The most Important reason why people prefer installing Thermowell on Elbow is because it saves from WFC (Wake frequency calculation)
 
Hence It is of paramount importance to effectively install Thermowell to achieve its desired purpose.
 
There are 4 main parameters to checked
1.The Direction of flow in pipe (Tip must face the direction of flow)
2. Acceptance from other discipline especially process department
3.Clearance space to remove the Temperature assembly outside
4.In case of Test well Ease of Accessibility

1.Why to check direction of flow

The Vortices are formed when a body is place perpendicular to flow.
 
Now when we install the Thermowell in Elbow our aim is to achieve as little contact of thermowell “perpendicular” to flow
 
Case one tip is facing downstream of elbow  

Apologies:Due to time constrain i had to draw these drawing by hand 

​It is clearly observed that the perpendicular area exposed to flow is more
 
Now compare that to tip facing Upstream of Elbow

We see that when tip is facing the upstream the area “perpendicular” to flow is very minimal
 
Hence very minimum von karman vortex and thus a less stress on thermowell
 
Thermowells mounted in an elbow with the tip pointing upstream, as shown are often preferable to a mounting with the tip pointing downstream…… Reference ASME PTC 19.3 TW-2016 Page no 28.
 
NOTE:  Major Petrochem companies of the world in their design bases mention that WFC should be in compliance with ASME PTC 19.3

2.Approval from other discipline?

​In the Below picture assume our thermowell is at this location 

​Now we might feel we can mount it on elbow but wait in-between there is another line joining our line.
 
So process might want to measure temperature of liquid before mixing and thus even though other considerations are fulfilled we still cannot go for Elbow installations.
 

3.Clearance space for Thermowell 

​This is simple to understand If you want to remove thermowell outside or install.
 
The has to be some clearance space to physically remove the Temperature assembly.
 
It should be around 610 mm (24 inches)
 
OR
 
Total length of thermowell + 76mm (3 Inches)  ….Whichever is greater ………….(Reference API 551 Page no 25 )

4. In case of Test well Ease of Accessibility

Its is recommended that Test wells must be very easily accessible and hence if Elbow is at a great height then it must be discussed and amicable solution is required.
 
In some cases I have notice client not accepting Elbow installation as they would want the test well to be readily accessible.
 
Thanks for reading !!

PS: This is as per best of my current understanding.
 
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