Strength calculation for thermowells

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Strength calculation for thermowells
                                                                                                     WIKA data sheet IN 00.15


■ The wake frequency calculation for thermowells serves as
   mathematical proof of the strength with respect to static
   and dynamic stress in relation to the operating tempera-

Special features

■ Calculation per ASME PTC 19.3 TW-2010 or Dittrich/
   Klotter as an engineering service
■ Recommendations for structural changes to the thermo-
   well where the permissible stress limits are exceeded can
   be derived.                                                   FEM representation of a thermowell in flow with stress
                                                                 representation at the tip and at the root


The calculation per ASME PTC 19.3 TW-2010 is used                For recommendations concerning structural changes where
for one-piece thermowells in tapered, straight or stepped        the permissible stress limits have been exceeded, the follow-
designs from solid materials, such as Model TW10, TW15,          ing information will be required in addition:
TW20, etc.
                                                                 ■ Inside diameter of the adapter
A calculation per Dittrich/Klotter is recommended for all        ■ Height of the adapter
thermowells in WIKA‘s portfolio, but especially for fabricated   ■ Inner diameter and wall thickness of pipeline/vessel

The process data required to perform a calculation in accord-
ance with both of the methods is as follows:

                                   SI unit   Imperial   Others
Flow rate                          m/s       ft/s       ---
Density of medium                  kg/m³     lb/ft³     ---
Temperature                        °C        °F         ---
Pressure                           bar       psi        ---
dynamic viscosity 1)               mm²/s     ft/1000s   cP
1) only required for ASME PTC 19.3 TW-2010

WIKA data sheet IN 00.15 ∙ 10/2010                                                                                 Page 1 of 4
ASME PTC 19.3 TW-2010                                                             Calculation methods per Dittrich/Klotter

ASME PTC 19.3 TW-2010 is divided into dynamic and static                          For fabricated thermowells, the calculation method per
calculation results.                                                              Dittrich/Klotter must be used because this construction is not
For gaseous media the previous limit frequency of rmax =                          covered by ASME PTC 19.3 TW-2010.
0.8, established from PTC 19.3-1974, is still valid. For liquid
media in many applications, the newly introduced limit                            The approach is based on calculating the stresses occurring
frequency of rmax = 0.4 for in-line resonance now applies.                        under load. These are compared with the allowable stresses
                                                                                  for the thermowell and safety factors.

 In-line resonance:                  Main resonance:
 „Drag Oscillation“                  „Lift Oscillation“
                                                                                  Recommendations for structural changes
                                                                                  when the permissible stress limits rmax
                                                                                  are exceeded
                                                                                  By exceeding the maximum, permissible limit frequency, rmax,
                                                                                  for the "In-line"- or main resonance, the following structural
                                                                                  changes should be made:

 rmax: 0.4 0.5                  rmax: 0.8      1                   r = fs/fn      a) Shortening the insertion length
                                                                                  This is the most effective method, (and the recommended
                                                                                  method from ASME PTC 19.3 TW-2010) for the improvement
                                                                                  of the frequency ratio r.
The evaluation of the dynamic results is made using the
damping factor NSC (The Scruton Number NSC, has a direct
                                                                                  b) Increasing the tip diameter
relationship to the permissible frequency ratio rmax from
                                                                                  By the enlargement of the tip diameter, the natural frequency
the wake frequency (fs) to the natural frequency (fn)). For
                                                                                  fs is reduced, as well as an optimisation of the frequency
gaseous media, a characteristic value is NSC > 2.5; fluids
                                                                                  ratio r.
typically have an NSC < 2.5.
                                                                                  c) Support through an anchor
                                                                                  Support of the thermowell through an anchor is generally not
                                                                                  recommended by ASME PTC 19.3 Points 6-7-(e), and lies
                   NSC > 2.5                                                      outside the valid range of the ASME Code. Against customer
                                                                                  requirements, an anchor can be used and the process side
                           Strength Res < Strength Perm.                          thermowell components below the anchor connection will
                                                                                  be designed in accordance with the design and calculation
     NSC < 2.5                                                                    criteria of ASME PTC 19.3 TW-2010, without, however, falling
                                                                      r = fs/fn
                                                                                  within the scope of ASME PTC 19.3 TW-2010. The operator
                 rmax: 0.4 r = 0.5                  rmax: 0.8   r=1
                                                                                  is responsible for a play-free support of the anchors in the
                           In-line resonance                    Main reso-        adapter. Due to this reason a guarantee cannot be given by

Whether the frequency ratio, r < 0.8, can also be used as
an evaluation limit with liquid process media, is determined                      Figure 1: Anchor support in adapter

through a consideration of the permissible stresses in the
thermowell material with respect to the actual stresses at
resonance. In addition an evaluation strength of the thermo-
                                                                                               Height of the adapter (HA)

well material with respect to the flexural fatigue stress in the
area of the thermowell mounting.
The static results of ASME PTC 19.3 TW-2010 can be
                                                                                                                                     Inside diameter of the
created from the maximum permissible process pressure
                                                                                                                                     adapter (IDA)
(dependent on the process temperature and the geometry
of the thermowell) and the bending stress in the area of the
thermowell root. The bending stress caused by the incident
flow on the thermowell depends on the shielded length of the                                                                        Flow
flange adapter.

                                                                                  Welded 3-point anchor (Standard)

Page 2 of 4                                                                                                                 WIKA data sheet IN 00.15 ∙ 10/2010
A welded or one-piece, 3-point anchor, as well as a one-piece                                    With an interference fit, the anchor is manufactured with a
ring anchor with a clearance fit or interference fit can be used.                                diameter that is 0.25 mm larger than the inner diameter of
With all variants, the correct adapter inner diameter and the                                    the adapter. The adjustment to a play-free seat, and method
adapter height to be used must be given by the customer. An                                      chosen for this, are the sole responsibility of the operator.
anchor with clearance fit has a gap of less than 0.15 mm to the
adapter wall.

Figure 2: Possible build configurations for the anchors

                     Insertion length

                                        Reduced length and

                                                         A-A                       B-B                                      C-C

                                                   Welded 3-point anchor                 One-piece                            One-piece ring
                                                   (Standard)                            3-point anchor                       beam

Design specification per ASME PTC 19.3-2010
                                                                    Tapered and straight designs                    stepped design
Description                                                         Minimum          Maximum                        Minimum                Maximum
Insertion length L                                                  63.5 mm                609.6 mm                 127 mm                 609.6 mm
Bore diameter d                                                     3.175 mm               20.9 mm                  6.1 mm                 6.7 mm
Tip diameter B                                                      9.2 mm                 46.5 mm                  ---                    ---
Taper ratio B/A                                                     0.58                   1                        ---                    ---
Step ratio B/A for B = 12.7 mm                                      ---                    ---                      0.5                    0.8
Step ratio B/A for B = 22.2 mm                                      ---                    ---                      0.583                  0.875
Bore ratio d/B                                                      0.16                   0.71                     ---                    ---
Cross-sectional ratio L/B                                           2                      ---                      2                      ---
Length ratio Ls/L                                                   ---                    ---                      0                      0.6
Min. wall thickness (B-D)/d                                         3 mm                   ---                      3 mm                   ---

Marking                          per ASME PTC                       in WIKA data                 If the thermowell dimensions, based on customer require-
                                 19.3 TW-2010                       sheets                       ments or for specific applications, lie outside the require-
                                                                                                 ments of ASME PTC 19.3 W-2010 the calculation results can
Insertion length                  L                                 U                            only be used for informative purposes. Due to this reason a
Bore Ø                            d                                 B                            guarantee cannot be given by WIKA.
Tip Ø                             B                                 V
Root Ø                            A                                 Q

WIKA data sheet IN 00.15 ∙ 10/2010                                                                                                                    Page 3 of 4
Provision of calculation data

The examples in the following table show how the process
and geometry data should be provided as an excel spread-
sheet for further electronic processing by WIKA.

Sample table including calculation data for 6 measuring points

 Tag No.         T          P          v           rho           dynamic viscosity L                      d     A     B      Tt      Material IDA       HA
                 in °C      in bar in m/s in kg/m³ in cP                                        in mm in mm in mm in mm in mm EN                in mm in mm
 TW-0301         220        1.5        23.6        2.4           0.013                          250       8.5   25    19     6.4     1.4435     38.3    220
 TW-0303         220        1.5        25.7        2.0           0.017                          250       8.5   25    19     6.4     1.4435     38.3    220
 TW-0305         235        10         19.6        6.1           0.015                          250       8.5   25    19     6.4     1.4435     38.3    220
 TW-0307         220        10         13          8.9           0.014                          355       8.5   25    19     6.4     1.4571     38.3    220
 TW-0309         235        30         8.9         28.3          0.013                          355       8.5   25    19     6.4     1.4571     38.3    220
 TW-0311         400        31.5       31.9        10.1          0.017                          355       8.5   25    19     6.4     1.4571     38.3    220

 Tag No.         Measuring point No.
 T               Temperature
 P               Pressure
 v               Flow rate
 rho             Density of process medium
 L               Insertion length
 Ød              Bore size
 ØA              Root diameter
 ØB              Tip diameter
 Tt              Tip thickness
 IDA             Inside diameter of the adapter
 HA              Height of the adapter

The specifications given in this document represent the state of engineering at the time of publishing.
We reserve the right to make modifications to the specifications and materials.

 Page 4 of 4                                                                                                                WIKA data sheet IN 00.15 ∙ 10/2010
                                                                                                                                                                 10/2010 GB

                                                                                                                     WIKA Alexander Wiegand SE & Co. KG
                                                                                                                     Alexander-Wiegand-Straße 30
                                                                                                                     63911 Klingenberg/Germany
                                                                                                                     Tel.   (+49) 9372/132-0
                                                                                                                     Fax    (+49) 9372/132-406

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