Model 4 (General)

Developing the Model

• Pressure loss in reactor
• Only one reaction: ammonia and oxygen combining to form nitric oxide and water
• Temperature changes in reactor due to heat generation at walls of reactor
• Parabolic flow profile in channel

Purpose of Model 4

There’s an important component to our reactor that we haven’t modeled yet: the actual flow of the gas stream flowing through the reactor. Gas flow, just like fluid flow, can be classified as either laminar or turbulent, depending on the geometry of the pipe, properties of the gas, and flow rate. In laminar flow, the stream lines do not change with time. Imagine putting five toy boats, one after each other, into a river and following their path downstream. If the flow is laminar, each boat will follow the one in front of it, tracing the same path. If the flow is turbulent, chances are that each boat will take a different route down the stream.

Knowing which kind of flow is present in a reactor is critical to knowing how to model that flow. Engineers have found that a good way of predicting if flow is laminar or turbulent is to calculate the Reynolds number. For most microreactors, including the one currently being discussed, the Reynolds number is low (<2000) and the flow is laminar.

What are the effects of flow ?

All of the previous models assumed that the flow rate was the same everywhere in the reactor. Real life, of course, is never that easy. The fluid close to the walls moves much more slowly than the fluid in the middle of the channel. This means that the fluid in the middle of the channel spends less time in the reactor that the fluid along the walls.

How to account for the effects of flow ?

As with the previous models, to account for an effect we need to model that effect. But our previous models are not well-suited to handling the very complicated fluid flow equations. So, we move on to a model just as complicated as the equations we are trying to solve, called a finite element model. Basically, we tell the computer what our reactor looks like and it then divides the reactor up into small sections and solves the complicated system of equations for each small section. By looking at small sections individually, the equations can be simplified to a more manageable level.

In the figure below, the large rectangular channel is the microreactor and the grey slice is the geometry that we described to the computer:

 Want to find out more? Click on the Expert Model 4 page.
 
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