5. example#

5.1. Example 1: Calculating the added mass matrix of a structure consisting of two concentric cylinders separated by an incompressible fluid#

The cylinders are each supported by springs. The added mass matrix is calculated for the first two modes of the structure, namely the rigid body modes of each of the cylinders in the Ox direction (cf. diagram). We are only going to present here the steps of the command file, because this example is inspired by test case FDLV101 [V8.01.101]. For the details of the syntax of the other operators, the user can therefore refer to the command file for this test case.

_images/10000F2600001DC4000017FA64ACE706587A5FD4.svg

  1. Assignment of the overall structure model (including the two cylinders and their support springs).

  1. Calculation of the natural modes of the structure in a vacuum

  2. Generalized numbering based on calculated mechanical modes

  3. Calculation of the added mass matrix of the matr_asse_gene_r type (operand NUME_DDL_GENE present). As a result, it is then possible to calculate the natural modes of the « wet » structure.

MACRO_MATR_AJOU (MAILLAGE = maya,

GROUP_MA_FLUIDE = 'grfluid',

GROUP_MA_INTERF = grunt,

MODELISATION = 'PLAN',

FLUIDE = _F (RHO = rho,

GROUP_MA = 'grtotal'),

DDL_IMPO = _F (GROUP_NO = 'noble',

PRES_FLUIDE = 0.),

MATR_MASS_AJOU = massage,

MODE_MECA = fashion,

NUME_DDL_GENE = number,

INFO =1)

  1. Calculation of generalized mass and stiffness matrices on generalized numbering based on the calculated mechanical modes numgen. These matrices are of type [matr_asse_gene_r]

  2. Calculation of the total mass matrix of the structure (generalized mass matrix plus added mass matrix)

  3. Calculation of the modes of the submerged structure.

  4. Restitution of « wet » modes on a physical basis.

5.2. Example 2: cylinder subjected to annular flow#

This case (very similar to test case FDLV106 [V8.01.106]) uses the calculation of mass, added damping, and added stiffness on a cylindrical structure subjected to an annular flow that is assumed to be potential. Initially, mass and damping added by the flow on the structure are calculated for various upstream speeds (4 m/s, 4.24 m/s and 6 m/s), this on a 3D model for the fluid and shell for the structure. The structure has a rotational movement around a pivot located at the downstream end of the cylinder with respect to the flow.

_images/1000312000003132000010F3EB4C772147E0570E.svg

  1. After modeling the cylindrical structure and calculating its modes in air, command MACRO_MATR_AJOU makes it possible to calculate the mass, stiffness and damping added by the flowing fluid to this structure:

MACRO_MATR_AJOU (MAILLAGE = MAYA,

GROUP_MA_FLUIDE = 'FLUIDE',

GROUP_MA_INTERF = 'INTERFACE',

FLUIDE = _F (RHO = 1000. ),

INFO = 2,

MODELISATION = '3D',

DDL_IMPO = (

_F (GROUP_NO = 'TEMPIMPO', PRES_FLUIDE = 0. ),

_F (GROUP_NO = 'NOSORT', PRES_SORTIE = 0. )),

ECOULEMENT = _F (GROUP_MA_1 = 'ENTREE',

GROUP_MA_2 = 'SORTIE',

VNOR_1 = -4. ,

VNOR_2 = 4.),

MATR_MASS_AJOU = CO (" MASSAJ "),

MATR_AMOR_AJOU = CO (" AMORAJ "),

MATR_RIGI_AJOU = CO (" RIGIAJ "),

MODE_MECA: = MODES,

NUME_DDL_GENE = NUMGEN,

)