TestTether.jl

Testing different approaches for tether chain models.

The following 4 models are considered

• Tether_07A.jl - the original (monolithic) version using MTK ecosystem - only the calculation of cross-section was corrected.
• Tether_07B.jl - a modified version (see PR)
• T7modia.jl - a Modia3D implementation - only for verification
• Tether_08.jl - an element based model - including friction in air and the impact of wind

Installation

It's assumed that the ModelingToolkit ecosystem is already installed.

It's recommended to use the latest versions from Modia and Modia3D

using Pkg
Pkg.add("https://github.com/ModiaSim/Modia.jl.git")
Pkg.add("https://github.com/ModiaSim/Modia3D.jl.git")
Pkg.add("Plots")
Pkg.add("JLD2")

Models

Do make it easier to compare, the original model was simplified.

The reel-out speed was set to zero. v_ro = 0.0 # reel-out speed [m/s], so the model was reduced to a multi-element pendulum. All other parameters remain unchanged. The results of the simulation (position of the last particle) is stored in a JLD2 structure for post-processing.

Tether_07A.jl

The original model with modified cross-section calculation.

This code (line #76) seems not to be correct. acc = force / mass

eqs2 = vcat(eqs2, acc[:, i+1] .~ se.g_earth + total_force[:, i] / 0.5*(m_tether_particle))

Tether_07B.jl

The modified model (see PR) with the assumption that the mass of the segment is located at the end. Elongation was considered in the model.

T7modia.jl

For this model the same approach was used.

Main difference to the MTK implementation:

• Elongation is ignored
• Revolution damping was considered

Tether_08.jl

Similar to Tether_07B.jl, but with an element-based approach. A model was created for a segment, and finally the segments are connected with a tether. The boundary conditions at the end of the tether can be defined.

Air friction of the moving segments was taken into account. The forces acting on the tether due to wind can also be investigated with this model.

performed Tests

For all 4 models tests procedures are defined. The position of the last segment is stored in a JLD2 structure.

model name	test routine	result HDF5
Tether_07A.jl	runTest7A.jl	T7A.hdf5
Tether_07B.jl	runTest7B.jl	T7B.hdf5
T7modia.jl	runT7modia.jl	T7modia.hdf5
Tether_08.jl	runTest8.jl	T8seg.hdf5

Running compareResults.jl: the results of the performed simulation can be shown in diagrams

julia> include("compareResults.jl")
[press: Enter=toggle, a=all, n=none, d=done, q=abort]
→ ⬚ T7A.hdf5
  ⬚ T7B.hdf5
  ⬚ T7modia.hdf5
  ⬚ T8seg.hdf5

comparison: Tether_07A.jl - Tether_07B.jl

The original implementation was compared with the modified MTK model. Result are shown below.

comparison: Tether_07B.jl - T7modia.jl

The modified MTK model was compared with a Modia3D implementation. Result are shown below. The results are more or less identical.

comparison: Tether_07B.jl - Tether_08.jl

Comparison of the monolithic model Tether_07B.jl with the element based model Tether_08.jl. The results are identical.

Discussion

rotational damping

Implementing rotational damping in MTK seems to be very difficult. To obtain correct results, torques and inertia of the masses must be taken into account. A correct implementation can be found in Modia3D.

Taking into account the air friction of the tether leads to more realistic results. The parameters used in the first draft of Tether_08.jl should be reviewed.

TODO's

initialization

Should be improved.

roll-in roll-out

Variation of length of a segment results in changing of the mass of the element.

Basically:

force  = der(impulse)
impulse = mass x speed
force = mass x der(speed) + speed x der(mass)

The impact of the additional dynamic force due to changing of the length of the tether should be studied.