# Strength calculation for thermowells by nikeborome

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Strength calculation for thermowells
WIKA data sheet IN 00.15

Applications

■ 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-
ture

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

Description

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
thermowells.

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

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
nance
WIKA.

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
3524951.01

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-

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
(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

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

Figure 2: Possible build configurations for the anchors

11611855
Insertion length

Reduced length and
anchor

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

Legend:
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

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
E-mail info@wika.de
www.wika.de

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