Hydrocarbon Processing - February 2022 - 70
Heat Transfer
On solving the same problem
using CFD software, the average
temperature at the bottom of the
trunnion support is (Eq. 26):
TH |CFD ≈ 560 K or 287°C (26)
Similarly, the temperature at
the bottom of the shoe support
has been calculated at various
air velocities and the results
have been compared with CFD
simulation results.
FIG. 6. Temperature contours for (a) shoe support and (b) trunnion support.
5. For the conductive heat loss rate
through the pipe shoe, Eq. 27
is used:
Q! =
10.3768 × 0.857534 ×
39.78 × 0.0076795.
(788−295).tanh
× 0.25
Or
10.3768 × 0.857534
39.78 × 0.0076795
Q ! = 710.32 W
Comparison of
FIG. 7. Comparison of results (average temperature at the bottom of the pipe support)
with CFD simulation results for (a) shoe support and (b) trunnion support.
1. For trunnion material, carbon
steel @ 788 K, k = 39.78 W/m-K
2. For an air velocity of 2 m/sec in a
forced convection case (Eq. 21):
1.225 × 2
Re =
ρvD
µ
Pr =
µCp
kair
=
× 0.2731
1.7894 ×
10 − 5
=
= 37392.14
1.7894 × 10 − 5
0.0242
Re × Pr = 27826.33
Nu = 0.3 +
⎡
⎣
⎢ 1+
⎛
⎝
Using Nu =
gives h =
⎛
⎝
⎜
⎜
⎜
where the trunnion height H =
250 mm or 0.25 m.
3. Given trunnion thickness t =
9.27 mm (Eqs. 22 and 23):
P = π × D = 857.534 mm =
0.857534 m
Ac = 0.25π × {(D2
0.0076795 mm2
= 0.74418
>0.2;
Churchill equation
is appliable
⎣⎡1+ 0.4/Pr)2/3 1/4
4/5
0.62Re1/2Pr1/3
(
Re
282000
hD
kair
;
Nu.kair
D
= 10.3768
70 FEBRUARY 2022 | HydrocarbonProcessing.com
⎞
⎠
5/8
⎤
⎦
⎥
⎦⎤
= 117.1031
cosh
(21)
On solving, we get Eq. 25:
TH
= 534.7 K or 261.7°C (25)
⎞
⎠
⎟
⎟
⎟
TH −T∞
Tb −T∞
cosh
=
cosh mH
1
or
⎛
⎜⎝
hP
kAc
TH −295
788−295
⎛
⎜⎝
=
cosh mH
1
10.3768 × 0.857534
39.78 × 0.0076795
⎞
⎟⎠
× 0.25
⎞
⎟⎠
H
1
=
(24)
- (D - 2t)2
(22)
} =
(23)
4. Using Eq. 10, we calculate Eq. 24:
1
=
(27)
results with CFD
analysis.
* Physical system and CFD
modelling: Dimensions of the
pipe support and input parameters
are taken as per respective
problem statements (FIGS. 4
and 5). The type of element
used for the simulation is a
" tetrahedral element " throughout
the computational domain.
This choice of elements is
advantageous with little distortion
in mesh for complex geometries.
The mesh is refined near the
solid fluid interface to accurately
capture the higher gradients
in properties. A coarse mesh
is otherwise used to save
simulation time.
This problem was studied
numerically by solving the
relevant governing equations
(i.e., conservation of momentum
equation, continuity equation
and energy equation) for the
given boundary conditions.
In the study, the following
assumptions were made:
° Fluid flow over the pipe support
is laminar and incompressible
° Heat loss due to radiation is
negligible
http://www.HydrocarbonProcessing.com
Hydrocarbon Processing - February 2022
Table of Contents for the Digital Edition of Hydrocarbon Processing - February 2022
Contents
Hydrocarbon Processing - February 2022 - Cover1
Hydrocarbon Processing - February 2022 - Cover2
Hydrocarbon Processing - February 2022 - Contents
Hydrocarbon Processing - February 2022 - 4
Hydrocarbon Processing - February 2022 - 5
Hydrocarbon Processing - February 2022 - 6
Hydrocarbon Processing - February 2022 - 7
Hydrocarbon Processing - February 2022 - 8
Hydrocarbon Processing - February 2022 - 9
Hydrocarbon Processing - February 2022 - 10
Hydrocarbon Processing - February 2022 - 11
Hydrocarbon Processing - February 2022 - 12
Hydrocarbon Processing - February 2022 - 13
Hydrocarbon Processing - February 2022 - 14
Hydrocarbon Processing - February 2022 - 15
Hydrocarbon Processing - February 2022 - 16
Hydrocarbon Processing - February 2022 - 17
Hydrocarbon Processing - February 2022 - 18
Hydrocarbon Processing - February 2022 - 19
Hydrocarbon Processing - February 2022 - 20
Hydrocarbon Processing - February 2022 - 21
Hydrocarbon Processing - February 2022 - 22
Hydrocarbon Processing - February 2022 - 23
Hydrocarbon Processing - February 2022 - 24
Hydrocarbon Processing - February 2022 - 25
Hydrocarbon Processing - February 2022 - 26
Hydrocarbon Processing - February 2022 - 27
Hydrocarbon Processing - February 2022 - 28
Hydrocarbon Processing - February 2022 - 29
Hydrocarbon Processing - February 2022 - 30
Hydrocarbon Processing - February 2022 - 31
Hydrocarbon Processing - February 2022 - 32
Hydrocarbon Processing - February 2022 - 33
Hydrocarbon Processing - February 2022 - 34
Hydrocarbon Processing - February 2022 - 35
Hydrocarbon Processing - February 2022 - 36
Hydrocarbon Processing - February 2022 - 37
Hydrocarbon Processing - February 2022 - 38
Hydrocarbon Processing - February 2022 - 39
Hydrocarbon Processing - February 2022 - 40
Hydrocarbon Processing - February 2022 - 41
Hydrocarbon Processing - February 2022 - 42
Hydrocarbon Processing - February 2022 - 43
Hydrocarbon Processing - February 2022 - 44
Hydrocarbon Processing - February 2022 - 45
Hydrocarbon Processing - February 2022 - 46
Hydrocarbon Processing - February 2022 - 47
Hydrocarbon Processing - February 2022 - 48
Hydrocarbon Processing - February 2022 - 49
Hydrocarbon Processing - February 2022 - 50
Hydrocarbon Processing - February 2022 - 51
Hydrocarbon Processing - February 2022 - 52
Hydrocarbon Processing - February 2022 - 53
Hydrocarbon Processing - February 2022 - 54
Hydrocarbon Processing - February 2022 - 55
Hydrocarbon Processing - February 2022 - 56
Hydrocarbon Processing - February 2022 - 57
Hydrocarbon Processing - February 2022 - 58
Hydrocarbon Processing - February 2022 - 59
Hydrocarbon Processing - February 2022 - 60
Hydrocarbon Processing - February 2022 - 61
Hydrocarbon Processing - February 2022 - 62
Hydrocarbon Processing - February 2022 - 63
Hydrocarbon Processing - February 2022 - 64
Hydrocarbon Processing - February 2022 - 65
Hydrocarbon Processing - February 2022 - 66
Hydrocarbon Processing - February 2022 - 67
Hydrocarbon Processing - February 2022 - 68
Hydrocarbon Processing - February 2022 - 69
Hydrocarbon Processing - February 2022 - 70
Hydrocarbon Processing - February 2022 - 71
Hydrocarbon Processing - February 2022 - 72
Hydrocarbon Processing - February 2022 - 73
Hydrocarbon Processing - February 2022 - 74
Hydrocarbon Processing - February 2022 - 75
Hydrocarbon Processing - February 2022 - 76
Hydrocarbon Processing - February 2022 - 77
Hydrocarbon Processing - February 2022 - 78
Hydrocarbon Processing - February 2022 - 79
Hydrocarbon Processing - February 2022 - 80
Hydrocarbon Processing - February 2022 - 81
Hydrocarbon Processing - February 2022 - 82
Hydrocarbon Processing - February 2022 - Cover3
Hydrocarbon Processing - February 2022 - Cover4
Hydrocarbon Processing - February 2022 - GP-1
Hydrocarbon Processing - February 2022 - GP-2
Hydrocarbon Processing - February 2022 - GP-3
Hydrocarbon Processing - February 2022 - GP-4
Hydrocarbon Processing - February 2022 - GP-5
Hydrocarbon Processing - February 2022 - GP-6
Hydrocarbon Processing - February 2022 - GP-7
Hydrocarbon Processing - February 2022 - GP-8
Hydrocarbon Processing - February 2022 - GP-9
Hydrocarbon Processing - February 2022 - GP-10
Hydrocarbon Processing - February 2022 - GP-11
Hydrocarbon Processing - February 2022 - GP-12
Hydrocarbon Processing - February 2022 - GP-13
Hydrocarbon Processing - February 2022 - GP-14
Hydrocarbon Processing - February 2022 - GP-15
Hydrocarbon Processing - February 2022 - GP-16
Hydrocarbon Processing - February 2022 - GP-17
Hydrocarbon Processing - February 2022 - GP-18
Hydrocarbon Processing - February 2022 - GP-19
Hydrocarbon Processing - February 2022 - GP-20
Hydrocarbon Processing - February 2022 - GP-21
Hydrocarbon Processing - February 2022 - GP-22
Hydrocarbon Processing - February 2022 - GP-23
Hydrocarbon Processing - February 2022 - GP-24
Hydrocarbon Processing - February 2022 - GP-25
Hydrocarbon Processing - February 2022 - GP-26
Hydrocarbon Processing - February 2022 - GP-27
Hydrocarbon Processing - February 2022 - GP-28
Hydrocarbon Processing - February 2022 - GP-29
Hydrocarbon Processing - February 2022 - GP-30
Hydrocarbon Processing - February 2022 - GP-31
Hydrocarbon Processing - February 2022 - GP-32
Hydrocarbon Processing - February 2022 - GP-33
Hydrocarbon Processing - February 2022 - GP-34
Hydrocarbon Processing - February 2022 - GP-35
Hydrocarbon Processing - February 2022 - GP-36
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