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Preliminary CFD Analysis of Entrance Length in Twisted Tube
Teoh Kuang Yee, Research & Application
Abstract
This paper aims to investigate the Entrance length in a twisted tube with CFD
simulation. Water is used as the flow media in the tube. Various entering velocities
have been studied, ranging from 1.5 m/s to 5 m/s. For a 700mm tube length, the
results show that only about 1/3 of the tube is needed for the fluid to be fully
developed. By avoiding the first 250mm of the tube, the remaining length of the tube
can be used in the actual physical experimentation to determine the tube performance
(e.g. fiction factor) under fully developed flow conditions.
Nomenclature
HD Hydraulic diameter
A Area
U Perimeter
I Turbulence intensity
Re Reynolds Number
critRe Critical Reynolds Number
avgu Mean velocity
'u Root-mean-square of the velocity fluctuations
µ Fluid viscosity
ρ Fluid density
El Entrance Length Number
el Entrance Length
1. Introduction
In general, an air conditioning unit has four main components – compressor,
condenser, expansion device and evaporator. Of these, the condenser and
evaporator are heat exchangers. A system designer engineer will need to design
and select the best heat exchanger sizes for optimum performance of the air-
conditioning system. However, such selection is often very challenging as it
involves the performance data of each component themselves.
For a water cooled air conditioner, the condenser is often manufactured from a
tube-in-tube pipe. The outer tube is usually a round smooth tube while the inner
tube has enhanced surfaces to improve the heat transfer. An example of tube-in-
tube condenser is shown in Figure 1. In order to make a good design selection of
this type of heat exchanger, it is important that the hydraulic and heat transfer
characteristics of the tube itself must be known. The heat transfer coefficient of
the tubes is one of the key properties for the system designer engineer in the
design of a water cooled heat exchanger.
Figure 1: A tube in tube heat exchanger
In order to obtain the heat transfer coefficient of a pipe, experiments have to
be carried out. It is important that this experiment is done when the flow is fully
developed. When the fluid enters the tube, it will take some distance for the
velocity profile to become fully developed. To ensure the data gathered from the
experiments are taken for fully developed flow, the fluid pressure drop is recorded
after the entrance length.
Recently, a new type of tube-in-tube pipe has been introduced in the market.
The pipe has a twisted inner tube (see Figure 2 and 3), which according to claims
from the manufacturer, helps to improve the heat transfer performance. In our
effort to characterize the performance of this tube, an experiment work has been
planned.
Inner tube, with
enhanced surfaces
Outer tube
Water
Due to the scarcity of resources, the pipe manufacturer is only able to provide
a short 0.7m straight piece of test specimen for the experiment. It is important to
determine if this short length is sufficient to accurately measure the hydraulic and
thermal performances in the fully developed region.
In view of this need, a CFD simulation approach is used to determine the
flow profile along the tube. By using some flow criteria, it is possible to estimate
the entrance length of this twisted pipe.
2. Geometry and Mesh
As a first approach, the twisted tube geometry has to be drawn. Due to the
complexity of the twisted surfaces, it is very difficult to reproduce the profile of
the tube in a CAD drawing. A simpler way of doing this would be to digitally scan
a short section of the tube.
Figure 2: 3D model of a small section of twisted tube
Figure 2 above shows the 3D scanned twisted tube. To model the internal
fluid flow, only the inner volume is needed. For this purpose, various methods
were used.
(a)
(b)
Figure 3: Solid Extrude Function in CAE 3D-modelling software
Initially, the scanned 3D model in IGES format is imported into CAE 3D-
modelling software. Using the inner perimeter, a solid extrusion (length
approximately 500mm) is created and exported in ACIS format. Exporting the
model in other format such as IGES or STEP will result in noise and damaged
geometry in gambit. Another hollow solid extrusion part is also created with the
inner perimeter as in Figure 3 (b). This will be used to prepare two different
regions for different mesh sizes.
Next, both geometries are imported into mesh generation software. Using
Boolean operation, the geometry in Figure 3(a) is split with geometry in Figure
3(b). The 2D auto-mesh function is then used on the faces of the split geometry
together with 3D drag function to create the mesh as shown in figure below:
(a)
(b)
Figure 4: Mesh generation with coarse and fine mesh
Fine Mesh
Coarse Mesh
Notice that the mesh is finer near the inner surfaces while coarse mesh is used
in the core of the pipe. This is necessary because of the narrow gaps between the
flutes of the pipe.
The completed mesh file is then imported into GAMBIT™ where the
boundary types are added to the mesh. See Figure 5. This is then ready to be
exported into FLUENT™.
Figure 5: Boundary type setup in GAMBIT™
3. CFD Numerical Modeling
In order to find the maximum possible Entrance length, the simulation had to
be run in turbulence mode since the application range falls in the turbulence
region.
Model Selection
Due to the computational cost constrain, the least expensive viscous model
with standard k-ε (epsilon) turbulence model has been selected. The k and ε are
the turbulence kinetic energy and its dissipation rate respectively. The k-ε model
constants are set with widely accepted default values: 44.11 =ε
C , 92.12 =ε
C ,
09.0=µ
C , 0.1=kσ , 3.1=ε
σ .
Boundary Conditions
Four boundary conditions have been applied to the model:
1. Velocity inlet boundary condition for inlet flow.
For the turbulence model, the calculations involved are:
Turbulence Intensity
81
)(Re16' −
=≡HD
avgu
uI (1)
The turbulence intensity, I , is defined as the ratio of the root-mean-square of
the velocity fluctuations, 'u , to the mean flow velocity, avgu .
Where
µ
ρ HavgDu=Re (2)
Hydraulic Diameter
U
ADH
4= (3)
The hydraulic diameter is the ratio of 4 times cross sectional area, A to the
wetted perimeter of the cross-section, U .
2. Pressure outlet boundary condition
The outlet boundary condition is set as pressure outlet. This boundary
condition often gives better convergence rate as compared with other outflow
conditions when backflow occurs during iteration. The gauge pressure at the
outlet is set to zero Pascal. Default values for backflow turbulence kinetic energy
and dissipation rate are used.
3. Wall boundary condition
Wall boundary condition is applied to the bound fluid flow region. The wall is
set as stationary wall with no slip shear condition.
4. Fluid condition
Default water-liquid from fluent database had been selected as the fluid.
4. Result and Analysis
Simulations were run with turbulence model coupled with different inlet
velocity ranging from 1.5 m/s to 5 m/s. Each inlet velocity produces a set of data
as shown in the graphs below.
Figure 6: Static Pressure Vs Position
The pressure drops rapidly from the inlet of the tube because the flow is still
developing. Then after some distance, the gradient become constant as the flow
becomes fully developed as in Figure 6. The entrance length is determined based
on the criteria that no further change of the rate of pressure drop along the length,
which will occur when the flow has been fully developed.
Figure 7: Finding entrance length
R2 = 1.0000
R2 = 0.9999
R2 = 0.9998
Since it is difficult to detect the transition point visually, a VBA macro
program is developed. Firstly five points at the near end position are selected and
plotted with a linear trend-line on the graph. Data points are added incrementally
one at a time. The R2 values for all the plots are recorded. The last point which
gives a R2 value not lower than 0.9999 is selected (as demonstrated in figure 7)
and the corresponding length position recorded in the table below:
Table 1: Entrance length for various entering velocity
Fluid Entering Velocity, m/s Entrance length, m
5 0.22
4 0.22
3.74 0.22
3 0.21
2 0.2
1.5 0.19
The plot above shows that the entrance length for up to 5m/s entering velocity
is less than 0.25m.
5. Validation
The entrance length can be expressed with the dimensionless Entrance Length
Number:
Dl
El e= (4)
The Entrance length number correlation with the Reynolds Number for
laminar flow and turbulent flow can be expressed accordingly as:
Re06.0min =arlaEl (5)
61
turbulent Re4.4=El (6)
Table 2: Analytical Solution
Hydraulic Diameter, m 9.40E-03 9.40E-03 9.40E-03 9.40E-03 9.40E-03 9.40E-03
Density, kg/m3 998.200 998.200 998.200 998.200 998.200 998.200
Velocity, m/s 5.00 4.00 3.74 3.00 2.00 1.50
Dynamic Viscosity, N.s/m
2 0.001002 0.001002 0.001002 0.001002 0.001002 0.001002
Re 46802 37441 35008 28081 18721 14041
El turbulent 26.414 25.449 25.166 24.258 22.673 21.611
length to fully developed velocity profile
el turbulent, m 0.248 0.239 0.236 0.228 0.213 0.203
Using equation 4 and 6, the analytical solution results were tabulated in table
2 above and validated with fluent simulation in Figure 8 below.
Figure 8: Entrance Length vs. Fluid Entering Velocity plot for Fluent
simulation and analytical solution.
The deviation of fluent simulation to analytical solution is found to have
RMSE of 8.55%
6. Other Observation
:
Figure 9: Pressure contour across the tube
From the simulation results, the pressure drop can be observed along the tube
length as in the Figure 9 contour plot. Pressure is gradually decreasing as fluid
flows from inlet to outlet.
Figure 10: Velocity contour across the tube
Figure 10 shows the velocity contour along the tube. The velocity profile at
the cross section becomes the same after some short distance from the inlet.
Beside that the velocity near wall is much lower than the center line.
Figure 11: Particle tracking showing swirling effect
Swirling effect can also be seen from the particle tracking plot as in Figure 11.
Particles at the center flow very much faster in Z direction compared to the
particles near the tube wall due to swirling effect. This can be explained by the
lower velocity but longer path traveled by the particles near the wall.
Conclusion
The tube length needed for the flow to be fully developed had been found by
using simulation. The results show that up to 5m/s entering fluid velocity, the
entrance length is around 0.25m. The deviation of simulation results compared to
analytical solution is found to have RMSE of 8.55%. The experiment with twisted
tube can be carried out by taken into consideration of the 0.25m entrance length.
References
[1] FLUENT™ 6.3 Manual, FLUENT™ Inc., 2006