flow field specification
DESCRIPTION
FLOW FIELD SPECIFICATION. Eulerian and Lagrangian descriptions:. Eulerian. Lagrangian. Velocity field and trajectories. Streamlines. Parallel (tangent) to the velocity vector → boundaries are streamlines. Represent velocity trajectories. slope of streamlines. - PowerPoint PPT PresentationTRANSCRIPT
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FLOW FIELD SPECIFICATIONEulerian and Lagrangian descriptions:
txVV ,
Eulerian
txVV ,0
Lagrangian
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Velocity field and trajectories
Streamlines Parallel (tangent) to the velocity vector → boundaries are streamlines. Represent velocity trajectories.
u
v
dx
dyslope of streamlines
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www.me.bme.hu/~karolyi/results/advect/advection.html
What can we say about these streamlines?
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Pathlines Trajectory of an identified water parcel – represent one particle at different times.
http://projects.ict.usc.edu/animation/fluidsim.htm
0
0
0
0
t
t
dtvyy
dtuxx
(e.g. progressive vector diagrams)
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Streaklines Pathlines that move more than a single point through the flow. Represent multiple particles at one time.
https://visualization.hpc.mil/wiki/Streaklines
Effective way to identify flow discontinuities through large separation of the points in the Streakline.
Streamlines = Pathlines = Streaklines if the flow is steady, i.e., 0t
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Stream function
In two dimensional flow we can define a stream function Ψ, such that:
xv
yu
,
http://www.atmos.albany.edu/student/gareth/diagnostics.html
x
y A
B
What is the mass flux ρQ across the line AB?
If AB II to y, thenQ = u dy
But in general AB can be defined by(dy,-dx), so that
Qvdxudydxdyvu ),(),(
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Qvdxudydxdyvu ),(),(
ddx
xdy
yQ
If A and B are on the same streamline, then Q = 0, so Ψ must be a constant along a streamline.
u
dx
v
dy
u
v
dx
dy ;Another way to look at it:
slope of streamlines
y
dx
x
dy
xv
yu
,
0
ddy
ydx
x
Ψ must be a constant along a streamline.
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Differentiating following a fluid parcel
dt
dz
z
Q
dt
dy
y
Q
dt
dx
x
Q
t
Q
dt
dQ
Adopting the Eulerian description, the rate of change of properties following a parcel:
wz
Qv
y
Qu
x
Q
t
Q
dt
dQ
Dt
DQQu
t
Q
dt
dQ
localadvective