A numerical study of flow fields of lobed hailstones falling in air

•Numerical solutions of unsteady Navier–Stokes equations for flow past lobed hailstones•Hailstone shapes are simulated by using a mathematical function to generate shapes with many lobes.•Flow characteristics are described to contrast with smooth spherical hailstones.•Drag coefficients are fitted with empirical formulas.

The characteristics of the flow fields around six falling lobed hailstones of diameters 1 to 10 cm are studied. The flow fields are obtained by numerically solving the time-dependent Navier–Stokes equations for flow past the six lobed hailstones created through a set of newly proposed mathematical expressions allowing us to precisely represent their shapes that can be easily meshed afterwards through stereolithography for the simulations performed herein. The range of Reynolds numbers is from 9560 to 388,000, which is believed to be close to the realistic physical range. The computed flow fields are characterized in terms of the streamtrace pattern, vertical velocity, pressure distribution, and vorticity fields. The computed results demonstrate that while the eddy lengths for the six lobed hailstones of equal size are almost the same, with more and longer lobes on a hailstone, the eddies inside the recirculation bubble shed more chaotically. In comparison with our previous numerical work, the spherical hailstones have higher drag coefficients than the three short lobed hailstones in the range of Reynolds numbers roughly between 25,000 and 122,000 while most long lobed hailstones we consider have greater drag coefficients than the spherical ones. However, compared with previous experimental data by others, the smooth spherical graupel and hailstone are both highly greater in drag coefficient than almost all the short and long lobed hailstones considered herein numerically.