CHAPTER 7 NUMERICAL MODELLING OF A SPIRAL HEAT EXCHANGER USING CFD TECHNIQUE

Transcription

1 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 60 o C (333 K) to 80 o C (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. 133

2 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) u v w 0 x y z (7.1) The relevant Navier-Stokes Equations (Momentum Equations) are presented in Equations (7.2) to (7.4) u u u u u u u p u v w ( ) t x y z x y z x (7.2) v v v v v v v p u v w ( ) t x y z x y z y (7.3) w w w w w w w p u v w ( ) t x y z x y z z (7.4) Energy Equation (7.5) for the fluid system is as follows: T T T T k T T T u v w ( ) t x y z c x y z p (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 c p, respectively 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 134

3 2 2 T k T T ( ) 2 2 t c x y p (7.6) This equation can be discretised to the following algebraic equation (7.7) a T a T a T a T a T a T (7.7) 0 0 p p E E W W N N S S p p where a E y ke, a ( x) e W y kw, a ( x) w N y kn, a ( x) n S y k 0 s, ap ( x) s x y ( cp) 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 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 W/m K, density of kg/m 3 and a specific heat of 502 J/kg K. 135

4 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 m 2 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 6 Core diameter of the heat exchanger 7 Outer diameter of the heat exchanger W/m K 273 mm 350 mm 8 Channel spacing 5 mm 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 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. 136

5 Fig Meshed cross sectional view of the Spiral plate Heat Exchanger grid Assumptions Fig Meshed 3D view of the Spiral plate Heat Exchanger. 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. 137

6 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 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 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 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 138

7 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 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. 139

8 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 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)

9 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 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 26 o C (299 K) and leaves at the central core of the heat exchanger at a temperature of 53.1 o C (326.1 K). On the other hand, the hot fluid enters into the central core of the heat exchanger with a temperature of 70 o C (343 K) and leaves it on the outer periphery of the heat exchanger with a temperature of o C (324.06) K. Fig Contours of static temperature (K) for Water-Water system corresponding to the case

10 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 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. 142

11 Fig.7.5. Comparison of experimental and CFD simulated hot fluid outlet temperatures of Water-Water system 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 26 o C (299 K) and leaves at the central core of the heat exchanger at a temperature of o C ( K). On the other hand, the hot fluid enters into the central core of the heat exchanger with a temperature of 70 o C (343 K) and leaves it on the outer periphery of the heat exchanger with a temperature of o C ( K). 143

12 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. 144

13 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. 145

14 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 26 o C (299 K) and leaves at the central core of the heat exchanger at a temperature of o C ( K). On the other hand, the hot fluid enters into the central core of the heat exchanger with a temperature of 70 o C (343 K) and leaves it on the outer periphery of the heat exchanger with a temperature of o C ( 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 It can be seen that the majority of the data falls within ± 6.17 % of the experimental data. 146

15 Fig Comparison of experimental and CFD simulated cold fluid outlet temperatures of Water- Sea Water (12%) system. Fig Comparison of experimental and CFD simulated hot fluid outlet temperatures of Water- Sea Water (12%) system. 147

16 Comparisons between the hot fluid outlet temperatures, obtained from the experiments with those calculated from the simulations, are shown in Fig It can be seen that the majority of the data falls within ± 4.26 % of the experimental data 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 It can be seen that the cold fluid enters into the outer periphery of the spiral heat exchanger with a temperature of 26 o C (299 K) and leaves at the central core of the heat exchanger at a temperature of o C ( K). On the other hand, the hot fluid enters into the central core of the heat exchanger with a temperature of 70 o C (343 K) and leaves it on the outer periphery of the heat exchanger with a temperature of o C ( K). Fig Contours of static temperature (K) for Water- Methanol system corresponding to the case

17 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 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 It can be seen that the majority of the data falls within ± 5.9 % of the experimental data. Fig Comparison of experimental and CFD simulated cold fluid outlet temperatures of Water-Methanol system. 149

18 Fig Comparison of experimental and CFD simulated hot fluid outlet temperatures of Water- Methanol system 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 It can be seen that the cold fluid enters into the outer periphery of the spiral heat exchanger with a temperature of 26 o C (299 K) and leaves at the central core of the heat exchanger at a temperature of o C ( K). On the other hand, the hot fluid enters into the central core of the heat exchanger with a temperature of 70 o C (343 K) and leaves it on the outer periphery of the heat exchanger with a temperature of 33.2 o C ( K). 150

19 Fig 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 It can be seen that the majority of the data falls within ± 4.73 % of the experimental data. 151

20 Fig Comparison of experimental and CFD simulated cold fluid outlet temperatures of Water- Butanol system. Fig Comparison of experimental and CFD simulated hot fluid outlet temperatures of Water- Butanol system. 152

21 Comparisons between the hot fluid outlet temperatures, obtained from the experiments with those calculated from the simulations, are shown in Fig It can be seen that the majority of the data falls within ± 8.96 % of the experimental data 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 It can be seen that the cold fluid enters into the outer periphery of the spiral heat exchanger with a temperature of 26 o C (299 K) and leaves at the central core of the heat exchanger at a temperature of o C ( K). On the other hand, the hot fluid enters into the central core of the heat exchanger with a temperature of 70 o C (343 K) and leaves it on the outer periphery of the heat exchanger with a temperature of o C ( K). Fig Contours of static temperature (K) for Water- Biodiesel system corresponding to the case

22 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 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 It can be seen that the majority of the data falls within ± % of the experimental data. Fig Comparison of experimental and CFD simulated cold fluid outlet temperatures of Water- Biodiesel system. 154

23 Fig 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. 155

24 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 ± Water-Sea Water (3%) ± 4.46 ± Water-Sea Water (12%) ± 6.17 ± Water-Butanol ± 3.69 ± Water-Methanol ± 4.73 ± Water-Biodiesel ± 3.77 ±