μ2). There are two particle resistors (in this work for simplicity we take h1 = h2 = h), that restrict the particle flows N1 and N2. The net result is a particle flow drop from N1 to an intermediate particle reservoir N3 and from N4 to N2. From the local stability analysis it was concluded that the ECR is stable for every value of h, C1 and τ = n x/n y. After a small perturbation, the system declines to the steady state with two different relaxation times both being proportional to C, h and τ. Finally, when the power output in the steady state versus τ is plotted, it demonstrates how an increment of τ can improve the system stability. This suggests a compromise between the stability and the engine energetic properties driven by τ.]]>
μ2). Adicionalmente, existen dos resistencias (en este trabajo por simplicidad tomamos h1 = h2 = h), que restringen los flujos de las partículas N1 y N2. El resultado neto es una caida en el flujo de partículas desde N1 hacia un almacen intermedio de partículas N3 y de N4 a N2. A partir del análisis de estabilidad local, se puede concluir que el ECR es estable para cada valor de h, C1 y τ = n x/n y. Después de una pequeña perturbación, el sistema decae hacia un estado estacionario con cualquiera dos tiempos de relajación diferentes ambos proporcionales a C, h y τ. Finalmente, cuando graficamos la potencia de salida en el estado estacionario contra τ, encontramos que un incremento de τ puede mejorar la estabilidad del sistema. Esto sugiere un compromiso entre la estabilidad del sistema y las propiedades energéticas del mismo manejados por τ.]]>
Dynamic stability in an endoreversible chemical reactor
Estabilidad dinámica de un reactor químico endoreversible
J.C. Chimal-Eguía*
* Centro de Investigación en Computación del IPN, Av. Juan de Dios Bátiz s/n esq. Miguel Othón de Mendizabal, col. San Pedro Zacatenco, C. P. 07738, México D. F., México. * Corresponding author. E-mail: jchimale@ipn.mx
]]> Received January 14, 2015;
Abstract
This article presents a local stability study for an endoreversible Chemical Reactor (ECR). The model consists of two particle reservoirs, one at high chemical potential μ1 and the other at low chemical potential μ2 (the terms "high" and "low" refer to the situation in which μ1 > μ2). There are two particle resistors (in this work for simplicity we take h1 = h2 = h), that restrict the particle flows N1 and N2. The net result is a particle flow drop from N1 to an intermediate particle reservoir N3 and from N4 to N2. From the local stability analysis it was concluded that the ECR is stable for every value of h, C1 and τ = nx/ny. After a small perturbation, the system declines to the steady state with two different relaxation times both being proportional to C, h and τ. Finally, when the power output in the steady state versus τ is plotted, it demonstrates how an increment of τ can improve the system stability. This suggests a compromise between the stability and the engine energetic properties driven by τ.
Keywords: endoreversible, chemical reactor, stability, steady state, power output.
Resumen
En este trabajo se presenta un análisis de estabilidad local de un Reactor Químico. El modelo consiste de dos almacenes de partículas uno a un potencial químico alto μ1 y el otro a un potencial químico bajo μ2 (los terminos "alto" y "bajo" se refieren a la situación en la que μ1 > μ2). Adicionalmente, existen dos resistencias (en este trabajo por simplicidad tomamos h1 = h2 = h), que restringen los flujos de las partículas N1 y N2. El resultado neto es una caida en el flujo de partículas desde N1 hacia un almacen intermedio de partículas N3 y de N4 a N2. A partir del análisis de estabilidad local, se puede concluir que el ECR es estable para cada valor de h, C1 y τ = nx/ny. Después de una pequeña perturbación, el sistema decae hacia un estado estacionario con cualquiera dos tiempos de relajación diferentes ambos proporcionales a C, h y τ. Finalmente, cuando graficamos la potencia de salida en el estado estacionario contra τ, encontramos que un incremento de τ puede mejorar la estabilidad del sistema. Esto sugiere un compromiso entre la estabilidad del sistema y las propiedades energéticas del mismo manejados por τ.
Palabras clave: endoreversibilidad, reactor químico, estabilidad, estado estacionario, potencia de Salida.
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Acknowledgements
The authors wish to thank "Consejo Nacional de Ciencia y Tecnología" (CONACyT), "Comisión de Operación y Fomento de Actividades Académicas del Instituto Politécnico Nacional" (COFAA-IPN, project number 20151704) and "Estímulos al Desempeño de los Investigadores del Instituto Politécnico Nacional" (EDI-IPN), for the support given for this work.
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