Engineering optimization of an improved plancha stove

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Engineering optimization of an improved plancha stove Gregory L. Urban, Kenneth M. Bryden, and Daniel A. Ashlock Department of Mechanical Engineering, 3030 H.M. Black Engineering Building Iowa State University, Ames, IA 50011-2161, USA

This paper presents an engineering model of an improved plancha stove and demonstrates the use of advanced numerical analysis to improve plancha stove effectiveness. The advanced numerical techniques used include coupling a genetic algorithm searcher with a computational fluid dynamics evaluation of the stove performance. The plancha stove is a popular stove design. Built from steel, brick, or cement, the plancha stove is a sealed stove with a steel or cast-iron cooking surface. This permits the combustion gases to be exhausted from the living quarters via a chimney. Frying of breads (i.e., tortillas) and other foods is performed directly on the cooking surface of the stove. In contrast, cooking operations requiring boiling or simmering are performed by placing a pot containing the food on the cooking surface. Because of this two-tiered arrangement (flame-stove, surface-pot-food), the plancha stove is thought to be less efficient than stoves in which the cookpot is in direct contact with the flame. There are several standard efficiency tests; in most cases these involve heating and boiling a given amount of water, measuring the fuel used, and accounting for latent and sensible heat. On this basis, efficiency is established as the ratio between the heat absorbed by the water and heat released by the fuel. Plancha stoves are used for a variety of cooking tasks, and many of these tasks conflict with one another. For example, cooking tortillas requires a large area heated to moderate temperatures (∼ ∼250ºC); simmering requires a small area of slightly higher temperatures (∼ ∼400ºC); and bringing a large pot to a quick hard boil is most efficient with very high temperatures (>600ºC). Because of this, traditional measures of efficiency do not provide a complete understanding of the fitness of the stove for specific applications. Using numerical modeling and experimental testing, this paper demonstrates how a measure of fitness can be used to provide a more complete understanding of plancha stove efficiency and effectiveness. This understanding can be used to assess various plancha stove designs and to determine which design provides the most benefit in a specific application. 1. Introduction Nicaragua, like many other developing tropical countries, relies heavily on wood for its energy needs. In 1997 fuelwood represented about 47 % of the internal gross primary supply of energy, while petroleum represented 24 %, electricity 25 %, and other biomass residues 3 %. Household cooking utilizes 90 % of the fuelwood consumption in Nicaragua [INE, 1997]. More than 95 % of the households use low-efficiency unimproved stoves [Proleña, 2000]. As a consequence, fuelwood consumption is high, resulting in deforestation and excessive fuel costs. Additionally, low-efficiency unventilated stoves have been linked to a number of increased health risks, including increased infant mortality, blindness, cancer, still births, and birth defects. Proleña – Nicaragua, working with Aprovecho Research Center, has developed an improved plancha stove, the EcoStove, that is planned for wide distribution in Nicaragua. During initial testing it was noted that the plancha surface of the EcoStove had wide spatial surface temperature variation with the coldest regions being as cool as 150ºC, while the hottest regions were hotter than 600ºC.

This paper presents a unique application of two First World engineering tools, computational fluid dynamics (CFD) and genetic algorithms, to improve the effectiveness of plancha stoves. CFD is a high-fidelity numerical analysis technique used to simulate fluid system performance on the basis of the differential conservation equations of mass, momentum, and energy for complex flows and thermal fluid systems. Genetic algorithms are programming methods inspired by biology that can be used to automate the optimization process of a problem. In this research, genetic algorithms are implemented in a way that allows the computer to randomly suggest solutions to the problem and evolve these guesses to better solutions. If implemented correctly, genetic algorithms are efficient at finding optimal solutions to many problems. In this paper, CFD is used to evaluate three-dimensional solutions to the EcoStove problem as they are evolved by the genetic algorithms. The use of this coupling between CFD and genetic algorithms for three-dimensional fluid systems with heat transfer is unique. In this research, a new technique for implementing genetic algorithms is utilized to reduce the search space and computational time.

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Figure 1. The plancha EcoStove

Genetic algorithms are used for optimization of many types of engineering problems. Recently, computers have become fast enough for genetic algorithms to be applicable to fluid mechanics problems. The coupling of evolutionary programming to computational fluid dynamics has been especially successful in the design of wings and turbo-machinery on aircraft. With this technique, researchers have been able to find good solutions to sophisticated problems such as optimizing wings for both low drag and high radar invisibility [Makinen et al., 1999] and optimizing missile inlet nozzles with very high speed flow [Blaize et al., 1998; Zha et al., 1997]. Some codes involve advanced techniques to aid the genetic algorithm in the search for the best solution. One researcher uses neural networks, another form of evolutionary computation, to manipulate the design structure during evolution by fixing the velocity distribution on the surface of a turbine blade [Fan, 1998]. Various techniques have been implemented in these projects to solve the problem of the high computational cost associated with solving the Navier-Stokes equations. The most common solution to this problem has been to use a lower-level fluids solver coupled to a genetic algorithm to do the initial design work, followed by a complete CFD solver coupled to a genetic algorithm to refine the solution [Foster et al., 1997; Zha et al., 1997]. 2. Background The EcoStove (Figure 1) is a plancha stove with an insu10

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lated rocket elbow [Still and Kness, 2000] made from locally available clay, shaped and fired using traditional pottery techniques. The insulation is locally available pumice. The support structure is made from angle iron and sheet metal, and the plancha cooking surface is a 54 cm × 54 cm × 3 mm thick stainless steel sheet formed to create a removable cooking surface to allow periodic cleaning of the baffle space between the pumice insulation and the cooking surface. Significant efficiency and reduced indoor emissions gains are realized by using the rocket elbow to place the reacting hot exhaust gas from the fire under the plancha surface. These hot gases travel through a 1.2-cm gap under the plancha surface and above the pumice insulation and exhaust from the stove pipe at the left rear corner of the plancha surface. This results in a high temperature band on the plancha surface running from the rocket-stove inlet to the chimney. The areas of the plancha stove not in this path are substantially cooler. The result is that only portions of the plancha are at the desired cooking temperature. The search for an improved stove has yielded a number of tests for determining the efficiency of the stove [Baldwin, 1987; Joshi et al., 1989; VITA, 1985]. Both BallardTremeer [1997] and Bially [1991] have discussed these tests in detail. In general a given amount of water is heated, and the energy absorbed by the water is measured and compared with the energy contained in the wood consumed. This provides a method for comparing various stoves and determining their relative suitability for tasks such as heating water or cooking beans, corn, or rice. However, most of these tasks are either short-term in nature or would be more effectively done using a hay box [Still, 1999]. The transient nature of short-term tasks means that the actual performance of the stove is not measured well by boiling water efficiency tests. Additionally, efficiency tests do not measure how well the stove meets local needs. A better measure of stove suitability is its effectiveness, that is, how well the stove does its job at a given energy cost. For example, car fuel usage is not measured in terms of efficiency. A car is not 10 % or 30 % efficient. Rather, car performance is measured in terms of kilometers (km) traveled per liter (l) of fuel for particular driving conditions, which is a measure of effectiveness. In the case of the EcoStove, the stove needs to perform three tasks. In many ways these tasks conflict with one another. The stove needs to be able to bring one or more pots of water to a boil in a relatively short time; it needs to simmer water and food for extended periods of time without excessive tending of the fire; and it needs to cook tortillas (flat cornmeal cakes). Tortilla-cooking requires a large area heated to moderate temperatures (∼250ºC); simmering requires a small area of slightly higher temperatures (∼400ºC); and bringing a large pot to a quick hard boil is most effective with very high temperatures (>600ºC). There are many ways to measure the effectiveness of a stove to perform these multiple tasks. As a starting-point this paper assumes that the stove is most effective when !

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the stove surface has one hot spot, and the remainder of the stove surface is uniform. This will permit the user to quickly heat water on the one hot spot, and simmer food or fry tortillas on the remaining surface. In each case the user will need to adjust the fuel feed rate to achieve the desired surface temperature. A uniform cooking surface temperature ensures that the maximum number of tortillas is cooked for the fuel used, that simmering is simplified, and that the minimum amount of heat is lost from the rest of the surface while the user is bringing a pot to a hard quick boil. Additionally, a uniform surface temperature simplifies the stove usage for the user, helping to ensure consumer acceptance. On this basis, the design problem to be solved is to provide a plancha surface with the most uniform temperature possible that can be easily manufactured. Because the direct path of the heated air from the stove inlet to the outlet causes the uneven surface heating, the problem can be eliminated or reduced if the flow can be redirected to other regions of the flow space. One simple method of doing this is to weld solid, flat metal baffles in the flow region to change the flow patterns of the hot air in the stove. Baffles can easily be welded to the underside of the stove surface using the same materials that are already used to manufacture the stove. This provides a practical, cost-efficient, and easy-to-manufacture solution to the problem. In addition, the baffles will have no impact on the consumer because the baffles are hidden underneath the cooking surface. The remaining problem is to determine the optimal number of baffles and the optimal locations and sizes of these baffles in the flow field so that the surface has one hot spot and the rest is evenly heated. The design must also be easily manufactured and maintained. This technique was implemented in the field with modest improvement of stove effectiveness. The goal of this work is to utilize computational techniques to significantly improve stove performance by optimizing the placement of baffles in the flow field. 3. Modeling techniques There are several approaches to improving the effectiveness of the EcoStove. A program of experimentation with a number of designs could be implemented. However, this approach is time-consuming and expensive and would result in at most 50 different designs being tested. With this small sample size relative to the larger solution space, it is unlikely that the best design could be chosen. In another approach, a generalized understanding of the temperature profiles could be developed from first principles and then used to develop better designs. This would still require the assembly and testing of a large number of designs, and the lack of engineering detail available would hamper the design process. A numerical model could be developed and then utilized to find the optimum stove design. The advantages of this approach are that time and cost are saved, and only a few physical models need to be built. However, this can often become a hunt-and-peck method of system optimization, in which each result is considered and then another guess is tried on the basis of the new

information. By coupling the numerical model with a genetic algorithm to search the design space, we can develop a program that optimizes the design without intervention. Once this program is built, differing stove designs can be optimized automatically. This is the technique discussed in this paper. The genetic algorithm will, in this case, attempt to create a design that has an optimal surface temperature distribution while remaining easy to manufacture by varying the size and placement of baffles in the flow space. A number of variables are used to describe this optimal solution. The first unknown is the number of baffles needed to significantly improve the effectiveness. This number is tightly coupled to the ease of manufacturability of the stove because the welding of a large number of baffles could become cumbersome. The length and depth of each of the baffles remains unknown. The depth corresponds to the distance the baffle penetrates into the flow space from the surface. Finally, these baffles need to be placed in their correct locations and orientations. The baffle thickness is assumed to be uniform. A problem can arise in counting the number of baffles if the algorithm allows two baffles to cross. In this case, an extra baffle is required to manufacture the design. 3.1. Genetic algorithms When trying to find the best locations for the baffles for optimizing wood use and the surface temperature profile in a stove, this optimization process starts with relatively little understanding of what arrangements of baffles are good. To locate good positions for the baffles, the solver thus starts with random positions for the baffles and draws on the biological paradigm of evolution to help us locate good positions for the baffles. For any given baffle design we can use CFD simulation to return a good prediction of the performance of a stove that has those baffles. With this performance metric available, we can compare designs and permit better designs to “reproduce”, i.e., those are the designs we copy and tweak to get new, and sometimes better, designs while we eliminate the less fit designs from the reproduction pool. A genetic algorithm operates on a population of structures that can be compared. Lower-quality structures are deleted, higher-quality structures are copied in their place, and then those copies are varied. The genetic structure of a copy is varied in the same way as in nature via reproduction and mutation. In reproduction, the design elements of portions of the two copies are exchanged, which is similar to the role of reproduction in biology. Also, small, random changes in the copies are made in analogy to mutation. Over time the designs in a population improve under the influence of variation and selection, just as they do in an evolving biological population. There are several advantages to this process. The inclusion of randomness permits discovery; there is room to “get lucky”. Heredity, via copying, ensures that the best designs located so far tend to stay in the “genetic” mix, and the very best design is always retained. Reproduction permits mix-and-match innovation, and mutation prevents stagnation. The genetic algorithm technique is also very simple

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Figure 2. The CFD model and temperature profile

Figure 3. Temperature profile of a square duct model

to program once the CFD code is available and can use as much computer time as is not taken up with other projects. This permits large computations to be “bootlegged” a bit at a time on whatever computers are available. 3.2. Computational fluid dynamics model A detailed numerical model utilizing Star-CD , a commercially available CFD software program, was used to create the model of the EcoStove. Star-CD incorporates all of the tools necessary to create the mesh of cells defined by grid points, specify the boundary conditions, generate the equations from these specifications, iterate the equations to a converged solution, and analyze the solution. The basis of CFD lies in discretization of the flow space and transforming the partial differential equations describing fluid mechanics and heat transfer into algebraic representations of the conservation equations for each of the many grid points that the flow field is divided into [Tannehill et al., 1997]. In the model, air flows into the stove at 3.88 m/s with a temperature of 977.4 K and a density of 0.357 kg/m3 to the outlet. The outlet is atmospheric air with a pressure of one atmosphere and a temperature of 298 K[1]. Turbu12

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lence is calculated using Star-CD ’s built-in K-ε model with an intensity of 0.1 and an entrance length of 0.0476 m. For the model, this inlet temperature and inlet air-flow rate was experimentally determined in the field, and the initial baffle-free model was validated by comparison with the known temperatures of the EcoStove surface. In practice, the inlet air temperature, inlet flow rate, and surface temperatures are functions of how the operator utilizes the stove. For example, fuel-wood moisture content, fuel-wood size, and feeding rate have significant impacts. However, once a uniform surface is achieved, variations in operator usage have only a small effect on surface temperature uniformity. After the optimization of the baffle locations, the effectiveness of the solution over a range of conditions was checked. Figure 2 shows the model along with the unmodified stove CFD temperature profile solution. The solution to the model shows that the lowest temperature on the surface of the model with these boundary conditions is 420 K in the upper right corner of the stove. This is a good match to the experimental value measured in the field in Nicaragua. The computational model of the flow space is 84 cells wide × 84 cells deep × 12 cells thick. The total number of grid cells including the ducts is 101,056. For the genetic algorithm to complete an extensive search for the best solution to the baffle problem, the CFD code evaluating the solutions as they are “born” must be called thousands of times. Therefore, the model used for optimization must be a compromise between computational costs and solution accuracy. Two simplifications were made to reduce these costs. The first was the replacement of the cylindrical inlet and outlet ducts with the simpler, more convergence-friendly square ducts. The inlet mass flow rate was adjusted by the ratio of the inlet cross-sectional area to ensure that the energy coming into the stove is the same for both cases. A test was completed to examine the effect of replacing the cylinders with square prisms. The result is shown in Figure 3. Although the details of the flow trends are somewhat different from the cylindrical solution of Figure 2, the major features of !

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Figure 4. Results of the grid dependency test

the flow field are consistent enough between the two models to be worth the saved computational cost. The second simplification was the reduction of the size of the grid. In most CFD problems, the errors inherent in the solution due to the discretization of the continuous partial differential equations are reduced as the number of cells increases [Tannehill et al., 1997]. However, more grid points significantly increase the computational cost of the solution. To test for grid dependence of the solution accuracy, models with cells half as large and twice as large as the original model were created. This results in models with one-eighth and eight times the number of cells of the base model because the distance is halved or doubled in three directions. The resulting square-duct models have 12,632 cells and 808,448 cells respectively. The CFD solutions are shown in Figure 4. Inspection of the results shows changes in the flow trends as the grid is refined; thus, there is some grid dependence in the 12,632-cell mesh. The standard 101,056-cell grid takes approximately eleven times as long to converge, and the 808,448-cell mesh takes approximately 290 times as long to converge. Additionally, the average surface temperature drops as more cells are added. This drop is relatively small; the temperature is approximately 10ºC less on the finest grid than on the coarsest grid. However, the major features of the temperature profile showing the problem of an uneven heating surface remain consistent between the fine and coarse grids. Because alteration of the major flow features is the underlying goal of this genetic algorithm, and the computational cost of a finer mesh is significant, the 12,632-cell mesh was used as the best model for coupling to the genetic algorithm. The 12,632-cell mesh has 1700 cell faces exposed as the cooking surface. The thermal resistance of this surface was calculated using a convective heat transfer coefficient[2] of 20 W/m2K, a thermal conductivity[3] of 30 W/mK, and a surface thickness of 0.16 cm. The remaining surface cell faces are assumed to be adiabatic. The mesh is broken into three parts: an 8×8×8-cell mesh for the inlet duct, a 42×42×6-cell mesh for the flow region, and an

Figure 5. Temperature profile of manually placed baffles

8×8×24-cell mesh for the outlet duct. The original circular duct model with an 84×84×12 flow region was used to confirm the final result upon completion of the genetic algorithm. In the field, two baffles were placed manually in the flow field in the configuration shown in Figure 5 in an attempt to improve stove performance. The baffles were placed above and to the left of the inlet to block an immediate flow path between the inlet and outlet ducts. Intuitively, it seems like a good solution to the flow problem. This configuration was also analyzed using the numerical model and yielded results similar to those obtained from the field test. However, inspection of Figure 5 indicates that this configuration does not result in a uniform temperature profile. This result does show that baffles in the flow region can have a significant effect on the surface profile. 3.3. Genetic algorithm set-up The first step in the design of the genetic algorithm is the specification of the structure that defines each member of the population. The structure used is an array of baffles,

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each of which is defined by five values that completely specify the baffle. The five values describing the baffle are the starting x and y positions of baffle generation, the direction of baffle generation, the length of the baffle, and the depth that the baffle penetrates into the flow field. Each of the values is in units of number of cells except for baffle generation direction, which is an integer between zero and three that represents right, left, up, and down, respectively. For the initial runs of the genetic algorithm, the maximum length of the baffle is the entire length of the stove, and the depth of the baffle is allowed to vary between two and six cells, the entire depth of the stove. Figure 6 gives an example that shows how the five values are decoded into a baffle in the flow regime. The likelihood of a structure passing to the next generation after a crossover event is determined quantitatively on the basis of the fitness function. The fitness function measures how well a particular solution creates an even temperature distribution across the stove surface. Two possible fitness functions were examined: Fitness = Σ (Ti – Tavg)2 (1) Fitness = Σ |Ti – Tavg| (2) In these equations, Ti represents the temperature at each cell and Tavg represents the average temperature on the stove surface. In both of these equations, structures with lower fitness values are more fit to be passed on to the

Figure 6. Coded structure of the genetic algorithm

next generation, and a fitness value of zero indicates a perfect temperature distribution. The squaring in Equation 1 and the absolute value in Equation 2 ensure the fitness value becomes larger for each cell in which there is temperature variation from the average. Equation 1 was used in the execution of the algorithm to force the code to discard designs with regions of extreme temperature variation. After completion of the algorithm, Equation 2 was used to analyze the results. These fitness functions leave out the design criterion that there needs to be a hot region on the surface of the stove for foods requiring very high temperatures to cook properly. However, as suggested by the results of the unaltered stove, all solutions will contain a well-defined hot spot directly above the inlet duct which cannot be eliminated by the addition of baffles perpendicular to the stove surface. The primary factor making the manufacture of a baffle design difficult is the number of baffles that are welded onto the underside of the stove surface. A large number of baffles would be difficult to manufacture because the welding space for adding a new baffle could become small as other baffles surround the space for the new baffle. Additionally, the heat from adding a new baffle may melt the weld of a previously welded baffle. Therefore, the fewer the number of baffles, the more manufacturable the design will be. However, too few baffles will not have a large enough impact on the flow field to satisfy the design criteria. In a preliminary genetic algorithm run, a three-baffle design was found to have a significant impact on the surface temperature distribution. Most three-baffle designs are easy to manufacture and have a significant enough impact on the flow to even the temperature distribution. However, if two of the baffles cross through one another, four baffles need to be welded to manufacture the design. Figure 7 describes this problem. Forcing the solution to consist of three baffles would require that the hangover portion of the design be deleted. Dropping a baffle in this way possibly removes significant flow features from the population. Thus, disallowing crossing baffles limits the ability of the genetic algorithm to find much better designs that are marginally more difficult to manufacture. To solve this problem, three baffles are used but a secondary

Figure 7. Baffle addition due to crossing baffles

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Figure 8. Diagram of a crossover operator

Figure 9. Temperature profile of the solution for non-penalized genetic algorithm

fitness function is included to penalize the design for each time it has a crossing baffle. For a three-baffle design, there is a maximum of five baffles because there are at most two baffle crossings. This allows the genetic algorithm to “experiment” with more than three baffles to check that the improvement would be worth making the design more difficult to manufacture. This secondary fitness function must be a measure of the added cost of manufacturability when more baffles are added. The population size and the number of mating events are important parameters in the execution of the code. Each generation consisted of 32 members. 1500 mating events were used. This provided a significant number of mating events within computationally bearable costs. Population graphing [Ashlock, 1999] is a technique that helps maintain diversity in small populations by forcing population members to interact only with certain other members. A five-dimensional hypercube [West, 2001] was used as the basis for the population graph. In each mating event, a population member is chosen and its mating group members are identified. Figure 8 shows the mating process used in this algorithm. Mating results in two new “children”. Each of these children is mutated. This helps bring into the population new features that were not present in the initial population. After mutation, the two new children’s fitness values are evaluated using the CFD solver. They then enter the population replacing the two

members of the mating group with the worst fitness. Additional technical details on the genetic algorithm and optimization routine are given in [Urban, 2001]. Complete details of the CFD solver are given in the Star-CD User’s Guide [CDI, 1999]. The preliminary runs were completed in serial execution on a Silicon Graphics Onyx 2 computer with 24 MIPS 400MHz R12000 processors and 12 GB of RAM. Execution of the code with 1500 mating events took between 4.5 and 11 days depending on the stability of the mesh generated after the addition of the baffles. 4. Results The solutions from three variations of the genetic algorithm are shown in the detailed grids in Figures 9 through 11. The difference between the solutions lies in the fitness evaluation. Figure 9 shows the results for a stove with no secondary manufacturability penalty. Figure 10 depicts the results when manufacturability is taken into account with a penalty of 10 % of the best structure’s fitness for each baffle crossing. Figure 11 shows the results with the variable fitness penalty that increases linearly from 0 % at the first mating event to 10 % at the 1000th mating event. The fitness penalty was held constant at 10 % for all mating events after the 1000th. All three codes were run to 1500 mating events. The results of the runs were re-evaluated using the

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Figure 10. Temperature profile of the solution for 10% fixed manufacturability penalty Table 1. Summary of genetic algorithm results Design

Fitness value

Adjusted fitness

Average surface temp (K)

Temp. difference per cell (K)

% surface within 15 % of average temp.

Unaltered

1.000

1.000

697.5

117.9

42.4

No penalty

0.452

0.407

744.7

47.9

94.0

10 % penalty

0.409

0.368

776.5

43.3

94.8

Variable penalty

0.439

0.439

767.5

51.8

88.3

Note Values do not include the hot spot on the stove surface directly above the inlet duct.

Figure 11. Temperature profile of the solution for variable manufacturability penalty

absolute value fitness function because the average surface temperature and the average temperature difference per cell is easier to calculate with this function. It also makes comparison between the small grid and the detailed grid more meaningful. Additionally, a 17×18-cell patch directly above the inlet duct was not included in the fitness evaluation to remove the hot spot from the analysis. This ensures that the temperature variations penalize a design only in the region where an even distribution is 16

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desired. Using this function, the unaltered plancha stove has a fitness of 795,661 and an average temperature difference of 118 K per cell from the average surface temperature. For analysis, the fitness values were normalized about the fitness value of the unaltered stove. Therefore, the unaltered stove has a fitness of 1.0, and a perfect temperature distribution results in a fitness of 0.0. Table 1 outlines the performance of the stove designs developed by the genetic algorithms. The adjusted fitness !

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Figure 12. Temperature profile of the manually enhanced stove design

Figure 13. Temperature profile for cooler inlet air condition

Figure 14. Temperature profile for warmer inlet air condition

removes the effect of adding the manufacturability penalty. All three designs have significantly better fitness values than the unaltered stove, suggesting that the stove surface temperature is much more uniform in the new designs. Additionally, the temperature of the air at the outlet is lower and the average surface temperature is warmer than that of the unaltered stove in each of these cases. This indicates that the new designs are more efficient because more energy is released for cooking from the same amount of fuel. On the the basis of the fitness values, the result from the constant penalty rate genetic algorithm (Figure 10) best accomplishes the task of raising the effectiveness while remaining manufacturable. It also has the lowest adjusted fitness value, suggesting that it is the best design when an even temperature profile is the only design criterion. Finally, the average surface temperature is the highest among all the designs, suggesting that it is the most efficient design. The average temperature is over 75 K higher than that of the unaltered stove as a result of fewer losses to the chimney, and nearly 95 % of the stove surface is within 15 % of the average temperature excluding the hot spot, suggesting high effectiveness. Inspection of Figures 9 through 11 shows that there are some important similarities between the new stove designs. Each of the solutions has found a deep, long baffle that passes longitudinally near the top of the inlet duct which acts to block the direct flow path from the inlet to the outlet. This pushes flow to the sides of the cooking surface by forcing the flow into a left-moving and a rightmoving stream. The remaining two baffles are used to vary the resistance to these two streams to achieve the optimal balance between the mass flow rate and the length of the flow path of the two streams. In each design, one baffle is used to vary the resistance to each of the two streams. The repeatability of these physical features suggests that the genetic algorithm has found an effective EcoStove design. The original, completely random

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Figure 15. Temperature profile for slowed inlet air condition

94 % of the stove surface is within 15 % of the average surface temperature. No design enhancements were discovered for the algorithms with manufacturability penalty functions. In everyday operation, the EcoStove is operated with various amounts of fuel to accommodate different needs. In the simulation, this is equivalent to changes in the inlet air temperature and flow rate. This means that a good baffle design will need to maintain the improved temperature distribution and efficiency when inlet conditions vary. Computational tests were completed to test the stove for different inlet conditions. The results are shown in Figures 13 through 16. These tests show that the overall effectiveness in the stove does not change as inlet conditions change because the major features of the flow field remain unaltered. This test was completed for the unaltered stove and the design from Figure 12. For each of the designs, the test results indicate that the design will retain its effectiveness as the operating conditions vary. 5. Conclusion and future work This paper presents an engineering model and optimization technique for improving the effectiveness of a plancha stove. This design is currently being field tested and will be implemented in Nicaragua. This work needs to be extended to create generalized optimization techniques and guidelines for a wide range of plancha stove configurations. This will enable the field optimization of plancha stoves. The next step in this process is to improve the optimization routine by reducing the computational time required. This will allow a larger number of stove geometries to be investigated and engineering design guidelines to be developed. Acknowledgements

Figure 16. Temperature profile for faster inlet air condition

populations of the three runs were all likely very different and developed along different evolutionary paths to come to similar conclusions. This leads to the assumption that runs with many more mating events will show even stronger similarities than the solutions presented here and come closer to the absolute best design. There is room for improvement in the stove designs since the genetic algorithms were not allowed, because of computational expense, to run to the point where evolution could no longer increase the stove fitness. At this point, the results of the genetic algorithm were used to help the designer make more intelligent design changes than would have been possible without this starting place. Design changes were made to the results of the threestove designs to attempt to increase the effectiveness of the stove. The enhancements to the solution from the algorithm without a manufacturability penalty are shown in Figure 12. The new design eliminates the baffle crossing and reduces the normalized fitness value to 0.394. The average surface temperature decreased to 744 K and the average temperature difference per cell dropped to 46 K. 18

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The help and encouragement of our friends Stuart Conway at Trees, Water and People and Rogerio Carneiro de Miranda at Proleña – Nicaragua is gratefully acknowledged. We extend our thanks to Larry Winiarski and Peter Scott who designed and built the EcoStoves in Nicaragua and gave us the opportunity to work on this problem. We also thank Chris House, an undergraduate mechanical engineering student at ISU, for building the grid and setting up the code that provided the CFD solutions. Notes 1. ºC = K - 273 2. The convective heat transfer coefficient is a measure of the rate at which the external .

air surrounding the stove removes heat. Specifically, Q conv , the rate of heat removal

. from the stove surface can be found from Q conv = hA(Tcs – Tair) , where h is the heat

transfer coefficient, A is the area, Tcs is the heated cooking surface of the stove, and Tair is the ambient air temperature.

3. Thermal conductivity is a measure of the ability of a material to conduct heat. Specifi.

cally, Q cond , the rate of heat transfer through the stove plancha can be found from

. Q cond , = kA (Ti – Tcs) where k is the thermal conductivity, A is the area, Ti is inner

surface of the plancha exposed to the hot combustion gases, and Tcs is the heated cooking surface of the stove. References

Ashlock, D.A., 1999. “Graph based genetic algorithms”, Proceedings of the 1999 Congress on Evolutionary Computation, Washington D.C., USA, pp. 1362-1368. Baldwin, S.F., 1987. Biomass Stoves: Engineering Design, Development, and Dissemination, Volunteers in Technical Assistance, Arlington, Virginia, USA. Ballard-Tremeer, G., 1997. Emissions of Rural Wood-burning Cooking Devices, Ph.D. dissertation, University of Witwatersrand, Johannesburg, South Africa. Bially, J., 1991. Evaluation Criteria for Improved Cookstove Programs: The Assessment of Fuel Savings, Environment and Policy Institute, East-West Centre, Hawaii, USA. Blaize, M., Knight, D., and Rasheed, K., 1998. “Automated optimal design of two-dimensional

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supersonic missile inlets”, Journal of Propulsion and Power, 14(6), pp. 890-898. Computational Dynamics, Inc. (CDI), 1999. Star-CD User Guide v3.10, Melvil, New York, USA. Fan, H.Y., 1998. “Inverse design method of diffuser blades by genetic algorithms”, Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 212(4), pp. 261-268. Foster, G.F., and Dulikravich, G.S., 1997. “Three-dimensional aerodynamic shape optimization and gradient search algorithms”, Journal of Spacecraft and Rockets, 34(1), pp. 36-42. Instituto Nicaragüense de Energia (INE), 1997. Memoria INE 1997, Managua, Nicaragua. Joshi, V., Venkataraman, C., and Ahuja, D.R., 1989. “Emissions from burning biofuels in metal cookstoves”, Environmental Management, 13(6), pp. 763-772. Makinen, R., Periaux, J., and Toivanen, J., 1999. “Multidisciplinary shape optimization in aerodynamics and electromagnetics using genetic algorithms”, International Journal for Numerical Methods in Fluids, 30(2), pp. 145-159. Proleña – Nicaragua (Proleña), 2000. Alternativas Viables Para Solucionar el Problema de Demanda de Leña en la Región Las Segovias, ed. Alves-Milho, S.F., Managua, Nicaragua.

Still, D., 1999. “The haybox for energy conservation”, Boiling Point, 43(10). Still, D., and Kness, J., 2000. Capturing Heat II, Aprovecho Research Center, Cottage Grove, Oregon, USA. Tannehill, J.C., Anderson, D.A., and Pletcher, R.H., 1997. Computational Fluid Mechanics and Heat Transfer, 2nd ed., Taylor and Francis, Washington D.C., USA. Urban, G.L., 2001. The EcoStove: a Case Study in Thermal System Optimization Based on Differential Analysis, MS dissertation, Iowa State University, Ames, IA, USA. Volunteers in Technical Assistance (VITA), 1985. Testing the Efficiency of Wood-burning Cookstoves: International Standards, Volunteers in Technical Assistance, Arlington, Virginia, USA. West, D.B., 2001. Introduction to Graph Theory, 2nd ed., Prentice-Hall, Upper Saddle River, New Jersey, USA. Zha, G., Ardoino, M., Zuccalli, G., Zanotti, L., Paorici, C., and Razzetti, C., 1997. “High performance supersonic missile inlet design using automated optimization”, Journal of Aircraft, 34(6), pp. 697-705.

Contributions invited Energy for Sustainable Development welcomes contributions from its readers. Energy for Sustainable Development, now twenty-seven issues old, is a venture in the field of journals on energy with a special focus on the problems of developing countries. It attempts a balanced treatment of renewable sources of energy, improvements in the efficiency of energy production and consumption, and energy planning, including the hardware and software (policy) required to translate interesting and useful new developments into action. With such a multi-disciplinary approach, Energy for Sustainable Development addresses itself to both specialist workers in energy and related fields, and decision-makers. It endeavours to maintain high academic standards without losing sight of the relevance of its content to the problems of developing countries and to

Energy for Sustainable Development

practical programmes of action. It tries to provide a forum for the exchange of information, including practical experience. Material for publication as articles, letters, or reviews may be sent to the Editor: Prof. K. Krishna Prasad, University of Technology, Faculty of Electrotechnical Engineering, EEG-Building 2.20, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands Tel: +31 40 2473168; Fax: +31 40 2464151 E-mail: [email protected] All other categories of material may be sent to the Executive Editor: Svati Bhogle, 25/5, Borebank Road, Benson Town, Bangalore - 560 046, India. Tel: +91 80 3536563 Fax: +91 80 3538426 E-mail: [email protected] For guidelines to authors on the preparation of the text and other material, see Page 4.

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