Preliminary design, optimization and CFD analysis of an organic rankine cycle radial turbine rotor
Introduction
With the increasing number of industrial activities, energy demand has increased continuously. Although there are sufficient natural resources such as oil, coal and water to meet the global electric power demand, these resources are increasingly depleted and cause adverse environmental impact.
Many lines of research in engineering have sought to develop designs that make possible the generation of energy from renewable sources. Greater attention has been given to renewable energy sources such as solar and geothermal energy, and heat from industrial waste. The latter is considered a potentially promising energy source, however this heat source cannot be converted efficiently to electricity by conventional power generation methods.
The organic Rankine cycle is the most common way to convert energy starting from low temperature sources (geothermal energy, waste heat processes, solar energy, etc.). In recent decades, it has been used to generate energy starting from high temperature heat sources (biomass burning and exhaust gases primary triggers) [1].
Applications based on ORC can be summarized as here: Biomass; Micro scale which includes small combined heat and power; solar desalination unit, ORC as micro gas turbine; bottoming cycle and ocean thermal energy conversion technology for ORC applications; Geothermal ORC; Waste heat recovery of some industries, e.g.: Steel, cement and ceramic industries or internal combustion engines or vehicles waste heat recovery; ORC are used as bottoming cycles of steam and gas turbines; Fuel cell; Solar – Larger solar power plants using ORC with possibility of storage systems; ORC in nuclear power plants; ORC for cooling [2]. They are characterized by electricity production from low temperature heat sources in the range of about 60 to 200 °C [3]. It has been estimated statistically that low-grade waste heat accounts for more than 50% of the total amount of heat generated in industry [4].
ORC is no longer confined to the laboratory, and has been widely applied since the 1980 s. In Europe more than 120 ORC plants are in commercial operation, with sizes ranging from 0.2 to 2.5 MW, which utilize the combustion heat of biomass [3].
The working fluid has a fundamental importance in the cycle. Not only must it have the necessary thermal and physical properties to match the application, but it must also possess adequate chemical stability in the desired temperature range. The fluid selection affects the system efficiency, operating conditions, environmental impact and economic viability. The selection criteria have been widely studied and established in the literature [5].
Rayegan [6] who developed a procedure to compare the capacities of working fluids when they are used in solar Rankine cycles with similar working conditions, 117 fluids in the Refprop 8.0 was investigated to provide more information on the effects on the system's operation, energy efficiency and impact on the environment.
Shengjun et al. [7] presents an investigation on parameter optimization and performance comparison of some fluids in ORC in a low temperature geothermal energy system (i.e, 80–100 °C). The results indicate that the choice of the working fluid varies the objective function and the value of the optimized operating parameters are not the same for different indicators such as: thermal efficiency, exergetic efficiency, recovery efficiency, and others.
The design of Ahmed et al. [1] studies an organic Rankine cycle combined with a gas turbine to convert the turbine's residual heat into electrical energy. The working fluid chosen is R134a. The exergetic analysis is performed using real data from the cement industry, showing that most of the loss of exergy is in the working part of the turbine. It was observed that the working fluid directly affects the efficiency of the cycle, so the choice of fluid is fundamental for a good performance of the cycle because the ideal thermal physical properties depend on the temperature of the source.
Drescher [8] developed a software to find thermodynamic suitable fluids for ORC in biomass power and heat plants.
This present work uses this knowledge to develop an efficient primary drive. The slope of the saturation curve of a working fluid in a t-s diagram can be positive (e.g. pentane), negative (e.g. R22) or vertical (e.g., R11), and the fluids are correspondingly called wet, dry and isentropic. Wet fluids such as water generally need to be superheated, while many organic fluids, which may be dry or isentropic, do not need superheating. Another advantage of organic working fluids is that the turbine constructed for ORC typically requires only a single expander stage, which results in a simpler plant which is more economical in terms of capital and maintenance costs [9].
Another important observation in Bao et al. [5] is that the thermodynamic properties of the working fluids affect the performance of ORC, as well as, a specific volume ratio. The work of Efstathiadis et al. [10] report that the influence of the chosen working fluid is strongly related to the turbine size. The work of Efstathiadis et al. [11] was developed an integrated model equations to evaluate the performance of an ORC for various working fluids, due to the importance they bring to the cycle efficiency. The inclinations and shapes of fluid saturation vapor curves affect the efficiency of the system.
Various studies have been conducted along these lines, some of which have used REFPROP 8.0 as a mathematical model to calculate the thermodynamic properties [12]. Others have developed their own mathematical models and used optimization techniques to simulate power plants operating with ORC to find optimal operation strategies with respect to thermal efficiency or net power generation in the network [13].
Few studies have shown an experimental investigation of an ORC turbine. Greater emphasis has been placed on the system rather than the machine that is the main efficiency generator in the cycle. Fiaschi et al. [14] briefly describes the design for a radial turbine using R-134a, cyclohexane, n-pentane, R-245fa, R-1234y and R-236fa as working fluid. In the expansion model the compressibility factor is used to take into account the properties of real gases. Hattiangadi [15] develops the design of a radial turbine rotor in FORTRAN, using values available in the literature for some parameters for gas turbines. According to the author, later studies of the model will only be possible if real experiments are performed with organic fluids in order to acquire the necessary loss coefficients and other dimensionless parameters. The nozzle design was not described in this work.
Rabar et al. [16] brings an optimization study for ORC for the radial turboexpander based on genetic algorithms, his line of reasoning seeks to identify the main variables that have significant effects on the turbine dimensioning, in order to achieve the smallest possible size, worked with 6 different fluids, of which R245fa and R236fa were present, an interesting point of his research shows that the refrigerant fluid R236fa was successful in the optimization process and resulted in the minimum total size of the turbine. Thus, this fluid was considered for use in the present work.
Rankine's organic cycle plays an important role in the study of technologies that aim at minimizing fuel consumption and CO2 emissions, they are the key piece with great potential in recovering energy from the engine exhaust in conversion to electrical energy. The good results of the ORC Investigations considered two important lines of work; i) the proper selection of the working fluid; ii) ORC system optimization to maximize efficiency, whether it is used in the global system, or in the components that integrate the cycle, with special attention to the design of the expander. The following are some of the most recent works that have considered the turbine to be a key part of energy extraction through heat recovery.
Alshammari et al. [17] discusses a design methodology for a radial turbine expander for a heavy-duty engine residual heat recovery system. In his work, a 1D code is used for the base geometry and is later used as an input for CFD analysis, achieving a maximum isentropic efficiency of 83% after the numerical simulation. The studies presented are similar to proposal in the present paper, although it does not provide more details on both the optimization of the 1D design and the numerical calculation used, and which working fluids used, but it is possible to notice that this approach significantly improves the cycle efficiency.
Fiaschi et al. [18] also implemented a one-dimensional model for the design of radial turboexpanders for ORC, referring to a typical small scale (50 kW) application considering, in particular, the estimate of losses and efficiency; worked with six different fluids, including refrigerants R236fa, R245fa, also chosen to work in this paper. The results show a 1.5–2.5% higher total to total efficiency percentage, and also shows that R236fa and R245fa fluids performed better.
Sarmiento et al. [19] developed a detailed preliminary 1D design based on the meanline and made comparisons performance characteristics obtained with the 3D CFD approach, verifying agreement with both models and validating the methodologies. The most recent work of Sarmiento et al. [20], a process for optimizing the blade geometry was performed using a response surface methodology created with radial Gaussian-based functions, the results were subsequently analyzed by CFD, the performance characteristics and the 3D flow field in the design and operation outside the design conditions showed that the optimization resulted in better loading of the blade and greater efficiency in the entire operational range studied.
According to Sarmiento et al. [20], 1D design is a starting point and that 3D analyzes are necessary to understand the three-dimensional flow field. In addition, it is possible to observe that the application of optimization processes that employs metamodels integrated CFD, significantly improves the design. The authors of this present work have their own experience of works developed with the use of metamodels [21], however, in a complementary and differentiated way, the authors developed an optimization methodology applied to the 1D design, that is, they have already improved the preliminary design with the use of tools with low computational cost. After, the result of the optimization process is evaluated with CFD. This methodology allows finding alternatives to avoid the high computational costs that yet constitute a bottleneck when it comes to direct optimization complex three-dimensional models.
Therefore, in a first approach, this work describes the development of a preliminary design methodology for a radial turbine rotor that operates in an organic Rankine cycle, for a small scale application, of approximately 50 kW, the results obtained are compared with the work of Fiaschi et al. [18], for the purpose of validating the proposed methodology. In this study, two working fluids (R236fa and R245fa) are chosen. In a second approach, a 1D design of a radial rotor of approximately 200 kW of power is obtained, a preliminary process is applied to this preliminary design. This comparison makes it possible to guarantee that the methodology can be extended to an experimental test future.
The principal purpose of this study is to design a radial turbine by considering the conditions of operation of the cycle and the thermodynamic properties of the working fluid, R245fa, in order to analyze their performance at the design point, making use of computational tools for optimization and numerical calculation, i.e. CFD. The R245fa has been selected as the working fluid because it provides the appropriate evaporation pressure, creates an overpressure in the condenser, and provides a good process efficiency. Moreover, it is not subject to emission standards for greenhouse gases, since it does not damage the ozone layer, and is non-flammable, non-toxic, and has satisfactory thermal stability [3].
This work deals with optimization in the preliminary design, for the future investigations an interesting approach would be the application of the optimization methodology based on the metamodels construction integrated to the 3D complex problem, and also to build a prototype and test it.
Section snippets
Preliminary design guidelines
The development of the design process of the radial turbine for use in ORC is based on an analysis of the thermodynamic cycle to establish the turbine operating conditions. The next step was to configure the stations, choosing the input and output of each component of the turbine (volute nozzle, rotor and diffuser) as illustrated in Fig. 1. At each station the appropriate thermodynamic properties and the conservation principles of the fluid dynamics apply to the main geometric parameters (blade
Rotor modeling
The circumferential velocity U4 in the inlet rotor can be calculated from the load coefficientψ (Eq. (1)), which is inlet data, as:
The Euler turbomachinery equation can be now written as:
In this way, the velocity triangles at the rotor inlet (state 4) can be completely defined by the relations:where ξ is the meridional velocity ratio. It has influence on the definition of the geometrical aspect of the inlet and outlet blade height, and is considered constant at ξ = 1. This
Loss models
The loss models are used to evaluate the performance of a radial turbine. The model implemented is derived from the sum of several contributions, and the evaluation cannot be replicated by advanced CFD methods, because it provides useful information about the performance of the turbine. On the other hand, CFD analysis can be useful for cross-checking the overall results of the efficiency and losses.
Methodology for optimization
In order to solve the optimization problem we propose the use of the Controlled Random Search Algorithm (CRSA). CRSA is an iterative, stochastic, population-set based algorithm which promotes the substitution of the worst point of the population by a better one at each iteration Price [34]. The CRSA version used in this paper adopts improvements introduced by Ali [35] and Manzanares-Filho et al. [36].
The original algorithm was developed in Fortran®, and performed the minimization of the
Results and discussion
The evaluation of radial turbine operating with ORC uses the meanline modeling approach. The thermodynamic properties are determined by REFPROP NIST version 9.1, while basic geometry and flow features are determined initially using a routine implemented in commercial code Matlab®.
Three routes were examined with the objective of studying how the methodology behaves when applied to designs with different operation parameters:
1.Applying the preliminary design methodology for a radial turbine that
Conclusion
We present a methodology for development of a radial rotor turbine that operates with organic fluid using a gas turbine methodology found in the literature [23]. Implementation of a loss correlation using correlations in the literature was realized. The preliminary design was based on the meanline, and the validation was carried out in comparison with the work of [18].
Subsequently, an optimization process was performed for the preliminary design for radial turbine of 220 kW, approximately. The
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The authors would like to thank the National Council for Scientific and Technological Development (CNPq), Swedish-Brazilian Research and Innovation Center (CISB) and Propulsion Aerodynamics & Performance, Saab AB for financial support. This work was carried out with support from search’s Group at the Future Energy Center of Mälardalen University, Västerås, Sweden and Hydraulic Virtual Laboratory of the Federal University of Itajubá, Brazil.
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