This document summarizes a CFD analysis of a tee-configured mixing pipe. The analysis varied the velocity of inlet 1 while keeping inlet 2 velocity fixed. It found that increasing inlet 1 velocity by 50% to 3.75 m/s produced the most homogeneous temperature distribution at the outlet. Visualizations of the temperature and velocity fields helped explain the mixing mechanisms and showed improved penetration of the cold stream into the hot stream with the higher inlet 1 velocity, enhancing mixing. The analysis also identified locations of maximum thermal stress within the pipe.

1. Jamie Fogarty Meng. Mechanical Engineering 10100598
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THERMAL ANALYSIS OF A TEE
CONFIGURED MIXING PIPE USING
COMPUTATION FLUID DYNAMICS
INTRODUCTION
Mixing pipes have various applications throughout many different sectors. Their dominant application
is the mixing of various flows, including single phase mixing, and double phase mixing e.g. liquid-gas,
in scope of blending, dilution, treatment, heat transfer, etc. Mixing is a common operation playing an
important, and sometimes controlling, role in industrial processes including biodiesel, chemical, and
petrochemical industries [Zahid et al., 2013]. Mixing vessels have been designed to contain no moving
parts, these are denoted static mixers. A static mixer consists of individual mixing elements stacked in
series. Each mixing element is oriented 90 degrees relative to the adjacent mixing element to create
homogeneous mixing in both the horizontal and vertical directions [Principles of Operation of Static
Mixers, 2015]. Other mixing units can achieve mixing without the use of any mixing elements and are
favoured, where applicable, due to the financial gain associated with the decreased pressure drop,
and reduced maintenance directly related to the reduced amount of mechanical parts. In these
applications the flows are typically introduced at 90° to one another, resembling a tee configuration.
The mixing mechanism is generally the turbulent shear introduced by the flow entering
perpendicular. This shear heightens the dispersion and increases mixing. Mixing pipes prove to be
efficient, low energy consumption, space conservative, easy to install and generate an automatic
process.
In the biodiesel industry, mixing pipes allow for shorter mixing time and lower energy consumption.
They are used when feeding hydroxide mixture into vegetable oil stream as it is recirculated through
the pipe mixer [Static mixing - pipe mixer, 2015]. Air mixing pipes are also utilised in air conditioning,
where it is required that air at atmospheric pressure and room temperature be mixed with
recirculating air of a higher pressure, temperature and velocity. The air is mixed to yield a specific
temperature that can be then circulated to areas of interest [Frederick, 1994].
The mixing pipe under analysis in this report is a mixing pipe with no mixing elements, figure 1. Air
flows through two inlets, configured perpendicular to one another, is mixed, and exits through the
outlet. The two air streams entering have different initial conditions i.e. temperature and velocity. The
mixing of hot and cold flow streams causes high cycle temperature fluctuations, resulting in high
temperature gradients in the mixing pipe structure that induce thermal stresses. These thermal
stresses are caused as a result of the thermal expansion of a material. Thermal differentials may
produce thermal stresses significant enough to limit material life and lead to failure by fatigue failure.
Analysing both the exit temperature gradient and the entire temperature gradient will allow the
insurance of homogeneous mixing and to devise where the main thermal stresses are located. This is
turn will allow modifications to be made, if necessary.

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FIGURE 1: MIXING PIPE GEOMETRY, MESH & MESH CONCENTRATION
Inlet 1
Inlet 2
Outlet
The analysis will be achieved using Computational Fluid Dynamics (CFD) software called Star CCM+.
CFD is an efficient tool in obtaining a better understanding of many processes, including detailed
knowledge of the flow characteristics. Such a detailed understanding of the process is essential for
equipment design and material selection. In the CFD analysis, inlet 2 velocity will be fixed, while the
velocity of inlet 1 will be increased in increments of 25%. The effects of this incremental increase on
the thermal homogeneity at the outlet, and the thermal gradient of the entire mixing section, will be
discussed and compared.
AIM
This report sets out to analyse the temperature gradient within a mixing pipe. The inlet 1 velocity will
be varied to investigate its consequence on the temperature gradient throughout the entire section
and at the outlet. For each scenario residuals, temperature gradients and velocity plots will be
generated. All the data will be compared and contrasted to indicate the most suitable velocity at the
inlet to achieve a homogeneous mixture.
OBJECTIVES
1. Define mesh characteristics
2. State flow conditions
3. Define boundary conditions
4. Ensure the turbulent flow through calculations of Reynolds number
5. Analyse results obtained
MESH CHARACTERISTICS
In order to run the analysis, a mixing pipe model was imported into Star CCM+. A quadrilateral mesh
structure was previously applied to the model upon importation and consists of 82,339 cells. The
mesh can be seen in figure 1. The mesh is not consistent throughout the section of the pipe. The
mesh is concentrated in specific areas, such as inlet 2. A mesh concentration is favourable in areas of
high gradients. Stream 1 and 2 will meet at inlet two, leading to high velocity and temperature
gradients. In order to maintain accuracy, it is required to concentrate the mesh in this area. The mesh
is not concentrated throughout the section as this would lead to high running time. Also, note that
the mesh is non-symmetrical in shape; instead, the mesh elongates in the direction of the flow. This
yields a greater numerical stability.
Inlet 1 Diameter 0.02m
Inlet 2 Diameter 0.01m
Outlet Diameter 0.02m
Mixing Pipe Length 0.17m
TABLE 1: MIXING PIPE DIMENSIONS

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CFD MODELLING
FLOW CONDITIONS
The working fluid in this analysis is air, both at inlet 1 & inlet 2. The working fluid is a slightly
compressible fluid that obeys the ideal gas equation of state. The flow itself is a non-isothermal,
steady, turbulent flow whose turbulent effects are represented using the 𝑘 − 𝜀 model. K-epsilon
model is one of the most commonly used turbulent models, which is a two-equation linear eddy
viscosity model. Two transported variables in k-epsilon model are turbulent kinetic energy (k) that
determines the energy in turbulence, and turbulence dissipation (ε) which determines the scale of the
turbulence. K-epsilon has wide application and convergence for it is relatively easy for stable
solutions. Finally, the problem is solved using segregated flow solver. The Reynolds number is
calculated at both inlets for each scenario to ensure turbulent flow is present. The material properties
are displayed in table 2.
Dynamic viscosity 𝜇 = 1.86𝑥10−5
𝑃𝑎 − 𝑠
Molecular weight 𝑚 = 28.97 𝑘𝑔/𝑘𝑚𝑜𝑙
Specific heat 𝐶 = 1003.62 𝐽/𝑘𝑔𝐾
Thermal conductivity 𝑘 = 0.026 𝑊/𝑚𝐾
Turbulent Prandtl number 𝑃𝑟 = 0.9
TABLE 2: MATERIAL PROPERTIES OF THE WORKING FLUID, AIR
BOUNDARY CONDITIONS
In order for Star CMM+ to conduct the analysis, it is appropriate to define the boundary conditions for
the general flow, the wall surface and both inlets. Table 3 specifies the conditions implemented for
the velocity and direction of the flow.
Flow direction specification Boundary-Normal
Velocity specification Magnitude + direction
TABLE 3: FLOW DIRECTION AND VELOCITY SPEFICIATION
Table 4 displays that the process is adiabatic, there is no friction at the wall, no tangential velocity
(which ensures that none of the velocity vectors are lost to different directions), and no slip for the
shear stress indicating that none of the stress dissipates.
Shear stress Specification No-slip
Tangential velocity specification none
Thermal specification adiabatic
Wall surface specification smooth
TABLE 4: CONDITIONS AT THE WALL OF THE MIXING PIPE
Note that the initial conditions of pressure and static temperature are; 𝑃 = 0 𝑃𝑎, 𝑇𝑠 = 293𝐾. The
turbulence kinetic energy is 𝑘 = 0.001 𝐽/𝑘𝑔 and the turbulence dissipation is defined as 𝜖 = 𝑚2
/𝑠3
.
Table 5 defines the inlet conditions for inlet 1 and 2.

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Inlet 1 Inlet 2
Static Temperature 𝑇𝑠 = 298𝐾 Static Temperature 𝑇𝑠 = 373𝐾
Turbulence Intensity 0.1 Turbulence Intensity 0.1
Turbulence length scale 0.001m Turbulence length scale 0.001m
Velocity magnitude 2.5 m/s Velocity magnitude 10 m/s
Reynolds Number 3245 Reynolds number 5328
TABLE 5: INITIAL CONDITIONS AT INLET 1 & 2
Note that in this analysis, the velocity at inlet 1 is incrementally increased as per table 6.
Increase Velocity Re
25% 3.125 m/s 4056
50% 3.75 m/s 4867
75% 4.375 m/s 5678
100% 5 m/s 6489
125% 5.625 m/s 7300
TABLE 6: PERCENTAGE INCREASE IN VELOCITY MAGNITUDE AND THE CORRESPONDING VELOCITY MAGNITUDE
AT INLET 1
Finally, the outlet default boundary type was set to flow-split outlet and the maximum steps, i.e.
running criteria, was set to 500 steps.
RESULTS
The residuals are fundamentally a measure of
an iterative solutions numerical convergence,
signifying that the lower the residual the less
the results will change with further iterations.
The residual plots were generated for each
incremental increase to ensure the accuracy
of the results. Figure 2 presents the residual of
the initial analysis i.e. inlet 1 velocity = 2.5m/s.
With the velocity of inlet 2 fixed, inlet 1 was
increased in increments of 25%, as per table 6.
Two probes were implemented at the outlet of
the mixing pipe. These probes were arranged so that one ran horizontally through the centre point
and the other vertically. These probes were used to gather the temperature gradient across the
outlet. From these temperature gradients the mean deviation from the average temperature for each
inlet velocity was obtained for both the horizontal and the vertical probe. From these then, the
average of both was generated and is plotted in figure 3.
FIGURE 2: RESIDUAL PLOT. 0% INCREASED VELOCITY

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FIGURE 3: MEAN DEVIATION FROM AVERAGE TEMPERATURE FOR EACH INLET VELOCITY
FIGURE 4: TEMPERATURE SCALAR SCENE:
OUTLET. 0% INCREASED VELOCITY
FIGURE 5: TEMPERATURE SCALAR SCENE:
OUTLET. 50% INCREASED VELOCITY
FIGURE 2: TEMPERATURE SCALAR SCENE: ENTIRE.
0% INCREASED VELOCITY
FIGURE 6: TEMPERATURE SCALAR SCENE: ENTIRE.
50% INCREASED VELOCITY
Using Star CCM+, instantaneous scalar scenes were generated. These are a convenient method for
visually interpreting results, as a colour scale is present to signify the values of the scalars of interest.
Figures 4 & 5 display the temperature scalar scenes at the outlet for inlet 1 velocity’s 2.5 m/s and 3.75
m/s.
The same temperature scalar scenes were used to locate the maximum thermal stresses in the mixing
pipe. This can be seen figures 5 & 6.
Instantaneous velocity scalar scenes, on a plane horizontally cut through the mid-section of the
mixing pipe, were generated for each simulation. The specific one of interest are displayed in figure 7
& 8.
5
6
7
8
9
10
2.5 3.125 3.75 4.625 5 5.625
MeanTemperature
Deviation(K)
Inlet 1 velocity (m/s)
Mean deviation from
average temperature

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FIGURE 7: VELOCITY SCALAR SCENE. 0%
INCREASED VELOCITY
FIGURE 8: VELOCITY SCALAR SCENE. 50%
INCREASED VELOCITY
DISCUSSION
Firstly, observing figure 2, it is evident that the solution numerically converges as the residuals arrive
significantly close to zero, inclining that the results obtained reserve some accuracy.
The aim of the mixing pipe is to achieve a homogenous temperature distribution at the outlet. Figure
3 plots the mean deviation from the average temperature. This plot quantifies the deviation of the
outlet temperature from the averaged value. The plot reveals that after a 50% increase in the velocity
magnitude of inlet 1, there is a convergence. Logical and economic sense indicates that no further
increase from 50% is required, as higher percentage increases achieve a similar homogeneity and are
less cost efficient i.e. pumping power. Consequently, the discussion will focus on the comparison of
both the initial inlet 1 velocity and the 50% increased velocity.
Figure 5 presents the instantaneous temperature gradient of the entire mixing section with an inlet 1
velocity of 2.5 m/s. This figure gives insight into the mechanism behind the mixing process. In order to
produce a uniform mixture by mixing, two things need to occur. First, there must be a bulk or
convective flow so as to avoid any dead/stagnant zones i.e. turbulent inlet stream 2. Secondly, there
must be an intensive or high-shear mixing zone, in which the homogeneities are broken down i.e. the
mixing section [Zahid et al., 2013]. The cold air enters inlet one, eventually meeting a divergence
zone. As the cold air initially diverges, the velocity decreases (by continuity) and the pressure
increases (by Bernoulli). This expansion results in an energy decrease corresponding to a decrease in
temperature, represented in figure 5 as the light blue zone at the neck of the divergence zone. The
hot stream is introduced perpendicular, at a velocity magnitude 4 times greater than the cold stream,
into the mixing section. This heightened velocity gives the hot stream a higher momentum inertia,
which carries it predominantly around the perimeter of the mixing section. This is quantified as the
green zones present near the walls of the mixing section in figure 7. The turbulence of the hot stream
yields velocity fluctuations that mix transported quantities of momentum and energy resulting in
heightened heat transfer from the hot stream to the cold stream. However, due to the momentum of
the stream and the position of introduction, the hot stream follows the boundary of the mixing pipe
in the axial direction, with minimal penetration of the cold stream, which resides in the centre. This is
verified in figure 7 by the green contour (hot stream) near the mixing section boundary and the blue
contour (cold stream) in the middle. As the two streams then converge, mixing is further induced as
the cold stream penetrates the hot stream. Analysing the outlet temperature scalar scene in figure 4,
the above stated is further signified. Despite the increased mixing due to the convergence of the
mixing pipe section, the hot air accommodates the perimeter with colder air filling the centre.

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When the inlet velocity increases by 50% to 3.75 m/s, in the mixing section, the heightened
momentum of the cold stream allows it to better penetrate the hot stream. This can be confirmed by
the reduction in velocity characterised by the comparison of the green zones near the mixing section
boundary in the velocity scalar scenes figure 7 & 8. The velocity near the boundary of the mixing
section in figure 8 is less than that of figure 7, indicating enhanced mixing of the hot and cold stream.
Further confirming this is the outlet temperature scalar scene shown in figure 5. The temperature
gradient is reduced and the streams have more homogeneity, as the colour gradient in the scalar
scene is diminished.
Observing the thermal stresses on the mixing pipe, schematically expressed as temperature gradients
in figure 5 & 6, it is evident that adjacent from the entry of the hot stream there is a high temperature
gradient independent of the cold stream inlet velocity. Dependant on the running agenda, i.e. fixed
running, periodic running, cyclic thermal stresses may be induced in the structure of the mixing pipe,
potentially initiating a crack and leading to failure by thermal fatigue loading. This analysis pinpoints
the area where the resilience of the mixing pipe requires focus, or gives the options of selecting a
material to suit the cyclic loading. Further from this, comparing figure 4 & 5, it is clear that at an inlet
1 velocity of 3.75 m/s the thermal gradient is reduced at the outlet. This velocity proves advantageous
as it would relieve thermal stresses further from the mixing pipe, reducing the risk of thermal fatigue.
CONCLUSION
From the analysis it can be concluded that:
 After an increased velocity of 50% in inlet 1 (3.75 m/s), the mean deviation from the average
temperature of the outlet converges.
 In the initial simulation, due to the heightened velocity and introductory position of inlet 2,
the hot stream flows predominantly around the boundary of the mixing section with minimal
penetration from the cold stream which fills the centre. Mixing primarily occurred as the
mixing section converges. As a result, a temperature gradient reflecting this was present at
the outlet.
 When the velocity of inlet 1 was increased to 3.75 m/s, improved penetration was observed
directly resulting in enhanced mixing in the mixing section and a more homogeneous outlet
mixture. Thermal stresses were relieved at the outlet as a consequence of this.
 Independent of the inlet 1 conditions, a large thermal gradient was present in the mixing
section. Depending on the running agenda of the mixing pipe, material choice or design
would have to be considered to minimise the risk of thermal fatigue.
Overall, increasing the velocity of inlet 1 by 50% proves an efficient method of ensuring a more
homogeneous mixture and decreasing the thermal gradient at the outlet. Although the pumping
power required would increase, depending on the application the homogeneity of the mixture may
be of more importance. To finally conclude, at an inlet velocity of 2.5 m/s, a thermal gradient was
present at the outlet. Contingent upon the distance the required mixture has to travel after the
outlet, the initial inlet 1 velocity may be sufficient to yield the required mixture, as further from the
mixing pipe, heat transfer will continue to occur.

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RECCOMENDATIONS
 If pressure drop was not a significant design parameter, having convergence occur over a
greater length would increase the mixing of the streams, and could potentially decrease the
thermal gradient present in the initial simulation i.e. inlet 1 velocity of 2.5 m/s. In saying this,
a balance would have to be stricken to ensure the pumping power requirement is lower than
that required for increasing the inlet 1 velocity by 50%, but still yielding the desired
homogeneity. Otherwise, this design change would not be feasible.
 Changing the introduction position and/or angle of inlet 2 may influence the mixing in the
mixing section in a positive way. A computational analysis could be conducted, fixing the
initial simulation conditions, and orientating the inlet 2 differently to try minimise its
peripheral flow and increase mixing.
REFERENCES
1. Zahid HI Khokhar, MA S Al-Harthi , BF Abusharkh , HH Al-Ali , RN Sharma , HD Zughbi , AA
Shaikh , HH Redhwi , A Abdurraheem , SU Rehman , SM J Zaidi , ZU Khan , IA Hussain and BS
Yilbas, 2013, ‘Heat and Mass Transfer Mixing Enhancements in Pipe-Line; Numerical CFD and
Experimental Chores: A Review’, International Journal of Engineering Science and Innovative
Technology (IJESIT), Volume 2, Issue 1, January 2013, pg. 1-11.
2. Principles of Operation of Static Mixers - StaMixCo Static Mixer Products & Technology.
2015. Principles of Operation of Static Mixers - StaMixCo Static Mixer Products & Technology.
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September 2015].
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