# Research on Simulation and Performance Optimization of Mach 4 Civil Aircraft Propulsion Concept

Authors: Min Chen; Zihao Jia; Hailong Tang; Yi Xiao; Yonghang Yang; Feijia Yin
Journal: International Journal of Aerospace Engineering
 (2019)

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## Abstract

Supersonic civil aircraft is of a promising area in the development of future civil transport, and aircraft propulsion system is one of the key issues which determine the success of the aircraft. To get a good conceptual design and performance investigation of the supersonic civil aircraft engine, in this article, a fast, versatile as well as trust-worthy numerical simulation platform was established to analyze the Mach 4 turbine-based combined cycle (TBCC) engine concept so as to be applied to the supersonic civil aircraft. First, a quick and accurate task requirement analysis module was newly established to analyze the mission requirement of the Mach 4 supersonic civil aircraft. Second, the TBCC engine performance simulation model was briefly presented and the number of engines on the supersonic civil aircraft was analyzed, considering single engine inoperative. Third, the Stone model and the DLR method were investigated to estimate the engine jet noise and the NOx emission of the Mach 4 supersonic civil aircraft. Finally, a multiobjective optimization tool made up of a response surface method and a genetic algorithm was developed to optimize the design parameters and the control law of the TBCC engine, in order to make the Mach 4 supersonic civil aircraft engine with better performance, lower noise, and lower emissions. The uniqueness of the developed analysis tool lies in that it affords a numerical simulation platform capable of investigating the task requirement analysis module of the supersonic civil aircraft, engine jet noise prediction model, and the NOx emission prediction model, as well as a multiobjective performance optimization tool, which is beneficial for the conceptual design and performance research of Mach 4 supersonic civil aircraft’s propulsion system.


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## Body

## 1. Introduction

Supersonic civil aircraft with higher speed can offer significant time savings in the long-range flight compared with the subsonic one. With the stop of the Concorde operation since 2003, the first generation of the supersonic civil aircraft has become a history. However, as the international communication is becoming more and more frequent, the long-range and short-time flight has a promising market potential. Research has shown that the supersonic civil aircraft could capture up to seventy percent of the long-haul markets in cases where it can offer significant time savings over a long-range subsonic aircraft [1]. For the broad market prospect, many aviation powers began to develop the supersonic civil aircraft. For example, America proposed the plan for high-speed civil transport aircraft, such as the supersonic transport (SST) and high-speed research (HSR) [2]. Europe put the first supersonic commercial aircraft into operation, which was stopped in 2003 due to the factors of safety consideration, economy, and noise problem, but it achieved in getting experience of the development in the supersonic aircraft production and the market operation. After that, a Long-Term Advanced Propulsion Concepts and Technologies (LAPCAT) program has been advanced for the supersonic passenger aircraft in Europe since 2005. Russia and Japan are also interested in the development of the supersonic civil aircraft, such as Russian T244, T344 development plans, Japanese National Experimental Supersonic Transport (NEXST), and hypersonic transport propulsion system research (HYPR) plans.Because the supersonic vehicles have a wide flight Mach range, the propulsion technology is one of the most important challenges in the process of meeting the flight mission requirement. Figure1 shows the specific impulse (Isp) comparison between different propulsion types with Mach number variation [3], where RBCC means a rocket-based combined cycle and specific impulse (Isp) means the thrust produced by the unit mass of propellant. From the chart, it is known that when the Mach number is from 0 to 3, the turbine engine has the highest specific impulse. When the Mach number varies from 3 to a higher level, the ramjet engine has the highest specific impulse. Since the supersonic civil aircraft has to operate from take-off to Mach number 5, the TBCC engine is one of the most optimal engine types, combined of the turbofan engine and the ramjet engine. Then, Figure 2 shows two typical TBCC engine configurations. Among these, the parallel type has independent engine operating modes due to the separate gas paths, greater windward area, and volume. In contrast with the parallel type, the tandem type has the advantages of more compact structure, lighter quality, and more complicated matching of aerodynamic performance to satisfy the wide flight range. Thus, this article selects the tandem-type TBCC engine (Figure 2(b)) as the research object.Figure 1
Specific impulse comparison between different propulsion types with Mach number variation [3].Figure 2
Two typical TBCC engine configurations ((a) parallel type; (b) tandem type).
(a)
(b)A variety of new generation supersonic civil aircraft concepts have been put forward in some literatures [4–21], for example, the conceptual design of Mach 5 TBCC engine which is applied into the supersonic civil aircraft has been investigated [22]. However, for Mach 5 TBCC engine, the inlet adjustment is more complicated, and the total inlet temperature can reach around 1300 K. So, it is more challenging to solve the airframe thermal protection problem based on the existing material and technology, due to the high stagnant temperature due to extremely high Mach. Meanwhile, the engine matching problem with the inlet and exhaust system under a wide flight Mach range also causes great troubles. Apart from these, assuming that the flight mission profile [22] is the same, with the increase of the Mach number, the time savings gradually decrease as shown in Figure 3. For example, the distance of the trans-Pacific flight from Shanghai to New York is about 13,800 km. According to Figure 3, the journey time for the Mach 5 supersonic civil aircraft is only about half an hour less than Mach 4. Thus, considering the above factors and referring to the requirements of the aircraft designers, in this article, the cruise Mach number of the supersonic civil aircraft is changed from Mach 5 to Mach 4.Figure 3
The flight time contrast at different speeds.In this article, a fast, versatile, and trustworthy numerical simulation platform has been established to analyze the Mach 4 TBCC engine concept for the supersonic civil aircraft, which includes the newly developed task requirement analysis module of the supersonic civil aircraft, engine jet noise, and the NOx emission prediction models, as well as a multiobjective optimization tool based on the response surface methodology. Firstly, Section 2 establishes the calculation module, which is used to analyze the mission requirement of the Mach 4 supersonic civil aircraft. Then, Section 3 presents the TBCC engine performance simulation module briefly and analyzes the number of engines for the supersonic civil aircraft, considering single engine inoperative. The two following sections conduct studies on the quick and trusted prediction models used to estimate the engine jet noise and the NOx emission of the supersonic civil aircraft. Section 6 proposes the multiobjective optimization tool to optimize the design parameters and control laws of the TBCC engine, in order to make the Mach 4 supersonic civil aircraft engine with better performance, lower noise, and lower emissions.


## 2. Task Requirement Analysis of the Mach 4 Supersonic Civil Aircraft

To put the concept design of the next generation supersonic civil aircraft and its propulsion system into practise, the mission requirement is essential, such as the cruise speed, the flight range, and the passenger capacity. To meet the major long-distance travel market requirement in China and to demonstrate the superior performance in time saving, trans-Pacific (from mainland China to United States West Coast), relative short-travelling-time (less than 4 hours) flight is of requirement. This mission requirement emphasizes that the range should be above 10,000 km according to the range survey in Figure4.Figure 4
Range survey.For all the aircraft concepts, economy is one of the most important factors that must be considered into the preliminary design stage. So, we use the fuel efficiency figure of merit (FOM) to evaluate the economy and define FOM as follows.(1)FOM=PAX⋅RWFblock,where PAX means passenger number, R means range, and WFblock means block fuel weight.Another important factor which must be considered in the preliminary design stage is take-off gross weight (WTO), because it is relative to the requirement of the propulsion system and can also meet the demand of an airport.However, in the previous investigations of the new generation supersonic civil aircraft, such as the 250-passenger, Mach 4 high-speed civil transport [4], influence that details of some important input parameters on FOM and WTO are not given, and these important parameters include flight range (R) and PAX, two technical parameters—cruise lift-to-drag ratio (L/D) and cruise specific fuel consumption (SFC). So, this section will analyze the influences of the important parameters on FOM and WTO, in order to analyze the task requirements of the Mach 4 supersonic civil aircraft. The published research data of the related supersonic civil aircraft are summarized in Table 1 [1, 3–5].Table 1
Data survey of the concept scheme of the supersonic civil aircraft [1, 3–5, 18, 19].
Ma
R (km)
PAX
WTO (kg)
WPL (kg)
WOE (kg)
WF (kg)
WPL/PAX (kg)
FOM (PAX·km/kg)
Mach 3
3.0
12,038
250
323,727
24,864
123,822
175,043
99
19.9
Mach 4
4.0
12,038
251
392,656
24,963
138,678
229,015
99
14.9
HSCT BOE MFTF5093
2.4
9260
300
320,051
29,433
124,141
166,477
98
18.8
HSCT BOE ACE701510
2.4
9260
300
323,914
29,434
123,918
170,562
98
18.5


### 2.1. Aircraft Preliminary Weight Estimation Method

In order to analyze the parameter FOM which is related toWFblock and WTO, we propose a preliminary aircraft weight estimation method.Generally,WTO consists of payload (WPL) and total fuel weight (WF) which includes WFblock and reserve fuel weight (WFreserve), as well as operating empty weight (WOE), shown as follows.
(2)WTO=WPL+WF+WOE.It can be rewritten as follows.(3)WTO=WPL1−WF/WTO−WOE/WTO.In3, WF/WTO means fuel weight coefficient, which is replaced by mf. WOE/WTO with the meaning of the operating empty weight coefficient is replaced by moe. Details of payload, total fuel weight, and operating empty weight estimation are presented as below.


#### 2.1.1. Payload (WPL)

Weight of each passenger including baggage is assumed to be 98 kg according to the existing research of the related supersonic civil aircraft in Table1 [1, 3–5]. If PAX is given, WPL can be calculated by using the following equation.
(4)WPL=98×PAX.


#### 2.1.2. Total Fuel Weight (WF)

Accurate estimation method of total fuel weight needs to split the flight profiles into many small sections, then integrate the fuel consumption of each section. However, this estimation method needs unavailable parameters of the aircraft and propulsion system at different flight conditions.In order to estimateWF quickly, it is divided into two parts—WFblock and WFreserve.ForWFblock, the flight mission profiles are segmented into 7 sections [23]: engine start and warm-up, taxi out, take-off, climb, cruise, descent, and taxi in. Ratio of aircraft weight (ROWi) (i = 1, 2, 3, 4, 5, 6, 7) is defined as ROWi=Wi/Wi−1, where Wi is the aircraft weight at the ending of one section, Wi−1 is the one at the start of this section, and W0 is WTO. For the 5th section, the ratio of cruise section is also written as ROWc. Then, the proportion of WFblock devoted to WTO is shown as follows.
(5)WFblockWTO=1−∏i=1i=7ROWi.ROWc can be gotten through Breguet range equation shown as follows.
(6)Rc=V0gSFCLDlnWstartWend=V0gSFCLDln1ROWc,where Rc is the range of the cruise section (km), g is gravity constant (m/s2), L/D is the cruise lift-to-drag ratio, SFC is cruise specific fuel consumption (kg/h/N), V0 is cruise velocity (km/h), Wstart is aircraft weight at the start of the cruise section, and Wend is aircraft weight at the end of the cruise section. And the relevant parameters for calculating WF are listed in Table 2. For long-range flight, noncruise range (Rnc) occupies 9.36% of the total range according to one investigated supersonic civil aircraft concept [3] and then Rc is 90.64% of the total range (R).Table 2
Values of relevant parameters for calculatingWF [1, 3–5].
RncR
RcR
ROWnc
WFreserveWTO
9.36%
90.64%
0.8584
6.51%For the noncruise sections, we multiply each noncruise section’sROWi written as ROWnc, as follows.
(7)ROWnc=ROW1×ROW2×ROW3×ROW4×ROW5×ROW6×ROW7.ROWnc is a given value referring to the relevant research of the supersonic civil aircraft [3]. So WFblock can be got by allying (5)~(7). For WFreserve, it is 6.51% of WTO which is given according to the statistical data of the supersonic civil aircraft [1, 3–5].So, fuel weight coefficientmf can be calculated as follows.
(8)mf=WFWTO=WFblockWTO+WFreserveWTO=1−∏i=1i=7ROWi+WFreserveWTO=1−ROWc+ROWnc+0.0651.Thus,WF can be calculated as follows:
(9)WF=mf×WTO.


#### 2.1.3. Operating Empty Weight (WOE)

WOE is commonly got by building the relation with WTO [23, 24]. According to the existing research data of the related supersonic civil aircraft in Table 1 [1, 3–5], the fitted relation is shown in Figure 5.Figure 5
The relation betweenmoe and WTO of the supersonic civil aircraft.So,WOE can be calculated as follows.
(10)WOE=moe×WTO,where moe signifies operating empty weight coefficient. The whole process of aircraft preliminary weight estimation is shown in Figure 6, which involves an iteration process.Figure 6
Aircraft preliminary weight estimation flow chart.


### 2.2. The Influence Analysis of PAX and SFC on FOM andWTO

Based on the related supersonic civil aircraft investigation [10], the Mach 4 supersonic reference cruise L/D is 7.79. Moreover, according to the existing research of the TBCC engine [22], Mach 4 TBCC engine reference cruise SFC is 2.00 kg/h/daN. By using the introduced aircraft preliminary weight estimation method and definition of FOM, influence of PAX and R on FOM and WTO is shown in Figure 7.Figure 7
Influence ofR and PAX on FOM and WTO.From the above figure, ifR keeps invariant, increasing PAX makes both FOM and WTO increase directly. According to the definition of FOM, it will be influenced by R, PAX, and WFblock. Increase of PAX makes both FOM and WFblock increase immediately. But the increase of WFblock results in the decrease of FOM. However, the effect of PAX outweighs the opposite effect of WFblock on FOM. Thus, in fact FOM is rising with the increase of PAX.IfPAX keeps constant, the increase of R makes FOM reduce and WTO increase, because the increase of R naturally makes WF and WOE increase, thus making WTO growing. Incremental R makes WFblock increase therefore makes FOM decrease. According to Figure 7, both R and PAX have severe influences on FOM and WTO.Because aircraft cruiseL/D and propulsion system cruise SFC represent the technical level of the aircraft and engine. The influences of the aircraft cruise L/D and engine cruise SFC on FOM and WTO should also be analyzed. The reference concept (R = 10,000 km, PAX = 300) should be treated as the research object. While in the reference concept, influences of cruise L/D and cruise SFC on FOM and WTO are shown in Figure 8.Figure 8
Influences of cruiseL/D and cruise SFC on FOM and WTO.
(a)
(b)As shown in Figure8(a), when cruise SFC keeps constant, increasing cruise L/D makes FOM increase and WTO decrease, vice versa. While on shown in Figure 8(b), if cruise L/D keeps constant, SFC reduction makes FOM increase and WTO reduce, vice versa. Both cruise L/D and cruise SFC have significant influence on FOM and WTO. Based on preceding analysis, improving cruise L/D and reducing cruise SFC are an effective method in reducing supersonic civil aircraft weight and improving the economy.


### 2.3. Sensitivity Analysis of Uncertain Variables on FOM andWTO

In the above shown aircraft preliminary weight estimation method, the noncruise ratio of aircraft weight (ROWnc) and the ratio of noncruise to total range (Rnc/R) are given as constant values, where ROWnc is 85.84% and Rnc/R is 9.36%. However, ROWnc and Rnc/R of different aircraft with different climbing and descent strategies are in a changing state. Thus, it is necessary to make sensitivity analysis of uncertain variables on FOM and WTO.Let reference concept (PAX = 300, R = 10,000 km, cruise L/D = 7.79, cruise SFC = 2.00 kg/h/daN, ROWnc = 85.84%, and Rnc/R = 9.36%) be a benchmark, the influences of ROWnc and Rnc/R on FOM and WTO are analyzed as shown in Figure 9.Figure 9
Sensitivity analysis ofROWnc and Rnc/R.From the figure, it can be seen thatROWnc has a great influence on both FOM and WTO. For example, −1% change of ROWnc makes FOM −4% and WTO +3%. Rnc/R also has certain influence on FOM and WTO but not as prominent as ROWnc. For example, +1% of Rnc/R makes FOM about +0.2% and WTO about −0.2%. Although ROWnc and Rnc/R have influence on absolute calculation results, they do not affect the trend of FOM and WTO resulting from the variation of PAX, R, cruise L/D, and cruise SFC. In the future in-depth investigation, accurate values of ROWnc and Rnc/R are needed to make the result more precise.Thus, to get a supersonic civil aircraft concept for trans-Pacific and relative short-travelling-time flight,R and PAX are recommended to be 10,000 km and 300 persons, respectively, which makes FOM 14.8 PAX·km/kg and WTO 407 tons.


## 2.1. Aircraft Preliminary Weight Estimation Method

In order to analyze the parameter FOM which is related toWFblock and WTO, we propose a preliminary aircraft weight estimation method.Generally,WTO consists of payload (WPL) and total fuel weight (WF) which includes WFblock and reserve fuel weight (WFreserve), as well as operating empty weight (WOE), shown as follows.
(2)WTO=WPL+WF+WOE.It can be rewritten as follows.(3)WTO=WPL1−WF/WTO−WOE/WTO.In3, WF/WTO means fuel weight coefficient, which is replaced by mf. WOE/WTO with the meaning of the operating empty weight coefficient is replaced by moe. Details of payload, total fuel weight, and operating empty weight estimation are presented as below.


### 2.1.1. Payload (WPL)

Weight of each passenger including baggage is assumed to be 98 kg according to the existing research of the related supersonic civil aircraft in Table1 [1, 3–5]. If PAX is given, WPL can be calculated by using the following equation.
(4)WPL=98×PAX.


### 2.1.2. Total Fuel Weight (WF)

Accurate estimation method of total fuel weight needs to split the flight profiles into many small sections, then integrate the fuel consumption of each section. However, this estimation method needs unavailable parameters of the aircraft and propulsion system at different flight conditions.In order to estimateWF quickly, it is divided into two parts—WFblock and WFreserve.ForWFblock, the flight mission profiles are segmented into 7 sections [23]: engine start and warm-up, taxi out, take-off, climb, cruise, descent, and taxi in. Ratio of aircraft weight (ROWi) (i = 1, 2, 3, 4, 5, 6, 7) is defined as ROWi=Wi/Wi−1, where Wi is the aircraft weight at the ending of one section, Wi−1 is the one at the start of this section, and W0 is WTO. For the 5th section, the ratio of cruise section is also written as ROWc. Then, the proportion of WFblock devoted to WTO is shown as follows.
(5)WFblockWTO=1−∏i=1i=7ROWi.ROWc can be gotten through Breguet range equation shown as follows.
(6)Rc=V0gSFCLDlnWstartWend=V0gSFCLDln1ROWc,where Rc is the range of the cruise section (km), g is gravity constant (m/s2), L/D is the cruise lift-to-drag ratio, SFC is cruise specific fuel consumption (kg/h/N), V0 is cruise velocity (km/h), Wstart is aircraft weight at the start of the cruise section, and Wend is aircraft weight at the end of the cruise section. And the relevant parameters for calculating WF are listed in Table 2. For long-range flight, noncruise range (Rnc) occupies 9.36% of the total range according to one investigated supersonic civil aircraft concept [3] and then Rc is 90.64% of the total range (R).Table 2
Values of relevant parameters for calculatingWF [1, 3–5].
RncR
RcR
ROWnc
WFreserveWTO
9.36%
90.64%
0.8584
6.51%For the noncruise sections, we multiply each noncruise section’sROWi written as ROWnc, as follows.
(7)ROWnc=ROW1×ROW2×ROW3×ROW4×ROW5×ROW6×ROW7.ROWnc is a given value referring to the relevant research of the supersonic civil aircraft [3]. So WFblock can be got by allying (5)~(7). For WFreserve, it is 6.51% of WTO which is given according to the statistical data of the supersonic civil aircraft [1, 3–5].So, fuel weight coefficientmf can be calculated as follows.
(8)mf=WFWTO=WFblockWTO+WFreserveWTO=1−∏i=1i=7ROWi+WFreserveWTO=1−ROWc+ROWnc+0.0651.Thus,WF can be calculated as follows:
(9)WF=mf×WTO.


### 2.1.3. Operating Empty Weight (WOE)

WOE is commonly got by building the relation with WTO [23, 24]. According to the existing research data of the related supersonic civil aircraft in Table 1 [1, 3–5], the fitted relation is shown in Figure 5.Figure 5
The relation betweenmoe and WTO of the supersonic civil aircraft.So,WOE can be calculated as follows.
(10)WOE=moe×WTO,where moe signifies operating empty weight coefficient. The whole process of aircraft preliminary weight estimation is shown in Figure 6, which involves an iteration process.Figure 6
Aircraft preliminary weight estimation flow chart.


## 2.1.1. Payload (WPL)

Weight of each passenger including baggage is assumed to be 98 kg according to the existing research of the related supersonic civil aircraft in Table1 [1, 3–5]. If PAX is given, WPL can be calculated by using the following equation.
(4)WPL=98×PAX.


## 2.1.2. Total Fuel Weight (WF)

Accurate estimation method of total fuel weight needs to split the flight profiles into many small sections, then integrate the fuel consumption of each section. However, this estimation method needs unavailable parameters of the aircraft and propulsion system at different flight conditions.In order to estimateWF quickly, it is divided into two parts—WFblock and WFreserve.ForWFblock, the flight mission profiles are segmented into 7 sections [23]: engine start and warm-up, taxi out, take-off, climb, cruise, descent, and taxi in. Ratio of aircraft weight (ROWi) (i = 1, 2, 3, 4, 5, 6, 7) is defined as ROWi=Wi/Wi−1, where Wi is the aircraft weight at the ending of one section, Wi−1 is the one at the start of this section, and W0 is WTO. For the 5th section, the ratio of cruise section is also written as ROWc. Then, the proportion of WFblock devoted to WTO is shown as follows.
(5)WFblockWTO=1−∏i=1i=7ROWi.ROWc can be gotten through Breguet range equation shown as follows.
(6)Rc=V0gSFCLDlnWstartWend=V0gSFCLDln1ROWc,where Rc is the range of the cruise section (km), g is gravity constant (m/s2), L/D is the cruise lift-to-drag ratio, SFC is cruise specific fuel consumption (kg/h/N), V0 is cruise velocity (km/h), Wstart is aircraft weight at the start of the cruise section, and Wend is aircraft weight at the end of the cruise section. And the relevant parameters for calculating WF are listed in Table 2. For long-range flight, noncruise range (Rnc) occupies 9.36% of the total range according to one investigated supersonic civil aircraft concept [3] and then Rc is 90.64% of the total range (R).Table 2
Values of relevant parameters for calculatingWF [1, 3–5].
RncR
RcR
ROWnc
WFreserveWTO
9.36%
90.64%
0.8584
6.51%For the noncruise sections, we multiply each noncruise section’sROWi written as ROWnc, as follows.
(7)ROWnc=ROW1×ROW2×ROW3×ROW4×ROW5×ROW6×ROW7.ROWnc is a given value referring to the relevant research of the supersonic civil aircraft [3]. So WFblock can be got by allying (5)~(7). For WFreserve, it is 6.51% of WTO which is given according to the statistical data of the supersonic civil aircraft [1, 3–5].So, fuel weight coefficientmf can be calculated as follows.
(8)mf=WFWTO=WFblockWTO+WFreserveWTO=1−∏i=1i=7ROWi+WFreserveWTO=1−ROWc+ROWnc+0.0651.Thus,WF can be calculated as follows:
(9)WF=mf×WTO.


## 2.1.3. Operating Empty Weight (WOE)

WOE is commonly got by building the relation with WTO [23, 24]. According to the existing research data of the related supersonic civil aircraft in Table 1 [1, 3–5], the fitted relation is shown in Figure 5.Figure 5
The relation betweenmoe and WTO of the supersonic civil aircraft.So,WOE can be calculated as follows.
(10)WOE=moe×WTO,where moe signifies operating empty weight coefficient. The whole process of aircraft preliminary weight estimation is shown in Figure 6, which involves an iteration process.Figure 6
Aircraft preliminary weight estimation flow chart.


## 2.2. The Influence Analysis of PAX and SFC on FOM andWTO

Based on the related supersonic civil aircraft investigation [10], the Mach 4 supersonic reference cruise L/D is 7.79. Moreover, according to the existing research of the TBCC engine [22], Mach 4 TBCC engine reference cruise SFC is 2.00 kg/h/daN. By using the introduced aircraft preliminary weight estimation method and definition of FOM, influence of PAX and R on FOM and WTO is shown in Figure 7.Figure 7
Influence ofR and PAX on FOM and WTO.From the above figure, ifR keeps invariant, increasing PAX makes both FOM and WTO increase directly. According to the definition of FOM, it will be influenced by R, PAX, and WFblock. Increase of PAX makes both FOM and WFblock increase immediately. But the increase of WFblock results in the decrease of FOM. However, the effect of PAX outweighs the opposite effect of WFblock on FOM. Thus, in fact FOM is rising with the increase of PAX.IfPAX keeps constant, the increase of R makes FOM reduce and WTO increase, because the increase of R naturally makes WF and WOE increase, thus making WTO growing. Incremental R makes WFblock increase therefore makes FOM decrease. According to Figure 7, both R and PAX have severe influences on FOM and WTO.Because aircraft cruiseL/D and propulsion system cruise SFC represent the technical level of the aircraft and engine. The influences of the aircraft cruise L/D and engine cruise SFC on FOM and WTO should also be analyzed. The reference concept (R = 10,000 km, PAX = 300) should be treated as the research object. While in the reference concept, influences of cruise L/D and cruise SFC on FOM and WTO are shown in Figure 8.Figure 8
Influences of cruiseL/D and cruise SFC on FOM and WTO.
(a)
(b)As shown in Figure8(a), when cruise SFC keeps constant, increasing cruise L/D makes FOM increase and WTO decrease, vice versa. While on shown in Figure 8(b), if cruise L/D keeps constant, SFC reduction makes FOM increase and WTO reduce, vice versa. Both cruise L/D and cruise SFC have significant influence on FOM and WTO. Based on preceding analysis, improving cruise L/D and reducing cruise SFC are an effective method in reducing supersonic civil aircraft weight and improving the economy.


## 2.3. Sensitivity Analysis of Uncertain Variables on FOM andWTO

In the above shown aircraft preliminary weight estimation method, the noncruise ratio of aircraft weight (ROWnc) and the ratio of noncruise to total range (Rnc/R) are given as constant values, where ROWnc is 85.84% and Rnc/R is 9.36%. However, ROWnc and Rnc/R of different aircraft with different climbing and descent strategies are in a changing state. Thus, it is necessary to make sensitivity analysis of uncertain variables on FOM and WTO.Let reference concept (PAX = 300, R = 10,000 km, cruise L/D = 7.79, cruise SFC = 2.00 kg/h/daN, ROWnc = 85.84%, and Rnc/R = 9.36%) be a benchmark, the influences of ROWnc and Rnc/R on FOM and WTO are analyzed as shown in Figure 9.Figure 9
Sensitivity analysis ofROWnc and Rnc/R.From the figure, it can be seen thatROWnc has a great influence on both FOM and WTO. For example, −1% change of ROWnc makes FOM −4% and WTO +3%. Rnc/R also has certain influence on FOM and WTO but not as prominent as ROWnc. For example, +1% of Rnc/R makes FOM about +0.2% and WTO about −0.2%. Although ROWnc and Rnc/R have influence on absolute calculation results, they do not affect the trend of FOM and WTO resulting from the variation of PAX, R, cruise L/D, and cruise SFC. In the future in-depth investigation, accurate values of ROWnc and Rnc/R are needed to make the result more precise.Thus, to get a supersonic civil aircraft concept for trans-Pacific and relative short-travelling-time flight,R and PAX are recommended to be 10,000 km and 300 persons, respectively, which makes FOM 14.8 PAX·km/kg and WTO 407 tons.


## 3. Engine Performance Simulation Model and Selection of the Engine Number considering Single Engine Inoperative

### 3.1. TBCC Engine Performance Simulation Module

This section describes the performance simulation model of the TBCC engine on the Mach 4 supersonic civil aircraft [22]. A zero-dimensional (0D) variable cycle TBCC engine model controlled by multiple variables is developed to provide a platform suitable for parametric cycle analysis, performance cycle analysis, control law study of the turbofan mode, the ramjet mode, and turbofan/ramjet mode transition. The engine model is viewed as a set of interconnected gas components, whose performance is described in terms of characteristic maps or empirical formulas. And the specific configuration of the TBCC engine is shown as the tandem type (Figure 2(b)). The gas components are coupled together through the balance relationships that are summarized as below.
(1)
Power-balance equation for each rotor with the rotor inertia term (turbine power = compressor power + parasitic power + acceleration power)
(2)
Flow compatibility between the connected gas components
(3)
Assurance of static pressure balance at the mixing surface boundary of the duct and core flowsThen, a multidimensional Newton Raphson iteration technique was employed to simultaneously satisfy all the balance relation functions to achieve cycle balance at each operation point. Other important features of the engine module are shown below.(1)
Component characteristics of the fan, high pressure compressor (HPCP), low pressure turbine (LPTB), and RJAB were proved by the rig tests [1, 2, 25, 26]
(2)
The characteristics of the inlet and nozzle are acquired through the analytical design method, which will be discussed later
(3)
Gas property differences, caused by the variation of the gas ingredients, ambient temperature, and ambient humidity, were considered
(4)
Other factors were also taken into account, such as the effect of altitude, Mach number, extraction and return of cooling air, and power set aside for aircraft accessories
(5)
Combined operation performance of the five variable geometries can be simulatedFinally, the fidelity of this module has been evaluated by the published reference and it is able to meet the requirements of the TBCC engine concept design.


### 3.2. Selection of the Engine Number considering Single Engine Inoperative

This section calculates the number of engines for the Mach 4 supersonic civil aircraft, considering single engine inoperative. For the existing subsonic aircraft, the engine performance in the take-off and climbing state is extremely important. However, for the supersonic civil aircraft, the thrust requirement in the Mach 4 supersonic cruising state must be satisfied; otherwise, it will decelerate and descend. Thus, if one aircraft engine is inoperative in the cruising state, it will be required to find the right number of engine to land in an alternate airport.To simplify the research process, the following assumptions are made before the study:(1)
A single engine inoperative occurs at cruising condition (23 km,Ma 4)
(2)
Within the range of 0.05 reduction of the flight Mach, the deceleration and the fuel flow remain unchanged
(3)
During the aircraft deceleration process, lift = gravityCl×1/2ρ×V2×A=W×g, where A = 356.31 m2 (calculated by the cruising lift = gravity) remains the same
(4)
When the difference between the engine thrust and the required aircraft thrust is less than 1 N, the iteration is considered to be completedFigure10 shows the flow chart of the algorithm for single engine inoperative process analysis, where the lift coefficient and the lift to drag ratio need to be checked on the Mach altitude characteristic diagram.Figure 10
Single engine inoperative analysis flow chart.According to Figure11, it can be seen that the abscissa values of the intersection are both more than 3, which means the Mach 4 aircraft can resume cruising condition with one engine inoperable, before the TBCC engines back to the turbofan mode. Meanwhile, the difference of iteration step has limited influence (around 0.5%) on the computational accuracy for the abscissa values (Mach number), and ΔMa = 0.05 can reduce iterations. So, ΔMa = 0.05 is chosen as the iteration step size.Figure 11
Influence of deceleration interval onMa-F relation.The following figures present the analysis and comparison of double, three, and four engine schemes under single inoperative process. The different engine configurations lead to the different aircraft weights and demanding thrusts. From Figure12, it can be seen that when the scheme with double engines occurs single engine inoperative, the engines’ total thrust cannot satisfy the aircraft required thrust. The aircraft will decelerate and descend quickly. Then, the engine will become the turbofan mode, where the Mach number is less than 3. Moreover, the maximum thrust of single engine of the turbofan mode is far less than the aircraft demanding thrust, which means the aircraft will decelerate and descend quickly, unable to find an alternate airport safely. When the three-engine one occurs single engine inoperative, the aircraft will decelerate and descend at first. Nevertheless, the gap between the engine thrust and the aircraft demanding thrust narrows; then, it can fly at a constant speed to find an alternate airport safely around Ma 3.55. When the four-engine one occurs single engine inoperative, because of the little difference between the aircraft demanding thrust and engine thrust, the aircraft can fly at a constant speed to find an alternate airport safely around Ma 3.89.Figure 12
Curve ofMa-F (double, three, and four engines).Thus, after the above calculation and analysis, considering single engine inoperative, it can be observed that three or four TBCC engines are needed for the Mach 4 supersonic civil aircraft in order to find an alternative airport safely. Then, considering the balance of the engine layout on the aircraft, four TBCC engines is a better choice for the Mach 4 supersonic civil aircraft.According to the main operation points and thrust requirements of the studied supersonic civil aircraft scheme [26], the reference cruise L/D (7.79) of the Mach 4 supersonic aircraft [10], and the average climbing rate (30.5 m/s) of the Mach 4 supersonic aircraft scheme from NASA [27], the thrust requirements of TBCC engines for the Mach 4 supersonic civil aircraft are listed in Table 3.Table 3
Thrust requirements of the TBCC engine at main operation points.
H (km)
Ma
Operation mode
Thrust (kN)
Take-off
0
0
Turbofan
4 × 240.2
Climb
20.9
3
Turbofan (design point)
4 × 150.6
Climb
25.0
4
Ramjet (design point)
4 × 137.2
Cruise
25.0
4
Ramjet
4 × 114.2


## 3.1. TBCC Engine Performance Simulation Module

This section describes the performance simulation model of the TBCC engine on the Mach 4 supersonic civil aircraft [22]. A zero-dimensional (0D) variable cycle TBCC engine model controlled by multiple variables is developed to provide a platform suitable for parametric cycle analysis, performance cycle analysis, control law study of the turbofan mode, the ramjet mode, and turbofan/ramjet mode transition. The engine model is viewed as a set of interconnected gas components, whose performance is described in terms of characteristic maps or empirical formulas. And the specific configuration of the TBCC engine is shown as the tandem type (Figure 2(b)). The gas components are coupled together through the balance relationships that are summarized as below.
(1)
Power-balance equation for each rotor with the rotor inertia term (turbine power = compressor power + parasitic power + acceleration power)
(2)
Flow compatibility between the connected gas components
(3)
Assurance of static pressure balance at the mixing surface boundary of the duct and core flowsThen, a multidimensional Newton Raphson iteration technique was employed to simultaneously satisfy all the balance relation functions to achieve cycle balance at each operation point. Other important features of the engine module are shown below.(1)
Component characteristics of the fan, high pressure compressor (HPCP), low pressure turbine (LPTB), and RJAB were proved by the rig tests [1, 2, 25, 26]
(2)
The characteristics of the inlet and nozzle are acquired through the analytical design method, which will be discussed later
(3)
Gas property differences, caused by the variation of the gas ingredients, ambient temperature, and ambient humidity, were considered
(4)
Other factors were also taken into account, such as the effect of altitude, Mach number, extraction and return of cooling air, and power set aside for aircraft accessories
(5)
Combined operation performance of the five variable geometries can be simulatedFinally, the fidelity of this module has been evaluated by the published reference and it is able to meet the requirements of the TBCC engine concept design.


## 3.2. Selection of the Engine Number considering Single Engine Inoperative

This section calculates the number of engines for the Mach 4 supersonic civil aircraft, considering single engine inoperative. For the existing subsonic aircraft, the engine performance in the take-off and climbing state is extremely important. However, for the supersonic civil aircraft, the thrust requirement in the Mach 4 supersonic cruising state must be satisfied; otherwise, it will decelerate and descend. Thus, if one aircraft engine is inoperative in the cruising state, it will be required to find the right number of engine to land in an alternate airport.To simplify the research process, the following assumptions are made before the study:(1)
A single engine inoperative occurs at cruising condition (23 km,Ma 4)
(2)
Within the range of 0.05 reduction of the flight Mach, the deceleration and the fuel flow remain unchanged
(3)
During the aircraft deceleration process, lift = gravityCl×1/2ρ×V2×A=W×g, where A = 356.31 m2 (calculated by the cruising lift = gravity) remains the same
(4)
When the difference between the engine thrust and the required aircraft thrust is less than 1 N, the iteration is considered to be completedFigure10 shows the flow chart of the algorithm for single engine inoperative process analysis, where the lift coefficient and the lift to drag ratio need to be checked on the Mach altitude characteristic diagram.Figure 10
Single engine inoperative analysis flow chart.According to Figure11, it can be seen that the abscissa values of the intersection are both more than 3, which means the Mach 4 aircraft can resume cruising condition with one engine inoperable, before the TBCC engines back to the turbofan mode. Meanwhile, the difference of iteration step has limited influence (around 0.5%) on the computational accuracy for the abscissa values (Mach number), and ΔMa = 0.05 can reduce iterations. So, ΔMa = 0.05 is chosen as the iteration step size.Figure 11
Influence of deceleration interval onMa-F relation.The following figures present the analysis and comparison of double, three, and four engine schemes under single inoperative process. The different engine configurations lead to the different aircraft weights and demanding thrusts. From Figure12, it can be seen that when the scheme with double engines occurs single engine inoperative, the engines’ total thrust cannot satisfy the aircraft required thrust. The aircraft will decelerate and descend quickly. Then, the engine will become the turbofan mode, where the Mach number is less than 3. Moreover, the maximum thrust of single engine of the turbofan mode is far less than the aircraft demanding thrust, which means the aircraft will decelerate and descend quickly, unable to find an alternate airport safely. When the three-engine one occurs single engine inoperative, the aircraft will decelerate and descend at first. Nevertheless, the gap between the engine thrust and the aircraft demanding thrust narrows; then, it can fly at a constant speed to find an alternate airport safely around Ma 3.55. When the four-engine one occurs single engine inoperative, because of the little difference between the aircraft demanding thrust and engine thrust, the aircraft can fly at a constant speed to find an alternate airport safely around Ma 3.89.Figure 12
Curve ofMa-F (double, three, and four engines).Thus, after the above calculation and analysis, considering single engine inoperative, it can be observed that three or four TBCC engines are needed for the Mach 4 supersonic civil aircraft in order to find an alternative airport safely. Then, considering the balance of the engine layout on the aircraft, four TBCC engines is a better choice for the Mach 4 supersonic civil aircraft.According to the main operation points and thrust requirements of the studied supersonic civil aircraft scheme [26], the reference cruise L/D (7.79) of the Mach 4 supersonic aircraft [10], and the average climbing rate (30.5 m/s) of the Mach 4 supersonic aircraft scheme from NASA [27], the thrust requirements of TBCC engines for the Mach 4 supersonic civil aircraft are listed in Table 3.Table 3
Thrust requirements of the TBCC engine at main operation points.
H (km)
Ma
Operation mode
Thrust (kN)
Take-off
0
0
Turbofan
4 × 240.2
Climb
20.9
3
Turbofan (design point)
4 × 150.6
Climb
25.0
4
Ramjet (design point)
4 × 137.2
Cruise
25.0
4
Ramjet
4 × 114.2


## 4. Engine Jet Noise Prediction Model

For the new generation of the supersonic civil aircraft, the engine noise is an essential factor that should be taken into consideration during the schematic design phase so as to meet the airworthiness requirements. When the Mach 4 supersonic civil aircraft takes off, the TBCC engine works at the turbofan operating mode with the small bypass ratio, which causes quite high exhaust velocity. If the exhaust velocity is not restricted, it may cause the engine jet noise to dissatisfy the airworthiness requirements. Therefore, the engine jet noise prediction model is required to develop to assess the noise level of the concept. The index for evaluating the engine jet noise is the effective perceived noise level (EPNL), which can be calculated as shown in Figure13 [28]. Firstly, based on the estimation of the engine jet noise prediction spectrum diagram, the perceived noise level (PNL) and perceived noise level with the tone correction (PNLT) as well as the effective perceived noise level (EPNL) can be calculated successively. Before the estimation of EPNL, the noise requirements of the Mach 4 supersonic civil aircraft should be determined. Based on Section 2, for the Mach 4 supersonic civil aircraft, it needs 4 TBCC engines and the WTO is 407 tons (897,281 pounds). In view of this, EPNL should be less than 103 EPNdB to satisfy the noise requirements of FAR Part 36 [29].Figure 13
A simple procedure for estimating effective perceived noise levels from the spectrum.


### 4.1. Engine Jet Noise Spectrum Prediction Model

This model provides the estimation of the engine jet noise spectrum for the Mach 4 supersonic civil aircraft. The commonly used prediction models include Stone model, Pao model, SAE model, and improved ICAO model [30]. In order to simplify the calculation and ensure the fidelity of the prediction model, these models should be compared with each other in order to choose the most suitable one. After comparison, only the Stone model input parameters can be achieved directly by the existing engine performance program and the measuring point layout of airworthiness requirements. In addition, the establishment of the Stone model is simpler when compared with other models, and its accuracy is also worth of trust. So, this section will use the Stone model to predict the Mach 4 TBCC engine jet noise spectrum. The flow chart of the engine jet noise spectrum prediction can be shown as Figure 14. The assumption of the Stone model is that the shock wave noise spectrum graphs of inner and bypass jet are independent, which could be calculated by the jet noise prediction method, respectively. Then, the integrated noise spectrum could be achieved by the superposition of the jet mixed noise, inner nozzle shock wave noise, and bypass nozzle shock wave noise [31, 32].Figure 14
Prediction flow chart of the jet noise spectrum.


#### 4.1.1. Subsonic Jet Noise Spectrum Prediction Model

This model is the spectrum prediction of subsonic jet noise of the Mach 4 TBCC engine. From Figure14, it can be seen that the subsonic jet mixed noise can be divided into the inner jet noise and the bypass jet noise. Firstly, we should investigate the subsonic inner mixed jet noise spectrum which means the relation of the sound pressure level (SPL), the frequency parameter logS1, and the pole direction angle θ [33, 34]. And some of these parameters could be found in Table 4, which shows the relative position symbol of measuring point and nozzle.Table 4
Relative position symbol of measuring point and nozzle.
Variable
Significance
R
Length between nozzle and measuring point
θ, theta
Pole direction angle (angle between engine axis and line connecting measuring point and nozzle)
ψ, psi
Modified pole direction angle (θ)
α, alpha
Engine angle of attack (angle between engine axis and flight direction)According to the input parameters from the existing engine performance program and the measuring point layout of airworthiness requirements, in order to calculate SPL, the uncorrected overall sound pressure level (UOL1) should be calculated in advance using the following equation [33, 34].
(11)UOL1=141+10logρaρISA2⋅cacISA4+10logA1R2+10logρ1ρaω+10logVeca7.5−15log1+Mc⋅cosθ2+0.04⋅Mc2−10log1−M0⋅cosφ+3log2A1π⋅D12+12,where symbol ρa and ca means the density (kg/m3) and the speed of sound (m/s) under atmospheric environment, ρISA and cISA means the density (kg/m3) and the speed of sound (m/s) under standard atmospheric conditions, A1 means the exit area of the inner nozzle (m2), ρ1 means the density (kg/m3) of the inner jet, M0 means the flight Mach number, and D1 means the nozzle exit diameter (m). These cycle parameters and dimension parameters could be calculated by the existing TBCC engine model [22]. And coefficient ω is defined in (12). Ve means the effective velocity of inner jet, which can be calculated in (13). Mc means the convective Mach number, which is defined in (14).
(12)ω=3Ve/ca3.50.6+Ve/ca3.5−1,(13)Ve=V11−V0V1cosα2/3,(14)Mc=0.62V1−V0cosαca,where V0 and V1 means the speed of the aircraft and inner jet and α means the angle between engine axis and flight direction. When engine axis and measuring points are on the same horizontal vertical plane, it means that α=θ−Ψ.After the calculation of the uncorrected overall sound pressure level, in order to get the frequency parameterlogS1, the Strouhal number S1 should be calculated in advance as follows.
(15)S1=f4A1/πVeD14A1/π0.41−M0cosφ×1+0.62V1−V0/cacosθ2+0.01538V1−V0/ca21/21+0.62V1−V/cacosθ2+0.01538V1/ca21/2.Finally, according to the relation ofSPL, the frequency parameter logS and the pole direction angle θ [33, 34], by interpolation, the relation of SPL, frequency f, and angle θ, could be got, which means the subsonic inner jet noise spectrum could be achieved.According to Figure14, it can be seen that the subsonic jet noise spectrum includes the inner jet noise spectrum and the bypass jet noise spectrum. After the estimation of the inner jet noise spectrum, the bypass jet noise spectrum should be calculated, which means that the area ratio, the temperature ratio, and the velocity ratio of inner and bypass should be considered to correct the corresponding parameters [35, 36]. By using the same method, the double jet mixed noise spectrum is achieved. It is also found that the influence of the bypass jet on spectrum is mainly reflected on the deviation of peak frequency of the sound pressure level. However, there is no monotonous relationship between the velocity ratio and the frequency deviation parameters [31, 32]. The bypass jet only affects slightly the inner jet mixed noise spectrum since the given area ratios are limited. In addition, as far as tandem-type TBCC engine applied in this article [22] is considered, the engine jet noise spectrum prediction model merely considers the influence of inner single jet without the bypass jet.In order to evaluate the fidelity of the subsonic jet noise spectrum prediction model, the typical model-scale experimental data are selected as the reference in Table5 [37], whose engine configuration is the dual-stream exhaust system with the subsonic jet. Meanwhile, the prediction results of the subsonic jet noise spectrum are compared with subsonic jet noise experimental data shown in Figure 15, where T1, T2, V1, V2, A1, and A2 mean the temperature, speed, and area of inner and bypass nozzle exit, which are determined by the experimental condition of jet noise [37]. From Figure 15, it can be seen that the prediction results agree well with the published experimental data. So, it proves that the fidelity of this noise spectrum estimation model is able to meet the requirements of the prediction of the engine jet noise.Table 5
Subsonic jet noise spectrum experimental data [37].
Frequency (Hz)
SPL (dB)
101.5967
84.13
196.1021
90.27
483.4218
96.93
957.1784
101.47
1898.007
103.60
6007.91
102.00
9579.603
100.13Figure 15
The check of the subsonic jet noise spectrum.Calculation condition is as follows:θ, theta = 90°, T1 = 1129 K, V1 = 593 m/s, T2 = 280 K, V2 = 216 m/s, and A2/A1 = 3.2.
(16)A1=14πD12=14×π×0.12=0.00785m2.


#### 4.1.2. Supersonic Jet Noise Spectrum Prediction Model

This model provides the prediction method of calculating the supersonic jet noise spectrum. From Figure14, it can be seen that when compared with the subsonic jet, the supersonic jet noise could be divided into the jet mixed noise and the shock wave noise. In order to estimate the shock wave noise spectrum, which is similar to the subsonic jet mixed noise, the sound pressure level SPL, the frequency parameter logS1, and the pole direction angle θ should be calculated in advance.Firstly, the uncorrected overall sound pressure level of shock wave noise (UOLs,j) can be calculated as follows [33, 34].
(17)UOLs,j=162+10logρaρISA2⋅cacISA4+10AjR2+10logMj2−121+Mj2−12−10log1−M0⋅cosφ+F⋅θ−θM,where Aj means the exit area of nozzle (m2) and Mj means the jet Mach number, which could be calculated by the existing TBCC engine performance model [22]. And parameters θM and F are defined in (18) and (19), respectively.
(18)θM=180deg−sin−11Mj,(19)F==0θ≤θM,=−0.75θ>θM.Then, the Strouhal numberSs,j can be calculated as follows:
(20)Ss,j=fDj0.7VjMj2−11−M0cosφ×1+0.7Vjca2+0.0196Vjca2,where Dj and Vj mean the exit diameter of the nozzle and the speed of the jet, which could be calculated by the TBCC engine performance model [17]. Based on the similarity with the calculation of subsonic jet noise spectrum, the shock wave noise spectrum could be achieved.Next, referring to the computing method of the subsonic jet mixed noise spectrum, the spectrum of supersonic jet noise could be got. Finally, the supersonic comprehensive jet noise spectrum can be achieved by a superposition of the jet mixed noise, inner nozzle shock wave noise, and bypass nozzle shock wave noise [31, 36].Being similar to the verification of the subsonic jet noise spectrum, in order to evaluate the accuracy and availability of the supersonic jet noise spectrum prediction model, the typical model-scale experimental data are selected as the reference in Table6 [37], whose engine configuration is a dual-stream exhaust system with the supersonic jet. What is more, the prediction results of the supersonic jet noise spectrum are compared with the published experimental data shown in Figure 16, where M1 means the Mach number of inner jet and the calculation condition is determined by the experimental condition of jet noise [37]. From Figure 16, it can be observed that the prediction results also match well with the experimental results. So, it proves that the accuracy of this noise spectrum estimation model is able to meet the requirements of the prediction of the engine jet noise.Table 6
Supersonic jet noise spectrum experimental data [37].
Frequency (Hz)
SPL (dB)
125.4961
96.63934
197.6471
98.48361
398.1072
101.5574
1287.031
108.1148
2592.38
112.8279
4082.808
118.1557
5123.763
118.9754
6552.973
115.6967
8223.723
115.082
10,320.45
113.8525Figure 16
The check of the supersonic jet noise spectrum.Calculation condition is as follows:θ, theta = 95°, T1 = 1127 K, V1 = 790 m/s, M1 = 1.38, T2 = 283 K, V2 = 218 m/s, and A2/A1 = 1.9
(21)A1=14πD12=14×π×0.1012=0.00801m2.


### 4.2. The Prediction Method of an Effective Sensory Noise Level

From Figure10, it can be seen that after the jet noise spectrum prediction model is built, PNL, PNLT, and EPNL could be calculated successively to evaluate the engine jet noise [28].


#### 4.2.1. Perceived Noise Level (PNL)

Based on the jet noise spectrum, to estimate PNL, the function of frequency and sound pressure levelNi, as well as accumulative total noise Nt should be introduced, which can be defined in (22) and (23), respectively.
(22)N=0SPL<A1,10B1SPL−A1−1A1≤SPL<A2,10B2SPL−A2A2≤SPL<A3,10B3SPL−A3A3≤SPL<A4,10B4SPL−A4A4≤SPL<150,(23)Nt=Nmax+0.15∑i=124Ni−Nmax=0.85Nmax+0.15∑i=124Ni,where A1, B1, etc. are all coefficients, which are determined by the central frequency of 1/3 frequency range. PNL means the single numerical expression of the noise annoyance level, which can be calculated as follows.
(24)PNL=40.0+10log2logNt=40.0+33.22logNt.


#### 4.2.2. Perceived Noise Level with Tone Correction (PNLT)

Because human auditory system has the predilection for following a single tone rather than the wide-band noise in the adjacent frequency range, the perceived characteristic of the single tone should be considered. The purpose of single tone correction is to detect the pure tone which includes 1/3 frequency range and to correct its influence at the same time. To achieve PNLT, the specific steps are shown as follows:(1)
The second-order elementary errors should be calculated
(2)
IfSPLi is local maximum, the average noise level or background noise level and their differences should be calculated
(3)
The discrete frequency correctionC should be determined, and its maximum Cmax should be found
(4)
PNLT could be calculated as follows
(25)PNLT=PNL+Cmax.


#### 4.2.3. Effective Perceived Noise Level (EPNL)

The basic evaluation criterion for aircraft noise qualification is EPNL, which involves the sound level, the frequency distribution, and the time variation of noise. More concretely, it needs to record the instant SPL per 0.5-second interval. Meanwhile, the period of time around the maximum value of PNLT has the greatest impact on EPNL. However, due to the lack of specific take-off track, in this section, the calculation of EPNL needs to be simplified. It is assumed that in the range of time recording, the maximum PNLT almost has no difference with all other PNLT and they are equivalent, which means EPNL equals to PNLT.Thus, the jet noise prediction model is achieved, which can estimate EPNL fast and simply. And its input parameters can be provided by the TBCC engine performance model [22]. So, a quick and trusted model is established in this section to predict the Mach 4 supersonic civil aircraft engine jet noise level.


## 4.1. Engine Jet Noise Spectrum Prediction Model

This model provides the estimation of the engine jet noise spectrum for the Mach 4 supersonic civil aircraft. The commonly used prediction models include Stone model, Pao model, SAE model, and improved ICAO model [30]. In order to simplify the calculation and ensure the fidelity of the prediction model, these models should be compared with each other in order to choose the most suitable one. After comparison, only the Stone model input parameters can be achieved directly by the existing engine performance program and the measuring point layout of airworthiness requirements. In addition, the establishment of the Stone model is simpler when compared with other models, and its accuracy is also worth of trust. So, this section will use the Stone model to predict the Mach 4 TBCC engine jet noise spectrum. The flow chart of the engine jet noise spectrum prediction can be shown as Figure 14. The assumption of the Stone model is that the shock wave noise spectrum graphs of inner and bypass jet are independent, which could be calculated by the jet noise prediction method, respectively. Then, the integrated noise spectrum could be achieved by the superposition of the jet mixed noise, inner nozzle shock wave noise, and bypass nozzle shock wave noise [31, 32].Figure 14
Prediction flow chart of the jet noise spectrum.


### 4.1.1. Subsonic Jet Noise Spectrum Prediction Model

This model is the spectrum prediction of subsonic jet noise of the Mach 4 TBCC engine. From Figure14, it can be seen that the subsonic jet mixed noise can be divided into the inner jet noise and the bypass jet noise. Firstly, we should investigate the subsonic inner mixed jet noise spectrum which means the relation of the sound pressure level (SPL), the frequency parameter logS1, and the pole direction angle θ [33, 34]. And some of these parameters could be found in Table 4, which shows the relative position symbol of measuring point and nozzle.Table 4
Relative position symbol of measuring point and nozzle.
Variable
Significance
R
Length between nozzle and measuring point
θ, theta
Pole direction angle (angle between engine axis and line connecting measuring point and nozzle)
ψ, psi
Modified pole direction angle (θ)
α, alpha
Engine angle of attack (angle between engine axis and flight direction)According to the input parameters from the existing engine performance program and the measuring point layout of airworthiness requirements, in order to calculate SPL, the uncorrected overall sound pressure level (UOL1) should be calculated in advance using the following equation [33, 34].
(11)UOL1=141+10logρaρISA2⋅cacISA4+10logA1R2+10logρ1ρaω+10logVeca7.5−15log1+Mc⋅cosθ2+0.04⋅Mc2−10log1−M0⋅cosφ+3log2A1π⋅D12+12,where symbol ρa and ca means the density (kg/m3) and the speed of sound (m/s) under atmospheric environment, ρISA and cISA means the density (kg/m3) and the speed of sound (m/s) under standard atmospheric conditions, A1 means the exit area of the inner nozzle (m2), ρ1 means the density (kg/m3) of the inner jet, M0 means the flight Mach number, and D1 means the nozzle exit diameter (m). These cycle parameters and dimension parameters could be calculated by the existing TBCC engine model [22]. And coefficient ω is defined in (12). Ve means the effective velocity of inner jet, which can be calculated in (13). Mc means the convective Mach number, which is defined in (14).
(12)ω=3Ve/ca3.50.6+Ve/ca3.5−1,(13)Ve=V11−V0V1cosα2/3,(14)Mc=0.62V1−V0cosαca,where V0 and V1 means the speed of the aircraft and inner jet and α means the angle between engine axis and flight direction. When engine axis and measuring points are on the same horizontal vertical plane, it means that α=θ−Ψ.After the calculation of the uncorrected overall sound pressure level, in order to get the frequency parameterlogS1, the Strouhal number S1 should be calculated in advance as follows.
(15)S1=f4A1/πVeD14A1/π0.41−M0cosφ×1+0.62V1−V0/cacosθ2+0.01538V1−V0/ca21/21+0.62V1−V/cacosθ2+0.01538V1/ca21/2.Finally, according to the relation ofSPL, the frequency parameter logS and the pole direction angle θ [33, 34], by interpolation, the relation of SPL, frequency f, and angle θ, could be got, which means the subsonic inner jet noise spectrum could be achieved.According to Figure14, it can be seen that the subsonic jet noise spectrum includes the inner jet noise spectrum and the bypass jet noise spectrum. After the estimation of the inner jet noise spectrum, the bypass jet noise spectrum should be calculated, which means that the area ratio, the temperature ratio, and the velocity ratio of inner and bypass should be considered to correct the corresponding parameters [35, 36]. By using the same method, the double jet mixed noise spectrum is achieved. It is also found that the influence of the bypass jet on spectrum is mainly reflected on the deviation of peak frequency of the sound pressure level. However, there is no monotonous relationship between the velocity ratio and the frequency deviation parameters [31, 32]. The bypass jet only affects slightly the inner jet mixed noise spectrum since the given area ratios are limited. In addition, as far as tandem-type TBCC engine applied in this article [22] is considered, the engine jet noise spectrum prediction model merely considers the influence of inner single jet without the bypass jet.In order to evaluate the fidelity of the subsonic jet noise spectrum prediction model, the typical model-scale experimental data are selected as the reference in Table5 [37], whose engine configuration is the dual-stream exhaust system with the subsonic jet. Meanwhile, the prediction results of the subsonic jet noise spectrum are compared with subsonic jet noise experimental data shown in Figure 15, where T1, T2, V1, V2, A1, and A2 mean the temperature, speed, and area of inner and bypass nozzle exit, which are determined by the experimental condition of jet noise [37]. From Figure 15, it can be seen that the prediction results agree well with the published experimental data. So, it proves that the fidelity of this noise spectrum estimation model is able to meet the requirements of the prediction of the engine jet noise.Table 5
Subsonic jet noise spectrum experimental data [37].
Frequency (Hz)
SPL (dB)
101.5967
84.13
196.1021
90.27
483.4218
96.93
957.1784
101.47
1898.007
103.60
6007.91
102.00
9579.603
100.13Figure 15
The check of the subsonic jet noise spectrum.Calculation condition is as follows:θ, theta = 90°, T1 = 1129 K, V1 = 593 m/s, T2 = 280 K, V2 = 216 m/s, and A2/A1 = 3.2.
(16)A1=14πD12=14×π×0.12=0.00785m2.


### 4.1.2. Supersonic Jet Noise Spectrum Prediction Model

This model provides the prediction method of calculating the supersonic jet noise spectrum. From Figure14, it can be seen that when compared with the subsonic jet, the supersonic jet noise could be divided into the jet mixed noise and the shock wave noise. In order to estimate the shock wave noise spectrum, which is similar to the subsonic jet mixed noise, the sound pressure level SPL, the frequency parameter logS1, and the pole direction angle θ should be calculated in advance.Firstly, the uncorrected overall sound pressure level of shock wave noise (UOLs,j) can be calculated as follows [33, 34].
(17)UOLs,j=162+10logρaρISA2⋅cacISA4+10AjR2+10logMj2−121+Mj2−12−10log1−M0⋅cosφ+F⋅θ−θM,where Aj means the exit area of nozzle (m2) and Mj means the jet Mach number, which could be calculated by the existing TBCC engine performance model [22]. And parameters θM and F are defined in (18) and (19), respectively.
(18)θM=180deg−sin−11Mj,(19)F==0θ≤θM,=−0.75θ>θM.Then, the Strouhal numberSs,j can be calculated as follows:
(20)Ss,j=fDj0.7VjMj2−11−M0cosφ×1+0.7Vjca2+0.0196Vjca2,where Dj and Vj mean the exit diameter of the nozzle and the speed of the jet, which could be calculated by the TBCC engine performance model [17]. Based on the similarity with the calculation of subsonic jet noise spectrum, the shock wave noise spectrum could be achieved.Next, referring to the computing method of the subsonic jet mixed noise spectrum, the spectrum of supersonic jet noise could be got. Finally, the supersonic comprehensive jet noise spectrum can be achieved by a superposition of the jet mixed noise, inner nozzle shock wave noise, and bypass nozzle shock wave noise [31, 36].Being similar to the verification of the subsonic jet noise spectrum, in order to evaluate the accuracy and availability of the supersonic jet noise spectrum prediction model, the typical model-scale experimental data are selected as the reference in Table6 [37], whose engine configuration is a dual-stream exhaust system with the supersonic jet. What is more, the prediction results of the supersonic jet noise spectrum are compared with the published experimental data shown in Figure 16, where M1 means the Mach number of inner jet and the calculation condition is determined by the experimental condition of jet noise [37]. From Figure 16, it can be observed that the prediction results also match well with the experimental results. So, it proves that the accuracy of this noise spectrum estimation model is able to meet the requirements of the prediction of the engine jet noise.Table 6
Supersonic jet noise spectrum experimental data [37].
Frequency (Hz)
SPL (dB)
125.4961
96.63934
197.6471
98.48361
398.1072
101.5574
1287.031
108.1148
2592.38
112.8279
4082.808
118.1557
5123.763
118.9754
6552.973
115.6967
8223.723
115.082
10,320.45
113.8525Figure 16
The check of the supersonic jet noise spectrum.Calculation condition is as follows:θ, theta = 95°, T1 = 1127 K, V1 = 790 m/s, M1 = 1.38, T2 = 283 K, V2 = 218 m/s, and A2/A1 = 1.9
(21)A1=14πD12=14×π×0.1012=0.00801m2.


## 4.1.1. Subsonic Jet Noise Spectrum Prediction Model

This model is the spectrum prediction of subsonic jet noise of the Mach 4 TBCC engine. From Figure14, it can be seen that the subsonic jet mixed noise can be divided into the inner jet noise and the bypass jet noise. Firstly, we should investigate the subsonic inner mixed jet noise spectrum which means the relation of the sound pressure level (SPL), the frequency parameter logS1, and the pole direction angle θ [33, 34]. And some of these parameters could be found in Table 4, which shows the relative position symbol of measuring point and nozzle.Table 4
Relative position symbol of measuring point and nozzle.
Variable
Significance
R
Length between nozzle and measuring point
θ, theta
Pole direction angle (angle between engine axis and line connecting measuring point and nozzle)
ψ, psi
Modified pole direction angle (θ)
α, alpha
Engine angle of attack (angle between engine axis and flight direction)According to the input parameters from the existing engine performance program and the measuring point layout of airworthiness requirements, in order to calculate SPL, the uncorrected overall sound pressure level (UOL1) should be calculated in advance using the following equation [33, 34].
(11)UOL1=141+10logρaρISA2⋅cacISA4+10logA1R2+10logρ1ρaω+10logVeca7.5−15log1+Mc⋅cosθ2+0.04⋅Mc2−10log1−M0⋅cosφ+3log2A1π⋅D12+12,where symbol ρa and ca means the density (kg/m3) and the speed of sound (m/s) under atmospheric environment, ρISA and cISA means the density (kg/m3) and the speed of sound (m/s) under standard atmospheric conditions, A1 means the exit area of the inner nozzle (m2), ρ1 means the density (kg/m3) of the inner jet, M0 means the flight Mach number, and D1 means the nozzle exit diameter (m). These cycle parameters and dimension parameters could be calculated by the existing TBCC engine model [22]. And coefficient ω is defined in (12). Ve means the effective velocity of inner jet, which can be calculated in (13). Mc means the convective Mach number, which is defined in (14).
(12)ω=3Ve/ca3.50.6+Ve/ca3.5−1,(13)Ve=V11−V0V1cosα2/3,(14)Mc=0.62V1−V0cosαca,where V0 and V1 means the speed of the aircraft and inner jet and α means the angle between engine axis and flight direction. When engine axis and measuring points are on the same horizontal vertical plane, it means that α=θ−Ψ.After the calculation of the uncorrected overall sound pressure level, in order to get the frequency parameterlogS1, the Strouhal number S1 should be calculated in advance as follows.
(15)S1=f4A1/πVeD14A1/π0.41−M0cosφ×1+0.62V1−V0/cacosθ2+0.01538V1−V0/ca21/21+0.62V1−V/cacosθ2+0.01538V1/ca21/2.Finally, according to the relation ofSPL, the frequency parameter logS and the pole direction angle θ [33, 34], by interpolation, the relation of SPL, frequency f, and angle θ, could be got, which means the subsonic inner jet noise spectrum could be achieved.According to Figure14, it can be seen that the subsonic jet noise spectrum includes the inner jet noise spectrum and the bypass jet noise spectrum. After the estimation of the inner jet noise spectrum, the bypass jet noise spectrum should be calculated, which means that the area ratio, the temperature ratio, and the velocity ratio of inner and bypass should be considered to correct the corresponding parameters [35, 36]. By using the same method, the double jet mixed noise spectrum is achieved. It is also found that the influence of the bypass jet on spectrum is mainly reflected on the deviation of peak frequency of the sound pressure level. However, there is no monotonous relationship between the velocity ratio and the frequency deviation parameters [31, 32]. The bypass jet only affects slightly the inner jet mixed noise spectrum since the given area ratios are limited. In addition, as far as tandem-type TBCC engine applied in this article [22] is considered, the engine jet noise spectrum prediction model merely considers the influence of inner single jet without the bypass jet.In order to evaluate the fidelity of the subsonic jet noise spectrum prediction model, the typical model-scale experimental data are selected as the reference in Table5 [37], whose engine configuration is the dual-stream exhaust system with the subsonic jet. Meanwhile, the prediction results of the subsonic jet noise spectrum are compared with subsonic jet noise experimental data shown in Figure 15, where T1, T2, V1, V2, A1, and A2 mean the temperature, speed, and area of inner and bypass nozzle exit, which are determined by the experimental condition of jet noise [37]. From Figure 15, it can be seen that the prediction results agree well with the published experimental data. So, it proves that the fidelity of this noise spectrum estimation model is able to meet the requirements of the prediction of the engine jet noise.Table 5
Subsonic jet noise spectrum experimental data [37].
Frequency (Hz)
SPL (dB)
101.5967
84.13
196.1021
90.27
483.4218
96.93
957.1784
101.47
1898.007
103.60
6007.91
102.00
9579.603
100.13Figure 15
The check of the subsonic jet noise spectrum.Calculation condition is as follows:θ, theta = 90°, T1 = 1129 K, V1 = 593 m/s, T2 = 280 K, V2 = 216 m/s, and A2/A1 = 3.2.
(16)A1=14πD12=14×π×0.12=0.00785m2.


## 4.1.2. Supersonic Jet Noise Spectrum Prediction Model

This model provides the prediction method of calculating the supersonic jet noise spectrum. From Figure14, it can be seen that when compared with the subsonic jet, the supersonic jet noise could be divided into the jet mixed noise and the shock wave noise. In order to estimate the shock wave noise spectrum, which is similar to the subsonic jet mixed noise, the sound pressure level SPL, the frequency parameter logS1, and the pole direction angle θ should be calculated in advance.Firstly, the uncorrected overall sound pressure level of shock wave noise (UOLs,j) can be calculated as follows [33, 34].
(17)UOLs,j=162+10logρaρISA2⋅cacISA4+10AjR2+10logMj2−121+Mj2−12−10log1−M0⋅cosφ+F⋅θ−θM,where Aj means the exit area of nozzle (m2) and Mj means the jet Mach number, which could be calculated by the existing TBCC engine performance model [22]. And parameters θM and F are defined in (18) and (19), respectively.
(18)θM=180deg−sin−11Mj,(19)F==0θ≤θM,=−0.75θ>θM.Then, the Strouhal numberSs,j can be calculated as follows:
(20)Ss,j=fDj0.7VjMj2−11−M0cosφ×1+0.7Vjca2+0.0196Vjca2,where Dj and Vj mean the exit diameter of the nozzle and the speed of the jet, which could be calculated by the TBCC engine performance model [17]. Based on the similarity with the calculation of subsonic jet noise spectrum, the shock wave noise spectrum could be achieved.Next, referring to the computing method of the subsonic jet mixed noise spectrum, the spectrum of supersonic jet noise could be got. Finally, the supersonic comprehensive jet noise spectrum can be achieved by a superposition of the jet mixed noise, inner nozzle shock wave noise, and bypass nozzle shock wave noise [31, 36].Being similar to the verification of the subsonic jet noise spectrum, in order to evaluate the accuracy and availability of the supersonic jet noise spectrum prediction model, the typical model-scale experimental data are selected as the reference in Table6 [37], whose engine configuration is a dual-stream exhaust system with the supersonic jet. What is more, the prediction results of the supersonic jet noise spectrum are compared with the published experimental data shown in Figure 16, where M1 means the Mach number of inner jet and the calculation condition is determined by the experimental condition of jet noise [37]. From Figure 16, it can be observed that the prediction results also match well with the experimental results. So, it proves that the accuracy of this noise spectrum estimation model is able to meet the requirements of the prediction of the engine jet noise.Table 6
Supersonic jet noise spectrum experimental data [37].
Frequency (Hz)
SPL (dB)
125.4961
96.63934
197.6471
98.48361
398.1072
101.5574
1287.031
108.1148
2592.38
112.8279
4082.808
118.1557
5123.763
118.9754
6552.973
115.6967
8223.723
115.082
10,320.45
113.8525Figure 16
The check of the supersonic jet noise spectrum.Calculation condition is as follows:θ, theta = 95°, T1 = 1127 K, V1 = 790 m/s, M1 = 1.38, T2 = 283 K, V2 = 218 m/s, and A2/A1 = 1.9
(21)A1=14πD12=14×π×0.1012=0.00801m2.


## 4.2. The Prediction Method of an Effective Sensory Noise Level

From Figure10, it can be seen that after the jet noise spectrum prediction model is built, PNL, PNLT, and EPNL could be calculated successively to evaluate the engine jet noise [28].


### 4.2.1. Perceived Noise Level (PNL)

Based on the jet noise spectrum, to estimate PNL, the function of frequency and sound pressure levelNi, as well as accumulative total noise Nt should be introduced, which can be defined in (22) and (23), respectively.
(22)N=0SPL<A1,10B1SPL−A1−1A1≤SPL<A2,10B2SPL−A2A2≤SPL<A3,10B3SPL−A3A3≤SPL<A4,10B4SPL−A4A4≤SPL<150,(23)Nt=Nmax+0.15∑i=124Ni−Nmax=0.85Nmax+0.15∑i=124Ni,where A1, B1, etc. are all coefficients, which are determined by the central frequency of 1/3 frequency range. PNL means the single numerical expression of the noise annoyance level, which can be calculated as follows.
(24)PNL=40.0+10log2logNt=40.0+33.22logNt.


### 4.2.2. Perceived Noise Level with Tone Correction (PNLT)

Because human auditory system has the predilection for following a single tone rather than the wide-band noise in the adjacent frequency range, the perceived characteristic of the single tone should be considered. The purpose of single tone correction is to detect the pure tone which includes 1/3 frequency range and to correct its influence at the same time. To achieve PNLT, the specific steps are shown as follows:(1)
The second-order elementary errors should be calculated
(2)
IfSPLi is local maximum, the average noise level or background noise level and their differences should be calculated
(3)
The discrete frequency correctionC should be determined, and its maximum Cmax should be found
(4)
PNLT could be calculated as follows
(25)PNLT=PNL+Cmax.


### 4.2.3. Effective Perceived Noise Level (EPNL)

The basic evaluation criterion for aircraft noise qualification is EPNL, which involves the sound level, the frequency distribution, and the time variation of noise. More concretely, it needs to record the instant SPL per 0.5-second interval. Meanwhile, the period of time around the maximum value of PNLT has the greatest impact on EPNL. However, due to the lack of specific take-off track, in this section, the calculation of EPNL needs to be simplified. It is assumed that in the range of time recording, the maximum PNLT almost has no difference with all other PNLT and they are equivalent, which means EPNL equals to PNLT.Thus, the jet noise prediction model is achieved, which can estimate EPNL fast and simply. And its input parameters can be provided by the TBCC engine performance model [22]. So, a quick and trusted model is established in this section to predict the Mach 4 supersonic civil aircraft engine jet noise level.


## 4.2.1. Perceived Noise Level (PNL)

Based on the jet noise spectrum, to estimate PNL, the function of frequency and sound pressure levelNi, as well as accumulative total noise Nt should be introduced, which can be defined in (22) and (23), respectively.
(22)N=0SPL<A1,10B1SPL−A1−1A1≤SPL<A2,10B2SPL−A2A2≤SPL<A3,10B3SPL−A3A3≤SPL<A4,10B4SPL−A4A4≤SPL<150,(23)Nt=Nmax+0.15∑i=124Ni−Nmax=0.85Nmax+0.15∑i=124Ni,where A1, B1, etc. are all coefficients, which are determined by the central frequency of 1/3 frequency range. PNL means the single numerical expression of the noise annoyance level, which can be calculated as follows.
(24)PNL=40.0+10log2logNt=40.0+33.22logNt.


## 4.2.2. Perceived Noise Level with Tone Correction (PNLT)

Because human auditory system has the predilection for following a single tone rather than the wide-band noise in the adjacent frequency range, the perceived characteristic of the single tone should be considered. The purpose of single tone correction is to detect the pure tone which includes 1/3 frequency range and to correct its influence at the same time. To achieve PNLT, the specific steps are shown as follows:(1)
The second-order elementary errors should be calculated
(2)
IfSPLi is local maximum, the average noise level or background noise level and their differences should be calculated
(3)
The discrete frequency correctionC should be determined, and its maximum Cmax should be found
(4)
PNLT could be calculated as follows
(25)PNLT=PNL+Cmax.


## 4.2.3. Effective Perceived Noise Level (EPNL)

The basic evaluation criterion for aircraft noise qualification is EPNL, which involves the sound level, the frequency distribution, and the time variation of noise. More concretely, it needs to record the instant SPL per 0.5-second interval. Meanwhile, the period of time around the maximum value of PNLT has the greatest impact on EPNL. However, due to the lack of specific take-off track, in this section, the calculation of EPNL needs to be simplified. It is assumed that in the range of time recording, the maximum PNLT almost has no difference with all other PNLT and they are equivalent, which means EPNL equals to PNLT.Thus, the jet noise prediction model is achieved, which can estimate EPNL fast and simply. And its input parameters can be provided by the TBCC engine performance model [22]. So, a quick and trusted model is established in this section to predict the Mach 4 supersonic civil aircraft engine jet noise level.


## 5. NOx Emission Prediction Model

Similar to the engine noise, the Mach 4 supersonic civil aircraft engine NOx emission is also an essential factor that should be considered in the schematic design phase. It is because the airworthiness regulations have strict restrictions on the engine NOx emission which could cause great damages to the ozone layer and lead to the serious environmental pollution. The index for evaluating the engine pollutant emission (EI) could be defined in (26) [38]. According to the NASA research program of the new generation of the supersonic aircraft, the target value of the NOx emission index should be less than 10 g/kg fuel consumption during cruise [39]. Thus, to meet the airworthiness regulations, after the comparison and the analysis of the NOx emission prediction method, the most appropriate way to estimate the Mach 4 supersonic civil aircraft engine NOx emission is shown as follows.
(26)EI=pollutantemissiongfuelconsumptionkg.


### 5.1. Comparison of Different NOx Emission Prediction Methods

At present, there are about three kinds of modeling methods for the NOx emission prediction: modified model method, reactor model method, and CFD numerical simulation method [40–42]. Compared with other methods, the input parameters of the modified model method could be achieved from the existing engine performance program directly and its modeling process is more concise. Based on the aforementioned analysis, the modified model method is chosen to estimate EINOx in this article. At the same time, the three emission prediction models of the modified model method will be analyzed and compared so as to choose the most accurate and suitable one to calculate EINOx of the supersonic civil aircraft engine.


#### 5.1.1.T3 Model Method

T3 model method is based on the NOx emission and the combustion chamber entrance total temperature Tt3, according to the study by Tsague et al. [38], which has a high fitting precision, and its relation could be shown as follows.
(27)EINOx=4×10−9Tt33.364.


#### 5.1.2. HSCT Method

HSCT method is based on the NASA research about the supersonic civil aircraft [43], whose prediction algorithm could be shown in (28), where subscript “toc” denotes the top-of-climb cycle conditions, Tt3max means the highest compressor discharge total temperature, Pt4 and Tt4 mean the combustor exit total pressure and temperature, Wa means the combustor airflow, and Tf means the combustor flame total temperature.WhenT3 < 611 K,
(28)EINOx=0.01555Tt3−8.3.WhenT3 ≥ 611 K,
(29)EINOx=2.899Tt3max1000−0.46Pt4Pt4tocTt4tocTt4WatocWa×exp−72.28+2.078Tf−0.014611Tf.


#### 5.1.3. DLR Fuel Method

The specific steps of the DLR fuel method can be shown as follows [44]. At first, the equivalent fuel mass flow Wf,cor of ground state should be calculated as shown in (30), where Wf means the fuel mass flow of the ground state, δt means the ratio of inlet entrance total pressure and atmospheric pressure, and θt means the ratio of inlet total temperature and standard atmospheric temperature. Then, EINOx of the reference state could be achieved by interpolation, due to its unique functional relationship with equivalent mass flow for the same engine. Finally, EINOx of the operating point could be calculated as shown in (31).
(30)Wf,cor=Wfδtθt,(31)EINOx=δtaθtbEINOx,ref,where a and b are the empirical fitting parameters, the range of a is 0.4–0.5, and b equals 3; meanwhile, the relation of EINOx and combustion chamber inlet temperature T3 and pressure P3 of the reference state could be shown as follows.
(32)EINOx,ref=constP3,coraT3,corb,where the combustion chamber inlet temperature T3 and pressure P3 of the reference state can be calculated in (33) and (34), respectively.
(33)P3,cor=P3δt,(34)T3,cor=T3θt.After the introduction of these EINOx prediction methods, several engines are used as cases to evaluate their accuracy and availability. Firstly, using the PW4056 engine [44] as an example to check the accuracy of the HSCT method, Figure 17 shows the effect of different Tf on emission prediction estimated by the HSCT method.Figure 17
Effect of differentTf on emission prediction.According to Figure17, it can be seen that the flame temperature has significant influence on EINOx when using the HSCT method. However, the flame temperature is difficult to estimate precisely in the TBCC engine performance model [22], so the HSCT method may not meet the requirements of accuracy.Then, ICAO database [45] is used to check the precision of T3 model and DLR fuel methods. The prediction precision comparison of the two methods is shown in Figure 18.Figure 18
Prediction precision comparison between the methods with ICAO database.According to Figure18, it is shown that the fitting curve of the DLR fuel method is more precise than the T3 method referring to ICAO data. Therefore, the DLR method is used to predict the EINOx of the Mach 4 supersonic civil aircraft engine.


## 5.1. Comparison of Different NOx Emission Prediction Methods

At present, there are about three kinds of modeling methods for the NOx emission prediction: modified model method, reactor model method, and CFD numerical simulation method [40–42]. Compared with other methods, the input parameters of the modified model method could be achieved from the existing engine performance program directly and its modeling process is more concise. Based on the aforementioned analysis, the modified model method is chosen to estimate EINOx in this article. At the same time, the three emission prediction models of the modified model method will be analyzed and compared so as to choose the most accurate and suitable one to calculate EINOx of the supersonic civil aircraft engine.


### 5.1.1.T3 Model Method

T3 model method is based on the NOx emission and the combustion chamber entrance total temperature Tt3, according to the study by Tsague et al. [38], which has a high fitting precision, and its relation could be shown as follows.
(27)EINOx=4×10−9Tt33.364.


### 5.1.2. HSCT Method

HSCT method is based on the NASA research about the supersonic civil aircraft [43], whose prediction algorithm could be shown in (28), where subscript “toc” denotes the top-of-climb cycle conditions, Tt3max means the highest compressor discharge total temperature, Pt4 and Tt4 mean the combustor exit total pressure and temperature, Wa means the combustor airflow, and Tf means the combustor flame total temperature.WhenT3 < 611 K,
(28)EINOx=0.01555Tt3−8.3.WhenT3 ≥ 611 K,
(29)EINOx=2.899Tt3max1000−0.46Pt4Pt4tocTt4tocTt4WatocWa×exp−72.28+2.078Tf−0.014611Tf.


### 5.1.3. DLR Fuel Method

The specific steps of the DLR fuel method can be shown as follows [44]. At first, the equivalent fuel mass flow Wf,cor of ground state should be calculated as shown in (30), where Wf means the fuel mass flow of the ground state, δt means the ratio of inlet entrance total pressure and atmospheric pressure, and θt means the ratio of inlet total temperature and standard atmospheric temperature. Then, EINOx of the reference state could be achieved by interpolation, due to its unique functional relationship with equivalent mass flow for the same engine. Finally, EINOx of the operating point could be calculated as shown in (31).
(30)Wf,cor=Wfδtθt,(31)EINOx=δtaθtbEINOx,ref,where a and b are the empirical fitting parameters, the range of a is 0.4–0.5, and b equals 3; meanwhile, the relation of EINOx and combustion chamber inlet temperature T3 and pressure P3 of the reference state could be shown as follows.
(32)EINOx,ref=constP3,coraT3,corb,where the combustion chamber inlet temperature T3 and pressure P3 of the reference state can be calculated in (33) and (34), respectively.
(33)P3,cor=P3δt,(34)T3,cor=T3θt.After the introduction of these EINOx prediction methods, several engines are used as cases to evaluate their accuracy and availability. Firstly, using the PW4056 engine [44] as an example to check the accuracy of the HSCT method, Figure 17 shows the effect of different Tf on emission prediction estimated by the HSCT method.Figure 17
Effect of differentTf on emission prediction.According to Figure17, it can be seen that the flame temperature has significant influence on EINOx when using the HSCT method. However, the flame temperature is difficult to estimate precisely in the TBCC engine performance model [22], so the HSCT method may not meet the requirements of accuracy.Then, ICAO database [45] is used to check the precision of T3 model and DLR fuel methods. The prediction precision comparison of the two methods is shown in Figure 18.Figure 18
Prediction precision comparison between the methods with ICAO database.According to Figure18, it is shown that the fitting curve of the DLR fuel method is more precise than the T3 method referring to ICAO data. Therefore, the DLR method is used to predict the EINOx of the Mach 4 supersonic civil aircraft engine.


## 5.1.1.T3 Model Method

T3 model method is based on the NOx emission and the combustion chamber entrance total temperature Tt3, according to the study by Tsague et al. [38], which has a high fitting precision, and its relation could be shown as follows.
(27)EINOx=4×10−9Tt33.364.


## 5.1.2. HSCT Method

HSCT method is based on the NASA research about the supersonic civil aircraft [43], whose prediction algorithm could be shown in (28), where subscript “toc” denotes the top-of-climb cycle conditions, Tt3max means the highest compressor discharge total temperature, Pt4 and Tt4 mean the combustor exit total pressure and temperature, Wa means the combustor airflow, and Tf means the combustor flame total temperature.WhenT3 < 611 K,
(28)EINOx=0.01555Tt3−8.3.WhenT3 ≥ 611 K,
(29)EINOx=2.899Tt3max1000−0.46Pt4Pt4tocTt4tocTt4WatocWa×exp−72.28+2.078Tf−0.014611Tf.


## 5.1.3. DLR Fuel Method

The specific steps of the DLR fuel method can be shown as follows [44]. At first, the equivalent fuel mass flow Wf,cor of ground state should be calculated as shown in (30), where Wf means the fuel mass flow of the ground state, δt means the ratio of inlet entrance total pressure and atmospheric pressure, and θt means the ratio of inlet total temperature and standard atmospheric temperature. Then, EINOx of the reference state could be achieved by interpolation, due to its unique functional relationship with equivalent mass flow for the same engine. Finally, EINOx of the operating point could be calculated as shown in (31).
(30)Wf,cor=Wfδtθt,(31)EINOx=δtaθtbEINOx,ref,where a and b are the empirical fitting parameters, the range of a is 0.4–0.5, and b equals 3; meanwhile, the relation of EINOx and combustion chamber inlet temperature T3 and pressure P3 of the reference state could be shown as follows.
(32)EINOx,ref=constP3,coraT3,corb,where the combustion chamber inlet temperature T3 and pressure P3 of the reference state can be calculated in (33) and (34), respectively.
(33)P3,cor=P3δt,(34)T3,cor=T3θt.After the introduction of these EINOx prediction methods, several engines are used as cases to evaluate their accuracy and availability. Firstly, using the PW4056 engine [44] as an example to check the accuracy of the HSCT method, Figure 17 shows the effect of different Tf on emission prediction estimated by the HSCT method.Figure 17
Effect of differentTf on emission prediction.According to Figure17, it can be seen that the flame temperature has significant influence on EINOx when using the HSCT method. However, the flame temperature is difficult to estimate precisely in the TBCC engine performance model [22], so the HSCT method may not meet the requirements of accuracy.Then, ICAO database [45] is used to check the precision of T3 model and DLR fuel methods. The prediction precision comparison of the two methods is shown in Figure 18.Figure 18
Prediction precision comparison between the methods with ICAO database.According to Figure18, it is shown that the fitting curve of the DLR fuel method is more precise than the T3 method referring to ICAO data. Therefore, the DLR method is used to predict the EINOx of the Mach 4 supersonic civil aircraft engine.


## 6. Multiobjective Optimization Module

After considering the aforementioned investigation of task requirement analysis, jet noise, and NOx emission prediction model of the Mach 4 supersonic civil aircraft TBCC engine, this module provides the optimization of the engine design parameters and control law, in order to get better engine performance, lower noise, and lower emissions. Due to the large quantities of engine variables (twelve variables) to be optimized, sensitivity analysis should be used first to conduct the preliminary screening and reduce the number of optimal variables. The polynomial combination of the response surface method is then used to simplify the target value calculation in the optimization process, based on the precise but time-consuming nonlinear component-based engine performance program. Considering the great number of optimization objectives (seven optimization objectives), the most mature, widely used multiobjective genetic algorithm is used to optimize the above performance index. Because the operating modes of the TBCC engine are divided into turbofan mode, ramjet mode, and mode conversion point, the optimization schemes should be divided into the above three modes as shown in Figure 19. And the specific optimization progress is presented as below.Figure 19
Optimization scheme of the TBCC engine.


### 6.1. Optimization of the Ramjet Mode

This section provides the optimization of the ramjet mode. Before the specific optimal calculation, the optimization objectives and constraints should be determined at first. The objective is to decrease SFC at ramjet design point and to reduce SFC and emissions at cruising point. Then, according to Table3, the constraints are summarized as follows.
(i)
Engine thrust to be kept more than 137.2 kN (design point)
(ii)
Engine thrust to be kept more than 114.2 kN (cruising point)According to the above content, it can be seen that there are several performance indicators needed to be analyzed and optimized. The sensitivity analysis should be made to preselect the design parameters and control law, in order to reduce the number of optimization goals and simplify the difficulty of optimization. The performance sensitivity analyses at ramjet mode design point are shown in Figures20 and 21 which also indicate the relative changes in performance influenced by the 5% increase of the independent variables. Moreover, the TBCC engine performance model is used to carry out the complete calculation [22].Figure 20
Sensitivity analysis of the ramjet mode at design point.Figure 21
Sensitivity analysis of the ramjet mode at cruising point.As shown in Figure20, for design point performance, decreasing the afterburner exit total temperature Tt7 makes the fuel consumption and emissions decrease. At the same time, increasing the inlet flow Wa makes thrust meet the demand.As shown in Figure21, for cruising performance, decreasing the control law of Tt7 (Tt7control) and control law of the nozzle throat area A8 (A8control) at off-design point makes the cruising fuel consumption decrease. At the same time, increasing the inlet flow Wa and Tt7 at design point makes the cruising thrust meet the constraints. However, it is found that Tt7 at cruising point corresponding to the minimum of cruising emissions changes with Tt7 at design point. Thus, the sensitivity analysis could not confirm the specific values of these parameters, and the automatic optimization of genetic algorithm should be used to find the optimum solution shown as below. To express more conveniently and improve the versatility of the optimization method, the range x1,x2 of independent variables is transformed into the coding interval −1,1 shown in (35), where x and xcode mean the previous value and the code value of the parameter, while x1,x2 means the adjustable interval of the parameter. The response surface method is also used for polynomial fitting to replace the difficult engine performance simulation, where the design point parameters and the control laws are the input variables. Finally, the multiobjective genetic algorithm is used to optimize the engine parameters of design point and cruising operating point as shown in Table 7. What is more, it can be seen that SFC and EINOx have significant decrease, the reduction of outlet temperature of combustion chamber could simplify its design, and increasing A8 and air mass flow makes it meet the thrust demand. According to the above content, the optimization of the ramjet mode achieves the optimization goals.
(35)xcode=x−x1x2−x1−1.Table 7
Ramjet mode optimization scheme (design and cruising point).
Ramjet design point
Before optimization
After optimization
Cruising operating point
Before optimization
After optimization
Flight altitude (km)
25
25
Flight altitude (km)
25
25
Flight Mach
4
4
Flight Mach
4
4
Thrust (kN)
138.3
138.4
Thrust (kN)
115.0
114.9
SFC (kg/daN/h)
2.00
1.97
SFC (kg/daN/h)
1.98
1.908
Air mass flow (kg/s)
208
227
Air mass flow (kg/s)
228
267
Outlet temperature of the combustion chamber (Tt7) (K)
2000
1909
Outlet temperature of the combustion chamber (Tt7) (K)
1730
1614
Maximum area ofA8 (m2)
2.3
2.4
A8 (m2)
0.95
1.06
EINOx (g/kg)
10.87
7.11
EINOx (g/kg)
4.97
4.74


### 6.2. Optimization of the Mode Transition Point

According to Figure19, after the optimization of the ramjet mode, this section provides the optimization of the mode transition point, which is also the design point of the turbofan mode. The optimization objectives are to minimize A8 of the ramjet mode at mode transition point to simplify its design difficulty. The constraints are summarized as follows, where the constraint of engine thrust at mode transition point refers to Table 3.
(i)
Enough surge margin for the fans and the compressors
(ii)
Total flow rate to be kept almost constant during the mode transition
(iii)
Engine thrust to be kept almost constant and more than 151.6 kNPerformance sensitivity analysis at the ramjet mode design point are shown in Figure22 which also indicates the relative changes in performance influenced by the 5% increase of the independent variables, where B means the bypass ratio and πf and πc mean the pressure ratio of fan and compressor, respectively. Except for A8, all the parameters belong to the turbofan mode. Similar to the ramjet mode, the sensitivity analysis of the mode transition point is made on the basis of the TBCC engine performance model [22]. Figure 22 shows that for mode transition point performance, increasing Wa, Tt4, and Tt7 makes the thrust and A8 increase. However, bypass ratio and pressure ratio have little influence on them and the compressor and fan surge margin is only influenced by their own pressure ratio at design point. Because the fan margin is adequate, the fan pressure ratio is set to be 1.3 without optimization referring to the TBCC engine performance model [22]. Increasing Tt4 leads to the increase of design point thrust but slightly increases of A8. Therefore, according to the above analysis, Tt4 is tentatively determined as a higher value of 2000 K [22]. Other optimization variables are difficult to value, so the response surface method and multiobjective genetic algorithm are used to calculate the performance parameters and optimize the above performance index. The turbofan mode optimization scheme is shown in Table 8, where increasing afterburner temperature and bypass ratio results in the increase of thrust. Then, according to the relationship between the thrust, air mass flow, and control law at mode transition point, the ramjet mode optimization scheme at mode transition point is shown as Table 9. According to the optimization constraint of the constant engine thrust at mode transition point, the Tt7 of the ramjet mode should be increased. To keep the mass flow constant through the outlet nozzle, the A8 should be increased, which can meet the optimization objective at mode transition point.Figure 22
Sensitivity analysis of the mode transition point (design point of the turbofan mode).Table 8
Turbofan mode optimization scheme.
Design point (mode transition point)
Before optimization
After optimization
Flight altitude (km)
20.9
20.9
Flight Mach
3
3
Thrust (kN)
151.8
157
SFC (kg/daN/h)
1.61
1.62
Air mass flow (kg/s)
318
318.5
Bypass ratio
0.7
0.74
Outlet temperature of the main combustion chamber (K)
2000
2000
Afterburner temperature (K)
1350
1377Table 9
Ramjet mode optimization scheme at mode transition point.
Before optimization
After optimization
Flight altitude (km)
20.9
20.9
Flight Mach
3
3
Thrust (kN)
151
157
SFC (kg/daN/h)
1.8
1.8
Air mass flow (kg/s)
318
318
Tt7 (K)
1400 K
1425 K
Maximum area ofA8 (m2)
2.3
2.4


### 6.3. Optimization of the Turbofan Mode

According to Figure19, after the above optimization, the turbofan mode is optimized successively. Before the specific optimal calculation, the optimization objectives and constraints should be determined at first. The objective is to get the reduction of the noise level and emission at take-off point. Then, the constraints are summarized as follows.
(i)
Constraints of engine thrust
(ii)
Constraints of margin of the fan and compressorThe polynomial combination of the response surface method is used to calculate the target value. The multiobjective genetic algorithm is used to optimize the engine performance index. The optimization scheme is shown in Table10. It can be observed that, increasing bypass ratio makes the exhaust velocity, SFC, and EINOx decrease. At the same time, the drawbacks of the increasing BPR is the reduction of inner flow capacity and specific thrust. But the increase of the outlet temperature of the main combustion chamber and the air mass flow makes the thrust satisfy its constraint. The reduction of EINOx and noise level makes the realization of the optimization objectives.Table 10
Turbofan mode optimization scheme.
Take-off operating point
Before optimization
After optimization
Flight altitude (km)
0
0
Flight Mach
0
0
Thrust (kN)
241.8
240.3
SFC (kg/daN/h)
0.82
0.817
Bypass ratio
1.24
1.4
Air mass flow (kg/s)
556
570
Outlet temperature of the main combustion chamber (K)
1545
1557
Exhaust velocity (m/s)
425.6
412
Noise level (EPNdB)
102.95
102.43
EINOx (g/kg)
6.37
5.47Thus, on the basis of the tandem TBCC engine performance model [22], the optimization of the TBCC engine is completed and its results could be seen in Figure 23. It can be seen that the EINOx, SFC, and exhaust velocity of the nozzle have been greatly reduced and the noise level also has a certain reduction. Thus, the developed multiobjective optimization tool is able to optimize the design parameters and the control law of the Mach 4 supersonic civil aircraft TBCC engine, in order to get its conceptual design with better performance, lower noise, and lower emissions. Finally, its task requirements could be satisfied.Figure 23
Optimization results of TBCC engine performance.


## 6.1. Optimization of the Ramjet Mode

This section provides the optimization of the ramjet mode. Before the specific optimal calculation, the optimization objectives and constraints should be determined at first. The objective is to decrease SFC at ramjet design point and to reduce SFC and emissions at cruising point. Then, according to Table3, the constraints are summarized as follows.
(i)
Engine thrust to be kept more than 137.2 kN (design point)
(ii)
Engine thrust to be kept more than 114.2 kN (cruising point)According to the above content, it can be seen that there are several performance indicators needed to be analyzed and optimized. The sensitivity analysis should be made to preselect the design parameters and control law, in order to reduce the number of optimization goals and simplify the difficulty of optimization. The performance sensitivity analyses at ramjet mode design point are shown in Figures20 and 21 which also indicate the relative changes in performance influenced by the 5% increase of the independent variables. Moreover, the TBCC engine performance model is used to carry out the complete calculation [22].Figure 20
Sensitivity analysis of the ramjet mode at design point.Figure 21
Sensitivity analysis of the ramjet mode at cruising point.As shown in Figure20, for design point performance, decreasing the afterburner exit total temperature Tt7 makes the fuel consumption and emissions decrease. At the same time, increasing the inlet flow Wa makes thrust meet the demand.As shown in Figure21, for cruising performance, decreasing the control law of Tt7 (Tt7control) and control law of the nozzle throat area A8 (A8control) at off-design point makes the cruising fuel consumption decrease. At the same time, increasing the inlet flow Wa and Tt7 at design point makes the cruising thrust meet the constraints. However, it is found that Tt7 at cruising point corresponding to the minimum of cruising emissions changes with Tt7 at design point. Thus, the sensitivity analysis could not confirm the specific values of these parameters, and the automatic optimization of genetic algorithm should be used to find the optimum solution shown as below. To express more conveniently and improve the versatility of the optimization method, the range x1,x2 of independent variables is transformed into the coding interval −1,1 shown in (35), where x and xcode mean the previous value and the code value of the parameter, while x1,x2 means the adjustable interval of the parameter. The response surface method is also used for polynomial fitting to replace the difficult engine performance simulation, where the design point parameters and the control laws are the input variables. Finally, the multiobjective genetic algorithm is used to optimize the engine parameters of design point and cruising operating point as shown in Table 7. What is more, it can be seen that SFC and EINOx have significant decrease, the reduction of outlet temperature of combustion chamber could simplify its design, and increasing A8 and air mass flow makes it meet the thrust demand. According to the above content, the optimization of the ramjet mode achieves the optimization goals.
(35)xcode=x−x1x2−x1−1.Table 7
Ramjet mode optimization scheme (design and cruising point).
Ramjet design point
Before optimization
After optimization
Cruising operating point
Before optimization
After optimization
Flight altitude (km)
25
25
Flight altitude (km)
25
25
Flight Mach
4
4
Flight Mach
4
4
Thrust (kN)
138.3
138.4
Thrust (kN)
115.0
114.9
SFC (kg/daN/h)
2.00
1.97
SFC (kg/daN/h)
1.98
1.908
Air mass flow (kg/s)
208
227
Air mass flow (kg/s)
228
267
Outlet temperature of the combustion chamber (Tt7) (K)
2000
1909
Outlet temperature of the combustion chamber (Tt7) (K)
1730
1614
Maximum area ofA8 (m2)
2.3
2.4
A8 (m2)
0.95
1.06
EINOx (g/kg)
10.87
7.11
EINOx (g/kg)
4.97
4.74


## 6.2. Optimization of the Mode Transition Point

According to Figure19, after the optimization of the ramjet mode, this section provides the optimization of the mode transition point, which is also the design point of the turbofan mode. The optimization objectives are to minimize A8 of the ramjet mode at mode transition point to simplify its design difficulty. The constraints are summarized as follows, where the constraint of engine thrust at mode transition point refers to Table 3.
(i)
Enough surge margin for the fans and the compressors
(ii)
Total flow rate to be kept almost constant during the mode transition
(iii)
Engine thrust to be kept almost constant and more than 151.6 kNPerformance sensitivity analysis at the ramjet mode design point are shown in Figure22 which also indicates the relative changes in performance influenced by the 5% increase of the independent variables, where B means the bypass ratio and πf and πc mean the pressure ratio of fan and compressor, respectively. Except for A8, all the parameters belong to the turbofan mode. Similar to the ramjet mode, the sensitivity analysis of the mode transition point is made on the basis of the TBCC engine performance model [22]. Figure 22 shows that for mode transition point performance, increasing Wa, Tt4, and Tt7 makes the thrust and A8 increase. However, bypass ratio and pressure ratio have little influence on them and the compressor and fan surge margin is only influenced by their own pressure ratio at design point. Because the fan margin is adequate, the fan pressure ratio is set to be 1.3 without optimization referring to the TBCC engine performance model [22]. Increasing Tt4 leads to the increase of design point thrust but slightly increases of A8. Therefore, according to the above analysis, Tt4 is tentatively determined as a higher value of 2000 K [22]. Other optimization variables are difficult to value, so the response surface method and multiobjective genetic algorithm are used to calculate the performance parameters and optimize the above performance index. The turbofan mode optimization scheme is shown in Table 8, where increasing afterburner temperature and bypass ratio results in the increase of thrust. Then, according to the relationship between the thrust, air mass flow, and control law at mode transition point, the ramjet mode optimization scheme at mode transition point is shown as Table 9. According to the optimization constraint of the constant engine thrust at mode transition point, the Tt7 of the ramjet mode should be increased. To keep the mass flow constant through the outlet nozzle, the A8 should be increased, which can meet the optimization objective at mode transition point.Figure 22
Sensitivity analysis of the mode transition point (design point of the turbofan mode).Table 8
Turbofan mode optimization scheme.
Design point (mode transition point)
Before optimization
After optimization
Flight altitude (km)
20.9
20.9
Flight Mach
3
3
Thrust (kN)
151.8
157
SFC (kg/daN/h)
1.61
1.62
Air mass flow (kg/s)
318
318.5
Bypass ratio
0.7
0.74
Outlet temperature of the main combustion chamber (K)
2000
2000
Afterburner temperature (K)
1350
1377Table 9
Ramjet mode optimization scheme at mode transition point.
Before optimization
After optimization
Flight altitude (km)
20.9
20.9
Flight Mach
3
3
Thrust (kN)
151
157
SFC (kg/daN/h)
1.8
1.8
Air mass flow (kg/s)
318
318
Tt7 (K)
1400 K
1425 K
Maximum area ofA8 (m2)
2.3
2.4


## 6.3. Optimization of the Turbofan Mode

According to Figure19, after the above optimization, the turbofan mode is optimized successively. Before the specific optimal calculation, the optimization objectives and constraints should be determined at first. The objective is to get the reduction of the noise level and emission at take-off point. Then, the constraints are summarized as follows.
(i)
Constraints of engine thrust
(ii)
Constraints of margin of the fan and compressorThe polynomial combination of the response surface method is used to calculate the target value. The multiobjective genetic algorithm is used to optimize the engine performance index. The optimization scheme is shown in Table10. It can be observed that, increasing bypass ratio makes the exhaust velocity, SFC, and EINOx decrease. At the same time, the drawbacks of the increasing BPR is the reduction of inner flow capacity and specific thrust. But the increase of the outlet temperature of the main combustion chamber and the air mass flow makes the thrust satisfy its constraint. The reduction of EINOx and noise level makes the realization of the optimization objectives.Table 10
Turbofan mode optimization scheme.
Take-off operating point
Before optimization
After optimization
Flight altitude (km)
0
0
Flight Mach
0
0
Thrust (kN)
241.8
240.3
SFC (kg/daN/h)
0.82
0.817
Bypass ratio
1.24
1.4
Air mass flow (kg/s)
556
570
Outlet temperature of the main combustion chamber (K)
1545
1557
Exhaust velocity (m/s)
425.6
412
Noise level (EPNdB)
102.95
102.43
EINOx (g/kg)
6.37
5.47Thus, on the basis of the tandem TBCC engine performance model [22], the optimization of the TBCC engine is completed and its results could be seen in Figure 23. It can be seen that the EINOx, SFC, and exhaust velocity of the nozzle have been greatly reduced and the noise level also has a certain reduction. Thus, the developed multiobjective optimization tool is able to optimize the design parameters and the control law of the Mach 4 supersonic civil aircraft TBCC engine, in order to get its conceptual design with better performance, lower noise, and lower emissions. Finally, its task requirements could be satisfied.Figure 23
Optimization results of TBCC engine performance.


## 7. Conclusion

The conceptual design and performance optimization of the propulsion system is extremely important for the Mach 4 supersonic civil aircraft. Integration of the most important calculation and analysis modules into one simulation platform provides the benefits which means the conceptual scheme, noise level, emission prediction, and performance optimization can be considered simultaneously and systematically. To meet the above objectives, a quick and trusted numerical simulation platform is established to analyze the Mach 4 TBCC engine concept for the supersonic civil aircraft, which includes the newly developed task requirement analysis module, engine jet noise, and the NOx emission prediction models, as well as a multiobjective optimization tool based on the response surface methodology. Therefore, some useful conclusions can be drawn.
(1)
Using an aircraft preliminary weight estimation method and the sensitivity analysis of parameters, a preliminary concept supersonic civil aircraft can be achieved with details of cruising Mach 4, range 10,000 km, capacity of 300 people, and fuel efficiency figure of merit 14.8 PAX·km/kg
(2)
The TBCC engine performance simulation model is used as the propulsion system of the Mach 4 supersonic civil aircraft. If one engine on the aircraft is inoperative during the cruising condition, considering the requirements of finding an alternative airport safely and the balance of the engine layout on the aircraft, four TBCC engines will be needed for the Mach 4 supersonic civil aircraft
(3)
Utilizing the developed platform, under the requirements of noise, emission, and engine thrust, as well as aerodynamic and structural compatibility of two modes, the main design parameters of the Mach 4 TBCC engine are shown as follows: at take-off point,Tt4 1557 K and bypass ratio 1.4; at mode conversion point, Tt4 2000 K, bypass ratio 1.62, fan pressure ratio 1.3, and compressor pressure ratio 2.7; at ramjet design point, Tt4 1909 K; and at cruising operating point, Tt4 1614 K
(4)
A multiobjective optimization tool can be used to optimize the conceptual design of Mach 4 TBCC engines with better performance, lower noise, and lower emissions, based on optimizing design parameters and control law of TBCC engines, which makesEINOx,design −35.49%, SFCdesign −1.50%, EINOx,cruise −4.62%, SFCcruise −3.64%, noiselevelground −0.51%, and exhaustvelocityground −3.15%. Finally, the optimized conceptual design of the TBCC engine could meet its task requirements



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*Source: 2918646-2019-01-14.xml*