As it known Fluent define the stream function as the mass rate of flow between the streamlines so it showing it in terms of (kg/s) in contours. My question how I can convert this unit into original units of stream function (i.e. to m2/s) ?
You can use the Custom-Field-Functions utility of FLUENT to do this.
Given that U=del(psi)/del(y), where U is streamwise velocity, psi is the stream function and del represents partial differentiation, it is seen that psi has a SI unit of m2/s. Now, in two-dimensions, psi would represent volume flow rate so that rho*psi (where rho is fluid density) represents mass flow rate (as you correctly point out) which is the case in FLUENT.
In order to obtain psi in terms of m2/s, you simply need to define a custom field function of the form psinew=psi/rho which should yield units of m3/s....which, in my opinion, is quantitatively equivalent to m2/s (the volume flow rate) in two dimensions.
You can use the Custom-Field-Functions utility of FLUENT to do this.
Given that U=del(psi)/del(y), where U is streamwise velocity, psi is the stream function and del represents partial differentiation, it is seen that psi has a SI unit of m2/s. Now, in two-dimensions, psi would represent volume flow rate so that rho*psi (where rho is fluid density) represents mass flow rate (as you correctly point out) which is the case in FLUENT.
In order to obtain psi in terms of m2/s, you simply need to define a custom field function of the form psinew=psi/rho which should yield units of m3/s....which, in my opinion, is quantitatively equivalent to m2/s (the volume flow rate) in two dimensions.