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Drag force on an accelerating submerged plate

  • E. J. Grift (a1), N. B. Vijayaragavan (a1), M. J. Tummers (a1) and J. Westerweel (a1)

Abstract

We present results on the drag on, and the flow field around, a submerged rectangular normal flat plate, which is uniformly accelerated to a constant target velocity along a straight path. The plate aspect ratio is chosen to be $AR=2$ to resemble an oar blade in (competitive) rowing, the sport which inspired this study. The plate depth, i.e. the distance from the top of the plate to the air–water interface, the plate acceleration and the plate target velocity are varied, resulting in a plate width based Reynolds number of $4\times 10^{4}\lesssim Re\lesssim 8\times 10^{4}$ . In our analysis we distinguish three phases; (i) the acceleration phase during which the plate drag is enhanced, (ii) the transition phase during which the plate drag decreases to a constant steady value upon which (iii) the steady phase is reached. The plate drag force is measured as function of time which showed that the steady-phase plate drag at a depth of $1/5$ plate height (20 mm depth for a plate height of 100 mm) increased by 45 % compared to the plate top at the surface (0 mm). Also, it is shown that the drag force during acceleration of the plate increases over time and is not captured by a single added mass coefficient for prolonged accelerations. Instead, an entrainment rate is defined that captures this behaviour. The formation of starting vortices and the wake development during the time of acceleration and transition towards a steady wake are studied using hydrogen bubble flow visualisations and particle image velocimetry. The formation time, as proposed by Gharib et al. (J. Fluid Mech., vol. 360, 1998, pp. 121–140), appears to be a universal time scale for the vortex formation during the transition phase.

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Copyright

This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

Corresponding author

Email address for correspondence: e.j.grift@tudelft.nl

References

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Adrian, R. J. & Westerweel, J. 2011 Particle Image Velocimetry. Cambridge University Press.
Barré, S. & Kobus, J. M. 2010 Comparison between common models of forces on oar blades and forces measured by towing tank tests. Proc. Inst. Mech. Engrs P 224 (1), 3750.
Bearman, P. W. 1971 An investigation of the forces on flat plates normal to a turbulent flow. J. Fluid Mech. 46 (1), 177198.
Bush, J. W. M. & Hu, D. L. 2006 Walking on water: biolocomotion at the interface. Annu. Rev. Fluid Mech. 38, 339369.
Caplan, N., Coppel, A. & Gardner, T. 2010 A review of propulsive mechanisms in rowing. Proc. Inst. Mech. Engrs P 224 (1), 18.
Caplan, N. & Gardner, T. N. 2007a A fluid dynamic investigation of the big blade and macon oar blade designs in rowing propulsion. J. Sports Sci. 25 (6), 643650.
Caplan, N. & Gardner, T. N. 2007b Optimization of oar blade design for improved performance in rowing. J. Sports Sci. 25 (13), 14711478.
Cohen, I. M. & Kundu, P. K. 2007 Fluid Mechanics. Academic.
Coppel, A., Gardner, T., Caplan, N. & Hargreaves, D. 2008 Numerical modelling of the flow around rowing oar blades (P71). In The Engineering of Sport 7, pp. 353361. Springer.
Coppel, A., Gardner, T. N., Caplan, N. & Hargreaves, D. M. 2010 Simulating the fluid dynamic behaviour of oar blades in competition rowing. Proc. Inst. Mech. Engrs P 224 (1), 2535.
Crowe, C. T., Schwarzkopf, J. D., Sommerfeld, M. & Tsuji, Y. 2011 Multiphase Flows with Droplets and Particles. CRC Press.
Dickinson, M. H. & Götz, K. G. 1993 Unsteady aerodynamic performance of model wings at low Reynolds numbers. J. Expl Biol. 174 (1), 4564.
Fage, A. & Johansen, F. C. 1927 On the flow of air behind an inclined flat plate of infinite span. Proc. R. Soc. Lond. A 116 (773), 170197.
Fernandez-Feria, R. & Alaminos-Quesada, J. 2018 Unsteady thrust, lift and moment of a two-dimensional flapping thin airfoil in the presence of leading-edge vortices: a first approximation from linear potential theory. J. Fluid Mech. 851, 344373.
Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121140.
Hemmati, A., Wood, D. H. & Martinuzzi, R. J. 2016 Effect of side-edge vortices and secondary induced flow on the wake of normal thin flat plates. Intl J. Heat Fluid Flow 61, 197212.
Hoerner, S. F. 1965 Fluid-dynamic Drag: Practical Information on Aerodynamic Drag and Hydrodynamic Resistance. Hoerner Fluid Dynamics.
Hsieh, S. T. 2003 Three-dimensional hindlimb kinematics of water running in the plumed basilisk lizard (Basiliscus plumifrons). J. Expl Biol. 206 (23), 43634377.
Jacobs, A. F. G. 1985 The normal-force coefficient of a thin closed fence. Boundary-Layer Meteorol. 32 (4), 329335.
Kim, H., Jeong, K. & Seo, T. 2017 Analysis and experiment on the steering control of a water-running robot using hydrodynamic forces. J. Bionic Engng 14 (1), 3446.
Koumoutsakos, P. & Shiels, D. 1996 Simulations of the viscous flow normal to an impulsively started and uniformly accelerated flat plate. J. Fluid Mech. 328, 177227.
Krasny, R. & Nitsche, M. 2002 The onset of chaos in vortex sheet flow. J. Fluid Mech. 454, 4769.
Leroyer, A., Barré, S., Kobus, J. M. & Visonneau, M. 2010 Influence of free surface, unsteadiness and viscous effects on oar blade hydrodynamic loads. J. Sports Sci. 28 (12), 12871298.
Lian, Q.-X. & Huang, Z. 1989 Starting flow and structures of the starting vortex behind bluff bodies with sharp edges. Exp. Fluids 8 (1–2), 95103.
Luchini, P. & Tognaccini, R. 2002 The start-up vortex issuing from a semi-infinite flat plate. J. Fluid Mech. 455, 175193.
Luff, J. D., Drouillard, T., Rompage, A. M., Linne, M. A. & Hertzberg, J. R. 1999 Experimental uncertainties associated with particle image velocimetry (PIV) based vorticity algorithms. Exp. Fluids 26 (1–2), 3654.
Matsuuchi, K., Miwa, T., Nomura, T., Sakakibara, J., Shintani, H. & Ungerechts, B. E. 2009 Unsteady flow field around a human hand and propulsive force in swimming. J. Biomech. 42 (1), 4247.
Meirovitch, L. 2001 Fundamentals of Vibrations. McGraw-Hill.
Patton, K. T.1965 An experimental investigation of hydrodynamic mass and mechanical impedances. MS Thesis, Univ. of Rhode Island.
Payne, P. R. 1981 The virtual mass of a rectangular flat plate of finite aspect ratio. Ocean Engng 8 (5), 541545.
Prandtl, L. 1904 Über flussigkeitsbewegung bei sehr kleiner reibung. In Verhandl. III, Internat. Math.-Kong., pp. 484491. Teubner.
Pullin, D. I. 1978 The large-scale structure of unsteady self-similar rolled-up vortex sheets. J. Fluid Mech. 88 (3), 401430.
Ringuette, M. J., Milano, M. & Gharib, M. 2007 Role of the tip vortex in the force generation of low-aspect-ratio normal flat plates. J. Fluid Mech. 581, 453468.
Robert, Y., Leroyer, A., Barré, S., Rongre, F., Queutey, P. & Visonneau, M. 2014 Fluid mechanics in rowing: the case of the flow around the blades. Proc. Engng 72, 744749.
Savitzky, A. & Golay, M. J. E. 1964 Smoothing and differentiation of data by simplified least squares procedures. Analyt. Chem. 36 (8), 16271639.
Schneider, K., Paget-Goy, M., Verga, A. & Farge, M. 2014 Numerical simulation of flows past flat plates using volume penalization. Comput. Appl. Maths 33 (2), 481495.
Schubauer, G. B. & Dryden, H. L.1937 The effect of turbulence on the drag of flat plates. NACA Annu. Rep. 22, pp. 129–133.
Sliasas, A. & Tullis, S. 2009 Numerical modelling of rowing blade hydrodynamics. Sports Engng 12 (1), 3140.
Tullis, S., Galipeau, C. & Morgoch, D. 2018 Detailed on-water measurements of blade forces and stroke efficiencies in sprint canoe. Proceedings 2 (6), 306.
West, G. S. & Apelt, C. J. 1982 The effects of tunnel blockage and aspect ratio on the mean flow past a circular cylinder with Reynolds numbers between 104 and 105. J. Fluid Mech. 114, 361377.
Williamson, C. H. K. 1996 Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28 (1), 477539.
Xu, L. & Nitsche, M. 2015 Start-up vortex flow past an accelerated flat plate. Phys. Fluids 27 (3), 033602.
Yu, Y. T. 1945 Virtual masses of rectangular plates and parallelepipeds in water. J. Appl. Phys. 16 (11), 724729.
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JFM classification

Type Description Title
VIDEO
Movies

Grift et al. supplementary movie 1
The hydrogen bubble flow visualisation is shown for the case of the fully submerged plate (h= 100 mm), at plate velocity V = 0.30 ms-1, and plate acceleration a = 0.82 ms-2. During the acceleration phase (t < 0.35 s) a vortex ring is formed that is stretched and shed during the transition phase (0.35 s < t < 3.4 s). The wake is fully developed after reaching the steady phase (t > 3.4 s).

 Video (9.5 MB)
9.5 MB
VIDEO
Movies

Grift et al. supplementary movie 2
The hydrogen bubble flow visualisation is shown for the case where the top of the plate coincides with the free surface (h = 0 mm) at plate velocity V = 0.30 ms-1, and plate acceleration a = 0.82 ms-2. During the acceleration phase (t < 0.35 s) a u-shaped vortex is formed that causes large surface depressions, which during the transition phase (0.35 s < t < 3.4 s) starts to lag behind the plate and is eventually shed. The shedding of the vortex is clearly visible through the flattening of the bottom of the surface depressions (t ≈ 0.7 s). The wake is fully developed after reaching the steady phase (t > 3.4 s).

 Video (9.6 MB)
9.6 MB
VIDEO
Movies

Grift et al. supplementary movie 3
The hydrogen bubble flow visualisation is shown for the case where the plate is submerged 1/5 plate height (h = 20 mm) at plate velocity V = 0.30 ms-1, and plate acceleration a= 0.82 ms-2. During the acceleration phase (t < 0.35 s) both a vortex ring and large surface depressions are observed; apparently a mixture of the flow phenomena seen in the visualisations of the cases h = 100 mm and h = 0 mm. During the transition phase (0.35 s < t < 3.4 s) the vortex ring quickly disintegrates after which a circulation region is formed in the top part of the wake of the plate, which remains present during the steady phase (t > 3.4 s) significantly increasing drag; see figure 4.

 Video (9.5 MB)
9.5 MB
VIDEO
Movies

Grift et al. supplementary movie 4
The vorticity ω*z is shown as function of time at plate velocity V = 0.30 ms-1, and plate acceleration a = 0.82 ms-2 for (a) h = 100 mm, (b) h = 0 mm, and (c) h = 20 mm, as discussed in section 3.9. The plate location x* is identical to t*. During the acceleration phase (t < 0.35 s) all wakes are similar. During the transition phase (0.35 s < t < 3.4 s) the wakes start to differ significantly. For h = 100 mm at t ≈ 2 s an `inward pinch-off’ is observed where two vortex cores touch and disintegrate. During the steady phase (t > 3.4 s) for the case of h = 100 mm the start of a characteristic oscillating tail is observed.

 Video (9.2 MB)
9.2 MB

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