2. 1 INTRODUCTION
This report will look at designing a cross flow heat exchanger to meet a design brief. It
will look at some useful calculations before the CFD simulation process, the CFD simulation
process and analysis of results gotten from the CFD process.
2 DESIGN BRIEF
A cross flow heat exchanger is needed for a building’s heating system. The heat exchanger
will be supplied with oil, at 55o
C (548.15o
K), from a combined heat and power plant, and
needs to be capable of providing 0.025m3
/s of water at 55o
C (328.15o
K).
3 THEORY
3.1 Overview
A heat exchanger is an equipment used to transfer heat from one fluid, at temperature T1,
to another at temperature T2. The temperature di↵erence is key to the operation of the heat
exchanger. Heat exchangers can be classified by their:
1. Transfer Processes
2. Geometry of Construction
3. Heat Transfer Mechanism, and
4. Flow Arrangement
we are interested in the flow arrangement, specifically the cross flow system.
3.2 Design Process
The goal of a heat exchanger, as stated above, is to transfer heat between two or more flowing
fluids. This implies that there will be a change in temperature between the heat exchanger
inlet and outlet.
Values of importance in the design process are; the relationship between the inlet, TIN, and
outlet, TOUT, temperatures, the overall, U, and individual, Cp, heat transfer coe cients, and
the heat transfer rate, Q, for the fluids involved (in this case, oil and water).
3.3 Heat Transfer Rate, Q
Heat transfer rate is the rate of heat energy transferred through a surface area. This gives
the amount of heat transferred between the oil in the pipes and the water, it is assumed there
are no heat losses between the pipes and the oil, i.e. the pipe walls are at 548.15o
K.
2
3. The design brief above, states the required outlet temperature is 328.15o
K, and, if water
at the inlet is taken to be at room temperature (298.15o
K), then the heat exchanger has to
achieve a change in temperature, 4T, of 30o
K. 4T is given as:
4T =
Q
Cp ⇥ ˙m
(1)
We know the required 4T, the heat transfer coe cient, Cp, of water (4183W/(m2
⇥ K)) and
the mass flux, ˙m (0.025m3
/s). Therefore, equation (1) can be rearranged to get the required
heat transfer rate, Q.
Q = 4T ⇥ Cp ⇥ ˙m
Q = 30 ⇥ 4183 ⇥ 0.025 = 3137.25W
3.4 Total Surface Area, Atotal
With heat exchangers, the greater the contact area between the fluids, the greater the heat
transferred. In this case, water is flowing along the surface of cylinders, so working out the
surface area of each cylinder and summing up will give the total contact surface. A better way
to go will be to relate the calculated heat transfer rate to the total surface area, i.e. use the
heat transfer rate, Q, calculated in 4.1 to find the required total surface area to achieve the
design temperature.
Total surface area, Atotal, is related to Q via the overall heat transfer coe cient, U, and is
given as:
Atotal =
Q
U ⇥ 4TLM
(2)
Where 4TLM , the log mean temperature di↵erence between the inlet and outlet, is:
4TLM =
4TA 4TB
ln 4TA ln 4TB
(3)
Where 4TA is the temperature di↵erence between the fluids at the inlet, and 4TB is the
di↵erence at the outlet. 4TLM gives a logarithmic average of the temperature di↵erence
between the heat exchanger inlet and outlet. A large 4TLM means large heat transfer.
3.4.1 Overall Heat Transfer Coe cient, U
The overall heat transfer coe cient depends on the fluids and transmission material, and
their individual properties. To find the overall heat transfer coe cient, U, the individual heat
coe cients of oil and water, and the resistance of the pipe material are needed. U is given as:
1
U ⇥ A
=
X 1
h ⇥ A
+
X
R (4)
Where R is the thermal resistance in the pipe and is given as:
R =
x
kA
(5)
Where A is the total area of the heat exchanger, x is the wall thickness and k is the thermal
conductivity of the pipe material. Assuming a really thin pipe (x < 0.0005m), then R ⇡ 0.
Therefore:
1
U ⇥ Atotal
=
1
hoil ⇥ Apipes
+
1
hwater ⇥ Aheatexchanger Apipes
We need an approximate value for Atotal so we can take an approximate value for U.
3
4. U = 60 300W/m2
K ([9], heavy oils & water) and 4TA = 250o
K and 4TB = 220o
K, 4TLM
can be approximated as:
4TLM =
30
ln 250 ln 220
= 234.68o
K
and thus Atotal, for U = 60W/m2
, is
Atotal =
3137.25
60 ⇥ 234.68
= 0.222m2
and, for U = 300W/m2
,
Atotal =
3137.25
300 ⇥ 234.68
= 0.04456m2
Therefore Atotal ⇡ between 0.222m2
and 0.04456m2
.
4 METHOD
The CFD simulation process was done using Ansys workbench starting with a very simple
2D model, figure 1. The model, a 1m ⇥ 0.2m flat plate, consisted of three pipes and symmetry
boundary conditions at the top and bottom of the plate, an inlet, to the left, and an outlet, to
the right.
Figure 1.
Next, the various boundaries where named using Named Selections. The pipe walls were
set a pipe walls, the inlet and outlet edges as inlet and outlet respectively and the top and
bottom walls as symmetry (this means the walls are infinitly long long the y-axis upwards and
downwards).
Then, the finished part had to be meshed. To start o↵, a mesh size of 0.005m (a mesh
refinement study is done in section 5 below) was chosen and the mesh generated. Figure 2,
below, shows the mesh at 0.005m.
4
5. Figure 2.
The final settings where made in fluent. The viscous model was set to k ✏, because of the
turbulent nature of the flow, the fluid was specified as water, and boundary conditions, for the
inlet and pipes, where set. The inlet velocity and temperature where set to 0.0125m/s and
298.15o
k respectively, and the pipe temperature set to 548.15o
K. Fluent was also set to solve
for the internal energy of the fluid.
Before the calculations could be performed, the tolerance was lowered to 0.00001 and the
calculation was set to perform 1000 iterations, at which point convergence would be been
reached.
After the calculations, values relating to the mass fluxes, total heat transferred etc., where
extracted from fluent using Fluxes under Reports.
5 RESULTS & CALCULATIONS
5.1 Numerics
5.1.1 Mesh Refinement Study
The first step, towards refining the design, was to perform a mesh refinement study. The
mesh refinement study provided an reasonable guide to choosing a mesh size that would give
accurate results in an e↵ective time frame. A very fine mesh (small element size) would very
accurate result approximations at the cost of very high processing power, so the most e cient
case would be a mesh small enough to give results within an acceptable accuracy/tolerance
level, but big enough to run with very little computing power and time requirements.
5
6. Figure 3.
Figure 3 shows the mesh at 0.05m, cells around the curves, especially the center circle, are
polygonal (instead of round), because the cell size is too big to accurately define them. Figures
4 and 5 show the mesh at 0.002m and 0.001m respectively. Although the 0.001m mesh is finer,
it only gives a 2% increase in accuracy, compared to the 56% increase from the 0.05m mesh.
Figure 4.
Figure 5
Before the analysis could run, the boundary conditions had to be set. The inlet temperature
was set to room temperature and the outlet temperature was set to 548.15o
K. The inlet flow
velocity, vI, also had to be set. To do this, vI was calculated by rearranging equation (6), below,
and solving for vI when volumetric flow rate, ˙V = 0.025m3
/s (from the design brief), and the
6
7. area of the inlet, Ainlet, = 0.2m2
(the inlet was assumed to be 1m thick, and 0.2m).
˙V = vI ⇥ A (6)
This gives an inlet velocity of 0.125m/s. The mesh refinement study was performed for values
between 0.05m and 0.001m, at increments of 0.01m, between 0.01m and 0.05m, and 0.001m
between 0.001m and 0.009m. Table 1, below, shows the values for outlet temperature, TOUT ,
for di↵erent mesh sizes, where x is mesh size in meters.
MESH REFINEMENT
x(m) TIN (K) ˙m kg/s Q (W) 4T (K) TOUT (K)
0.05 298.15 25 309775 2.97 301.12
0.04 298.15 25 308925.4 2.96 301.11
0.03 298.15 25 401368.64 3.85 302.00
0.02 298.15 25 533509.75 5.11 303.26
0.01 298.15 24 682983.54 6.67 304.82
0.009 298.15 25 687097.2 6.58 304.73
0.008 298.15 25 706218.3 6.77 304.92
0.007 298.15 25 701844.6 6.72 304.87
0.006 298.15 25 703599.57 6.74 304.89
0.005 298.15 25 704299.1 6.75 304.90
0.004 298.15 25 699115.5 6.70 304.85
0.003 298.15 25 704136.1 6.75 304.90
0.002 298.15 25 708133.1 6.79 304.94
0.001 298.15 25 724694.8 6.94 305.09
Table 1.
From table 1, 4T can be seen to be converging at ⇡ 7o
K as the mesh gets finer, however,
after 0.002m, the calculation times increase significantly, which indicated increased processing
power. However, from graph 1, the graph is levelling o↵ and can be expected to give relatively
similar temperature values at mesh size 0.0005m (for example) as at 0.002m; therefore, it is
reasonable to use a mesh size of 0.002m.Graph 1, below, illustrates the levelling out of the
temperature values.
7
8. Graph 1: TOUT(K) against mesh size (m)
5.1.2 Inlet Turbulence Conditions
Another test of convergence was to change the inlet turbulence conditions; the temperature
results where not expected the change significantly. Table 2 and graph 2 below show the results
converging as turbulence intensity increases. Where % is turbulence intensity.
INLET TURBULENCE
% TOUT(K)
1 306.92
2 305.95
3 305.4
4 305.09
5 304.9
6 304.77
7 304.68
8 304.61
9 304.57
10 304.53
11 304.5
12 304.47
13 304.45
14 304.43
15 304.42
Table 2.
8
9. Graph 2: Outlet Temperature, TOUT(K) against Turbulence Intensity %.
5.2 2D Designs
Confident that fluent was generating accurate and reliable results, the original simple design
could be modified to achieve requirement set out in the design brief.
5.2.1 Pipe Spacing
The 1st
variable, in the design process, was the pipe spacing. A pipe spacing study was
performed on five di↵erent variations of a simple design (figure 6 above), all with 3 pipes of
radius 0.075m. Graph 3, shows a plot of the pipe oulet temperature against spacing.
Graph 3: Outlet Temperature, TOUT(K) against Pipe Spacing (m).
The shape of Graph 3 indicates, generally, the smaller the pipe spacing, the better the the
heat transfer, however, there is a dip in the curve, which indicates that pipe spacing is not the
only factor a↵ecting heat transfer. Figures 6 and 7, show the geometry at spacings 0.15m and
0.35m respectively.
9
10. Figure 6
Figure 7
5.2.2 Angle of Attack
Another factor, a↵ecting heat transfer, is the angle at which the inlet flow engages with the
pipes. Various resources [2] on heat exchanger design quote 30o
as the angle to set the pipes at
for maximum e ciency. Working on an even simpler model than the one used in 5.2.1 above,
with 2 pipes of radius 0.03m, we can investigate the e↵ect the angle of attack has on heat
transfer.
Figure 8
Figure 8, above, shows the pipe arrangement at 30o
. Graph 4, below, shows the outlet temper-
ature for di↵erent angles of attack. We can see that, the best heat transfer occurs at 0o
mark,
but at 30o
we have a similar value.
10
11. Graph 4: TOUT(K) against Angle of Attack (o
)
To explain this, we examine the velocity contours of the flow in 30o
and 50o
cases (figures 8.1
and 8.2 below). In the 30o
case, flow over the top pipe can be seen to be interacting with the
flow over the second pipe a lot more than in the 50o
case; these interactions aid heat transfer.
Therefore, a design with pipes at an angle around 30o
would be ideal.
Figure 8.1
Figure 8.2
5.2.3 Reverse Flow
Reverse flow occurs when flow of fluid changes direction and flows opposite to it’s predefined,
or desirable direction. When running the pipe spacing study, it was discovered that, at a certain
distance from the inlet and outlet, reverse flow began to occur. Reverse flow occurs when flow
is fully turbulent and has not had adequate time to adjust after coming in contact with an
obstacle.
11
12. Case 1
The design in case one is the simple first case used for the mesh refinement study in 5.1.1
above. Using a mesh size of 0.002m, 1000 iterations where calculated, at turbulence intensity
5, and the temperature at the outlet was worked out using equation (1) in section 3.3 above.
Design 1 gave an outlet temperature of 304.94o
K.
Case 2
In case two, the number of pipe was increased from 3 to 9, and the pipe spacing, angle of
attack, and pipe radii where changed. This design had an outlet temperature of 309.29o
K.
Figure 9
Case 3
Case 3 built on case 2, with more pipes being added, even more variation in pipe radii,
and smaller gaps between the pipes. The outlet temperature for this design was 352.11o
K,
23.96o
K more than the required outlet temperature specified in the brief; this gives room for
discrepancies that my arise when the part is extruded to 3D (for example, the 3D case will not
have symmetry conditions at the walls and will have the walls set at room temperature). Case
3 will be the main design going forward.
Figure 10
The design in case 3 pulled together everything discussed in the above sections. The pipe
spacing is very small, to get as much interaction as possible, there are no empty spaces at the
top an bottom of the heat exchanger, where water could avoid the pipes, and there are smaller
pipes in spaces between the larger ones to increase the maximum total surface area, and thus
increase heat transfer. Also, there a huge amount of the heat exchanger left over for turbulent
flow to settle such that reverse flow either does not occur at the outlet or is kept to a minimum.
12
13. 5.3 3D Design
Having achieved the design brief in 2D, the next step was to run the simulation in 3D.
5.3.1 Creating the Model
To create the model, the geometry was thin extruded, in design modeller, and, to save
processing time, the thickness was set to 0.1m. This meant that the inlet velocity had to be
recalculated, and the new vI(1m/s) had to be set as the boundary condition in fluent. After
generating the 3D part and defining the inlet, outlet walls and pipes, a 0.002m mesh was
generated and the calculations where set up in fluent and run. Figure 11 shows the meshed 3D
part.
Figure 11
Figure 12, below, shows the highlighted section from figure 11. This shows how detailed the
mesh is, especially at the spaces between the pipes.
Figure 12
It can be seen that the mesh is not small enough, in the pipe spacings, to give the best values,
especially where there is only one cell between the pipes. A finer mesh was tried, to better
describe the spaces, but the meshing process ran for too long, so in an attempt to get a better
mesh, the thickness of the 3D part was reduced further to 0.05m. Figure 13 shows a zoomed
in image of the refined mesh (0.0015m) for the part.
Figure 13
13
14. With the 0.002m mesh, the outlet temperature for the 3D model was 343.44o
K.
5.3.2 Reynold’s Number
To understand the nature of the flow through the heat exchanger, we need to work out the
Reynold’s number. At Re< 2300, flow is laminar, at 2300 <Re< 4000, the flow is transient,
and at Re> 4000 we have turbulent flow[3]. In our design, the flow is expected to be turbulent,
thus Re> 4000. For a heat exchanger, Reynolds number is given as [4]
Re =
⇢vDH
µ
(7)
Where the hydraulic diameter of the pipe, DH, is given as:
DH =
4A
P
Where A is the cross-sectional area of the heat exchanger and P is the wetted perimeter.
⇢ = 997.04, V= 2m/s (from equation (6) at thickness= 0.05m),
µ = 0.001003kg/m 2
, and
DH =
4 ⇥ 0.05 ⇥ 0.25
2 ⇥ 0.05 + 0.25
=
1
12
Therefore, Reynolds number for the 3D design is:
Re =
997.04 ⇥ 2 ⇥ 1/12
0.001003
= 165676.3
Re> 4000, therefore the flow is turbulent, as expected.
5.3.3 Total Surface Area, Atotal
In section 3.4, the total surface area to achieve the design brief was approximated as 0.222m2
.
This section will compare the theoretical results with the result received experimentally.
The design in case 3 consists of a pattern of pipes of di↵erent radii. There are 14 pipes of
radius 0.03m, 2 of radius 0.017m, 12 of radius 0.016m, 2 of radius 0.015m, 12 of radius 0.013m,
and 12 of radius 0.01m. Total surface area for a cylinder is given as:
Atotal = 2⇡r(r + h) (8)
The pipes are 0.05m long, therefore, Atotal can be calculated for each case using equation (8).
Table 3 below shows the total surface area for each pipe radius. Comparing the result here
with theoretical Atotal, ⇡ between 0.222m2
and 0.04456m2
, we can see the design should and
does fit the design brief from a mathematical point of view.
14
15. r (m) No. Atotal (m)
0.03 14 0.211115026
0.017 2 0.014313096
0.016 12 0.079620524
0.015 2 0.012252211
0.013 12 0.061751145
0.01 12 0.045238934
Total = 0.4243m2
Table 3.
6 ANALYSIS
This section includes analysis of the performance of case 3’s 3D design.
6.1 Contours & Vectors
6.1.1 Temperature
Figure 14 shows the variation of temperature between the inlet and outlet. As expected, the
temperature is highest at the pipe walls and there is an increase in temperature from the inlet
to the outlet, which shows the water is getting heated.
Figure 14
6.1.2 Turbulence
The turbulence contour gives a visual representation of nature of the flow. The turbulent
energy of the flow is high at the top and bottom pipes and at the points (top and bottom)
where the flow exists the pipe system, due to vorticies formed by the unsteady separation of
the flow around the pipes (von Karman vortex sheet or vortex shedding [5]). These vortices
are undesirable as they set up cross wind forces, which lead to vibrations. The e↵ect can be
reduced by using oval pipes, instead of circular ones, or by fitting fins down stream from the
pipes. In case 3, it would not be possible to fit fins on the pipes due the the pipe spacing,
using slightly more oval or aerofoil shaped pipes could be possible. Oval pipes will be more
streamline and, therefore, allow flow to pass around easier, thereby avoiding (or minimizing)
the vortices.
15
16. Figure 15
The flow can then bee seen to settle as it approaches the outlet.
6.1.3 Velocity
Figures 17.1 and 17.2 below show the velocity vector of the whole heat exchanger and a
zoomed in section, respectively. Zooming in on figure 17.1 (figure 17.2), we can see the flow
around the cylinders is fast, and without and reverse flows.
Figure 17.1
Figure 17.2
16
17. 6.2 Pipe Temperature
One assumption made early on in the design process, was that the pipes had constant
temperature of 548.15o
K; this is very unlikely to be the case. Oil is supplied to the heat
exchanger at 548.15o
K, it is unknown what material the heat exchanger is made of, and thus,
impossible to work out the thermal conductivity of the pipes. Also, as water flows through the
heat exchanger, the oil looses heat to the water, and thus the temperature of the oil begins to
drop a certain distance from the inlet. However, to account for losses in temperature to the
surrounding was also ignored, the outer walls where set to room temperature when during the
3D analysis.
6.3 Boundary Layer & Pipe Sizes
A boundary layer is a region around a wall where the e↵ects of surface friction are significant
enough to slow down the flow; at the wall boundary, the flow velocity is zero. The e↵ects of the
boundary layer where ignored during the design process and thus it is possible that some of the
pipes chosen are too small to e↵ectively flow oil through. In reality, the type and properties of
the oil (e.g. thermal resistance) would be known, and study would have been done for di↵erent
pipe sizes [6][7][8].
6.4 Cost
The design brief does not address the financial restrictions of the heat exchanger and thus,
it is possible an equally e cient heat exchanger could be manufactured for a fraction of the
current design. For example, case 3 uses di↵erent sized pipes, but, because the heat transferred
is more of a function of the total contact area (i.e. total surface area of the pipes), then a design
with the same sized pipes could be designed could be designed to meet the design brief.
7 CONCLUSION
In conclusion, a heat exchanger capable of heating water at room temperature to 55o
C
(328.15o
K) has been successfully designed using CFD simulation. However, although the design
has been analysed and adjusted for any discrepancies between the CFD approximation and the
real world part, as stated in the analysis, the design brief lacked a number of real world
specification, which would have lead to a more accurate design, and as such there may be
errors in the calculations, which could prove costly.
References
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17
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