# Navier-Stokes equations through a orifice [closed]

I have reactor that looks as follows :

In the first part, my reactants flow in. The reaction is started and generates heat as a result.

It then expands slightly into the second part where after it is forced through a smaller opening, compressing the gases. The compressed gas then once again expands.

The reactor kinetics are not that important for now, I can do that. However, I do not know how to use NS-equations where the fluid expands, compresses and then expands.

I only ask that someone throws me in the right direction so that I may further research this.

## closed as too broad by tpg2114♦, ACuriousMind♦, John Rennie, Brandon Enright, BMSFeb 4 '15 at 20:53

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• Are you wanting to know how to use/solve the NS equations numerically or analytically in the region? – Kyle Kanos Feb 4 '15 at 13:52
• What level of answer are you looking for? An analytical solution? RANS, LES, DNS? This is a problem that could take months on a massive super computer to solve correctly depending on what kind of analysis you are trying to do. – tpg2114 Feb 4 '15 at 13:52
• Chapter III Turbulance models may help you, but as fellow commenters have suggested, it is a tough problem to crack. See waset.org/publications/4244/… – Autolatry Feb 4 '15 at 13:55
• Given your last sentence and the fairly broad nature of the question (i.e., whole books are written on the subject), I've added in a resource-recommendation tag to prevent closure (and seems to be in-line with what you want). – Kyle Kanos Feb 4 '15 at 13:58
• I see now that it is a bit vague. I have a gas, entering at approximately 1300C. A reaction then takes place, which causes a temperature increase down the reactor. The pressure drop in the horizontal direction can be determined by the Ergun equation as far as I know. – 22134484 Feb 4 '15 at 13:59