THERMOWELL VIBRATION

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. However, as the wake frequency (fw) approaches the natural frequency (fn) of the thermowell (within 20%), 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 Murdock calculations (and companion ASME PTC 19.3) 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 0.8 to eliminate the possibility of resonance. Although the oscillating drag force is small, it can force the thermowell into resonance at lower velocities because it occurs at twice the wake frequency. For high-density fluids (liquids and high pressure steam), the Murdock analysis is not adequate. When the oscillating drag component is included, the velocity rating can be reduced by up to 50%.

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. Other variables, like corrosion, should be evaluated and influence the decision.

THERMOWELL VIBRATION

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. However, as the wake frequency (fw) approaches the natural frequency (fn) of the thermowell (within 20%), 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 Murdock calculations (and companion ASME PTC 19.3) 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 0.8 to eliminate the possibility of resonance. Although the oscillating drag force is small, it can force the thermowell into resonance at lower velocities because it occurs at twice the wake frequency. For high-density fluids (liquids and high pressure steam), the Murdock analysis is not adequate. When the oscillating drag component is included, the velocity rating can be reduced by up to 50%.

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. Other variables, like corrosion, should be evaluated and influence the decision.

Thermowell Velocity Rating(Program Ver. 4.2a)

Company: Tag #: Project No: Date:

Reference: Rev:

U

B

d A

FLUID DATA CONSTANTS Fluid Air 2.01 0.01

Operating Temperature 2200 ºF 0.079 0.01

Operating Pressure 200 psig 15.7 3.5

Fluid Velocity V 85 ft/sec 2.679 3.5

v 4.586

WELL DATA CALCULATIONS

Well Material 304 424 Hz

Unsupported Length U 10.00 in Wake Frequency 299 Hz

Bore Diameter d 0.500 in Frequency Ratio r 0.71

Tip Diameter B 0.750 in Magnification Factor Fm 1.99

Root Diameter A 0.760 in Max Length @ V (r=0.8) Um 10.6 in

w 0.112 Max Velocity @ U (r=0.8) Vm 96 ft/sec

E 50.0 Max Static Pressure Pm 3167 psig

S 40.0 Max Stress Length Ls 40.32 in

Max Stress Velocity Vs 342.8 fps

NOTES

Wall thickness is less than recommended

Well taper is less than recommended

These calculations are performed according to the paper "Power Test Code Thermometer Wells" by J. W. Murdock, and also

meet the requirements of ASME PTC 19.3-1998. The program supplies results which should only be used as a guide for

thermowell design. Thermo-Kinetics assumes no responsibility for failure of a well based on the results of these calculations,

and accepts no liability direct or consequential, arising from error or misinformation supplied herein, or due to program misuse.

Kf t/A

To K1 t/B

Po K2 FA

K3 FB

ft3/lb

Natural Frequency @ To fn

fw

Specific Weight @ To lb/in3

Mod of Elasticity @ To psi x 106

Allowable Stress @ To psi x 103

TABLES

Material Code 70ºF 700ºF 900ºF 1100ºF 1300ºF 1500ºF

C.Steel 105 0.284 0.280 0.279 0.278

304 SS 304 0.290 0.286 0.285 0.284 0.283 0.281

310 SS 310 0.290 0.286 0.285 0.284 0.283 0.281

316 SS 316 0.290 0.286 0.285 0.284 0.283 0.281

FLUID VELOCITY CALCULATED from FLOW DATA 321 SS 321 0.290 0.286 0.285 0.284 0.283 0.281

446 SS 446 0.270 0.267 0.266 0.264 0.263

Fluid Air V = 3.0558×Q/ID² F22 SS F22 0.290 0.286 0.285 0.284 0.283 0.281

Pipe I.D. ID 2.000 in Hast B-3 HSB-3 0.334 0.330 0.328 0.326 0.325 0.324

Flow Rate Q 10.0 SCFM Hast C-22 HSC-22 0.323 0.319 0.317 0.316 0.314 0.313

Velocity V 7.6 ft/sec Hast C-276 HSC-276 0.323 0.319 0.317 0.316 0.314 0.313

Hast C-4 HSC-4 0.323 0.319 0.317 0.316 0.314 0.313

Hast X HSX 0.297 0.293 0.291 0.290 0.289 0.287

Inconel INC 0.307 0.302 0.300 0.299 0.297 0.296

Monel MON 0.319 0.313 0.311 0.308 0.306

1 60 100 200 300 400 500 600 700 Nickel NIK 0.322 0.316 0.315 0.313 0.311 0.309

0.016 0.016 0.016 0.017 0.017 0.018 0.020 0.024 0.037 Titanium TIT 0.163 0.162 0.161

Material UNS# Code 70ºF 200ºF 300ºF 400ºF 500ºF 600ºF 700ºF 800ºF 900ºF 1000ºF 1100ºF 1200ºF 1300ºF 1400ºF 1500ºF C.Stl SA-675 105 29.5 28.8 28.3 27.7 27.3 26.7 25.5 24.2 22.4 20.4 18.0 HR160 N12160 160 30.6 29.8 29.4 29.1 28.6 28.3 27.8 27.2 26.6 26.0 25.6 24.9 24.3 23.6 22.8 304 SS S30400 304 28.3 27.7 27.1 26.6 26.1 25.4 24.8 24.1 23.4 22.7 22.0 21.3 20.7 19.3 17.9 310 SS S31008 310 28.3 27.7 27.1 26.6 26.1 25.4 24.8 24.1 23.4 22.7 22.0 21.3 20.7 19.3 17.9 316 SS S31600 316 28.3 27.7 27.1 26.6 26.1 25.4 24.8 24.1 23.4 22.7 22.0 21.3 20.7 19.3 17.9 321 SS S32100 321 28.3 27.7 27.1 26.6 26.1 25.4 24.8 24.1 23.4 22.7 22.0 21.3 20.7 19.3 17.9 446 SS S44627 446 29.2 28.7 28.3 27.7 27.0 26.0 24.8 23.1 21.1 18.6 15.6 12.2 F22 SS K21590 F22 30.6 29.8 29.4 28.8 28.3 27.7 27.1 26.3 25.6 24.6 23.7 22.5 21.1 19.4 Hast B-3 N10675 HSB-3 31.4 30.6 30.1 29.8 29.3 29.0 28.6 27.9 27.3 26.7 26.2 25.6 25.0 24.2 23.4 Hast C-22 N06022 HSC-22 29.9 29.2 28.7 28.4 28.0 27.7 27.2 26.6 26.0 25.4 25.0 24.4 23.8 23.0 22.3 Hast C-276 N10276 HSC-276 29.8 29.1 28.6 28.3 27.9 27.6 27.1 26.5 25.9 25.3 24.9 24.3 23.7 22.9 22.2 Hast C-4 N06455 HSC-4 29.8 29.1 28.6 28.3 27.9 27.6 27.1 26.5 25.9 25.3 24.9 24.3 23.7 22.9 22.2 Hast X N06002 HSX 28.5 27.8 27.4 27.1 26.6 26.4 25.9 25.4 24.8 24.2 23.7 23.2 22.6 21.9 21.2 Inconel N06690 INC 30.3 29.5 29.1 28.8 28.3 28.1 27.6 27.0 26.4 25.8 25.3 24.7 24.1 23.3 22.6 Monel N04400 MON 26.0 25.4 25.0 24.7 24.3 24.1 23.7 23.1 22.6 22.1 21.7 21.2 20.7 20.0 19.4 Nickel N02200 NIK 30.0 29.3 28.8 28.5 28.1 27.8 27.3 26.7 26.1 25.5 25.1 24.5 23.9 23.1 22.4 Titanium R50400 TIT 15.5 15.0 14.6 14.0 13.3 12.6 11.9 11.2

Material UNS# Code 70ºF 200ºF 300ºF 400ºF 500ºF 600ºF 700ºF 800ºF 900ºF 1000ºF 1100ºF 1200ºF 1300ºF 1400ºF 1500ºF

C.Steel SA-675 105 14.3 14.3 14.3 14.2 13.6 12.8 11.9 9.4 5.0 HR160 N12160 160 23.3 20.5 18.3 16.5 15.0 14.1 13.6 13.5 13.5 13.5 11.0 7.5 5.1 3.6 2.5 304 SS S30400 304 20.0 16.7 15.0 13.8 12.9 12.3 11.7 11.2 10.8 10.4 9.8 6.1 3.7 2.3 1.4 310 SS S31008 310 20.0 17.6 16.1 15.1 14.3 13.7 13.3 12.9 12.5 9.9 316 SS S31600 316 20.0 17.3 15.6 14.3 13.3 12.6 12.1 11.8 11.5 11.3 11.1 7.4 4.1 2.3 1.3 321 SS S32100 321 20.0 18.0 16.5 15.3 14.3 13.5 13.0 12.6 12.3 12.0 6.9 3.6 1.7 0.8 0.3 446 SS S44627 446 18.6 18.5 18.3 18.2 18.1 18.0 17.9 F22 SS K21590 F22 21.4 21.4 20.9 20.6 20.5 20.4 20.0 19.3 15.8 7.8 3.2 1.2 Hast B-3 N10675 HSB-3 31.4 31.4 30.3 28.8 27.4 26.3 25.4 24.8 Hast C-22 N06022 HSC-22 28.6 26.7 24.6 22.9 21.5 20.4 19.6 19.0 18.6 18.3 17.5 9.6 Hast C-276 N10276 HSC-276 27.3 24.9 23.0 21.3 19.9 18.7 17.8 17.1 16.7 16.5 15.0 9.8 Hast C-4 N06455 HSC-4 26.7 24.6 23.0 21.7 20.8 20.1 19.6 19.1 Hast X N06002 HSX 23.3 21.0 19.2 17.7 16.5 15.7 15.1 14.7 14.5 Inconel N06690 INC 23.3 21.1 19.9 19.1 18.6 18.4 18.2 18.0 Monel N04400 MON 16.7 14.6 13.6 13.4 13.2 13.1 13.0 12.7 8.0 Nickel N02200 NIK 10.0 10.0 10.0 10.0 10.0 10.0 Titanium R50400 TIT 14.3 12.4 10.3 8.8 7.6 6.5

CONVERSION FACTORS

From To X Water 62.4 82.3 Air 0.0764 Hydrogen 0.006

m ft 3.281 Sea Water 64.2 95.4 Acetylene C2H2 0.073 Hydrogen Chloride HCl 0.095

mm in 0.03937 Amyl Alcohol 55.0 114.7 Ammonia 0.044 Hydrogen Sulphide 0.096

m/s ft/s 3.281 Butyl Alcohol 45.3 71.0 Argon Ar 0.103 Methane 0.045

16.018 Benzine 56.0 Nitric Acid (95%) 93.5 Butane 0.162 Methyl Chloride 0.133

Mpa psi 145.04 Gasoline 42.0 Nitric Acid (7%) 64.7 Butylene 0.148 Nitrogen 0.075

Kpa psi 0.145 Kerosine 50.5 HCl (10%) 66.5 Carbon Dioxide 0.113 Nitric Oxide NO 0.078

g/cc 0.03613 Carbon Monoxide CO 0.078 Nitrous Oxide 0.114

0.06243 Chlorine 0.184 Oxygen 0.082

USGPM IGPM 0.8327 Ethane 0.081 Pentane 0.088

Ethylene 0.073 Propane 0.118

0.113 60 0 0.113 Helium He 0.010 Sulphur Dioxide 0.179

SPECIFIC WEIGHT (lb/in3)

Specific Volume of Water (ft3/lb) (T in ºF)

MODULUS of ELASTICITY (x 106 psi)

ALLOWABLE STRESS (x 103 psi)

DENSITY of LIQUIDS (lb/ft3) DENSITY of GASES at STP (60 ºF & 14.7 psia) (lb/ft3)

Caustic Soda (30%) H2

Caustic Soda (50%)

H2SO4 (100%) NH3 H2S

H2SO4 (20%) CH4

m3/kg ft3/lb C4H10 CH3Cl

C4H8 N2

CO2

lb/in3 N2O

kg/m3 lb/ft3 Cl2 O2

Gas Density Calculation (STP = 60ºF & 14.7 psia) C2H6 C5H12

Density (@ STP) To (ºF) Po (psig) Dens (@To/Po) C2H4 C3H8

SO2

PIPE DIMENSIONS

Size O.D.SCHEDULE

5S 10S 10 20 30 STD 40 60 XH 80 100 120 140 160 XXH1/2" 0.840 0.710 0.674 0.674 0.622 0.622 0.546 0.546 0.466 0.252

3/4" 1.050 0.920 0.884 0.884 0.824 0.824 0.742 0.742 0.612 0.434

1" 1.315 1.185 1.097 1.097 1.049 1.049 0.957 0.957 0.815 0.599

1-1/4 1.660 1.530 1.442 1.442 1.380 1.380 1.278 1.278 1.160 0.896

1-1/2 1.900 1.770 1.682 1.682 1.610 1.610 1.500 1.500 1.338 1.100

2 2.375 2.245 2.157 2.157 2.067 2.067 1.939 1.939 1.687 1.503

2-1/2 2.875 2.709 2.635 2.635 2.469 2.469 2.323 2.323 2.125 1.771

3 3.500 3.334 3.260 3.260 3.068 3.068 2.900 2.900 2.624 2.300

3-1/2 4.000 3.834 3.760 3.760 3.548 3.548 3.364 3.364

4 4.500 4.334 4.260 4.260 4.026 4.026 3.826 3.826 3.624 3.438 3.152

5 5.563 5.345 5.295 5.295 5.047 5.047 4.813 4.813 4.563 4.313 4.063

6 6.625 6.407 6.357 6.357 6.065 6.065 5.761 5.761 5.501 5.189 4.897

8 8.625 8.407 8.329 8.329 8.125 8.071 7.981 7.981 7.813 7.625 7.625 7.437 7.187 7.001 6.813 6.875

10 10.750 10.482 10.420 10.420 10.250 10.090 10.020 10.020 9.750 9.560 9.562 9.312 9.062 8.750 8.500 9.750

12 12.750 12.438 12.390 12.390 12.250 12.090 12.000 11.938 11.626 11.750 11.374 11.062 10.750 10.500 10.126 11.750

14 14.000 13.688 13.624 13.500 13.250 13.376 13.250 13.124 12.812 13.000 12.500 12.124 11.812 11.500 11.188

16 16.000 15.670 15.624 15.500 15.500 15.376 15.250 15.000 14.688 15.000 14.312 14.938 13.562 13.124 12.812

18 18.000 17.670 17.500 17.500 15.376 17.124 17.250 16.876 16.500 17.000 16.126 15.688 15.250 14.876 14.438

20 20.000 19.624 19.500 19.500 19.250 19.000 19.250 18.814 18.376 19.000 17.938 17.567 17.000 16.500 16.064

22 22.000 21.624 21.624 21.500 21.250 21.000 21.250 20.250 21.000 19.750 19.250 18.750 18.250 17.750

24 24.000 23.572 23.500 23.500 23.250 22.876 23.250 22.626 22.064 23.000 21.564 20.938 20.376 19.876 19.314

26 26.000 25.376 25.000 22.876 25.750 25.000

28 28.000 27.376 27.000 26.750 27.750 27.000

30 30.000 29.500 29.376 29.376 29.000 28.750 29.750 29.000

32 32.000 31.376 31.000 30.750 31.750 30.624 31.000

34 34.000 33.376 33.000 32.750 33.750 32.624 33.000

36 36.000 29.376 35.376 35.000 34.750 35.750 34.500 35.000

42 42.000 41.750 41.000

Pipe Inside Diameter - inches (Welded & Seamless Steel Pipe)

THERMOWELL VELOCITY RATING

Pressure(psia) 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500

10 0.016 38.85 44.99 51.04 57.04 63.03 69.01 74.98 80.95 86.92 92.88 98.84 104.8 110.76 116.72

15 0.016 0.017 29.90 33.96 37.99 41.99 45.98 49.96 53.95 57.93 61.91 65.88 69.86 73.83 77.81

20 0.016 0.017 22.36 25.43 28.46 31.47 34.47 37.46 40.45 43.44 46.42 49.41 52.39 55.37 58.36

25 0.016 0.017 17.86 20.34 22.78 25.20 27.60 30.01 32.40 34.80 37.19 39.58 41.98 44.37 46.76

30 0.016 0.017 14.81 16.89 18.93 20.95 22.95 24.95 26.95 28.94 30.94 32.93 34.92 36.95 38.90

35 0.016 0.017 12.65 14.45 16.21 17.94 19.66 21.38 23.09 24.80 26.51 28.22 29.93 31.63 33.34

40 0.016 0.017 11.04 12.62 14.17 15.67 17.20 18.70 20.20 21.70 23.19 24.69 26.18 27.68 29.17

45 0.016 0.017 9.782 11.21 12.58 13.94 15.28 16.62 17.96 19.29 20.62 21.95 23.28 24.61 25.94

50 0.016 0.017 8.769 10.06 11.31 12.53 13.74 14.95 16.15 17.35 18.55 19.75 20.94 22.14 23.33

65 0.016 0.017 6.678 7.698 8.667 10.18 10.55 11.49 12.41 13.34 14.26 15.19 16.11 17.03 17.95

75 0.016 0.017 0.017 6.645 7.494 8.320 9.135 9.945 10.75 11.55 12.36 13.16 13.95 14.75 15.55

100 0.016 0.017 0.017 4.936 5.588 6.217 6.834 7.446 8.053 8.658 9.260 9.862 10.46 11.06 11.66

200 0.016 0.017 0.017 2.361 2.725 3.059 3.379 3.693 4.003 4.310 4.615 4.918 5.221 5.522 5.823

250 0.016 0.017 0.017 1.861 2.154 2.430 2.693 2.948 3.198 3.446 3.692 3.936 4.179 4.421 4.663

300 0.016 0.017 0.017 0.019 1.767 2.005 2.227 2.442 2.653 2.861 3.066 3.270 3.474 3.676 3.878

400 0.016 0.017 0.017 0.019 1.285 1.477 1.651 1.817 1.978 2.136 2.292 2.446 2.600 2.753 2.905

500 0.016 0.017 0.017 0.019 0.993 1.159 1.304 1.441 1.573 1.701 1.827 1.952 2.076 2.199 2.321

600 0.016 0.016 0.017 0.019 0.795 0.946 1.073 1.190 1.302 1.411 1.518 1.623 1.726 1.830 1.932

675 0.016 0.017 0.017 0.018 0.693 0.829 0.946 1.053 1.154 1.252 1.347 1.441 1.534 1.627 1.718

700 0.016 0.016 0.017 0.019 0.020 0.793 0.908 1.011 1.109 1.204 1.296 1.387 1.477 1.566 1.654

800 0.016 0.016 0.017 0.019 0.020 0.678 0.783 0.877 0.964 1.048 1.130 1.211 1.290 1.368 1.446

900 0.016 0.016 0.017 0.019 0.020 0.587 0.686 0.771 0.850 0.926 1.000 1.072 1.143 1.213 1.283

1000 0.016 0.016 0.017 0.019 0.020 0.514 0.609 0.688 0.761 0.831 0.898 0.963 1.028 1.091 1.154

1200 0.016 0.017 0.017 0.019 0.020 0.402 0.491 0.562 0.626 0.686 0.743 0.798 0.853 0.906 0.959

1400 0.016 0.017 0.017 0.018 0.020 0.318 0.406 0.472 0.529 0.582 0.632 0.681 0.728 0.774 0.820

1550 0.016 0.017 0.017 0.018 0.020 0.272 0.357 0.420 0.473 0.522 0.568 0.613 0.656 0.699 0.740

1600 0.016 0.017 0.017 0.018 0.020 0.024 0.342 0.403 0.456 0.503 0.548 0.592 0.634 0.677 0.716

1800 0.016 0.017 0.017 0.018 0.020 0.023 0.291 0.350 0.399 0.443 0.484 0.524 0.562 0.599 0.635

2000 0.016 0.017 0.017 0.018 0.020 0.023 0.249 0.307 0.353 0.394 0.432 0.468 0.503 0.537 0.570

2500 0.016 0.017 0.017 0.018 0.020 0.023 0.169 0.230 0.272 0.308 0.340 0.370 0.399 0.427 0.454

3000 0.016 0.016 0.017 0.018 0.020 0.023 0.098 0.176 0.216 0.249 0.277 0.304 0.329 0.353 0.376

3100 0.016 0.016 0.017 0.018 0.020 0.023 0.092 0.167 0.208 0.240 0.268 0.293 0.318 0.341 0.364

3500 0.016 0.016 0.017 0.018 0.020 0.023 0.031 0.136 0.176 0.207 0.233 0.256 0.278 0.300 0.320

4000 0.016 0.016 0.017 0.018 0.020 0.022 0.029 0.105 0.146 0.175 0.199 0.221 0.241 0.260 0.279

5000 0.016 0.016 0.017 0.018 0.020 0.022 0.027 0.059 0.104 0.131 0.153 0.172 0.189 0.205 0.220

7500 0.016 0.016 0.017 0.018 0.019 0.021 0.025 0.032 0.051 0.074 0.092 0.107 0.121 0.133 0.144

10000 0.016 0.016 0.017 0.018 0.019 0.021 0.023 0.027 0.036 0.050 0.063 0.076 0.087 0.096 0.105

15000 0.016 0.016 0.017 0.017 0.018 0.019 0.022 0.024 0.028 0.034 0.041 0.048 0.055 0.062 0.069

STEAM TABLES (extracted from ASME Steam Tables for Industrial Use, 1997 Edition)

Specific Volume (ft3/lb) (w)

Temperature (ºF)