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Assessment of the validity of a log-law for wall-bounded turbulent bubbly flows

Bragg, A.; Liao, Y.; Fröhlich, J.; Ma, T.


There has been considerable discussion in recent years concerning whether a log-law exists for wall-bounded,
turbulent bubbly flows. Previous studies have argued for the existence of such a log-law, with a modified von
K´arm´an constant, and this is used in various modelling studies. We provide a critique of this idea, and present
several theoretical reasons why a log-law need not be expected in general for wall-bounded, turbulent bubbly
flows. We then demonstrate using recent data from interface-resolving Direct Numerical Simulations that when
the bubbles make a significant contribution to the channel flow dynamics, the mean flow profile of the fluid can
deviate significantly from the log-law behaviour that approximately holds for the single-phase case. The departures
are not surprising and the basic reason for them is simple, namely that for bubbly flows, the mean flow is
affected by a number of additional dynamical parameters, such as the void fraction, that do not play a role for the
single-phase case. As a result, the inner/outer asymptotic regimes that form the basis of the derivation of the loglaw
for single-phase flow do not exist in general for bubbly turbulent flows. Nevertheless, we do find that for
some cases, the bubbles do not cause significant departures from the unladen log-law behaviour. Moreover, we
show that if departures occur these cannot be understood simply in terms of the averaged void fraction, but that
more subtle effects such as the bubble Reynolds number and the competition between the wall-induced turbulence
and the bubble-induced turbulence must play a role.

Keywords: Bubbly flow; Log-law; Wall-bounded turbulent flows



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