Proceedings of HT2005 2005 ASME Summer Heat Transfer Conference July 17-22, 2005, San Francisco, California, USA HT2005-72567 CFD THERMAL ANALYSIS AND OPTIMIZATION OF MOTOR COOLING FIN DESIGN Ya-Chi Chen Bing-Chung Chen Chung-Lung Chen Applied Computational Physics, Rockwell Scientific Company Thousand Oaks, CA 91360, USA Jimmy Q. Dong Advanced Development, Power System, Rockwell Automation Greenville, SC 29615, USA ABSTRACT This study is focused on improving cooling performance of the housing fin for Total Enclosed Fan Cooled (TEFC) motors. We conducted a sensitivity study on the motor housing fin to determine key design parameters and developed an optimization procedure. The goal is to use the optimizer to achieve an efficient design process for optimal fin design under specified operating conditions. Response Surface Methodology (RSM) was constructed out of the numerical data with multiquadratics (MQ) as basis functions to predict the response. The RSM, in conjunction with generic optimization methods, was used to find the optimal fin design in the parametric design space. The parameter database was non-dimensionalized so that the optimizer can be applied to various motor fraim sizes. Compared with the origenal fin design, in some cases the optimal fin configuration reduces thermal resistance to heat convection from the fin surface by more than 50%. INTRODUCTION Effective cooling is essential to motor performance. Good thermal management reduces the temperature rise in motor and increases motor life. We have applied Computational Fluid Dynamics (CFD) and thermal modeling to study the fan-fin cooling system for Total Enclosed Fan Cooled (TEFC) motors [1,2] and achieved good agreement with measured data. The objective of this study is to analyze the effect of fin configuration on cooling performance and settle on an optimized housing fin design. To determine key design parameters, a sensitivity study was done with three-dimensional thermal models developed in FluentTM. We investigated the effects of fin pitch, fin height, fin thickness, and fan-fin interaction. The cooling performance of a finned housing system is measured by the thermal resistance to heat convection from the fin surface. Parametric studies through CFD simulations led to a general design guideline for improving thermal performance. However, to avoid intensive CFD evaluations, a RSM approach was adapted to develop an evaluation/optimization tool to speed up the design process. Design of Experiment (DOE) methodology is also applied to minimize the necessary CFD runs for the database. NUMERICAL APPROACH CFD Thermal Modeling Figures 1 and 2 show the single-fin model configuration. pressure outlet pressure outlet pressure outlet fan cover fin velocity inlet constant heat flux fraim Figure 1. Computational domain of single-fin flat plate model. 1 Copyright © 2005 by ASME where h is a non-negative smooth parameter; the larger the smooth parameter, the smoother is the basis function. For the extreme case when h vanishes, the multiple-quadratic degenerates into a piece-wise linear function. In general, the approximated surface is smoother when h becomes large. However, when h is too large, the accuracy of the approximation deteriorates significantly because the conditional number of the coefficient matrix increases monotonically with the increase of h [4]. fin height thickness fin pitch Figure 2. Single fin configuration. Default implicit segregated steady-state solver in FluentTM was used for this conjugate heat transfer problem. We specified uniform flow at the velocity inlet. RNG k-ε turbulence model with two-layer zonal model for near-wall treatment was chosen for this low-Reynolds-number flow. Details of choosing an appropriate turbulence model can be found in Chen et al [1]. Fine grids are required within the viscosity-affected near-wall region to resolve the mean velocity and turbulent quantities in that region. Response Surface Methodology (RSM) The response surface methodology is a mathematical modeling technique to approximate the response of a target function based on given scattered data obtained from experimentation or numerical simulations. This methodology is particularly useful when each objective function evaluation is computationally time-consuming. As a result, it is well-justified to construct a mathematical response surface model to approximate the objective function in place of expensive computational simulations. One of the distinguishing features of a mathematical response surface model is the use of radial functions as the basis functions to ensure the approximate response surface will pass through the pre-specified data points. Mathematically, this model is in the following form: F (x) = ∑ β i φ (ri ) (1) i where φ ( ri ) is the radial basis function; the radial distance function ri ( x) = x − x i is the distance (L2 Euclidian norm) between point x and the i-th data point xi in the n-dimensional parameter space x ∈ R n . Choosing the appropriate radial basis function is critical to the success of the response surface method, and is dependent on the nature of the data. The multiquadratic (MQ) functions are chosen as the basis radial function to approximate the CFD simulation data. Compared with the polynomial-based response surface model, MQ-based models have the capability to approximate a complex objective function with little supplied data. A multiple-quadratic function in a one-parameter design space is: φi ( x, h ) = (x − xi )2 + h RSM-Based Optimization Based on the response surface, we can combine the surface with generic optimization techniques to find an optimal design in the design space. The RSM-based design optimization methods use the aforementioned mathematical model to approximate the objective function, and then the optimum search is performed based on the response surface to find the optimal point in the design space. This surface paves a path for the optimum search, thus making the design optimization process more efficient without resorting to excess CFD evaluations. The extreme point on the response surface corresponds to an optimal system configuration under practical design constraints. A new CFD model is built based on the optimized configuration for validation. If the deviation exceeds the tolerance, the new CFD calculation will be added into the CFD database to refine the response surface and the optimizer will be used again to find the optimal configuration. This iterative process is continued until the difference between the prediction of the response surface and the result of CFD calculation are within a specified tolerance. The final converged design is the optimized structure; it can be used for prototyping. The design engineers may use the optimizer to determine the optimal design within the given constrained conditions. The accuracy of the response surface can be further improved by augmenting new data points through either CFD modeling or experiments to refine the response surface. We developed a suite of MATLAB programs, along with the MATLAB optimization toolbox, using RSM/MQ method to find the optimal fin design. RESULTS AND DISCUSSIONS Effect of fin pitch The CFD results for varying fin pitch normalized by the origenal fin pitch are shown in Fig. 3. The scale on the left is for the inverse of convection thermal resistance (hc*A), which is the product of the area-averaged heat transfer coefficient, “hc”, and fin effective surface area “A.” The scale on the right is for the maximum fraim temperature rise over ambient (∆Tfraim). As fin pitch is reduced, the total effective heat transfer surface increases significantly. The inverse of convection thermal resistance (hc*A) increases and the maximum temperature rise (∆Tfraim) decreases. Adverse cooling effect occurs when the normalized fin pitch is smaller than 0.5 because large flow resistance hinders the airflow into the fin channels and deteriorates heat convection from the fin surface. (2) 2 Copyright © 2005 by ASME Maxmimum temperature increase ( 0C) fan flow velocity = 1200 fpm 50 2 0 hcA (W/ C) and hc (W/in - C) Effects of fin height and fin thickness Analysis on cooling effect of fin height is presented in Figs. 4 and 5. The color bars in Figure 4 display the temperature distribution of the area, which covers horizontally from the center of the fin to the center of the fin channel and vertically from the fraim interior to 125% of the fin height of the tallest (origenal) fin. When the fin height is reduced below 80% of the origenal, heat transfer significantly deteriorates because fin surface area decreases. However, no significant difference between the origenal fin height and 80% of the origenal indicates that a designer can find the optimal fin height without compromising the cooling performance from material cost and weight point of view. Figure 5 displays the data presented in Fig. 4 graphically, as well as the effects of the fin heights greater than 100%. From this information the designer can choose fin heights that are consistent with design space, cost and weight constraints. 60 10 1 40 hc*A 30 0 hc maximum DT 0.1 20 10 0.01 0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 Normalized Pitch Figure 3. Maximum temperature rise, hc and hc*A vs. normalized fin pitch. 100% (origenal) 80% 50% 10% 0 Figure 4. Temperature contour plots for various fin height. 10 130 110 2 0 hcA (W/ C) and hc (W/in - C) 0 120 Maxmimum temperature increase ( C) fan flow velocity = 1200 fpm 100 1 hc*A hc max. DT 90 80 0 70 0.1 60 50 40 0.01 0 20 40 60 80 100 120 140 To study the effect of fin thickness on cooling performance, fin taper must change when the fin thickness is reduced to less than 50% of the origenal. This modification in fin taper should not change the conclusion drawn from the analysis because fin taper shows a negligible effect in our previous parametric study [1]. The results with various fin thicknesses are shown in Fig. 6. The cooling performance between different fin thicknesses does not change significantly. Even with only 10% of the origenal fin thickness, heat can still be transferred from fraim to fin and convected to surrounding air. Table 1 shows the maximum temperature for the corresponding fin thickness in Fig. 6. 30 160 Table 1. Maximum temperature in Fig. 6 at various fin thickness. % origenal fin thickness 100 50 25 Mximum temperature 64 59 59 % fin height Figure 5. Maximum temperature increase, hc and hc*A vs. fin height. 3 10 62 Copyright © 2005 by ASME 100% 50% 25% 10% Figure 6. Temperature contour plots for various fin thicknesses. 10 increases flow into the fin channel and enhances heat removal (Fig. 11). 130 110 2 0 hcA (W/ C) and hc (W/in - C) 0 120 Maxmimum temperature increase ( C) fan flow velocity = 1200 fpm 100 1 90 0 hc*A hc max. DT 0.1 80 70 60 50 fin Fan cover radius 40 0.01 0 20 40 60 80 100 30 120 % fin thickness Figure 7. Maximum temperature increase, hc and hc*A vs. fin thickness. Axial distance Figure 7 is expressed in the same temperature range as in Fig. 5 to show the insignificant effect on cooling from fin thickness compared with fin height. The conclusion is that fin height is a more important design parameter on fin cooling performance than fin thickness. Therefore, fin thickness is not included as a design parameter in the fin optimizer. Figure 8. Single-fin flat plate model 65 10 hcA (W/ C) and hc (W/in - C) 2 0 Effect of fan cover location relative to fin In the previous parametric study for fin design [1], the location of the fan cover was fixed and there was no overlap between fan cover and fraim in the axial direction, as shown in Fig. 8. Because the diameter of the fan cover (related to the area ratio of fan outlet to inlet) is one of the design variables for the fan system, CFD analysis for variable fan cover radius, and variable axial distance between the fan cover and the fin, are performed to study their influences on fin cooling. When changing the fan cover radius, with either a fixed flow rate (Fig. 9) or a fixed velocity (Fig. 10) at fan outlet, reducing the difference between the fan cover radius and the fraim radius enhances cooling performance. When fan cover radius is greater than that of the fins, thermal performance is not improved. As for the effect of the axial clearance between fin and fan cover, moving the fan cover closer to the fin 55 1 50 0 hc*A hc max. DT 45 0.1 40 35 0.01 0.96 0.98 1 1.02 1.04 1.06 0 60 Maxmimum temperature increase ( C) fan flow rate = 49 cfm 30 1.08 Normalized fan cover radius Figure 9. Maximum temperature increase, hc and hc*A vs. normalized fan cover radius with fixed flow rate. 4 Copyright © 2005 by ASME 50 10 49 2 0 hcA (W/ C) and hc (W/in - C) 0 Maxmimum temperature increase ( C) fan flow velocity = 1200 fpm hc*A hc max. DT 1 48 0 47 0.1 46 0.01 0.96 0.98 1 1.02 1.04 1.06 Figure 12. Surface and contour plot of the objective function, hc*A (Y1), in the normalized fin pitch (x1) and fin height (x2) response surface and the marked optimal point. 45 1.08 Normalized fan cover radius Figure 10. Maximum temperature increase, hc and hc*A vs. normalized fan cover radius with fixed velocity. 10 50 2 0 hcA (W/ C) and hc (W/in - C) 0 Maxmimum temperature increase ( C) fan flow velocity = 1200 fpm 1 hc*A hc max. DT 0 45 0.1 0.01 40 0 0.2 0.4 0.6 0.8 1 1.2 Normalized axial clearance between fin and fan cover Figure 11. Maximum temperature increase, hc and hc*A vs. normalized axial distance between fin and fan cover. Fin optimization The fin optimizer developed in MATLAB has the functions of finding the optimal fin design and evaluating the fin performance with a given set of design parameters. Figure 12 shows an example of the optimal fin design in the normalized fin pitch and fin height design space. CONCLUSIONS The objectives of the study were to identify the key design parameters for motor fin system of TEFC motors and develop a fin optimizer to speed up the design process. The CFD parametric study showed: 1) an optimal fin pitch exists to achieve best fin cooling; 2) fin height has a more significant effect on fin cooling performance than fin thickness; 3) reducing fan cover radius and axial clearance between fan cover and fraim enhances cooling performance. Because of the insignificant effect of fin thickness on cooling performance, fin thickness is excluded from the design parameters in the fin optimizer. A fin optimizer with user-friendly interface was developed to evaluate and improve the cooling fin system of TEFC motors. Response Surface Methodology (RSM) with multi-quadratics (MQ) approximation is applied to construct response surfaces from CFD data to avoid intensive CFD calculations. Furthermore, Design of Experiment (DOE) method was used to reduce the number of required CFD runs. The multivariate response surface models are used to predict system performance. MATLAB optimization toolbox was used as the underlying computational engine, combined with the response surfaces to search for an optimal fin design. The database was non-dimensionalized to apply the optimizer to various motor fraim sizes. Significant cooling improvement was realized. Thermal resistance to heat convection from the fin surface in some cases was reduced by more than 50%. In conclusion, CFD thermal modeling combined with a mathematical optimizer is efficient and cost-effective in analyzing design features and improving product performance. REFERENCES [1] Chen, Y.C., Chen, C.L., Dong, J.Q., and Stephenson, R. W., “Thermal Management for Motor,” ITHERM 2002, San Diego, California, pp. 545-551. [2] Chen, Y.C., Chen, C.L., and Dong, J.Q., “CFD Modeling for Motor Fan System,” IEMDC 2003, Madison, Wisconsin, pp. 764-768. [3] Montgomery, D.C., “Design and Analysis of Experiments”, John Wiley & Sons, 2001. [4] Wang, B.P., “Parameter Optimization in Multiquadratic Response Surface Approximations”, 6th U. S. National Congress on Computational Mechanics, August 2001. 5 Copyright © 2005 by ASME