【作者】 张大彭；

【导师】 宋??；

【作者基本信息】 天津大学 ， 化学工程， 2004， 硕士

【摘要】 在共沸精馏模拟中共沸点的准确预测起着举足轻重的作用，传统的预测方法，有的采用经验关联式，但是其适用范围有限；而采用基于多元汽－液相平衡数据的共沸点预测方法，目前一般采用局部收敛性的Newton法求解。同伦方法具有大范围收敛性，对初值要求不高的优点，但收敛速度慢；Newton法具有收敛速度快的优点，但对初值要求苛刻。本文将两种算法优势互补，提出了预测共沸点的新算法同伦-Newton联合算法。同伦－Newton联合算法首先采用同伦方法把满足共沸条件的方程转化为微分连续同伦函数，并由此变成一个常微分方程的初值问题。对于转化以后的常微分初值问题，分别采用了中点求积公式和Euler预估－Newton校正法对其进行求解。以此解作为牛顿法的初值，然后采用Newton方法得到方程的精确解。在本文中，分别采用Newton法、同伦法、同伦-Newton联合算法预测了二元物系和三元物系等十余种强非理想性物系的共沸点，结果表明，相对牛顿法，同伦-Newton联合算法的收敛范围有了明显的扩大，收敛迭代过程的稳定性也有了很大的改善；而与同伦法相比，同伦-Newton联合算法的收敛速度和精度明显地提高。更多还原

【Abstract】 It is important to predict azeotropic temperature and composition in distillation. The traditional predictive methods include experiential methods and multicomponent vapor-liquid equilibrium methods, etc. But the applicable scope is finite, or the convergence scope is finite. Because the convergence of homotopy methods is larger than Newton methods, so it can make up for this disadvantage. In this thesis, authors combine the advantage of homotopy methods with Newton methods to form new homotopy-Newton united methods.In the first, the equations are being transformed to a differential homotopy-continuation function, and being a initial value problem of ordinary differential equation. Prediction-corrector methods are adopted in this thesis to solve ordinary differential equation. At last we adopt Newton methods to get the precision answer.In the thesis, new homotopy-Newton united methods、Newton methods and homotopy methods are adopted to predict azeotropic temperature and composition. Compare with Newton methods, the convergence scope of the new homotopy-Newton united methods is being enlarge and robust. Compare with homotopy methods, The new homotopy-Newton united methods, precision and rapidity are make a progress.更多还原