Bubble velocity

As stated in the Kunii and Levenspiel book, the bubble rise velocity in a dense bed can be calculated as

\[u_{br} = 0.711(g d_b)^{1/2} \quad \text{where} \quad d_b/d_t < 0.125\]

Wall effects can slow the rise of bubbles when \(d_b/d_t > 0.125\); as such, the rise velocity is calculated as

\[u_{br} = \left[0.711(g d_b)^{1/2}\right]1.2\,exp\left(-1.49 \frac{d_b}{d_t}\right) \quad \text{where} \quad 0.125 < d_b/d_t < 0.6\]

For conditions where \(d_b/d_t > 0.6\), the fluidized bed is considered to be slugging.

Nomenclature

\(d_b\) - Diameter of sphere having same volume as spherical cap bubble, effective bubble diameter (m)
\(d_t\) - Bed or tube diameter (m)
\(g\) - Acceleration due to gravity, 9.81 m/s²
\(u_{br}\) - Rise velocity of single bubbles in a fluidized bed (m/s)

Source code

chemics.bubble_velocity.ubr(db, dt)[source]

Rise velocity of single bubbles in a fluidized bed from Equations 5.3 and 5.4 in Kunii and Levenspiel book 1.

Parameters
  • db (float) – Diameter of sphere having same volume as spherical cap bubble, referred to as the effective bubble diameter [m]

  • dt (float) – Bed or tube diameter [m]

Returns

ubr (float) – Rise velocity of single bubbles in fluidized bed [m/s]

Example

>>> ubr(0.05, 0.6)
0.4979

References

1

Daizo Kunii and Octave Levenspiel. Fluidization Engineering. Butterworth-Heinemann, 2nd edition, 1991.