Direct numerical simulation of turbulent heat - HAL UPEC

Direct numerical simulation of turbulent heat - HAL UPEC

Direct numerical simulation of turbulent heat transfer in
annuli: Effect of heat flux ratio
Meryem Ould-Rouiss, L. Redjem Saad, Guy Lauriat
To cite this version:
Meryem Ould-Rouiss, L. Redjem Saad, Guy Lauriat. Direct numerical simulation of turbulent
heat transfer in annuli: Effect of heat flux ratio. International Journal of Heat and Fluid Flow,
Elsevier, 2009, 30 (4), pp.579-589. <10.1016/j.ijheatfluidflow.2009.02.018>. <hal-00734060>
HAL Id: hal-00734060
https://hal-upec-upem.archives-ouvertes.fr/hal-00734060
Submitted on 21 Sep 2012
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
List of Figures
1
2
3
4
5
6
7
8
9
10
11
12
13
Shemati of the omputational domain. . . . . . . . . . . . . . . . . . . . .
Two-point orrelations in the axial diretion. . . . . . . . . . . . . . . . . . .
Two-point orrelations in the azimuthal diretion. . . . . . . . . . . . . . . .
Mean veloity prole. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
RMS veloity utuations: (a) streamwise, (b) radial, () azimuthal. . . . .
Positions of zero total shear stress r0 and maximum veloity rmax . . . . . .
Mean temperature proles. (a) inner ylinber, (b) outer ylinder . . . . . .
RMS of temperature utuations for q ∗ = 1. . . . . . . . . . . . . . . . . . .
RMS of temperature utuations for various heat ux ratios. (a) q ∗ ≤ 1,
(b) q ∗ ≥ 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Turbulent heat uxes for q ∗ = 1. (a) streamwise omponent, (b) wall-normal
omponent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Streamwise turbulent heat ux for various heat ux ratios. (a) q ∗ ≤ 1, (b)
q∗ ≥ 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Wall-normal turbulent heat ux for various heat ux ratios. (a) q ∗ ≤ 1, (b)
q∗ ≥ 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Position of zero wall-normal turbulent heat ux versus heat ux ratio. . . .
17
18
19
20
21
22
23
24
25
26
27
28
29
30
R1
R2
L
Figure 1: Shemati of the omputational domain.
18
(a)
1
vz
Θ
0.8
Rvv(z)
0.6
0.4
0.2
0
inner
-0.2
0
(b)
2
4
6
z/δ
8
10
12
1
vz
Θ
0.8
Rvv(z)
0.6
0.4
0.2
0
outer
-0.2
0
2
4
6
z/δ
8
Figure 2: Two-point orrelations in the axial diretion.
19
10
12
(a)
1
vz
Θ
0.8
Rvv(θ)
0.6
0.4
0.2
0
-0.2
inner
-0.4
0
(b)
0.02
0.04
0.06
rθ/δ
0.08
0.1
0.12
1
vz
Θ
0.8
Rvv(θ)
0.6
0.4
0.2
0
outer
-0.2
0
2
4
rθ/δ
6
Figure 3: Two-point orrelations in the azimuthal diretion.
20
8
1.5
(a)
vz/ub
Chung et al. (2002)
vz/ub
1
0.5
0
0
0.5
1
1.5
2
y/δ
25
inner
outer
(b)
20
+
+
vz =2.5 ln (y )+5.5
vz
+
15
10
+
5
0 0
10
+
vz =y
10
1
y
+
Figure 4: Mean veloity prole.
21
10
2
3
(a)
2.5
+
v’z(rms)
2
1.5
1
Interne
Externe
Chung et al (2002)
0.5
0
0
20
40
y+
60
80
100
1
(b)
0.8
+
v’r(rms)
0.6
0.4
0.2
Interne
Externe
Chung et al (2002)
0
20
40
y+
60
80
100
1.2
(c)
+
v’θ(rms)
0.8
0.4
Interne
Externe
Chung et al (2002)
0
0
20
40
y+
60
80
100
Figure 5: RMS veloity utuations: (a) streamwise, (b) radial, () azimuthal.
22
1.5
1.5
(a)
v’zv’r
v’zv’r+1/Re(dvz/dy)
y/δ=0.64
1
2
v’zv
v’zr/(u
/uτb)e
1
0.5
y/δ=0.61
0
0.5
-0.5
-1
0
0
0.5
0.5
11
1.5
1.5
y/δ
2
1.5
1.5
DNS
y/δ=0.64
v’zv’r
v’zv’r-1/Re(dvz/dy)
1
b
2
v’zv’vr/(u
/u τ)e
1
0.5
z
y/δ=0.61
0
0.5
-0.5
(b)
-10
00
0.5
0.5
11
1.5
1.5
y/δ
Figure 6: Positions of zero total shear stress
23
r0
and maximum veloity
22
rmax .
20
*
q =1
*
q =0.01
*
q =100
Θ =(1/0.362)ln(y )+1.8
+
+
Θ+
15
10
Θ =Pr.y
+
5
+
0 0
10
10
1
+
10
2
10
2
y
20
*
q =1
*
q =0.01
*
q =100
Θ =(1/0.362)ln(y )+1.8
+
+
Θ+
15
10
5
Θ =Pr.y
+
0 0
10
+
10
1
+
y
Figure 7: Mean temperature proles. (a) inner ylinber, (b) outer ylinder
24
5
inner
outer
inner
Chung et al. (2003)
outer
Redjem et al. (2007)
4.5
}
4
3.5
Θ’+rms
3
2.5
2
1.5
1
0.5
0
0
20
+
40
y
Figure 8: RMS of temperature utuations for q ∗ = 1.
25
60
0.03
(a)
q*=1
*
q =0.5
*
q =0.25
q*=0.1
*
q =0.01
Θ’rms
0.02
0.01
0
0
0.5
1
y/δ
1.5
(b)
2
q*=1
*
q =2
*
q =5
q*=10
q*=100
0.15
Θ’rms
0.1
0.05
0
0.5
1
1.5
2
y/δ
Figure 9: RMS of temperature utuations for various heat ux ratios. (a) q ∗ ≤ 1, (b)
q∗ ≥ 1
26
10
(a)
inner
outer
inner
outer Chung et al. (2003)
Redjem et al. (2007)
}
8
v’zΘ’+
6
4
2
0
0
20
y+
40
60
1.5
(b)
inner
outer
inner
outer Chung et al. (2003)
Redjem et al. (2007)
}
v’rΘ’+
1
0.5
0
0
20
+
40
60
y
Figure 10: Turbulent heat uxes for q ∗ = 1. (a) streamwise omponent, (b) wall-normal
omponent
27
0.003
(a)
*
q =1
q*=0.5
*
q =0.25
*
q =0.1
*
q =0.01
v’zΘ’
0.002
0.001
0
0
0.5
1
1.5
2
y/δ
0.018
(b)
*
q =1
q*=2
*
q =5
*
q =10
*
q =100
v’zΘ’
0.012
0.006
0
0
0.5
1
1.5
2
y/δ
Figure 11: Streamwise turbulent heat ux for various heat ux ratios. (a) q ∗ ≤ 1, (b)
q∗ ≥ 1
28
0.0004
*
q =1
*
q =0.5
*
q =0.25
*
q =0.1
*
q =0.01
v’rΘ’
0.0002
0
(a)
-0.0002
0
v’rΘ’
0.0005
0.5
1
y/δ
1.5
2
(b)
0
-0.0005
*
q =1
q*=2
*
q =5
*
q =10
q*=100
-0.001
-0.0015
0
0.5
1
y/δ
1.5
Figure 12: Wall-normal turbulent heat ux for various heat ux ratios. (a) q ∗ ≤ 1, (b)
q∗ ≥ 1
29
2
10
1
y/δ
*0.53
y/δ=0.46q
0
y/δ
10
10-1
10-2 -2
10
10
-1
0
10
*
10
1
10
2
q
Figure 13: Position of zero wall-normal turbulent heat ux versus heat ux ratio.
30