Thermowell Wake Frequency Calculation
Table of Contents
- Transition of Thermowell Calculation
- Technical Background of the Effect of a Vortex Protection Tube.
- Thermowell Vibration in Two-phase Flow
TRANSITION OF THERMOWELL CALCUATION
１．Transition of Thermowell Calculation
It is thought that we started our thermometer Protection Tube strength calculation in the 1970s with manual calculation based on the strength calculation materials of a customer. At the time we performed calculations of the natural frequency, forced frequency with fluid and bending stress with fluid, etc. based on mechanical engineering handbooks, etc. Then, it became standard with jobs for overseas for calculation to be performed based on ASME PTC19.3 materials and the method was the main one for a long time.
However, since the Monju Na leakage accident which occurred in 1995 was caused by the damage on a thermometer Protection Tube (sensor casing), the method was suddenly focused on and in 1998 JSME (Japan Society of Mechanical Engineers) issued a guideline for the strength calculation. This guideline includes not only the evaluation with Kármán vortices but also the resonance calculation with symmetric vortices which were assumed to be a cause of the damage on the Protection Tube in Monju. Currently many domestic users calculate the strength with this guideline.
Furthermore, ASME (American Society of Mechanical Engineers) issued PTC 19.3 TW-2010, a revision of PTC 19.3, in 2010, which allowed the symmetric vortex evaluation in the same way as JSME. Based on the background above, the transition of the strength calculation method from the past to the present is described below.
(1) 1960s: Domestic Thermal Power Plant
Sometime around 1960, a main steam line Protection Tube breakage occurred in a domestic thermal power plant and with almost the same method as ASME PTC19.3 mentioned later the cause was looked for with three types of evaluation: external pressure strength consideration, bending strength consideration with fluid and resonance consideration with Protection Tube natural frequency fn and forced frequency fs with Kármán vortices. There were several evaluation results; however, commonly it could be said that breakage had occurred with Kármán vortices resonance in fluid relatively in high density (30 kg/m3).
(2)ASME PTC 19.3-1974
Based on the taper Protection Tube natural frequency fn described in the report of Power Test Code Thermometer Wells/Journal of Engineering for Power, Trans. ASME, vol. 81, 1959, Oct. (2) by J. W. Murdock issued in 1959, non-matching conditions are obtained in comparison with fs, the forced frequency with Kármán vortices occurred in the wake flow of the Protection Tube. Normally it is called ASME PTC 19.3; however, just four pages of the text “Performance Test Code – Part 3: Temperature Measurement” (1) which covers the general temperature measurement have the description of the Protection Tube strength calculation.
We perform the strength calculation with this method; however, we have added our following original method in accordance with customers’ request.
Since for light gases, stress on resonance is small, the usable over resonance area 1.4 < fs/f
Considering that the drag coefficient CD becomes large with high viscosity fluid, CD is calculated as a function of Re number so that Protection Tubes which are not bent even with a high viscosity can be designed.
The strength calculation guideline issued by Japan Society of Mechanical Engineers in 1998 with the Protection Tube breakage accident in “Monju” as a trigger is JSME S012-1998 Guideline for evaluation of flow-induced vibration of a cylindrical structure in a pipe (4). Conventionally the strength calculation has evaluated only Kármán vortices; however, with this guideline, the drag direction resonance generated with symmetric vortices can also be evaluated. The calculation base is ASME BPVC SEC. III N-1300 (3). Also the evaluation procedure looks greatly different from the conventional one; however, the basic evaluation is the comparison of the Protection Tube natural frequency to the forced frequency with the evaluation of fluid density added.
Evaluation and judgment are performed based on the new concepts of conversion fluid speed Vr and conversion attenuation factor Cn and Vr is determined with the vibration ratio fs/fn and Strouhal number St and Cn is determined with the fluid density p, attenuation coefficient ratio ζ and Protection Tube mass m, which are dimensionless numbers. In this guideline, since the resonance by the symmetric vortices in the drag direction occurs with fs/fn = 0.4 to 0.6 (Vr = 2 to 3) and the resonance by Kármán vortices in the lift direction occurs with fs/fn = 1 (Vr = 5), judgment is made to avoid usage near the resonance area each depending on the fluid density.
In other words, the use condition is to satisfy any of the conditions below.
・Vr < 1 (for Cn ≦ 2.5)
・Cn > 64
・Vr < 3.3 and Cn > 2.5
When it is expressed with the vibration ratio, fs/fn < 0.2 (Vr < 1) is satisfied for the high density fluid (Cn ≦ 2.5), fs/fn < 0.66 (Vr < 3.3) is satisfied for the medium density fluid (Cn > 2.5) and there is no problem for the low density fluid (Cn > 64) since the stress is extremely small even with resonance.64) since the stress is extremely small even with resonance.
Figure Synchronous Vibration Avoidance/Suppression Condition (Extracted from JSME S 012)
(4)ASME PTC19.3 TW-2010(5)
Revised conventional ASME PTC19.3:1974 issued by American Society of Mechanical Engineers in 2010, which has been rewritten overall in detail as a new document.
In these specifications, vibration with the symmetric vortices in the drag direction is evaluated in the same way as JSME S012 greatly different from the conventional calculation method. The force with Kármán vortices in the lift direction is called Transverse Force and the force with symmetric vortices in the drag direction is called In-line Force. Refer to Figure Force Received from Fluid.
Figure Force Received from Fluid
However, the calculation method and evaluation method are greatly different form JSME. The features of the revised version are described below.
The Scruton number NSc has been introduced and the concept is same as the conversion attenuation factor Cn; however, since the attenuation coefficient ratio ζ value used for calculation is smaller than JSME by one digit, the calculation result and judgment result are greatly different from JSME.
The resonance in the drag direction (In-line) is evaluated; however, the forced frequency in the drag direction is half of the number of Kármán vortices and the resonance point in the drag direction is fs/fn = 0.5.As a result, when the stress on resonance in the drag direction exceeds the allowance, the available vibration ratio area for the high density fluid is fs/fn < 0.4 and the resonance area which is unavailable with the JSME judgment is available. (For NSc ≤ 2.5 or Re ≥ 10^5).
When the stress on resonance in the drag direction does not exceed the allowance, it is enough if fs/fn < 0.8 is satisfied; however, to avoid resonance in the drag direction, it is recommended to avoid the vibration ratio 0.4 < fs/fn < 0,6 (for NSc > 2.5 and Re < 10^5). As a result, the available conditions are greatly narrowed.
Since the calculation method for the natural frequency has been greatly revised, the calculation accuracy for the natural frequency was improved and the value became closer to the actual natural frequency.
Figure Resonance Area with Flow-induced Vibration
As the description above, since the criteria of the ASME PTC19.3 TW-2010 differ from the one of the JSME S012, even if a product becomes available with the calculation result of ASME PTC19.3 TW-2010, the product may become unusable when the JSME S012 calculation is performed.For example, if the Protection Tube which was broken at Monju is calculated for the strength, it will become unusable with JSME S012, but it will become usable with ASME PTC19.3 TW.The calculation method comparison above is described in “Protection Tube Vortex-induced Vibration-related Strength Calculation Method Comparison.”
２．Technical Background of the Effect of a Protection Tube with a Helical Rod
When thermometer Protection Tubes are used in various plants, recently “strength calculation” to evaluate resonance with Kármán vortices, etc. occurring in the wake flow of Protection Tubes is being performed increasingly. As a result, changing dimensions of the Protection Tubes and installation methods are required depending on the operational conditions; however, when the flow rate is high, the conditions may not be satisfied by changing the Protection Tube dimensions/installation methods.
Before we have provided support in such cases with Protection Tubes with collars; however, the actual natural frequency is unclear with the ones with collars and when another nozzle inner diameter is not as in the design, the product was not be able to be installed at sites in some cases. Furthermore, recently issued ASME PTC 19.3 TW-2010 clearly stated that ones with collars are not recommended so that currently they are not adopted in most cases.
We have been manufacturing Protection Tubes with helical rods as per customers' proposal and the technical background of their effect has come to be requested; therefore, we have actively been performing investigation of various documents, testing with actual fluid and other theoretical analysis, etc. The details of adopting Protection Tubes with helical rods, our experiment results with actual fluid and theoretical analysis are reported below.
(2) Details of Adoption
The adoption started from the introduction of the measures with helical rods in some customer’s internal standard. Then the Protection Tube with a helical rod has been introduced as the Kármán vortex preventive method in the JSME S012 guideline, furthermore, we have designed and adopted helical rods based on the experiment results published in the following paper and the dimensions/shapes applied to chimneys specified in the BS standard. Then replying to an inquiry “Is there confirmation data for helical rods to be valid not only in air (for chimneys) but also in liquid ? ”,we have carried out flow-induced experiments using a liquid for Protection Tube with a helical rod.
1) JSME S012-1998 “Guideline for evaluation of flow-induced vibration of a cylindrical structure in a pipe” Page B84
Figure Kármán Vortex Preventive Method
2) Helical Strake for Vortex Excited Vibration Suppression Adopted to Chimney
As indicated with the experiment results in “The Efficiency of Helical Strakes for the Suppression of Vortex Excited Oscillation of Steel Stacks,” Architectural Inst. of Japan Structural System Papers/Reports #354 Aug. 1985, by Tadayuki Shimada (IHI), Hiroshi Hara (IHI) and Hatsuo Ishizaki (Kyoto University), it is understood that installing helical strakes suppresses resonance with Kármán vortices. Recently most chimneys have helical strakes installed to prevent vortex excited vibration and we have many results.
Figure Extraction of Paper Details
3)BS 4076: 1989 Specification for Steel chimneys
Specifications of shapes and dimensions for helical strakes installed in chimneys established in the BS standard. The details are almost same as the paper in (6). (Also introduced in JSME S012)
|Hight of side plate||: 0.1 - 0.12D (D: Cylindrical diameter)|
|Number of side plate||: 3 spirals|
|Pitch of parallel winding side plate||: The 5D (it winds, suitable to the angular 58°)|
|Istallation range of the side plate||: In range of top 1/3 of cylindrical condition structure installation|
|Drag coefficient||: Cd=1.2|
(3) Experimental Verification
Our experimental results are described below. The symmetric vortices have been observed near fs/fn = 0.4 in both domestic and overseas experiments; however, their impact has not been recognized with the Protection Tubes with helical rods.
1) Water Flow Experiment in Tamagawa University
We borrowed the hydrodynamic vibration experimental facility of Tamagawa University and checked the effect of helical rods under actual water flow in August, 2006. Taking videos and measuring displacement at the upper part of a Protection Tube, we confirmed that the effect of helical rods is demonstrated sufficiently even under water. This experiment results were described in “Piping Engineering” magazine in Aug., 2007.
For Kármán vortices, we have executed a re-productive experiment only domestically and confirmed that Protection Tubes without helical rods break in a relatively short time. Since excessive stress is applied to the root part on Kármán vortex resonance, if a crack occurs at the root part, the natural frequency will change and resonance will stop.
The Protection Tubes with helical rods have almost no resonance even with Kármán vortices when compared with ones without helical rods; however, it was confirmed that there was slight vibration at the resonance point. Therefore, for high density fluid, we recommended that the product be used with the vibration ratio fs/fn < 0.8 even with helical rods.
Figure Tamagawa University Testing Apparatus Overall Diagram and Apparatus Photo
2) Actual Liquid Flow Experiment Using Oil by TUV SUD NEL, Glasgow, UK
The experiment entrusted to a testing agency in the UK was stopped partway. This was because the distortion gauge installed only in the drag direction was broken with the resonance by symmetric vortices; however, the flow rate was increased near the vibration ratio fs/fn = 0.47.As a result, it was confirmed that the maximum value of the resonance amplitude with symmetric vortices is near the vibration ratio fs/fn = 0.4 and the displacement characteristic with vibration in the drag direction indicated in the JSME S012 guideline was demonstrated. For Protection Tubes with helical rods, the stress increase with symmetric vortices were not recognized and the value near the calculated static stress value was detected with the distortion gauge.
Figure TÜV Testing Apparatus
Figure Result of Hydrodynamic Experiment with Oil
Figure JSME S012 Cylindrical Vibration Shape
(4) Theoretical Verification
We have entrusted the comparison CFD (Computational Fluid Dynamics) analysis of normal hollowed out Protection Tubes and Protection Tubes with helical rods to Cygnet Development Services Ltd. in UK in addition to the documents and experimental results above. In the report, the conclusion summary was “It was observed that adding the helical rib greatly decreased vortices induced around the thermowell. For the specific model, there was no regular vortex behavior.” This agrees with all other papers which mention that the helical rib decreases the vortex discharge behavior. The flow line comparison is indicated in Figure-7.
Figure Protection Tubes with CFD Comparison
Figure-7 Flow Line Comparison with CFD
[Material Download] TD-1469 Protection Tube with Helical Rod Technical Data.pdf:PDF of this material
ASME PTC 19.3 PART 3 Temperature Measurement/ Instruments and apparatus
Power Test Code Thermometer Wells / J.W. Murdock , Journal of Engineering for Power, Trans . ASME, vol.81, 1959.Oct. /P407-P409
ASME BOILER & PRESSURE VESSEL CODE SECTION III DIVISION 1 APPENDICES APPENDIX N-1300
JSME S012-1998 Guideline for evaluation of flow-induced vibration of a cylindrical structure in a pipe
ASME PTC 19.3 TW-2010 Thermowells Performance Test Codes
The Efficiency of Helical Strakes for the Suppression of Vortex Excited Oscillation of Steel Stacks, Architectural Inst. of Japan Structural System Papers/Reports, Shimada, Hara, Ishizaki, Aug. 1985
Hydrodynamic Vibration Consideration and Measures, Okazaki Manufacturing Company, Kazeoka, Saijo, Michinoshita, Japan Industry Publishing, Piping Engineering, Sep., 2007
Computational Fluid Dynamics Modeling、Cygnet Development Services Ltd、T.Oakes、23/06/2008
THERMOWELL VALIDATION TESTS VortexWell, Evaluation Report : E 1937 X 12, TÜV SUD NEL, Glasgow, UK
Thermometer Protection Tube Validation Test, Evaluation Report: E 1937 X 12, TÜV SUD NEL, Glasgow, UK (Japanese translation of (7))
Water Flow Simulation of the Flow-induced Vibration Phenomenon of the Thermowell in the Prototype-FBR "Monju", JAERI-Tech 96-028, Japan Atomic Energy Research Institute
Remarks: Reference documents (7) to (10) are our hydrodynamic test results/reports. We will make them available to customers who are interested in them, please contact us. Note that we will not make them available to persons other than our customers or those adjudged to be from our competitors. (11) is available on the Web.
３．Protection Tube Vibration in Two-phase Flow
In spring 2012, at a certain petroleum refining plant, a Protection Tube with a helical rod attached for a Kármán vortex measure had a resonance. The product has been designed to attach “a helical rod” for vibration countermeasures since the fluid has two phases of gas and liquid with high flow rate. We found the vibration statuses below.
In-line vibration in the same direction as the flow.
The vibration level was extremely high, the surface of the sheathed thermocouple attached was in contact with the inside of the Protection Tube and many scratches were observed.
Vibration was confirmed with the Protection Tubes of two different types of shapes and use conditions and both vibration frequencies were near the Protection Tube natural frequency; therefore, the resonance status due to an outer force was assumed.
The flow ratios of the liquid and gas were the mass flow ratio GL/GV = 10.7 and GL/GV = 4.6 and the volumetric flow ratio QL/QV = 0.11 and QL/QV = 0.08 and the average density was 81.5 kg/m3 and 63.3 kg/m3.
Based on the results above, we checked our documents. As a result, for the cylinder put in the two-phase flow, the document of  has an item of “Vibration with Two-phase Flow” with the description below.
“On the other hand, in the flow direction, if the void ratio is large, vibration which is larger than one in single phase water flow occurs.” For Protection Tubes in the two-phase flow, even though the detailed conditions are unknown, the Protection Tube resonance may occur in the flow direction depending on the two-phase flow conditions. Figure-A shows the resonance (lock-in) in two-phase flow of gas and liquid.
Figure-A Lock-in in Gas/Liquid Two-phase Flow
Although the same document introduces the two-phase flow patterns in Figure-B, we absolutely cannot predict the actual flow within a tube at this point. If the slag flow or froth flow in the diagram goes within a tube, the liquid hits the Protection Tube in the flow direction discontinuously and if the cycle is the integral multiplication or 1/(integer) of the natural frequency of the Protection Tube, it is assumed that the Protection Tube may have resonance.
From the results above, the strength calculation for Kármán vortices in two-phase flow has no meaning at all depending on the flow pattern status and it is predicted that vibration occurs not with vortices occurring in the wake flow of the Protection Tube but with the liquid phase which hits the Protection Tube discontinuously (intermittently) depending on the flow status.
Furthermore, after subsequent verification, another Protection Tube used in the two-phase flow was found to be bent; however, when the Kármán vortex was calculated with the hypothetical calculation fluid density with the two-phase complete mixture, the vibration ratio fs/fn < 0.8 and the product was deemed usable based on the calculation with the vortex induced vibration. Although the Protection Tube was bent, the bending stress was equal to the allowance or less.
From the results above, for the two-phase flow, it is thought that only liquid flow may directly hit the Protection Tube depending on the flow pattern and it is predicted that there will be an unexpected load depending on the flow rate. Further repeated hits may generate resonance whose mechanism is different from the one generated in the wake flow of the Protection Tube; therefore, it can be said that the strength calculation method for Kármán vortices and symmetric vortices explained in this document cannot be used.
Since we handle the strength calculation for the two-phase flow we execute assuming it to be a single-phase flow with the average density of a complete mixture, it must be understood that the calculation result is only for reference. Sufficient attention must be paid to usage.
Figure-B Flow Pattern in Two-phase Flow
The following description is used for the strength calculation sheet.
Since calculation of a 2 phase flow assumes that it is a single phase flow in mean density, please consider that the result is an object for reference.
 Flow Induced Vibrations: Classification and Lessons from Practical Experiences, edited by Japan Society of Mechanical Engineers, Gihodo Shuppan