modeling of sloshing problems broca

ANSYS, Inc. Proprietary© 2006 ANSYS, Inc.

Modeling of Sloshing ProblemsFree Surface with Advanced FSIModeling of Sloshing ProblemsFree Surface with Advanced FSI

Sheldon ImaokaTechnical Support EngineerANSYS, Inc.


Overview of Analysis

• Two containers partially-filled with a dense fluid undergoing 3Gs in 1 second

• The objective is to review the structural response of the containers

Rigid housing Containers

FluidThe containers are half-filled with a dense fluid.

Besides self-weight, the system experiences a 3G loading in the axial direction


Advanced FSI Capability

• Although the structural response is desired, an FSI analysis required– If the fluid were treated either as solid

elements with negligible shear stiffness or as added mass, the change in fluid distribution would not be accounted for

If this were treated as a purely structural analysis, the dynamic loading of the fluid would not considered correctly.


Model of Structure

• Structural analysis used ANSYS 10.0:– Containers meshed with SOLSH190 with

multilinear isotropic plasticity– Housing is assumed to be rigid– Contact with friction defined between all

three bodiesSOLSH190 is a 8-node solid-shell element.Multilinear isotropic hardening plasticity assumed for the containers.5% damping included in the model.


Model of Fluid

• CFD analysis performed in CFX 10.0:– Fluid and air modeled as free surface flow– Initially, it is assumed that the dense fluids

are at rest and take up half of the tank• Initial VF and pressures defined via CEL

Because the model is fully enclosed, pressure levels have to be specified.

Two separate domains exist, so reference pressure locations specified via CCL


MFX – Overview

• The MFX solution capability allows complex FSI problems to be solved:– Within each timestep, a stagger loop sends

results of one analysis as input to the other– Displacements from ANSYS modify fluid

domain in CFX. Forces (from pressure and shear stresses) in CFX become loading in ANSYS.

– (Thermal capability also supported with MFX)


MFX – Analysis Details

• The MFX solver was used to solve this fluid-structure interaction problem– Loading: constant gravity (1G) in y-

direction, acceleration loading (3G) ramped in 1 second, held for 1 second

– Boundary conditions: symmetry about yzplane assumed

– Simulation time was 2 seconds with constant timesteps of 0.01 seconds


MFX – Load Transfer

• The outside of the fluid and the inside of the container transfer loads– Displacements and forces are sent

between ANSYS and CFX during solution


MFX – Load Transfer

• Mapping resultscan be reviewed– Information on

mapping is shownin the output file

– Mapped forces anddisplacementsare postprocessedon the right


Solution Convergence

• Different measures of convergence:• ANSYS: in a given substep, if force equilibrium

is not achieved within specified number of equilibrium iterations, bisection occurs or solution stops (if max substeps reached)

• CFX: in a given coefficient loop, if residuals do not go below specified criteria within maximum number of iterations, solution continues

• MFX: in a given stagger loop, if transferred (load) quantities do not converge (per equation on left with e<0) within maximum stagger iterations, solution goes to next timestep

ΦΦ

ΦΦ

=

min

max

min

log

loge


Solution Convergence

• ANSYS, CFX, and MFX runs can all be monitored during solution:

CFX Solver Manager ANSYS Results Tracker


Results


Analysis Runs

• Three cases considered:– Case 1: CFD analysis only– Case 2: FSI analysis with linear elastic

materials and high coefficient of friction– Case 3: FSI analysis with plasticity and low

coefficient of friction• Case 3 is analysis of interest, but Cases

1 and 2 serve to verify model setup


Case 1: CFX only

• In the CFD-only case, the walls are assumed to be rigid.

In this animation, 3G loading is ramped in 1 second, held for another second, then ramped down. (Total simulation time is 5 seconds, although only first 2 seconds is of interest.)Note that the response is very similar (symmetric) for the two containers, as expected.


Case 2: MFX with linear elastic

• Total axial (z-dir) force is compared:Total Z-Force vs. Time

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00 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Time (s)

Forc

e (N

)

CFX (CFD) CFX 1 (MFX) ANSYS 1 (MFX)With linear elastic material properties and a high coefficient of friction, the resulting deflections are relatively small. Consequently, the CFX forces do not change significantly between the CFD-only case (rigid walls) and MFX case (elastic walls).The forces in ANSYS include the mass of the containers, so that accounts for the slightly larger forces.


Case 2: MFX with linear elastic

• When comparing total z-force (sum of forces on all walls), the previous two cases provided similar results– This verifies the model setup since there

should not be large strains or finite sliding for Case 2.

– With the verification step complete, the case of interest (next) can be approached with greater confidence.


Case 3: MFX with plasticity

• Animation of volume fraction for Case 3:

Note that at the point of contact between the two containers, there is significant deformation occurring because of plastic straining.Also, between the left container and housing, there is also permanent deformation.This results in free surface responses that are not exactly the same (symmetric) between the two containers.



• Note mesh deformation in highlighted two regions:



• Total axial (z-dir) force for Case 3:Total Z-Force vs. Time

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00 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Time (s)

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)

CFX (CFD) CFX 2 (MFX) ANSYS 2 (MFX)

With plasticity and a smaller coefficient of friction, there are finite strains as well as sliding.These effects make the dynamic response less smooth during impact between the containers and between the containers and rigid housing.



• Animation of equivalent stresses:Z force of left rigid wall of housing is plotted in upper-right corner (this differs from previous slide, as that was the sum of Z forces on all walls of rigid housing).Note sliding occurring on the right container. Also, large strains exist in the left container, as seen earlier.During the analysis, although acceleration loading is ramped, the force loading is not linear because of the dynamic loading from the fluid.


Conclusion

• The ANSYS MFX Solver is demonstrated with this sloshing example– ANSYS Advanced FSI capabilities make it

possible to account for large-deformation, free surface flow coupled problem

– In situations such as these, only through the coupled treatment can loading be accurately modeled

modeling of sloshing problems broca

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