Modeling a kayak paddle stroke using a Body force Method

Joe Banks, Dr Alex Phillips and Prof. Stephen Turnock6th OpenFOAM Workshop, Penn State

Why simulate a paddle stroke?

• Calculate forces generated by a Paddle.

• Simulate interactions between paddle blade and hull.

• Understand the dynamic forces acting on a kayak.

• Optimise hull and blade design for dynamic race conditions.

2

Why use a body force model?• Self propelled kayak is a complex problem:

• Moving geometries & free surface

• A body force propulsion model simulates the impact of the paddle blade by inducing accelerations in the fluid.

– Removes the need for dynamic mesh.

3

– Reduces cell count and allows for increased time-step as resolution of blade geometry not required.

• Similar method previously used for modelling a ship’s propeller [1].

[1] A.B. Phillips, M.E. Furlong and S.R. Turnock, Accurate capture of rudder-propeller interaction using a coupled blade element momentum-RANS approach. Ship Technology Research (Schiffstechnik), Vol 57, pp 128-139. (2010).

Simple Paddle stroke model

• Angular velocity:

• Advance velocity:

• Radius: r

• Normal velocity on the blade is:

• Therefore the force at a given radius is:

4

Calculating Momentum sources

• Divide stroke path into sectors

• Determine total volume of cells within each sector

5

• When the blade passes through a sector the blade force is calculated at its centre

• The momentum source term for each cell within that sector is: Fn/SectorVolume

• This volume vector field is then added to the Uegn.H in interFoam

Experimental data for Paddle stroke

6

• Student project performed towing tank tests on a paddle

• Dynamic Swing test applied a constant torque via a dropping weight

• Blade angle and Horizontal forces (Thrust & Side force) measured using towing Tank Dynamometer

• Various angles of attack

Experimental data for Paddle stroke

7

Comparing simple blade model to experimental data

8

Simulating the Paddle within OpenFOAM

• Blade modelled as a flat plate:

• Length = 0.54 m, Breadth = 0.2 m

• Drag coefficient = 1.2

• Centre of rotation placed on the surface of the water

• Stroke path divided into 18 angular and 8 radial divisions

9

• 740 cells out of 40,000 within sectors

• Angular velocity constant throughout the stroke

Thrust generated at a constant RPM

10

Thrust generated for varying RPM

11

Improvements needed for paddle model

• Unsteady effects:

• Added mass due to acceleration

• Changes in thrust due to Vortex generation

12

• Affects of radial flow on the blade

• In the meantime increase drag coefficient to match experimental data

Thrust generated for modified Cd

13

Simulating a self-propelled kayak

14

Naked hull resistance• Advance speed = 2m/s

• L=4m, B=0.6m, D=0.25m

15

Property MeshType of mesh Unstructured (Hexahedral)

No. of elements Approximately 1.2M

y+ on the hull 10-15

Domain PhysicsHomogeneous Water/Air

multiphase, kOmegaSST turbulence model, Automatic wall function

Boundary physics:Inlet Free stream velocity

Outlet Zero gradient

Bottom/side wall Wall with free stream velocity

Top OpeningHull Wall with no slip condition

Solver settings:Transient scheme 1st order EulerGrad (U) Scheme Gauss linear

Div (U) Gauss limitedLinearV 1Pressure coupling PISO

Convergence criteriaP 1e-7, U 1e-6, k 1e-8, omega 1e-8

Multiphase control Volume fraction couplingTimestep control max Courant No = 0.4

Processing Parameters:

Computing System

Iridis 3 Linux Cluster (University of Southampton)

Run typeParallel (9 - 24 Partitions run on 5x8 core nodes each with 23 Gb RAM)

Bow Stern

Naked hull resistance 22.68 N

16

Determine Required Stroke Rate

17

• Vary angular velocity throughout stroke to approximate a constant Torque Condition.

• Average thrust over half a stroke cycle =22.60 N

Self Propelled Simulation

• Continued run from naked hull case

• Applied two paddle models, one on each side but out of phase, with their centre of rotation 0.5 m from hull centre line.

• Naked hull resistance = 22.68 N

• Average Thrust over = 22.60 N

18

Paddle Induced Velocities 0.5m from hull

19

Pressure on hull during Left paddle stroke

20

Forces acting on the hull during paddle strokes

21

Right (+) Left (-) Left (-)Right (+)

Average self Propelled resistance = 21.5 (N)

Moments acting on the hull during paddle strokes

22

Right (+) Right (+)Left (-) Left (-)

Conclusion

• A simple methodology has been developed for investigating the paddle and hull interaction in kayaking.

• To allow more realistic stroke techniques to be modelled a more sophisticated paddle model needs to be developed including:

• Unsteady 3D effects on force coefficients,

• Lift and drag forces for varying angles of attack,

• Generic stroke paths allowing translation and rotation

23

Thank you for listening?

Are there any questions?

24