Research PaperDevelopment of three-dimensional optimization of a small-scale radial turbine for solar powered Brayton cycle application
Introduction
The demand for energy is continually increasing day after day, but at the same time, investigations around the world into sustainable sources of power are growing in number. Solar energy is considered one of the main renewable energy sources which can play an important role in decreasing CO2 emissions. It can be efficiently used to generate electricity using different types of thermal power cycles, such as the Brayton cycle.
Moreover, small scale turbines are considered as a promising technology because of their low initial costs, low maintenance, durability and simple construction. Furthermore, they can offer a solution for the power generation demand in domestic or even remote areas. In order to increase the cycle efficiency, one of the main effective ways is to improve the turbines’ performance.
Much research has been carried out regarding both the solar Brayton cycle thermodynamic analysis and the selection of the appropriate boundary conditions of energy as heat sources such as [1], [2], [3], [4]. For example, an attempt to enhance the overall efficiency of the small-scale solar Brayton cycle, by optimizing both the receiver and the parabolic concentrator, has been achieved by Le Roux et al. [5]. Riazi and Ahmed [6] studied the effect of specific heat ratios for three different working fluids and for air, helium and tetrafluoromethane, on the efficiency of small scale solar energy. A regenerative closed Brayton cycle was analysed in terms of the influence of temperature ratio and the minimum to maximum gas temperature. Their results showed that the higher the specific ratio of the analysed fluid, the higher the cycle efficacy. Moreover, they also suggested that for small-scale Brayton cycles, the performance of lower specific ratios is better as this scale only accumulates a small amount of heat. However, the performance of turbines was not included in all the studies mentioned above as on the shelf turbines were used. Two important parameters have to be carefully considered, as they lead to better preliminary design. Both the loading coefficient and the exit flow coefficient contribute in [7]. Intensive analyses in order to enhance the performance of scroll expander were conducted in [8], [9], [10]. Mean line analysis for radial turbines for organic Rankin cycle applications was achieved by many researchers [11], [12], [13], [14], [15], [16]. However, no more 84% Total-To-Static efficiency for the studied models of radial turbine have been attained [12]. It is clear that the 3D computational fluid dynamics (CFD) leads to more enhancement in the aerodynamic performance. Three-dimensional optimization design work on ORC radial turbines was demonstrated in [17], [18], [19]. On the other hand, modelling and optimization of axial turbines was conducted in [20], [21]. Sauret [22] carried out intensively numerical work on a high pressure radial turbine. The author started his study from the preliminary design passing through 3D simulation; then the impact of tip clearance as well as the importance of the diffuser on the turbine’s performance was examined at wide range of boundary conditions. The author then validated her design against some experimental data from the literature. Regarding the compressed air radial turbine, it can be seen that only some efforts have been made by different researchers who studied the performance of radial turbines with different design factors as well as boundary conditions. With the aim of identifying the possible acoustic sources which occurs, Marsan and Moreau [23] studied the effect of stator wakes and trailing edge on the impeller blades of radial turbine. In their study the authors showed that the interface regime between the stator and rotor causes pressure fluctuations to the flow passes through these surfaces. They emphasized that the tip clearance losses should not be neglected in analytical studies. Together CFD and FE analysis of relatively high pressure ratio and low inlet temperature, 5 bar and 400 K, radial turbine was conducted in [24]. The output power and efficiency of the investigated turbine were 36.4 and 85% respectively. With comparatively accepted deviation, the authors validated their simulation work using an experimental data. For compressed air turbine optimizations, Tsalicoglou1 and Phillipsen [25] used an iterative method that conducted in-house and commercial CFD codes to decrease the amount of working fluid mass flow rate. This results in changing the turbine blade geometry modifications with some improvement in efficiency. However, with the limitation of the allowed number of design parameters’ evaluations, multiple runs were required. As a single objective function, particle swarm optimization was used in their study. An integrated optimization of a 100 kW radial turbine was reported by Lei Fu et al. [26]. In their study, an enhancement in terms of aerodynamic and structural performance was achieved. However, the optimization carried out on the rotor while the stator was not considered in their study. Also, each part of optimization was completed separately in two different codes and that might be the reason for the relatively low maximum efficiency value that has been achieved, 82%. Zhang and Ma [27] used the multi-objective algorithm technique for optimizing only the rotor of a radial turbine. Even though the authors claimed the optimized rotor experienced better performance especially in off-design conditions with about an 8% increment in its efficiency, the maximum value that the turbine reached was also low, about 77%.
An intensive study on the relation between optimization of computational time and the chosen range of the database, as well as the selection of the suitable optimization method was reported in [28]. In his study the author emphasized that selecting the closer setting to the optimum parameters not only results in further improvements of the convergence, but also contributes to better rotor geometry performance. Three-dimensional multi-objective optimization for a turbocharger radial turbine impeller designed for automotive applications was applied in [29]. With the aim of maximizing its total-to-static efficiency and the impeller moment of inertia, and at the same time keeping mechanical stresses below a maximum allowable value, the maximum value of efficiency reached was only 80%.
To the best of the authors’ knowledge no work has been published on the 3D multi-objective optimization of the two main parts of radial turbines: the stator and rotor, together especially for this scale of turbines. So, this paper tries to focus on design; such as turbine design which creates as high as possible efficiency and output power to the cycle but with keeping both the rotational speed and the mass flow rate at their minimum values.
Section snippets
Methodology
In this study the computational fluid dynamic CFD techniques, using ANSYS®15 VISTA, was utilized in order to first initiate a Mean Line (ML) design for the Small Scale Radial Turbine SSRT with relatively sufficient performance. Then, 3-D model was improved using ANSYS®15 CFX tool, which precisely figure out the aerodynamic flow behaviour, analyse were followed in order to have more accurate and better outcomes for the SSRT. After the best design shape for both the stator and rotor was achieved,
Thermodynamic analysis of brayton cycle
The traditional thermal Brayton cycle consists of the compressor, the combustion chamber, the turbine to extract the air’s potential energy and transfer it to mechanical energy; and a pre-heater to exploit the exhaust energy, which will be otherwise lost to the environment and also to preheat the cold air before entering the source of heat. However, the solar powered Brayton cycle shown schematically in Fig. 1, consists of a compressor (1−2), thermal receiver (3–4) and a turbine (4–5). A
Mean line design of radial turbine [12,31–41]
The initial shape blade as well as its dimensions such as nominal hub and shroud diameters, the blade number and thickness, the trailing and leading edges can be determined using the ML design [41]. Together Fig. 3, Fig. 4 show the velocity triangles and their relative thermodynamic processes. The two dimensionless parameters that have been used in the ML design of radial turbine are the loading (ψ) and flow (ϕ) coefficients. These two parameters are together used to determine the exact
Numerical analysis of the model
Once the ML design of the SSRT, using the Vista RTD tool, was completed, all the relevant information for building the blade geometry of the rotor was prepared. So, the next step was to export these dimensions in order to create the rotor blade geometry using the Blade-Gen feature in ANSYS CFX. This tool in fact can be used to construct the stator blade as well as the rotor for the studied turbine. The CFX Turbo-Grid was employed in order to generate the required elements for the turbine’s
Validation
Because they have relatively sufficient data, the Refs. [45], [46] have been chosen and deeply investigated in order to validate the current work. The validation results showed good agreement between the current work and the two chosen ones. While the first validation, which was with Ref. [45], the CFD technique was used in order to validate the current work, however, in the second validation, with Ref. [46], only the 1Dimensional approach was used because relatively little information was
Results of the base-line design
Fig. 10 compares the CFD results of the base-line design against the ML design analysis at nominal boundary conditions, shown in Table 1. The values of output power and isentropic efficiency were compared for three different cases: inlet temperature, rotational speed and pressure ratio. Specifically, Fig. 10A and A/ show the values of output power and efficiency at different values of turbine inlet temperatures. In this figure the relative over estimation for the ML analysis in terms of both the
Multi-objective optimization and genetic algorithm
Engineers still need to search for the best design among the available possible designs. Yet, the term ‘best’ can come with many meanings and what is excellent in some terms or applications may not be the best in other applications; thereby this term does not have an absolute meaning. Therefore, understanding the optimization procedure in depth will certainly lay the groundwork for optimization of the turbines; especially the Small Scale Turbines (S.S.T.) whose sizes might add to the challenge
Results of Brayton cycle analysis
Using the Brayton cycle analysis in Eqs. (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11) to calculate the cycle efficiency for the various boundary conditions, the cycle efficiency at nominal and other boundary conditions, as well as the enhancement that the cycle has achieved is clear in Fig. 18. These improvements are delivered by 3D CFD results and inserted in the cycle modelling as inputs to calculate the overall cycle efficiency. This improvement, which is not constant for all the
Conclusions
Numerical simulation was carried out to optimize a small-scale radial turbine with output power in the range of 1.5–7.5 kW. A one-dimensional Mean Line approach and three-dimensional CFD simulations, using three-dimensional RANS with the SST turbulence model in ANSYS®15- CFX, were employed to achieve the best turbine performance; and consequently, the highest reachable efficiency for the small-scale solar powered Brayton cycle. This paper demonstrated the following important outcomes:
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The CFD
Acknowledgement
The author thanks the Higher Committee of Developing Education in Iraq HCED for funding this project.
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