Keywords

1 Introduction

Aerospace scientists have noticed the air-breathing propulsion vehicles, since several decades ago. Supersonic combustion chambers (scramjets) have great ability in high speed hence have acquired high level of recent research interest in all over the world [1, 2]. Due to high fuel impulse, scramjets can be considered as one of economic choice in long-distance flights [3]. However, scramjets are not very appropriate for accelerating missions since their net thrust is lower than a rocket [4]. Whereas, scramjet technology face up to many challenges such cooling management of high working temperature, onboard fuel storage restriction, flight condition sustainability etc. Accordingly, prevailing over these challenges can be purpose of developed research centers.

High heat flux level in scramjet combustion chambers demands a reliable cooling system. Heat flux range of 0.5–2.5 MW per unit of area in working temperature of 500–2000 K for Mach number of 8 flight condition is reported [5]. Due to such high temperature, even the most developed composite materials cannot withstand a work properly [6]. Regenerative cooling systems (RCC) especially open cooling cycle (OCC) is introduced as one of the most efficient and feasible solution encountering heat management challenge. Utilizing the high heat absorption of hydrogen to cool down the scramjet is the innovative point of this method. Over-temperature of the wall in the scramjet systems is a crucial phenomenon through the cooling process which can be avoided by preheating of the fuel before entering the cooling channel [7]. Thus, an appropriate cooling treatment prevents the heat transfer deterioration at the entrance region. This process may be repeated in various times that is called multi-OCC (M-OCC). OCC is also applicable to both hydrocarbon and hydrogen-fueled scramjet engines.

The ancillary set-ups, including circuit measuring, fuel injection, and tracking controller set-ups on aircrafts and aerospace vehicles need a definite deal of electrical energy. Thus, for such a high speed enormous vehicles, it is completely important to provide an energy recovery set-up to address its surplus electricity need [8]. In recent years, recovering energy and implementing energy-saving methods for producing power, useful products and other required commodities have been utilized in numerous energy conversion systems [9]. Consequently, co-production systems are introduced as the most efficient and pragmatic solutions for energy recovery purposes when low-quality heat resources (such as waste heat) are pondered [10, 11]. Using co-production systems render the feasibility of producing other useful forms of energies such as heating, cooling, purified water and hydrogen alongside the power production [12,13,14]. Co-production (also known as co-generation) systems have higher energy efficiency and low exergy destruction than the single-production systems under a same condition, as shown by Onovwiona and Ugursl [15]. Dincer et al. [16] carried out a thermodynamic study of a high degree set-up electrolysis (HDSE) for cogeneration of H2 and electricity, including a solar tower, a Brayton system, a Rankine system, and an organic Rankine system. Based on the results, the total efficiencies. Ghaebi et al. [17] recommended two novel combined cycles for electricity and H2 co-production using huge value of wasted heat of the city gas post (CGP) regulators in which the high pressure NG is decreased to an acceptable pressure for consumption. These set-ups are integrated by a combination of a Rankine system (RS) and CGP system as well as an absorption power system (APS) as an alternative electricity unit. In both systems, PEM electrolyzer is utilized to generate hydrogen. The power sub-cycle is actuated by waste heat of CGP and PEM is operated by a fair segment of net output electricity. An executive and comparative 4E (energy, exergy, economy and environment) analysis of both systems have been fulfilled. The outcomes of assessment have demonstrated 6.868 and 6.351 kg/h hydrogen production as well as 8.571 and 7.618 MW electricity generation for the CGP-RS and CGP-APS set-ups, correspondingly. The exergy destruction study has demonstrated that the generator of system has introduced as the highest exergy destructive component (in both systems). Li and Wang [5] have performed a theoretical study on producing power from the waste energy of scramjet. In their study, a thermoelectrical generator (TEG) is assimilated with a regenerative cooling cycle of scramjet engine for power production. The results of this study revealed power production of 61.69 kW and exergy efficiency of about 22% for fuel flow rate of 0.4 kg/s. And a parametric analysis which has been accomplished in their investigation denoted that the pressure ratio of turbine has a significant effect on the exergy efficiency.

Hydrogen has higher-ranking properties compared to all kinds of carbon based fuels such as substantial flame stability for combustion and high ignitability. These intrinsic profits nowadays have captured a great attention in recent studies of H2-fueled scramjet engines [7, 10, 18]. H2 production process c is performed by biomass conversion water splitting or steam methane reforming. Splitting water is a thermochemical process which is called electrolysis. There are three conventional forms for electrolyzing process, consist of the alkaline, oxidation of solid, and proton exchange membrane (PEM) electrolysis. Hydrogen generation by PEM electrolysis has several benefits especially in renewable-based procedures, including: being compact, low environmental effect, zero hazardous chemicals and extremely pure hydrogen [19]. PEM is the most widespread procedure of hydrogen production in energy set-ups with low grade energy sources because of its high compatibility with these systems and is introduced as the commendable hydrogen production method for future utilities accordingly [20, 21]. Marangio et al. [22] presented a model for theoretical study of the PEM cells in which a complicated pattern of Ohmic losses in electrodes and membrane. They have validated the presented model using available experimental data. In the other study presented by Ahmadi et al. [23], a PEM electrolyzer which is actuated by solar energy, has been assimilated with an OHEC (ocean heat energy conversion) system to extract H2. Energy and exergy assessment have been performed in the recommended model and it is concluded that the extracted hydrogen rate is 1.2 kg/h with exergy and thermodynamic efficiencies of 23% and 3.6%, respectively.

The importance of thermal management of the scramjet and its effects on operation of this hypersonic vehicle has drawn attention of many researches about it in more recent years. The M-OCC is known as one of the most feasible system for cooling of scramjet engines. On the other hand, some studies have tried to examine the exergy aspect of utilizing this kind of cooling system for co-production aims such as a limited exergy based study conducted by Li and Wang. Despite all efforts to study and outstrip these cooling systems and conducting thermodynamic analysis of these systems, the lack of an exclusive thermodynamic and exergy analysis of the M-OCC and investigating the effects of multi-expansion process is also indispensable. Moreover, no thoroughgoing investigation for producing electricity and hydrogen from waste heat of scramjet via PEM electrolyzer is presented up to yet.

The aim of present work is to advance a novel multi-stage OCC in order to produce electricity and hydrogen and cooling the scramjet engine as well. Additionally, a thoroughgoing study on multi-expansion effects is accomplished from thermodynamic standpoint. In the proposed set-up, the PEM is driven by a portion of net output power the cooling cycle, whilst the waste heat of scramjet is pondered as the heat source of the multi cooling cycle.

2 System Expression

Figure 12.1 shows a comprehensive illustration of system layout. Two prominent systems, Power and PEM electrolyzer cycles, are operating in this system. Hydrogen as working flow, is streamed through scramjet cooling pass entry by pump (state 2). Coolant absorbs the combustion chamber heat and changes to superhot gas quickly. Afterwards, the superhot hydrogen gets on the turbine number 1 (state 3). By entering to the turbine the hydrogen as working fluid not only produce electric power but also the temperature decreases to \({T}_{4}\). Hydrogen produced power, by circulating in turbine, and now is cooled down. Thus it is again ready to absorb the heat and cool down through the second cooling passage and turbine number 2, respectively. This process of chilling the scramjet wall down and expanding through turbine to extract electricity from the heated coolant continues two times again in order to attain a high performance. Finally hydrogen enters to the combustion chamber of scramjet as fuel after streaming into last cooling passage to close the power sub-cycle.

Fig. 12.1
figure 1

Simple schematics of proposed system

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Electricity and heat energy are two main inputs of PEM electrolyzer to produce hydrogen. Some portion of produced electricity in the power sub-cycle supplies the electricity need of PEM and high heat flux of scramjet meets heat needs of PEM. A simple electrolyzing process of water separation occurs in the PEM. Electric voltage difference make to anode and cathode sides. Hydrogen is produced in cathode side then is storied in a special tank (state 15). In the anode side the separated oxygen is accumulated and transferred to a storage tank (state 16). The surplus water is recirculated to the PEM and closes the PEM sub-cycle.

3 Methodology and Assumptions

3.1 Considered Suppositions

Some of the main assumptions of the suggested system are made as following [24,25,26,27,28]:

  • Mathematical modeling is zero dimensional steady state

  • Specific heat is considered constant.

  • After the first cooling passage, the coolant is assumed perfect gas.

  • Any energy and pressure drops are not considered through joints and transfer lines.

  • Any losses is not considered by heat transfer process in the turbine.

  • 298 K and 0.101 MPa are reference temperature and presure, respectively.

  • Any energy losses is not considered through PEM electrolyzer.

3.2 The Mathematic Simulation of Scramjet

The thermodynamic analysis based modeling of scramjet is conducted in present modeling. Therefore, two main parameters consisting of the scramjet's entry pressure ratio (\({{{\pi}}}_{{{i}}{{n}}}\)) and fuel equivalence ratio are needed to evaluate the average temperature of scramjet combustion chamber wall. The mean wall combustor temperature is calculated by averaging TD and TC, which means the outlet and inlet combustor temperatures (Fig. 12.2):

Fig. 12.2
figure 2

Ideal scramjet Schematic condition

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$${T_{ave}} = \frac{{{T_c} + {T_D}}}{2}$$
(12.1)

Figure 12.2 indicates a schematic plot of an ideal scramjet, which includes four prominent zones of inlet, nozzle, isolator, and combustor. The combustor is supplied by hydrogen.

3.3 Cycle Analysis for the Scramjet Engine Modeling

As demonstrated in Fig. 12.3, the ideal scramjet system is drawn on a T-s plot. A-C process indicates the adiabatic compression from the static temperature to the combustor inlet temperature. A-B and B-C indicate air compression in the enter section and isolator. C-D shows the energy receiving operation in to combustor, performing at a consistent static pressure. Process D-E occurs isentropically in the nozzle. Also, process E-A is only an unreal constant static pressure event. Based on energy conversion principle, heat is wasted from nozzle outlet to the atmosphere at D-A process. The Three main sectors in scramjet modeling are described extensively.

Fig. 12.3
figure 3

T-s diagram of an ideal scramjet system

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3.3.1 Compression Process

The amount of compression in the scramjet inlet section defines as inlet pressure ratio \(({{{\pi}}}_{{{i}}{{n}}})\). At cruise situations, the freestream circumstances (\({{{P}}}_{{{t}}{{A}}}\), \({{{T}}}_{{{t}}{{A}}}\) and \({{{M}}{{a}}}_{{{A}}}\)) are expressed. However, the steady flow through the inlet compression part may be written as below [29, 30]:

$${{{P}}}_{{{t}}{{B}}}={{{P}}}_{{{t}}{{A}}}$$
(12.2)
$${{{T}}}_{{{t}}{{B}}}={{{T}}}_{{{t}}{{A}}}$$
(12.3)
$$M{a_B} = \sqrt {{{\left[ {{{\left( {\frac{{{P_{tA}}}}{{{\pi _{in}}{P_A}}}} \right)}^{(k - 1/k)}}} \right]} \mathord{\left/ {\vphantom {{\left[ {{{\left( {\frac{{{P_{tA}}}}{{{\pi _{in}}{P_A}}}} \right)}^{(k - 1/k)}}} \right]} {\left( {\frac{{k - 1}}{2}} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\frac{{k - 1}}{2}} \right)}}}$$
(12.4)

Also, \({{k}}\) is the specific heat capacity ratio of air.

The isolator compression is followed by a shock train. The empirical relations are described by Billig et al. [31, 32]:

$$\frac{L}{H} = \frac{{\left[ {50\left( {\frac{{P_{C} }}{{P_{B} }} - 1} \right)^{2} + 170\left( {\frac{{P_{C} }}{{P_{B} }} - 1} \right)^{2} } \right]}}{{\left( {Ma_{1}^{2} - 1} \right)}}.\frac{{\sqrt {{\theta \mathord{\left/ {\vphantom {\theta H}} \right. \kern-\nulldelimiterspace} H}} }}{{\sqrt[4]{{Re_{\theta } }}}}$$
(12.5)

where, \({{{R}}{{e}}}_{{{\theta}}}\) is the inlet Reynolds number, \({{\theta}}\) is the thickness of boundary layer momentum, and \({{L}}/{{H}}\) is the of shock train length to isolator height ratio. The consistent coefficient (\({{C}})\) is defined for brevity targets. The amounts of \({{L}}/{{H}}\), \({{\theta}}/{{H}}\) and \({{{R}}{{e}}}_{{{\theta}}}\) are estimated 10, 0.02 and 10,000, respectively [30].

$$C = {{\frac{L}{H}} \mathord{\left/ {\vphantom {{\frac{L}{H}} {\frac{{\sqrt {{\theta \mathord{\left/ {\vphantom {\theta H}} \right. \kern-\nulldelimiterspace} H}} }}{{\sqrt[4]{{\text{Re} _{\theta } }}}}}}} \right. \kern-\nulldelimiterspace} {\frac{{\sqrt {{\theta \mathord{\left/ {\vphantom {\theta H}} \right. \kern-\nulldelimiterspace} H}} }}{{\sqrt[4]{{\text{Re} _{\theta } }}}}}}$$
(12.6)

The isolator exit pressure is defined by manipulating Eqs. (12.5) and (12.6) [30]:

$${{{P}}}_{{{C}}}={{{P}}}_{{{B}}}.\frac{\sqrt{680.{{C}}.\left({{{M}}{{a}}}_{{{B}}}^{2}-1\right)+2500}+290}{340}$$
(12.7)

The whole pressure and temperature at the isolator outlet are given as [29]:

$${{{T}}}_{{{t}}{{C}}}={{{T}}}_{{{t}}{{B}}}={{{T}}}_{{{t}}{{A}}}$$
(12.8)
$${{{P}}}_{{{t}}{{C}}}={{{P}}}_{{{C}}}.{\left(1+\left({{k}}-1\right).\frac{{{{M}}{{a}}}_{{{C}}}^{2}}{2}\right)}^{({{k}}/{{k}}-1)}$$
(12.9)
$$\frac{{{{P}}}_{{{t}}{{C}}}}{{{{P}}}_{{{t}}{{B}}}}=\left[{ \left(\frac{1+\frac{\left({{k}}-1\right)}{2}.{{{M}}{{a}}}_{{{C}}}^{2}}{1+\frac{\left({{k}}-1\right)}{2}.{{{M}}{{a}}}_{{{B}}}^{2}}\right)}^{({{k}}/{{k}}-1)}\right].\left[\frac{1+{{k}}.{{{M}}{{a}}}_{{{B}}}^{2}}{1+{{k}}.{{{M}}{{a}}}_{{{C}}}^{2}}\right]$$
(12.10)

The static temperature at C is obtained from [29]:

$${{{T}}}_{{{C}}}={{{T}}}_{{{t}}{{C}}}/\left(1+\left({{k}}-1\right).\frac{{{{M}}{{a}}}_{{{C}}}^{2}}{2}\right)$$
(12.11)

3.3.2 Heat Addition Process

Based on the energy conversation relation at steady state condition for the combustor, the Eq. (12.12) is written [30]:

$$\left({\dot{{{m}}}}_{{{A}}}+{\dot{{{m}}}}_{{{f}}}\right){{{h}}}_{{{t}}{{D}}}={\dot{{{m}}}}_{{{A}}}{{{h}}}_{{{t}}{{C}}}+{\dot{{{m}}}}_{{{f}}}{{{L}}{{H}}{{V}}}_{{{{H}}}_{2}}$$
(12.12)

where, \({{{L}}{{H}}{{V}}}_{{{{H}}}_{2}}\) is the hydrogen combustion low heat value and is reported 120.11 \(\mathrm{MJ}/\mathrm{kg}\).

The Eq. (12.12) can be expressed in the other way as below:

$${\dot{{{m}}}}_{0}{{{C}}}_{{{p}}}{{{T}}}_{{{t}}{{C}}}+{\dot{{{m}}}}_{{{f}}}{{{L}}{{H}}{{V}}}_{{{{H}}}_{2}}={\dot{{{m}}}}_{0}{{{C}}}_{{{p}}}{{{T}}}_{{{t}}{{D}}}$$
(12.13)

or

$$\mathop m\limits^{.} _{f} LHV_{{H_{2} }} = \mathop m\limits^{.} _{A} C_{p} T_{{tD}} \left( {{{T_{{tC}} } \mathord{\left/ {\vphantom {{T_{{tC}} } {T_{{tD}} - 1}}} \right. \kern-\nulldelimiterspace} {T_{{tD}} - 1}}} \right) = \mathop m\limits^{.} _{A} C_{p} \left( {T_{{tD}} - T_{{tC}} } \right)$$
(12.14)

The whole temperature ratio is introduced as:

$$\tau = {{T_{{tC}} } \mathord{\left/ {\vphantom {{T_{{tC}} } {T_{{tD}} }}} \right. \kern-\nulldelimiterspace} {T_{{tD}} }}$$
(12.15)

The stoichiometric hydrogen-air reaction is described as [33]:

$$2{{{H}}}_{2}+{{{O}}}_{2}+3.76{{{N}}}_{2}\to 2{{{H}}}_{2}{{O}}+3.76{{{N}}}_{2}$$
(12.16)

The highest demand of hydrogen \({\dot{{{m}}}}_{{{f}}{{s}}}\), takes place in the stoichiometric situation with Eq. (12.17):

$${\dot{{{m}}}}_{{{f}}{{s}}}=\frac{{\dot{{{m}}}}_{{{A}}}\times 4\times 0.21}{1\times 32}\cong {\dot{{{m}}}}_{{{A}}}/40$$
(12.17)

Also, the fuel equivalence ratio \((\mathbf{\varnothing })\) is introduced as below:

$$\mathbf{\varnothing }=\frac{{\dot{{{m}}}}_{{{f}}}}{{\dot{{{m}}}}_{{{f}}{{s}}}}$$
(12.18)

Moreover, the total temperature ratio may be described as below:

$${{\tau}}=1+\frac{\boldsymbol{\varnothing }\boldsymbol{ }{{{L}}{{H}}{{V}}}_{{{{H}}}_{2}}}{40\boldsymbol{ }{{{C}}}_{{{p}}}{{{T}}}_{{{t}}{{A}}}}$$
(12.19)

In the constant pressure process:

$${{{P}}}_{{{D}}}={{{P}}}_{{{C}}}$$
(12.20)

Then, whole pressure \({{{P}}}_{{{t}}{{D}}}\) is denoted as [29]:

$${{{P}}}_{{{t}}{{D}}}={{{P}}}_{{{D}}}.{\left(\left({{k}}-1\right).\frac{{{{M}}{{a}}}_{{{D}}}^{2}}{2}+1\right)}^{\left({{k}}/{{k}}-1\right)}$$
(12.21)
$${{\tau}}=\left[\frac{1+{{k}}.{{{M}}{{a}}}_{{{C}}}^{2}}{1+{{k}}.{{{M}}{{a}}}_{{{D}}}^{2}}\right].\left[\frac{{{{M}}{{a}}}_{{{D}}}^{2}}{{{{M}}{{a}}}_{{{C}}}^{2}}\right].\left[{\left(\frac{1+\frac{\left({{k}}-1\right)}{2}.{{{M}}{{a}}}_{{{D}}}^{2}}{1+\frac{\left({{k}}-1\right)}{2}.{{{M}}{{a}}}_{{{C}}}^{2}}\right)}^{({{k}}/{{k}}-1)}\right]$$
(12.22)

By simultaneous solving of Eq. (12.21) and (12.22), the Mach number) and after that static temperature at the pint D are calculated.

$${{{T}}}_{{{D}}}={{{T}}}_{{{t}}{{D}}}/\left(1+\left({{k}}-1\right).\frac{{{{M}}{{a}}}_{{{D}}}^{2}}{2}\right)$$
(12.23)

3.3.3 Expansion Process

Expansion process has been occurred isentropically in the nozzle as the followed relations [29]:

$${{{P}}}_{{{E}}}={{{P}}}_{{{A}}}$$
(12.24)
$${{{P}}}_{{{t}}{{E}}}={{{P}}}_{{{t}}{{D}}}$$
(12.25)
$$M{a_E} = \sqrt {{{\left[ {{{\left( {\frac{{{P_{tE}}}}{{{P_E}}}} \right)}^{(k - 1/k)}} - 1} \right]} \mathord{\left/ {\vphantom {{\left[ {{{\left( {\frac{{{P_{tE}}}}{{{P_E}}}} \right)}^{(k - 1/k)}} - 1} \right]} {\left( {\frac{{k - 1}}{2}} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\frac{{k - 1}}{2}} \right)}}}$$
(12.26)

3.4 Performance Criteria of Open Cooling Cycle

Decreasing in the fuel flow rate for refrigeration by rising the heat absorption of fuel is the prominent target of the OCC.

One of the main parameters is the multiplication ratio of the fuel heat absorption (δ), which is obtained from the first passage cooling per second passage cooling amounts as Eq. (12.27) [34].

$${{{\delta}}}_{1}=\frac{{{{Q}}}_{2}}{{{{Q}}}_{1}}$$
(12.27)

By the similar definition, \({{{\delta}}}_{2}\), \({{{\delta}}}_{3}\), and \({{{\delta}}}_{4}\) are introduced for the third, fourth and fifth cooling passages, correspondingly:

$${{{\delta}}}_{2}=\frac{{{{Q}}}_{3}}{{{{Q}}}_{1}+{{{Q}}}_{2}}$$
(12.28)
$${{{\delta}}}_{3}=\frac{{{{Q}}}_{4}}{{{{Q}}}_{1}+{{{Q}}}_{2}+{{{Q}}}_{3}}$$
(12.29)
$${{{\delta}}}_{4}=\frac{{{{Q}}}_{5}}{{{{Q}}}_{1}+{{{Q}}}_{2}+{{{Q}}}_{3}+{{{Q}}}_{4}}$$
(12.30)

The other main parameter is introduced as reduction ratio of mass flow rate (ϕ). The increasing of the fuel heat absorption load is explained as decreasing in the mass flow rate of fuel. Particularly, direct effect of utilizing OCC in performance of the scramjet cooling unit is decreasing of the essential fuel flow rate. Moreover, the reduction ratio of the second cooling passage is described as below [34]:

$${{{\phi}}}_{1}=\frac{{{{Q}}}_{2}}{{{{Q}}}_{1}+{{{Q}}}_{2}}$$
(12.31)

Similarly,\({{{\phi}}}_{2}\), \({{{\phi}}}_{3}\), and \({{{\phi}}}_{4}\) are introduced for the third, fourth and fifth cooling passages, as written:

$${{{\phi}}}_{2}=\frac{{{{Q}}}_{3}}{{{{Q}}}_{1}+{{{Q}}}_{2}+{{{Q}}}_{3}}$$
(12.32)
$${{{\phi}}}_{3}=\frac{{{{Q}}}_{4}}{{{{Q}}}_{1}+{{{Q}}}_{2}+{{{Q}}}_{3}+{{{Q}}}_{4}}$$
(12.33)
$${{{\phi}}}_{4}=\frac{{{{Q}}}_{5}}{{{{Q}}}_{1}+{{{Q}}}_{2}+{{{Q}}}_{3}+{{{Q}}}_{4}+{{{Q}}}_{5}}$$
(12.34)

3.5 PEM Electrolyzer Equations

The structure of PEM electrolyzer is drawn in the bottom section of Fig. 12.1. The main relations of the PEM set-up are described comprehensively in our other works [24, 35].

3.6 Thermodynamic Assessment

The governing format of the energy and mass balance at steady state condition may be explained as below [28, 36,37,38]:

$$\sum {\dot{{{m}}}}_{{{i}}{{n}}}=\sum {\dot{{{m}}}}_{{{o}}{{u}}{{t}}}$$
(12.35)
$$\dot{{{Q}}}-\dot{{{W}}}=\sum {\dot{{{m}}}}_{{{o}}{{u}}{{t}}}{{{h}}}_{{{o}}{{u}}{{t}}}-\sum {\dot{{{m}}}}_{{{i}}{{n}}}{{{h}}}_{{{i}}{{n}}}$$
(12.36)

The energy performance of the suggested set-up is calculated from the summing the net generated power and produced hydrogen as products of the system divided by input heat as below:

$${{{\eta}}}_{{{e}}{{n}}}=\frac{(1-{{{\eta}}}_{{{G}}}) \cdot {\dot{{{W}}}}_{{{n}}{{e}}{{t}}}{+\boldsymbol{ }{{L}}{{H}}{{V}}}_{{{{H}}}_{2}} \cdot {\dot{{{m}}}}_{15}}{{\dot{{{Q}}}}_{{{t}}{{o}}{{t}}{{l}}{{a}}}}$$
(12.37)

where, \({\dot{{{Q}}}}_{{{t}}{{o}}{{t}}{{a}}{{l}}}\) is the scramjet’s whole cooling utilized as the system heat source.

Some of the important thermodynamic relations which extracted from energy balance are tabulated in Table 12.1.

Table 12.1 Energy balance relations for each constituents of the recommended unit
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Total exergy rate (\({\dot{{{E}}{{x}}}}_{{{t}}{{o}}{{t}}{{a}}{{l}}}\)) has four major part: physical exergy (\({\dot{{{E}}{{x}}}}_{{{P}}{{H}}}\)), potential exergy (\({\dot{{{E}}{{x}}}}_{{{P}}{{T}}}\)), kinetic exergy (\({\dot{{{E}}{{x}}}}_{{{K}}{{N}}}\)), and chemical exergy rate (\({\dot{{{E}}{{x}}}}_{{{C}}{{H}}}\)) [38, 39]:

$${\dot{{{E}}{{x}}}}_{{{t}}{{o}}{{t}}{{a}}{{l}}}={\dot{{{E}}{{x}}}}_{{{P}}{{H}}}+{\dot{{{E}}{{x}}}}_{{{P}}{{T}}}{+\dot{{{E}}{{x}}}}_{{{K}}{{N}}}+{\dot{{{E}}{{x}}}}_{{{C}}{{H}}}$$
(12.38)

Also, potential and kinetic exergies can be assumed negligible. The physical and chemical exergies are given as below [40]:

$${\dot{{{E}}{{x}}}}_{{{P}}{{H}}}=\dot{{{m}}}\left({{h}}-{{{h}}}_{0}-{{{T}}}_{0}({{s}}-{{{s}}}_{0})\right)$$
(12.39)
$${\dot{{{E}}{{x}}}}_{{{C}}{{H}}}=\dot{{{m}}}\left[\sum_{{{i}}=1}^{{{n}}}{{{y}}}_{{{i}}}{{{e}}{{x}}}_{{{C}}{{H}},{{i}}}^{0}+{{R}}{{{T}}}_{0}\sum_{{{i}}=1}^{{{n}}}{{{y}}}_{{{i}}}\mathbf{ln}{{{y}}}_{{{i}}}\right]$$
(12.40)

For each constituent, the exergy balance relation is denoted as [39, 41]:

$${\dot{{{E}}{{x}}}}_{{{F}}}^{{{i}}}={\dot{{{E}}{{x}}}}_{{{P}}}^{{{i}}}+{\dot{{{E}}{{x}}}}_{{{D}}}^{{{i}}}$$
(12.41)

In the above equation, \({\dot{{{E}}{{x}}}}_{{{D}}}^{{{i}}}\) is the exergy destruction,\({\dot{{{E}}{{x}}}}_{{{P}}}^{{{i}}}\) and \({\dot{{{E}}{{x}}}}_{{{F}}}^{{{i}}}\) are product and fuel exergies, respectively.

Exergetic efficiency of the constituents is written as:

$${{{\eta}}}_{{{e}}{{x}}}^{{{i}}}={\dot{{{E}}{{x}}}}_{{{P}}}^{{{i}}}/{\dot{{{E}}{{x}}}}_{{{F}}}^{{{i}}}$$
(12.42)

Destruction rate of each component can be expressed by exergy destruction ratio as below [39]:

$${{{Y}}}_{{{D}},{{i}}}={\dot{{{E}}{{x}}}}_{{{D}},{{i}}}/{\dot{{{E}}{{x}}}}_{{{D}},{{t}}{{o}}{{t}}{{a}}{{l}}}$$
(12.43)

The overall exergetic efficiency of the set-up can be written as following

$${{{\eta}}}_{{{e}}{{x}}}^{{{total}}}={\dot{{{E}}{{x}}}}_{{{P}}}^{{{total}}}/{\dot{{{E}}{{x}}}}_{{{F}}}^{{{total}}}$$
(12.44)

Some of the necessary exergy relations of the recommended set-up is tabulated in Table 12.2

Table 12.2 Exergy equations of the main components of the simulated system
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3.7 Multi-criteria Optimization

In this investigation, optimization procedure is applied to maximize the energy and exergy efficiencies simultaneously. The multi-criteria optimization procedure is utilized via genetic algorithm (GA) which is a strong approach compared to other methods [42].

Two Thermodynamics factor, consisting of the energy and exergy efficiencies have been determined as objective functions, while the six parameters are presented as the prominent decision variables. The multi-criteria function is presented in Eq. (12.45), and the major target of optimization is maximizing the suggested function.

$${{M}}{{a}}{{x}}\left({{M}}{{C}}{{F}}={{{w}}}_{1}\times {{{\eta}}}_{{{e}}{{n}}}+{{{w}}}_{2}\times {{{\eta}}}_{{{e}}{{x}}}\right),$$
(12.45)
$${w}_{1}+{w}_{2}=1 , 0\le {w}_{1},{w}_{2}\le 1$$
$$200\le {{{T}}}_{1}\left({{K}}\right)\le 250$$
$$200\le {{{T}}}_{15}\left({{K}}\right)\le 250$$
$$0.1\le {{{P}}}_{1}\left({{M}}{{P}}{{a}}\right)\le 0.4$$
(12.46)
$$15\le {{{P}}}_{2}\left({{M}}{{P}}{{a}}\right)\le 25$$
$$5\le {{{M}}{{a}}{{c}}{{h}}}_{{{A}}}\le 7$$
$$0.5\le {{\eta}}_{{{G}}}\le 0.7$$

Moreover, Table 12.3 shows some main accountable parameters applied in the GA.

Table 12.3 Some main accountable parameters applied in the GA [43,44,45,46]
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4 Result and Arguments

Based on coding in EES software, the recommended set-up is analyzed from energy and exergy standpoint. Table 12.4 expressed the initial parameters for modeling the set-up. The calculated outcomes regarding to prominent thermodynamic flow properties are written in Table 12.5. The properties consist of pressure, temperature, mass flow rate, enthalpy, entropy, and exergy rate at each state.

Table 12.4 Input data for simulation of the set-up
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Table 12.5 Thermodynamic properties in each state of the set-up
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4.1 Results of Thermodynamic Simulation

This section reveals the results of simulation, in which 4840 kW and 59.45 kg/h power and hydrogen are produced and 13.87% total energy efficiency is achieved for uniform condition of \({{m}}=0.4\,\,\mathrm{kg}/\mathrm{s}\), \({{{M}}{{a}}}_{{{A}}}=6,\,\,{{{T}}}_{{{A}}}=223\,\text{K},\,\,{{{P}}}_{{{A}}}=2.56\,\text{kPa}\) when 65% of the generated electricity is consumed in the PEM electrolyzer. The quantity of hydrogen production is satisfying compared to that of other similar systems, which can be widely used in aerospace industry (Table 12.6).

Table 12.6 The outcomes of the energy assessment
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Table 12.7 and Fig. 12.4 demonstrate the results of exergy analysis. Accordingly, the overall exergy efficiency is 17.48%, and the PEM electrolyzer and the first cooling pas-sage account for the highest exergy destruction, with 72.47% and 10.67% proportional exergy destruction ratio caused by chemical reaction and high temperature difference, respectively [47]. There is a direct relation between the temperature difference and exergy destruction [39]. Also, the highest exergy efficiency belongs to the pump in the system.

Table 12.7 Exergy results of the equipment
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Fig. 12.4
figure 4

Diagram of exergy destruction in different fixtures of the system

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4.2 Optimization Results

In this section, optimized outcomes are reported and the comparison be-tween base scenario and multi-criteria optimizing scenario (MCO) have been presented in the Fig. 12.5. Accordingly, the energy efficiency increases from 13.87% to 20.7% (49.24% improvement) and exergy efficiency rises from 17.87% to 26.09% (45.98% improvement). Also. The last column of the results shows the optimized amounts of decision variables.

Fig. 12.5
figure 5

Comparison of major parameters for base and optimum scenarios

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5 Noteworthy Conclusions

In our previous work [19] a novel M-OCC system is proposed and its analytic modeling developed. The previous study showed that the proposed system not only is able to aid scramjet in managing the heat properly but also has great potential in producing other variant useful energy forms such as electric power and hydrogen as fuel, by recovering a useless waste heat. Accordingly, the necessity of conducting a research work to improve the performance of the proposed system is comprehensible. Thus the present study focused on the optimization of novel M-OCC system. The present study had been accomplished to have a better understanding from the system's operation. The following outlines can be expressed as brief:

  • The energy efficiency of the system have been increased from 13.87 to 20.7%.

  • The exergy efficiency of the system have been increased from 17.87 to 26.09%.

  • The overall improvement of the system performance is more than 45% which is really considerable.