Numerical simulation of two-dimensional flows over a circular ...

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366 A.L.F. Lima E Silva et al. / Journal of Computational Physics 189 (2003) 351–370distribution, plotted over the central streamline downstream of the cylinder. Fig. 18 shows these distributionsas a function of y, for different values of Reynolds number. The second point, over this streamline,where the velocity is zero gives the L w measure. Fig. 19 shows the L w distribution as a function of theReynolds number. Comparisons of the present results with those of other authors [13,14] demonstrate goodagreement.The drag coefficient as a function of the dimensionless time for different values of the Reynolds numberis shown in Fig. 20. These results were obtained using Eq. (24).Fig. 21 shows the lift coefficient as a function of time for different Reynolds numbers. These results wereobtained using Eq. (28). It should be noted that for Re ¼ 45 the flow is still stable. As the Reynolds numberincreases the flow becomes unstable. The critical Reynolds number is approximately Re ¼ 47, as predictedby the linear theory of stability.The h orientation angle, illustrated by Fig. 22, varies from 0 to 180°, between the two stagnation points.Fig. 23 shows the pressure coefficient on the cylinder surface, defined as C p ¼ p k =0:5qU1 2 [22], as a functionof the angle h, as illustrated by Fig. 22. The pressure is taken on the Lagrangian points ~x k . U 1 is the freestream velocity.The comparison of the drag coefficient, obtained in the present work, with other numerical and experimentalresults, is presented in Table 2. Very good agreement has been obtained [5,11,23,26].Fig. 17. Length of the bubble recirculation.Fig. 18. Vertical velocity component ðvÞ as a function of y. L w determination.
A.L.F. Lima E Silva et al. / Journal of Computational Physics 189 (2003) 351–370 367Fig. 19. Bubble recirculation length ðL w =dÞ as a function of the Reynolds number.Fig. 20. Drag coefficients as a function of the dimensionless time: (a) Re ¼ 10, 20, 40 and 50; (b) Re ¼ 80, 100, 150 and 300.Fig. 21. Variation of lift coefficients with time: (a) Re ¼ 45 and 47; (b) Re ¼ 50 and 80.
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