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College notes Advanced fluid dynamics (ME45042) Fluid Mechanics, ISBN: 9780124059351 R128,30   Add to cart

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College notes Advanced fluid dynamics (ME45042) Fluid Mechanics, ISBN: 9780124059351

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Lecture notes from the TU Delft course Advanced fluid dynamics AFD. Covers most of chapters 5 to 11 of fluid mechanics from Kundu

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  • October 13, 2022
  • 35
  • 2020/2021
  • Class notes
  • Daniel tam
  • All classes
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Advanced Huid Dynamics
College 1
Part 4
Vorticity Dynamics
Vorticity and circulatie

Definition

Consider a flow ,
character ized b III. t ) =
( v.v ,
w )

the work
City as the Carl of the
Velocity
ad ( E. t) × ICE t ) ,




In cartesion coordinator




÷:
÷




Hou is a related to it ?


↳ ( Io t ) =L ( Xo ) t
É ( Ik -


Ik ) DX t É ( It If
-
it ) DX
try
-

translation
¥ rate of Strain tensor

= deflatie
= Rotaties




÷
÷÷÷÷: ÷
÷
÷




.




In -




DI = É e X EX
-
Rotatie where
rotatie vector is te




ij -

,-




couette flow : d- '



µ)

â








IEË H -




÷÷÷÷÷÷÷÷÷÷÷:*
F-


ZD
-




:
§ tal


Congothe
C-
flow
-



ytly
# g
ctfdlt


t to
- -







g- y
- -




¥ XÉIX
T
§ Edf ! kaft ! Edf
dftsudf
=
=




-
Lidl dealt
= dx Î
=D
g


ÏÏ . . .




ydx
"
t dig "
t .
. .




VJDX
0




.jp#nseIEE
Stokester ( correctie between
workcity
& circulatie )
,




#
F-
§ tot


=




notie
vorti
Cityfield e
( Aftands )
.




ijij IJ

, t.us#F
Examt ê




=


§ Vêêdxdy
-




} Vdxdy =
✓ DX
B
-

= -




Irrotational flow :

A flow such that
{ If ¥] ( Carl of vetocity )
( no
vorticity)




ij

, Advanced Huid Dynamics
College 2


Vorti
City equator


assumep =
constant (incompressie flow)

assume inertie frame of reference



bodyforce f a Conservative :
f =
-


I 4
( mits)
µ dynamic viscose ( kg 1ms) ✓ %
=
:



,




The is defined ( I. t) I X UCI t)
vorticity as : =
,




px (Pl # te Ilt ) = -



IP thee -14 )
① ② ③ ④ ⑤


① px (E) =p Elixir ) =p # e



②I X (PHIL ) =P ( t.hu ) -



text) Ik HIHI -



)
xd


incontest
te te
µ
A- Ik
-
-


Peek I. e- o (




⇐÷÷÷÷÷÷÷÷÷
⑤ Extra ) 0
1=0
=


§ Idf →
[ ( Ixftnds
I XD


③ Ix (IP ) = 0




④ Extra ) =D (Ixus )
'
'
e



p 3¥ PEI =p ⇐ Ik twee

IE t
the =
elk twee



DIE =
E- Ik

Source
twee
(
term
/ mits =
diffusie constant
adrector of
vorticity
(
vorticity transported
with the flow)

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