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

135

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.

136

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.

137

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.

138

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

139

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

141

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.

142

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.

143

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.

146

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.

147

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.

148

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.

149

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.

150

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).

151

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.

154

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.

156

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