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

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 less than or equal to Re less than or equal to 603. For 210.5 less than or equal to Re less than or equal to 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 less than or equal to Re less than or equal to 603 the flow is unsteady and periodical but again with non-zero time-averaged lift/side and torque moment coefficients. Only for Re greater than or equal to 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 less than or equal to Re less than or equal to 400. For 2100 less than or equal to Re less than or equal to 300 obtained periodical 3D flows are corresponding to known mode A (with periodical structures along the axis of a cylinder equal to 3.5d less than or equal to lambda less than or equal to 4d, where d is the diameter of the cylinder). The regime with large dislocations previously discovered in experiments was obtained numerically for 220 less than or equal to Re less than or equal to 260. For 300 less than or equal to Re less than or equal to 400 obtained periodical structures have length 0.8d less than or equal to lambda less than or equal to 0.9d 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. (C) 2002 Elsevier Science Ltd. All rights reserved.