Determining appropriate time steps for a CFD simulation involving rotating blades is crucial for achieving accurate and stable results. In this calculator, we will use typical scenario for a rotating blade (fan, turbine, blower, etc) with specific rotational speed, blade numbers, and desired iteration input to determine the timestep required and total number of iterations.
Formula to Determine Timesteps
To determine the timesteps, we must first determine the time required for the system to achieve a complete single rotation, or its frequency:
frequency = time/rotation = 1/rotational speed [Hz]
The rotational speed must be in rev/s, if you have the rpm data, just divide the rpm by 60 to get rev/s.
Then, calculate time required for one blade achieve the next blade location, which can be calculated by dividing the frequency by the number of blade:
blade-to-blade time = frequency/number of blade [s]
This value is the “maximum” time step that you might apply to your simulation. By inputing this value, you cannot capture the blade motion within the simulation. Then, we must specify the number of motion (in the animation) for blade to achieve its next position. You also must consider the number of autosave for your setup, the “appeared” timestep in your post processing will be your inputed timestep times the autosave/timestep, which ultimatelly can be calculated as follows:
time step = blade-to-blade time/(blade-to-blade motion*autosave) [s]
After you have your time-step value, you can calculate the total number of iteration based on your total desired revolution, internal iteration (iteration per number of motion) and your timetep as follows:
end time = frequency*total rotation [s]
total iteration = (end time/timestep)*internal iteration [iterations]
These equations illustrated in the Image below (3 motions blade-to-blade):
Rotation Speed Unit conversion:
1 rad/s ~ 9.549 rpm
1 deg/s = 0.166667 rpm
1 rev/s = 60 rpm
1 Hz = 60 rpm