Performance assessment of an integrated power generation and refrigeration system on hypersonic vehicles

Aerospace Science and Technology 89 (2019) 192–203

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Performance assessment of an integrated power generation and refrigeration system on hypersonic vehicles Kunlin Cheng a , Jiang Qin a,∗ , Hongchuang Sun a , Chaolei Dang a , Silong Zhang a , Xiaoyong Liu b , Wen Bao a a b

Harbin Institute of Technology, Harbin 150001, People’s Republic of China Beijing Power Machinery Institute, Beijing 100074, People’s Republic of China

a r t i c l e

i n f o

Article history: Received 17 February 2019 Received in revised form 2 April 2019 Accepted 2 April 2019 Available online 5 April 2019 Keywords: Closed-Brayton-cycle Thermoelectric generator Power generation Refrigeration Hypersonic vehicle Cascade utilization of cold source

a b s t r a c t Hypersonic vehicle as next generation aircraft/spacecraft has broad applications, but its power supply and refrigeration are strictly limited by finite cold source. In this article, an integrated power generation and refrigeration system is developed, in which low-temperature fuel is utilized as cold source and hightemperature fuel is used as heat source. A novel combined generator based on closed-Brayton-cycle (CBC) and thermoelectric generator (TEG) is proposed to enhance electric power through extending the available temperature range of cold source. The integrated system model which consists of a refrigerator, a simple recuperated CBC and a three-stage TEG, is established to assess performance. Results indicate that the combined CBC-TEG generator has great potential in electric power enhancement. The power has an increase of 18.2% compared with single CBC. Power increase percentage of combined generator reduces with fuel outlet temperature in primary cooler. Moreover, decoupling the cooling and heating process of the combined generator is beneficial for the matching between its cold source and heat source. This research provides an innovative technical solution for the power generation and refrigeration on hypersonic vehicles under finite cold source conditions. © 2019 Elsevier Masson SAS. All rights reserved.

1. Introduction Hypersonic vehicles [1–3] driven by the ramjet [4], scramjet [5–9], combined cycle [10–12] or pre-cooled engines [13], are designed for the commercial applications and military missions [14] in or cross the atmosphere. There is a huge electric demand mainly caused by the fuel feeding, radar system [15] and flight control actuation [16] on hypersonic vehicles. For existing aircrafts, electricity is supplied by the generators attached to the rotating shafts of main engines [17] or batteries [18]. Nevertheless, these mature technologies of power supply can hardly be applied on hypersonic vehicles. Firstly, the main engines of hypersonic vehicles cannot always drive the generators, because their main components are not rotational or their rotational parts do not work at high flight Mach numbers. Secondly, the relatively low energy density of battery will lead to a huge mass of the electricity supply system in a long-endurance flight, which is clearly unacceptable for hypersonic vehicles. Besides, some air-breathing power generation units, such as the auxiliary power unit (APU) [19], ram air turbine (RAT)

*

Corresponding author. E-mail address: [email protected] (J. Qin).

https://doi.org/10.1016/j.ast.2019.04.006 1270-9638/© 2019 Elsevier Masson SAS. All rights reserved.

[20] and fuel cell [21], also have difficulties in the air-intake and compression at high Mach numbers. Therefore, it is essential to develop suitable power generation technology for hypersonic vehicles. Because of the high-speed flight and high-intensity combustion, hypersonic vehicles can provide enough high-quality heat source for power generation, such as the aerodynamic heat and the combustion heat dissipation through engine walls. The rich heat, as the by-product of air-breathing hypersonic flight in the atmosphere, can be somewhat treated as low-cost or even cost-free, because it is supposed to be isolated or transferred for thermal protection. Therefore, the power generation technology based on the heat-toelectricity conversion is quite appropriate for hypersonic vehicles. Compared with the power generation devices in which airflow acts as the working fluid (APU, RAT), closed thermodynamic cycle may be a better choice. Firstly, high-temperature air or gas only provides heat for closed-cycle power generator, which decreases the demand on total pressure of heat source. Secondly, the working fluids of closed-cycle systems, such as helium and water, have better heat transfer property and higher specific power than the working fluids in open-cycles (air or fuel vapor [15]), which brings benefits to performance enhancement.

K. Cheng et al. / Aerospace Science and Technology 89 (2019) 192–203

193

Nomenclature A Dh H I K Pc Pe Q R T cp Cd h l m n p u w x

Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m2 Hydraulic diameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m Convection heat transfer coefficient . . . . . . . . . W/(m2 K) Electric current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Thermal conductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . W/K Refrigeration power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kW Electric power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kW Heat transfer rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kW Electric resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K Specific heat capacity at constant pressure . . . . J/(kg K) Drag coefficient, dimensionless Specific enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J/kg Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m Mass flow rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kg/s Number, dimensionless Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pa Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m/s Specific work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J/kg Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m

Greek

α γ ε η θ λ ζ

π ρ σ ϕ

Seebeck coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V/K Ratio, dimensionless Effectiveness of heat exchanger, dimensionless Efficiency, dimensionless Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m Thermal conductivity . . . . . . . . . . . . . . . . . . . . . . . . . W/(m K) Relative pressure loss, dimensionless Pressure ratio, dimensionless Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kg/m3 Electric conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 1/( m) Percentage increase, dimensionless

Subscript C CBC CE G HT HX L N

Compressor of CBC Closed-Brayton-cycle Refrigeration to electric power Generator Heater of CBC Heat exchanger Load N-type

Owing to the compact size and high efficiency, closed-Braytoncycle (CBC) becomes one of the most promising closed thermodynamic cycles for air-based applications [22]. Noble gas (He, He-Xe) and carbon dioxide are the common working fluids of CBC, and recuperation process is necessary due to limited cycle pressure ratios. Some remarkable progresses on the CBC-based space power generation have been made. Barrett and Reid [23] built a CBC space power system model to study the performance trends in a trade space characteristic of interplanetary orbiters. Gallo and ElGenk [24] developed the models of Brayton rotating units with centrifugal-flow compressor and radial-inflow turbine, and presented the performance results of a space power system with segmented, gas cooled fission reactor heat source. A peak thermal efficiency of 26% and corresponding electric power of 122.4 kW were achieved at the compressor and turbine inlet temperatures of 400 and 1149 K. Besides, Qin [25] proposed a thermal management system based on closed-Brayton-cycle, and remarkably reduced the fuel flow for the regenerative cooling of scramjets through converting part heat absorption of fuel into electricity.

P PC REC REF T TEG act cc cp ele f f0 f1 f2 f3 f4 f5 f6 f7 fc fh h h1 h2 h3 h4 h5 h6 hc in int jc jh max n n1 n2 out s tot wc wh

P-type Primary cooler of CBC Recuperator of CBC Refrigerator Turbine of CBC Thermoelectric generator Actual Cooling channel Ceramic plate Thermoelement Fuel Storage in fuel tank Inlet of refrigerator for fuel Inlet of CBC’s primary cooler for fuel Inlet of TEG’s cooling channel Inlet of wall cooling channel Inlet of CBC’s heater for fuel Inlet of TEG’s heating channel Outlet of TEG’s heating channel Cold fuel Hot fuel Helium Inlet of CBC’s compressor Outlet of CBC’s compressor Inlet of CBC’s heater for helium Inlet of CBC’s turbine Outlet of CBC’s turbine Inlet of CBC’s primary cooler for helium Heating channel Inlet Internal Cold junction Hot junction Maximum Nitrogen Inlet of refrigerator for nitrogen Outlet of refrigerator for nitrogen Outlet Isentropic Total Cold wall Hot wall

Thermoelectric generator (TEG), which converts heat into electricity directly based on the Seebeck effect, is another potential technology of power generation for hypersonic vehicles [26,27]. Benefiting from the simple structure, small vibration and high reliability, TEGs have been widely applied on spacecraft [28] and automobile [29] for power supply and heat recovery. Moreover, the requirements on the temperatures of cold source and heat source for TEGs are much lower than general thermodynamic cycles, which brings benefits to establishing combined systems with other power generation devices. Shu et al. [30] proposed a combined TEG-ORC (Organic-Rankine-Cycle) used in the exhaust heat recovery of internal combustion engines. The results indicated that TEG-ORC system was suitable for recovering waste heat from engine exhaust, because the temperature range of heat source was extended by TEG. Li and Wang [31] proposed an integrated TEG and fuel vapor turbine power generation system on the basis of the regenerative cooling system of scramjet. The results of exergy analysis showed that the output power and exergy efficiency

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were 61.69 kW and 21.88% respectively with the fuel flow rate of 0.4 kg/s. Enough electricity supply is just a precondition for the normal operation of onboard electric devices, and effective cooling is indispensable to achieve high stability and high efficiency. More or less, part of electricity will be converted into waste heat, which has to be transferred away from onboard electric devices. In conventional aircrafts, ram air and fuel oil are the common coolants for electric devices. However, airflow not only cannot be utilized as coolant but also causes a serious aerodynamic heating [32] for hypersonic vehicles flying at high Mach numbers, due to its high total temperature. Meanwhile, it is difficult to cool all the onboard electric devices directly by liquid fuel, because of the extremely complex flow path and relatively low reliability of liquid cooling, as well as the unacceptable pressure drop for fuel. Hence, the mature gas cooling may be a more realistic choice. Another advantage of gas cooling is that gaseous coolants are more convenient for cooling rotating machinery, such as turbine blades. One way to achieve the gas cooling is carrying additional cooling gas at high pressures, which will be exhausted directly after cooling electric devices. Nevertheless, the cooling capacity of this open cooling system is strictly limited by the mass and temperature of cooling gas. Another option is building a closed cooling system in which stable gaseous fluid acts as coolant and fuel serves as its cold source. In this way, the cooling capacity depends on the mass and temperature of fuel rather than gaseous coolant. Unfortunately, the cold source essential for closed power generation and gas cooling systems, is finite on hypersonic vehicles. As mentioned above, airflow is no longer the cold source in hypersonic flights. Fuel will be the only cold source onboard, if no additional coolant is carried. Kerosene [18] and liquid hydrogen (LH2) [33] are common fuels for hypersonic vehicles. Kerosene can be stored conveniently and safely at normal temperatures using compact fuel tanks. However, kerosene can only provide little cooling capacity in its low temperature range, before thermal cracking occurs [34]. Specifically, considering the upper temperature of kerosene is strictly limited by the onboard equipment, the available temperature difference for refrigeration is quite small at its relatively high original temperature [22]. Liquid hydrogen has extremely high heat value per unit mass and huge physical heat sink, leading to a high specific impulse and excellent thermal protection performance at high flight Mach numbers (Ma > 10) [33]. Nevertheless, the technical complexity of its super-lowtemperature storage (below 30 K) enhances the difficulty in the application on hypersonic vehicles. Due to the low density of liquid hydrogen, its huge fuel tank becomes a challenge for the aerodynamic design of hypersonic vehicles. Besides, the high cost of hydrogen becomes another disadvantage, when it is applied on a reusable hypersonic vehicle. Therefore, both kerosene and liquid hydrogen are not ideal fuels in the view of cold source. Over the past decade, liquid methane (LCH4) has strongly attracted the attentions of the researchers in the aeronautics [35] and astronautics [36], because of its properties between kerosene and LH2 in the storage, thrust and specific impulse. Particularly, high-purity methane can be separated easily from natural gas, making it lowcost. Hence, liquid methane as a definitely promising fuel/cold source for hypersonic vehicles, is chosen as the fuel in this paper. It is necessary to take full advantage of the fuel’s cooling capacity for power generation and refrigeration, since the cold source on hypersonic vehicles is so finite. Expending the available temperature range as cold source is a possible method. However, it is not easy to increase the terminal temperature of cold source. A higher terminal temperature of cold source always decreases efficiency in single cycles, and thus reduces the power enhancement achieved by the larger temperature range of cold source

Fig. 1. Schematic diagram of a simple recuperated CBC system.

[22]. Building a combined system composed by different cycles suitable for different temperature ranges, is a common way to expend temperature range. Unlike conventional combined systems, the purpose of this study is to increase the temperature range of cold source, rather than heat source [30,37]. Combining the advantages on the efficiency and power density of CBC, as well as the cold source adaptability of TEG, a combined generator in which CBC and TEG are used as its topping and bottoming cycle respectively, is a potential approach for power enhancement with finite cold source. The present study focuses on the electricity supply and refrigeration with finite cold source on hypersonic vehicles. An innovative integrated system for power generation and refrigeration based on a combined CBC-TEG generator is proposed to meet the double demands of electricity and cooling for hypersonic vehicles. The integrated system model mainly composed by a simple recuperated CBC model, a three-stage TEG model and a refrigerator model, is established for performance assessment. The maximum electric power of TEG and CBC is obtained at constant temperature range of cold source. The effects of fuel outlet temperature in primary cooler on the electric power, efficiency and power increase percentage of CBC-TEG are investigated at different ratios of refrigeration to electric power. In addition, the limitations caused by the direct heating through high-temperature fuel are discussed in this study. 2. System description 2.1. Combined CBC-TEG generator In the combined CBC-TEG generator, closed-Brayton-cycle is utilized as the main power generation device. Helium is applied as the CBC working fluid, since it cannot be liquefied by LCH4. Although intercooled design is an effective method for performance enhancement in helium-CBC system, simple recuperated cycle exhibits better on weight and size [38]. Thus, a simple recuperated helium-CBC is used as the topping cycle of combined generator. As illustrated in Fig. 1, the closed-Brayton-cycle system is mainly composed by a compressor, a turbine, a generator and three heat exchangers, namely the primary cooler, recuperator and heater. The compressor and turbine are connected with the generator via a single shaft to achieve compact size. Firstly, helium is supercharged by the compressor, before entering into the recuperator to absorb heat from the expanded helium. Next, helium is heated into a higher temperature by heat source in the heater, and then flows into the turbine. The expanded helium is still at high temperature caused by a relatively small pressure ratio, so a recuperation process is built to utilize its remaining heat for preheating. Finally, helium is fully cooled by fuel in the primary cooler, before entering the compressor for next loop. Note that the generator produces

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195

Fig. 2. Sketch of three-stage thermoelectric generator.

either alternating current or direct current, which depends on the need of onboard electric devices. It is also as the motor when the system gets started. Thermoelectric generator is used as the assistant power generation equipment in the combined generator. Considering the large temperature difference between the heat source and cold source (over 400 K), it is predictable that multi-stage TEGs behave better than single-stage TEG [39]. The stage number is set as three to achieve the balance between the conversion performance and structural complexity. As shown in Fig. 2, a number of thermoelectric elements connected electrically in series by metallic connectors and thermally in parallel, are sandwiched by the ceramic plates to compose the thermoelectric module (TEM). Meanwhile, TEM is sandwiched between cooling and heating channel to obtain the necessary temperature gradient. The relatively lowtemperature fuel as cold source flows into the cooling channel, in which its temperature raises significantly through absorbing the heat release from thermoelectric module. The hot fuel in the heating channel provides heat for thermoelectric conversion. It should be mentioned that the non-uniformity of fuel along the flow direction is taken into account in this paper, considering the significant temperature change occurs in the cooling and heating channel with limited fuel flowrate. In addition, TEG is divided into two modules, namely the lowtemperature module and high-temperature module, for a better adaptation to the dramatic temperature change along fuel flow direction. In the low-temperature module, the thermoelectric material of the stage close to cooling channel is set as the nanostructured bismuth antimony telluride bulk alloys, which exhibits excellent thermoelectric conversion performance in the low temperature range (below 480 K) [40]. Meanwhile, a high-performance thermoelectric material suitable for middle-temperature range (480–800 K), cubic AgPb18 SbTe20 [41], is applied in the other two stages. For the high-temperature module, the cubic AgPb18 SbTe20 is utilized in the all three stages, because all thermoelectric elements are within the middle temperature range. Two modules can be arranged flexibly, in layer upon layer to shorten total length, or end to end to decrease total height.

2.2. Integrated power generation and refrigeration system The integrated power generation and refrigeration system produces electricity and cooling gas by means of the combined CBCTEG generator and refrigerator, which is actually a heat-exchanger transferring heat from cooling gas to liquid methane. Nitrogen, which cannot be liquefied by LCH4, is selected as the cooling gas, because of its good stability and low cost. Fuel plays a major role in this integrated system. As shown in Fig. 3, the low-temperature fuel is utilized as the cold source for the refrigeration and power generation, and the mid-temperature fuel serves as the coolant of engine walls. Finally, the high-temperature fuel acts as the heat source for combined CBC-TEG generator. Firstly, liquid methane pressurized by an electric pump, enters into the refrigerator for cooling nitrogen. Then, the fuel with a temperature rise flows into the primary cooler of CBC, in which its temperature increases significantly. The next destination for methane is the cooling channel of TEG, in which the fuel temperature is much higher than the general cold source temperatures for power generation. Then, to reach a higher temperature, the methane at middle temperatures cools the engine walls through absorbing the engine heat dissipation in the wall cooling channels. After that, the high-temperature methane is inputted into the heater of CBC and the heating channel of TEG to provide heat for power generation. Finally, the still hot methane is injected into the combustor for the mixing and combustion with airflow. In this way, a cascade utilization of cold source is achieved by the serial connection of the refrigerator, CBC and TEG in the fuel flow path, as shown in Fig. 4. That is, the cooling capacity of fuel in different temperature ranges is utilized by the refrigerator, CBC and TEG sequentially and fully. The fuel temperature in the cooling channel of TEG is much higher than the cold source temperatures of general thermodynamic cycles. Thus, the temperature range of cold source is expanded by TEG. Note that the helium is heated by the high-temperature fuel in the heater, rather than the combustion heat dissipation through engine walls directly. It is because if helium acts as the coolant of engine walls, a huge pressure loss may occur in the wall cooling channels, which is unacceptable for

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Fig. 3. Schematic diagram of integrated power generation and refrigeration system.

Taking no account of the detailed engine wall cooling; Ignoring the coking issues of methane at high temperatures; The cooling of turbine blades is ignored; The properties and configurations of the p- and n-type elements are identical; 6. The electric resistances of metallic connectors and wires are negligible; 7. Methane behaves as ideal gas after entering the cooling channel of TEG.

2. 3. 4. 5.

3.1. CBC model For a zero-dimensional CBC model, the enthalpies and entropies of working fluid, which are determined by the corresponding temperatures and pressure, are essential for calculation. The following equations are used to obtain the pressures. According to the definition of compressor pressure ratio, the outlet pressure of compressor is given by Fig. 4. Energy flow of fuel as cold source and heat source.

CBC. What is more, the mature design methods on regenerative cooling [42] will be used as references easily, if the engine walls are still cooled by fuel. It should be mentioned that the wall cooling performance of fuel is not taken into account in this paper. Of course, it is predictable that the relatively high temperature of fuel at the inlet of wall cooling channel makes the wall cooling design much more difficult. Besides, the pressure loss of nitrogen in the cooling process is supplied by a cooling gas fan.

p h2 = p h1 · πC

The outlet pressure of heat exchanger is calculated by the corresponding inlet pressure and relative pressure loss, which is defined as the ratio of the pressure difference to inlet pressure (ξ = ( p in − p out )/ p in ) [43]. Thus, the outlet pressure is expressed as

p out,HX = p in,HX (1 − ξHX )

1. The integrated system is in steady-state;

(2)

The pressure ratio of turbine determined by the pressure ratio of compressor and the pressure loss of all heat exchangers, is exhibited as follows:

3. Mathematic modeling The integrated system model is composed by a simple recuperated CBC model, a three-stage TEG model and a refrigerator model. The flow and heat transfer process in the heating and cooling channel of TEG is described in quasi-one-dimension. The system model is based on the following assumptions:

(1)

πT =

p h4 p h5

= πC

n  (1 − ξi )

(3)

i =1

According to Ref. [44], the effectiveness of heat exchanger is defined as the ratio of the actual heat exchange capacity to the maximum value. It should be noted that the specific heat in the cold side is smaller than that of hot side. It means that the cold side reaches the pinch point of heat transfer first (T h3 will reach

K. Cheng et al. / Aerospace Science and Technology 89 (2019) 192–203

T h5 before T h6 = T h2 ). Thus, the effectiveness of CBC recuperator is given by

εREC =

Q act Q max

=

The governing equations of fuel in the cooling and heating channel are set as follows:

1 ρ f

hh3 − hh2

(4)

h( T h5 , p h3 ) − hh2

The electric power generated by CBC system is the product among the mass flowrate and specific work (work difference between turbine and compressor) of helium, as well as the generator efficiency.

PeCBC = mh ( w T − w C )ηG

1 u f

=0 u f x u f p f 1 Cd +A + mf uf = 0 mf x 2 Dh x c p T f u f Q hc,cc = +uf mf x x x 1 ρ f 1 T f 1 p f

ρ f x

+

=

p f x

  = mh (hh4 − hh5s )ηT − (hh2s − hh1 )ηC ηG

197

+

ρ f x

(11) (12) (13) (14)

T f x

where Q CBC is the heat transfer rate inputted into CBC system ( Q CBC = m f (h f 5 − h f 6 ) = mh (hh4 − hh3 )).

where Eq. (11) is the conservation of mass, Eq. (12) is the conservation of momentum in the x direction, Eq. (13) is the conservation of energy, and Eq. (14) is the equation of state. It should be noted that the cross sectional area of all channels is a constant, so the area differential, d A, is omitted in the conservation of mass. According to the Newton’s law of cooling, the heat transfer rate between thermoelectric module and fuel in the conservation of energy is expressed as follows:

3.2. TEG model

i i Q hc = − A hc H hc T f h (i ) − T wh (i )

(15)

i Q cc

(16)

(5)

The electricity generation efficiency of CBC system is defined as

ηCBC =

PeCBC Q CBC

× 100%

(6)



Classic thermal resistance thermoelectric generator model is applied for the performance assessment of three-stage TEG. Meanwhile, the flow and heat transfer process of fuel is described in quasi-one-dimension, in order to represent the temperature nonuniformity along the flow direction. By combining the equations of heat transfer rate, the junction temperatures can be expressed as a matrix form as follows. The detailed derivation is shown in Ref. [39].

B·T =C

(7)

The matrix B, in which j = 1, 2, 3, is expressed as:

B= ⎡A H

⎢ ⎣

1 1 (i ) − K cp hc hc (i ) + K cp (i ) j j j j − K cp (i ) α I + K cp (i ) + K (i ) i

ele

j − K (i ) ele 0

0 0

=

 T wc (i ) − T f c (i )

The Dittus–Boelter equation is applied to predict the forced convection coefficient:

H=

Nu · λ f

(17)

Dh

Nu = 0.023Re0.8 Pr0.4

Uo =







αij T jhj (i ) − T jcj (i )

(19)

j

⎤

Similarly, the total internal resistance is the electric resistance sum of thermoelectric couples in all stages:

⎥ ⎦

R in =

0 0 j − K (i ) 0 ele j j +1 j j +1 −α I + K cp (i ) + K (i ) − K cp (i ) i ele 4 (i ) 4 (i ) − K cp A cc H cc (i ) + K cp

i

where the Seebeck coefficient of thermoelement is the Seebeck coefficient difference between the P- and N-type thermoelectric leg (α = α P − α N ), the thermal conductance of each thermoelement is the sum of two type legs (K ele = λ P A P /l P + λ N A N /l N ), and K cp is the thermal conductance of insulated ceramic plates (K cp = λcp A cp /θcp ). The vector of temperatures is given by

j

Ri

(20)

j

The electric power output is the product of the load voltage and current:

PeTEG = U L · I = U o2

RL

(21)

( R L + R int )2

The total heat transfer rate into thermoelectric module is given by

Q TEG = m f (h f 6 − h f 7 ) =

⎤

T wh (i ) ⎢ T j (i ) ⎥ ⎢ ⎥ T = ⎢ jh ⎥ ⎣ T jcj (i ) ⎦ T wc (i )

(18)

The open-circuit voltage is the electrodynamic force sum of all thermoelements:

i

(8)

⎡



i A cc H cc







i A hc H hc T fh (i ) − T wh (i )

(22)

i

( j = 1, 2, 3)

(9)

In this way, the thermoelectric conversion efficiency of TEG is the ratio of electric power to heat transfer rate:

ηTEG =

PeTEG Q TEG

× 100%

(23)

The vector C is expressed as

⎡ ⎢ ⎢ C =⎢ ⎣

A hc H hc (i ) T f h (i ) j 0.5I R i j 0.5I 2 R i A cc H cc (i ) T f c (i ) 2

⎤ ⎥ ⎥ ⎥ ⎦

3.3. Refrigerator model

( j = 1, 2, 3)

(10)

where the internal electric resistance of thermoelectric element (R) is the sum of the P- and N-type leg (R = l P /σ P A P + l N /σ N A N ).

The model of refrigerator is quite simple. A dimensionless parameter, ratio of refrigeration to electric power (γC E ), as defined as follows, is introduced to measure the required refrigeration power for cooling electronic devices.

γCE = Pc/Pe

(24)

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K. Cheng et al. / Aerospace Science and Technology 89 (2019) 192–203

Fig. 5. Solution strategy block diagram of integrated power generation and refrigeration system.

The mass flow rate of cooling gas, namely nitrogen, is expressed as follows:

mn =

Pc

(25)

hn1 − hn2

3.4. System performance and coupling The physical properties of helium and nitrogen, as well as the methane in the refrigerator and primary cooler, are based on the NIST-REFPROP [45]. After absorbing heat in the primary cooler, methane behaves closer to ideal gas, so its physical properties are supplied by CHEMKIN-II [46]. The main performance parameters of integrated system are exhibited as follows. Obviously, the total electric power is the power sum of CBC and TEG:

Petot = PeCBC + PeTEG

(26)

The percentage increase of electric power achieved by CBC-TEG against CBC under the same conditions is defined as:

ϕ=

Petot − PeCBC PeCBC

=

PeTEG PeCBC

× 100%

(27)

The total conversion efficiency from heat to electricity of combined CBC-TEG generator is:

ηtot =

PeCBC + PeTEG Q CBC + Q TEG

× 100%

(28)

For a better understanding for calculation process, the solution strategy of the integrated power generation and refrigeration system is given in Fig. 5. The optimal thermoelement number in each stage (nele ) for PeTEG , and the inlet fuel temperature in the primary cooler (T f 2 ) to achieve the required ratio of refrigeration to electric power, are obtained by iterations. The optimal compression ratio and recuperation effectiveness for maximum PeCBC are achieved by the Genetic Algorithm (GA) optimization [22]. In addition, a more detailed calculation flowchart of TEG has been described in Ref. [47]. 4. Results and analysis 4.1. Basic input parameters As illustrated in Table 1, the liquid methane temperature in the fuel tank is set as 113 K, which is a common value for LCH4 storage [48]. The storage pressure of fuel is designed as 1 MPa to

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Table 1 Basic parameters on fuel supply. Parameter

Value

Storage temperature of liquid methane Storage pressure of liquid methane Mass flowrate of fuel, m f Efficiency of fuel pump Outlet temperature of fuel pump, T f 1 Outlet pressure of fuel pump, p f 1

113 K 1 MPa 1 kg/s 0.5 114.9 K 3 MPa

Table 2 Basic parameters of refrigerator. Parameter

Value

Inlet temperature of cooling gas, T n1 Outlet temperature of cooling gas, T n2 Relative pressure loss

350 K 285 K 0.01

Table 3 Basic input parameters of CBC-TEG. Parameter CBC Inlet temperature of compressor, T h1 Inlet pressure of compressor, ph1 Isentropic efficiency of compressor, ηC Isentropic efficiency of turbine, η T Relative pressure loss Heater High-pressure side of recuperator Low-pressure side of recuperator Primary cooler TEG Thickness of ceramic plate Thickness of metal connector Gap between thermoelements Total height of thermoelectric module Width and height of channels

Fig. 6. TEG electric power vs. stage thermoelement number (T f 6 = 920 K). Value 300 K 500 kPa 0.873 0.887 0.02 0.015 0.006 0.01 0.2 mm 0.1 mm 0.4 mm 25 mm 2 mm

diminish the fuel tank size and pump power, although a higher storage pressure may lead to a heavier fuel tank. It should be noted that the parameters on fuel storage are just initial values, and the optimal storage conditions of liquid methane for hypersonic vehicles will be investigated in our future research. The outlet pressure of fuel pump is 3 MPa, so that the terminal pressure in the injector is high enough for supersonic mixing. For the refrigerator, the inlet and outlet temperature of nitrogen, as well as the relative pressure loss, are listed as Table 2. The working temperature of cooling gas has a remarkable effect on the operation efficiency of onboard electronic devices. The electronic equipment based on semiconductor will be inefficient if the cooling gas is too hot or too cold. In this paper, the temperature range of nitrogen refers to the cooling air values on conventional aircrafts. The main input parameters of combined CBC-TEG generator are listed in Table 3, which mainly refer to Ref. [24]. The inlet temperature of compressor is designed as 300 K to achieve high power and efficiency [22]. The values of relative pressure losses are relatively large, considering the limited size of onboard heat-exchanger makes it difficult to reduce pressure loss. Besides, the geometrical parameters of thermoelectric module, including the thickness of ceramic plate and metal connector, the air gap between two adjacent thermoelements, as well as the total height, refer to Ref. [47]. The width and height of the heating and cooling channel are as same as the values in Ref. [34]. 4.2. Analysis on maximum electric power On a hypersonic vehicle, heat source is relatively rich, but cold source is definitely finite. Hence, how to achieve maximum elec-

Fig. 7. Conversion efficiency and heat absorption at various nele (T f 6 = 920 K).

tric power with limited fuel mass becomes the primary objective. For thermoelectric generators, the thermoelement number in each stage (nele ) has a significant effect on electric power. As shown in Fig. 6, the electric power of TEG (PeTEG ) when m f = 1 kg/s increases with the stage thermoelement number first, and then decreases at a larger nele . Thus, there is an optimal nele for electric power at constant inlet temperature of cooling channel (T f 3 ) and heating channel (T f 6 ). It is because that a larger nele means more thermoelectric elements are applied for thermoelectric conversion, and meanwhile the heating and cooling channels become longer, leading to more heat absorbed by TEM for power generation, as illustrated in Fig. 7. Nevertheless, as another result of channel length increase, more heat of hot fuel is transferred into the cold source. It causes a higher outlet temperature of cooling channel and a lower terminal temperature in the heating channel. Thus, the available temperature gradient for TEM decreases with nele , leading to lower ηTEG , as shown in Fig. 7. The combined effect of heat absorption and conversion efficiency causes such variation of PeTEG with nele . Moreover, the electric power drops dramatically when T f 3 increases. The reason is that a higher T f 3 reduces the available temperature gradient between the hot and cold junctions of TEM. For closed-Brayton-cycle, the recuperation effectiveness (εREC ) and compressor pressure ratio (πC ) are main influencing factors on power and efficiency. As illustrated in Fig. 8, at constant T h4 , T f 2 and εREC , both electric power at unit fuel mass flowrate and efficiency increase with πC firstly and reach their peaks. After

200

Fig. 8. Variation of 175 K).

K. Cheng et al. / Aerospace Science and Technology 89 (2019) 192–203

η and P e with πC at different εREC for CBC (T h4 = 1073 K, T f 2 =

Table 4 Maximum electric power of CBC at various

Effectiveness of primary cooler (εPC )

εREC

0.50

0.9 0.8 0.7

350.20 332.57 322.04

0.60 420.24 399.09 386.44

Table 5 Terminal temperature of cold source and temperature difference of cooling channel vs. T f 3 .

ε P C and εREC .

PeCBC,max (kW)

0.70 490.28 465.60 450.85

Fig. 9. Electric power comparison at various T f 3 for CBC and CBC-TEG (T f 6 = 920 K, T h4 = 1073 K).

0.80 560.32 532.12 515.26

0.90

T f 3 (K)

370

390

410

430

450

630.37 598.63 579.66

T f 4 (K)  T cc (K)

651.2 281.2

662.4 272.4

673.2 263.2

680.1 250.1

687.2 237.2

that, the power and efficiency become lower. The reason is that the increase of πC provides a higher π T , which is beneficial to power enhancement. However, the compressor work also improves with πC . The net work of CBC will decrease if πC is too high, leading to lower PeCBC and ηCBC . Obviously, a higher recuperation effectiveness brings benefits to power and efficiency improvement, due to a more effective utilization of heat source. The optimal πC decreases with εREC , because the increase of εREC reduces the demand of πC . Specifically, at a higher εREC , the recuperator can recovery the remaining heat after expansion more fully to reduce heat rejection, and thus a lower πC is allowable. Besides, the optimal πC for electric power is always higher than that for efficiency. It is because the increasing rate of heat absorption from heat source (denominator of efficiency) is higher than the power enhancement rate (numerator of efficiency), when πC is larger than its optimal value for efficiency. The variation of the electric power (m f = 1 kg/s) at the optimal πC with the effectiveness of primary cooler and recuperator, is shown in Table 4. It is obvious that the maximum electric power increases with εPC and εREC . The influence of εPC is much more significant than εREC , because fuel cooling capacity used by CBC mainly depends on the former. To achieve better power generation performance, the effectiveness of recuperator is set as 0.9 in the following analysis. 4.3. Effect of fuel outlet temperature in primary cooler (Tf3 ) The fuel outlet temperature in the primary cooler of CBC, namely the inlet temperature of TEG cooling channel, determines the cooling capacity proportions of fuel for CBC and TEG, and strongly influences the TEG performance. As shown in Fig. 9, the electric powers at the fuel flowrate of 1 kg/s for the combined CBC-TEG generator and single CBC are compared at different T f 3 and ratio of refrigeration to electric power (γC E ). These two power generation systems have same CBC parameters. Obviously, CBC-TEG behaves better than CBC in electric power, due to a larger temperature range of cold source achieved by TEG. As listed in Table 5,

the terminal temperature of fuel as cold source (T f 4 ) increases with T f 3 . It indicates that more cooling capacity of fuel is utilized for refrigeration and power generation, which is beneficial to more electricity at a fixed γCE . For both CBC and CBC-TEG, the electric power increases with T f 3 . In single CBC system, a higher T f 3 provides a larger cooling capacity of fuel to generate electricity. For the combined CBC-TEG generator, increasing T f 3 is beneficial to PeCBC improvement, but meanwhile reduces PeTEG . It is because both the fuel cooling capacity utilized by TEG and available temperature gradient for TEM decrease when T f 3 increases and T f 6 decreases, leading to lower ηTEG and PeTEG . Fortunately, the power enhancement of CBC is more than the power decrease of TEG, since ηCBC is much higher than ηTEG . Thus, the increase percentage of combined generator reduces with T f 3 , because the performance degradation of TEG decreases its numerator and the power enhancement of CBC increases its denominator respectively, according to Eq. (27). The electric power with unit fuel flowrate becomes lower at a larger ratio of refrigeration to electric power, because more cooling capacity of fuel is utilized for refrigeration rather than power generation. However, the power increase percentage of combined generator is higher when γCE = 1.5 than γCE = 0.3, because the power increase achieved by TEG is much more significant at a lower PeCBC . The value of increase percentage is over 18.2% when T f 3 = 370 K and γCE = 1.5. It indicates the combined CBC-TEG generator is very effective in electric power enhancement under finite cold source conditions. The cooling capacity fraction of fuel utilized for refrigeration and power generation at different γCE is shown in Fig. 10. When γCE = 0.3, the fraction of CBC power generation is the largest, and increases with T f 3 significantly. Correspondingly, the fraction of TEG power generation decreases as the increase of T f 3 . It is because T f 3 changes the temperature ranges of fuel for cooling CBC and TEG. The fraction variation of refrigeration improves with T f 3 but not obviously. Because the refrigeration power has little change with the electric power, due to a relatively low γCE . The variation trends are similar when γCE changes from 0.3 to 1.5. However, the fraction of CBC power generation becomes smaller, because more

K. Cheng et al. / Aerospace Science and Technology 89 (2019) 192–203

Fig. 10. Fraction of cooling capacity at various T f 3 : (a)

Fig. 11. Variation of T f 5 with

γCE = 0.3; (b) γCE = 1.5.

γCE at different T f 6 (T h4 = 1073 K, T f 3 = 450 K).

cooling capacity of fuel is utilized for refrigeration. At low T f 3 , the largest fraction belongs to TEG. With the increase of T f 3 , the refrigerator takes advantage of the most cooling capacity of fuel. It should be mentioned that an amount of cooling capacity is utilized by TEG, but its electric power is relatively low due to the low ηTEG . Nevertheless, the combined CBC-TEG generator has a strong potential in the power enhancement with finite cold source, considering the thermoelectric performance will be improved significantly by the great progresses on thermoelectric material. 4.4. Limitation on direct heating by fuel Although the direct heating by fuel is beneficial to decreasing the pressure drop of helium, it causes some limitations in the meanwhile. On the one hand, the fuel inlet temperature in heater (T f 5 ) decreases with γCE , making it too close to T h4 at a large γCE , as shown in Fig. 11. It is because less cooling capacity of fuel is utilized for power generation when γCE increases, and thus the corresponding requirement of heat input becomes smaller, too. Due to the constant m f , the only way to reduce heat input is decreasing the temperature difference of fuel (T f 5 − T f 6 ) in the heater.

201

Fig. 12. Power increase percentage of CBC-TEG vs. 1073 K, T f 6 = 920 K).

γCE at different T f 3 (T h4 =

Considering T f 6 is an essential parameter for TEG, it is more reasonable to vary the fuel temperature difference in heater through changing T f 5 . If γCE is extremely large, T f 5 will be too low for heat transfer at constant T f 6 . Besides, a higher T f 6 causes the increase of T f 5 , and thus improves the upper limit of γCE . It should be noted that a too-high T f 5 raises the risk of coking and carbon deposit for hydrocarbon fuel, including methane, which is quite dangerous in a practical application. On the other hand, the power increase percentage achieved by combined generator (ϕ ) is strictly limited by the direct heating of fuel. As illustrated in Fig. 12, the increase percentage improves with γCE , because PeCBC becomes lower but PeTEG remains the same. In this way, the increase percentage is limited by γCE , due to the limitation of T f 5 as discussed above. Meanwhile, a higher T f 3 will improve PeCBC but reduce PeTEG , and thus decreases ϕ . The fundamental cause for these limitations is that a strong coupling between the cooling and heating process occurs, when fuel is utilized as both cold source and heat source. Hence, decoupling

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the cooling and heating process becomes the key to break through these limitations. 5. Conclusion An integrated power generation and refrigeration system on hypersonic vehicles, in which a combined CBC-TEG generator is established for the power generation with finite cold source, is proposed in this paper. The maximum electric power of TEG and CBC, as well as the effects of fuel outlet temperature in primary cooler on system performance are investigated. In addition, the limitations caused by the direct heating of fuel are discussed in this study. The main conclusions are summarized as follows: 1. There is an optimal stage thermoelement number for the electric power of TEG, under the influence of the conversion efficiency and heat absorption; 2. Effectiveness of primary cooler has a more dramatic impact on the electric power of CBC than recuperation effectiveness, because fuel cooling capacity used by CBC is mainly dependent on the former; 3. Compared with single CBC, the combined CBC-TEG generator exhibits better on electric power through extending the temperature range of cold source, the power increase percentage of which exceeds 18.2% when T f 3 = 370 K and γCE = 1.5; 4. Power increase percentage of combined generator reduces with fuel outlet temperature in primary cooler, due to the performance degradation of TEG and the power enhancement of CBC; 5. Due to the too-small temperature difference at heater hot end, the direct heating by high-temperature fuel limits the ratio of refrigeration to electric power and power increase percentage, and decoupling the cooling and heating process of combined generator is essential to break through these limitations. This article provides a novel technical solution to achieve the power generation and refrigeration on hypersonic vehicles under finite cold source conditions. Conflict of interest statement The authors declare there is no conflict of interest regarding the publication of this paper. Acknowledgements This research work is supported by General Program (No. 51476044) and Program (No. 51606051) of National Natural Science Foundation of China. References [1] Z.-t. Zhao, W. Huang, B.-b. Yan, L. Yan, T.-t. Zhang, R. Moradi, Design and high speed aerodynamic performance analysis of vortex lift waverider with a widespeed range, Acta Astronaut. 151 (2018) 848–863. [2] F. Deng, F. Xie, N. Qin, W. Huang, L. Wang, H. Chu, Drag reduction investigation for hypersonic lifting-body vehicles with aerospike and long penetration mode counterflowing jet, Aerosp. Sci. Technol. 76 (2018) 361–373. [3] S. Di Giorgio, D. Quagliarella, G. Pezzella, S. Pirozzoli, An aerothermodynamic design optimization framework for hypersonic vehicles, Aerosp. Sci. Technol. 84 (2019) 339–347. [4] M. Ou, L. Yan, J.-f. Tang, W. Huang, X.-q. Chen, Thermodynamic performance analysis of ramjet engine at wide working conditions, Acta Astronaut. 132 (2017) 1–12. [5] W. Huang, Transverse jet in supersonic crossflows, Aerosp. Sci. Technol. 50 (2016) 183–195. [6] W. Huang, L. Yan, Numerical investigation on the ram–scram transition mechanism in a strut-based dual-mode scramjet combustor, Int. J. Hydrog. Energy 41 (2016) 4799–4807.

[7] S. Zhu, X. Xu, Q. Yang, Y. Jin, Intermittent back-flash phenomenon of supersonic combustion in the staged-strut scramjet engine, Aerosp. Sci. Technol. 79 (2018) 70–74. [8] Z. Cai, J. Zhu, M. Sun, Z. Wang, Effect of cavity fueling schemes on the laserinduced plasma ignition process in a scramjet combustor, Aerosp. Sci. Technol. 78 (2018) 197–204. [9] W. Huang, Z.-b. Du, L. Yan, R. Moradi, Flame propagation and stabilization in dual-mode scramjet combustors: a survey, Prog. Aerosp. Sci. 101 (2018) 13–30. [10] W. Huang, L. Yan, J.-g. Tan, Survey on the mode transition technique in combined cycle propulsion systems, Aerosp. Sci. Technol. 39 (2014) 685–691. [11] J. Liu, H. Yuan, Z. Hua, W. Chen, N. Ge, Experimental and numerical investigation of smooth turbine-based combined-cycle inlet mode transition, Aerosp. Sci. Technol. 60 (2017) 124–130. [12] D. Yan, G. He, F. Qin, D. Zhang, L. Shi, Effect of the heat release on the component coordination in the rocket-based combined cycle engine, Acta Astronaut. 151 (2018) 942–952. [13] X. Yu, C. Wang, D. Yu, Precooler-design & engine-performance conjugated optimization for fuel direct precooled airbreathing propulsion, Energy 170 (2019) 546–556. [14] Y. Xi, Y. Meng, Adaptive actuator failure compensation control for hypersonic vehicle with full state constraints, Aerosp. Sci. Technol. 85 (2019) 464–473. [15] D. Zhang, J. Qin, Y. Feng, F. Ren, W. Bao, Performance evaluation of power generation system with fuel vapor turbine onboard hydrocarbon fueled scramjets, Energy 77 (2014) 732–741. [16] S. Song, W. Liu, D. Peitsch, U. Schaefer, Detailed design of a high speed switched reluctance starter/generator for more/all electric aircraft, Chin. J. Aeronaut. 23 (2010) 216–226. [17] J. Dollmayer, N. Bundschuh, U.B. Carl, Fuel mass penalty due to generators and fuel cells as energy source of the all-electric aircraft, Aerosp. Sci. Technol. 10 (2006) 686–694. [18] J.M. Hank, J.S. Murphy, R.C. Mutzman, The X-51A Scramjet Engine Flight Demonstration Program, AIAA Paper 2540, 2008. [19] Y. Zhang, L. Wang, S. Wang, P. Wang, H. Liao, Y. Peng, Auxiliary power unit failure prediction using quantified generalized renewal process, Microelectron. Reliab. 84 (2018) 215–225. [20] L.M. Surhone, M.T. Tennoe, S.F. Henssonow, Ram Air Turbine, Betascript Publishing, 2010. [21] D.F. Waters, C.P. Cadou, Engine-integrated solid oxide fuel cells for efficient electrical power generation on aircraft, J. Power Sources 284 (2015) 588–605. [22] K. Cheng, J. Qin, C. Dang, C. Lv, S. Zhang, W. Bao, Thermodynamic analysis for high-power electricity generation systems based on closed-Brayton-cycle with finite cold source on hypersonic vehicles, Int. J. Hydrog. Energy 43 (2018) 14762–14774. [23] M.J. Barrett, B.M. Reid, System mass variation and entropy generation in 100-kWe closed-Brayton-cycle space power systems, AIP Conf. Proc. 699 (2004) 445–452. [24] B.M. Gallo, M.S. El-Genk, Brayton rotating units for space reactor power systems, Energy Convers. Manag. 50 (2009) 2210–2232. [25] J. Qin, W. Zhou, W. Bao, D. Yu, Thermodynamic analysis and parametric study of a closed Brayton cycle thermal management system for scramjet, Int. J. Hydrog. Energy 35 (2010) 356–364. [26] K. Cheng, D. Zhang, J. Qin, S. Zhang, W. Bao, Performance evaluation and comparison of electricity generation systems based on single- and two-stage thermoelectric generator for hypersonic vehicles, Acta Astronaut. 151 (2018) 15–21. [27] C.L. Gong, J.J. Gou, J.X. Hu, F. Gao, A novel TE-material based thermal protection structure and its performance evaluation for hypersonic flight vehicles, Aerosp. Sci. Technol. 77 (2018) 458–470. [28] G. Bennett, J. Lombardo, R. Hemler, G. Silverman, C. Whitmore, W. Amos, E. Johnson, A. Schock, R. Zocher, T. Keenan, J. Hagan, R. Englehart, Mission of daring: the general-purpose heat source radioisotope thermoelectric generator, in: 4th International Energy Conversion Engineering Conference and Exhibit (IECEC), San Diego, California, 2006, pp. 1–23. [29] J.-H. Meng, X.-D. Wang, W.-H. Chen, Performance investigation and design optimization of a thermoelectric generator applied in automobile exhaust waste heat recovery, Energy Convers. Manag. 120 (2016) 71–80. [30] G. Shu, J. Zhao, H. Tian, X. Liang, H. Wei, Parametric and exergetic analysis of waste heat recovery system based on thermoelectric generator and organic rankine cycle utilizing R123, Energy 45 (2012) 806–816. [31] X. Li, Z. Wang, Exergy analysis of integrated TEG and regenerative cooling system for power generation from the scramjet cooling heat, Aerosp. Sci. Technol. 66 (2017) 12–19. [32] W. Huang, Z. Chen, L. Yan, B.-b. Yan, Z.-b. Du, Drag and heat flux reduction mechanism induced by the spike and its combinations in supersonic flows: a review, Prog. Aerosp. Sci. 105 (2019) 31–39. [33] R.T. Voland, L.D. Huebner, C.R. McClinton, X-43A hypersonic vehicle technology development, Acta Astronaut. 59 (2005) 181–191. [34] S. Zhang, J. Qin, K. Xie, Y. Feng, W. Bao, Thermal behavior inside scramjet cooling channels at different channel aspect ratios, J. Propuls. Power 32 (2016) 57–70. [35] R. Lemoyne, Fundamental analysis of a first stage ramjet-rocket combined cycle and second stage hydrolysis propulsion system with trajectory weighting,

K. Cheng et al. / Aerospace Science and Technology 89 (2019) 192–203

in: 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, San Francisco, California, 2011, pp. 1–12. [36] Y. Kano, T. Tsujimoto, I. Kubota, T. Munenaga, M. Ishii, Y. Sato, Overview of LNG propulsion system development, in: 63rd International Astronautical Congress, Naples, Italy, 2012, pp. 1–6. [37] C. Zhang, G. Shu, H. Tian, H. Wei, X. Liang, Comparative study of alternative ORC-based combined power systems to exploit high temperature waste heat, Energy Convers. Manag. 89 (2015) 541–554. [38] X. Yan, K. Kunitomi, T. Nakata, S. Shiozawa, GTHTR300 design and development, Nucl. Eng. Des. 222 (2003) 247–262. [39] K. Cheng, J. Qin, Y. Jiang, S. Zhang, W. Bao, Performance comparison of singleand multi-stage onboard thermoelectric generators and stage number optimization at a large temperature difference, Appl. Therm. Eng. 141 (2018) 456–466. [40] B. Poudel, Q. Hao, Y. Ma, Y. Lan, A. Minnich, B. Yu, X. Yan, D. Wang, A. Muto, D. Vashaee, X. Chen, J. Liu, M.S. Dresselhaus, G. Chen, Z. Ren, High-thermoelectric performance of nanostructured bismuth antimony telluride bulk alloys, Science 320 (2008) 634–638. [41] K.F. Hsu, S. Loo, F. Guo, W. Chen, J.S. Dyck, C. Uher, T. Hogan, E. Polychroniadis, M.G. Kanatzidis, Cubic AgPbmSbTe2+ m: bulk thermoelectric materials with high figure of merit, Science 303 (2004) 818–821.

203

[42] J. Ma, J. Chang, J. Zhang, W. Bao, D. Yu, Control-oriented unsteady onedimensional model for a hydrocarbon regeneratively-cooled scramjet engine, Aerosp. Sci. Technol. 85 (2019) 158–170. [43] M.J. Barrett, Expectations of closed-Brayton-cycle heat exchangers in nuclear space power systems, J. Propuls. Power 21 (2005) 152–157. [44] M.T. Dunham, B.D. Iverson, High-efficiency thermodynamic power cycles for concentrated solar power systems, Renew. Sustain. Energy Rev. 30 (2014) 758–770. [45] E.W. Lemmon, M.L. Huber, M.O. McLinden, NIST Reference Fluid Thermodynamic and Transport Properties–REFPROP, version, 2002. [46] R.J. Kee, F.M. Rupley, J.A. Miller, Chemkin-II: A Fortran Chemical Kinetics Package for the Analysis of Gas-Phase Chemical Kinetics, Sandia National Labs., Livermore, CA (USA), 1989. [47] K. Cheng, J. Qin, Y. Jiang, C. Lv, S. Zhang, W. Bao, Performance assessment of multi-stage thermoelectric generators on hypersonic vehicles at a large temperature difference, Appl. Therm. Eng. 130 (2018) 1598–1609. [48] D. Haeseler, C. Mäding, A. Götz, V. Roubinski, S. Khrissanfov, V. Berejnoy, Recent developments for future launch vehicle LOXHC rocket engines, in: 6th International Symposium Propulsion for Space Transportation of the XXIst Century, Versailles, France, 2002, pp. 1–9.