Laminarising Turbulence by Minimising Transient Growth

  • Chu, Shijun (University of Sheffield)
  • Willis, Ashley (University of Sheffield)
  • Marensi, Elena (University of Sheffield)

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Turbulent friction drag is an important factor limiting the performance of many fluids engineering systems, which has led to extensive research for both active and passive methods for drag reduction. Kuhnen et al., found that a flattened base profile can make the turbulence decay, and attributed this to reduced transient growth. Transient growth, related to the non-orthogonality of normal modes, is thought to be essential for sustaining turbulence for linear stable flow. Motivated by these points, this paper adopted the recent development of variational methods to design the optimal base flow by minising transient growth, to eliminate turbulence at Re=2400 and Re=3000. The body force is then calculated corresponded to the modified optimal base flow and introduced to transient turbulence. 30 arbitrary turbulent initial conditions are used to check the robustness of the body force. The flattened base profile which can laminarise turbulence is firstly reproduced theoretically by reducing optimal transient growth in m=1 at Re=2400. A quite promising net-power saving (about %33) is obtained, while the most net-power saving of the body force constructed by Song can achieve is about %32. Further attempt to eliminate turbulence at Re=3000 failed when optimisation reduces transient growth of only the first azimuthal wave number. It is found that the base flow constructed by Song, which is proved to be efficient for laminarising turbulence, reduces the transient growth of all low azimuthal wave numbers. Inspired by this point, it is realized that the streaks of higher wave number (m>1) may be still active enough to sustain turbulence. Thus, the key point to eliminate turbulence is making sure that all active streaks cannot be sustained. The variational method is adopted again to design the base flow, with a new objective functional constructed to achieve reducing the transient growth of each active wave number. The results show that the body force calculated according to the optimal base flow can effectively laminarise turbulence at Re=3000. Also, a little higher net-power saving (about %28) can be obtained, compared with the body force designed by Song(about %27). Although the net-power saving of our body force does not improve a lot, the significant outcomes are the theoretical method we used to construct the base profile and the deeper understanding to the sustaining mechanism of turbulence.