Converging-Diverging Nozzles

Here is something that I believe to be interesting. It is often of common sense to think that as the area normal to a fluid flow gets reduced, the fluid velocity increases. We observe this behavior all the time with garden hoses as we use reduction fittings to get a faster water flow coming out of the hose. Incompressible fluids, like water or any other liquid, follow this behavior since for conservation of mass to be satisfied the velocity must increase, but what happened to compressible flows. A very different type of behavior can be observed with compressible flows if the geometry and the conditions are right. I am not going to get into very much detail in this topic; however I will show you a CFD (Computational Fluid Dynamics) experimental study that was performed using a compressible fluid (air). Using a CFD computer software called StarCD, the first step was to generate the geometry and the mesh. To save computational time, only half of the nozzle was created and a symmetry boundary condition was imposed on the middle cut. 
As observed from the picture above, this nozzle converges to maximum reduction section called “the throat” and then it starts to diverge again, thus the name Converging-Diverging nozzle. As the flow enters the convergence section of the nozzle, the flow accelerates to exactly a mach number of 1 exactly at the throat (see picture below). If the pressure conditions are right, a shock wave will occur at the throat of the nozzle expanding the fluid and the flow will continue to accelerate in the divergence section of the nozzle reaching velocities higher than mach1.
The imposed atmospheric pressure boundary condition at the outlet was such that the flow then had to slow down lower than mach 1 before reaching the outlet (however on better designs and under other conditions the flow can exit at supersonic speeds) . This is just one example in which a flow can be accelerated through a section of increasing cross-sectional area although common sense might tell us the opposite. This behavior is also a results of the law of conservation of mass. I should add that if instead of increasing the area after the throat, one continues to decrease it; the flow will never reach supersonics speeds. Now you know why supersonic vehicles like space shuttles have the nozzle shape like that.

No comments:

Post a Comment