follows the principle of large values matching.
In order to reveal the physical concepts and the laws of performance optimization of heat exchanging system, directional derivative method is adopted. Firstly, the concept and the mathematical forms of directional derivative method are introduced, and the relationship between directional derivative method and lagrange multiplier method is illustrated. Secondly, based on the concept of entransy-dissipation-based thermal resistance and the principle of thermal resistance network, the paper analyzes the heat exchanger networks in independent, series and parallel composition respectively by directional derivative method. For the network of two independent heat exchangers,when the total heat transfer amount reaches a maximum, the derivatives of heat transfer amount with respect to thermal conductance(or heat capacity rate) of two heat exchangers are equal. It is a kind of discrete field synergy of derivative. Finally, the optimization calculations of heat exchanger network with both series and parallel units are carried out by directional derivative method and the optimal values of design parameters are obtained. Analysis finds that the thought of system classification and equivalence can guide and simplify the optimal design of heat exchanging system. System performance optimization depends on the optimal allocation of resources(like thermal conductance and heat capacity rate). That is, it follows the principle of large values matching.
引文
[1] GUO Zengyuan, ZHU Hongye, LIANG Xingang.Entransy—a Physical Quantity Describing Heat Transfer Ability[J]. International Journal of Heat and Mass Transfer, 2007, 50(13/14):2545-2556
[2] CHEN Qun, LIANG Xingang, GUO Zengyuan. Entransy Theory for the Optimization of Heat Transfer-a Review and Update[J]. International Journal of Heat and Mass Transfer, 2013, 63(15):65-81
[3]柳雄斌,孟继安,过增元.基于(火积)耗散的换热器热阻分析[J].自然科学进展,2008, 18(10):1186-1190LIU Xiongbin, MENG Ji'an, GUO Zengyuan. Analtsis of Thermal Resistance in Heat Exchanger Based on Entransy Dissipation[J]. Progress in Natural Science, 2008,18(10):1186-1190
[4]柳雄斌,过增元.换热器性能分析新方法[J].物理学报,2009, 58(7):4766-4771LIU Xiongbin, GUO Zengyuan. A Novel Method for Heat Exchanger Analysis[J]. Acta Physica Sinica, 2009, 58(7):4766-4771
[5] CHEN Qun. Entransy Dissipation-based Thermal Resistance Method for Heat Exchanger Performance Design and Optimization[J]. International Journal of Heat and Mass Transfer, 2013, 60(1):156-162
[6] CHEN Qun, FU Ronghuan, XU Yunchao. Electrical Circuit Analogy for Heat Transfer Analysis and Optimization in Heat Exchanger Networks[J]. Applied Energy, 2015,139:81-92
[7]方倩珊,吴全荣.多元函数条件极值的求法探究[J].福建师大福清分校学报,2014(2):5-10FANG Qiansian,Wu Quanrong. Discussions about Calculation of Conditional Extreme of Multivariate Function[J]. Journal of Fuqing Branch of Fujian Normal University,2014(2):5-10
[8]唐军强,杨庆玺,马小霞,耿世佼.用方向导数法求解多元函数条件极值[J].科技创新导报,2008(19):246-247TANG Junqing, YANG Qingxi, MA Xiaoxia, GENG Shijiao. Solving the Conditional Extremum of Multivariate Function by Directional Derivative Method[J]. Science and Technology Innovation Herald, 2008(15):246-247
[9] CHEN Qun, HAO Junhong, ZHAO Tian. An Alternative Energy Flow Model for Analysis and Optimization of Heat Transfer Systems[J]. International Journal of Heat and Mass Transfer, 2017, 108:712-720
[10]过增元.换热器中的场协同原则及其应用[J].机械工程学报,2003,39(12):1-9GUO Zengyuan. Principle of Field Coordination in Heat Exchangers and its Applications[J]. Chinese Journal of Mechanical Engineering, 2003, 39(12):1-9
[2] CHEN Qun, LIANG Xingang, GUO Zengyuan. Entransy Theory for the Optimization of Heat Transfer-a Review and Update[J]. International Journal of Heat and Mass Transfer, 2013, 63(15):65-81
[3]柳雄斌,孟继安,过增元.基于(火积)耗散的换热器热阻分析[J].自然科学进展,2008, 18(10):1186-1190LIU Xiongbin, MENG Ji'an, GUO Zengyuan. Analtsis of Thermal Resistance in Heat Exchanger Based on Entransy Dissipation[J]. Progress in Natural Science, 2008,18(10):1186-1190
[4]柳雄斌,过增元.换热器性能分析新方法[J].物理学报,2009, 58(7):4766-4771LIU Xiongbin, GUO Zengyuan. A Novel Method for Heat Exchanger Analysis[J]. Acta Physica Sinica, 2009, 58(7):4766-4771
[5] CHEN Qun. Entransy Dissipation-based Thermal Resistance Method for Heat Exchanger Performance Design and Optimization[J]. International Journal of Heat and Mass Transfer, 2013, 60(1):156-162
[6] CHEN Qun, FU Ronghuan, XU Yunchao. Electrical Circuit Analogy for Heat Transfer Analysis and Optimization in Heat Exchanger Networks[J]. Applied Energy, 2015,139:81-92
[7]方倩珊,吴全荣.多元函数条件极值的求法探究[J].福建师大福清分校学报,2014(2):5-10FANG Qiansian,Wu Quanrong. Discussions about Calculation of Conditional Extreme of Multivariate Function[J]. Journal of Fuqing Branch of Fujian Normal University,2014(2):5-10
[8]唐军强,杨庆玺,马小霞,耿世佼.用方向导数法求解多元函数条件极值[J].科技创新导报,2008(19):246-247TANG Junqing, YANG Qingxi, MA Xiaoxia, GENG Shijiao. Solving the Conditional Extremum of Multivariate Function by Directional Derivative Method[J]. Science and Technology Innovation Herald, 2008(15):246-247
[9] CHEN Qun, HAO Junhong, ZHAO Tian. An Alternative Energy Flow Model for Analysis and Optimization of Heat Transfer Systems[J]. International Journal of Heat and Mass Transfer, 2017, 108:712-720
[10]过增元.换热器中的场协同原则及其应用[J].机械工程学报,2003,39(12):1-9GUO Zengyuan. Principle of Field Coordination in Heat Exchangers and its Applications[J]. Chinese Journal of Mechanical Engineering, 2003, 39(12):1-9