Reference problem
=====================


Geometry
---------


.. image:: images/Object_1.svg
    :width: 602
    :height: 207


.. _RefImage_Object_1.svg:

:math:`L=50m`

:math:`{R}_{i}=1m`

:math:`{R}_{e}=1.1m`

:math:`C`: pivot point of the external structure (pivoting around :math:`\mathrm{Cx}`)


Material properties
------------------------

**fluid:** density :math:`{\rho }_{1}=1000{\mathrm{kg.m}}^{-3}`; :math:`{\rho }_{2}=750{\mathrm{kg.m}}^{-3}`;

**Structure:** :math:`{\rho }_{s}=7800\mathrm{kg}/{m}^{3}`; :math:`E=2.1{10}^{11}\mathrm{Pa}`;; :math:`\nu =0.3` (steel).


Boundary conditions and loads
-------------------------------------

**Fluid:**


1. to simulate the permanent flow, a normal speed of :math:`–4m\mathrm{/}s` is imposed on the fluid inlet face (by thermal analysis, a normal heat flow equivalent to :math:`–4` is imposed);


2. to model the variation in density, a condition of continuity of the flow rate is imposed at the interface;


3. to calculate the fluid disturbance caused by the movement of the external cylinder, a Dirichlet boundary condition is imposed at a fluid node.

**Structure:**


1. the external cylinder is subjected to a displacement of the type

    .. image:: images/Object_11.svg
        :width: 602
        :height: 207


    .. _RefImage_Object_11.svg:

at the nodes of the mesh of this cylinder.