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Correct method for calculating time step size

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Old   February 9, 2016, 04:49
Default Correct method for calculating time step size
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Hello Everyone,

I am a newbie to FLUENT & CFD. I wanted to calculate time step size for unsteady flow around a circular cylinder of dia = 0.01m in the Reynolds number of 45 to 50. The working fluid is water with viscosity = 0.001003 kg/ms and density = 998.2 kg/m3.

I came across several posts related to this and many methods to calculate the time step size.

1) From Strouhal number (0.2 for circular cylinder- approx)

Sr (0.2) = (frequency x diameter) / velocity
From the above equation find the frequency. The total time period, T = 1/frequency. Hence, time step \Deltat = T/25 (approx).

2) From CFL condition
\Delta t = C_m X \Delta x / velocity
where, C_m = 1 (approx) and \Delta x = minimum cell size.

3)From domain length
\Delta t = domain length / (20 x velocity)

1) Which of the above method is correct ?
2) How to calculate the suitable time step size for my condition?
3) Please explain.

Thanks in advance.
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Last edited by Aarthy Meena; February 9, 2016 at 05:50.
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Old   February 9, 2016, 05:25
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the time step is constrained by stability criteria that are based not only on the cfl condition but also on the visicous terms.

Furthermore, each discretization has a specific stability region
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Old   February 9, 2016, 05:28
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Dear Sir,

Can you please explain me the method for my flow scenario around a circular cylinder.
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Old   February 9, 2016, 05:36
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The numerical stability depends upon the method you use for the integration and the sizes of the mesh (in all directions), does not depend on a specific flow problem.
Assuming you are using non-dimensional equations, the velocity magnitude is no more than O(1) so that you can use that as estimation in the (multidimensional) CFL condition
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Old   February 9, 2016, 05:46
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Thank you sir,

Actually am very new to FLUENT and I do not understand your reply. In FLUENT, I am using dimensional form of the governing equations. Kindly please suggest me some material where I can learn about this topic.
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Old   February 10, 2016, 04:20
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A theoretical advice:
The CFL-number and the according "condition" are only part of the stability analysis of numerical schemes. A good introduction (for Finite Difference methods) can be found on:
https://en.wikipedia.org/wiki/Von_Ne...ility_analysis

Basically the stability depends on the equation you discretise (including all the terms in it - as FMDemaro added), as well as the discretisation scheme you use. As a "rule of thumb": lower order discretisation schemes (e.g.: Upwind schemes) and implicit time-dependent solution are very stable, whereas the more accurate methods tend to be unstable. For the Finite Element method, this can be proven analytically for certain cases - An example is also contained in the link.

A practical advice:
I am not familiar with ANSYS Fluent but I guess, that you will use Finite Volume Method with an implicit solver. The theoretical advice from above might therefore be tough to prove for your problem. I would advise you to have look on the user manual and see, if there is any hint. A cylinder in cross flow is also very well researched and there might be a lot of data and advice for your example already available.

Regards,
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Old   February 10, 2016, 05:46
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I am trying to do a transient analysis of flow through a bifurcation of penstock pipe (wye) using ansys cfx . Here i need to specify the conditions that the valves of the turbine are closed within a 5 seconds of time. I thought of giving pressure inlet and mass flow rate at the outlet. Now i need to vary the mass flow rate at the outlet from 4650kg/s to 0 within a 5 seconds of time and i dont know how to do that in ansys CFX. Can anybody help me please ??
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Old   May 7, 2019, 08:56
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Dear Aarthy Meena,
did you find a good average to calculate the time step and time step size?
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circular cylinder, fluent 14.5, time step size, transient simulations

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