Averaging effects in models of three-dimensional two-phase flows

In order to avoid the treatment of individual particle motion in two-phase flow description, one can use volume averaged descriptors. However, if the averaging volume is too small then individual particles can cause large undulations of the averages. In this report the amplitude of such undulations is estimated by a bound. It is shown that in general, one must average over 30-150 particles in order to obtain reasonably smooth averages. A consequence for interior ballistics calculations is that volume averages may be used to model the core flow but in general they cannot be used to resolve radial structures in two phases. Also presented are examples of the representation of a gas-particle aggregate boundary in terms of the gas volume fraction, and an approximate expression is derived for the transition curve.