The Theoretical And Numerical Study On The Mathematical Model Of Micro-Channel Reactor

The micro-channel reactors have many important applications in the areas of biology, chips, chemical engineering and material science. This thesis focuses on two kinds of micro-channel reactor--the co-flowing micro-channel reactor and the rotating liquid film reactor, which have different structure and reaction mechanism. So far, although many good results have been obtained, there are still many problems that are not fully solved.As to the co-flowing micro-channel reactor, we mainly study on the upper part of it, i.e. the annular pipe. Due to the fact that the stability of the flow in the annular pipe is a key factor to the final product, this thesis mainly investigates the behavior of the flow in it. From the literatures, we find there are many similarities between the Orr-Sommerfeld equation and the stability of the flow in the annular pipe, thus the method used in this thesis is analogous to that used in solving the Orr-Sommerfeld equation.Firstly, an analytical expression of velocity profile of the laminar flow in the annular pipe has been given in the section 2.3. Secondly, we simplify the governing equations of the flow in annular pipe and turn the stability problem into the searching of the eigenvalue of a linear system of equations. Finally, the critical Reynolds number and some other properties of the critical Reynolds number have been studied via the numerical solution of the linear system. In order to examine the reliability of the method, we apply it in solving one similar problem in the real number field and another one in the complex field.As to the rotating liquid film reactor, we just do some research on the critical volume flow rate and the critical tilt angle. After the analysis and some comparisons of the numerical results, we find there is a critical tilt angle which makes the volume flow rate of the reactant reach its maximum when the rotator of the reactor is fixed. Based on this fact, a further study has been made on the effect of the speed of the rotator and the gap size on the change of the critical tilt angle and we have gained some good results.