Pipeline agglomerator design as a model test case

Design of a pipeline agglomerator to facilitate collection of submicron flame-synthesized aerosol powder post-quench must consider simultaneous aggregation and breakup to arrive at the appropriate pipe diameter to achieve desired cyclone efficiency under pressure drop constraints. The authors have used this problem in teaching population balances to classes in particle technology. The class solved the problem using a sectional method. Here, alternative moment solutions are discussed, including reconstruction of the distribution for comparison with the sectional result. The power of using both types of methods is illustrated in the additional insight available. The solution to the problem can be anticipated from the equilibrium solution for the zeroth moment alone. Insight into what is happening along the system trajectory can be seen more clearly in the moments but is reflected in the trajectory of sectionally obtained distributions. The moment model for this problem is an open set of equations requiring closure. Two different approaches, polynomial interpolative closure (MOMIC) and closure by quadrature (QMOM), are illustrated and the sensitivity of distribution reconstruction to the number of moments included in each type of model is probed. For both approaches, a model based on 10 moment equations resulted in a reconstructed distribution in reasonable agreement with the distribution computed directly from a 25-bin sectional model. Comparing on the same platform, solution time was the shortest for the MOMIC approach. The sectional method took 2–3 times longer than MOMIC while the QMOM method took 35% longer.