scholarly journals The aerodynamics of jumping rope

2011 ◽  
Vol 468 (2139) ◽  
pp. 720-730 ◽  
Author(s):  
Jeffrey M. Aristoff ◽  
Howard A. Stone
Keyword(s):  
Shape Change ◽  
Nonlinear Differential Equations ◽  
Reynolds Numbers ◽  
Relative Magnitude ◽  
Relative Reduction ◽  
Centrifugal Forces ◽  
Dimensionless Groups ◽  
Out Of Plane ◽  
High Reynolds ◽  
Jump Rope

We consider the influence of aerodynamic forces on the shape of a whirling filament that is held at both ends, i.e. a jump rope. At high Reynolds numbers, the rope curls out of the plane and towards the axis of rotation—a feature we demonstrate via experiment. We derive a pair of coupled nonlinear differential equations that characterize the steady-state shape of the rope, and the resulting eigenvalue problem is solved numerically. The solution depends on two dimensionless groups: the ratio between the length of the rope and the distance between its ends, and the relative magnitude of the aerodynamic to centrifugal forces. As the latter ratio is progressively increased, the tension in the rope and the out-of-plane deflection increases, until eventually the rope reaches a limiting shape. Finally, we show that the airflow-induced shape change leads to a relative reduction in drag and has implications for successful skipping.

Low Reynolds number k—ε modelling with the aid of direct simulation data

1993 ◽  
Vol 250 ◽  
pp. 509-529 ◽  
Author(s):  
W. Rodi ◽  
N. N. Mansour
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Eddy Viscosity ◽  
Reynolds Numbers ◽  
Relative Magnitude ◽  
Direct Simulation ◽  
Simulation Data ◽  
Layer Flow ◽  
High Reynolds ◽  
Improved Model

The constant Cμ and the near-wall damping function fμ in the eddy-viscosity relation of the k–ε model are evaluated from direct numerical simulation (DNS) data for developed channel and boundary-layer flow, each at two Reynolds numbers. Various existing fμ model functions are compared with the DNS data, and a new function is fitted to the high-Reynolds-number channel flow data. The ε-budget is computed for the fully developed channel flow. The relative magnitude of the terms in the ε-equation is analysed with the aid of scaling arguments, and the parameter governing this magnitude is established. Models for the sum of all source and sink terms in the ε-equation are tested against the DNS data, and an improved model is proposed.

TRANSONIC CROSS FLOW (M∞ = 0.8) OVER A CIRCULAR CYLINDER AT HIGH REYNOLDS NUMBERS

2012 ◽  
Vol 43 (5) ◽  
pp. 589-613
Author(s):  
Vyacheslav Antonovich Bashkin ◽  
Ivan Vladimirovich Egorov ◽  
Ivan Valeryevich Ezhov ◽  
Sergey Vladimirovich Utyuzhnikov
Keyword(s):  
Circular Cylinder ◽  
Cross Flow ◽  
Reynolds Numbers ◽  
High Reynolds Numbers ◽  
High Reynolds

Oscillatory control of separation at high Reynolds numbers

AIAA Journal ◽  
1999 ◽  
Vol 37 ◽  
pp. 1062-1071 ◽  
Author(s):  
A. Seifert ◽  
L. G. Pack
Keyword(s):  
Reynolds Numbers ◽  
High Reynolds Numbers ◽  
High Reynolds

Turbulent vortex breakdown at high Reynolds numbers

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 825-834
Author(s):  
F. Novak ◽  
T. Sarpkaya
Keyword(s):  
Vortex Breakdown ◽  
Reynolds Numbers ◽  
Turbulent Vortex ◽  
High Reynolds Numbers ◽  
High Reynolds

Drag Measurements on Long Thin Cylinders at Small Angles and High Reynolds Numbers

2004 ◽  
Author(s):  
William L. Keith ◽  
Kimberly M. Cipolla ◽  
David R. Hart ◽  
Deborah A. Furey
Keyword(s):  
Reynolds Numbers ◽  
High Reynolds Numbers ◽  
High Reynolds

An Experimental and Numerical Study of Heat Transfer and Pressure Loss in a Rectangular Channel With V-Shaped Ribs

2006 ◽  
Author(s):  
Michael Maurer ◽  
Jens von Wolfersdorf ◽  
Michael Gritsch
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Enhancement ◽  
Thermal Performance ◽  
Pressure Loss ◽  
Numerical Study ◽  
Rectangular Channel ◽  
Reynolds Numbers ◽  
Transfer Enhancement ◽  
High Reynolds Numbers ◽  
High Reynolds

An experimental and numerical study was conducted to determine the thermal performance of V-shaped ribs in a rectangular channel with an aspect ratio of 2:1. Local heat transfer coefficients were measured using the steady state thermochromic liquid crystal technique. Periodic pressure losses were obtained with pressure taps along the smooth channel sidewall. Reynolds numbers from 95,000 to 500,000 were investigated with V-shaped ribs located on one side or on both sides of the test channel. The rib height-to-hydraulic diameter ratios (e/Dh) were 0.0625 and 0.02, and the rib pitch-to-height ratio (P/e) was 10. In addition, all test cases were investigated numerically. The commercial software FLUENT™ was used with a two-layer k-ε turbulence model. Numerically and experimentally obtained data were compared. It was determined that the heat transfer enhancement based on the heat transfer of a smooth wall levels off for Reynolds numbers over 200,000. The introduction of a second ribbed sidewall slightly increased the heat transfer enhancement whereas the pressure penalty was approximately doubled. Diminishing the rib height at high Reynolds numbers had the disadvantage of a slightly decreased heat transfer enhancement, but benefits in a significantly reduced pressure loss. At high Reynolds numbers small-scale ribs in a one-sided ribbed channel were shown to have the best thermal performance.

scholarly journals Aerodynamics of smooth and rough square-section prisms at incidence in very high Reynolds-number cross-flows

2021 ◽  
Vol 62 (3) ◽  
Author(s):  
Nils Paul van Hinsberg
Keyword(s):  
Reynolds Number ◽  
Cross Sections ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Surface Boundary ◽  
Experimental Proof ◽  
Surface Boundary Layer ◽  
Pitch Moment ◽  
The Mean ◽  
High Reynolds

Abstract The aerodynamics of smooth and slightly rough prisms with square cross-sections and sharp edges is investigated through wind tunnel experiments. Mean and fluctuating forces, the mean pitch moment, Strouhal numbers, the mean surface pressures and the mean wake profiles in the mid-span cross-section of the prism are recorded simultaneously for Reynolds numbers between 1$$\times$$ × 10$$^{5}$$ 5 $$\le$$ ≤ Re$$_{D}$$ D $$\le$$ ≤ 1$$\times$$ × 10$$^{7}$$ 7 . For the smooth prism with $$k_s$$ k s /D = 4$$\times$$ × 10$$^{-5}$$ - 5 , tests were performed at three angles of incidence, i.e. $$\alpha$$ α = 0$$^{\circ }$$ ∘ , −22.5$$^{\circ }$$ ∘ and −45$$^{\circ }$$ ∘ , whereas only both “symmetric” angles were studied for its slightly rough counterpart with $$k_s$$ k s /D = 1$$\times$$ × 10$$^{-3}$$ - 3 . First-time experimental proof is given that, within the accuracy of the data, no significant variation with Reynolds number occurs for all mean and fluctuating aerodynamic coefficients of smooth square prisms up to Reynolds numbers as high as $$\mathcal {O}$$ O (10$$^{7}$$ 7 ). This Reynolds-number independent behaviour applies to the Strouhal number and the wake profile as well. In contrast to what is known from square prisms with rounded edges and circular cylinders, an increase in surface roughness height by a factor 25 on the current sharp-edged square prism does not lead to any notable effects on the surface boundary layer and thus on the prism’s aerodynamics. For both prisms, distinct changes in the aerostatics between the various angles of incidence are seen to take place though. Graphic abstract

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