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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?