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Optimizing the Design of Radiator using Genetic Algorithms

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Optimizing the Design of Radiator using Genetic Algorithms

Optimizing the Design of Radiator using Genetic Algorithms

    ( Real World Application )

Puneet Saxena Charles L. Karr Keith A. Woodbury

    Graduate Student Associate Professor Associate Professor

     Industrial Engineering Dept. Aerospace Engineering and Mechanical Engineering Dept.

    The University of Alabama Mechanics Dept. The University of Alabama Tuscaloosa, AL 35487 The University of Alabama Tuscaloosa, AL

    Email: saxen001@bama.ua.edu Tuscaloosa, AL Email: woodbury@me.ua.edu

    Phone: (205) 348 1659 Email: ckarr@coe.eng.ua.edu

    Phone: (205) 348 0066

    overall heat transfer coefficient and the total heat transfer Abstract area.

    The design optimization problem involves both explicit constraints (such as fixed frontal area) and implicit This paper describes the application of genetic constraints (such as those specifying the heat transfer algorithms to achieve the optimal design of a coefficient). Once the geometry is selected, additional radiator used in automobiles so as to achieve not constraints such as minimum and maximum values for the only the required performance but also to find a fin pitch, minimum and maximum number of tubes and cost effective solution. The performance of an the cross-section of the tubes are imposed, and thereafter automobile radiator is a function of overall heat the problem reduces to that of solving the problem within transfer coefficient and total heat transfer area. the ranges of variables specified to achieve the optimal The basic thermodynamic equations are utilised design. The overall heat transfer coefficient is dependent to enable the calculation of the overall heat on the number of tubes; in general, as the number of tubes transfer coefficient of the vehicle radiator core increases the heat transfer coefficient improves. However, and thereafter the genetic algorithm is used for additional factors such as vibration damage (if the tubes manipulating the design parameters to achieve are very close together), the need to access the outer the optimal solution. surface of tubes for cleaning, and the limit on pressure

    drop across the radiator affect the decision on the number

    of tubes. Fins are attached to the tubes by brazing or 1 INTRODUCTION soldering, thereby imparting strength to the whole

    assembly and enabling the exchanger to withstand high Radiators are heat exchangers responsible for controlling

    pressure. Fins not only enhance the overall heat transfer engine-operating temperatures. The heat carried by the

    coefficient but also significantly increase the total heat cooling water jacket is generally 30% of the total energy

    transfer area and thus help enhance the performance of a produced in the engine. This energy must be removed

    radiator. However, if the fin pitch is high, the fluid in constantly through the use of a heat exchanger, or a

    between the fins will move at a lower velocity (for radiator. A suitable radiator is used to achieve not only

    constant pumping power) giving more time for fouling to the efficient performance of the engine but also the cost-

    occur and it further becomes difficult to clean the effective solution for the cooling system. In radiators, heat

    assembly. It is costly to have high fin pitch. Thus, fouling, carried by the coolant fluid is transported by convection

    maintenance, manufacturing, and cost considerations limit and conduction to the fin surface and from there by

    the fin pitch. The profile of the tube plays an important thermal radiation into the atmosphere-free space. The hot

    role as it affects the contact area between the two fluids and cold fluids are separated by an impervious surface

    without adding much cost, but the manufacturing process and hence they are also referred to as surface heat

    again limits the kinds of profiles that can be adopted exchangers. In the case of a radiator, the hot fluid flows

    economically. inside the tubes and so the hot fluid is unmixed. However,

    the cold fluid flows over the tubes and is free to be mixed. The factor most often used to evaluate the performance of The mixing tends to make the fluid temperature uniform the radiator is the product of overall heat transfer in transverse direction; therefore, the exit temperature of a coefficient, U, and the total heat transfer area, A. The mixed stream exhibits negligible variation. The total heat overall heat transfer coefficient is a function of the heat transfer rate between the fluids is dependent on the

    transfer coefficient and a fouling factor. The fouling 2 PROBLEM STATEMENT factor is a constant for given environmental conditions It is generally desired to find a solution for radiator design while the heat transfer coefficient can be calculated by that simultaneously meets both the performance using the following set of equations: requirements and cost targets. Since a number of parameters affect both the performance and the cost, it is 2/3PrSt;;important to evaluate the search space thoroughly to Heat Transfer Coefficient, h = ;;Gcp2/3obtain the best possible solution. The radiator heat Prtransfer model is linearized about a known configuration 14from a flattened tube / fin array (surface 9.68 0.87). DGhReynolds Number, Re = This paper presents a solution approach in which a genetic algorithm manipulates the parameters to find a

    near-optimum solution. This study reveals the details of 'Avthe approach that solves the problem of searching the Mass Velocity, G = cost-effective design of an automotive radiator for a pre-ACdefined level of performance of a radiator. This is

     accomplished by providing the details of the

    configuration of the tubes and the fins along with the where c is specific heat at constant pressure, A' is frontal pdetails of the cross-section of the tube for the specific area of radiator, is density of air, v is velocity of air at design problem. inlet, A is free-flow area of radiator, Pr is Prandtl number, cD is hydraulic diameter, St is Stanton number, and is h3 LITERATURE REVIEW the dynamic viscosity of the radiator fluid.

    The total surface area through which heat exchange The automobile industry is a field in which an abundance occurs is dependent on the profile of both the tubes and of research has been conducted. Since radiators play an the fins, the number of tubes, the fin pitch and the number integral role in the operation of an automobile, these of rows. The configuration of fins and tubes also affects devices have been explored extensively. The the performance, but the current study is confined to only concentration has always been on evaluating the radiator 4straight fins and inline tubes. Figure 1 shows the radiator together with the cooling system of the engine. A work in core having straight fins and tubes. the early 1970’s focused on heat dissipation from a 1radiator to cool vehicle engines. Further, during that time

    a computer program for selecting a radiator to provide a

    desired level of engine cooling and for predicting the

    engine cooling performance with a given radiator was 2formulated. Simulations were developed for evaluating

    the performance of a radiator as a single part of an entire

    cooling system. As time passed researchers started

    analyzing the material of the radiator and now aluminum

    is considered to produce the best performance based upon

    the statistics available because of a better method of 3manufacturing and new metallurgical combinations. 9Chiou conducted a study to understand the effect of the

    tube length on the heat transfer capability of a heat 10exchanger. Further, Emmaenthal and Hacho presented a

    method to design the cooling system of an automobile

    where the individual components were first described

    using experimental data and then the study was carried

    out to achieve the low cost design. But, genetic

    algorithms have not been previously applied to the

    problem of optimizing the design of a radiator.

     4 GENETIC ALGORITHM

     PARTICULARS

    Figure 1: Radiator core showing the straight fins and 4.1 CODING SCHEME tubes with air and water flowing at right angles to each

    other. As described above the goal of the current effort is to find

    a cost-effective design of the radiator having a desired

    5performance using a genetic algorithm. In this study the k = a weighting factor of 10 2 3parameters that define the performance and cost are the k = a weighting factor of 10 3

    number of tubes (n), the fin pitch (p), the length of the k = a weighting factor of 10 tf4

    cross-section of tube (l) and the width of the cross-section k = a weighting factor of 1 t5of tube (w). The length of the binary string, which tThe difference between the UA and UAis weighted desired represents these four parameters using standard binary by maximum factor as radiator’s under-performance and concatenated coding, is found by specifying the accuracy over performance is highly undesired, while the higher of each parameter. The minimum and maximum values weightage is given to number of tubes represented in the for each parameter are problem specific and depend on string, p represents the fin pitch value in the string while fthe constraints that exist on the design. Table 1 shows the higher weightage is given to the number of tubes as pertinent information about the coding used in this study. compared to the fin pitch the number of tubes affect the cost more severly. The profile of tube is given a low Table 1: Sub-string length for each parameter based on penalty for poor design. chosen accuracy and maximum and minimum values.

    In the solution of this problem, a genetic algorithm first SUBSTRING PARAMETER A U U pminmaxgenerates a population of strings of given length using the LENGTH user-defined constraints. Each string is decoded to yield n 1 29 60 5 tactual parameters. The fitness of each string in the p (per inch) 1 8 11 2 fpopulation is found by evaluating the fitness function as l (mm) 1 8 15 3 t -1defined in Equation (1). Then, reproduction using w(mm x 10) 1 15 30 4 t tournament selection, single-point crossover, and

    mutation are used to generate subsequent generations and search for acceptable values for n, p, l and w which tfttThe sub-string lengths of each of the four parameters are minimise the fitness function of Equation (1). Tournament concatenated, resulting in the total string length of fifteen. selection is executed by picking 15% of the strings from Each string represents one possible solution to the the current population at random and comparing their problem. The number of tubes and the fin pitch fitness values. The string with the lowest fitness value is significantly affect the performance and cost of the placed into the mating pool for the new population. radiator. Thus, these two parameters are placed adjacent Single-point crossover is accomplished by randomly to one another to reduce the likelihood of destroying good picking two strings from the mating pool; then randomly combinations of these two parameters by crossover. picking the crossover location in the string length based Therefore the binary string obtained is described in Table on a probability of crossover of 0.9 and crossing the 2. strings at the location. A mutation operator with a probability of 0.01 is used to introduce new genetic Table 2: Position of each parameter in string. material into the population.

    PARAMETER n p l w tftt

    Positioning in string 1 - 5 6 - 7 8 - 10 11 - 14 5 RESULT The accuracy of the genetic algorithm is tested by

    comparing the solution obtained using a genetic algorithm 4.2 FITNESS FUNCTION to the known practical result; one that is implemented The parameters are sent to a mathematical model for successfully in 1998 in India. evaluation of the performance and the cost effectiveness The goal set for the of the genetic algorithm was to of the radiator, and in return a fitness value is assigned provide a cost-effective solution for the radiator, when the defining the quality of solution represented by a given performance desired from the radiator is 817 WC (product binary string. The genetic algorithm then attempts to of overall heat transfer coefficient and total heat transfer achieve the desired performance with the minimum area). The genetic algorithm was run for twenty-five number of tubes and fin pitch combination together with generations, using single-point crossover and a simple the best profile of the cross-section of the tube. Here the mutation operator. An initial population of 100 strings fitness function is defined as was randomly selected, where each string represented one possible solution. The fitness value of the best string in a 21/2Minimise {k*[(UA - UA) +1] + k*n + k* p + 1desired2t3fgeneration is plotted against the function evaluations. The k*(17 -l) + k*(5-w) } …(1) 4t5tresults of this case are displayed in Figure 2. where

     UA = desired value of UA for radiator performance desired7 k = a weighting factor of 10 1

    When the genetic algorithm was run and compared to the

    known practical solution the following results were

    obtained (Table 3): 8075 7065Table 3: Comparison of genetic algorithm to the known 60 )55practical solution for the 3-row radiator with straight fins 55045( x 10and inline tubes. (population size=100, number of 4035generations=25, probability of crossover=0.9, probability 30Fitness 25of mutation=0.01) 2015GENETIC Minimum 10PARAMETER PRACTICAL Fitness5ALGORITHM 00Number of Tubes 48 51 100200Fin pitch (per inch) 10 11 300Function Evaluation400( Number of generation x Population size )Length of cross-50012 11 600section of tube 700800Width of cross-900 2.5 1.8 1000section of tube 1100Figure 2: Best Fitness produced by the genetic algorithm 1200Fitness Value 1481052.5 1511163.2 1300vs. function evaluation 1400 1500 1600Particulars of Simple Genetic Algorithm: 1700The configuration resulting from the genetic algorithm is 1800Population size=100 1900slightly less economical than the practical known solution. 2000Number of generations=25 2100However, the result is near optimal and hence the genetic 2200Probability of crossover=0.9 2300algorithm is successful in providing a near-optimal Probability of mutation=0.01 2400solution to the problem. Chromosome length=15

    Tournament size =15 Based on these results, the genetic algorithm can be used Desired performance of radiator =817 WC to determine the configuration of a radiator, for which we

    have no solution, when the performance desired from the radiator is know, say 1500 WC (product of overall heat As seen in Figure 3, the offline performance shows better transfer coefficient and total heat transfer area). Here a convergence than the online performance. This is because genetic algorithm is run for forty generations with a of the larger pool of diverse schemata are available in population size of 50, initially selected at random. The larger population. results of this case are displayed in Figure 4.

    900

    80070657006055600)550 )545500(x 1040Online Performance( x 1040035Fitness 3030025Fitness 2020015101005Offline Performance0000100100200200300Function Evaluation300Function Evaluation400400( Number of generation x Population size )(Number of generation x Population size) 500500600600 700700800800Figure 4: Best Fitness produced by the genetic algorithm Figure 3: Comparison of online and offline performance 9009001000vs. function evaluation 1000of genetic algorithm vs. function evaluation 110011001200 1200 130013001400 140015001500160016001700170018001800190019002000200021002100220022002300230024002400

    10. K. D. Emmenthal and W. Hucho. A Rational The configuration of radiator obtained after running the

    Approach to Automotive Radiator Systems Design, genetic algorithm is given in Table 4.

    Society of Automobile Engineers 740088

    Table 4: Solution provided by genetic algorithms for the 11. D. E. Goldberg (1989). Genetic Algorithms in Search, 5-row radiator with straight fins and inline tubes. Optimization, and Machine Learning. (population size=100, number of generations=100, 12. C. L. Karr, J. C. Phillips. Scheduling and Resource probability of crossover=0.9, probability of mutation=0.1) Allocation with Genetic Algorithms, Presentation at the SOLUTION Society of Mechanical Engineers Annual Meeting. PROVIDED BY rdPARAMETER edition) Analysis 13. B. K. Hodge, Robert P. Taylor, (3GENETIC & Design of Energy Systems. ALGORITHM ndNumber of Tubes 52 14. W. M. Kays and A. L. London, 2 ed. (1964), Fin pitch (per inch) 9 Compact Heat Exchangers.

    Length of cross-section of tube 10 Width of cross-section of tube 3 Fitness Value 1520972

6 CONCLUSIONS

    A genetic algorithm was developed to search for the optimal design of a radiator with pre-defined performance characteristics and cost constraints. The validity of the approach was tested against a problem with a known solution. The genetic algorithm produced near-optimum result for the problem; a solution which matched the best-known practical solution. Thereafter, the genetic algorithm is used for finding the optimal design parameters for a radiator with desired performance criteria and cost constraints. Therefore, it is concluded that a genetic algorithm can be used successfully to find near-optimum solutions in the realm of radiator design. References

    1. R. A. Beard and G. J. Smith, A Method of Calculating

    the Heat Dissipation from Radiators to Cool Vehicle Engines, Society of Automobile Engineers 710208

    2. Charles N. Kurland, Computer Program for Engine

    Cooling Radiator Selection, Society of Automobile

    Engineers 710209

    3. Performance of Aluminium Automotive Radiators,

    Society of Automobile Engineers 790400

    4. Engine Cooling System Design for Heavy Duty Trucks, Society of Automobile Engineers 770023.

    5. J. P. Holman (1986). Heat Transfer.

    6. P. L. Balaney. Thermal Engineering.

    7. G. F. Hewitt, G. L. Shires and T. R. Bott. Process Heat

    Transfer.

    8. M. Necati Ozisik (1985). Heat Transfer - A Basic

    Approach, New York, McGraw-Hill Inc.

    9. Jiunn P. Chiou. Correction Factor to Unit Core Heat

    Transfer Capability of Heat Exchanger Core Due to Variation of Tube Length, Society of Automobile

    Engineers 750884

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