This test enures that the inertia loads calculated by the Morison equation match those published by Suja-Thauvin (2019a)

## 1 Test description

This test uses a monopile in regular waves. To check that the inertia loads are calculated correctly, we compare the total inertia force applied on the monopile to the analytical solution published by Suja-Thauvin (2019a). In this publication, the analytical solution for the inertia load of the Morison equation with linear regular waves in finite water depth is presented.

## 2 Model

This test uses the Support structure - offshore monopile template
The CSV file to run this test can be downloaded from here.
The monopile has a constant diamater of
$$D = 5.78\text{ m}$$
and at a depth
$$d = 27\text{ m}$$
. The water density is taken equal to
$$\rho = 1000\text{ kg}\cdot\text{m}^{-3}$$
and the inertia coefficient is
$$C_M = 1.8$$
.
Two regular wave conditions are modelled:
• H = 5 m, T = 7 s
• H = 10 m, T = 12 s
For each regular wave, the simulation is run four times, with the following parameters:
• Loads only: the simulation does not take Newton's second law into account, therefore the structure will not be affected by the hydrodynamic loads
• Fixed: the loads are computed based on the initial position of the monopile
• Partly: the loads are computed based on the position of the monopile at the beginning of the time step
• Moving: the loads are computed based on the position of the monopile updated during the time step
For bottom fixed wind turbines, it is expected that all these options will produce very similar results. For more details see the Hydrodynamics document.

## 3 Benchmarked solution

From Suja-Thauvin (2019a) the amplitudes of the inertia loads for both wave conditions are given:
• for the H = 5 m, T = 7 s case, a load amplitue of 1.134 MN is expected
• for the H = 10, T = 12 s case, a load amplitude of 1.759 MN is expected
The results from Ashes are compared to a sinusoidal load with the corresponding period and amplitude. Since Ashes outputs the magnitude of the force, the absolute value of the sinusoid is taken.

## 4 Results

A simulation of 30 seconds is run for each case. The results are considered passed if the results from Ashes are within 2% of the expected solution.

The report for this test can be found on the following link: