Abstract
An experimental study was conducted on the wakes around three different obstacles confined between two parallel walls: semi-ellipsoids with the major axes of the base ellipses aligned in the streamwise and transverse directions, and a sphere. The Reynolds number was \(1.78 \times 10^4\) based on obstacle height, H. Common to each of these geometries is a convex surface of the obstacle intersecting one or more boundaries, which was shown to result in a wall jet in the vicinity of the junction. Large streamwise counter-rotating vortex structures were found to be a robust feature of the wakes, which are referred to as lobes, due to their resemblance to previously coined lobe structures identified in the wake of a deeply submerged sphere. Inner lobe structures, of opposite sense to the primary lobes, were also observed in all cases, and it is proposed that the primary and inner lobe structures are formed by the wall jet deforming vorticity shed by the obstacle into a hairpin-like loop. Wavelet analysis of velocity time series on both sides of the wake revealed approximately antisymmetric vortex shedding in the ellipsoid wakes; however, intermittent in-phase shedding was observed in the wake of the sphere. This study showed that the shape of the obstacle junction (convex vs. flat) plays an important role in the behavior of the wake.
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Some or all data, models or code that support the findings of this study are available from the corresponding author upon reasonable request.
Abbreviations
- f :
-
Frequency of velocity fluctuations in the wake, Hz
- H :
-
Obstacle height, mm
- D :
-
Maximum transverse dimension, mm
- AR:
-
Aspect ratio, \(\text{AR} = H/D\)
- \(U_{\infty }\) :
-
Free-stream velocity, m/s
- d :
-
Flow depth, mm
- RS:
-
Relative submergence, the ratio of flow depth to obstacle height
- x, y, z :
-
streamwise, transverse and spanwise (vertical) directions
- \(\omega\) :
-
Vorticity, s−1
- \(\omega ^*\) :
-
Dimensionless vorticity, \(\omega ^*= \omega D / U_{\infty }\)
- \(\Gamma\) :
-
Circulation, mm2/s
- \(\Gamma ^*\) :
-
Dimensionless circulation, \(\Gamma ^* = \Gamma /(U_{\infty }D)\)
- \(\text{Re}_H\) :
-
Reynolds number, \(\text{Re}_H = \frac{U_{\infty } H}{\nu }\)
- \(\nu\) :
-
Kinematic viscosity, m2/s
- \(f^*\) :
-
Dimensionless frequency, \(f^*=f D/U_{\infty }\)
- \(f_{0}\) :
-
Dominant frequency
- St:
-
Strouhal number, \(St = f_{0} D/U_{\infty }\)
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This work was supported by the United States National Science Foundation under award number CBET-1033732.
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Hajimirzaie, S.M., Buchholz, J.H.J. Flow patterns around confined low-aspect-ratio obstacles. Exp Fluids 64, 139 (2023). https://doi.org/10.1007/s00348-023-03675-y
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DOI: https://doi.org/10.1007/s00348-023-03675-y