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Characteristic Diameter D* for an FDS Grid

The characteristic diameter D* and the cell size range from which an FDS grid sensitivity study begins.

Where Q̇ comes from

Q̇ here is the design fire peak and not an instantaneous rate. If you have already calculated it in one of the other tools, you can take it from there rather than typing it again.

Where Q̇ comes from

Design fire peak

Ambient conditions

ρ∞ and T∞ are derived from it. c_p stays at 1.0 kJ/kg·K as in the FDS User Guide, so the result can be compared against the source.

What these numbers are not

Validity range

The conditions that determine whether the correlation applies. Crossing them changes the state of the result.

  • The correlation has no practical upper bound. A very large fire gives a large D* and a coarse starting grid — that is a correct answer rather than an anomaly, and the tool invents no ceiling.

Model limits

What the model does not describe, even within its validity range. These always hold.

  • They are not a cell size to choose from. D* divided by n, with n between 4 and 16, is the range a grid sensitivity study starts from — that is how the FDS User Guide presents it. The tool shows both ends and does not choose between them.
  • A convergence check is required. Run at least two resolutions within the range and compare. If the results differ materially the grid has not converged, and the answer depends on the grid rather than on the physics.

The equation

D* = ( Q̇ / (ρ∞ · c_p · T∞ · √g) )^(2/5)

1.829 / 16 … 1.829 / 4

D* [m]
Characteristic diameter
Q̇ [kW]
Design fire peak
T∞ [°C]
Ambient temperature

FDS User Guide, NIST — public domain

Result

Result with a caveat

There is a result, and there is a caveat to read before using it.

Opening range for a grid sensitivity study — D*/16 to D*/4

Fine

0.114 m

Coarse

0.457 m

Characteristic diameter D*
1.829 m
Design fire peak used
5,000 kW
Derived ρ∞ and T∞
1.2041 kg/m³ · 293.15 K
  • These values are not a recommended cell size but a starting point for a grid sensitivity study, as the FDS User Guide presents them. Run at least two resolutions within the range and compare the results; if they differ materially the grid has not converged, and the answer depends on the grid rather than on the physics.
  • The Q̇ entered here is the design fire peak, not an instantaneous rate. A grid derived from an instantaneous value suits that instant only.
  1. Density and absolute temperature — derived from the ambient temperatureρ∞ from the gas law, T∞ = 20 + 273.151.2041 kg/m³ · 293.15 K
  2. The denominator — ρ∞ · c_p · T∞ · √g1.2041 · 1 · 293.15 · √9.806651,105.4
  3. The characteristic diameter — D* = (Q̇ / the denominator)^(2/5)(5,000 / 1,105.4)^(2/5)1.829 m
  4. The opening range — D*/16 to D*/41.829 / 16 … 1.829 / 40.114 m … 0.457 m

Source

FDS User Guide, NIST — public domain.

c_p = 1 kJ/kg·K per the guide; ρ∞ and T∞ are derived from the ambient temperature entered, so the two are consistent with each other and a cold or hot space can be described too.

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