Comparison of very-large-scale motions of turbulent pipe and boundary layer simulations

A direct numerical simulation of a fully developed turbulent pipe flow was performed to investigate the similarities and differences of very-large-scale motions (VLSMs) to those of turbulent boundary layer (TBL) flows. The Reynolds number was set to ReD = 35 000, and the computational domain was 30 pipe radii in length. Inspection of instantaneous fields, streamwise two-point correlations, and population trends of the momentum regions showed that the streamwise length of the structures in the pipe flow grew continuously beyond the log layer (y/?? 3??), and the maximum length of the VLSMs increased up to ~30??. Such differences between the TBL and pipe flows arose due to the entrainment of large plumes of the intermittent potential flow in the TBL, creating break-down of the streamwise coherence of the structures above the log layer with the strong swirling strength and Reynolds shear stress. The average streamwise length scale of the pipe flow was approximately 1.5-3.0 times larger than that of the TBL through the log and wake regions. The maximum contribution of the structures to the Reynolds shear stress was observed at approximately 6?? in length, whereas that of the TBL was at 1??-2??, indicating a higher contribution of the VLSMs to the Reynolds shear stress in the pipe flow than in the TBL flow.open1

Scale growth of structures in the turbulent boundary layer with a rod-roughened wall

Direct numerical simulation of a turbulent boundary layer over a rod-roughened wall is performed with a long streamwise domain to examine the streamwise-scale growth mechanism of streamwise velocity fluctuating structures in the presence of two-dimensional (2-D) surface roughness. An instantaneous analysis shows that there is a slightly larger population of long structures with a small helix angle (spanwise inclinations relative to streamwise) and a large spanwise width over the rough-wall compared to that over a smooth-wall. Further inspection of time-evolving instantaneous fields clearly exhibits that adjacent long structures combine to form a longer structure through a spanwise merging process over the rough-wall; moreover, spanwise merging for streamwise scale growth is expected to occur frequently over the rough-wall due to the large spanwise scales generated by the 2-D roughness. Finally, we examine the influence of a large width and a small helix angle of the structures over the rough-wall with regard to spatial two-point correlation. The results show that these factors can increase the streamwise coherence of the structures in a statistical sense.open

Direct numerical simulation of a 30R long turbulent pipe flow at Re=3008

A direct numerical simulation of a turbulent pipe flow at a high Reynolds number of Re-tau = 3008 over a long axial domain length (30R) was performed. The stream-wise mean velocity followed the power law in the overlap region (y(+) = 90-300; y/R = 0.03-0.1) based on the power law indicator function. The scale separation of the Reynolds shear stresses into two components of small-and large-scale motions (LSMs) revealed that the LSMs in the outer region played an important role in constructing the constant-stress layer and the mean velocity. In the pre-multiplied energy spectra of the streamwise velocity fluctuations, the bimodal distribution was observed at both short and long wavelengths. The k(x)(-1) region associated with the attached eddies appeared in lambda(x)/R = 2-5 and lambda(x)/y = 18-160 at y(+) = 90-300, where the power law was established in the same region. The k(z)(-1) region also appeared in lambda(z)/R = 0.3-0.6 at y(+) = 3 and 150. Linear growth of small-scale energy to large-scale energy induced the k(x)(-1) region at high Reynolds numbers, resulting in a large population of the LSMs. This result supported the origin of very-large-scale motions in the pseudo-streamwise alignment of the LSMs. In the pre-multiplied energy spectra of the Reynolds shear stress, the bimodal distribution was observed without the k(x)(-1) region.open