TestChain.jl

Based on the works of Uwe Fechner Tethers.jl. In addition to this monolithic model, a segmented chain model is introduced.

All simulations are implemented in Julia programming language using

• ModelingToolkit.jl and
• Modia.jl

Modeling assumption for the chain:

• Chain was divided into segments with the same length and mass
• No rotational friction between segments
• Total length of teh chain remains unchanged (no, reel in/out)

Modeling assumption for a segment:

• strian due to forces with a defined stiffness and damping
• segment has only one mass and no inertia
• on the connection points only forces are considered - no torques are applied on the segment
• no friction due to movement in the air

Modeling approach

The models are reduced to make it easier to compare the results. At the beginning, a very simple approach was used (level 0). In the future, the restrictions will be removed step by step.

level	comment
level 0	a simplified model - see description above
level 1	air friction considered coming soon
level 2	??

Testcase - level 0

For testing the various models, the original parameter settings were used with a few changes.

@with_kw mutable struct Settings3 @deftype Float64
    g_earth::Vector{Float64} = [0.0, 0.0, -9.81] # gravitational acceleration     [m/s²]
    v_wind_tether::Vector{Float64} = [2, 0.0, 0.0]
    rho = 1.225
    cd_tether = 0.958
    l0 = 50                                      # initial tether length             [m]
    v_ro = 2                                     # reel-out speed                  [m/s]
    d_tether = 4                                 # tether diameter                  [mm]
    rho_tether = 724                             # density of Dyneema            [kg/m³]
    c_spring = 614600                            # unit spring constant              [N]
    rel_compression_stiffness = 0.01             # relative compression stiffness    [-]
    damping = 473                                # unit damping constant            [Ns]
    segments::Int64 = 5                          # number of tether segments         [-]
    α0 = π/10                                    # initial tether angle            [rad]
    duration = 10                                # duration of the simulation        [s]
    save::Bool = false                           # save png files in folder video
end

modification

se = Settings3(; segments=5,v_ro=0.0, v_wind_tether=[0.00,0.0,0.01], rho=0.0)

Modeling

The following 3 models are considered

• Tether_07mod0.jl - the original (monolithic) version using MTK ecosystem
• SegMTKLev0.jl - acausal model with connected segments using MTK ecosystem
• SegModiaLev0.jl - acausal model with connected segments using Modia ecosystem

All the simulation are producing a HDF5 file with the position of all the nodes in the defined time range.

Comparison of results

For comparison all the results are shown in a diagram (only the position of the last segment).

Appendix

Installation modeling environment

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

It's recommended to use the latest versions from Modia

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