## hydrodinamics in cm scale

MOHID Water forum. Questions and discussion around MOHID Water
ruedabayona@gmail.com
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### hydrodinamics in cm scale

Dear mohid team,

I'm working on my Master research thesis, and I interested in modelling ocean currents in cm scale interacting with obstacles (piles, fixed structures). What is the minimum cm scale for modelling that? could you give me and advice for achieve good currents results in a 3d grid with 25 cm of spacing?

thank you

Juan Rueda

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### Re: hydrodinamics in cm scale

Dear Juan,

Depending on what exactly you're trying to simulate, you'll need good boundary conditions to provide to your 25 cm resolution model.

Regarding the piles/fixes structures:

Regarding obstacle drag coefficients, MOHID considers obstacles as pillars. Water flow when reaching a pillar is distorted around it, resulting in the reduction of the current velocity. This was included in the model, as an extra term in the equations, acting a negative force in the balance. As MOHID uses a semi-implicit algorithm, this negative term can be simulated implicitly, thus enabling numerical stability.

However, the simulation of each single pillar leads to the integration of a scale of centimetres that is unaffordable in terms of computational costs. Thus, the effect of the pillars had to be parameterized and included in the forces balance in the 3D primitive equations, by including a drag force (F) applied on the flow by influence of the pillars. This drag effect was adapted from Morison’s equation (Morison et al, 1950) for flow past a vertical cylinder, as described below.

Fi = 0.5 Cd * ρ * D * |u| * ui

Where Fi is the drag force (N/m) in the i direction per unit of length, Cd is the drag coefficient, ρ is the water density (kg/m3), D is the diameter of the pillar (m), |u| is the velocity modulus (m/s), ui is the velocity in the i direction.
Additionally, the effect of the pillars has to be adjusted to the grid resolution of the model, i.e. defining the pillars density per horizontal grid cell. Also, the effective drag force has to be integrated to the pillars’ length, which in practical terms, is achieved by integrating the drag force per unit of length over the size (in the vertical axis) of each grid cell.

Fd = n * INTEGRAL z=zcellbottom to zcelltop (Fi) dz

Where Fd is the effective drag force (N), n is the number of pillars per grid cell and zcellbottom and zcelltop are respectively the bottom and top vertical coordinates of a grid cell.

The model assumes there is a homogeneous distribution of pillars. The definition of the pillars is made through a pre-processed 3D grid data file where a drag coefficient is given in the grid cells that form the area of the structure and set to a null value in the rest of the domain. The values defined in the data file are previously computed based on pillar diameter, pillar length and pillar density and the reference dimensionless drag coefficient for a flow past a vertical cylinder. Pillar density in each grid cell is computed based on the horizontal resolution of the model pillar length in each grid cell is computed based on the vertical resolution. Drag coefficient values for a flow past a vertical cylinder were obtained from literature and range around 1-2. Nevertheless, this parameter can be seen as a tuning factor.

Cheers,
Luis

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### Re: hydrodinamics in cm scale

thank you very much Luis