power of francis turbine's runner
hi all, i'm designing francis turbine right now. i'm using cfd software to see the velocity and pressure distribution in the runner of francis turbine in order to calculate the power of it.what i'm doing is to obtain the velocity triangle from every point in the cell of entry and exit of the runner, so i can get " P= u1cu1u2cu2". I wonder if anybody can give me advices or another way to calculate the power.
kind regards NIzam 
Re: power of francis turbine's runner
(1). I don't know you are doing right now. But I think, you are more likely running a cfd code. (2). You need to review the turbomachinery books first,and make sure that you know what you are doing. This is because working in the rotating frame of reference can be very confusing. (3). In the stationary frame of reference, the work done by the torque of the turbine shaft is equal to the angular momentum change between the inlet and the exit. (4). Once you have the velocity field in the stationary frame of reference, integrate the angular momentum in the inlet plane to give you the inlet value. Do th same thing at the exit, and then find the difference. (5). I still think, you need to review the books to make sure that you are getting the right formula. It has been a trap for many engineers from the cfd side.

Re: power of francis turbine's runner
Hi Nizam,
To calculate the power of the turbine you have to multiply your formula with the mass flow rate. But you can also use the following equation: P = M times omega, with M the torque [Fu x r] and omega the angular velocity. Fu represents the circumferential component of the (integral) forces along the turbine blades (friction and pressure). Dietmar 
Re: power of francis turbine's runner
For designing hydro turbine you have to first calculate specific speed by assuming head and flow after finding specific speed then you have to decide type of runner . Then find out diameter of shaft / runner. To get blade shape you have to construct velocity diagram at hub, mean and at tip section for entry and exit section.
power = mass flow x work done (i.e from velocity diagram at each section hub, mean and tip) After getting intial dimension (i.e shaft, blade dimension) then you have to go for CFD analysis. regards sameer mohrir 
Re: power of francis turbine's runner
the asme paper fedsm973328 is worth a check the computation of fluidinduced forces on centrifugal impellers rotating and whirling in a volute casingauthors rggkm aarts and jb jonker [university of twente].basic fluid book by j fay also could be helpful on equations and stationayrotating reference frames as pointed out by j.chien.
also paper epflscr no9 capa unsteady simulations of impellerdiffuser interactions in cent pump. hope this helpful. 
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