Transcript MODELISATION DES ECOULEMENTS EN LITS COMPOSES

‫الــمدرســــة الــوطــــنــيــة للــمــهــنــدســيــن بــتــونــس‬
école nationale d'ingénieurs de Tunis
Laboratoire de Modélisation en Hydraulique et Environnement
NUMERICAL SIMULATIONS
OF A PASSIVE SCALAR
TRANSPORT IN A JET FLOW
Prepared by :
Nabil MRABTI
Presented by :
Zouhaier HAFSIA
Plan
Introduction.
Mathematical model (chen profile at the inlet).
Rodi adjusments of the standard k-ε constants
Numerical results.
Conclusions.
2
INTRODUCTION
An important progress was made in the CFD
It is possible to simulate a very large varieties of flow transport processes
It is necessary to validate the transport model in a simple case : monophasic
jet, for example
Chen in 1979 adjust turbulence intensity at the inlet of the jet flow with
Gaussian profile
Since 1980, Rodi showed that the constants of the (k-eps) model depends on
the decelaration of axial velocity
We use the CFD code PHOENICS for numerical simulations.
Numerical results are compared to experimental data of Hu (2000)
associated with the establishment zone of the jet flow.
3
THE JET FLOW PARAMETERS
D= 30 mm; Win = 0.20 m/s
4
GOVERNING EQUATIONS
For a stationary single-phase flow and with no buoyancy for a quasi-parallel
flow having axial symmetry, the transport equations is :
- Momentum
- Mass conservation
 (U j Ui )
 Ui
0
x i
x j

 u 'i u ' j
1 p
 ²U i


 x i
x jx j
x j
II
I
III
IV
- Kinetic equation :
Ui
 Ui  U j 2
k
 t  k

(
)   t ((

) ) 
 xi
 x i k  x i
 x j  xi
IV
I
II
III
- ε equation :

 t  
  Ui  U j 2
2
Ui

(
)  C1 ((

) )  C 2
 x i  x i   x i
k  x j  xi
k
I
II
III
- Scalar transport equation :

C
( U jC  
)  SC
 xj
 xj
IV
C  Ck  0.09 ; C1  1.44 et C2  1.92
5
The model in its form described previously has been applied with success in a lot
of type of flow but the universality of its constants cannot be expected. The field of
application of this model can be extended thus if its constants are substituted by
functions of parameters of the flow. In this context comes the setting of Rodi and al.
(1980) relative to jet flows which the constants are replaced by the equations:
C  0.09  0.04 f
C2  1.92  0.0667 f
   U c U c
f 


x
 U max  x



0.2
Umax : Maximal velocity
  ye  yc: (c: center and e: ambient fluid)
The manipulation of the constants of the model can be done by the technique
"PLANT" relative to PHOENICS.
PLANT is an attachment to the PHOENICS-SATELLITE that allows the users
to place in their files of entry, the formulas for which it cannot have an
equivalent there in the source program.
6
RODI ADJUSMENTS
 Y   W  Wc  
C  0.09  0.04*  1%   c  

 Wc   Z  Z  
0.2
Wc is the longitudinal mean velocity on the axis of the jet and
width of the jet when the W is equal to 1%.
The gradient of velocity term is approximated by :
Y1% is the
Wc Wi  Wi 1

z
zi  zi 1
U
E
E
S  C V     C1   t
k
C  4* C2 *

V 
(3k )
i, j
 U j ,i 
2
2

4
Thus, we can modify the term directly source of the dissipation rate while substituting,
in the expression of, by:
C2   1.92  0.0677 *
 Y1%
W
 c
 
Wc
z

Wc
z




0.2
7
BOUNDARY CONDITIONS :
- Standard inlet conditions :
For the kinetic energy and the dissipation rate at the inlet :
kin  k Win2
Win3
in   
d
These two coefficients are adjusted numerically in order to reproduce the
experimental data.
  0.01   0.006

k
- Chen profile at inlet (gaussian profile ) :
k  k in exp -1.7 y 2 
  in exp -1.7 y 2 
0
y
d
2
- For a plane of symetry :
 (U, W, k, )
0
y
8
Longitudinal variation of
C
0,091
0,090
Cμ
0,089
0,088
0,087
0,086
0,085
0
10
Z/D
20
30
9
Longitudinal variation of
C2 
1,920
1,918
C 2ε
1,916
1,914
1,912
1,910
0
10
Z/D
20
30
10
Mean velocity profiles
exp de Hui Hu
1,2
(k-e)
(k-e) modified
1,0
W1/W in
0,8
0,6
0,4
0,2
0,0
0,0
0,5
1,0
1,5
2,0
Y/D
Fig. 4 : Velocity Profile at : Z=2D.
11
Mean velocity profiles
exp de Hui Hu
1,2
(k-e)
(k-e) modified
1,0
W1/Win
0,8
0,6
0,4
0,2
0,0
0,0
0,5
1,0
1,5
2,0
Y/D
Fig. 5 : Velocity Profile at : Z=3D.
12
RESULTS OF SIMULATIONS
Mean velocity profiles
exp de Hui Hu
1,2
(k-e)
(k-e) modified
1,0
W1/Win
0,8
0,6
0,4
0,2
0,0
0,0
0,5
1,0
1,5
2,0
Y/D
Fig. 6 : Velocity Profile at : Z=4D.
13
Turbulence Intensity profiles
exp de Hui Hu
0,25
(k-e)
(k-e) modified
w'w''^ 0.5/W in
0,20
0,15
0,10
0,05
0,00
0,0
0,5
1,0
1,5
2,0
Y/D
Fig.(5-a): Velocity fluctuations profiles at Z=2D.
14
Turbulence Intensity profiles
exp de Hui Hu
0,25
(k-e)
(k-e) modified
w'w'^0.5/W in
0,20
0,15
0,10
0,05
0,00
0,0
0,5
1,0
1,5
2,0
Y/D
Fig.(5-a): Velocity fluctuations profiles at Z=3D.
15
Turbulence Intensity profiles
exp de Hui Hu
0,25
(k-e)
(k-e) modified
w'w'^0.5/W in
0,20
0,15
0,10
0,05
0,00
0,0
0,5
1,0
1,5
Y/D
2,0
Fig.(5-a): Velocity fluctuations profiles at Z=4D.
16
Concentrations profiles
1,2
exp de Hui Hu
(k-e)
1,0
(k-e) modified
Cc//Cin
0,8
0,6
0,4
0,2
0,0
0,0
0,5
1,0
Y/D
1,5
2,0
Fig.(5-a): Concentration profiles at Z=2D
17
Concentrations profiles
exp de Hui Hu
1,2
(k-e)
(k-e) modified
1,0
C1/Cin
0,8
0,6
0,4
0,2
0,0
0,0
0,5
1,0
Y/D
1,5
Fig.(5-a): Concentration profiles at Z=3D
2,0
18
Concentrations profiles
exp de Hui Hu
1,2
(k-e)
(k-e) modified
1,0
C1/Cin
0,8
0,6
0,4
0,2
0,0
0,0
0,5
1,0
Y/D
1,5
2,0
Fig.(5-a): Concentration profiles at Z=4D
19
CONCLUSIONS
* The monophasic jet transporting a passive scalar is affected by the
conditions at the injection which describe the nature of the nozzle.
* The Rodi adjustments for the jet flow provided significant
improvements of hydrodynamic jet structure : for the mean velocity
profiles and of the turbulent intensity at three sections in the
establishment zone; however the concentrations profiles remain not
acceptable.
* Although, the modelling of the scalar transport by models which are
based on a direct proportionality between diffusivities of momentum and
that of the passive scalar appears insufficient. In fact, many authors such
us Feath and al (1995) showed that the Schmidt number is variable
through the cross-section of the stream discharge.