Numerical Optimization of Domestic Hot Water Systems Based on Global Cost Lucas Paglioni Pataro Faria 1 e-mail: lppf@ig.com.br Rudolf Huebner e-mail: rudolf@ufmg.br Universidade Federal de Minas Gerais, Anto ˆnio Carlos Avenue, 6627, Pampulha, Belo Horizonte, Minas Gerais 31270-901, Brazil Elizabeth Marques Duarte Pereira Centro Universita ´rio UNA, Raja Gaba ´glia Avenue, 3950, Estoril, Belo Horizonte, Minas Gerais 30494-310, Brazil e-mail: bethduarte00@gmail.com Ivan Magela Corgozinho Pontifı ´cia Universidade Cato ´lica de Minas Gerais, Dom Jose ´ Gaspar Avenue, 500, Building 50, Belo Horizonte, Minas Gerais 30535-901, Brazil e-mail: ivanmagela@yahoo.com.br The scope of this work is motivated by the large number of solar heaters recently installed by the government in joint housing developments for the low-income population in Brazil, the techni- cal challenges inherent in deploying domestic hot water systems, and innovative new models of sustainability technology being developed in Brazil. Computational algorithms were developed to establish the criteria for optimization, such as minimizing the required recycling, the energy consumption in pumping, and the diameter of the pipes in the secondary circuit of the distribution network. The numerical method adopted, the conjugate gradient method combined with a genetic algorithm, has exhibited a very satisfactory degree of convergence, even though high-oscillation amplitudes were observed, which are attributed to slight varia- tions in the pipe diameters (commercial). [DOI: 10.1115/1.4023967] Keywords: solar energy, domestic, hot, water, optimization 1 Introduction By the year 2000, there were approximately 400 solar heating systems installed in social interest housing in Brazil. By 2001, there were already 625 installed systems, and approximately 2100 systems were installed per year in the ensuing years. Many of these systems were installed in low-income communities by the electric power companies. The number of low-income households serviced by solar heating systems is expected to increase further in the coming years. In 2000, a project coordinated by the Study Group on Energy at the Catholic University of Minas Gerais, Brazil installed solar systems in 100 houses in the Sapucaias neighborhood of Contagem/Minas Gerais and monitored them for 5 years. Compared to systems that work only with electricity for water heating, the average electric power consumption savings observed in the monitored houses was 36.4%, and the monetary savings exceeded 50% of the energy bill in some households [1]. Given the technical challenges of equipment installation, mainte- nance, and even the sale of some systems by community residents, the proposal is an unprecedented project in Brazil, aiming to iden- tify the critical variables of a domestic hot water system (DHWS) through the development of an optimized mathematical model. The study aims to establish the minimum standards for hot water supply to low-income houses, develop optimized systems of hot water distribution, develop programs and applications for control and design of the facilities, and possibly build a monitored DHWS unit in a place of strategic interest in the state of Minas Gerais, Brazil, while also solving the technical difficulties of today’s solar heating systems in low-income houses. 2 Bibliographic Review Several parameters influence the performance and feasibility of district heating systems and DHWS. Several authors, mentioned below, have studied the modeling and optimization of these systems. Pulido-Calvo et al. [2] studied how to select the best combina- tion of tube diameters in a water distribution network for a fish farm. Fraisse et al. [3] compared various optimization criteria for a solar domestic hot water system. Cho et al. [4] showed that optimization of combined cooling, heating, and power (CCHP) systems’ operation commonly focuses only on energy cost. Wang et al. [5] analyzed the energy flow of a CCHP system. In the Wang et al. [5] study, the capacity and operation of CCHP sys- tems were optimized by a genetic algorithm. Lygnerud and Ojala [6] studied the efficiency of providing district heating to small houses in Finland and Sweden. The results indicate that Finnish companies, overall, are more efficient when offering district heat to small-house customers compared to large-house customers. Reverberi et al. [7] proposed an algorithm for the minimization of a suitable cost function. Prasanna and Umanand [8] proposed a hybrid solar cooking system, where the solar energy is transported to the kitchen. In that study, the diameter of the pipe was selected to optimize the overall energy transfer. Young-Deuk et al. [9] optimized the long-term performance of an existing active- indirect solar hot water plant using a microgenetic algorithm in conjunction with a relatively detailed model of each component in the plant and a solar radiation model based on the measured data. Although extremely widespread in Europe and the United States, such simulation and optimization tools and DHWS them- selves are new in Brazil, Latin America, and in most tropical and subtropical countries. Therefore, it is necessary to develop tools adapted to this type of country and, particularly, consider the pro- file of the low-income consumer. 3 Mathematical Modeling and Optimized Implementation of the Global Cost Function of the DHWS The contribution of this work complements the previous studies by developing a numeric and economic evaluation of the fluid dynamic behavior optimized at the secondary circuit of a DHWS for low-income houses. A major mark of this work is that the opti- mization algorithm, based on the gradient method, works together with a genetic optimization that has the function to select which segments of the pipe network will be optimized by the gradient method. The genetic model basically creates a more representative “search space” that allows the gradient method to work better. The implementation methodology of the genetic algorithm is not described in this article. However, its omission does not affect the 1 Corresponding author. Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING. Manuscript received June 26, 2012; final manuscript received February 24, 2013; published online May 23, 2013. Assoc. Editor: Gregor P. Henze. 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