Numerical Simulation of Distributed Parameter Processes

Analytical Modeling of an 15N Isotope Separation Column by Second-Order Quasi-Linear Equations with Two Independent Variable

“…Among the multiple approximate solutions associated with the isotopic separation phenomena expressed in relation to the time (t) and the propagation space (s), it is considered the following overdamped version represented in the following equation [1], [2]: (1) The two exponentially increasing evolutions represented in the following figure are limited to being approximated by two time constants respective and two space constants respective .…”

“…Taking into consideration the relations (2) respectively (3), (1) is presented as follows [2], [4]: (4) Considering the elements of the Cartesian system, namely p = 0 and q = 0, it follows that s = r corresponds to the height of the column, respective represents the final height of the column. With and are noted the initial and final moments of the isotopic separation process.…”

“…(1), the partial derivatives expressed in relation (6) lead to much more unitary and systematized expressions than those resulting in , presented in [3], directly associated with Cohen's equation. (6) As a result, the following relations will be presented as follows [1], [2], [4]: (7) ) (…”

“…As a result, these partial derivatives in relation to (t) and (s) are also obtained from the pivot element in the general form [ The approximation of these parameters is based on knowing the abscises ( , and ordinate resulting the aproximation of both and , but also knowing the abscises , and ordinate resulting the aproximation of both and . This is based on the numerical solution of the following transcendent equation [1], [2], [5], [6]:…”

“…From (16), (17), (18) For the usual propagation case with stationary values and , it is observed that . As a result, for this propagation inertia, which is increasing at the output in comparison to the input , it follows that for the time constants the following relation is noted [1], [2], [5], [6]:…”