Eduardo Uresti Waldo Arcos - Tec48 N. León-Rovira, E. Uresti and W. Arcos Waldo Arcos received the...

Int. J. Computer Applications in Technology, Vol. 30, Nos. 1/2, 2007 47

Copyright © 2007 Inderscience Enterprises Ltd.

Fan-shape optimisation using CFD and genetic algorithms for increasing the efficiency of electric motors

Noel León-Rovira* Center for Innovation in Design and Technology, Tecnológico de Monterrey, Campus Monterrey. Ave. Eugenio Garza Sada # 2501, Colonia Tecnológico, CP 64841 Monterrey, Mexico E-mail: [email protected] *Corresponding author

Eduardo Uresti Center for Artifitial Intelligence, Tecnológico de Monterrey, Campus Monterrey. Ave. Eugenio Garza Sada #2501, Sucursal de Correos ‘J’, Colonia Tecnológico, CP 64841 Monterrey, Mexico E-mail: [email protected]

Waldo Arcos Center for Innovation in Design and Technology, Tecnológico de Monterrey, Campus Monterrey. Ave. Eugenio Garza Sada # 2501, Colonia Tecnológico, CP 64841 Monterrey, Mexico E-mail: [email protected]

Abstract: The electric motor efficiency represents the effectiveness with which the motor converts electrical energy into mechanical energy. As the energy losses are converted into heat, which is dissipated by the motor frame aided by internal and external fans, a better cooling system adds up to better efficiency. In recent years, improvements in motor efficiency have been achieved but at higher costs. By using Genetic Algorithms (GAs), changes are introduced to the fan shape looking for a better aerodynamic performance. The evaluation of the achieved fan efficiency with the modified shapes is performed with Computational Fluid Dynamics (CFD) simulation software.

Keywords: shape optimisation; genetic algorithms; shape parameterisation; CFD.

Reference to this paper should be made as follows: León-Rovira, N., Uresti, E. and Arcos, W. (2007) ‘Fan shape optimisation using CFD and genetic algorithms for increasing the efficiency of electric motors’, Int. J. Computer Applications in Technology, Vol. 30, Nos. 1/2, pp.47–58.

Biographical notes: Noel León-Rovira is a Professor at the Center for Innovation in Design and Technology at Mexico’s Tecnológico de Monterrey. He holds a Degree in Mechanical Engineering, as well as a PhD in Mechanical Engineering (Summa cum Laude), both from the Dresden University of Technology, Germany. He also made Postdoctoral studies on design methodology and computer-aided design. He is the Director of the Research Program Creativity, Inventiveness and Innovation in Engineering. He specialises in product design, design methodology and computer-aided engineering.

Eduardo Uresti is a Professor at the Center for Intelligent Systems at Mexico’s Tecnológico de Monterrey. He holds a degree in Mathematics, a master degree in Mathematics and a PhD in Computer Science. He has served as professor in the Physics and Mathematics School (ESFM) of the National Politechnical Institute (IPN) and also in the Physics and Mathematics Faculty at UANL Mexico. His current interests include the use of genetic algorithms for multi-modal and multi-objective optimisation (new algorithms and their applications) and the application of Artificial Intelligent strategies in teaching and learning.

48 N. León-Rovira, E. Uresti and W. Arcos

Waldo Arcos received the BS Degree in Mechanical with Minor in Electrical Engineering from the Autonomous University of Nuevo León, Nuevo Leon, Mexico, and the Master’s Degree in Manufacturing Systems from Tecnológico de Monterrey, Nuevo Leon, Mexico, in 2002 and 2006, respectively. He is currently responsible for the mechanical and electrical design of electric motors in an electric motors company.

1 Introduction

Improving the energy use in electric motors is relevant because improved efficiency leads to slower growth in electricity demand. In the following sections, a way is shown of obtaining a higher efficiency of electric motor with a better heat dissipation that is achieved by a better fan aerodynamic performance.

Losses due to electrical resistance in electric motors take the form of heat, which has to be dissipated. Improvements in motor efficiency are achieved by reducing losses. In electric motors, reduction of losses is achieved in various ways, such as higher core-steel grade, higher slot fill, slots redesign and reduced windage design. All these options have been used throughout the years, but even though these methods have achieved increments in electric motor efficiency, the consequence has incremented total motor costs. The objective of achieving higher efficiency through fan-shape optimisation using GAs is obtaining the same benefits but without increasing the costs. GAs have been successfully applied in other shape optimisation cases for optimising aerodynamic shapes (Marco et al., 2004; Obayashi et al., 2000a; 2000b; Olhofer et al., 2001; Kelner et al., 2005). In this case, the application starts from a shape optimisation of a fan, which used at first only straight-line blades’ cross sections.

Using CFD software, it is possible to simulate the effect of changing the fan blades’ shapes with GAs. However, for optimisation purpose, the CFD simulation time required is tremendous. In a recent study, Kelner et al. (2005) relate a study where the CFD simulation time was greatly reduced, based on the differentiation and high-order Taylor-series expansion of the discretised Reynolds-Averaged Navier–Stokes (RANS) equations around an independently computed reference flow solution.

In the present study, the simulation time was reduced taking advantage of the periodicity of the geometry, simulating only one-eighth of the fan rotor. Moreover, in order to reduce the total computational time, two different commercially available CFD packages were compared and the one which require less computational time was used.

The objective is to increase the efficiency of a Total Enclosed Fan-Cooled (TEFC) induction motor, using the same raw materials and manufacturing processes. The electrical design of the motor is not subject of analysis.

2 Innovation as concept optimisation Based on former publications, it may be stated that product innovation may also be implicit as “optimisation

not restricted to parametric variation” but extended to ‘constrained concept variations’. As has been shown in several case studies, an extended parametric optimisation is achieved by adding shape and topology as possible search directions. This extended optimisation has been achieved by allowing shape variation substituting the original shapes, which were based on straight lines and arcs, with spline curves (Leon et al., 2004).

The current fan blade profile has two identical parallel straight lines. The new fan blade design proposed in this paper, although starting from the same straight profiles, is represented by splines, shape of which may be modified for finding new profiles beyond the limits than would be possible using only straight-line profiles. New constraints have been added to the GA that restricts the minimum permitted thickness of the fan blade profile to avoid possible flexion due to the air impact over the fan blades.

3 Basic thermal consideration Thermal issues affect the performance of a motor. The coil temperature rise, that is, the temperature difference of stator coil over an ambient temperature, depends on two factors:

• the temperature gradient between stator coil and housing for conductive heat flow, which can be solved analytically

• the temperature difference between housing and air for heat flow by convection and radiation.

For a TEFC machine, the problem of heat transfer from housing to air for a given temperature gradient is associated with the aerodynamic flow pattern. This part is difficult to solve analytically, and, because of this, an empirical relation has been established, based on data available from test results.

Conduction of losses inside the motors is particularly important in areas that include air gaps and voids, for example inside the coil insulation between conductors and cores and between the stator core and housing of totally enclosed motors. A totally enclosed machine is one so enclosed as to prevent the free exchange of air between the inside and the outside of the case, but not sufficiently enclosed to be termed airtight. There are different types of enclosures and its use depends upon the application and the working environment. For this research, a TEFC electric motor enclosure is used. In this type of enclosure, an external fan pulls air in through a fan cover and blows it over the external motor surface. Heat transfer occurs by forced convection.

Fan shape optimisation using CFD and genetic algorithms 49

4 Genetic Algorithms (GAs) GAs are search algorithms based on the mechanics of natural selection and natural genetics. They combine survival of the fittest among string structures with a structured yet randomised information exchange to form a search algorithm with some of the innovative flair of human search. In every generation, a new set of artificial creatures (strings) or individuals is created using the fittest as parents. While randomised, GAs are no simple random walk. They efficiently exploit historical information to speculate on new search points with expected improved performance (Goldberg, 1989).

Normally, when a GA is used for function optimisation, each individual in the population represents a point in the search space of the problem to be solved. The aptitude of an individual is closely related to the value of the function in the point being represented by the individual. Different types of GAs have been proposed, from the simple GA (Goldberg, 1989) to others with special selection schemes as Genitor (Whitley, 1989). In the simple GA, the whole population is replaced by a new set of individuals each generation. The new set of individuals is produced in pairs. In order to produce two new individuals, a pair of parents is selected from the current population. Those individuals with a better aptitude have more chances of being selected. Once a pair of individuals is selected, crossover and mutation are applied. The crossover consists of constructing a pair of new individuals by taking parts of the genetic material from both parents. The expected effect is the combination of the characteristics present in both parents. In the simplest case, the genetic material of an individual consists of the string and the crossover consists of randomly taking a point in which both parents can simultaneously be divided and then joining the first part of the first parent with the second part of the second parent. The second individual can be constructed with the remaining parts of the genetic material of the parents. Mutation consists of making changes in the genetic material in both resulting new individuals. Compared with the simple GA, Genitor has some differences, as it produces one new individual each generation, which replaces the worst individual in the current population. As in the simple GA, two parents are selected, but they are selected according to their ranking in the population: the whole population is ordered according to the value of the function evaluation.

In some GA applications, it may be more convenient to use a real vector as genetic material instead of a string of characters (Wright, 1991; Barone et al., 2002; Bleier, 1998; Capello and Mancuso, 2003; Chapman, 2004; Goldberg, 1989; Eshelman and Schaffer, 1993), in such applications, the use of different crossover operators is required.

5 AC motor losses Electric motor efficiency is a measure of the effectiveness with which a motor converts electrical energy to mechanical

energy. It is defined as the ratio of power output to power input or as the ratio of output to output + losses (http://www.reliance.com/mtr/b7087_5/b7087_5_2.htm.):

.Output OutputMotor Efficiency = =Input Output + losses

AC motor losses are classified in components. Electrical losses are converted into heat, which is dissipated by the motor housing aided by internal or external fans. Stator and rotor losses are caused by current flowing through the motor winding and are proportional to the squared current times the winding resistance (I2R). Hysteresis and eddy current losses are confined to the laminated core of the stator and rotor and can be reduced by utilising steels with low core loss characteristics, as found in high-grade silicon steel. Friction and windage losses are due to all sources of friction and air movement in the motor and may be appreciable in large high-speed or TEFC motors. The stay load losses are due mainly to high-frequency flux pulsations, caused by design and manufacturing variations (http://www.reliance.com/mtr/ b7087_5/b7087_5_2.htm.).

There are two basic ways for increasing the efficiency of an electric motor based on its fan characteristics. One way is by minimising windage losses while maintaining the airflow rate. In that case, the rest of the losses will not be benefited. The efficiency increase is due only to the reduction of windage losses. Another way to boost electric motor efficiency is by increasing the airflow rate provided by the fan, without increasing the energy required for driving the fan. This way will benefit the rest of the losses mentioned earlier, while the windage losses remain constant.

Fan size augmentation is a straightforward way for increasing airflow (Bleier, 1998). However, fan size is constrained by the space available in the fan cover and it increases the energy required for driving the fan. By varying the shape of the fan blades, the fan efficiency can be enhanced in such a way that the airflow is increased and a better cooling effect reduces the stator losses, core losses and rotor losses without increasing the energy absorbed for driving the fan. Therefore, shape variations generated with GAs may be useful in achieving best results considering the size constraints.

6 Identifying the influence of the fan performance

For better identifying the effect of increasing the fan efficiency, two preliminary experiments were made: the first was a laboratory test and the second was an analytical calculation. In the first case, a motor was tested in a laboratory, eliminating the energy consumption of the fan by using an external fan cooling system. The internal fan was removed from the motor; therefore, the fan energy consumption was zero (an ideal situation). The efficiency increase measured was 1.09%.


In the second case, the airflow was increased in the analytical model by 50%, without considering any increase of the energy consumption of the fan. The efficiency increase calculated was 1.35%. It became evident that the efficiency of the motor could be more benefited through efficiency augmentation of the fan.

7 Simulation using CFD simulation software integrated into 3D CAD system with meshing capabilities

Two commercial CFD simulation programs were compared. In the first case, a 3D CAD system for modelling the geometry and CFD software with dedicated mesh generation software were used. The analysis time was approximately 4 h. Then the same case study was performed using CFD simulation software integrated into a 3D CAD system with meshing capabilities. The analysis time was about 40 min. The second package was selected, as it performed the analysis up to ten times faster than the first with similar results.

Taking advantage of the periodicity of the geometry, only one-eighth of the fan geometry was modelled. This way the total computational time is reduced accordingly.

The geometry was constructed as a single blade centred within the region divided by two even adjacent passages.

The mesh was generated inside of the 3D CAD system using an interface provided by the CFD software. The grid is set up with periodic boundaries on either side of the domain. The upstream boundary is defined by velocity and the downstream boundary by pressure. The single blade centred is assumed to be rotating, while the two even adjacent passages are stationary. The z-axis is used as a rotation axis for the reference frame. The fan spins clock-wise (looking from the positive end of the z-axis) at constant rotational speed. The fan rotation speed is defined by the motor at full load. The standard k –ε turbulence model (Abbott, 1989) and sea-level conditions were used. The 3D CAD model and the mesh generated are shown in Figure 1.

The simulations were performed based on the defined boundary conditions. The simulation stops after convergence criteria are met. The convergence criteria are shown in the Figure 2. Each curve should become horizontal as criterion that the convergence was reached. A guideline followed is that the quantities in the calculation progresses change <5% over the last 20% of the total iterations.

Figure 3 shows the velocity vectors as found at the midspan of the rotational area. The velocity vector plot provides insight into the behaviour of the flow around the fan blade. This analysis is the basis for finding the variations of blade profiles that increase the airflow.

The pressure distribution on the blade is shown in Figure 4.

Figure 1 (a) 3D CAD geometry and (b) mesh model in CFD program

(a)

(b)


Figure 2 Plot curve convergence

Figure 3 Velocity vectors (second simulation)

Figure 4 Pressure distribution on the blade


The contour plots illustrate the pressure rise on the fluid caused by the fan blade. Positive pressure values occur on the surface, where the fan blade pushes the air and negative pressures (suction) on the other surface.

7.1 Profile modification

As the purpose of this paper is to look for new designs that increase the efficiency of the electric motor using shape optimisation through GAs, the blade profiles are required to

be modified during the optimisation run. For a first trial, the straight profile of the fan blade was substituted by a curved profile as shown in Figure 5.

This analysis shows an increment in the velocity vector’s magnitude. The results are shown in Figure 6.

The velocity vector’s magnitude was increased 4.7% with respect to the current design. The increment of the parameters measured shows that it is possible to get higher airflow provided by the fan over the motor. By increasing the airflow the electric motor efficiency can be improved, as was discussed in Section 5.

Figure 5 Fan profile modification

Figure 6 (a) Velocity vectors (profile curve-simulation) and (b) pressure distribution on the blade (profile curve simulation)

(a)


Figure 6 (a) Velocity vectors (profile curve-simulation) and (b) pressure distribution on the blade (profile curve simulation) (continued)

(b)

8 Representation of fan blade for optimisation Shape optimisation deals with variations of the form: find a shape (in two or three dimensions) that is optimal in a certain sense, while satisfying certain requirements and constraints. In the present case study, as was already mentioned, advantage was taken of the periodicity of the geometry and only one fan blade was simulated. In order to simplify the shape optimisation problem, only the profile half way up the fan blade will be modified, as shown in Figure 7. The fan blade profile analysed in Section 7 will be codified below as chromosome in the GA.

Figure 7 Fan blade profile

The population is represented by individuals with different fan profile shapes, where each fan profile shape is

evaluated and represents a possible solution. Following a strategy adopted by several researches (Lamping, 2003; Leon et al., 2004, 2005; Marco et al., 2004; Michalewicz, 1992; Obayashi et al., 2000a) and the concepts studied in the preceding sections, the shape parameterisation is based on B-spline curves. B-splines are commonly used to define curved bodies and profiles. In some cases (Marco et al., 2004), Bézier curves are used, and the parameters constituting the chromosome are coded as binary string. The smoothness properties of Bézier curve permits to avoid non-feasible shapes by the crossover operator.

In this case study, non-feasible shapes are controlled by using constraints added in the GA, which are discussed briefly in the last paragraph of this section. Six control points are used in this case to control the whole fan profile shape modification by the crossover operator, as shown in Figure 8.

Figure 8 Control points along the profile


The control points shown above (P1–P6) are defined by their x- and y-coordinates, respectively; thus, P1 = (x1, y1), …, P6 = (x6, y6). For simplifying the shape parameterisation, the x values are fixed, and only the y-coordinates are allowed to vary. This way, P1 = y1, P2 = y2, …, P6 = y6 represent the search space, while Pi, Pi′, Pf and Pf′ are fixed. Several approaches have been proposed for controlling the geometry through control points; for example, in Obayashi et al. (2000a), the airfoil geometry is split into a mean camber line and thickness distribution. Some points are used for the camber line and other points are used for the thickness distributions. In this case, the extreme points have to be fixed to avoid a new fan blade profile being thinner than the current profile. Therefore, the chromosome will be represented only by the y-coordinates:

1 2 3 4 5 6Upper Lower

Chromosome = , , , , , .y y y y y y

The GA introduces changes on the position of the control points, resulting in profile variations. Traditionally, GAs use binary numbers to represent such strings: a string has a finite length, and each bit of a string can be either 0 or 1. For real-valued function optimisation, however, it is more natural to use real numbers (as might be done with evolution strategies or evolutionary programming), as suggested in Obayashi et al. (2000b), where the length of the real-number strings corresponds to the number of design variables. Real-number coding is used here.

Genitor is the GA selected for sampling the search space, but in this case individuals of the population are not removed. In order to keep the selection pressure high, the selection bias parameter is dynamically set to be 1.5 in a growing population. In the present investigation, the operator BLX-α is used (Goldberg, 1989):

New = α × P1 + (1 – α) × P2

where P1, P2 are the parents, New is the new individual and α is a random number in the real interval [–0.5, 1.5]. Mutation operations consist of adding to the new individual a vector of small random numbers.

Normally, in a real application, some individuals produced by the GA correspond to impossible configurations and such individuals receive reduced evaluations or penalties. In this case, such individuals were mapped to valid individuals by swapping the corresponding y-coordinates, in order to preserve the restrictions y1 > y6, y2 > y5 and y3 > y4, and minimum permitted thickness. Individuals with smaller thickness are considered invalids by the GA.

9 Evaluation procedure Using the GA described, the process flow is constituted by the steps shown in Figure 9. An initial population of 25 individuals was generated, which were seeded. As the evaluation process is complicated and the cycle could not be

done yet automatically (because actual CFD software lacks scripting capabilities), it was necessary to use an evaluation team. The evaluation team was a group of specialists (volunteer Master degree students in the Computer-Aided Engineering course), where the simulation results of each population member was assigned for evaluation to one person of this team.

Figure 9 Process flow diagram from Genetic Algorithms

GA depends on the data reported after the evaluation from each new individual has been done. Thus, it was constructed using PHP language where it runs on a web server, taking PHP code (GA) and a MySQL database as input and creating a web page to manage the information of the simulation.

When a new evaluation is reported to the GA by any member of the team, the PHP script stores the information parameter and images related to the simulation process into the databases. A new individual is created, and the new parameters (six control points) are sent via e-mail to the team member with less evaluations pending.

In order to assure that evaluations in the CFD package are consistent, a step-by-step manual was created and provided to each team member and exercises were performed before starting with the actual evaluation. Figure 10(a) shows how the members of this team report the results obtained in the analysis. All data obtained in the analysis were saved in the databases and it can be easily retrieved as a web page.


Figure 10 (a) Report of results and (b) GA population

(a)

(b)


Figure 10(b) shows some individuals of the GA population in the web page. The best fan profile design generated by the GA is shown into the red circle. It will be discussed in the next section. The web page can be accessed in the following link http://lizt.mty.itesm.mx/~euresti/genetico/ home.htm.

10 Results The best fan profile generated by the GA presents a significant increase in the velocity vector’s magnitude of 9.4%, with respect to the current design, while the profile curve presented in Section 7.1 had an increment of 4.7%. Due to the time limits, the GA was not run until its final convergence; however, the best fan profile obtained from

GA shows that introducing changes in the profile it is possible to get a better aerodynamic performance than the results obtained by former profile curves. The results are shown in Figure 11.

In Figure 12, the changes in the new fan profile generated by GA are shown. This kind of variation obtained by GA optimisation procedures is finer than the changes obtained by trial and error variations of experienced designers, who commonly do not have the patience and time for such minimal changes. The use of splines for changing profiles that are initially modelled with only circular arcs and lines seems to be a better solution for shape optimisation by using genetics algorithms for controlling the geometry through control points (Lamping, 2003).

Figure 11 (a) Velocity vectors (profile generated by GA) and (b) pressure distribution on the blade (profile generated by GA)

(a)

(b)


Figure 12 (a) Original profile and (b) profile generated by GA

11 Conclusions Although requiring experimental validation, the results obtained by simulation indicate that optimising the fan blade shape through GAs increases the airflow in the motor. This improvement can be achieved by small shape modifications. The obtained shapes are not more expensive to manufacture than the original ones, as the fan is produced by injection moulding and the cost increment of the mould is negligible. The economic benefits obtained through efficiency increment may be substantial. The present research represents a step forward towards a new way of increasing the efficiency of TEFC induction motors through shape optimisation, using genetic algorithms and CFD techniques.

Acknowledgements The authors acknowledge the support received from Tecnológico de Monterrey through grant number CAT043, Research Chair Creativity and Innovation in Engineering of the Center for Innovation in Products and Technology (CIDYT) to carry out the research reported in this paper.

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Websites http://www.usmotors.com/. http://www.reliance.com/mtr/b7087_5/b7087_5_2.htm.

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