Extension of the two-fluid model to bubble size distribution moment velocities

Moment methods exist as a computationally affordable way to model particle population balance in combination with the two-fluid model. For simplicity, it is often assumed that all moments are advected using the dispersed phase velocity of the two-fluid model. However, interfacial forces, and therefore also particle velocities, are generally size-dependent functions. We refer to this phenomenon as poly-celerity. This can be accounted for in moment methods by having different advection velocities for the different moments under consideration. In this work, we present a momentum balance equation for the advection velocity of a moment of arbitrary order. The equation is derived in such a way that it remains consistent with the two-fluid model momentum balance equation. This consistency is crucial, since the volume fraction computed by the two-fluid model is often taken as one of the moments used for closure in moment methods. In order to test the presented model, a hypothetical air–water bubbly pipe flow is simulated. We show that the resulting poly-celeric moment method is capable of predicting the same size distribution dynamics as a highly accurate reference size group method, at a significantly lower computational cost. The low computational cost can be explained by the fact that the present model only requires two additional balance equations to be solved in order to account for poly-celerity, while the reference method requires, in our specific case, 15 (one per velocity group). Additionally, we show that the correct size distribution dynamics are entirely lost when the effect of poly-celerity is left out of the model.