How to calculate the strength/energy of vortex in Joules
 

I would like to evaluate the strength of vortex in lid driven cavity flow. i am simulating the cases in Fluent. Although stream function (m^2/s)indicates the strength of vortex, I want to know vortex strength in Joules. How is it possible?

You can differentiate your stream function to get your velocity field (http://web.mit.edu/16.unified/www/FA...ctures/f12.pdf) which is then integrated around a closed loop to get your vortex strength (http://web.mit.edu/16.unified/www/SP..._Notes/f18.pdf).

For lid driven cavity flow, you will probably not get a constant circulation moving radially inward and will probably have to integrate or average several radial locations to get a global result. (unless I am totally wrong about that, but i doubt it.)

Also, unless I misunderstand your question I don't believe you can convert a circulation (vortex strength) to joules. Joule is a measurement of energy, circulation is not a measurement of energy. Dimensional analysis of the joule (kg-m^2/s^2) gives (M^1)(L^2)(T^-2) while circulation (m^2/s) gives (L^2/T^-1). Therefore you cannot convert between the two units...