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9.9 Fluid-Structure Interaction

Flow elements in a model for fluid-structure interaction require the input of some special material parameters.

Fluid medium (syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...[}\>\texttt{CSOUND}\>\texttt{\textit{c}}$_{r}\,${]} \end{tabbing} \end{figure}$

CONDUC

cf is the conductivity c_F of the fluid. ( c_F $\ge$ 0 )This parameter is a necessary but `dummy' input to generate the element conductivity matrix K_F^e .

K_F^e = $\displaystyle \int_{{\Omega_{\mathrm{F}}}}^{}$ $\displaystyle \nabla$ N^TN d $\displaystyle \Omega$

(9.12)

CSOUND

c is the sonic speed c in the fluid medium for compression effects. (c > 0 )From this value DIANA calculates the element compression matrix M_F^e .

M_F^e = $\displaystyle {\frac{{ 1 }}{{ c^{2} }}}$ $\displaystyle \int_{{\Omega_{\mathrm{F}}}}^{}$ N^TN d $\displaystyle \Omega$

(9.13)

These matrices may be applied in a direct frequency response or hybrid frequency time domain response fluid-structure interaction analysis.

Fluid boundary (syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...\>\>\texttt{CSOUND}\>\texttt{\textit{c}}$_{r}\,$\,) \end{tabbing} \end{figure}$

GRAVAC

gracce is the acceleration of gravity g applied for free surface waves or radiation boundary effects. (g > 0 )If only GRAVAC is specified, DIANA calculates the element gravity convection matrix M_F^e to model the free surface wave effects.

M_F^e = $\displaystyle {\frac{{ 1 }}{{ g }}}$ $\displaystyle \int_{{\Gamma_{\mathrm{s}}}}^{}$ N^TN d $\displaystyle \Gamma$

(9.14)

These matrices may be applied in a direct frequency response or hybrid frequency time domain response fluid-structure interaction analysis.

DSBOUN

depths is the fluid depth h with respect to the surface. (h > 0 )If both GRAVAC and DSBOUN are specified, DIANA calculates the frequency dependent sonic speed c_s due to radiation.

c_s = $\displaystyle {\frac{{ g }}{{ \omega }}}$ tanh $\displaystyle {\frac{{ \omega h }}{{ c_{\mathrm{s}} }}}$

(9.15)

with $\omega$ as angular speed. From this c_s DIANA calculates the element radiation convection matrix C_F^e to model the radiation boundary effects.

C_F^e = $\displaystyle {\frac{{ 1 }}{{ c_{\mathrm{s}} }}}$ $\displaystyle \int_{{\Gamma_{\mathrm{e}}}}^{}$ N^TN d $\displaystyle \Gamma$

(9.16)

These matrices may be applied in a direct frequency response or hybrid frequency time domain response fluid-structure interaction analysis.

CSOUND

c is the sonic speed c in the fluid medium for bottom absorption effects. (c > 0 )

ALPHAB

alphab is the wave reflection coefficient for the bottom $\alpha_{{\mathrm{B}}}^{}$ . ( -1 $\leq$ $\alpha_{{\mathrm{B}}}^{}$ $\leq$ 1 )From this value and the sonic speed c in the fluid medium DIANA calculates the element bottom absorption matrix

C_F^e = $\displaystyle {\frac{{ 1 - \alpha_{\mathrm{B}} }}{{ c(1+\alpha_{\mathrm{B}}) }}}$ $\displaystyle \int_{{\Gamma_{\mathrm{b}}}}^{}$ N^TN d $\displaystyle \Gamma$

(9.17)

For rigid reservoir bottom materials $\alpha_{{\mathrm{B}}}^{}$ = 1 . For very soft reservoir bottom materials $\alpha_{{\mathrm{B}}}^{}$ = - 1 These matrices may be applied in a direct frequency response or hybrid frequency time domain response fluid-structure interaction analysis.

A fluid boundary element can either represent a bottom absorption, free surface or a radiation boundary. DIANA assumes a bottom absorption boundary if both ALPHAB and CSOUND are specified. DIANA assumes a free-surface boundary if only GRAVAC is specified. DIANA assumes a radiation boundary if both GRAVAC and DSBOUN are specified. No element gravity convection matrix will be set up for radiation absorption boundary elements.

Next: 10. Model Code Libraries Up: 9. Special Models Previous: 9.8 Wöhler Diagrams Contents Index

DIANA-9.3 User's Manual - Material Library
First ed.

Copyright (c) 2008 by TNO DIANA BV.