A Finite Volume Procedure on Unstructured Meshes for Fluid-Structure Interaction Problems
Flow through micro and mini channels requires relatively
high driving pressure due to the large fluid pressure drop
through these channels. Consequently the forces acting on the walls of
the channel due to the fluid pressure are also large. Due to these forces
there are displacement fields set up in the solid substrate containing
the channels. If the movement of the substrate is constrained at some
points, then stress fields are established in the substrate. On the other
hand, if the deformation of the channel shape is sufficiently large
then its effect on the fluid flow is important to be calculated. Such
coupled fluid-solid systems form a class of problems known as fluidstructure
interactions. In the present work a co-located finite volume
discretization procedure on unstructured meshes is described for
solving fluid-structure interaction type of problems. A linear elastic
solid is assumed for which the effect of the channel deformation
on the flow is neglected. Thus the governing equations for the
fluid and the solid are decoupled and are solved separately. The
procedure is validated by solving two benchmark problems, one from
fluid mechanics and another from solid mechanics. A fluid-structure
interaction problem of flow through a U-shaped channel embedded
in a plate is solved.
[1] I. Demirdzic and S. Muzaferija, "Numerical method for coupled fluid
flow, heat transfer and stress analysis using unstructured moving meshes
with cells of arbitrary topology", Comput. Methods Appl. Mech. Engrg.,
vol. 125, pp. 235-255, 1995.
[2] Michael Schafer and Ilka Teschauer, "Numerical simulation of coupled
fluid-solid problems", Comput. Methods Appl. Mech. Engrg., vol. 190,
pp. 3645-3667, 2001.
[3] A. W. Date, "Solution of transport equations on unstructured meshes
with cell-centered colocated variables: Part I: Discretization, International
Journal of Heat and Mass Transfer, vol. 48, pp. 1117-1127, 2005.
[4] S. V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere
Publishing Corp.: New York, 1980, ch. 6.
[5] A.W. Date, "Fluid dynamical view of pressure checkerboarding problem
and smoothing pressure correction on meshes with colocated variables",
International Journal of Heat and Mass Transfer, vol. 46, pp. 4885-4898,
2003.
[6] K. C. Karki, K. M. Kelkar, P. S. Sathyamurthy and S. V. Patankar,
"Accurate solutions for laminar flow and heat transfer in a channel with
a backward-facing step, benchmark problems for heat transfer codes",
ASME HTD, vol. 222, pp. 35-43, 1992.
[7] I. Demirdzic, S. Muzaferija and M. Peric, "Benchmark solutions of some
structural analysis problems using finite-volume method and multigrid acceleration",
International Journal for Numerical Methods in Engineering,
vol. 40, pp. 1893-1908, 1997.
[1] I. Demirdzic and S. Muzaferija, "Numerical method for coupled fluid
flow, heat transfer and stress analysis using unstructured moving meshes
with cells of arbitrary topology", Comput. Methods Appl. Mech. Engrg.,
vol. 125, pp. 235-255, 1995.
[2] Michael Schafer and Ilka Teschauer, "Numerical simulation of coupled
fluid-solid problems", Comput. Methods Appl. Mech. Engrg., vol. 190,
pp. 3645-3667, 2001.
[3] A. W. Date, "Solution of transport equations on unstructured meshes
with cell-centered colocated variables: Part I: Discretization, International
Journal of Heat and Mass Transfer, vol. 48, pp. 1117-1127, 2005.
[4] S. V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere
Publishing Corp.: New York, 1980, ch. 6.
[5] A.W. Date, "Fluid dynamical view of pressure checkerboarding problem
and smoothing pressure correction on meshes with colocated variables",
International Journal of Heat and Mass Transfer, vol. 46, pp. 4885-4898,
2003.
[6] K. C. Karki, K. M. Kelkar, P. S. Sathyamurthy and S. V. Patankar,
"Accurate solutions for laminar flow and heat transfer in a channel with
a backward-facing step, benchmark problems for heat transfer codes",
ASME HTD, vol. 222, pp. 35-43, 1992.
[7] I. Demirdzic, S. Muzaferija and M. Peric, "Benchmark solutions of some
structural analysis problems using finite-volume method and multigrid acceleration",
International Journal for Numerical Methods in Engineering,
vol. 40, pp. 1893-1908, 1997.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:62414", author = "P I Jagad and B P Puranik and A W Date", title = "A Finite Volume Procedure on Unstructured Meshes for Fluid-Structure Interaction Problems", abstract = "Flow through micro and mini channels requires relatively
high driving pressure due to the large fluid pressure drop
through these channels. Consequently the forces acting on the walls of
the channel due to the fluid pressure are also large. Due to these forces
there are displacement fields set up in the solid substrate containing
the channels. If the movement of the substrate is constrained at some
points, then stress fields are established in the substrate. On the other
hand, if the deformation of the channel shape is sufficiently large
then its effect on the fluid flow is important to be calculated. Such
coupled fluid-solid systems form a class of problems known as fluidstructure
interactions. In the present work a co-located finite volume
discretization procedure on unstructured meshes is described for
solving fluid-structure interaction type of problems. A linear elastic
solid is assumed for which the effect of the channel deformation
on the flow is neglected. Thus the governing equations for the
fluid and the solid are decoupled and are solved separately. The
procedure is validated by solving two benchmark problems, one from
fluid mechanics and another from solid mechanics. A fluid-structure
interaction problem of flow through a U-shaped channel embedded
in a plate is solved.", keywords = "Finite volume method, flow induced stresses, fluidstructureinteraction, unstructured meshes.", volume = "5", number = "7", pages = "1482-7", }