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