THERMOWELL VIBRAT VIBR ATION ION When fluid flows past a thermowell, the change in fluid momentum creates a turbulent wake behind the well. Vortices form in this wake, and shed from alternate sides of the well. The vortex shedding frequency (or Wake frequency is linear with flow velocity and inversely proportional to thermowell tip diameter. These shedding vortices impose on the thermowell, a periodic force comprising two components ! (i a lift force, normal to direction of flow, oscillating at the wake frequency, and (ii a smaller drag force, parallel to flow, oscillating at twice the wake frequency. These vortex"induced forces, which cause thermowell vibration, are normally small with the magnitude of the vibrations generally negligible. #owever, as the wake frequency (fw approaches the natural frequency (fn of the thermowell (within $%&, it can shift and lock"in to the natural frequency. When fw ' fn, the thermowell goes into resonance, and vibrating forces increase rapidly. The resultant vibrations can cause mechanical failure of the well. The urdock calculations (and companion )*+ T- /.0 consider only the oscillating lift force as the cause of thermowell vibration. The ratio of wake to natural frequency is restricted to a maximum of %.1 to eliminate the possibility of resonance. )lthough the oscillating drag force is small, it can force the thermowell into resonance at lower velocities because it occurs at twice the wake frequency. 2or high"density fluids (liquids and high pressure steam, the urdock analysis is not adequate. When the oscillating drag component is included, the velocity rating can be reduced by up to 3%&. The calculations included herein are modified to include in"line resonance due to the oscillating drag force, correction for the magnification ratio and use of the actual natural frequency of the well rather than the estimated value. The results of these calculations should only be used as a guide in the selection of the correct thermowell. 4ther variables, like corrosion, should be evaluated and influence the decision.
Thermowell Velocity Rating (Program Ver. 4.2a)
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Fluid Operating Temperature
To
Operating Pressure
Po
Fluid Velocity
@
2.01
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0.01
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@1
0.079
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0.01
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/A t!sec
84T+*
%all t+ic,ness is less t+an recommended %ell taper is less t+an recommended
T+ese calculations are perormed according to t+e paper :Poer Test ;ode T+ermometer %ells: and also meet t+e re-uirements o &8 PT; 19.3?199$. T+e program supplies results +ic+ s+ould only and accepts no lia arising rom error or misinormation supplied +erein> or due to program misuse.
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0.$#0 1.050 1.315 1.""0 1.900 2.375 2.$75 3.500 #.000 #.500 5.5"3 "."25 $."25 10.750 12.750 1#.000 1".000 1$.000 20.000 22.000 2#.000 2".000 2$.000 30.000 32.000 3#.000 3".000 #2.000
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1.1$5 1.530 1.770 2.2#5 2.709 3.33# 3.$3# #.33# 5.3#5 ".#07 $.#07 10.#$2 12.#3$ 13."$$ 15."70 17."70 19."2# 21."2# 23.572
1.097 1.##2 1."$2 2.157 2."35 3.2"0 3.7"0 #.2"0 5.295 ".357 $.329 10.#20 12.390 13."2# 15."2# 17.500 19.500 21."2# 23.500
29.500
29.37"
1.097 1.##2 1."$2 2.157 2."35 3.2"0 3.7"0 #.2"0 5.295 ".357 $.329 10.#20 12.390 13.500 15.500 17.500 19.500 21.500 23.500 25.37" 27.37" 29.37" 31.37" 33.37" 35.37"
29.37"
%$$.125 10.250 12.250 13.250 15.500 15.37" 19.250 21.250 23.250 25.000 27.000 29.000 31.000 33.000 35.000
0%
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*T9 0."22 0.$2#
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1.0#9 1.3$0 1."10 2.0"7 2.#"9 3.0"$ 3.5#$ #.02" 5.0#7 ".0"5 7.9$1 10.020 12.000 13.250 15.250 17.250 19.250 21.250 23.250 25.750 27.750 29.750 31.750 33.750 35.750 #1.750
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30."2# 32."2# 3#.500
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D# 0.5#" 0.7#2 0.957 1.27$ 1.500 1.939 2.323 2.900 3.3"# 3.$2" #.$13 5.7"1 7."25 9.5"0 11.750 13.000 15.000 17.000 19.000 21.000 23.000 25.000 27.000 29.000 31.000 33.000 35.000 #1.000
1% 0.5#" 0.7#2 0.957 1.27$ 1.500 1.939 2.323 2.900 3.3"# 3.$2" #.$13 5.7"1 7."25 9.5"2 11.37# 12.500 1#.312 1".12" 17.93$ 19.750 21.5"#
%%
7.#37 9.312 11.0"2 12.12# 1#.93$ 15."$$ 17.5"7 19.250 20.93$
%$3."2# #.5"3 5.501 7.1$7 9.0"2 10.750 11.$12 13.5"2 15.250 17.000 1$.750 20.37"
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7.001 $.750 10.500 11.500 13.12# 1#.$7" 1".500 1$.250 19.$7"
A% 0.#"" 0."12 0.$15 1.1"0 1.33$ 1."$7 2.125 2."2#
DD# 0.252 0.#3# 0.599 0.$9" 1.100 1.503 1.771 2.300
3.#3$ #.313 5.1$9 ".$13 $.500 10.12" 11.1$$ 12.$12 1#.#3$ 1".0"# 1 7.750 19.31#
3.152 #.0"3 #.$97 ".$75 9.750 11.750
T#+:4W+== V+=4->TC :)T>8E
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(extracted from )*+ *team Tables for >ndustrial ;se, //@ +dition
*pecific Volume (ft0 Flb Temperature (B2
ressure
(w
(psia
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0%%
?%%
3%%
A%%
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1%%
/%%
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0.01"
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##.99
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57.0#
"3.03
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0.01" 0.01" 0.01" 0.01" 0.01" 0.01" 0.01"
0.017 0.017 0.017 0.017 0.017 0.017 0.017
29.90 22.3" 17.$" 1#.$1 12."5 11.0# 9.7$2
33.9" 25.#3 20.3# 1".$9 1#.#5 12."2 11.21
37.99 2$.#" 22.7$ 1$.93 1".21 1#.17 12.5$
#1.99 31.#7 25.20 20.95 17.9# 15."7 13.9#
#5.9$ 3#.#7 27."0 22.95 19."" 17.20 15.2$
#9.9" 37.#" 30.01 2#.95 21.3$ 1$.70 1"."2
53.95 #0.#5 32.#0 2".95 23.09 20.20 17.9"
57.93 #3.## 3#.$0 2$.9# 2#.$0 21.70 19.29
"1.91 #".#2 37.19 30.9# 2".51 23.19 20."2
0.01" 0.01" 0.01" 0.01"
0.01"
0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.01" 0.017 0.01" 0.01" 0.01" 0.01" 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.01" 0.01" 0.01" 0.01" 0.01" 0.01" 0.01"
$.7"9 "."7$ 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017
10.0" 7."9$ "."#5 #.93" 2.3"1 1.$"1 0.019 0.019 0.019 0.019 0.01$ 0.019 0.019 0.019 0.019 0.019 0.01$ 0.01$ 0.01$ 0.01$ 0.01$ 0.01$ 0.01$ 0.01$ 0.01$ 0.01$ 0.01$ 0.01$ 0.01$
11.31 $.""7 7.#9# 5.5$$ 2.725 2.15# 1.7"7 1.2$5 0.993 0.795 0."93 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.019 0.019
12.53 10.1$ $.320 ".217 3.059 2.#30 2.005 1.#77 1.159 0.9#" 0.$29 0.793 0."7$ 0.5$7 0.51# 0.#02 0.31$ 0.272 0.02# 0.023 0.023 0.023 0.023 0.023 0.023 0.022 0.022 0.021 0.021
13.7# 10.55 9.135 ".$3# 3.379 2."93 2.227 1."51 1.30# 1.073 0.9#" 0.90$ 0.7$3 0."$" 0."09 0.#91 0.#0" 0.357 0.3#2 0.291 0.2#9 0.1"9 0.09$ 0.092 0.031 0.029 0.027 0.025 0.023
1#.95 11.#9 9.9#5 7.##" 3."93 2.9#$ 2.##2 1.$17 1.##1 1.190 1.053 1.011 0.$77 0.771 0."$$ 0.5"2 0.#72 0.#20 0.#03 0.350 0.307 0.230 0.17" 0.1"7 0.13" 0.105 0.059 0.032 0.027
1".15 12.#1 10.75 $.053 #.003 3.19$ 2."53 1.97$ 1.573 1.302 1.15# 1.109 0.9"# 0.$50 0.7"1 0."2" 0.529 0.#73 0.#5" 0.399 0.353 0.272 0.21" 0.20$ 0.17" 0.1#" 0.10# 0.051 0.03"
17.35 13.3# 11.55 $."5$ #.310 3.##" 2.$"1 2.13" 1.701 1.#11 1.252 1.20# 1.0#$ 0.92" 0.$31 0."$" 0.5$2 0.522 0.503 0.##3 0.39# 0.30$ 0.2#9 0.2#0 0.207 0.175 0.131 0.07# 0.050
0.01"
0.01"
0.017
0.017
0.01$
0.019
0.022
0.02#
0.02$
0.03#
0.01" 0.01" 0.01" 0.01" 0.01" 0.01" 0.01" 0.01" 0.01" 0.01" 0.01" 0.01" 0.01" 0.01" 0.01" 0.01" 0.01" 0.01" 0.01" 0.01" 0.01" 0.01" 0.01" 0.01"
%%%
%%
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10#.$
110.7"
11".72
"5.$$ #9.#1 39.5$ 32.93 2$.22 2#."9 21.95
"9.$" 52.39 #1.9$ 3#.92 29.93 2".1$ 23.2$
73.$3 55.37 ##.37 3".95 31."3 27."$ 2#."1
77.$1 5$.3" #".7" 3$.90 33.3# 29.17 25.9#
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