Turbulent and Thermal Mixing in T-junctions 

Introduction

The mixing process of hot and cold fluids in a tee junction is chaotic (turbulent) in nature and can result in high cycle thermal fatigue of the junction. This random quasi steady state phenomenon of hot and cold shocks can lead to fatigue cracks and possible leakage, causing a structural integrity and process safety concern. Standard Computational Fluid Dynamics (CFD) two parameter turbulence models (Reynolds Averaged Navier Stokes Models) cannot predict this phenomenon, and advanced analysis, specifically Large Eddy Simulation (LES) is required to obtain meaningful results. This paper presents a comprehensive analysis of a petrochemical industry mixing point, including LES, a standard two parameter CFD turbulence model, finite element stress analysis, fatigue and fatigue crack growth approaches. This investigation is driven by extensive analysis of operational data, and is rigorously benchmarked against the observed in-service failure of the mixing tee.

Theory and Applications

The turbulent mixing problem is one of the most studied CFD problems, both computationally and experimentally. Its applications are widespread in the chemical, petrochemical, HVAC and other industries. One of the most common household application is the mixing of hot and cold water streams, probably available in all the houses.

In industrial applications, it is most widely used in the HVAC industry to get an optimum temperature in a living space. The cold stream of air from the air conditioning system can be mixed with the ambient air to get a desired temperature. The desired temperature can be controlled by varying the mass flow rates of the streams.

Thus, due to its wide applications a computational study has been performed in the present work using Ansys Fluent Student Version (Version 2020 R2).

Project Discription

In this project, We have worked upon how two different fluid having different temperature gets mixes with each other and produces a diffused flow into the domain of tube having T-shape or in simpler words, how diffusion takes place in T-joint tube. Here, Both fluid have different inlet velocity, fluid which comes from y axis inlet and velocity which comes from x axis inlet. The main aim behind this mixing of two different fluid in T-shape tube is to anlayse that how diffusion and turbulence take place between the two fluid.

To fulfill such desire, We have made up a model whose geometry is in T-shape. The model have been created and developed in CAD package 'Solidworks'. In CAD package, We basically have created two types of model i.e short mixing Tee and long mixing Tee. Then this models have been imported in Ansys simulation package, Where geometry have been cleaned up, meshed, setup and finally post-processed the results.

Here, We have imported two different configuration of geometry in Space-claim :-

One is short mixing tee whose dimension is approx 0.26 m

and, another one is long mixing tee 0.19 m

Since, We are interested in knowing that what happens when diffusion takes in T-joint tube rather how it happens within the T-joint tube. Hence, We have performed steady state solution which gives final state solution.

 

Procedure

 

Preprocessing 

Imported Geometry 

In this, We imported the geometry(Tee-shape tube) in Space-claim, where the geometry was in raw state as created in CAD package software. Here, We have represented the geometry in trimetric view given below:-

Cleaned up geometry in Space-claim

Since Geometry was in solid state where the body was having thickness which need to be remove so as to make geometry simple and can be converted into volumetric form. The newly updated geometry in volumetric form was as given below,

Meshed geometry in Ansys Mesher

Here, We imported the volumetric geometry created in Space-claim after cleaning up the geometry. Here, we applied meshing on the volumetric region with base mesh size. We also make sure that mesh quality should be of good quality.

After importing 3D cad geometry in ansys mesher the first step is to name the boundries by selecting the surfaces and rt clicking and slecting "Create Name Selection" or just by click N on the selected surface. There are two inlets i.e X-inlet which is along the X- axis (as shown in geometry) and other inlet is perpendicular it called Y- Inlet and the other end of pipe is Outlet. After this the element size is provided and mesh is created.

The created mesh is using element type as tetrahydral mesh in this study which is unstructured type of mesh.

 

Solving / Setup

Ansys Fluent is used as the solver. Here, We have created the setup for simulation where we have provided double precision and displayed mesh after reading so that We can visualize the mesh obtained in design moduler.

Single precision means that the floating point numbers will be represented in 32 bit system whereas double precision means that they will be represented in 64 bit system. So Calculation in double precision will be more accurate. Though the performance of CPU takes a hit as it takes longer solution time for solving 64 bit floating point numbers as well the solution requires more RAM to store those nos.

A steady state computational study has been performed using a pressure based solver. Air was used as the fluid entering from both the inlets. The default physical properties defined in Fluent were used.

Selecting boundary markers shows that what are the inlets and outlet. Blue Colours arrows shows inlet and red colour shows outlet.

Turbulence Model

RANS based two turbulence models are used to analyze the mixing effectiveness of the mixing tee.

1. K-epsilon realizable Turbulence model with standard wall function

An immediate benefit of the realizable k-ɛ model is that it provides improved predictions for the spreading rate of both planar and round jets and captured turbulence in the bulk flow. While wall function added here which capture the information near the wall.

Pros: Robust, Easy to implement. Valid for fully turbulent flows only. Suitable for bulk flow, initial screening of alternative designs, and parametric studies.
Cons: Performs poorly for complex flows involving severe pressure gradient, separation, strong streamline curvature. And wall shear stress overestimated by wall function so that delay in separation occurs. Another shortcoming is numerical stiffness when equations are integrated through the viscous sublayer which is treated with damping functions that have stability issues.

2. SST K-Omega Turbulence Model
Shear Stress Transport (SST) is a variant of the standard k–ω model and used when there are wall effects present within the case.
Pros:  The SST model accounts for the transport of turbulent shear stress and gives highly accurate predictions of the onset and the amount of flow separation under adverse pressure gradients. SST is recommended for high accuracy boundary layer simulations.
Cons: Dependency on wall distance makes this less suitable for free shear flows compared to standard k-w. It requires mesh resolution near the wall.

 

 Boundary conditions - Momentum ratio of 2 and 4 have been used in the study. The hot stream enters in the main pipe (larger diameter) while the colder stream enters from the secondary inlet.

                                                                                                     Table 1. Boundary conditions

	Velocity of hot air stream (m/s)	Velocity of cold air stream (m/s)	Temperature of hot air stream (oC)	Temperature of cold air stream (oC)
Case 1	3	6	36	19
Case 2	3	12	36	19

(i) Inlet velocity for x -axis :- 

Here, We have given value of velocity for x-axis 3 m/s and gauge pressure 0 Pa and value for all other parameters have been taken default.

   

(ii) Inlet velocity for y -axis :- 

Here, We have assumed value of velocity for y axis 6 m/s and gauge pressure 0 Pa whereas value for all other parameters have been taken default.

 

(iii) Wall condition for pipe :-

Wall conditions have been taken in the following way :-

• Stationary wall motion
• No Slip condition for shear stress
• Standard Roughness Model have been assumed at the surface
• Other parameters have been default value

(iv) Outlet condition for pipe :-

Here, values have been assumed by default for all the conditions.

 

Case I - Short Mixing Tee Caliberation

• Mesh independent study 

Element Size = 5e-3m

The above image shows the cut section of meshed mixing Tee geometry with element Size = 5e-3m

 

Mesh Element Quality

the above graph shows the element metrics vs no. of elemnts, this is use to define the quality of mesh in between 0 to 1. The element quality should not be lower than 5% in above ghaph and the min. mesh quality is 26%this we can say the mesh quality is good.

Residuals

If we take look at the residuals, std. deviation of temperature and area-weighted avg. of temp. then we can see that the after 1000 iteration the fluctuation in the resudals increases also the std. deviation of temp. along iterations falls down and area weighted avg. of temp. keeps on increaseing. thus these results are not sutiable to find out any definite inference out of it. Thus to get the proper results and to define the mesh size should be reduce.

Element Size = 4e-3m

The above image shows the cut section of meshed mixing Tee geometry with element Size = 4e-3m

Mesh Element Quality

the min. mesh quality is 31% this we can say the mesh quality is good.

As compare to element Size = 5e-3m the residuals are bit stable in case of element Size = 4e-3m and the temp. graphs also shows steady trends. Area weighted avg. temp. get sconstant at 30.25 C and the std. deviation of temp. is also gets steady to 1.6C. 

 

Element Size = 2e-3m

The above image shows the cut section of meshed mixing Tee geometry with element Size = 2e-3m

Mesh Element Quality

the min. mesh quality is 23% this we can say the mesh quality is good.

• Using K-e Turbulent Model For Momentum Ratio 2

Residuals

from the above results for element size of 2e-3m mesh we can see the results are nearly similar to the results of element size 4e-3 thus we can say that results are indepent up mesh size.

In all the above three different mesh sizes we can see that as the mesh becomes finner the the result accuracy increases and on further refinements the result remains unaffected thus this is the purpose of trying (studying) different mesh size for same physics setup is to find the out the optimum mesh size for a set physics just to make minimum use of resorces.

The element size 0f 2e-3m mesh is used for all other cases.

Temperature Contours

Using Global scale

 

Using user define scale (min. temp. = 5 C & max. temp. = 40 C)

Temperature contours shows how temperature is changes with the mixing flow physics. If we see above pitures then there are two images of temperature contours with a global and user define representation of temperatures. The global temp. representation shows the all the temperature in the flow where as the user-define shows temp. on the pipe with in the given limits.

Thus we can see in a contours that hot fluid mixes with a cold fluid with a different velocities and combines forms a fluid with different temperature.

Velocity Contours

Velocity contours shows the low to high velocity distribution throughout the domain. Velocity entering from x-inlet is 3 m/s and from y-inlet is 6m/s wich mixes and fromed new velocity of around 7 to 8 m/s but as the flow propogates from one end to another the velocity reduces upto 4.5m/s.

 

Temperature & Velocity Distribution along Line

horizental and vertical lines are taken to plot a temperature and velocity distribution along that line as shown below.

 X-distribution

 

  

graph shows that temperature and velocity along the horizantal line in which temperature after mixing reduces the value and on further propogation and mixing it rises.

Velocity profile along horizental shows before mixing, flow velocity from x-inlet is low and after mixing it increases.

Y- distribution

  

 Temperature and velocity profile along the vertical axis shows that temp. is reduces and becomes constant from higher to lower end of pipe and velocity keeps on increasing from higher to lower end.

 

•  Using K-e Turbulent Model For Momentum Ratio 4

Residuals

 

from the residuals we can see that on increasing momemtum ratio the fluction in flow increases. The avarage temp. noted on area weighted avarage of temp. graph is 27 C with a 1.5 std. deviation.

Contours

Contours shows that two different velocity flowes mixes and propogates along the length of pipe. In this case momemtum ratio is 4 that means cold fluid velocity i higher thus this can be clearly shown in the above contours.

Temperature and Velocity Distribution over a line

  

 

 comparing both the cases with 2 and 4  mometum ratios we can say that as the cold flow velocity increases the better fluid mixing takes place as we can see for 2 momemtum ratio the outlet temperature is 30 C and for 4 momemtum ratio 27 C so we get more cooler air at outlet. But both of these cases are simulated using k-e model. what difference the turbulent model can made is studied further.

 

• Using K-w Turbulent Model For Momentum Ratio 2

Residuals

If we compare this case result with the momemtum ratio 2 with k-e model case then we can see that Residuals are seems to be more fluctuating in case of using k-w model with a same momemtum ratio and avarage temperature at outlet is almost same i.e. 30.5 C but th deviation is increases from 1.7 to 2.48 and this is due to using k-w turbulence model

Contours

Velocity and temperature contours shows that how the two different temperature and velocity flows mixes and propogates along the length of tube.

Temperature and Velocity Distribution over a line

 

 

 

  

 Temperature and velocity profiles are drawn along the vertical and horizantal line positioned in above figure which shows how fluid behaves after mixing.

 

• Using K-w Turbulent Model For Momentum Ratio 4

Residuals

 

If we compare this case with momemtum ratio 4 with k-e turbulence model then residuals shows fluctuation at greater interval of time as compare to k-e model case which is have fluctuations with smaller or imidiate interval of time. Avarage temperature at outlet is slight increase by 0.5 C i.e 27.5 C  with a higher std. deviation of 2.1.

Contours

 Velocity and temperature contours shows that cold fluid coming with highger velocity than hot fluid mixes and form fluid with different temperature and velocity.

Temperature and Velocity Distribution over a line

 

 

  

 therefore we can say that by changing the turbulence models will affect the temperature deviation but not affects the results. 

 

Case II -  Long Mixing Tee Caliberation

While simulating short pipe we have see that the std. deviation of temp. is less in case of k-e model as compare to k-w model and we are intrested in the outlet temperature thus we will use the k-e model for the long pipe configureation simulation.

•  For Momentum Ratio 2

Residuals

 

residuals shows the steady fluctuations in simulation thus solution is concidered to be in steady state.

 

the avarage temperature for momemtum ratio 2 is 30.5 deg. with the std. temp. deviation of 1.8

Contours

Above contours shows the mxixing effect of hot and cold fluid with different velocities and temperature.

Temperature and Velocity Distribution over a line

 

 

 

The temperature and velocity distribution shows that variation in temp. and velocity over a drawn line while mixing

 

• For Momentum Ratio 4

Residuals

the steady residuals shows that simulation achived the steady state and for higher momemtum ratio fluction is less in the residuals.

As the flow velocity increases there is a better mixing obtained in the simulation as the avg. temperature graph shows 27.5 deg. of temp. at outlet with the std. deviation of 1.

Contours

Temperature and Velocity Distribution over a line

 

 

 

 

 Conclusions

•  K-e turbulent model gives less temperature deviation as compare to k-w model thus if we are intrested in accurate temperature at outlet thus we will require lesser deviation and therefore we concider k-e turbulent model sutiable for this simulation.
• To get a good mxing, the velocity of chilled air is very important. By increasing the velocity of chilled air by twice the velocity of 1st case we are able to reduce the outlet temp. quite nicely.
• The long pipe configuration is not at all helpful becoz it gives same results as 1st configuration.