The Formula
For cold air discharge into a warmer space:
Fr = v / √(g × L × ΔT/T)
Where:
- v = air velocity (m/s)
- g = gravitational acceleration (9.81 m/s²)
- L = characteristic length (metres)
- ΔT = temperature difference between cold air and ambient (K)
- T = ambient temperature (K)
What Froude Number Tells You
Fr > 3: Momentum dominates. Cold air travels in the direction it’s discharged, maintaining horizontal trajectory across the refrigerated space.
1 < Fr < 3: Transition zone. Buoyancy forces become significant. Cold air begins curving downward while still traveling forward.
Fr < 1: Buoyancy dominates. Cold air falls regardless of discharge direction. Horizontal throw distance is severely limited.
Why Froude Number Matters for Refrigeration
Cold air discharged from a roof-mounted
evaporator at 5 m/s starts with a high
Froude number (typically Fr ≈ 9-10 at the discharge point). However, air velocity decays rapidly with distance as the jet spreads. In a typical 2.4m courier loadbox,
Froude number can drop below 1 before cold air reaches the rear doors.
This explains why
dead zones form predictably in upper rear corners—cold air intended for those areas has already fallen to the floor due to buoyancy takeover.
Design Implications
Increasing discharge velocity extends the throw distance before buoyancy dominates. However, higher velocities require more powerful fans (energy cost) and may create noise issues. Ducted discharge systems can maintain higher velocities over longer distances by preventing jet spreading.
T-bar floor channels in refrigerated vehicles work with buoyancy rather than against it—accepting that cold air will sink to floor level and creating return paths that pull circulation through the cargo space.
Related Research
Studies of tunnel ventilation and
thermal stratification use
Froude number (or the related Richardson number, Ri ≈ 1/Fr²) to predict stratification stability. When Fr < 0.66 (Ri > 2), stable stratification develops with distinct temperature layers.
See our technical article on
dead zones and temperature distribution for practical applications of
Froude number analysis.]]>
