heat conduction is very small due to the small thickness of the metal foil and the low conductivity of the rod ... determined from the measurements of the current and the voltage drop along the rods with an ... not as good as that of the x-wires, which are run in the Constant Temperature Ane- mometer-mode ...... 0.620 321.200.
Forschungszentrum Karlsruhe Technik und Umwelt Wissenschaftliche Berichte FZKA 5582
Measurements of Turbulent Velocity and Temperature in a Wall Channel of a Heated Rod Bundle T. Krauss, L. Meyer Institut tür Neutronenphysik und Reaktortechnik
Mai 1995
Forschungszentrum Karlsruhe Technik und Umwelt Wissenschaftl iche Berichte FZKA5582
Measurements of Turbulent Velocity and Temperature in a Wall Channel of a Heated Rod Bundle T. Krauss, L. Meyer Institut für Neutronenphysik und Reaktortechnik
Forschungszentrum Karlsruhe GmbH, Karlsruhe
1995
Als Manuskript gedruckt Für diesen Bericht behalten wir uns alle Rechte vor Forschungszentrum Karlsruhe GmbH Postfach 3640, 76021 Karlsruhe
ISSN 0947-8620
Measurements of Turbulent Velocity and Temperature in a Wall Channel of a Heated Rod Bundle Abstract Turbulent air flow in a wall sub-channel of a heated 37-rod bundle (P/D=1.12, W/D=1.06) was investigated. Measurements were performed with a hot-wire probe with x-wires and a temperature wire. The mean velocity, the mean fluid temperature, the wall shear stress and wall temperature, the turbulent quantities such as the turbulent kinetic energy, the Reynolds-stresses and the turbulent heat fluxes were measured and are discussed with respect to data from isothermal flow in a wall channel and heated flow in a central channel of the same rod bundle. Also, data on the power spectral densities of the velocity and temperature fluctuations are presented. These data show the existence of large scale periodic fluctuations of velocity and temperature in the gap region of two adjacent rods or between rods and the wall. These fluctuations are responsible for the high intersubchannel heat and momentum exchange.
Messungen der turbulenten Geschwindigkeit und Temperatur in einem Wandkanal eines beheizten Stabbündels Zusammenfassung Turbulente Strömung durch einen Wandkanal eines beheizten 37-Stabbündels (P/D=1.12, W/D=1.06) wurde untersucht. Die Messungen wurden mit einer Hitzdrahtsonde mit x-Drähten und einem Temperaturdraht durchgeführt. Die mittleren Strömungsgeschwindigkeiten und -temperaturen, Wandschubspannungen und Wandtemperaturen, Turbulenzgrößen wie die turbulente kinetische Energie, die Reynoldschen Schubspannungen und die turbulenten Wärmeströme wurden gemessen und werden mit den Ergebnissen bei isothermer Strömung in einem Wandkanal und bei beheizter Strömung in einem Zentralkanal dieses Stabbündels verglichen. Spektrale Leistungsdichten der Geschwindigkeits- und Temperaturschwankungen werden ebenfalls dargestellt. Sie weisen auf die Existenz von periodischen großskaligen Schwankungen der Geschwindigkeit und Temperatur im Spalt zwischen zwei benachbarten Stäben oder zwischen Stäben und der Wand hin. Diese Schwankungen sind für den großen Wärme- und Impulsaustausch zwischen den Unterkanälen verantwortlich.
CONTENTS
1. II\ITRODUCTION ............................................................................................ 1
2. EXPERIMENTAL APPARATUS AND PROCEDURE..................................... 2
3.
RESllLT .........................................................................................................5 3.1. Wall shear stress and wall temperature distribution .............................. 5 3.2. Mean velocity and temperature distribution ........................................... 6 3.3. Turbulent intensities and kinetic energy ................................................. 7 3.4. Reynolds shear stress ............................................................................ 8 3.5. Turbulent heat flux ................................................................................. 9 3.6. Eddy diffusivities of heat and momentum ............................................. 10 3.7. Tripie correlations ................................................................................ 12 3.8. Skewness and flatness ......................................................................... 13 3.9. Frequency analysis .............................................................................. 14
4. COI\lCLUSIOI\l .............................................................................................. 15
5.
NOMENCLATURE ....................................................................................... 16
6. REFERENCES ............................................................................................. 18
-1-
1. INTRODUCTION The prediction of the temperature distribution within the rod bundle of a nuclear reactor is of major importance in nuclear reactor design. The thermal-hydraulic analysis is performed by solution of the conservation equation for mass, momentum and energy. Recently developed codes [1] applying a distributed parameter analysis need empirical information on turbulent transport properties of both momentum and energy transport. A large number of experiments has been performed in various rod bundle geometries with isothermal flow (for a review see Ref. 2). It has been found that distributions of the turbulence intensities in rod bundles are unusual and different from those in tubes and parallel plates [3,4,5]. The highest turbulence intensities were observed at positions of greatest distance from the walls in the gap region. The eddy viscosities parallel to walls are considerably higher than those normal to walls and depend strongly on the pitch to diameter ratio of the rod bundle. The high mixing rates between subchannels of rod bundles have been explained by the effects of secondary flow for a long time, although Rowe [6,7] in 1973 had noticed that a nongradient macroscopic flow process, possibly flow pulsation, affects the mixing between subchannels. Detailed turbulence measurements of the axial flow through closely-spaced rod bundles have confirmed the observations of Rowe and have shown that an energetic and almost periodic flow pulsation exists through the gaps between the rods and between rods and channel walls, respectively [8,9]. It was demonstrated that these flow pulsations are the reason for the high mixing rates between the subchannels of rod bundles [10,11] and secondary flows in subchanneis do not contribute significantly to the mixing rates. In arecent investigation on turbulent flow through compound rectangular channels [12] it was shown that these large scale flow pulsations or vortices are a general phenomenon existing in any longitudinal slot or groove in a wall or a connecting gap between two flow channels, provided its depth is more than approximately twice its width. Thus, the momentumand heat transfer processes in the rod-gap area for turbulent flow through closely spaced rod arrays are governed by a low frequency quasi-periodic fluctuation of the velocity component directed through the gap.
-2-
To model correctly the heated flow it is necessary to know the turbulent quantities of the velocity and those of the temperature such as the eddy diffusivity of heat in all directions. No such data were available for flow through rod bundles. In carrying on the 15 years of research on turbulent flow through rod bundles at Kernforschungszentrum Karlsruhe (KfK) the investigations were continued at a heated 37-rod bundie. The results of the measurements in a central channel have been published earIier [13]. Here we present the main results of the measurements in a wall subchannel and discuss them with respect to those results in the central channel and with isothermal flow in the wall channel [14].
2. EXPERIMENTAL APPARATUS AND PROCEDURE A rod bundle of 37 parallel rods (0.0. 0 ::: 140 mm) arranged in triangular array in a hexagonal symmetrie chan ne I was built (Fig.1). The position of the channel is horizontal. The total length of the working section is L::: 11.50 m with an unheated entrance length of
L iso :::
4.60 m and a heated length of
L heat :::
6.90 m. The pitch to di-
ameter ratio ofthe rods is P/O::: 1.12 (W/O::: 1.06), which gives a length to hydraulic diameter of central channel ratio for the heated part of
Lheat/Oh,c :::
128. The rods are
made of epoxy reinforced with fiberglas, sheathed with a 50 J.1m foil of monel metal, which serves as resistance heating element. It is heated by low voltage, high direct current to temperatures in the range of 60° to 100
oe. Since the metal foil has a very
accurate thickness the heat flux is uniform around the perimeter of the rods. The heat conduction is very small due to the small thickness of the metal foil and the low conductivity of the rod material. Thus, the circumferential temperature variations due to different heat transfer will not be eliminated by conduction. The wall heat flux was determined from the measurements of the current and the voltage drop along the rods with an estimated error of ±1.5 %.
The channel walls are made of aluminum covered with a thick insulation at the outside to minimize the heat losses. The whole bundle is made up from five sections, each 2.30 m long. The rod gap spacers were made of 4 mm thick and 15 mm wide
-3-
(in axial direction) steel with rounded edges. Oue to extremely small manufacturing tolerances the deviations from the nominal bundle geometry are less than 0.2 mm, including the bending of the rods. The fluid is air at atmospheric pressure and room temperature at the entrance. The air is driven bya centrifugal blower. Before entering the working section it passes through a filter to remove particles greater than 1 !-tm and an entrance section of 5 m length with a honeycomb grid and a number of fine grid screens. The measurements are performed at a position 20 mm Upstream of the outlet. The time-mean values of the axial velocity and the wall shear stresses are measured by Pitot and Preston tubes (0.0. d=0.6 mm), respectively, the mean temperatures are measured by sheathed thermocouples (0.0. d=0.25 mm). The wall temperatures are measured by an infrared pyrometer (Heimann KT 4), which has a range of 0°C-100°C and a target area of 5 mm diameter at 1 m distance. Mainly due to difficulties with ca libration the uncertainty is ±1 K.
The turbulent quantities are measured by hot wire anemometry using a three-wire probe. This probe consists of an x-wire probe with an additional cold wire perpendicular to the x-wire plane for simultaneous measurement of two components of instantaneous velocity and temperature. The x-wires have a length of 1.1 mm, a diameter cf 2.5 !-tm and a spacing of 0.35 mm. The cold wire has a diameter of 1 J..lm, a length of 0.9 mm and is positioned 0.1 mm upstream of the x-wire prong tips. The measuring volume is approximately 1 mm3 • The probe was fabricated in our laboratory. The calibration and evaluation method uses look-up tables as described by Lueptow et al. [15], extended by the temperature dimension [16]. Since the cold wire is run in the Constant Current Anemometer-mode (CCA) the frequency response is not as good as that of the x-wires, which are run in the Constant Temperature Anemometer-mode (CTA). The attenuation and phase shift of the temperature signal leads to errors in all correlations of u, v and e. A rough estimate for a 1 !-tm wire gives the following maximum errors: e2 is 2%, ue is 4% and anet uv are 4% too large and there is a negligible error in v 2
•
va
is 6% too smalI; u2
-4-
Apart from these errors there are several errors typical for x-probes, such as the errar due to the velocity component normal to the x-plane and the errors due to the finite length of the wires and the distance between them. The velocity component normal to the x-plane will result in the evaluation of tao high axial components u2 , while the finite length of and the distance between the wires leads to errors in v 2
,
w 2 and in the correlations such as uv. Those latter errors depend on the velocity and temperature gradient [16]. The performance of the measurements is fully automated; the mass flow rate, the heating power and the traversing of the measuring probe are contra lied by a 486-PC. The tripie wire probe is run by two CTA- and one CCA-bridge of an AN-1003 anemometer system. The signals were digitized at sampie rates of 7 kHz per channel by a OT2829-card, which provided sampie and hold digitization with 16-bit resolution. The total number of sampies taken in a continuous stream were 49152 per channel, with a measuring time of 7 seconds. The raw data were loaded into extended memory of the computer by OMA. The evaluation of all correlations takes approximately 20 seconds. At each measuring point the probe is turned into eight positions to measure a" six Reynolds stresses, three turbulent heat fluxes and ten tripie products [17]. To evaluate the above correlations it is necessary to roll the probe about its axis to the positions 0'\ 45°, 90° and 135° with respect to the start. The positions 180°, 225°, 270 0 and 315° are used to compute the average between two corresponding positions, 00 and 180° for example, in order to minimize possible errors in the radial or azimuthai components. In a wall channel measurements at 636 positions (Fig. 2) were taken under nonisothermal conditions, which took approximately forty hours. The data of the heated experiment were: Reynolds number in the wall channel Re ::: 6.5 X 104 , hydraulic diameter
Dh,w:::
0.0488 m with a bulk velocity Ub ::: 19.4 mls and a bulk temperature
Tb::: 29.1 °C. The wall heat flux in the present experiment was 1.39 kW/m2 •
-5-
3.RESUlTS
3.1. Wall shear stress and wall temperature distribution
Fig.3 shows the measured wall shear stress distribution of the 37 -rod bundle in comparison to the results of a 4-rod bundle. The shear stress was calculated by Preston's method. The properties of air were evaluated at the fluid temperature at y=O.3 mm, which is the radius of the Preston tube.
The wall shear stress reduced by the average wall shear stress of the wall and the rod ('t'w.av = 1.21 N/m 2 ) shows no relevant difference between the heated and isothermal data in a wall subchannel of the 37 -rod bundle. Even the shear stress distribution in the 4-rod bundle shows good agreement with these results, which confirms the similarity of flow through wall channels of 4-rod- and 37-rod bundles. Compared to the data obtained in a heated central channel of the 37 -rod bundle, the wall shear stress in the wall channel of the bundle is about 13% larger. The minimum value of 't w
occurs in the rod-to-wall gap region and the maximum value at the position of
maximum channel width.
In FigA local wall temperatures of the heated and unheated wall bounding the wall channel are plotted versus mean temperatures of each boundary. As expected, the temperature gradient along the unheated wall is very small due to excellent thermal conductance of the wall material. The values of this unheated wall showa maximum in the rod-to-wall gap and decrease gradually with increasing distance from the gap. In contrast to this the temperature distribution of the heated rod varies over a wider range with the minimum appearing at the position of maximum wall shear stress. The highest temperatures are reached in the rod-to-rod gap region.
-6-
3.2. Mean veloeity and mean temperature distribution
Isoline and x-y-plots of the time mean velocity are shown in Figs. 5 and 6. Time mean velocities are related to the bulk velocity of the wall channel Ub= 19.4 m/s. The distribution of time mean temperature is shown in Figs. 7 and 8. The bulk temperature in the wall subchannel was Tb = 29.1°C and the difference (Tw-Tb) was 19.55°C. There is no relevant difference in the velocity data between the isothermal and the heated case. The temperature differences in the wall ehannel are very large compared to a central channel, due to the proximity of an unheated wall. As expected, the temperature reaches its maximum value in the rod-to-rod gap region. The logarithmie plots of the radial velocity distribution, computed with local frietion velocities (Figs. 9 and 10) follow the law of the wall u+=2.5Inl+5 with reasonable agreement at most azimuthai positions. The logarithmic temperature profiles are shown in Figs. 11 and 12, together with the lines T+=2.5Iny+, displaced by 1 K every second angular position. Fig. 11 shows the logarithmic temperature profiles ealculated with loeal friction velocities in aceordance with the calculation of u+. Previous measurements in a heated central channel of our 37-rod-bundle have shown that the logarithmic temperature profiles at different azimuthai positions would not collapse if local friction veloeities were used. Therefore temperature profiles computed with the friction velocity averaged over the perimeter of the heated rod are presented in Fig. 12. The logarithmic profiles in Fig. 12 are slightly higher compared to Fig. 11, but the tendency to change its slope at different angular positions remains the same. The slope of the profiles is higher in the rod-to-wall gap and lower in the gap between two heated rods, the latter also being tound in central channels. The temperature profiles, calculated with local frietion veloeities can be fitted by logarithmic laws that gradually change from 3.69Iny+-6.21 in the rod-to-wall gap to 2.32Iny+-0.25 in the gap between two heated rods. The reason tor the deviation of these temperature profiles from a single logarithmie law is the extremely asymmetrie temperature distribution in the wall channel.
-7-
3.3. Turbulent intensities and kinetic energy
All quantities displayed in isoline plots were scaled by values of the friction velocity and temperature that are averaged over the perimeter of the rod and along the wall. All data are shown for the heated case. The differences between the unheated ca se and the heated case were negligible. Compared to the data from measurements in central channels the variation of all three velocity components in azimuthai direction is larger. All turbulent intensities except for the radial velocity component are higher in the wall chan ne I.
The turbulent intensities in axial direction
-tJ./ u
L - I_ - - , - .
40
20
--.t.-
bun
(J'I
CP
0
~---
70
symn1etry line
Fig. 14 Contour plot of relative axial intensity
·--
1
1
[ z [mm )
[!J
(9
.9
~.
-l
~
0 0 5 7 10 13
+
15 X 20 25 30 X 35 Z 40 y 45
+
> (!I
-~
.8
P
Ä
50 70
z
55 78 60 65
*
:::s
111 •
.7
20 26 33 40 47 55 62
Ä
70 75
.9
>
.8
(!I
-~ t.i'
:::s
.7
'f' 80 ~ 65 •
.6
.5
f-
o
.6
.5 .25
.5
.75
1
90
~-I
\
"~
I
1
y/y Fig. 15 Turbulent intensity of the radial velocity component
o
.25
.5
y/y
.75
1
c.:>
0
I
-31-
o relative radial intensity
-Jv
2
/ u,&,av
10
20
30
50
60
I
=::::-Q;-.l
70
-
~
.... 0.9--...
symmetry Une
Fig. 16 Contour plot of relative radial intensity
2.5
2.5
-
4l [grd )
----
z [mm]
CJ (!)
2.1
I-
I
-j
~
+ X ~
0 0 5 7 10 13
2.1
15 20 20 26 25 33
"" 30 40
X 35
z
~
> 1.7 (IS ~
:::I
~
y Ä
50 70
*Z
......
~7
40 55 45 62
55 76 60 l1li 65 • 70 ... 75
1.3
> 1.7 (IS
~
::::1
......
~
1.3
'f' 60 .... •
.9
.5
~~
I-
o
65 90
.5
.75
I\J
I
.9
.5 .25
I
I
(AI
1
y/y Fig. 17 Turbulent intensity of the azimuthai velocity component
o
.25
.5
y/y
.75
1
-33-
o relative azimuthai intensity
-Jw
2
5
I U... av
10
20
40
50
60 co
70
(J1
symmetry line
Fig. 18 Contour plot of relative azimuthai intensity
~
--
5
5
41 [grdJ z [mm J
[!]
(!) ~v
4.2 I-
'---'"
.ö
+
x
~
3.4
r
+
~
~'-,
2.6 l-
~"", "--
1 ~
X
o
Z
40 55 45 62 ):( 50 70
3.4
y
*X l1li 11
55 78 60 65 70 75
+
~
2.6
'f' 60 .... 65 .. 90
'\
I
w
~
"'J"
1.8
1 .25
.5
.75
y/y Fig.19
4.2
15 20 20 26 25 33
'" 30 40 X 35 47
Ä
~,,~
1.8
1
-rr
I-~'~
0 0 5 7 10 13
kinetic energy
1
o
.25
.5
y/y
.75
1
-35-
o 5
relative kinetic energy k
10
+
20
30 (ij 40 ~
9'6'
~
60
50
60
symmetry Une
Fig. 20 Contour plot of relative kinetic energy
2.6
2.6
----
ql
[de
z [mm]
[!]
2.2
I-
-----.
-~
~.,.:
C)
4l.
0 0 5 7 10 13
+
15 X 20 25 30 J1: 35 :2 40 y 45 )( 50
+
~ 1.8
-~ I-~
*X
20 26 33 40 47 55 62 70
55 78 60 11 65 .. 70 At. 75
1.4
"
2.2
>
-~
1.8
111
I-~
1.4-
50
... 65 .. 90
I
1
.6
l 1\ o
~
r
J
1
.6 .25
.5
.75
1
y/y Fig. 21 Turbulent intensity of temperature
o
.25
.5
y/y
.75
1
I
(.:I (J)
I
-37-
o relative intensity of temperature
10
-J82 I T'\:,av 20
30
50
60
70
symmetry Une
Fig.22 Contour plot of relative intensity of temperature
·9
.9
-
ql
[grd]
z [mm]
Cl .t,
0 0 5 7 10 13
+
15 20
(!)
.7
I-~
-j
.7
X
20 26 25 33 4" 30 40 ~
"
>
.5
t\:I
Nt-l'"
::::s .......
> :::J .3
z
~
y ~
*
Z
111
"" ~
~ '\.."-
I-
e -j
V •
-.1
I-
.5
50 70
> t\:I
55 78 60 65 70
Nt-l'"
:::J
.......
I~
A 75 ,
0
I
-41-
:
---..... o
5~
relative azimuthai shear stress uw
IU't,av2 10
~
10
20
30
co
3:
'9'6"
50
~
....l
-l
CX>
~
6b
~ 60
0
(J'\
70
(J1
~
'0,
"'0.4,
symmetry Une
Fig.26 Contour plot of relative azimuthai shear stress
A)
.4
.4
-
!p
[gr d J
z [mm]
!:I C9
.2
I-
I
P"/ß -l
0
ffi
0 5 ~ 10 + 15 X 20 ~ 25 30 ;:;:: 35 Z 40 Y 45 Ä 50
*
N~
:::::s
0 7 13 20 26 33 40 47 55 62 70
55 76 Z 60 111 65 • 70 ... 75
.......
I~ -.2
.2
0
ffi
N~
:::::s
.......
I~ -.2
,~~
'f' 60 . N
I
-43-
o
relative planar shear stress vw / u~,av
10
20
. 50
. 60
0.05
symmetry line
Fig.28 Contour plot of relative planar shear stress
2
2
--
!jl
[grd J
I
-I
I
I
I
1
I
z [mm]
~
C)
b
1.6
10 13
1.6
15 20 X 20 26 25 93
x:
1.2
~+
35 47
x:
=-ce
X1-., ~ " ~Y A "4111~ +
.8
Ä
*
Z
• *111 Z
1.2
.5
[!J
~zx:~ I-'~
~
*\-zx: $
'
*~
+
Yll'. "'.
Xb
o
~***
+
~)!():( )!X~
11
~,. ..
~[!]* * ..:!:. C)..:!:.(l;h..:!:. C)
*
~
Yr< y ~-t ~
~..:J!
~
~~~ *Z
-.1
Z,,"
::!e
Z Z
-fJ
+
yv
,'"
r
i?
"'&.
~.
*
~
€
v
""
X
X
*
50 70
55 78
Z
60 65
*z
11
70
&.
75
C)
~
(!)
'" 80 t.>
+
X
)!(
11
[!]
[!]A
X)!( X):(
. i!>
11
)!(
[!] X )!(
[!][!]
o
65 .. 90
x
-
I-
::l
I--I-
+
~
Y Z ""
I-
30 40 3S 47
X Z 40 55 Y 4S 62
111
-
.2
+
"'"
-
I-
-.1
~ * * *" A~C)~ ..:!:.~ ~
~
):( * ):(x
yyy
*0
I
+
X
x y
"" y
z
X
z
x y
-.2
-.2
o
.25
.5
.75
Z 1
y/y 31 Azimuthai gradient of time mean velocity
o
.25
.5
y/y
.75
I
~
1
-47
o 5
azimuthai gradient of mean velocity aUla
10
~
10 20
30
40
50
60 co (J1
70
symmetry line
Fig. 32 Contour plot of the azimuthai gradient of time mean velocity
~
----
1.5
1.5
41 [gr d]
z [mml
r::J
(!)
.9
> (11
I-
~
#~~
+
'"'
:::;,
CD
~
-.3
-1.5
~-.~
40 47 55 62
50 70
l1li
55 7B 60 65
.,
70
.& 75
-.9 I- "F_~""-:;:atC
.9
33
):(
*Z
> 111
-
10 13
z
~p
0 7
15 20 20 26
X 25 + 30 X 35 40 y 45
~-
.3
0 5
V
80
"'"
85
•
90
> t'G
~ >
.3
111
-
'"' I~
r
:::;,
-.3
~
r
l
-.9
-f
-1.5
o
.25
.5
.75
1
y/y Fig. 33 Relative turbulent heat flux in azimuthaI direction
o
.25
.5
y/y
.75
1
.j>.
co
I
-49-
5
relative azimuthai heat flux
we IU't,avT't,av
-
o 10
20
30
40
'57'6-
~
60
50
60
70
symmetry line
Fig. 34 Contour plot of relative azimuthai heat flux
m $:
4
--
4
lJl [
z [mm
3.2
x
l-
~~,~
-I
[!J
0
(!)
7
0 5 & 10 + 15 X 20 ~ 25 + 30 ~ 35 40 y 45 Ä 50
z
~ 2.4 I-~-
~
-
~
::J
I~ 1.6
13 20 26 33 40
3.2
47
55 62
~
*
70
I-~
55 76
~
X 111 .. AI.
60 65 70 75
-
2.4
~
::J
I~
1.6
'" 80 30 40
~
::R Z
.5
35 47 40 55
Y 45 62
~.
t---:> 111
-
~
50 70
j--f
li
55 7B 60 65
~ p:;:,
.. 70 ... 15
I~ .3
111
Ä
* :&
:;:,
.5
>
-
I~ .3
//T
'V 80
.1
-.1
~
l 1\ o
...
85
•
90
.1
-.1
.25
.5
.75
1
y/y Fig. 37 Relative turbulent heat flux in radial direction
o
.25
.5
y/y
.75
1
0'1
I\J
I
-53-
o relative radial heat flux va lu'r; avT'r; av !
10
!
20
30
40
50 60 -l
_~~'---------co
01
CIl 0
(J'\
("
' ......
symmetry Une
Fig. 38 Contour plot of relative radial heat flux
I
C
o' 70
\
~
3
I
I
I
I
I
---
z [mm)
[!J
f-
-
(!)
A
[!]
2.4
+
f-
.,.
I-
8
-f
f-
~
A
+
'\!>
(!)
A
+
'\!>
f-
«::>
1.2
I-
+
~111_.".+ ~ Z
.,.
r~_~~....
I-
.6
I-
III
"
•
+
X
~ ~
" .....
+
~.t. "z ~ Z ::x:
~)(11~
\)( Y
• l1li>
A
10 13
+
15 20
2.4
X 20 26 0 25 33
+
30 40
::x:
35 47
Z
40 55
x
+
cfl
A
x
'.:7" t::.....
o
+
Ä 50 70 ,.; 55 78 X 60
~~
1+ A
+ X
+
~~~ I
o
7
1.8
~ j;: «::>
1.2
~
I
"
60 65 .. 90
..
,
[!] (!)
A
+
.6
x
~
~~Y~Y~r)( "1 .... ~
I-
o
0
5
111 65
AC!)
~
+
0
C!)
: 1'" -l
[!]
*,-,y
T
(!) A
X
[!J
Y 45 62
[!J
X L ul5.",...
*..rv
.
X
~'\!> )iif."\.,.
~ j;:
_'
[!J
x
+
....I
(!)
x
3
41 (
I
.25
.5
.75
1
y/y Fig. 39 Radial gradient of time mean temperature
o
o
.25
.5
y/y
.75
1
-55
o radial gradient of mean temperature aT/ar
10
20
30
40
50
60
."
I' symmetry Une
Fig.40 Contour plot of the radial gradient of time mean temperature
70
~
.2
.2
--
lJl (
~
-----
z [mm ]
x
0.1
~
I
I-
I
~
++
Z
6~@6@
++ + Xx X
o I-
~~~
r
9~
~
- .1
I-
~+
~~
~ ~
:Q: ~~ ~ ZZZ ~ Z Z ~ Yy Y Y Ä):( ):( Y
~ * ):():(
*
-... . .. Z*
i*
liliiii 111111
~
AU..t.. .t..
Z
.t..
-.2 IVf""VV ~
4:,. 4:,.+ + + ~
X
i' i'
......... .. +
~
cEJ
X
X
~
~
*
~
X 6
*Zy Z
Z
Z
):(
):(
0
'1
13 20 26 33 40 47 55 62 70
55 78 Z 60 111 65 .. 70 .t.. 75
Y
):(
0 (9 5 6 10 + 15 X 20 ~ 25 + 30 ~ 35 Z 40 y 45 ):( 50
*
Y
Y
e:J
):(
i'
0.1
~
l1li
111
*
*~ .t..
~ V
)J!( ~
~
60
0
-1 0"
•
70
~
O'
'-symmetry line
Fig.42 Contour plot of the azimuthai gradient of time mean temperature
~
.25
.25
--
41 [
z [mm J
1\ .2
I-
I
J
..
I-
)C:
.1
0.05
o
~ YA
~
o
A.
.XC
++~ ~ + ~ .)(
I-
I
4-
.l1li
I
..
7
15 X 20 25 l' 30 )C: 35
X
+
~
•
Z
Z
Y
:.'j~
~*
Ä
Y
..
X
.
~~
55 78 Z 60 l1li 65 • 70 A. 7S
+
T
6
*
.2
20 26 33 40 41
)C:
4-
40 55 45 62 50 10
* Ä
x
10 13
+
T
+E CJ.:)
0
5
6
Z
...
0
(!)
1
111
.15
rJ
~
80 85
•
90
)C:
... +E
Z
~ ~ ~"iYK 6 +
CJ.:)
. ~ ~ Y)(
.75
1
y/y Fig. 43 Dimensionless eddy viscosity in radial direction
+
Ä
)(
+~~[!I ~ ~
.1
XX
~-!
('l'1
00
I
~ rJ
~j~ 0.05
o .5
+y
-1
.25
X
.15
Z
o
.25
.5
y/y
.75
1
.25
[grd]
z
Cl (!)
.2
f-
I
~
-1 Y
.15
Z'l'- A ~
f-
~
+~
CiJ
.,
je .1
•
f-
~~ ..
~*
~-~
~ 0.05
f-
X
~ ... X Ä )(Z
z 30 l\ 35 40 y 45
11 • ~
If-
.2
20 26 33 40 47 55 62
f-
.15
50 70
* 55 7B Z 60
x*
•
+
~
V
•
~
[mrn 1
0 0 5 7 10 13
z
'I
y
l\ 111
...
.25
---
I}l
A
65 70 75
V ... •
80 85 90
*
Ä
+.c CiJ
*
.1
yÄ y~
~Z
~
~'l'-x +~ *-i~
~
y
r
Z
Z
f
Cl
l\ Lf Ä*cHJ Zl\~ ~ ~
0.05
zr
Yr"~ *
f
~+
y
l
ClZ
~~ ~
't-
'l'-
..
~x~
(!)
X
l\
+ X
~
~
,*
0
0 0
.25
.5
.75
1
0
y/y Fig. 44 Dimensionless eddy diffusivity of heat in radial direction
.25
.5
y/y
.75
1
cn
co
I
(Jl
B
4 ['J C)
2
~
""
2
* l:.~~~
8 6
"'Y,..:~
2
~~
4.1J.
4 0
6
5 7 10 13
2 10 B 6
4
Y 45 62 );( 50 70
2
55 78 X 60 l1li 65 • 70 4. 75 ,.. 80
___ X +~_
+
XX
,, x
-"'l-"/
4' _____ -
4' (15
+E CI.')
1
B 6
z
4
....
~
I
2
85 .. 90
,(
A.~A
+6
20 26 33 40
::x:. 35 47 Z 40 55
*
);(
4
0
15 X 20 25 4' 30
~
C)
4
1
-
+
+~ +
B 6
tI)
6
6
10
+E
6 6
z [mm
6
(15
[grd J
.1
.1
8 6
8 6
4
4
2
2 0.01
0.01
0
.25
.5
.75
1
y/y Fig. 45 Dimensionless eddy viscosity in azimuthai direction
0
.25
.5
y/y
.75
1
,
---
4l [grd]
10~ 6 5 4 3
(!I
e.
5 10 13
5 4 3
+
15 20
2
(!)
3
+.c
0 7
I!J
2~
~6
z [mm 1
6 5 4
I
0
X 20 26
~
~
~
25 33 30 40
10~
::x:: 35 47
Z 40 55 Y
45 62
Ä
50 10
*Z
55 18 60 11 65 • 70 .A. 75 .., BO
+
~~ (!) X
2
~
4'
IR 7
...
65
•
90
!f
(!I
(!) (!)
e.
3
+.c ~
2
I
'" -
'-'
""
'"
~
~
1,
6 5 4 3
6
2
2
5 4
3
0.1
0.1
0
.25
.5
.75
1
0
y/y Fig. 46 Dimensionless eddy diffusivity of heat in azimuthai direction
.25
.5
y/y
.75
1
·5
ql
.5
[grd] z [mm]
.2
't"~
I-
-I
[::J
0
0
(!)
5
7
.:!:. .10 13
+
15 20
X
20 26
.2
25 33
-0.1
30 40
::x:
35 47
Z
40 55 45 62
y
~
-I~
+
):( 50 70
*z
('t)p
::::s
-.4
41
70
... 75
-.7 I-
-1
111
55 78 60 65
o
\
\\
'v
-I
"
....
80 85
•
90
-0.1 ~
-
('t)p
::::s
I~
-.4
.5
.75
1
\~I
-.7
-1 .25
~
o
.25
y/y Fig. 47 Tripie correlation of two axial components and the radial component
.5
y/y
.75
1
m
I\)
I
4.2
4.2
4l [gr d ]
[!]
(!)
~
3 f
~_
-:i.
+ X
0 0 5 7 10 13
3
15 20 20 26
25 33 .,. 30 40 X
1.8 > ('11 (t)t:->
-I~
35 47
Z 40 55 y
45 62
Ä
50 70
*Z
~
55 76 60 111 65 11 70 A., 75
.6
~
-I~
1.8
Mt:-> ~
"
.6
~~7/
'" 60 .. 65 • 90
-.6
-1.8
l-
o
V'
~
-1
0) (..)
I
-.6
-1.8 .25
.5
.75
1
o
.25
y/y Fig. 48 Tripie correlation of two axial components and the, azimuthai component
.5
y/y
.75
1
-64-
o 5 .....,./
correlation coefficient u2w /U-r, ,av 3
~ 10
( f 20
30
40
96'
~
öO
~&C _o~ symmetry Une
Fig. 49 Contour plot of the tripie correlation of two axial components and the azimuthai component
50
60
70
~
.5
.5
-
ql
[grdJ
z [mm ]
.3
f-
~
~
~
0
C9
5
~
+
0 7
10 13
X
15 20 20 26
~
25 33
.3
'" 30 40 J ('iJ
-
40 55 45 62
~
50 70
*
C')p
:::::I
N
y
Z
>
11
:::::I
•
-0.1
~
..." •
-.5
iii
P :::J
C')
I~
-0.1
60 65 90
-.5
o
.25
.5
.75
r~~~~l
-.3
~
-.3 I-
55 76 60 65 70 75
.1
1
o
.25
y/y Fig. 50 Tripie correlation of the axial component and two radial components
.5
y/y
.75
1
I
0) Q'I
I
-66-
o 5
correlation coefficient uv2 IU-c,av3
10
10
20
30
40
50
60
70
symmetry line
Fig. 51 Contour plot of the tripie correlation of the axial component and two radial components
~
.2
[grd]
z
0.1
.2
---
(jl
~~
I-
(mm]
[!]
0
0
C9
5
7
A
-I +
10 13
0.1
15 20
X 20 26 25 33 "I" 30 40 ::5
-.3
o
.25
.5
.75
1
o
.25
y/y Fig. 52 Tripie correlation of the radial component and two azimuthai components
.5
y/y
m
--l
I
·25
.25
--
ql
,----~~I
[grd]
---
z [mm)
I::l CJ
.15
/
I-
a--+ 6+ X
0 0 5 7 10 13
.15
15 20 20 26
25 33 4' 30 40 X 35 47
~
Z
0.05
y
Pt 50 70
*
(")~
~
.......
I~
40 55 45 62
z 111 11 A
-0.05
55 78 60 65 70 75
0.05
.,
ili
("):t .......
'I~
"0,05
-~
'V 60 ... •
-.15
-.25
I
4'""
f'
/fi)
-l
Cl 00
I
65 90
-.15
-.25
o
.25
.5
.75
1
o
.25
y/y Fig. 53 Tripie correlation of two radial components and the azimuthai component
.5
y/y
.75
1
.5
qJ___ [grdJ
.5
z [mm J
f2J 0)
.3
~
/ /'.fi"
0 5
0 7
e. 10 13
ff + X ~
15 20
•
3
20 26 25 33
4' 30 40 X 35 47
L
1
/ff./
~
~ -j
•
z:
1
40 55
Y
45 62
}{
50 70
... •
85 90
~
•
~-O.l t~l!!"II_O.l I"~~T .3 f-
-1
\
-.3
-.5
-.5
o
.25
.5
.75
1
o
y/y Fig. 54 Tripie correlation of the axial, the radial and the azimuthai component
~
2
2
---
ql
[grd]
z [mm]
I::J
1.2
I
~
~
C9 L!l.
+ X
0
0 5 7 10 13
1.2
15 20 20 26
25 33 4' 30 40 ){ 35 47
Z
40 55 45 62 ):( 50 70
.4
iii
-I~
.4
y
*
(t)tJ'
::I
z l1li
• A
-.4
55 78 60 65 70 75
> 111
-I~' (t) ",-
::s
::s -.4
~~
" 80 ... 85 .. 90
-1.2
-2
I-
_A
""
~
1.2
-2
o
.25
.5
.75
1
o
y/y
Fig. 55 Tripie correlation of the axial and two azimuthai components
.25
.5
y/y
.75
1
""-I
0
I
-71
30 40 )( 35 47
-.2 I-
-
(')::1
b
1('):::1
-.5
-.8
*' "'x: "v
Z 40 55
1
~
l I 1\
..,
'y
y
45 62
~
50 70
z 60 *'''' Ä
65 70 75
" .....
80 85
•
90
l1li
•
~
"\
-.2
-
(')::1
b
1('):::1
-.5
i
.75
1
.8
ql
-1.1
-1.1
o
~\ \
.25
.5
.75
1
y/y Fig. 57 Skewness of the axial velocity component
o
.25
.5
y/y
~
I'IJ
I
-73
o
(
skewness of u
•
10
20
30
40
50
60
symmetry Une
Fig. 58 Contour plot of the skewness of the axial velocity component
~
.4
.4
-
ql
[grd]
z [mm]
[!) C)
.2
I-
#/:.
-..b
0 7
10 13
+
.2
40 55 45 62
~
50 70
55 78 60 l1li 65 G 70 A 75
z
I(".)?; 0
.4
20 26 33 40 47
y
*
T
(".)::
.2
-..b
I(".)?; 0
r
'Y 80
...
85 .. 90
-.2 I-
-.4
A
-l
-.2
-.4
o
.25
.5
.75
1
y/y Fig. 61 Skewness of the azimuthai velocity component
o
.25
.5
y/y
.75
1
-..j
CI>
I
-77-
o skewness of w
10
20
30
~ '$76'
~
60
50
60 -l
70
symmetry line
Fig.62 Contour plot of the skewness of the azimuthai velocity component
1.5
1.5
--
41 [deg] z [mm]
.9
I-
-::L
[!]
0
(!)
5
0 7
.&.
10 13
+
15 20
X
20 26
.9
25 33 .,. 30 40
.3 I-
~~~.r:
-l
;:;
25 33
4.4
b
I..q->
3.8
.5
.75
1
y/y
Fig. 67 Flatness of the radial velocity component
~
o
.75
3.5
3.2 .25
I 1~~
.25
.5
y/y
1
Cl:>
I\)
I
-83-
o flatness of v
10
20
40
50
GO
o
/\ synlmetry line
Fig. 68 Contour plot of the flatness of the radial velocity component
70
~
4.2
ql
4.2
[grdJ
----
z [mm]
~
C)
~
3.8
3.4 I-
-
""'~ b
I""'~
3
/" /7-""-
~~~-
~~
A
~
Z
0 7
3.8
1013 15 20 X 20 26 25 33 "I' 30 40 ::>2
utw'l u"
-y'W" u"
SM
K(u)
SM
KM
S(w)
Klw)
apsv
0,068 0,077 0,091 0,113 0,136 0,181 0,226 0,272 0,362 0,453 0,566 0,679 0,906 1,000
108,000 121,600 141,900 175,900 209,800 277,700 345,700 413,600 549.400 685,200 855,000 1024,800 1364,300 1505,500
0,964 0,977 0,994 1,023 1,046 1,078 1,105 1,130 1,170 1,196 1.217 1,236 1,255 1.262
16,660 16,890 17,180 17,680 18,080 18,630 19,110 19,540 20,230 20,670 21,030 21,370 21,700 21,820
3,323 3,285 3,297 3,192 3,128 2,993 2,776 2,633 2,287 1.989 1,723 1,533 1.351 1,308
1,904 1,900 1,903 1,877 1,858 1,812 1,759 1,711 1,601 1,490 1,389 1,309 1,232 1,210
0,853 0,850 0,845 0,841 0,836 0,832 0,830 0,828 0,812 0,792 0,781 0,767 0,769 0,774
1.514 1.496 1,503 1.467 1.452 1,417 1,330 1,285 1.164 1,063 0,952 0,874 0,770 0,743
0,727 0,738 0,740 0,734 0,720 0,689 0,639 0,638 0,532 0.439 0,356 0,269 0,133 0,082
0,173 0,177 0,219 0,216 0,161 0,155 0,161 0,151 0,078 0,025 -0,039 -0,088 -0,143 -0,136
-0,156 -0,131 -0,121 -0,092 -0,064 -0,029 -0,015 0,017 0,032 0,044 0,056 0,066 0,055 0,050
0,071 0,075 0,069 0,037 0,020 -0,031 -0,108 -0,147 -0,210 -0,259 -0,267 -0,248 -0,272 -0,302
2,756 2,748 2,729 2,714 2,701 2,694 2,701 2,719 2,780 2,858 2,912 2,941 2,964 3,014
-0,275 -0,236 -0,200 -0,168 -0,137 -0,145 -0,148 -0,194 -0,206 -0,192 -0,162 -0,140 0,026 0,111
3.658 3,588 3,541 3,518 3,372 3,382 3,398 3,311 3,371 3,397 3.453 3,567 3,654 3,761
-0,049 -0,046 -0,018 0,010 0,043 0,096 0,137 0,191 0,269 0,296 0,344 0,280 0,134 0,071
3,180 3,203 3,157 3,129 3,099 3,118 3,180 3,263 3,378 3,574 3,743 3,833 3,818 3,626
0,028 0,030 0,034 0,040 0,046 0,059 0,067 0,077 0,081 0,107 0,159
y/ymax
y+
(Tw-TII ITw-Tb)
T'/P
-u'T'l
v'T'1
Sm
eptv
eptw
u'2y'1 u"
u"w" u"
u'y"1 u"
u'v'zi u"
v"w'l u"
V'W'2/
u+T*
w'T'1 u·T*
K(T)
u+T*
u"
u'v'w'f u"
0,068 108,000 0,077 121,600 0,091 141.900 0,113 175,900 0,136 209,800 0,181 277,700 0,226 345,700 0,272 413,600 0,362 549,400 0,453 685,200 0,566 855,000 0,679 1024,800 0,906 1364,300 1,000 1505,500
0.492 0,517 0,554 0,597 0,637 0,683 0,749 0,786 0,843 0,892 0,942 0,977 1,044 1.062
2,132 2,141 2,131 2,125 2,147 2,153 2,120 2,102 2,077 2,038 2,023 2,018 2,032 2,001
2,444 2,406 2,394 2,304 2,313 2,215 2,099 2,004 1.826 1.639 1,499 1.394 1.285 1.186
0,418 0,425 0,444 0,450 0,476 0,504 0,501 0,542 0,495 0,452 0.427 0,390 0,340 0,303
-0,893 -0,872 -0,845 -0,802 -0,869 -0,833 -0,695 -0,649 -0,575 -0,512 -0,481 -0,477 -0,507 -0,488
0,069 0,099 0,170 0,227 0,265 0,409 0,521 0,543 0,700 0,752 0,715 0,663 0,809 0,808
2,802 2,809 2,820 2,804 2,808 2,791 2,835 2,816 2,889 2,942 2,955 2,924 2,951 2,931
-0,176 -0,198 -0,235 -0,211 -0,259 -0,328 -0,376 -0.415 -0,408 -0,393 -0,337 -0,267 -0,113 -0,043
-0,103 -0,117 -0,190 -0,159 -0,110 -0,139 -0,058 0,015 0,019 0,049 0,037 0,001 -0,062 -0,102
-0,202 -0,180 -0,168 -0,147 -0,149 -0,160 -0,189 -0,199 -0,204 -0,192 -0,181 -0,155 -0,138 -0,143
0,414 0,345 0,275 0,127 0,072 -0,042 -0,150 -0,247 -0,249 -0,259 -0,198 -0,174 -0,148 -0,129
-0,074 -0,067 -0,065 -0,038 -0,028 -0,012 0,005 0,026 0,028 0,060 0,043 0,017 -0,008 0,002
0,041 0,033 0,020 0,007 -0,005 -0,010 -0,023 -0,026 -0,037 -0,045 -0,040 -0,049 -0,045 -0,035
0,057 0,043 0,046 0,044 0,038 0,018 0,030 0,048 0,Q18 0,018 0,011 0,004 0,000 -0,017
TABLE I cont.
0,014 0,016 0,019 0,024 0,030 0,043 0,053 0,069 0,084 0,096 0,115 0,125
0,396 0,380 0,362 0,338 0,360 0,336 0,250 0,207 0,186 0,162
epsw
..... 0
I\)
I
WALL SUBCHANNEL ANGULAR POSITION 70° Reference wall temperature Tw=48,65°C Local friction velo city u'=1,078m/s Average frietion velo city u' =1,019 m!s Average velocity in the wall eha Ub = 19,4 mfs
y/ymax
y+
U/Ub
REFERENCE: lOCAl Wall heat flux loeal frietion temperature Average frietion temperature Average fluid temperature
U+
k+
u'fu'
v'/v*
w'/w'
u'v'J u'%
u'w'/
1,908 1,903 1.893 1,881 1,851 1,807 1,753 1,687 1,569 1,471 1,390 1,382
0,849 0,834 0,822 0,809 0,797 0,790 0,786 0,780 0,784 0,799 0,812 0,833
1,334 1.320 1,301 1,280 1,257 1,214 1,176 1,110 1,001 0,922 0,844 0,816
0,725 0,719 0,712 0,709 0,682 0,649 0,608 0,570 0,479 0,370 0,223 0,135
sm -0,425 -0,403 -0,355 -0,276 -0,276 -0,125 -0,002 0,114 0,279 0,456 0,511 0,512
0,108 0,123 0,145 0,181 0,217 0,289 0,361 0,434 0,578 0,723 0,904 1,000
105,000 118,200 138,000 171.100 204,100 270,100 336,200 402,200 534,300 666,400 831,500 919,500
0,933 0,943 0,966 0,988 1,013 1,048 1,074 1,097 1,124 1,145 1,160 1,162
16,590 16,760 17,160 17,570 18,010 18,620 19,090 19,500 19,970 20,350 20,610 20,650
3,071 3,031 2,977 2,915 2,820 2,681 2,537 2,344 2,039 1,826 1,652 1,634
y/ymax
y+
ITw-TJI ITw-Tb)
T'/T*
-uT/
v'T'/
w'T'/
u"'T*
U+T4
u"T*
0,293 0,318 0,348 0,400 0,429 0,498 0,538 0,580 0,643 0,683 0,698 0,720
2,306 2,337 2,316 2,340 2,354 2,384 2,390 2,346 2,325 2,261 2,220 2,189
2,793 2,794 2,776 2,771 2,727 2,661 2,540 2,375 2,154 1,931 1,751 1,713
0,396 0,400 0,417 0,448 0,445 0,469 0,456 0,464 0,443 0,408 0,360 0,318
-0,943 -0,936 -0,946 -0,997 -0,982 -1,051 -1,042 -0,968 -0,850 -0,810 -0,768 -0,724
0,108 0,123 0,145 0,181 0,217 0,289 0,361 0,434 0,578 0,723 0,904 1,000
105,000 118,200 138,000 171,100 204,100 270,100 336,200 402,200 534,300 666,400 831,500 919,500
TABLE I cont.
REYNOLDS NUMBER = 65000 q 1,39 kW!m' T* =1,124 K T' =1,193 K Tb=29,1°C
-v'w'! u"
S(uJ
K(uJ
SM
KM
S{w)
KIwI
epsv
-0,038 -0,022 -0,036 -0,062 -0,065 -0,094 -0,113 -0,128 -0,152 -0,232 -0,296 -0,319
-0,110 -0,083 -0,082 -0,066 -0,040 0,003 0,009 0,024 0,041 0,042 0,018 0,002
0,113 0,122 0,116 0,104 0,082 0,033 -0,009 -0,018 -0,029 0,010 0,070 0,088
2,813 2,787 2,781 2,759 2,744 2,697 2,718 2,755 2,803 2,824 2,803 2,782
-0,269 -0,237 -0,208 -0,176 -0,182 -0,178 -0,167 -0,168 -0,141 0,019 0,159 0,221
3,630 3,610 3,517 3,475 3,497 3,462 3.399 3,514 3,594 3,665 3,839 3,766
-0,015 0,Q10 0,021 0,097 0,093 0,217 0,282 0,306 0,377 0,362 0,322 0,278
3,301 3,315 3,305 3,332 3,312 3,360 3,417 3,455 3,613 3,704 3,670 3,584
0,042 0,046 0,051 0,060 0,068 0,085 0.102 0,126 0,186 0,118
Km
eptv
eptw
ut '2v 'l u"
u"w'/
u'v t2j u"
u'v"/ u"
v"w'/
u"
v'w"/ u"
u'v'w'j
u"
2,642 2,606 2,600 2,574 2,524 2,506 2,483 2,483 2,506 2,591 2,612 2,670
0,022 0,025 0,031 0,041 0,049 0,069 0,084 0,102 0,131 0,148
-0,169 -0,138 -0,131 -0,138 -0.169 -0,272 -0,341 -0,339 -0,316 -0,247 -0,105 -0,008
0,025 -0,003 0,059 0,077 0,034 0,118 0,164 0,132 0,143 0,070 0,012 -0,037
-0,192 -0,168 -0,148 -0,116 -0,127 -0,140 -0,148 -0,149 -0,132 -0,121 -0,113 -0,120
0,466 0,470 0,459 0,397 0,291 0,201 0,111 0,023 -0,040 -0,030 0,002 0,009
-0,077 -0,071 -0,049 -0,031 -0,014 0,012 0,040 0,042 0,059 0,094 0,104 0,095
0,035 0,027 0,036 0,008 0,004 -0,016 -0,051 -0,077 -0,084 -0,108 -0,063 -0,039
0,073 0,076 0,066 0,058 0,055 0,049 0,085 0,052 0,065 0,071 0,049 0,057
u"
0,479 0,472 0,471 0,494 0,483 0,514 0,477 0,419
epsw
0,126 0,176 0,180 -'"
0
(,J
I u"
WAll SUBCHANNEl Reference wall temperature loeal friction veloeity Average frietion veloeity Average veloeity in the wall eha
ANGULAR POSITION 80° Tw=48,65°C u' =1,044 mfs u' =1,019 mfs Ub 19,4 m/s
REFERENCE: lOCAl Wall heat flux loeal frietion temperature Average frietion temperature Average fluid temperature
REYNOLDS NUMBER q=1,39 kW/m' T' =1,161 K P=1,193 K Tb=29,1°C
= 65000
yfymax
y+
U/Ub
U+
k+
u'/u'
v'{v'
w'/w'
u'v'{ u"
u'w'f u"
-v'w'l u' 2
Slul
KM
SM
KM
S(w)
KiwI
epsv
epsw
0,159 0.180 0,212 0.265 0,317
101,800 114,600 133,700 165,700 197,700 261.700 325,700 389,700 517,700 610,700
0,906 0,917 0,937 0,960 0,986 1,021 1,043 1,063 1,082 1,088
16,630 16,830 17,200 17,620 18,080 18,720 19,140 19,490 19.850 19,960
2,806 2,748 2.655 2,540 2,434 2,219 2,027 1,847 1,598 1,523
1.871 1,853 1,831 1.803 1.763 1.682 1,600 1,514 1,381 1.343
0.842 0,826 0,803 0,773 0,754 0,728 0,711 0,692 0,692 0,704
1,184 1.176 1.146 1,110 1,091 1,038 0,994 0,961 0,900 0,864
0,688 0,685 0,667 0,647 0,612 0,544 0,473 0,386 0,224 0,117
-0.195 -0.212 -0,179 -0,234 -0,251 -0,306 -0,340 -0,379 -0,389 -0,399
-0,102 -0.088 -0,077 -0,058 -0.049 -0,036 -0,037 -0,032 -0,066 -0,088
0,086 0.092 0,094 0,082 0,052 0,022 0,039 0,074 0,227 0,283
2,828 2,826 2,808 2,812 2,793 2,853 2,913 2,976 3,017 3,026
-0.306 -0,255 -0,243 -0,224 -0,211 -0,199 -0,211 -0,158 0,088 0,289
3ß76 3,609 3,594 3,536 3,540 3,540 3,694 3,762 4,044 4.116
-0.064 -0,029 0,011 0,091 0.118 0,223 0,223 0,289 0,298 0,339
3,379 3,438 3,352 3,383 3,385 3,463 3,456 3,542 3,441 3,480
0.063 0,066 0,069 0,076 0,083 0,110 0,143 0.106
OA85 0,540 0,455 0,514 0,802 0,780 0,746
OA23
0,529 0,635 0,846 1,000
0
"'I" y/ymax
y+
ITw-Tl/ (Tw-Tbl
T'/T'
0,058 0,083 0.112 0.166 0,208 0,280 0.306 0,359 0,398 0,410
2.363 2,390 2,382 2.435 2,444 2,496 2,491 2,512 2,462 2,471
0.159 101.800 0,180 114.600 0.212 133.700 0,265 165,700 0,317 197,700 0,423 261,700 0,529 325,700 0,635 389.700 0,846 517,700 1,000 610,700
TABLE I cont.
-u'T'1 u"T*
u·T*
v'TI
2,917 2,896 2,871 2,880 2.810 2,718 2.532 2,377 2.047 1,958
0,360 0,374 0,381 0,408 0,399 0,439 0,426 0.399 0,346 0,315
w'T'1
u"T+
-0,789 -0,864 -0,803 -0.917 -0,974 -1,103 -1.137 -1.214 -1,216 -1.200
Sm -1,109 -1,143 -1.102 -1.060 -1.115 -0,969 -0,916 -0,905 -0,735 -0,728
Km 2,627 2,607 2,578 2,485 2,468 2,331 2,264 2,201 2,137 2,128
eptv 0,031 0,036 0,043 0.057 0.067 0.098 0,120 0,134
eptw 0,450 0,491 0,457 0.522 0,554 0,630 0,649
u'2y'1 u"
u''w'f
u'v"l u' 3
u'v"l
v'''w'f
u"
u"
u"
v'w'" u"
u'v'w u"
-0.219 -0,211 -0.159 -0,213 -0,253 -0,300 -0,306 -0,256 -0,107 0,054
0.160 0,243 0.184 0,200 0.257 0,294 0.260 0,228 0,217 0.196
-0,222 -0.185 -0.168 -0,153 -0,153 -0.142 -0,137 -0,098 -0,057 -0.048
0,264 0,324 0,258 0,250 0,207 0,152 0,080 0.077 0,080 0,110
-0,089 -0,078 -0.060 -0,049 -0,016 0.015 0.056 0,091 0,178 0,185
0,040 0,043 0,018 0,011 -0,001 -0.034 -0.050 -0,090 -0.089 -0,089
0,049 0,060 0,061 0.058 0.050 0.053 0,043 0,039 0,025 0,012
f
/
ANGULAR POSITION 90° Tw=48,65°C u· '" 1.029 m/s Average friction velo city u' =1,019 m/s Average velo city in the wall eha Ub = 19,4 mts
REFERENCE: LOCAL Wall heat flux Loc
yJymax
Y+
UJUb
U+
k+
u'/u"
Vi/V'"
0,186 0,211 0,248 0,310 0.372 0,496 0.620 0,744 0,993 1,000
100,300 113,000 131.900 163,400 195,000 258.100 321.200 384,300 510,500 514,300
0,871 0,883 0,903 0,928 0,956 0,991 1.019 1.035 1,052 1,050
16,210 16,440 16,790 17,270 17,790 18,430 18,950 19,260 19,570 19,530
2,464 2,394 2.288 2,156 1,999 1.794 1.582 1,410 1,233 1,210
1,710 1,692 1.665 1,621 1,567 1,466 1,361 1,259 1,145 1,135
0,849 0,826 0.797 0,764 0,733 0,684 0.648 0,611 0,581 0,578
REYNOLDS NUMBER = 65000 q=1,39 kWJm 2
P"'U77K
T" =1, 193 K Tb=29,1°C
w'/w"
U'y'J u' 2
u'w'J u"
-v'w'J u· 2
S(ul
KM
SM
KM
Slwl
K(wl
epsy
1,133 1.115 1.081 1,050 1,003 0,985 0,945 0,928 0,904 0,892
0,676 0,668 0.630 0,609 0,551 0.445 0,349 0,236 0.030 0,024
-0,189 -0,167 -0.161 -0,189 -0,187 -0,215 -0,202 -0,217 -0,197 -0,194
-0,098 -0,090 -0,077 -0,064 -0,059 -0,040 -0,046 -0,043 -0,046 -0,057
0,012 0,029 0,025 0.007 -0.008 -0,051 -0.056 0,010 0,210 0,189
2,839 2,854 2.852 2,854 2,899 3,005 3,127 3.309 3,326 3,310
-0,333 -0,295 -0.282 -0,244 -0,248 -0,292 -0,284 -0,257 0,036 0,056
3,691 3,591 3,539 3,454 3,437 3,532 3,582 3,739 3,852 3,884
-0,130 -0,126 -0,096 -0,010 0,012 0,091 0,119 0,199 0,261 0,255
3,393 3,313 3,347 3,391 3,333 3,395
0,077 0,074 0.070 0,076 0.084 0,095 0,100 0,175
30444
3,454 30418
3,409
epsw
... 0
(J't
I yJymax 0,186 0,211 0,248 0,310 0,372 0,496 0,620 0,744 0,993 1,000
y+
(Tw-Tl( tTw-Tbl
TJT"
-0,165 -0.136 -0,102 -0,056 -0,014 0,063 0,105 0,143 0,162 0,164
1,983 2,010 2,010 2,057 2,084 2,092 2,066 2,090 2,061 2,046
100,300 113,000 131,900 163,400 195,000 258,100 321,200 384,300 510,500 514,300
TABLE I cant.
-u'T'1 u+T"
v'TI
w'T'J
u*T*
u'T'
2,054 2,030 2,003 1,975 1,912 1,739 1,517 1,365 1,166 1,131
0,333 0,339 0,331 0,342 0,329 0,303 0,259 0,208 0,092 0,082
-0,613 -0,610 -0,596 -0,697 -0,704 -0,861 -0,858 -0,965 -1,026 -0,956
sm
Km
-U!B5 -1,966 -2,015 -2,114 -2,215 -2,356 -2,359 -2,440 -2,550 -2,449
3,543 3,540 3,544 3,466 3,450 3.478 3.431 3,379 3,422 3,350
eptv 0,035 0,040 0,046 0,060 0,069 0,085 0,093 0,092
eptw
u"y'J u"
u"w'J
-0.292 -0.264 -0,253 -0,255 -0,259 -0,290 -0,274 -0,207 0,019 0,019
0,216 0,237 0,235 0,249 0,246 0,295 0,250 0,267 0,265 0,231
uH
u'v"J u··
u'v"J u"
y''w'J u"
V 1 W'2/
-0,263 -0,237 -0,201 -0,177 -0,159 -0,155 -0,139 -0,107 -0,063 -0,062
0,129 0,145 0,114 0,151 0,111 0,164 0,187 0,238 0,306 0,261
-0,101 -0,090 -0,083 -0,062 -0,058 -0,027 0,038 0,068 0,128 0,113
0,023 0,032 0,026 -0,002 -0,009 -0,026 -0,045 -0,031 -0,012 -0,009
u"
0.047 0,040 0,038 0,046 0,028 0,020 0,036 0,029 0,012 0,016
