Direct numerical simulation of the transitional separated fluid flows around a sphere and a circular cylinder

Abstract For the investigation of transitional (from 2D to 3D unsteady) regimes of separated fluid flows around a sphere and a circular cylinder the direct numerical simulation is used. Transitional (from 2D axisymmetrical to 3D unsteady) regimes for a sphere were obtained for 210.5⩽ Re ⩽603. For 210.5⩽ Re ⩽297 the flow is steady but not axisymmetrical with non-zero lift/side and torque moment coefficients (the so-called double-thread wake). For 298⩽ Re ⩽603 the flow is unsteady and periodical but again with non-zero time-averaged lift/side and torque moment coefficients. Only for Re ⩾604 these time-averaged coefficients are equal to zero. The calculated vortex structure of the wake is successfully used for flow visualisation. An analysis of the dynamics of these structures for Re =880 reveals a sequence of shed hairpin vortices in combination with a sequence of secondary vortex loops around the legs of the hairpin vortices. Transitional regimes of separated fluid flows around a circular cylinder were obtained for 200⩽ Re ⩽400. For 200⩽ Re ⩽300 obtained periodical 3D flows are corresponding to known mode A (with periodical structures along the axis of a cylinder equal to 3.5 d ⩽ λ ⩽4 d , where d is the diameter of the cylinder). The regime with large dislocations previously discovered in experiments was obtained numerically for 220⩽ Re ⩽260. For 300⩽ Re ⩽400 obtained periodical structures have length 0.8 d ⩽ λ ⩽0.9 d approximately, which is in agreement with known mode B. For Re =300 obtained both modes A and B are existing simultaneously. The splitting on physical factors method for incompressible fluid flows (SMIF) with hybrid explicit finite difference scheme (second-order accuracy in space, minimum scheme viscosity and dispersion, capable of work in wide range of Reynolds numbers and monotonous) and O-type grids were used.