Parcel-number-density control algorithms for the efficient simulation of particle-laden two-phase flows

Highlights: • Modified variants of stochastic PNDCs are proposed. • A new deterministic PNDC is proposed combining the pair and ternary schemes. • Many available PNDCs are evaluated for EL particle-laden flow simulations. • A new challenging test case for the PNDC algorithm assessment is devised. • The closeness in the movement direction is the best parcel selection criterion. -- Abstract: The efficient reduction of statistical error and achieving numerically convergent solutions in Eulerian–Lagrangian (EL) simulations necessitate the use of Parcel-Number-Density Control (PNDC) algorithms. Many PNDC algorithms have been proposed in other fields, like plasma simulations, which have not been evaluated for particle-laden two-phase flows. In this research, for the assessment of different deterministic and stochastic PNDCs, a new test case is devised in which the statistical error can be filtered out to measure the level of inconsistency imposed by a PNDC. The results show that the closeness of the movement direction is the best criterion for the parcel selection in the merging process, compared to similar position or weight criterion. Here, a new blended deterministic PNDC, which has the least error among deterministic PNDCs, is proposed by combining the pair merging and ternary merging schemes. In addition, modified variants of stochastic PNDCs based on the two-value PDF concept are proposed which satisfy all consistency requirements. These stochastic PNDCs are proved to be much more promising for more challenging situations, like poly-dispersed flows or particles with larger Stokes numbers. The computational overhead of these algorithms are compared and the best algorithm is recommended. Finally, it is proved that a convergent EL solution with a controlled statistical error can be obtained using these PNDCs.