numerical modelling of a spiral heat exchanger...
TRANSCRIPT
133
CHAPTER 7
NUMERICAL MODELLING OF A SPIRAL HEAT EXCHANGER
USING CFD TECHNIQUE
In this chapter, the governing equations for the proposed numerical model with
discretisation methods are presented. Spiral plate exchanger geometry is created in
Gambit environment and is imported into Fluent software to predict the temperature
profiles of the spiral plate heat exchanger. Simulations are carried out for all the six
fluid systems for all the cases (15 cases per fluid system). The temperature data for
the outlet conditions are computed and the corresponding temperature profile of the
particular experimental condition is also obtained. The predicted temperature data are
compared with those of the experimental data in order to validate the generated CFD
model.
7.1 NUMERICAL MODELLING
A spiral plate heat exchanger is numerically modelled to account for the fluid flow
and heat transfer characteristics under the specified hot and cold fluid flow rates and
hot fluid inlet temperature conditions. A computational fluid dynamics software
package (FLUENT 13.0.) is used to predict the temperature profiles of the spiral plate
heat exchanger. Flow rates for hot and cold fluid are varied from 0.1 to 0.9 kg/s and
hot fluid inlet temperatures are varied from 60oC (333 K) to 80
oC (353 K). The outlet
temperatures for the hot and cold fluids are calculated for counter flow configurations.
The three-dimensional governing equations for momentum, continuity, and heat
transfer are solved using a finite volume based computational fluid dynamics (CFD)
code. Validation of the simulations is done by comparing the temperature data
predicted by FLUENT with those of the experimental data.
In the process of validation of the experimental data with the simulated data, the
outlet temperatures of the hot fluid and cold fluid are considered for comparison. This
is due to the fact that FLUENT does not give the overall heat transfer coefficient
value directly. Therefore, the temperature data, which are the dominant variables in
the calculation of the overall heat transfer coefficient, are taken for comparison to
validate the CFD model.
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7.1.1 Governing Equations
The physical phenomena of fluid flow and heat transfer of a process fluid system
with constant density ρ, viscosity μ can be described in Cartesian Coordinates
(x, y, z) by the following Continuity equation (7.1)
0u v w
x y z
(7.1)
The relevant Navier-Stokes Equations (Momentum Equations) are presented in
Equations (7.2) to (7.4).
2 2 2
2 2 2( )
u u u u u u u pu v w
t x y z x y z x
(7.2)
2 2 2
2 2 2( )
v v v v v v v pu v w
t x y z x y z y
(7.3)
2 2 2
2 2 2( )
w w w w w w w pu v w
t x y z x y z z
(7.4)
Energy Equation (7.5) for the fluid system is as follows:
2 2 2
2 2 2( )
p
T T T T k T T Tu v w
t x y z c x y z
(7.5)
p, T represents the pressure and temperature and u, v, and w represent velocities
in the x, y, and z directions, respectively. The thermal properties such as thermal
conductivity and specific heat are represented by the symbols, k and cp, respectively.
7.1.2 Discretisation of the Governing Equations
In computational fluid dynamics (CFD) software, the above equations are solved
simultaneously using a numerical procedure. Once the domain is determined, the
domain is divided into numerous cells and the partial differential equations are then
applied to each cell. Therefore, within each cell that makes up the domain, the above
partial differential equations are first discretised and then applied to the cell.
Discretisation of the equations is often based on approximating the differential
equations by truncated Taylor series expansions.
The governing differential Equation (7.6) for unsteady state conductive heat
transfer without heat generation is
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2 2
2 2( )
p
T k T T
t c x y
(7.6)
This equation can be discretised to the following algebraic
equation (7.7)
0 0
p p E E W W N N S S p pa T a T a T a T a T a T (7.7)
where
( )E e
e
ya k
x
,
( )W w
w
ya k
x
,
( )N n
n
ya k
x
,
( )S s
s
ya k
x
, 0 ( )p p
x ya c
t
(7.8)
Thus, an algebraic expression for the temperature of every cell can be formulated in
the form of equation (7.7), which is simply a function of all the surrounding
temperatures and the environmental properties such as thermal conductivity and
specific heat. The temperature distribution may now be determined by solving the set
of algebraic equations, given the appropriate boundary conditions. This is a simplified
version of the calculation procedure that does not consider fluid flow. Even though
this approach to systems with fluid movement is more difficult to solve, the same
basic approach is used for the solutions.
7.2 CFD MODELLING
Geometries for the spiral plate heat exchanger are created in GAMBIT 2.4.6. The
specifications of the spiral heat exchanger are shown in Table 7.1. The spiral plate
heat exchanger is essentially made up of two flat plates wound into a double spiral,
with room between them to accommodate fluid flow. The space between the plates is
kept by welding bolts to form the channels for the flow of the fluids. They have only
one channel per process stream, which to some extent prevents the uneven
distribution of fluid flow. In single phase applications, it is common for the hot stream
to enter the exchanger through the central part of the exchanger and to exit at the
periphery. The cold fluid, on the other hand, enters the unit from the outermost part of
the unit and circulates to eventually exit the exchanger from the centre. Properties of
the spiral plate material are set to those of stainless steel, with a thermal conductivity
of 15.364 W/m K, density of 7881.8 kg/m3 and a specific heat of 502 J/kg K.
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Table 7.1. Specifications of the Spiral plate Heat Exchanger for
CFD input.
S.No. Parameter Value Unit
1 Total heat transfer area 2.24 m2
2 Width of the channel plate 304 mm
3 Thickness of the channel
plate
1 mm
4 Material of the channel plate 316 Stainless steel
5 Thermal conductivity of the
channel plate
15.364 W/m K
6 Core diameter of the heat
exchanger
273 mm
7 Outer diameter of the heat
exchanger
350 mm
8 Channel spacing 5 mm
7.2.1 Meshing
Meshing is carried out to represent a finite number of elements of the geometric
structure. The presence of more elements ensures higher accuracy. But, more
elements consume more computational time to find a solution. A 3D model of the
spiral plate heat exchanger is created and exported to GAMBIT for meshing. The
removal of sharp corners, internal features, unnecessary edges, etc. is done to greatly
speed up CFD analysis. Pave mesh is used in the core region and map mesh is used
for all other parts of the spiral plate heat exchanger.
Until a grid independent heat transfer prediction is obtained, grid adoptions based
on velocity gradients are performed after each solution. The final grid consisted of
6, 63,044 cells, 20,58,186 faces and 7, 31,709 nodes. A portion of the spiral plate heat
exchanger grid is shown in Fig. 7.1. The 3D meshed CFD model is shown in Fig.7.2.
This meshing is appropriate enough, for the solution accuracy. The model is imported
to FLUENT 13.0., a commercial computational fluid dynamics software based on
control volume-finite difference formulation.
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Fig. 7.1. Meshed cross sectional view of the Spiral plate Heat
Exchanger grid.
Fig. 7.2. Meshed 3D view of the Spiral plate Heat Exchanger.
7.2.2 Assumptions
The effects of the change of velocity at the entrance and exit of the
exchanger is neglected.
A pure counter flow arrangement is assumed.
Steady state conditions prevail.
The heat transfer coefficient is constant along the length
of the heat exchanger.
Ambient losses are negligible.
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7.2.3 Boundary Conditions
It is critical to specify the correct or realistic boundary conditions. At the inlet, a
uniform velocity boundary condition is specified since the inlet turbulence can
significantly affect the downstream flow. At the outlet, the thermal boundary conditions
are also specified.
7.2.3.1 Velocity Inlet Boundary Conditions
Velocity inlet boundary conditions are used to define the flow velocity, along with
all other relevant scalar properties of the flow, at the flow inlets. As the total
properties of the flow are not fixed, they will rise to whatever value is necessary to
provide the required velocity distribution. This type of boundary condition at inlet is
intended to be used in incompressible flow. It requires the specification of the velocity
magnitude and direction, the velocity components or the velocity magnitude normal to
the boundary. In this case, the velocity normal to boundary specification method is
used. There are several ways in which the code allows the definition of the turbulence
parameters for turbulent calculations. The method of specifying the turbulent intensity
and hydraulic diameter is used for turbulence modelling purposes. Since the flow is
found to be in the turbulent region for most cases, an intensity of 5 % is used.
7.2.3.2 Pressure Outlet Boundary Conditions
The pressure outlet boundary conditions require the specification of gauge
pressure at the outlet. All other flow quantities are extrapolated from the interior. A
set of the backflow conditions are also specified, if at all reverse flow occurs at the
exit during the solution process. The convergence difficulties are reduced by
specifying realistic values of the backflow quantities. To set the static pressure, the
appropriate gauge pressure should be entered. Backflow temperature and turbulence
parameters are set normal to the boundary with a realistic value. At the pressure
outlets, FLUENT uses the boundary condition pressure input as the static pressure of
the fluid at the outer plane, and extrapolates all other conditions of the interior of the
domain.
7.2.3.3 Thermal Boundary Conditions
When choosing to solve an energy equation, it is required to define the thermal
boundary condition at the walls. Since the wall zone here is a two sided wall (a wall
that forms the interface between two regions, such as the fluid/solid interface) a
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conjugate heat transfer problem is encountered. The code allows us an option to
choose whether or not the two sides of the wall are coupled. When the coupled option
is chosen, no other additional thermal boundary conditions are required, because the
solver will calculate the heat transfer directly from the solution in the adjacent cells.
But when performing the two-dimensional numerical simulation, the temperature
boundary conditions are chosen, which requires the specification of the wall surface
temperature.
7.2.4 Physical Properties
The first step while setting up the numerical model is to define the physical
properties. For the solid materials, since the segregated solver is used, only the
thermal conductivity value is required for the calculations. But, for the fluid materials,
the values of density, thermal conductivity, viscosity, and specific heat capacity is
required for calculation purposes. The physical properties may be dependent or
independent of temperature depending upon the type of approach chosen.
When there is a large temperature difference between the fluid and the surface, the
assumption of constant fluid transport properties may cause some errors because the
transport properties of most fluids vary with temperature. These property variations
will then cause a variation of velocity and temperature throughout the boundary layer
or over the flow cross section of the duct. For most liquids, the specific heat, thermal
conductivity, and density are nearly independent of temperature, but the viscosity
decreases with an increase in temperature.
All calculations are performed in a double precision segregated steady state
solver. In the simulations of flows, two different models are employed for turbulence
modelling, namely the k-ε model and the Reynolds Stress Transport model (RES). In
the case of the Finite Volume method, two levels of approximations are needed for
surface integrals. The integral is approximated in terms of the variable values at one
location on the cell face by employing the midpoint rule. The cell face values are
approximated in terms of the nodal values and the linear interpolation is used in this
task. The volume integrals are approximated by a second-order approximation
replacing the volume integral of the product of the mean value and the control
volume.
140
7.2.5 Simulation
Simulations are performed using water as the hot fluid and water, sea water (3%),
sea water (12%), methanol, butanol and biodiesel as cold fluids. For different hot and
cold fluid flow rates, the temperatures at the inlet and outlet of hot and cold fluids are
noted. The flow conditions of 0.1, 0.5 and 0.9 kg/s and the temperature conditions of
60º C, 70º C and 80º C are used. The experimental conditions proposed by RSM are
used for simulation also. All the RSM proposed flow and temperature conditions are
simulated. The case numbers and the corresponding process variables of the 15
experimental runs are tabulated in Table 7.2. Second order discretisation is used.
Solutions are considered to have converged when the residuals of continuity,
components of velocity and energy components are less than 10-6
.
Table 7.2. Input process parameters for CFD simulation
corresponding to the 15 cases.
Case No.
Hot Fluid
Flow Rate
(kg/s)
Cold Fluid
Flow Rate
(kg/s)
Hot Fluid Inlet
Temperature
(°C)
1 0.5 0.5 70
2 0.5 0.5 70
3 0.5 0.1 80
4 0.5 0.1 60
5 0.9 0.9 70
6 0.9 0.5 80
7 0.1 0.5 60
8 0.5 0.9 70
9 0.1 0.1 70
10 0.9 0.5 60
11 0.1 0.5 80
12 0.5 0.9 60
13 0.9 0.1 70
14 0.1 0.9 70
15 0.5 0.5 70
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7.3 NUMERICAL RESULTS AND DISCUSSION
Simulations for the chosen fluid systems are performed for all the 15 cases by
incorporating the flow and temperature conditions proposed by the RSM. The
temperatures at the inlet and outlet of both the cold and hot fluids are found out by
simulation and are compared to those of the experimental values in order to validate
the developed CFD model.
7.3.1 Water - Water System
Simulations are performed using water as the hot and cold fluid. The temperature
contour corresponding to the hot fluid flow rate of 0.9 kg/s and cold fluid flow rate of
0.9 kg/s and hot fluid inlet temperature of 70ºC (case 5) is shown in Fig.7.3. It can be
seen that the cold fluid enters into the outer periphery of the spiral heat exchanger
with a temperature of 26oC (299 K) and leaves at the central core of the heat
exchanger at a temperature of 53.1oC (326.1 K). On the other hand, the hot fluid
enters into the central core of the heat exchanger with a temperature of 70oC (343 K)
and leaves it on the outer periphery of the heat exchanger with a temperature of
51.06oC (324.06) K.
Fig. 7.3. Contours of static temperature (K) for Water-Water system
corresponding to the case 5.
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Simulations for all the 15 cases are carried out and the respective temperature
contours are shown in Annexure I indicating their respective cases.
Comparisons between the cold fluid outlet temperatures, obtained from the
experiments with those calculated from the simulations, are shown in
Fig. 7.4. It can be seen that the majority of the data falls within ±2.72 % of the
experimental data.
Comparisons between the hot fluid outlet temperatures, obtained from the
experiments with those calculated from the simulations, are shown in
Fig.7.5. It can be seen that the majority of the data falls within ±2.52 % of the
experimental data.
Fig.7.4. Comparison of experimental and CFD simulated cold fluid
outlet temperatures of Water-Water system.
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Fig.7.5. Comparison of experimental and CFD simulated hot fluid
outlet temperatures of Water-Water system.
7.3.2 Water - Sea Water (3%) System
Simulations are performed using water as the hot fluid and sea water (3%) as the
cold fluid. The temperature contour corresponding to the hot fluid flow rate of 0.9
kg/s and cold fluid flow rate of 0.9 kg/s and hot fluid inlet temperature of 70ºC
(case 5) is shown in Fig.7.6. It can be seen that the cold fluid enters into the outer
periphery of the spiral heat exchanger with a temperature of 26oC (299 K) and leaves
at the central core of the heat exchanger at a temperature of 55.83oC (328.83 K). On
the other hand, the hot fluid enters into the central core of the heat exchanger with a
temperature of 70oC (343 K) and leaves it on the outer periphery of the heat
exchanger with a temperature of 51.06oC (324.06 K).
144
Fig.7.6. Contours of static temperature (K) for Water- Sea water (3%)
system corresponding to the case 5.
Simulations for all the 15 cases are carried out and the respective temperature
contours are shown in Annexure II indicating their respective cases.
Comparisons between the cold fluid outlet temperatures, obtained from the
experiments with those calculated from the simulations, are shown in
Fig.7.7. It can be seen that the majority of the data falls within ±4.46 % of the
experimental data.
145
Fig.7.7. Comparison of experimental and CFD simulated cold fluid
outlet temperatures of Water- Sea Water (3%) system.
Fig.7.8. Comparison of experimental and CFD simulated cold fluid
outlet temperatures of Water- Sea Water (3%) system.
Comparisons between the hot fluid outlet temperatures, obtained from the
experiments with those calculated from the simulations are shown in
Fig.7.8. It can be seen that the majority of the data falls within ± 6.02 % of the
experimental data.
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7.3.3 Water - Sea Water (12%) System
Simulations are performed using water as the hot fluid and sea water (12%) as the
cold fluid. The temperature contour corresponding to the hot fluid flow rate of
0.9 kg/s and cold fluid flow rate of 0.9 kg/s and hot fluid inlet temperature of 70ºC
(case 5) is shown in Fig.7.9. It can be seen that the cold fluid enters into the outer
periphery of the spiral heat exchanger with a temperature of 26oC (299 K) and leaves
at the central core of the heat exchanger at a temperature of 57.59oC (330.59 K). On
the other hand, the hot fluid enters into the central core of the heat exchanger with a
temperature of 70oC (343 K) and leaves it on the outer periphery of the heat
exchanger with a temperature of 44.17oC (317.17 K).
Fig.7.9. Contours of static temperature (K) for Water- Sea Water (12%)
system corresponding to the case 5.
Simulations for all the 15 cases are carried out and the respective temperature
contours are shown in Annexure III indicating their respective cases.
Comparisons between the cold fluid outlet temperatures, obtained from the
experiments with those calculated from the simulations, are shown in
Fig.7.10. It can be seen that the majority of the data falls within ± 6.17 % of the
experimental data.
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Fig.7.10. Comparison of experimental and CFD simulated cold fluid
outlet temperatures of Water- Sea Water (12%) system.
Fig.7.11. Comparison of experimental and CFD simulated hot fluid
outlet temperatures of Water- Sea Water (12%) system.
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Comparisons between the hot fluid outlet temperatures, obtained from the
experiments with those calculated from the simulations, are shown in
Fig. 7.11. It can be seen that the majority of the data falls within ± 4.26 % of the
experimental data.
7.3.4. Water - Methanol System
Simulations are performed using water as the hot fluid and Methanol as the cold
fluid. The temperature contour corresponding to the hot fluid flow rate of 0.9 kg/s and
cold fluid flow rate of 0.9 kg/s and hot fluid inlet temperature of 70ºC (case 5) is
shown in Fig.7.12. It can be seen that the cold fluid enters into the outer periphery of
the spiral heat exchanger with a temperature of 26oC (299 K) and leaves at the central
core of the heat exchanger at a temperature of 59.59oC (332.59 K). On the other
hand, the hot fluid enters into the central core of the heat exchanger with a
temperature of 70oC (343 K) and leaves it on the outer periphery of the heat
exchanger with a temperature of 38.52oC (311.52 K).
Fig.7.12. Contours of static temperature (K) for Water- Methanol system
corresponding to the case 5.
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Simulations for all the 15 cases are carried out and the respective temperature
contours are shown in Annexure IV indicating their respective cases.
Comparisons between the cold fluid outlet temperatures, obtained from the
experiments with those calculated from the simulations, are shown in
Fig.7.13. It can be seen that the majority of the data falls within ± 3.69 % of the
experimental data.
Comparisons between the hot fluid outlet temperatures, obtained from the
experiments with those calculated from the simulations, are shown in
Fig.7.14. It can be seen that the majority of the data falls within ± 5.9 % of the
experimental data.
Fig.7.13. Comparison of experimental and CFD simulated cold fluid
outlet temperatures of Water-Methanol system.
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Fig.7.14. Comparison of experimental and CFD simulated hot
fluid outlet temperatures of Water- Methanol system.
7.3.5 Water - Butanol System
Simulations are performed using water as the hot fluid and Butanol as the cold
fluid. The temperature contour corresponding to the hot fluid flow rate of 0.9 kg/s and
cold fluid flow rate of 0.9 kg/s and hot fluid inlet temperature of 70ºC (case 5) is
shown in Fig.7.15. It can be seen that the cold fluid enters into the outer periphery of
the spiral heat exchanger with a temperature of 26oC (299 K) and leaves at the central
core of the heat exchanger at a temperature of 57.13oC (330.13 K). On the other hand,
the hot fluid enters into the central core of the heat exchanger with a temperature of
70oC (343 K) and leaves it on the outer periphery of the heat exchanger with a
temperature of 33.2oC (306.20 K).
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Fig.7.15. Contours of static temperature (K) for Water- Butanol system
corresponding to the case 5.
Simulations for all the 15 cases are carried out and the respective temperature
contours are shown in Annexure V indicating their respective cases.
Comparisons between the cold fluid outlet temperatures, obtained from the
experiments with those calculated from the simulations, are shown in
Fig.7.16. It can be seen that the majority of the data falls within ± 4.73 % of the
experimental data.
152
Fig.7.16. Comparison of experimental and CFD simulated cold
fluid outlet temperatures of Water- Butanol system.
Fig. 7.17. Comparison of experimental and CFD simulated hot
fluid outlet temperatures of Water- Butanol system.
153
Comparisons between the hot fluid outlet temperatures, obtained from the
experiments with those calculated from the simulations, are shown in
Fig. 7.17. It can be seen that the majority of the data falls within ± 8.96 % of the
experimental data.
7.3.6 Water - Biodiesel System
Simulations are performed using water as the hot fluid and Biodiesel as the cold
fluid. The temperature contour corresponding to the hot fluid flow rate of 0.9 kg/s and
cold fluid flow rate of 0.9 kg/s and hot fluid inlet temperature of 70ºC (case 5) is
shown in Fig.7.18. It can be seen that the cold fluid enters into the outer periphery of
the spiral heat exchanger with a temperature of 26oC (299 K) and leaves at the central
core of the heat exchanger at a temperature of 46.73oC (319.73 K). On the other hand,
the hot fluid enters into the central core of the heat exchanger with a temperature of
70oC (343 K) and leaves it on the outer periphery of the heat exchanger with a
temperature of 31.46oC (304.46 K).
Fig. 7.18. Contours of static temperature (K) for Water- Biodiesel
system corresponding to the case 5.
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Simulations for all the 15 cases are carried out and the respective temperature
contours are shown in Annexure VI indicating their respective cases.
Comparisons between the cold fluid outlet temperatures, obtained from the
experiments with those calculated from the simulations, are shown in
Fig. 7.19. It can be seen that the majority of the data falls within ± 3.77 % of the
experimental data.
Comparisons between the hot fluid outlet temperatures, obtained from the
experiments with those calculated from the simulations, are shown in
Fig. 7.20. It can be seen that the majority of the data falls within ± 10.29 % of the
experimental data.
Fig.7.19. Comparison of experimental and CFD simulated cold
fluid outlet temperatures of Water- Biodiesel system.
155
Fig. 7.20. Comparison of experimental and CFD simulated hot
fluid outlet temperatures of Water- Biodiesel system.
7.4 SUMMARY OF RESULTS
In this chapter, the CFD based geometric model is created in Gambit environment
and is imported into Fluent software in order to evaluate the temperature profiles. The
temperature profiles of all the six fluid systems considered for evaluation are
analysed. The temperature data of the outlet conditions for both the hot and cold flow
agree well with those of the experimental data. The percentage variation of most of
the fluid systems is found to be less than ±10.5 %. The summary of the results are
tabulated in Table 7.3. Therefore, the generated CFD model can be considered to
possess sufficient accuracy for analysis.
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Table 7.3. Summary of CFD simulation results.
Sl.
No. Fluid System
% Variation between Experimentation and
CFD Simulation
For Cold Fluid
Outlet Temperature
For Hot Fluid
Outlet Temperature
1 Water-Water ± 2.72 ± 2.52
2 Water-Sea Water (3%) ± 4.46 ± 6.02
3 Water-Sea Water (12%) ± 6.17 ± 4.26
4 Water-Butanol ± 3.69 ± 5.9
5 Water-Methanol ± 4.73 ± 8.96
6 Water-Biodiesel ± 3.77 ± 10.29