Turbulent flow around a square cylinder at Reynolds number 22,000: A DNS study

Abstract

The turbulent flow around a square cylinder at Reynolds number 22000 (based on the cylinder diameter and the inflow velocity) is studied by means of direct numerical simulation. An overview of the numerical methods and the methodology used to verify the simulation is presented with special emphasis to determine the proper domain size and time-integration period.

The turbulence cascade in the near wake of a square prism

“…While all references agree that the peak of u ′ 1 should occur just after x 1 ≈ d, the actual value of u ′ 1 /U ∞ at its peak varies between 0.28 and 0.56. We find the peak value of u ′ 1 /U ∞ to be close to 0.41 which is in agreement with the results of Lyn et al (1995) and Trias et al (2015) which were obtained at a larger Re. Lee & Kim (2001a) are shown in Lee & Kim (2001b).…”

“…This is in line with the results reported in Voke (1996) and Sohankar (2006) where LES simulations at Re = 22000 are compared with the reference data of Lyn et al (1995). On the other hand, significant differences are also observed in the recovery velocity: while the present results and those of Lyn et al (1995), Lee & Kim (2001b) and Trias et al (2015) show a very slow increase of U 1 /U ∞ along x 1 /d from the value of about 0.6 at x 1 /d ≈ 3 to around 0.7 at x 1 /d ≈ 8 others find the mean velocity to be over 20% higher. It is unlikely that these differences are solely due to wind tunnel blockage and free-stream turbulence.…”

“…Although Lee & Kim (2001b) did not measure sufficiently downstream, their results seem to agree with the present DNS and that of Trias et al (2015) in a slower decrease of u ′ 2 /U ∞ with x 1 /d in comparison to Durão et al (1988) and Lyn et al (1995). with x 1 /d, while the present DNS at Re = 3900 shows the same profile of u ′ 3 /U ∞ as in Trias et al (2015) whose results refer to Re = 22000. In the DNS, the peak of u ′ 3 /U ∞ on the centreline appears to be at the same location as the mean stagnation point (where…”

“…In fact, the distance from the prism to the location of the peak of u ′ 2 /U ∞ is used to define the vortex formation length. Both the present results and those of Trias et al (2015) show a vortex formation length extending to x 1 /d ≈ 1.5, while the experiments of Durão et al (1988), Lyn et al (1995) and Lee & Kim (2001b) place this further downstream, at x 1 /d ≈ 1.9. Apart from the PIV results of Lee & Kim (2001b), the peak value of u ′ 2 /U ∞ is reported to be close to 0.9 both in the present results and Lyn et al (1995) and Trias et al (2015) and just over 0.8 in Durão et al (1988).…”

“…It is unlikely that these differences are solely due to wind tunnel blockage and free-stream turbulence. Lyn et al (1995), Lee & Kim (2001b) and Arslan et al (2012) reported a blockage of 7% but Hu et al (2006) and Trias et al (2015) report a blockage of about 2% even though there are differences in their results. The free-stream turbulence on the other hand appears to have a more significant effect on U 1 /U ∞ in the experiment of Durão et al (1988) who report 6% free-stream turbulence; this explains the differences observed in the incoming profiles.…”