CHAPTER 4 CFD ANALYSIS

Transcription

1 52 CHAPTER 4 CFD ANALYSIS The finite volume based Computational Fluid Dynamics (CFD) technique is used to predict the flow and heat transfer aspects in a cross flow heat exchanger, used in an automobile application.the radiator on which the experiments were carried out, is a cross flow type compact heat exchanger, with water flowing inside tubes, and air cross flowing over the tubes through louvered fins. To understand the flow and thermal characteristics of fluids inside the radiator, a numerical analysis using the computational fluid dynamics tool (CFD) is carried out. The numerical method used for validating the computational results with those of the experiments is discussed in detail in this chapter. 4.1 PHYSICAL AND CFD MODEL The physical domain considered for the CFD analysis is shown in Figure 4.1(d) Figure 4.1(a) identifies the front and top view directions of the radiator. Figure 4.1(b) shows the top view of the radiator, with the two rows of tubes shaded. The geometry periodicity of the radiator in the tube pitchwise (lateral) direction can be easily observed. Figure 4.1.c shows a small region of the radiator in the front view. The fins positioned between the tubes are seen. The fin geometry indicates that it has a periodicity in the tube height-wise (span) direction.

2 53 The computational domain is confined to one fin pitch in the spanwise direction and one tube pitch in the lateral direction, as shown in Figure 4.1(b) and Figure 4.1(c) respectively, which is highlighted with a dashed red line. The length, breadth and height of the computational domain are mm, 9.6 mm (tube pitch) and 3 mm (fin pitch) respectively. To minimize the error due to flow oscillations and flow reversing effects, which are induced due to the numerical algorithm, the inlet and outlet of the computational domain are extended, as shown in Figure 4.1(d Gambit software is used to model the computational domain. Tetrahedral mesh elements are used for meshing the computational model. Surface mesh element sizes are controlled to obtain fine mesh elements close to the fin and louvers. The mesh grows in size outward from the fin and louver to the tubes and extended domains. Top view Outlet towards ambient air Computational domain Front view Inlet from wind tunnel (a) Radiator view directions (b) Top view of radiator Figure 4.1 (Continued)

3 54 Water tubes 4 Air out Water in 3 Computational domain A A Span-wise periodic domain Air in Extended air domain upstream of radiator 2. Water tube row 1 3. Water tube row 2 4. Extended air domain downstream of radiator (c) Front view of radiator (d) Isometric view of computational domain Figure 4.1 Details of Computational domain 4.2 MATHEMATICAL MODEL The commercial version of the CFD software Fluent is employed to perform the simulation. This software uses the finite volume method of discretizing the transport equations. The assumptions made in the CFD simulation are (a) that the flow is stable in the computational domain, and (b) that the fluid in the domain is steady and incompressible. The problem under consideration is governed by the steady three dimensional form of continuity, the Reynolds-Average Navier-Stokes equation (RANS), and the energy equation, along with the equations for modelling the turbulent quantities. follows: The governing equations are given in Equations 4.1 to 4.4 as Mass conservation:. ( v ) = 0 (4.1)

4 55 Momentum conservation:.( vv ) = - p +.( ) + g + F (4.2) Energy conservation:. v E p where =. kt. v (4.3) = + (4.4) The temperature distribution inside the solid regions of the model, such as the tube walls and fin, is obtained by solving the energy Equation 4.5 as given below. (k s T s ) = 0 (4.5) The equation will allow to obtain the temperature, not only inside the fin, but also along its surface. The turbulent quantities are modeled using the k- model to capture the large fluid strains more effectively. 4.3 BOUNDARY CONDITIONS The analysis is carried out by considering the water flowing through the tube, and the simultaneous heat transfer occurs through the finned surface. Hence, a conjugate analysis is performed, by estimating the conduction and convection parameter, using the solver based on the local flow and thermal conditions. The various boundary conditions used for the present CFD analysis where both hot water and cold air make cross flows in the domain are given below:

5 56 1. Inlet and outlet conditions Air side Inlet v = v in, u = 0 and w = 0 T = T in,a Outlet p = p atm T = T out (Applicable only to the grid cells occurs) where back flow Water side Inlet w = -w in, u = 0 and v = 0 T = T in,w Outlet T = T out (Applicable only to the grid cells where back flow occurs) 2. Boundary Surfaces Upper and Lower side = Periodicity Left side and Right side = Periodicity 3. Tube, Fin and Louver walls u = 0, v = 0 and w = 0 No separate temperature boundary condition is needed, as the solver calculates the thermal information in a coupled way.

6 57 The air and water entry flow and thermal conditions are specified as boundary conditions for the computations. All internal flows and thermal conditions are calculated in a conjugate manner. Thus the fin, louver and tube surface heat transfer rates are all calculated, and not specified as boundary conditions. The property values of the air, water and solid materials used in the analysis are given in Table 4.1. Table 4.1 Material properties Fluid material properties Property Water Air Density, (kgm -3 ) Specific heat, C p (Jkg -1 K -1 ) Thermal conductivity, k (Wm -1 K -1 ) Viscosity, µ (kgm -1 s -1 ) e-05 Solid material properties Property Aluminium Copper Density, (kgm -3 ) Specific heat, C p (Jkg -1 K -1 ) Thermal conductivity, k (Wm -1 K -1 ) The commercial CFD code Fluent 6.3 is used for simulations in the present conjugate heat transfer analysis. The continuity, momentum and energy equations for three dimensional, incompressible flows are solved on the double periodic domain. The code uses a pressure correction based finite volume solver. Thefluid domain is the air which cross flows over the water tubes, and the solid domain is modeled to effect the conjugate heat transfer. The second order up-winding scheme is used to have higher order accuracy. The homogeneous method of conjugate heat transfer is employed by fluent

7 58 which facilitates the direct coupling of the fluid zone and solid zone, using the same discretization and numerical approach. Hence, it is possible to have an interpolation-free crossing of the heat fluxes between the neighboring cell faces. Among several options for turbulence models, the standard k- model of wilcox is chosen after several trials, by comparing the computational results.the local and averaged heat transfer coefficient values on the wall surfaces are estimated, based on the thermal and flow turbulence calculations by the solver. 4.4 GRID INDEPENDENCE TEST The computational domain is extended both upstream and downstream of the core, and the potential back flow is avoided. Initially, the mesh density finalization is done for the computational domain. Tetrahedral mesh elements are used for meshing the computational model. The surface mesh element sizes are controlled to obtain fine mesh elements close to the fin and louvers. The mesh grows in size outward from the fin, and louver to the tubes and extended domains. Different mesh configurations, starting with very coarse to very fine are taken at a particular Reynolds number, and analysed using the Fluent. Three different grids were tested with 0.6, 1.63 and 2.26 million cells, using different meshing parameters. The results were obtained from the computational domain along the axial length, along a line passing through the center of the channel. The line is highlighted as a red dashed line in the inset of Figure 4.2. Figure 4.2 shows the total pressure variation along the chosen axial line, and it has negligible variation across all the three mesh densities tested. The domains with three mesh densities show the differences in the total pressure at the channel inlet. This is due to the boundary conditions used for the numerical study, and the difference in the calculation of the near wall flow features, which will vary with the mesh density.

8 59 Since the outlet boundary condition is atmospheric, which is specified on the radiator outlet, the system pressure drop in the radiator is amplified back to the radiator inlet. Among the three mesh densities tested, the variation between the 1.63 and 2.26 million cells is less. A further analysis of the thermal characteristics along the same chosen line will help in deciding the final mesh parameters to be used Mi Million Mi Million Mi Million Water in Air out Pressure (Pa) Upstream side HEX Core Air in Position along air stream-wise direction (m) Downstream side Figure 4.2 Pressure variation along a line passing through the computational domain The variation of the static temperature along the chosen horizontal line between the different mesh densities of 0.6, 1.63 and 2.26 million cells, is shown in Figure 4.3. Good agreement in the local values of temperatures is observed, between the grids of 1.63 million and 2.26 million cells. Since the variation in temperature between these two mesh densities is negligible, it was decided to proceed with the meshing settings and parameters used for the 1.63 million cells for further analysis. For all the cases, the value of the dimensionless distance y + is always maintained at less than 1.

9 60 The homogeneous method of a conjugate heat transfer is employed, which facilitates the direct coupling of the fluid and solid zone, using the same discretization and numerical approach. Hence, it is possible to adopt an interpolation-free crossing of the heat fluxes between the neighbouring cell faces. Temperature (K) Upstream side Mi Million Mi Million Mi Million HEX Core Position along air stream-wise direction (m) Downstream side Figure 4.3 Temperature variation along a line passing through the computational domain The scaled residuals for solution convergence are set to 10-5 for all governing equations, and turbulence quantities, and 10-7 for energy, and once met, the solution is considered to be converged. After the analysis, post processing is done for the mass weighted average temperatures and pressures, at the inlet and outlet over the computational domain. The pressure, temperature and velocity profiles are taken at the various sections of the fin, for the corresponding Reynolds number. This temperature difference between the inlet and outlet of the core, in turn, is used for calculating the energy transfer, using the basic equation.

10 VALIDATION AND PARAMETRIC ANALYSIS In order to validate the numerical procedure adopted in the CFD analysis, initially the three data sets used in the experiments are used to generate the CFD results, and the results of the analysis are compared with the experimental results. The three sets of CFD data which are validated with the experimental results are given in Table 4.2.Simulations are carried out for the heat exchanger models with different geometrical parameters. The data sets used for the parametric analysis are given in Table 4.3. Validation Cases Table 4.2 Summary of the data sets used for CFD validation Air velocity (ms -1 ) Inlet air temp (K) Water Flow Rate (kgs -1 ) Inlet water temp (K) VC VC VC Table 4.3 Summary of data sets used for parametric analysis SL. NO. Fin Pitch (F P ) (mm) Transve rse Tube Pitch (T P ) (mm) Longitudi nal Tube Pitch(T L ) (mm) Louver Pitch (L P ) (mm) Louver Angle (L a ) (Deg) Number of Longitudina l Tube Rows (N t )

11 62 Table 4.3 (Continued)

12 DATA REDUCTION FOR THE EVALUATION OF f AND j FACTORS In the present work, the heat transfer and flow characteristics of the test heat exchanger are presented in terms of the Colburn j factor and Fanning friction f factor versus Reynolds number. In addition, the f and j factors are also determined using the existing correlations available in the literature as given in the table 1 and compared with the experimentally determined f and j factors. The equations employed in evaluation of the Fanning friction f factor and Colburn j factor are given below. (i) Fanning friction f factor is defined on the basis of an equivalent shear force in the flow per unit heat transfer area and it is represented by Equation 4.6 f = (P/2L) (D h / air v 2 ) (4.6) where P is air-side pressure drop (Pa), air is density of air (kgm -3 ), v is inlet air velocity (ms -1 ). (ii) The dimensionless Colburn j factor is represented by Equation 4.7 j = St x Pr 2/3 = (D h /4L) [ln (T i T w )/ (T o T w )] Pr 2/3 (4.7) where St is the Stanton number [dimensionless], Pr is the Prandtl number [dimensionless], T i is the air inlet temperature [ C], T o the is air outlet temperature [ C] and T w is the tube wall temperature [ C]. (iii) Hydraulic diameter of the louvered fin is defined as given in Equation 4.8 D h = 4LA min / A s (4.8)

13 64 where D h is the hydraulic diameter (mm), L is the flow length or Heat transfer matrix depth in the air flow direction (mm), A min is the minimum free flow area (mm 2 ), A s is the total area for heat transfer on the air-side (mm 2 ). (iv) The dimensionless Reynolds Number based on hydraulic diameter is represented by Equations 4.9 and 4.10 Re Dh = G D h /µ (4.9) G = A f v / A min (4.10) where A f is frontal area of the heat exchanger (mm 2 ) and G is the mass flux or mass velocity (kgm -2 s -1 ). (v) The dimensionless Reynolds number based on louver pitch is represented by Equation 4.11 Re Lp = G L p /µ (4.11) where L p is louver pitch (mm)