The parabolic dish reflects and concentrates the sun's rays onto the receiver aperture so that solar heat can be absorbed by the inner walls of the receiver. With reference to Fig. 6.1, the compressor (1–2) increases the air pressure before it is heated in the recuperator (3–4) and solar receiver (5–6). In the recuperator, hot turbine exhaust air (9–10) is used to preheat the compressed air. The compressed and heated air expands in the turbine (7–8), which produces rotational shaft power for the compressor and the electric load. The compressor, turbine, and generator are mounted on a single shaft and all spin at the same rate [2,3]. It is simple, robust, and easy to maintain. A recuperated STBC allows for lower compressor pressure ratios [4], higher efficiency [1], and a less complex solar receiver, which operates at lower pressure.

The open Brayton cycle uses air as working fluid, which makes this cycle very attractive for use in water-scarce countries. The hot exhaust air coming from the recuperator can be used for cogeneration, such as water heating. The use of cogeneration makes the cycle more efficient and highly competitive. Intercooling and reheating can also be applied to increase efficiency. The use of local small-scale power generation means that transmission lines do not have to cross vast stretches of land to bring electricity to isolated areas.

The STBC can be supplemented with natural gas as a hybrid system [5] for continuous operation when the sun is not shining. Storage systems such as packed rock bed thermal storage [6] can also be coupled to the cycle. Cameron et al. [7] showed how lithium fluoride could be used in the solar receiver of an 11-kW earth-orbiting STBC with recuperator to store heat for as much as 38 min during full power operation. The small-scale dish-mounted STBC also has an advantage in terms of bulk manufacturability and cost. Microturbines can be adapted as turbochargers from the vehicle market off the shelf [8], which allows for lower costs due to high production quantities [9].

According to Pietsch and Brandes [1], experimental testing of the STBC has proved high reliability and efficiencies above 30% with turbine inlet temperatures of between 1033K and 1144K. Dickey [10] also presented experimental test results of an STBC (20–100 kW), an initiative from HelioFocus Ltd. and Capstone Microturbine at the Weizmann Institute. A proprietary pressurized volumetric solar receiver was used in the experiment. A system efficiency of 11.76% was achieved with a solar receiver exit temperature of 871°C. The system generated 24.04 kW of electricity with the microturbine spinning at 96,000 rpm. Heller et al. [11] tested an open STBC without a recuperator and found that a volumetric pressurized receiver can produce air of 1000°C to drive a gas turbine. According to [11], the cost and performance of this cycle looks promising for future solar power generation. According to Chen et al. [12], the Brayton cycle is definitely worth studying when comparing its efficiency with those of other power cycles. Mills [9] predicted that small-scale Brayton microturbines might become more popular than Stirling engines due to high Stirling engine costs.

As shown earlier, the STBC has much potential and its efficiency can be improved using various methods. Another method to improve the efficiency of the cycle is through design optimization. When designing the STBC, there is a compromise between allowing effective heat transfer and keeping pressure losses in the components small. Heat losses and pressure losses in the components of the cycle decrease the net power output of the cycle. Limiting factors to the performance of the STBC include maximum receiver surface temperature and recuperator weight. The Brayton cycle and the optimization thereof have been studied by many authors; however, not many have studied the STBC with recuperator. Zhang et al. [13], for example, studied the performance of a closed STBC without a recuperator. Solar receivers and recuperators have been designed and optimized individually for the Brayton cycle and the STBC [14–16]; however, various studies such as [17] have emphasized the importance of the optimization of the global performance of a system, instead of optimizing components individually. To obtain the maximum net power output of the cycle, a combined effort of heat transfer, fluid mechanics, and thermodynamic thought is required. The method of entropy generation minimization combines these thoughts [18]. Jubeh [19] has done an exergy analysis of specifically the open STBC with recuperator.

Optimization of the geometry variables of cycle components using the method of total entropy generation minimization is considered to be a holistic optimization approach and has been applied to the STBC in recent work for maximum net power output [20–23]. In this chapter, the method is applied to a recuperated STBC with low-cost dish optics and low-cost tracking. Furthermore, three different off-the-shelf turbochargers from Garrett [8] are investigated for use in the STBC.

According to Ref. [4], the focal length of a parabolic dish is defined by Eq. (6.1). The rim angle of a parabolic dish determines where its focal point is. A rim angle of 45° is paramount for concentrators with focal plane receivers [4].

Solar receivers can be divided into tubular, volumetric, and particle receivers. A number of high-temperature and high-efficiency receivers are available from the literature, mostly for use in large-scale (10–200 MW) applications [27,28]. Typical receiver efficiencies and experimental data that have been obtained with pressurized volumetric receivers and tubular receivers are summarized in Ref. [24]. These receivers are mostly not optimized to perform well in a dish-mounted STBC with recuperator. A solar receiver might be designed for high efficiency, but if it is not optimized to achieve a common goal together with other components, it might not perform well in a recuperated Brayton cycle.

Most Brayton cycles are not self-sustaining at operating temperatures below 480°C [4]. For the STBC, the maximum receiver surface temperature and turbine inlet temperature are very important. The higher these temperatures, the better the Brayton cycle will perform, but more heat will be lost to the environment [21]. The maximum turbine inlet temperature of commercial off-the-shelf turbochargers is more or less 950°C [8,29], whereas for ceramic microturbines a temperature of 1170°C is envisaged [30]. The higher the turbine inlet temperature, the less material choices are available for the receiver.

The open-cavity tubular solar receiver (see Fig. 6.2) consists of a coiled stainless steel tube through which pressurized air travels. The depth of the receiver is equal to 2a. The receiver is covered with ceramic fiber insulation. Reflected solar beam irradiance gets absorbed at the inner walls of the cavity. The receiver has been tested at low temperatures in a low-cost solar dish with the use of weld-on thermocouples [32].

The heat loss from the receiver consists of convection, radiation, and conduction and can be modeled with the Koenig and Marvin heat loss model [33] presented by Harris and Lenz [31]. The heat loss per tube section is determined with Eq. (6.4). The larger the cavity aperture, the more heat can be lost, but more heat can also be intercepted.

A counterflow plate-type recuperator is considered as shown in Fig. 6.4 [22]. The channels with length L_reg and aspect ratio a/b are shown. The recuperator effectiveness is modeled using an updated ε-NTU (effectiveness – number of transfer units) method [42]. This method takes the heat loss to the environment into consideration when calculating the recuperator efficiency, since the recuperator operates at a very high average temperature. According to Ref. [42], the hot side and cold side efficiencies can be calculated with Eq. (6.14) and Eq. (6.15) and the equations below.

The heat loss rate from the hot side and cold side of the recuperator is calculated with Eq. (6.22) and Eq. (6.23) and the following equations.

The finite heat transfer and pressure drop in the compressor, turbine, recuperator, receiver, and other tubes are identified as entropy generation mechanisms. When doing an exergy analysis of the system at steady state and assuming V₁ = V₁₁ and Z₁ = Z₁₁ (see Fig. 6.1), the objective function is assembled as shown in Eq. (6.31). The function to be maximized (the objective function), is W˙net (the net power output). Eq. (6.32) shows the total entropy generation rate in terms of the temperatures and pressures at different locations in the cycle (with reference to Fig. 6.1). The entropy generation rate of each component is added as shown in Eq. (6.32). T^∗ is the apparent sun's temperature as an exergy source as described in Ref. [23]. Note that Q˙∗−Q˙loss=Q˙net. For validation, the net power output can also be calculated with the first law of thermodynamics using a control volume around the microturbine and also around the system.

As optimization, different combinations of three turbochargers by Garrett [8], three different receiver tube diameters, and 625 differently sized recuperators are used as parameters and variables to determine the net power output of the system. MATLAB [51] is used to determine the variables that will give the best results. The recuperator variables are the width of the recuperator channel, a, the height of a recuperator channel, b, the length of the recuperator, L, and the number of flow channels in one direction, n. The maximum receiver surface temperature is constrained to 1200K. The recuperator total plate mass is restricted to 300, 400, or 500 kg. The temperatures and pressures at every point of the STBC are found with iteration and by modeling every component [23] and using isentropic efficiencies of the compressor and turbine as well as recuperator and receiver efficiencies.

In the following results, a solar dish with diameter of 4.8 m was considered and a solar direct normal irradiance (DNI) of 1000 W/m² was assumed. For a fixed area ratio of A′ = 0.0035, the available solar power at the aperture of a receiver with a = 0.25 m (aperture area of 0.25 m × 0.25 m) is shown in Fig. 6.6 for different tracking errors and optical errors. Fig. 6.6 shows that the available solar power decreases as the optical error and tracking error increase. However, at a tracking error of 3°, the available solar power increases as the optical error increases, since the focal image increases as the optical error increases. Note that the available solar power stays almost constant when the tracking error is between 0° and 1° and the optical error below 10 mrad.

Fig. 6.7 shows the average net heat transfer rate at the cavity receiver inner wall. The net heat transfer rate is the available solar power minus the heat loss rate from the cavity receiver to the environment. Note that a dish reflectivity of 85% was assumed. Fig. 6.7 also shows that an optical error of 10 mrad or less with a tracking error of 1° or less is required to have an acceptable net heat transfer rate. A tracking error of 2° would thus not be acceptable for the collector.

Eq. (6.31) was used as an objective function in MATLAB to determine the maximum net power output of the cycle by optimizing the receiver tube diameter and counterflow plate-type recuperator geometries. A 4.8-m-diameter parabolic dish, rim angle of 45°, 1° tracking error, 10 mrad optical error, a = 0.25, solar receiver emissivity of 0.7, a solar DNI of 1000 W/m², and a dish reflectivity of 85% was used to generate the results. It was also assumed that all tubing in the cycle has 10 mm insulation thickness and conduction heat transfer coefficient of 0.18 W/mK. For the open-cavity tubular receiver, efficiencies of between 43% and 70% were obtained with mass flow rates of between 0.06 and 0.08 kg/s, tube diameters of between 0.05 and 0.0889 m, and air inlet temperatures of between 900K and 1070K [24]. In Figs. 6.8–6.10 the maximum net power output of the STBC at steady state was found as a function of turbine pressure ratio. It is shown that the maximum net power output of the system can be found when a large receiver tube diameter is used, for all three of the microturbines. Note that each data point represents a maximum, which is achieved using a unique recuperator as shown in Table 6.1 for the GT2860RS turbocharger with a receiver tube diameter of 0.0833 m (compare with Fig. 6.9). From Table 6.1, a recuperator with a = 0.225 m, b = 2.25 mm, L = 1.5 m, and n = 45 was the best-performing recuperator since it gave the highest maximum net power output of 1.77 kW (Table 6.1). Note that in these results the recuperator mass was restricted to 500 kg and the receiver surface temperature restricted to 1200K.

The GT1241 provides the highest maximum power output of 2.11 kW and a conversion efficiency of 12% (Fig. 6.10). This efficiency compares well with photovoltaic panels. It should be noted that this efficiency can be improved in many ways. Note that in this chapter, low-cost tracking and solar optics were considered, which decrease the efficiency of the receiver. In this work, only standard off-the-shelf turbochargers were considered, which are not necessarily optimized to perform as a power-generating unit but rather for performance in a vehicle. However, the low cost of these units justifies the research into its application in this field. Further investigation into the correct matching of turbocharger compressors and turbines to improve efficiency should be done. The overall efficiency of the cycle can also be improved with the use of cogeneration. It should also be noted that higher efficiencies have already been obtained with state-of-the-art systems, as mentioned in Section 6.1.

For larger receiver tube diameters, a higher maximum net power output can be achieved at high turbine pressure ratios. Note that in Ref. [24], it was found that the highest second law efficiencies for the receiver were achieved when the tube diameter and inlet temperature were large and the mass flow rate small. This combination of variables would also create a very high surface temperature. When the surface temperature is then restricted to 1200K, a larger mass flow rate and lower inlet temperature can still provide high second law efficiencies, when a large tube diameter is chosen.

The larger the mass of the recuperator, the higher the net power output of the system as shown in Fig. 6.11. When the recuperator mass is constrained to 400 kg, a recuperator with a = 150 mm, b = 2.25 mm, L = 1.5 m, and n = 45 was found to be the recuperator with the most common optimum dimensions. When the recuperator mass is constrained to 300 kg, a recuperator with a = 150 mm, b = 2.25 mm, L = 1.5 m, and n = 37.5 is best.

From Fig. 6.12 it is shown that it is optimum for the maximum receiver tube surface temperature to decrease with increasing turbine pressure ratio and with decreasing receiver tube diameter. At high turbine pressure ratios, the large receiver tube diameter has a higher surface temperature and it allows for higher net power output of the small-scale STBC.

Future possibilities of the STBC include hybridization and thermal storage for continuous power generation, as was also mentioned in Section 6.1. Hot exhaust air leaving the STBC can be used to heat water or to run an absorption chiller. If the exhaust gas is not utilized, it is very important that the exhaust air is exposed of correctly and that it is not sucked in again at the compressor. Furthermore, commercial turbine operating temperatures might be increased in future with the use of ceramic materials, which will allow for higher STBC efficiencies.

The cycle is faced with low compressor and turbine efficiencies, heat losses, and pressure losses, which decrease the net power output of the system. In this chapter, a recent development in the minimization of these losses was presented. The power output of the small-scale dish-mounted STBC with recuperator, off-the-shelf turbocharger, and low-cost optics was modeled and maximized using the method of total entropy generation minimization. A receiver and recuperator were optimized to perform in the cycle. Results showed that higher maximum net power output can be achieved at high turbine pressure ratios, when a large receiver tube diameter is used. It was found that a recuperator with a = 225 mm, b = 2.25 mm, L = 1.5 m, and n = 45 gives the best results for the setup with the recuperator mass constraint and receiver maximum surface temperature constraint. The larger the mass of the recuperator, the higher the power output of the system.

Results showed that solar-to-mechanical efficiencies of up to 12% could be achieved when using a standard off-the-shelf turbocharger and low-cost optics. The efficiency is low compared with other solar technologies; however, there are many ways in which the efficiency can be improved. Note that the current work only considered commercial turbochargers with an already-combined compressor and turbine. This combination is chosen for performance in a vehicle rather than for power generation. Further compressor and turbine matching should be performed to identify better combinations of these units for significant efficiency improvement. It should also be noted that a very simple solar receiver was used for the modeling. With the use of high absorptivity and low emissivity coatings, the efficiency of the receiver can be increased. It is recommended that high-temperature, low-emissivity receiver coatings and materials should be investigated further experimentally to improve efficiency. The efficiency can be further improved by having more precise tracking and dish optics and higher dish reflectivity. Note that, in this chapter, a receiver aperture area of 0.25 m × 0.25 m and a dish with poor tracking (1° error) and poor dish optics (10 mrad error) were assumed. According to Ref. [24], the receiver efficiency can be increased up to 71% when both the optical error and tracking error are changed to 5 mrad and 0°, respectively, and the aperture area to 0.1 m × 0.1 m. By adding water heating using the hot exhaust air, the overall efficiency will be increased even further.

Furthermore, it is recommended that a cost-versus-efficiency study should be done regarding the small-scale dish-mounted STBC. With further research, the small-scale open STBC could become a competitive off-the-grid small-scale solar energy solution for small communities. It is recommended that the cycle should be further developed experimentally and investigated as a clean energy technology.