Comparison of methods for computing the concentration field of a particulate flow

• We compare five methods for concentration definition in multiphase flows.
• A range of desirable properties are introduced by which to compare the methods.
• Common definitions exhibit excess noise and/or lack of discrete conservation.
• Even moment-preserving methods fail to be conservative for wall-bounded flows.
• New conservative blob method yields smooth, conservative fields in all flows.

Concentration computation from known particle positions is important for post-processing of Lagrangian multiphase flow computations and for calculation of particle-induced body force in computations with two-way fluid-particle coupling. Some existing methods for particle concentration calculation exhibit excessive noise, negative concentration values, or lack of discrete conservation of the particle volume in various situations. The current paper examines the performance of five concentration computation methods based on satisfaction of a set of desirable properties. The methods are examined for three different test cases, including situations with and without boundaries in the particle domain. Of the concentration computation methods examined, the standard particle-counting method and the moment-preserving M4′ method exhibit significant amounts of noise as the ratio of grid increment to particle diameter decreases to less than a critical value. The M4′ method produces non-physical negative concentration values. The concentration blob method violates the discrete-conservation property, which specifies that the total particle volume be equal to the numerical integral of the concentration field. A smooth moment-preserving Gaussian blob method is examined that discretely conserves the zeroth and first concentration moments (as well as higher-order moments) in an unbounded domain, but leads to lack of conservation in a bounded domain. A new conservative concentration blob method is presented which is positive and discretely-conservative in both unbounded and bounded domains with little spurious noise, but requires that the blob diameter be sufficiently large compared to the grid increment size.