The influence of the Reynolds number on the natural transition of boundary layers over underwater axisymmetric bodies is studied using numerical approaches. This is a fundamental problem in fluid mechanics, and is of great significance in practical engineering problems. The transition locations are predicted over diameter Reynolds numbers ranging from 1.79×105 to 2.32×108 for eight different forebody shapes. The transition onsets are predicted using the semi-empirical eN method based on the linear stability theory (LST), and the wall pressure fluctuation spectra are estimated. The effects of the forebody shapes and the Reynolds numbers on the transition location are studied. At the same Reynolds number, the forebody shape has great influence on transition. As the Reynolds number increases, the changes in the dimensionless transition location are qualitatively similar for the different forebody shapes. The dimensionless transition location shifts closer to the leading edge as the Reynolds number increases, and is more sensitive at lower Reynolds numbers. However, the quantitative changes in transition location for different forebody shapes are distinctly different. Consequently, the sequential order of the transition locations for the eight forebody shapes is not fixed, but changes dramatically with increasing Reynolds number. This irregularity in the sequential order of the transition locations is called the "Reynolds number effect." Finally, the fundamental causes of this effect are analyzed.
The natural transitions of bow boundary layers over underwater axisymmetric bodies are investigated using numerical methods. The laminar flow fields over the underwater axisymmetric bodies are first calculated, and then the linear stability of the boundary layers is analyzed considering both the streamwise and circumferential curvatures of the wall. Based on the stability results, the eN method is employed to predict the transition locations. Numerical calculations are performed for seven forebody shapes under six oncoming flow velocities, allowing the influences of the forebody shapes and the oncoming flow velocities on the transition to be investigated. For the different forebody shapes, the boundary layer stability is generally the same behind the streamwise location of twice the forebody length, but varies within in the range of twice the forebody length. The transition locations are significantly different for the different forebody shapes. As the oncoming flow velocity increases, the dimensional unstable zone expands significantly, and the transition location moves upstream. The SUBOFF forebody shape proposed by Groves et al. [“Geometric characteristics of DARPA SUBOFF models (DTRC model numbers 5470 and 5471),” Report No. DTRC/SHD-1298-01 (David Taylor Research Center, West Bethesda, MD, 1989)] has a particularly late transition location and a large diameter close to the leading edge. This delayed transition location is caused by two separated unstable zones. Considering multiple factors, our analyses indicate that the SUBOFF forebody shape is quite valuable for practical engineering problems.
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