Phase averaged Turbulent statistics in drag reduced pipe flow at low and moderate Reynolds number with Transverse Wall Oscillations

Transverse wall oscillations is a drag reduction mechanism studied in this work. We investigate the turbulent statistics in a pipe flow with transversely oscillated walls as a function of the phase angle of the wall oscillations through Direct Numerical Simulation at two different Reynolds Numbers. At Re_τ = 340, a total drag reduction of 36% is achieved. At this Reynolds number, the Stokes solution to the Navier-Stokes equations matches perfectly with the mean azimuthal velocity up to the Stokes layer. The Reynolds shear stress exhibits a characteristic decrease all throughout the domain. Similarly, for the Re_τ = 720 case, 34% drag reduction is achieved and a Stokes solution matches reasonably well with the mean azimuthal velocity albeit with a larger deviation. Likewise with the Reynolds stresses, the mean shear stress exhibits a decrease. Phase averaging indicates that, phase to phase, the stress is always reduced compared to the non-oscillated pipe, a Stokes solution is a valid representation of the mean azimuthal velocity below the Stokes layer, and the streamwise fluctuations exhibit reduced peak rms values.