The flow structure in the lee of an inclined 6:1 prolate spheroid

Abstract

Particle displacement velocimetry is used to measure the velocity and vorticity distributions around an inclined 6: 1 prolate spheroid. The objective is to determine the effects of boundary-layer tripping, incidence angle, and Reynolds number on the flow structure. The vorticity distributions are also used for computing the lateral forces and rolling moments that occur when the flow is asymmetric. The computed forces agree with results of direct measurements. It is shown that when the flow is not tripped, separation causes the formation of a pair of vortex sheets. The size of these sheets increases with increasing incidence angle and axial location. Their orientation and internal vorticity distribution also depend on incidence. Rollup into distinct vortices occurs in some cases, and the primary vortex contains between 20 % and 50 % of the overall circulation. The entire flow is unsteady and there are considerable variations in the instantaneous vorticity distributions. The remainder of the lee side, excluding these vortex sheets, remains almost vorticity free, providing clear evidence that the flow can be characterized as open separation. Boundary-layer tripping causes earlier separation on part of the model, brings the primary vortex closer to the body, and spreads the vorticity over a larger region. The increased variability in the vorticity distribution causes considerable force fluctuations, but the mean loads remain unchanged. Trends with increasing Reynolds number are conflicting, probably because of boundary-layer transition. The separation point moves towards the leeward meridian and the normal force decreases when the Reynolds number is increased from 0.42 × 106 to 1.3 × 106. Further increase in the Reynolds number to 2.1 × 106 and tripping cause an increase in forces and earlier separation.

Asymmetries in the wake of a submarine model in pitch

“…A primary pair of streamwise counterrotating vortices are seen to form on the leeward side of the model. Similar flow fields have been observed over a wide range of Reynolds numbers by, for example, Han & Patel (1979) for a 4.3:1 spheroid and Vatsa, Thomas & Wedan (1989), Fu, Shekarriz & Huang (1994), Chesnakas & Simpson (1997), Karlsson & Fureby (2009) and Feymark et al (2012) for a 6:1 prolate spheroid. Werlé (1962), Hornung & Perry (1984) and Bippes (1987) described the separation topologies over similar bodies at low and moderate angles of attack, but here we are concerned with the evolution of the streamwise counter-rotating vortices which comprise the turbulent wake of such bodies in pitch.…”

“…These elements were placed at different azimuthal (100 • < θ < 170 • ) and axial locations (0.2 < x/L < 0.4), upstream of the separation point, which is in the range 0.6 < x/L < 0.7, as reported by Fu et al (1994). The buttons were placed on the left and right sides of the body in symmetric and asymmetric configurations, as listed in table 2; for example, x/L = 0.2(l) and x/L = 0.4(r) correspond respectively to an array of roughness elements at x/L = 0.2 on the left side and one at x/L = 0.4 on the right side, which is the configuration shown in figure 12.…”

A Fourier-Chebyshev spectral collocation method for simulating flow past spheres and spheroids

“…Note that since the grid spacing in the p-direction is significantly larger near the body than in the other two directions, the viscous terms in this direction can be treated explicitly and this leads to a simpler operator on the left side of Equation (9). In fact, when the above equation is transformed in the -direction, we obtain a set of one-dimensional Helmholtz equations, which can be solved quite easily using the matrix diagonalization technique [31].…”

“…In fact, the bulk of our knowledge about three-dimensional separated wake flows rests on surface oil flow patterns [4] and dye visualization [5][6][7][8]. Advances in experimental techniques have, however, allowed researchers to obtain more quantitative information and recently detailed measurements of the wake of spheroids have been made [9,10].…”

Towing PIV and its application on the juncture forms of stern appendage with main-body

“…The world's first stationary PIV system was built in the 140-fl towing basin at the DTRC1 at the era of 90's , which has been used to measure flow separation and vortex structure around submarine-like bodies11, and to investigate the flow structure in the lee side of a spheroid ( 6: 1 prolate) [2] and also to investigat the structure of bow waves on a ship model [3j•…”