Thermal stratification

Effect of non-uniform temperature distribution over the height of piping system cross-section

The thermal stratification arises in the horizontal segments of the piping system as a result of mixing the two flows of the working fluid with different temperatures and low velocities. Under certain operating conditions, due to this effect, the non-linear temperature distribution occurs over the height of piping system cross-section, which leads to additional temperature stress that can be divided into the following two categories:

It should be noted that the existing strength analysis codes for piping systems do not consider stratification as the design load, however in the course of operation of the piping system the stratification effect can influence on supports and equipment as well as on the fatigue strength.

Similar to the approach given in ASME NB-3653.2 for the temperatures gradient over the wall thickness of the piping system, the temperature distribution over the cross-section height of the piping can be presented by superposition of the following three parts: T – constant part, V – linear portion with zero average value and ΔT3 – a non-linear portion with zero average value and a zero first moment across the pipe diameter.

Decomposition of Stratification Temperature Distribution Range.

The following formula can be used for determination of the above-mentioned parameters:

where

T(r,θ) – function of distribution of temperature over the cross-section depending upon the radius and the 

angle, °C,

ro – outside radius of pipe, mm

ri – internal radius of pipe, mm

θ – angle to be counted from the horizontal central line of the cross-section

r – coordinate along the radiusAfter determination of the values of V and ΔT3, the program will compute the distributed bending moment Meq, which complements the load from thermal expansions:

where

E  – Young modulus (of elasticity) of the pipe material (MPa);

I   –  moment of inertia of the piping cross-section (mm4);

α  –  temperature expansion coefficient (mm/mm/°C);

V  – linear component of the temperature distribution,°C;

D0 – outside diameter of the pipe, mm. 

In conducting the estimation of the fatigue strength according to the ASME NB-3600 Codes, equation 11 (NB-3653.2), the calculation of local peak stress shall be supplemented by the f

ollowing part: Eα|ΔT3 | where |ΔT3| is the maximum value of the non-linear component of the stratification temperature distribution, °C.

Thermal stratification has caused several piping failures. The thermal effects of stratified flow at injection nozzle in piping systems are normally investigated by using a coupled CFD and FE method. Since CFD analyses as well as stress analysis are performed to find the time dependent temperature profile and peak stresses to evaluate fatigue strength considering these fluctuating temperature phenomena. Numerical results show that the most critical factor governing thermal stratification and that temperature distribution according to the conditions of process, operating and injection configuration. Also, if the flow pattern shows thermal stratification almost over all piping system or longer span, analyses may be necessary to carry out against bowing like phenomena. Simulation of Peak Stresses and Bowing Phenomena during the Cool Down of a Cryogenic Transfer System https://www.modelica.org/events/modelica2008/Proceedings/sessions/session6c1.pdf Coke Drum http://www.cbi.com/images/uploads/technical_articles/PTQq32006.pdf