Thrust calculation from cfd data(Numerical Integration)
 

I am doing CFD analysis on the supersonic nozzle, I need to calculate the thrust of the nozzle from CFD data. I don't know how to calculate the thrust numerically. The equation for thrust calculation is


please help

Hi,

If you use a particular software, maybe you have the integration option somewhere in the post processor. However, in order to evaluate that surface integral numerically, you consider constant the integrand over each cell face composing the patch where you need to evalute the momentum fluxes. Doing this your integral will be: \sum_{1}^{N} mf*Uf*Af, where Uf is the face center value for the velocity, Af the face area while mf is the mass flow rate throught the patch.The sum extends to all the patch faces. Hope this help.

Numerical integration is simple, because it can be reduced to a summation (as Ali mentioned). The problem here is to define a appropriate surface for the integral. If it encompass a too large volume, some of the thrust is transformed in heat (via turbulence) and your value gets too low.

take the gage pressure at the nozzle interior surface and element area normal to thrust direction and add the momentum of the flow of the upstream boundary of the nozzle. (the viscous forces on parallel surface may be insignificant....depends on the level of accuracy that your require).

thanks for suggestions I will look and get back if some problem comes.