Modelling of the skin friction and heat transfer in turbulent two- component bubbly flows in pipes.

*(English)*Zbl 0621.76063The skin friction and heat transfer in turbulent two-component bubbly flows in pipes are modelled under the following conditions.

The flow is assumed to be vertical, steady, fully developed and to circulate in the upward direction. The modelling is based on two main arguments: firstly the persistence of the logarithmic velocity and temperature profiles near the wall for low values of the void fraction; secondly the similarity of the modifications caused by the bubbles on these profiles and those created by a grid in a single-phase turbulent boundary layer. The form of the friction and heat-transfer laws derived is in principle valid at low gas concentrations. However, comparisons with the local measurements presently available in this field and with the correlations of R. W. Lockhart and R. C. Martinelli [Chem. Eng. Prog. 45, 39-48 (1949)] and R. C. Martinelli and D. B. Nelson [Trans. ASME 79, 695-702 (1948)] show that the model works pretty well up to 0.2-0.3 void fractions.

The flow is assumed to be vertical, steady, fully developed and to circulate in the upward direction. The modelling is based on two main arguments: firstly the persistence of the logarithmic velocity and temperature profiles near the wall for low values of the void fraction; secondly the similarity of the modifications caused by the bubbles on these profiles and those created by a grid in a single-phase turbulent boundary layer. The form of the friction and heat-transfer laws derived is in principle valid at low gas concentrations. However, comparisons with the local measurements presently available in this field and with the correlations of R. W. Lockhart and R. C. Martinelli [Chem. Eng. Prog. 45, 39-48 (1949)] and R. C. Martinelli and D. B. Nelson [Trans. ASME 79, 695-702 (1948)] show that the model works pretty well up to 0.2-0.3 void fractions.

##### MSC:

76F99 | Turbulence |

76T99 | Multiphase and multicomponent flows |

76M99 | Basic methods in fluid mechanics |

80A20 | Heat and mass transfer, heat flow (MSC2010) |