Zimoch ES 240 Presentation

8/9/2019 Zimoch ES 240 Presentation

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Sloshing liquid in a

rectangular tankPawel Zimoch

ES 240 Fall 2008Photo: http://bulgar.no-ip.inf o/downloads/snimki/wall/Afternoon%20Offshores,%20Hermosa%20Beach,%20California.jpg

Modeling approaches and failures


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Motivation

Great practical importance, especially intransport (tankers, trucks)

Personal interest


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Initial goals

Simulate vibrations of coffee in a mugCylindrical tankNewtonian fluidHorizontal harmonicforcing

Expected result:

Animation by Shreyas Madre


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Software

Chose COMSOL due to adviceCOMSOL supports moving mesh which

allows modeling of free fluid surfacesA basic sloshing liquid model exists in thebuilt in model library


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COMSOLs basic model

Response of a body of fluid under rotationof the gravity vector

Rectangular subdomainFluid modeled using incompressibleNavier-Stokes equations

Liquid: glycerol Denisty: 1270 kg/m^3 Dynamic viscosity: 1.49 Pa s


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Subdomain Geometry1m x 0.3 m Rectangle

Automatically generated mesh


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Boundary Conditions

Sides and bottom: slip/symmetry Normal component of velocity =0 Tangential component of viscous force = 0

Top: neutral Total force = 0 (free boundary)

Navier-Stokes


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Boundary Conditions

Sides: constrained in x-directionBottom: constrained in x and y-directionTop: mesh follows deformations of the liquid Velocity of the mesh in the direction parallel to its

normal equals the velocity of the fluid

Moving Mesh

nun

TTTT

y!y]


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Modeling approach

Adopt similar boundary conditions to 3DgeometryFailed In cylindrical coordinates system was

underdetermined In rectangular coordinates, solver could not

handle the constraints (freeze)Therefore, decided to model in rectangular 2D, investigate


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Physical situation

Constant horizontal acceleration 1m/s^2for 2 seconds, then release

E.g breaking of a truck with a fluid tankFind out: Extreme positions of vertical boundaries

Pressures on the walls Total force on the tank


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Resultvorticity


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Total horizontal forcehorizontal force on all

6

6

6

time [s]

t o t a l f o r c e o n w

a l l s

i n

[ N / m ]

Force from abody of the ame ma : 3 N/mConlcu ion: 5 % greater force in ca e of a liquid


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Displacement of liquid on vertical

boundariesRight boundary

Left boundary


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Pressure on walls

Right Bottom (x=0)

Middle (x=0.15) Top (x=0.3)

40% reduction inpressure fromx=0.15 to x=0(statically 50%)


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Pressure on walls

Left Bottom (x=0)

Middle (x=0.15) Top (x=0.3)


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Is the model accurate?

Fluid is glycerol very viscousThe vibrations experience almost no

damping.Energy should be dissipated due toviscous friction model does notrepresent physics accuratelySolution try to implement no-slipboundary condition


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Model with no-slip boundary

conditionsModel vertical andbottom boundary asno-slip. Top boundaryremains neutral.Result:

QuickTime and adecompressor

are needed to see this picture.


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Finer mesh

ickTime n ec m ress r

re nee e t see this ict re.


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Very fine mesh

To represent no-slip condition accurately, mesh around the verticalboundaries (especially around the corners) would need to be extremely fine.


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Less viscous fluidwater


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Conclusions

While the model seems to show generalbehavior of a fluid well, its much worse atrepresenting a given fluidTo accurately represent viscous fluids, no-slip boundary condition must be possibleto enforce.


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Interesting failures (1)


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Interesting failures (2)


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AcknowledgmentsThanks to Ben Jordan for useful

hints on COMSOL


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Questions?

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