This preview shows pages 1–8. Sign up to view the full content.
1
Turbulence & mixing
Turbulence & mixing
4
th
lecture
FACE 8 2007
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 2
Turbulence & mixing
·P
r
o
g
r
a
m
▫
08:1508:45 Lecture: The LES approach
▫
08:4509:00 Exercise: RANS+ Questions
▫
09:0009:15 Break
▫
09:1510:00 Lecture: Smagorinsky SGS model
▫
10:0011:30 Exercise: Test case in Fluent
▫
11:2012:00 presentations in plenum
·L
i
t
e
r
a
t
u
r
e
▫
Frölich and Rodi’s introduction to LES
Suggested reading:
▫
Fluent user guide
▫
Sagaut’s LES for incompressible flows
3
Turbulence & mixing
· Turbulence structure
· How to simulate this?
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 4
Turbulence & mixing
· DNS
(Direct Numerical Simulation)
▫
Idea: Just use the NSequations…
▫
Problem: Need to resolve the time and length scales of turbulence
/
▫
Conclusion: Not practical possible for most problems
·L
E
S
(Large Eddy Simulation)
▫
Idea: Okay, let just resolve the larger time and length scales then
▫
Problem: Still very demanding + difficult to setup
▫
Conclusion: We only want to use LES for specific problems
·R
A
N
S
(Reynolds Averaged Navier Stokes)
▫
Idea: Lets forget about eddies and whirls and try to find some way
to model the effect of turbulence on the overall flow
▫
Problem: This is an oversimplification of the problem which yields
erroneous results and require an insight to use
▫
Conclusion: This is the fast solution and we must be skeptical of the
result; but we’ll probably be using RANS models most of the time!
More time
More computational demanding
5
Turbulence & mixing
·R
A
N
S
· Boussinesq approximation
· Mixing length
()
ij
i
ij
i
j
i
jj
j
uu
u
P
S
tx
x
x
ρ
τ
ρρ
∂
∂
−∂
∂
′′
+=
+−
+
∂∂
∂
∂
Turbulent stress or
Reynolds stresses:
τ
T
j
i
TT
j
i
u
u
xx
τμ
⎛⎞
∂
∂
≈+
⎜⎟
⎝⎠
Turbulent or eddy viscosity
T
l
u
μ∝
Velocity scale
Length scale
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 6
Turbulence & mixing
· Structure of turbulence
▫
Energy is extracted from the main flow to produce large eddies
▫
Energy is transferred from larger eddies to smaller eddies
▫
The smallest eddies dissipates due to the viscosity of the flow
7
Turbulence & mixing
· Local isotropy
▫
Large eddies transport the majority of the turbulent kinetic energy
▫
Large eddies are
problem dependent
; they are dictated by the
geometry/ boundaries of the flow
▫
Large eddies are more
anisotropic
▫
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 09/16/2011 for the course ME 563 taught by Professor Staff during the Spring '11 term at Auburn University.
 Spring '11
 Staff

Click to edit the document details