123
Appendix A - List of assumptions
Steady-state simulations
Influence of temperature is negligible.
Heat exchanger central plane taken as symmetry plane.
Differential window-zone flow area in square and rotated triangular configurations is
negligible.
Simulations are split into three separate sections.
Nozzle connections are omitted, as they have negligible influence.
Baffle rod supports are omitted, as they have negligible influence.
Baffle-shell and baffle-tube leakages are omitted.
Smooth wall roughness has negligible influence.
Convergence is reached when residuals and change in pressure drop fall below 10
-3
and 0,1
Pascal per iteration, respectively.
Transient simulations
The geometry is simplified in order to lessen computational requirements.
The majority of the deposition of particles will be concentrated in the first four compartments
and transportation of sediment downstream will only commence after significant deposits
have already formed in the initial compartments.
A comparison of trends within simplified geometries will be sufficient.
Inlet velocity that is decreased, enhances convergence behaviour.
150 internal iterations sufficient to allow for general convergence
Sediment is modelled as fired clay.
Sediment inlet concentration is assumed to be 30%.
Particle size is assumed to be 1 mm.
ΔP
34969.58
ΔP
c
2407.692
ΔP
34969.58
ΔP
ec
8361.513
ΔP
wz
2262.008
ΔP
n
997.561
N
u
6
ρ
s
997.561
ΔP
c
2407.692
ΔP
wz
2262.007925
ΔP
ec
8361.513
ΔP
n
997.561
f
0.424861
f
0.424861
ΔP
cdn
1989.614644
L
0.3955
L
0.3955
ΔP
b
409.4846711
u
sc
0.81094
θ
0.944711
A
wz
0.089172637
P
p
0.027712
B
c
28.26923
α
2.237571076
θ
0.944711
u
sc
0.81094
A
bm
0.134124457
N
c
14
A
sc
0.179076
d
bs
0.413246371
D
s
0.91
γ
1.148160499
B
s
0.858
r
b
0.382275571
B
c
28.26923
θ
B
1.69054331
H
0.25725
u
wz
1.62852783
V
0.14522
k
2
0.066813331
A
sc
0.179076
k
1
0.242741662
D
0
0.890647
k
0.309554993
d
0.025
A
1.006031511
P
0.032
B
0.241286341
P
t
0.032
r
b/dbs
0.925054877
Re
s
18267.77
C
f
0.149163
f
l
1
A
wz
0.089173
α
Rad
2.237571
α
Deg
128.2034
D
b
0.9055
N
wt
128
A
bm
0.134124
d
bs
0.413246
i γ
Rad
1.14816
γ
Deg
65.78475
r
b
0.382276
θ
B,rad
1.690543
θ
B,deg
96.861
k
0.309555
u
wz
1.628528
k
2
0.066813
k
1
0.242742
k
0.309555
A
1.006032
i B
0.241286
N
w
16
i
i
i
Variables
Nozzle
Cross Flow
Triangular
Window Zone
End Cross Flow
ΔP
33249.2
ΔP
Q
1432.214
ΔP
33249.2
S/D
0.942857 Valid
t/d
1.28 Valid
ΔP
QE
2304.447
H/D
0.282692 Valid
D/d
36.4 Valid
ΔP
F
3413.612
R
B
0 Valid
Re
18267.77 Valid
ΔP
S
997.561
N
u
6
ΔP
Q,0
1432.214
ΔP
Q
1432.214
ΔP
QE
2304.447
ΔP
F
3413.612
ΔP
S
997.561
f
L
1
ΔP
Q,0
1432.214
ΔP
QE,0
2304.447
n
WF
7.426168
w
S
1
f
B
1
w
e
0.650978
A
E,E
0.2314
d
g
0.032203
ξ
0.483992
A
E
0.22308
w
e,E
0.627572
A
F
0.089173
n
w
14
A
inlet
0.14522
Re
E
1.76E+04
U
F
11.07621
w
e
0.650978
V
0.14522
ξ
E,f
0.488743
A
FG
0.152004
ρ
997.561
a
1.28
ξ
E,v
0.488787
A
FR
0.062832
V
0.14522
b
1.108513
ξ
lE
0.012683
w
z
1.029629
A
E
0.22308
e
0.007
ξ
tE
0.476103
w
P
1.628528
S
0.858
e
1
0.024
f
z,lE
1
L
E
0.26
L
E
0.26
f
z,tE
1
d
S
0.43
ξ
l
1.22E-02
A
inlet
0.14522
ξ
t
0.471765
e
0.007
f
z,l
1.00E+00
e
1
0.024
f
z,t
1
e
c
0.022
Re
1.83E+04
a
1.28
f
a,l,f/v
223.3609
b
1.108513
f
a,t,f
0.696263
s
q
0.032
f
a,t,v
5.484626
s
l
0.027713
ξ
f
4.84E-01
d
a
0.025
ξ
v
4.84E-01
D
i
0.91
f
L
0.707826
n
tubes
26
f
B
1
ξ
l
0.012227
R
M
0.231714
ξ
t
0.471765
R
L
0.079708
f
z,l
1
A
SMU
0.00412
f
z,t
1
A
SG
0.017781
i Re
18267.77
A
SRU
0.013661
f
a,l,f/v
223.3609
γ
2.248605
f
a,t,f/v
5.484626
r
0.615243
η
0.000889
R
B
0
η
w
0.000889
A
B
0
R
M
0.231714
D
B
0.890647
R
L
0.079708
A
SMU
0.00412
A
SG
0.017781
A
SRU
0.013661
n
556
i n
f
256
d
B
0.0258
D
L
0.9055
γ
Rad
2.248605
γ
Deg
128.8356
H
0.25725
r
0.615243
β
3.7
R
B
0
R
S
0
A
B
0
i D
B
0.890647
S
E
0.89
n
WE
24
ΔP
QE,0
2304.447
A
E,E
0.2314
w
e,E
0.627572
Re
E
17610.95
ξ
E
0.488787
ξ
lE
0.012683
ξ
tE
0.476103
i f
z,lE
1
f
z,tE
1
w
z
1.029629
n
WF
7.426168
d
g
0.032203
A
F
0.089173
U
F
11.07621
A
FG
0.152004
i A
FR
0.062832
w
P
1.628528
ξ
S
2
w
S
1
Window
Nozzle
Variables
Triangular
Crossflow
End Crossflow
33.00E+00 3.28E+00 43.28E+00 SimulationBase Size Prism Layer
ThicknessRelative Minimum Size Relative Target
Size Total Number of Cells Pressure Drop 1 40 mm2.5% (1 mm)40% (16 mm) 100% (40 mm) 749837 5.698805
Range V < 0 05 V < 0 05 0 05 < V < 0 1 0 05 < V < 0 1 0 1 < V < 0 15 0.1 < V < 0.15 0 15 < V < 0 2 0.15 < V < 0.20.2 < V < 0.250.2 < V < 0.250.25 < V < 0.50.25 < V < 0.50.5 < V 0.5 < V Range V < 0.05 V < 0.05 0.05 < V < 0.1 0.05 < V < 0.1 0 1 < V < 0 0 1 < V < 0 1 0 15 < V < 0 0.15 < V < 0.20 2 < V < 0 25 0.2 < V < 0.250.25 < V < 0.5 0.25 < V < 0.5 0.5 < V 0.5 < V Baffle 1Baffle 2Baffle 3Baffle 4Baffle 5Baffle 6Single_6178.7121Double_6182.3049DnD_6166.6419 RangeVolume# Elements SP Velocity> 0 5+0.5+
Main0.5+ NoSP
2 20 mm5% (1 mm)40% (8 mm) 100% (20 mm)2154792 8 785818 Single 61 0 036 0 036 0 079 0 079 0 127 0 127 0 176 0 176 0 225 0 225 0 356 0 355 1 112 1 022Single 61 0 002 0 002 0 009 0 0090 0180 0180 025 0 024 0 026 0 025 0 087 0 084 0 169 0 117Single 601 7961 9821 8521 8941 9401 876Single 6273 6421Double 6295 1519DnD 6272 5053 Single 610 336993693953 28223 3413 3413 341 3 20 mm5% (1 mm)30% (6 mm) 100% (20 mm)2918746 8 314031 Single 62 0 035 0 035 0 079 0 079 0 127 0 127 0 177 0 177 0 226 0 226 0 369 0 368 1 284 1 149Single 62 0 003 0 003 0 011 0 0100 0190 0180 025 0 024 0 030 0 029 0 133 0 128 0 245 0 188Single 901 6831 7981 7141 7231 7421 728Single 6353 8872Double 63115 3627DnD 6382 9183 Single 620 4661133156104 13094 1313 1953 308 4 12 mm5% (0 6 mm)40% (4 8 mm) 100% (12 mm)4885949 7 283291 Single 63 0 035 0 035 0 078 0 078 0 127 0 127 0 176 0 176 0 226 0 226 0 381 0 381 1 446 1 284Single 63 0 002 0 002 0 008 0 0070 0130 0120 018 0 017 0 021 0 021 0 097 0 092 0 177 0 138Double 601.7671.9991.9131.9241.9752.029Single_9156.9690Double_9155.1849DnD_9173.6303 Single_630.336293498863.81083.8902.9933.551 5 15 mm5% (0 75 40% (6 mm) 100% (15 mm)5894761 7 981239 Si l 91 0 035 0 035 0 078 0 078 0 126 0 126 0 175 0 175 0 225 0 225 0 363 0 362 1 019 0 992Si l 91 0 003 0 003 0 013 0 0130 0200 0190 022 0 022 0 024 0 023 0 099 0 095 0 171 0 145D bl 901.7571.8791.8281.7991.9201.841Single_9252.9033Double_9284.1546DnD_92107.9423 Single_910.352994775062.91333.7093.7093.709 Final 10 mm10% (1 mm)40% (4 mm) 100% (10 mm)9369395 7 594238 Single 92 0 034 0 035 0 078 0 078 0 126 0 126 0 175 0 175 0 225 0 225 0 373 0 372 1 117 1 060Single 92 0 005 0 005 0 018 0 0170 0240 0230 026 0 025 0 029 0 027 0 129 0 122 0 262 0 205DnD 601 7271 8381 9131 9241 9051 798Single 9381 3876Double 9389 1466DnD 9383 8502 Single 920 4924133400203 19903 2002 7022 986 Single_93 0.034 0.035 0.078 0.078 0.126 0.126 0.175 0.175 0.225 0.225 0.379 0.378 1.224 1.169Single_93 0.004 0.003 0.012 0.0110.0150.0140.018 0.017 0.020 0.019 0.098 0.091 0.185 0.150DnD_901.7511.8751.7471.7821.9051.823 Single_930.352795140623.03013.6143.1623.614 Double_61 0.025 0.022 0.043 0.040 0.036 0.034 0.024 0.023 0.019 0.018 0.057 0.052 0.114 0.071Double_61 0.025 0.022 0.043 0.0400.0360.0340.024 0.023 0.019 0.018 0.057 0.052 0.114 0.071 Single 60 Double 60 Double 6 Double 60 Double 6 Double 60 Double 610.3187115174404.03983.1114.0404.040 Double_62 0.029 0.029 0.072 0.072 0.123 0.123 0.174 0.175 0.225 0.225 0.379 0.380 0.952 0.928Double_62 0.042 0.039 0.058 0.0520.0390.0340.028 0.024 0.022 0.019 0.077 0.067 0.198 0.164 Single_61 3.247Double_61 3.387DnD_61 2.551Single_61 3.282Double_61 3.112DnD_612.924 Double 620.4644171363903.97874.1324.1324.132 Double_63 0.029 0.028 0.074 0.075 0.656 0.541 0.175 0.175 0.224 0.224 0.359 0.359 1.173 1.145Double_63 0.024 0.023 0.033 0.0310.0300.0260.025 0.022 0.021 0.018 0.061 0.052 0.126 0.100 Baffle 1Baffle 2Baffle 3Baffle 4Baffle 5Baffle 6Single_62 3.308Double_62 4.114DnD_62 4.310Single_62 4.131Double_62 3.973DnD_624.330 Double 630.3187115322705.92556.3285.5165.516 Double_91 0.030 0.030 0.073 0.073 0.125 0.125 0.175 0.175 0.225 0.225 0.368 0.367 0.859 0.837Double_91 0.027 0.025 0.045 0.0420.0360.0340.029 0.027 0.023 0.021 0.066 0.056 0.111 0.072Single_602.7202.9403.2983.2823.0703.337Single_63 3.551Double_63 5.096DnD_63 5.342Single_63 3.890Double_63 6.328DnD_635.342 D bl 910.3367117597703.43882.7893.4393.439 Double_92 0.028 0.028 0.070 0.070 0.123 0.124 0.175 0.175 0.225 0.225 0.384 0.384 0.849 0.835Double_92 0.032 0.029 0.058 0.0520.0440.0390.032 0.028 0.026 0.022 0.088 0.077 0.211 0.174Single_902.6242.5593.0222.8862.6902.758Single_91 3.441Double_91 3.325DnD_91 3.383Single_91 3.030Double_91 3.232DnD_913.048 D bl 920.4903181932403.63173.9303.9303.930 Double_93 0.039 0.036 0.035 0.029 0.023 0.019 0.018 0.015 0.016 0.014 0.055 0.047 0.152 0.118Double_93 0.027 0.026 0.040 0.0350.0320.0280.024 0.021 0.020 0.017 0.064 0.052 0.130 0.107Double 602.6173.3112.9973.2834.4805.162Single_92 2.986Double_92 3.917DnD_92 4.078Single_92 3.200Double_92 3.698DnD_924.018 Double 930.3364121132104.43344.9494.9494.949 DnD_61 0.032 0.032 0.076 0.076 0.124 0.124 0.175 0.175 0.225 0.239 0.363 0.361 0.893 0.872DnD_61 0.008 0.007 0.024 0.0240.0310.0300.030 0.029 0.026 0.025 0.081 0.071 0.117 0.073Double 902.4062.5662.8282.8934.0633.060Single_93 3.614Double_93 4.928DnD_93 5.030Single_93 3.031Double_93 4.563DnD_934.838 DnD_610.3191108502002.68413.0443.0443.044 DnD_62 0.024 0.023 0.070 0.070 0.124 0.124 0.175 0.175 0.225 0.225 0.382 0.384 0.982 0.957DnD_62 0.034 0.031 0.046 0.0420.0370.0340.030 0.028 0.025 0.023 0.088 0.079 0.205 0.167DnD_602.3972.5012.3072.5865.1133.122 DnD_620.4643169896304.34424.3303.8344.071 DnD_63 0.031 0.031 0.074 0.074 0.125 0.125 0.175 0.175 0.225 0.225 0.376 0.375 1.153 1.125DnD_63 0.011 0.009 0.018 0.0170.0220.0210.022 0.021 0.021 0.020 0.081 0.074 0.144 0.111DnD_902.6512.5102.2702.4734.6212.930 DnD_630.3187114771205.08265.3424.6175.342 DnD_91 0.029 0.029 0.075 0.074 0.126 0.126 0.174 0.174 0.224 0.224 0.368 0.366 0.685 0.681DnD_91 0.012 0.012 0.031 0.0290.0360.0340.035 0.033 0.029 0.027 0.081 0.071 0.114 0.072 Si l 60 D bl 60 Single_60D bl 60 DnD_60D bl 60 Single_61 1.237Double_61 0.863DnD_61 1.039Single_61 1.005Double_61 0.816DnD_611.039 DnD_910.3366117825303.38302.7273.3833.286 DnD_92 0.025 0.024 0.071 0.071 0.122 0.122 0.174 0.174 0.225 0.225 0.382 0.384 0.969 0.962DnD_92 0.057 0.050 0.062 0.0560.0440.0400.031 0.029 0.024 0.022 0.079 0.067 0.195 0.158 Single_62 1.239Double_62 0.750DnD_62 0.775Single_62 1.078Double_62 0.719DnD_620.893 DnD_920.4912170297604.01904.0783.9744.078 DnD_93 0.028 0.027 0.074 0.074 0.125 0.125 0.175 0.175 0.225 0.225 0.376 0.375 1.096 1.090DnD_93 0.010 0.008 0.022 0.0200.0240.0220.024 0.022 0.024 0.022 0.089 0.081 0.144 0.111 Single_63 1.260Double_63 0.993DnD_63 1.235Single_63 1.119Double_63 0.849DnD_631.005 DnD_930.3361124172604.71855.0304.5645.030
Single_91 1.023Double_91 0.839DnD_91 1.076Single_91 0.964Double_91 0.790DnD_910.680 Single_92 0.987Double_92 0.731DnD_92 0.751Single_92 0.908Double_92 0.688DnD_920.835
Range V < 0.05 V < 0.05 0.05 < V < 0.1 0.05 < V < 0.1 0 1 < V < 0 15 0.1 < V < 0.15 0 15 < V < 0 2 0.15 < V < 0.20.2 < V < 0.250.2 < V < 0.250.25 < V < 0.50.25 < V < 0.50.5 < V 0.5 < V Range V < 0.05 V < 0.05 0.05 < V < 0.1 0.05 < V < 0.1 0 1 < V < 0 0 1 < V < 0 0 15 < V < 0 0.15 < V < 0.20 2 < V < 0 25 0.2 < V < 0.250.25 < V < 0.5 0.25 < V < 0.5 0.5 < V 0.5 < V Single_93 1.012Double_93 0.869DnD_93 1.207Single_93 0.999Double_93 0.724DnD_930.960 RangeVolume# Elements Velocity < 0 Velocity < Velocity < Velocity < 0.5
Single_60 0.03532 0.03517 0.07849 0.078640.12679 0.126890.17619 0.17624 0.22558 0.22561 0.36861 0.36817 1.28089 1.15154Single_60 0.00786 0.00753 0.02753 0.026240.049570.047430.06755 0.065130.07734 0.075080.317730.303230.591590.44268 Single_601.13932034891 4.1314.1313.3413.551 Single_90 0.03469 0.03491 0.07800 0.078070.12590 0.125990.17527 0.17528 0.22541 0.22541 0.37152 0.37065 1.12009 1.07360Single_90 0.01254 0.01116 0.04358 0.040980.059200.056470.06609 0.063480.07203 0.069260.326480.307330.618080.49977 Single_901.19832331588 3.1993.7093.7093.709 Double_60 0.02754 0.02652 0.06304 0.062120.27185 0.232450.12464 0.12422 0.15595 0.15549 0.26500 0.26356 0.74668 0.71474Double_60 0.09001 0.08388 0.13431 0.122030.105380.093730.07722 0.068950.06172 0.054370.194900.171060.438230.33499 Single_60 3.551 Single_601.245 Single_60 4.131 Single 601.068 Double 601.10240186100 5.9256.3285.5165.516 Double_90 0.03233 0.03114 0.05959 0.057520.09013 0.088960.12248 0.12164 0.15528 0.15465 0.26901 0.26606 0.61981 0.59652Double_90 0.08666 0.08044 0.14250 0.129190.111950.101320.08502 0.076220.06814 0.060190.216740.184680.452360.35272 Single_90 3.614 Single_901.007 Single_90 3.200 Single 900.957 Double 901.16342066220 4.4334.9494.9494.949 DnD_60 0.02882 0.02864 0.07351 0.073600.12437 0.124410.17496 0.17504 0.22487 0.22952 0.37396 0.37317 1.00961 0.98478DnD_60 0.05254 0.04758 0.08859 0.082160.090260.085170.08267 0.078230.07261 0.068170.249810.225080.465640.35148 D bl 60 5.096 D bl 600.868 Double_606.328 D bl 60.795 DnD_601.10239316950 5.0835.3424.6175.342 DnD_90 0.02731 0.02689 0.07309 0.073170.12442 0.124600.17465 0.17471 0.22490 0.22490 0.37523 0.37492 0.91654 0.91091DnD_90 0.07849 0.06985 0.11443 0.104890.103830.096700.08991 0.083810.07603 0.070240.248960.218730.452250.34083 Double 90 4.928 Double 900.813 Double_904.563 Double 90.734 DnD_901.16441229550 4.7195.0304.5645.030
DnD_60 5.342 DnD_601.016 DnD_60 5.342 DnD_600.979 DnD_90 5.030 DnD_901.012 DnD_90 4.838 DnD_900.825 DnD_60 Single_60 Double_60 Single_60 Single_60 Double_90 Single_90 Double_90
Range V < 0.05 V < 0.05 0.05 < V < 0.1 0.05 < V < 0.1 0 1 < V < 0 0 1 < V < 0 0 15 < V < 0 0.15 < V < 0.20 2 < V < 0 25 0.2 < V < 0.250.25 < V < 0.5 0.25 < V < 0.5 0.5 < V 0.5 < V Configuration BypassBundle Configuratio BypassBundle Single_60 0.690 0.661 2.417 2.3034.3514.1645.930 5.718 6.789 6.591 27.891 26.618 51.930 38.858 Single_60 4.9373.341 Single_60 4.857 3.341 Single_90 1.047 0.932 3.638 3.4214.9414.7145.516 5.299 6.013 5.781 27.252 25.653 51.593 41.717 Single_90 4.6343.709 Single_90 3.852 3.709 Double_60 8.169 7.614 12.190 11.0769.5648.5087.009 6.258 5.602 4.934 17.689 15.526 39.775 30.404 Double_60 4.7695.516 Double_604.761 5.516 Double_90 7.449 6.915 12.249 11.1059.6238.7107.308 6.552 5.857 5.174 18.630 15.874 38.883 30.319 Double_90 4.5624.949 Double_903.875 4.949 DnD_60 4.767 4.317 8.038 7.4558.1907.7287.501 7.098 6.588 6.186 22.666 20.422 42.250 31.892 DnD_60 4.3254.617 DnD_60 4.238 4.617 DnD_90 6.743 6.002 9.832 9.0128.9218.3087.725 7.201 6.532 6.034 21.390 18.792 38.856 29.283 DnD_90 4.4524.564 DnD_90 4.162 4.564 Single_60 1.580 Single_60 1.277 Single_90 1.194 Single_90 1.061 Double_60 0.980 Double_600.890 Double_90 0.890 Double_900.810 0.187595658 0.212154 0.198461953 1.273205977 13.0717423 DnD_60 1.000 DnD_60 1.065 0.227605307 0.217262 0.231201289 1.59826468 9.87542025 DnD_90 1.018 DnD_90 3.484 1.056861889 0.751154 0.667893417 2.163482663 9.37048291 0.913703873 0.756294 0.683304777 2.755747406 8.56434 0.461740116 0.403258 0.402586381 2.243710776 10.3582714 0.612269 0.523861 0.4975292 2.59797039 9.572746475
ConfigurationNb f Base sizeP i lR l ti i i R l ti t Pressure drop 1508057 50 8 40 250 9.78042 2785953 40 8 40 250 10.52572 3853773 30 10 50 250 10.47048 41135974 30 6 34 250 11.15531 51988564 25 6 40 200 11.08486 62973626 25 6 34 250 11.16434
verage bundle-shell velo Velocity Averages Velocity Averages Total volume for threshold above the specified range
Velocity Averages Velocity Averages Total volume for threshold above the specified range
Average baffle cut veloctiy
Maximum bundle-shell veloc Average bundle-shell veloc Maximum baffle cut veloctiy##dd93
Maximum bundle-shell velo
Max Velocities and volumes and number of elements
Max Velocity Average bundle-shell bypass velocity different sections of configurations
Maximum wall Y+ values for different sections of configurations
Maximum bundle-shell bypass velocity different sections of configurationsMaximum pass-partition bypass velocity different sections of configurations Average pass-partition bypass velocity different sections of configurations
Maximum pass-partition velocity Average bundle-shell velocity Average pass-partition veloc
Mesh independence study of the transient multiphase simulations
Maximum bundle-shell velocity Total volume for threshold above the specified range
0 1 2 3 4 5 6 7 8 9 10 0100000020000003000000400000050000006000000700000080000009000000 10000000 Pre ss ure drop Number of elements Mesh sensitivity study
Pressure Drop 0.000 5.000 10.000 15.000 20.000 25.000 30.000 35.000 40.000 45.000 0 1 2 3 4 5 6 7 8 Single_60 Single_90 Double_60 Double_90 DnD_60 DnD_90 9.6 9.8 10 10.2 10.4 10.6 10.811 11.2 11.4 0 1000000200000030000004000000 Pre ssure dro p (kP a) Number of elements Mesh sensitivity study
Series1
