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Choosing a suitable physical timescale in CFX calculation

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For a single phase turbulent flow with or without heat transfer, the 'Auto Timescale' should be used. If you have more complicated physics, such as multiphase flow, flow resistance, or flow with reactions, then you should choose a physical timescale that is appropriate for your physics.

Most physical models require additional source terms and the timescale can often be estimated from them. For example, if we consider a quadratic flow resistance on a filter of length scale, d, then the momentum equation would be:

density*dv/dt = ... + 0.5*Cd*density*(v^2)/d

The timescale, dt, implied by this model is estimated from

v/dt = 0.5*Cd*(v^2)/d or dt = 2*d/(Cd*v)

So if d = 1 mm, Cd = 0.6 and v = about 10 m/s, dt = 3 x 10^-4 s.

The form of the source term can be obtained from the ANSYS CFX theory manual.

Once you have run a first case then look at the last number on the right in the residual table for each iteration in the out file. For example:

----------------------------------------------------------------------

| Equation | Rate | RMS Res | Max Res | Linear Solution |

+----------------------+------+---------+---------+------------------+

| U-Mom-Bulk | 0.84 | 6.3E-05 | 3.4E-03 | 1.6E-03 OK|

| V-Mom-Bulk | 0.87 | 1.4E-04 | 6.5E-03 | 4.4E-03 OK|

| W-Mom-Bulk | 0.84 | 6.3E-05 | 3.8E-03 | 1.5E-03 OK|

| P-Vol | 0.77 | 2.4E-06 | 1.0E-04 | 9.0 2.9E-03 OK|

+----------------------+------+---------+---------+------------------+

| Mass-Fluid1 | 0.91 | 2.3E-05 | 1.2E-03 | 10.7 3.3E-08 OK|

The numbers in the 'Linear Solution' column (1.6E-3, 4.4E-3, etc) tell you the residual from the linear solver but they can also be considered to be the fraction of non-linearity in the equation. Ideally, you want to choose the timescale so that the non-linearity is about 1 or 2% (i.e. 1e-2). If you increase the timescale, the amount of non-linearity also increases in proportion. In the above example, the timescale for u, v, w and p could be increased by a factor of 3 to get faster convergence. However, the mass fraction called 'Mass-Fluid1' has a non-linearity of only 3.3e-8, which is very small. The timescale for this equation (in CFX Pre Solver Control > Equation Class Settings) could be increased by almost 1,000 times, and the calculation would still be stable.

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