Fig 1.
Visualization of hydrodynamic effects of seal whisker geometry.
Isosurfaces of nondimensional Q-criterion value 0.4, colored by positive (red) and negative (blue) z-vorticity. Flow over a smooth ellipse (top) compared with the flow over the seal whisker model (bottom) reveal distinctly different flow structures and hydrodynamic responses as a result of the undulations.
Fig 2.
Geometric parameters of the baseline model as originally defined by Hanke et al. [2] create two coordinating sets of spanwise undulations along the z-axis. The seal whisker model is created from two different sized ellipses a distance M apart, major radii a and k, minor radii b and l, inclined at incident angles α and β with respect to the x-axis. Nominal values for harbor seal whiskers are M = 0.91 mm, a = 0.595 mm, b = 0.240 mm, k = 0.475 mm, l = 0.290 mm, α = 15.27 degrees, and β = 17.60 degrees [2].
Fig 3.
Schematic of baseline whisker model.
Schematic shows the hydrodynamic-based geometric parameters that define the undulation features as described in Table 1. Top view (top panel) and front view (bottom panel), where flow is along the positive x-axis.
Table 1.
Description of geometric parameters.
Table 2.
Low and high geometric parameter values.
Fig 4.
Figure shows mesh used for simulation of baseline model using LES at (equivalent to ReT = 500). Mesh details are listed in Table 4.
Table 3.
Comparison of mesh variations with previous literature.
Fig 5.
Contours of time-averaged streamwise velocity.
Comparison of LES model with fully resolved DNS at (equivalent to ReT = 500). Contours of time-averaged streamwise velocity are shown at peak and trough cross-sections of the baseline model. (a) LES peak cross-section. (b) DNS peak cross-section. (c) LES trough cross-section. (d) DNS trough cross-section.
Table 4.
Mesh variation by geometry class.
Fig 6.
Three Pareto charts summarize the effects of modifications to geometric parameters on each of the response variables. Gray shaded regions indicate a positive correlation and the red shaded regions indicate a negative correlation. γ, AC, AT, and λ are seen to have the largest effects. (a) Response (b) CL,RMS Response (c) St Response.
Table 5.
Measured response variables by model and geometric variation.
Fig 7.
Geometry of models with low and high AT values.
Directly comparing a low AT and high AT model with three views: top view in the x-z plane, front view in the y-z plane, and side view in the x-y plane. Flow is along the positive x-axis. (a) EL1 (low AT). (b) EL2 (high AT).
Fig 8.
Flow comparison between low and high AT geometries.
EL1 (low AT) in the left column, EL2 (high AT) in the right column. (a) The comparison of time-averaged streamwise velocity contours for low AT (left) and high AT (right) models shows considerable variation between recirculation length at peak and trough cross sections. Contours are shown at equally spaced spanwise locations where peak and trough correspond to AT undulations. (b) Velocity streamlines at peak and trough spanwise locations denoted in 8a demonstrate more spanwise transport for the high AT model. (c) Isosurfaces of nondimensional Q-criterion value 0.8, colored by positive (red) and negative (blue) z-vorticity. Isosurfaces display long, coherent structures at low AT and breakup at high AT.
Fig 9.
CL spectra for low and high AT geometries.
The CL spectra for EL1 (low AT) and EL2 (high AT) geometries shown in Fig 7 are directly compared with a smooth elliptical cylinder. The EL1 frequency spectrum shows a spectra more similar to the cylindrical case while the EL2 response is smaller in magnitude with a peak at lower frequency.
Fig 10.
Geometry of models with low and high AC values.
Directly comparing a low AC and high AC model with three views in the same configuration as Fig 7. (a) CL2 (low AC). (b) CL4 (high AC).
Fig 11.
Flow comparison between low and high AC geometries.
CL2 (low AC) in the left column, CL4 (high AC) in the right column. (a) The comparison of time-averaged streamwise velocity contours for low AC (left) and high AC (right) models shows a relative similarity between the two models. Contours are shown at equally spaced spanwise locations where peak and trough correspond to AT undulations. (b) Velocity streamlines at peak and trough spanwise locations denoted in 11a demonstrate the similarity in the streamwise flow component and a modest increase in spanwise flow for the high AC model. (c) Isosurfaces of nondimensional Q-criterion value 1.6, colored by positive (red) and negative (blue) z-vorticity. Isosurfaces display a noticeable break towards the center of the high AC model.
Fig 12.
CL spectra for low and high AC geometries.
The CL spectra for the CL2 (low AC) and CL4 (high AC) geometries shown in Fig 10 are directly compared with a smooth circular cylinder. A gradual decrease in St occurs as AC increases.
Fig 13.
Flow structure comparison among various λ geometries.
Isosurfaces of Q-criterion colored by positive (red) and negative (blue) spanwise vorticity show a larger wavelength allows for break up of flow structures while flow structures from low λ models continue to resemble those of their smooth cylindrical counterparts. (a) Circular geometries (low γ); nondimensional Q-criterion value 1.6. From left to right: no undulations, CS2 (low λ), CL2 (high λ). (b) Elliptical geometries (high γ); nondimensional Q-criterion value 0.8. From left to right: no undulations, ES2 (low λ), EL2 (high λ).
Fig 14.
Frequency spectra for low and high λ geometries.
The frequency spectra for low and high values of λ and γ are compared with the smooth cylinder cases showing St similarity between low λ and smooth models. (a) Circular aspect ratio. (b) Elliptical aspect ratio.
Fig 15.
Flow visualization for high ϕ and ϵ geometry.
Flow visualization reveals disjointed vortex structures and a preferential direction for the spanwise velocity. (a) EL4 (high ϵ and high ϕ): top view in the x-z plane, front view in the y-z plane, and side view in the x-y plane. (b) Velocity streamlines at equally spaced spanwise locations as described in Fig 11. (c) Isosurfaces of nondimensional Q-criterion value 0.8, colored by positive (red) and negative (blue) z-vorticity. (d) Mean spanwise velocity in x-z plane.