Optimal design of dual-pressure turbine in OTEC system based on constructal theory

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Highlights

  • Optimal design of a dual-pressure turbine in OTEC system is performed.

  • Total power output of turbines is chosen as the optimization objective.

  • Constructal theory is applied with constraint of fixed total volume of turbines.

  • Optimal performance and optimal constructs of are obtained.

  • Influences of five parameters on constructal optimization results are analyzed.

Abstract

Based on constructal theory, the optimal design of a dual-pressure turbine in OTEC system is performed under the condition of fixed total volume of the turbines. The total power output of the turbines is chosen as the optimization objective, and the volume fraction, ratio of wheel diameter and relative flow angle at rotor outlet are employed as the optimization variables. The optimal performance and optimal constructs of the dual-pressure turbine with the same and different structural parameters are obtained, respectively. Besides, the influences of five parameters on the constructal optimization results of the dual-pressure turbines are analyzed. The results show that compared with the initial design point, the total power output of the turbines after primary, twice and triple constructal optimizations are increased by 0.69%, 1.82% and 2.02%, respectively. The optimal volume fraction, ratio of wheel diameter and relative flow angle at rotor outlet of the turbines after triple constructal optimization are 0.243, 0.49 and 28°, respectively. The total power output of the turbines will increase with the increases of the inlet pressure of the low-pressure turbine, mass flow rate ratio of the working fluids, total volume of the turbines and absolute flow angle at rotor inlet, and will decrease with the increase of the reaction degree. The constructal optimization results of the high-pressure and low-pressure turbines with the same and different structural parameters are similar. The maximum total power outputs of the two cases are both 50.38 kW, and the largest difference is that the optimal volume fraction is reduced by 4.33%. The obtained results can provide theoretical guidelines for the optimal designs of the dual-pressure turbines in OTEC systems.

Introduction

Faced with a series of problems caused by fossil energy consumption, many countries are vigorously developing new alternative energies. Ocean thermal energy conversion (OTEC) technology, which was proposed by the French D’Arsonval [1], has been attracting much attention because the ocean thermal energy has the characteristics of large reserves, renewability, sustainability and no pollution. Claude [2] successfully conducted the OTEC experiment in 1926. Then many scholars have carried out researches on the OTEC, including the choices of working fluids (WFs) [3], [4], parameters optimizations [5], [6], performance analyses [7], [8] and hydrogen production [9], [10]. The above OTEC system adopts the single-pressure organic Rankine cycle (SPORC), which has a great deal of exergy loss [11], [12] because the heat-source temperature (HST) and the temperature of WF in evaporation process are mismatched. To diminish the irreversibility in evaporation process, the WF is separated to absorb heats from the low-temperature evaporator (LTE) and the high-temperature evaporator (HTE), respectively. This kind of cycle with two endothermic processes is called dual-pressure organic Rankine cycle (DPORC), in which the temperatures of evaporator and WF in endothermic and exothermic processes are more closely matched. Refs. [13], [14], [15] compared the performance differences between SPORC and DPORC with different HSTs and WFs, and optimized the heat recovery effectiveness, system efficiency and thermal-economic performance. Guzović et al. [16] and Shokati et al. [17] introduced the DPORC into a geothermal power plant, and found that DPORC can significantly improve the exergy efficiency, net power output and net produced electrical power compared to the other cycles. Ikegami et al. [18] applied the DPORC to the OTEC system, and found that DPORC has higher power and efficiency than the SPORC under the different conditions.

Turbine determines the conversion capability of heat to work. Because the HST and the mass flow rate (MFR) of WF are small in the OTEC system, the power output is also small. The radial-inflow turbine (RIT) still has a high efficiency when the power output and the MFR of WF are small. Therefore, the OTEC system generally adopts RIT [19]. Some studies on the RITs have been carried out in Refs. [20], [21], [22], [23], [24], [25], [26]. In these studies, the conventional WFs such as air, flue gas and steam are adopted, while the organic WFs are generally adopted in OTEC system. Thus, some scholars conducted some researches on the turbines of the OTEC systems [27], [28], [29], [30]. In addition, some scholars also obtained the optimal performance and optimal sizes of the RITs in ORC via the theoretical analyses [31], [32], [33], [34], [35], CFD simulations [36], [37] and experimental researches [38], [39], respectively. All of the above studies are related to one turbine, while the DPORC adopts two turbines, namely a high-pressure turbine (HPT) and a low-pressure turbine (LPT). Kang [40] designed a two-stage RIT device, and pointed out that the power and efficiency of the ORC with two-stage RIT device are enhanced. Du et al. [41] introduced the turbine losses into the performance calculation of a DPORC, and obtained the geometric parameters of the two RITs by using particle swarm optimization (PSO) algorithm. Li et al. [42] performed a comparison for the thermal-economic performance of two RITs with steam-additional and separate layout forms, and confirmed that the thermal-economic performance of the former is better than that of the latter. Sun et al. [43] demonstrated that the DPORC with two RITs has better performance than the SPORC with one RIT.

According to Refs. [22], [23], the performance of turbine is greatly affected by its structure. Therefore, it is necessary to perform structural design and optimization for the turbines. Constructal theory [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57], [58], [59], [60], [61], [62], [63], [64] is an emerging optimization design theory, and has been applied to the structural designs for living and non-living systems. The turbines can also be studied by constructal theory. Kim et al. [65], [66] first introduced constructal theory into the design of the turbine, and optimized the mass distribution ratio of two turbines and multiple turbines with a fixed total mass by maximizing the power. They obtained that the mass distribution ratio of the two turbines in series should be balanced, and the mass distribution ratio of the multiple turbines should be more distributed into the HPTs. Beyene and Peffley [67] applied constructal theory to design a low-speed turbine, and obtained an optimal trailing edge angle to make the power reach the maximum value. They found that the turbine with flexible blades has higher efficiency than that with standard rigid blades. Feng et al. [68] conducted constructal optimization for the gas-turbine blades, and indicated that the multi-scale constructal optimization results (CORs) are better than the single-scale CORs. Stanescu et al. [69] studied the performance of the turbine with “fog cooling” and “inter-stage water spraying” technologies based on constructal theory.

In this paper, the OTEC system adopts the DPORC since it has high power and efficiency characteristics under the condition of low HST. Turbine is a conversion component of heat to work and has a pivotal impact on the overall performance of the OTEC system. Hence, it is needed to research the performances and structures of the two turbines in the OTEC system. The above researches are mainly related to one turbine. Although the structural parameters of the two turbines were obtained in Ref. [41], while in which the two turbines adopted separate layout form. The structural optimization of the two turbines with steam-additional layout form [42] has not been publicly reported. In addition, the optimization of the volume distribution for the two turbines in the OTEC system with DPORC has not been publicly reported. This paper will establish a dual-pressure turbine model with steam-additional layout form for the OTEC system, and apply constructal theory to optimize the volume distribution, ratio of wheel diameter and relative flow angle at the rotor outlet for the two turbines with a fixed total volume by taking the maximum total power output as objective function. The optimal performance and optimal constructs will be obtained, and the effects of some important parameters on CORs will be analyzed. Two contributions of this paper are the applications of DPORC model and constructal theory into the turbine performance optimization of the OTEC system.

The structure of this manuscript is illustrated as follows. The dual-pressure turbine model and the calculations for performances and structures of the HPT and LPT are presented in Section 2. The verifications of the performance and structure for single turbine are organized in Section 3. The constructal designs for the dual-pressure turbine are conducted in Section 4. The conclusions and the future works are drawn in Section 5.

Section snippets

Dual-pressure turbine in OTEC system

DPORC can significantly improve the power output when the HST is low [13], [14], [15], [16], [17], [18] compared to SPORC. The power output is small because the HST is 25–30 °C in the OTEC system. To abate the exergy loss and improve the power output, OTEC system adopts DPORC and uses ammonia as WF [70] in general. Fig. 1 depicts a T-s diagram for the expansion process of DPORC, in which the WF is divided into two parts to absorb heats from the HTE and LTE, respectively. Part of WF first

Model verification

When the volume fraction (xV) of the two turbines and the MFR distribution ratio (xm) of the WF are 0, and the inlet pressure (pL) of the LPT is equal to the inlet pressure (pH) of the HPT, the two-turbine model can be simplified into the single turbine model. The flow and structural parameters of the simplified turbine can be obtained by taking xV=0,xm=0 and pL=pH, and taking the values of φ,ψ,χa,Ω,D¯,α1 and β2 as same as those in Ref. [71]. Comparing the obtained parameters with the

Constructal design of dual-pressure turbine with the same structural parameters

Fig. 8 depicts the relationship between the total power output (Pt,sum) and the volume fraction (xV). In the figure, as xV increases, Pt,sum first increases to a peak and then decreases, and the increased amplitude of Pt,sum is larger than its reduced amplitude. There is a primary optimal volume fraction (xV,opt=0.246) to make Pt,sum reach the primary maximum (Pt,sum,m=49.72kW). The reason for the variation range of xV being 0.11–0.32 is that the MFR of the WF in the HPT is smaller than that of

Conclusions

Turbine is a crucial component in OTEC system. Based on constructal theory, the constructal optimization for the dual-pressure turbine in OTEC system with the fixed total volume is performed by taking the maximum total power output (Pt,sum) as objective function and the volume fraction (xV), ratio of wheel diameter (D¯) and relative flow angle (β2) at the rotor outlet as design variables. The CORs of the two turbines in the dual-pressure turbine with the same and different structural parameters

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.

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant Nos. 51779262 and 51506220) and Independent Project of Naval University of Engineering (No. 425317Q017). The authors wish to thank the reviewers for their careful, unbiased and constructive suggestions, which led to this revised manuscript.

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