On the influence of computational domain length on turbulence in oscillatory pipe flow

We present results from direct numerical simulations (DNS) of oscillatory pipe flow at two different Womersley numbers (Wo ∈ {13, 26}) using a fully developed turbulent flow field as initial condition and different lengths of the computational pipe domain. By comparing high-frequency velocity signals and instantaneous flow fields for Wo=13, we found that the flow was conditionally turbulent for shorter pipe domains, while the flow completely laminarised in longer computational domains. This unforeseen observation is discussed in more detail by comparing spatial energy spectra, turbulence statistics and integral quantities calculated from the respective flow fields at different oscillation phases. We conclude that the critical maximum pipe length to maintain a conditionally turbulent flow lies within 3.54D < L < 5D for this special scenario characterised by Wo=13 and Re=11500. Interestingly, the occurring wall shear stress is slightly lower and the peak flow rate is slightly higher when the flow field is turbulent compared to the laminar scenario for the same set of control parameters. For Wo=26 we did not find such a critical domain length. The resulting flow field appears to be conditionally turbulent for L=1.25D and L=5D. Comparing two-point correlations for both Wo reveals a growing and shrinking behaviour of turbulent structures in the velocity field over the different phases of the oscillation cycle and how this mechanism is affected by the finite size of the periodic pipe domain. Further, this DNS study provides the important results that, first, the Floquet linear stability analysis of Thomas et al. (2012) is corroborated and second, that a minimum pipe length must be employed for DNS of oscillating pipe flow in the subcritical regime, otherwise there is questionable prediction of sustained turbulence.