2.1 Aerodynamic performance calculation

The turbofan engine model is shown in Fig. 1, in which the section numbers are defined in Table 1. The mathematical model used in this paper includes the following basic assumptions:

1. (1) The total pressure recovery coefficient of the burner, afterburner, and nozzle remained unchanged.

2. (2) The percentage of high and low-pressure turbine blade cooling gas in the total airflow of the engine remained unchanged, and the power separation remains unchanged, ignoring the air leakage.

3. (3) It was assumed that the internal flow of the engine was a quasi-one-dimensional ideal gas, and its specific heat changed with gas temperature and fuel-air ratio.

4. (4) Except the throat area and exit area of the nozzle, the other cross-sectional area of the engine was constant.

Figure 1. Turbofan engine using infrared stealth technology.

Behind the exhaust system, the infrared radiation at the exit of the low-pressure turbine, central cone, and the inner surface of the nozzle expansion section accounts for a large proportion. The targeted infrared suppression measure is to install the integrated fully shielded guiding strut (IFSGS) at the exit of the low-pressure turbine. The IFSGS integrates the guiding strut and the central cone, which makes the low-pressure turbine rotor completely invisible behind the engine. The IFSGS is hollow inside to pass cooling airflow. The air film cooling method was applied to the IFSGS (Fig. 2) and the inner surface of the nozzle expansion section (Fig. 3). The cooling air flows into the mainstream of the exhaust system through the densely packed tiny holes.

Figure 2. IFSGS with air film holes ^{Reference Wang and Ji5} .

Figure 3. Air film holes on nozzle surface of F119 engine ^{Reference Wang and Ji5} .

Considering the requirements of accuracy and real-time ability, the component level model of the engine was adopted, that is, first establish the model of each component according to the principle of aerodynamic thermodynamics and characteristic diagram of rotor components, and then integrate all single components into a complete engine mathematical model according to the matching relationship between each component, which can be expressed by the following six equations:

HP rotor power balance equation:

(1) \begin{equation}{E_{q1}} = \frac{{{H_{PT}}}}{{{H_{PC}}/{\eta _{mH}} + {H_{PEXT}}/{\eta _P}}} - 1\end{equation}

where H _PT is the power generated by the HP turbine, H _PC is the power consumed by the compressor, H _PEXT is the shaft power extraction of the HP turbine, $\eta$ _mH is the mechanical efficiency of the HP shaft, and $\eta$ _P is the power extraction efficiency.

LP rotor power balance equation:

(2) \begin{equation}{E_{q2}} = \frac{{{H_{PL}}}}{{{H_{PF}}/{\eta _{mL}}}}\end{equation}

where H _PL is the power generated by the LP turbine and H _PF is the power consumed by the fan, $\eta$ _mL is the efficiency of the LP shaft.

HP turbine inlet flow continuity equation:

(3) \begin{equation}{E_{q3}} = \frac{{{W_{g4c}}}}{{{W_{g41c}}}} - 1\end{equation}

where W _g4c is the inlet flow of the HP turbine and W _g41c is the outlet flow of the combustion chamber.

LP turbine inlet flow continuity equation:

(4) \begin{equation}{E_{q4}} = \frac{{{W_{g41c}}}}{{{W_{g45c}}}} - 1\end{equation}

where W _g45c is the inlet flow of the LP turbine.

Static pressure balance equation at the entry of the mixer:

(5) \begin{equation}{E_{q5}} = \frac{{{P_6}}}{{{P_{16}}}} - 1\end{equation}

where P ₆ is the core stream static pressure, and P ₁₆ is the bypass stream static pressure.

Total pressure balance equation at the tail nozzle throat:

(6) \begin{equation}{E_{q6}} = \frac{{{P_{t8c}}}}{{{P_{t8}}}} - 1\end{equation}

where P _t8c is the total pressure calculated according to the nozzle flow, and P _t8 is the total pressure at the outlet of the tail nozzle calculated according to the incoming flow.

Two cooling air streams with a mass flow of m _c and m _w are led out from the bypass duct to cool the surface of the IFSGS and the nozzle expansion section respectively. The cooling airflow fractions $\varepsilon$ _c and $\varepsilon$ _w are defined as follows:

(7) \begin{equation}{\varepsilon _c} = \frac{{{m_c}}}{{{m_3}}}\end{equation}

(8) \begin{equation}{\varepsilon _w} = \frac{{{m_w}}}{{{m_3}}}\end{equation}

where m _c and m _w respectively represent the mass flow of cooling air flowing through the IFSGS and nozzle expansion section; m ₃ is the air mass flow at the HP compressor exit. The residuals of the balance equations are affected by the cooling airflow fractions.

When the high-temperature wall is cooled, its surface temperature can be obtained by the following formula:

(9) \begin{equation}{\eta _c} = \frac{{{T_m} - {T_f}}}{{{T_m} - {T_{cool}}}}\end{equation}

where $\eta$ _c is the film cooling efficiency, T _m is the mainstream temperature; T _f is the wall temperature; T _cool is the cooling air temperature.

The blowing ratio M _br of the high-temperature wall is defined as follows:

(10) \begin{equation}{M_{br}} = \frac{{{\rho _c}{V_c}}}{{{\rho _m}{V_m}}}\end{equation}

where $\rho_{c}$ and V _c are the density and velocity of the cooling air; $\rho_{m}$ and V _m are the density and velocity of the mainstream.

The film cooling efficiency $\eta$ _c is a function of the blowing ratio M _br , and the form of the function is determined by the size and arrangement of the air film holes. The empirical formula used in this paper is:

(11) \begin{equation}{\eta _c} = 0.6672 \cdot \left({e^{ - 0.01156{M_{br}}}} - {e^{ - 52.79{M_{br}}}}\right)\end{equation}

When the control parameters (fuel flow rate, nozzle area, bleed air flow rate, etc.) of the engine is given, the Newton-Raphson method can be used to solve the balance equations. For the above six balance equations, the corresponding six unknowns are HP rotor speed n _H , LP rotor speed n _L , fan pressure ratio $\pi$ _F , compressor pressure ratio $\pi$ _C , HP turbine pressure ratio $\pi$ _HT , LP turbine pressure ratio $\pi$ _HL , so the balance equations can be expressed as the function of the six unknowns, and the system of equations to be solved is:

(12) \begin{equation}F\!\left(X\right) = \left\{ \begin{array}{c}{E_q}_1\!\left({n_H},{n_L},{\pi _F},{\pi _C},{\pi _{HT}},{\pi _{LT}}\right) = 0\\[4pt]{E_{q2}}\!\left({n_H},{n_L},{\pi _F},{\pi _C},{\pi _{HT}},{\pi _{LT}}\right) = 0\\[1pt] \vdots \\[1pt] {E_{q6}}\!\left({n_H},{n_L},{\pi _F},{\pi _C},{\pi _{HT}},{\pi _{LT}}\right) = 0\end{array} \right.\end{equation}

where, $X = {\left[ {{n_H}\quad {n_L}\quad {\pi _F}\quad {\pi _C}\quad {\pi _{HT}}\quad {\pi _{LT}}} \right]^T}$ . X will be iteratively computed until the residuals of the balance equations are less than 10^–6. The iteration formula of X is:

(13) \begin{equation}{X^{n + 1}} = {X^n} - {\left[ {F'({X^n})} \right]^{ - 1}}F({X^n})\end{equation}

(14) \begin{equation}F'({X^n}) = \left[ {\begin{array}{c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c}{\dfrac{{\partial {E_{q1}}}}{{\partial {n_H}}}} & {\dfrac{{\partial {E_{q1}}}}{{\partial {n_L}}}} & {\dfrac{{\partial {E_{q1}}}}{{\partial {\pi _F}}}} & {\dfrac{{\partial {E_{q1}}}}{{\partial {\pi _C}}}} & {\dfrac{{\partial {E_{q1}}}}{{\partial {\pi _{HT}}}}} & {\dfrac{{\partial {E_{q1}}}}{{\partial {\pi _{LT}}}}}\\[12pt]{\dfrac{{\partial {E_{q2}}}}{{\partial {n_H}}}} & {\dfrac{{\partial {E_{q2}}}}{{\partial {n_L}}}} & {\dfrac{{\partial {E_{q2}}}}{{\partial {\pi _F}}}} & {\dfrac{{\partial {E_{q2}}}}{{\partial {\pi _C}}}} & {\dfrac{{\partial {E_{q2}}}}{{\partial {\pi _{HT}}}}} & {\dfrac{{\partial {E_{q2}}}}{{\partial {\pi _{LT}}}}}\\[9pt] \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\[8pt] {\dfrac{{\partial {E_{q6}}}}{{\partial {n_H}}}} & {\dfrac{{\partial {E_{q6}}}}{{\partial {n_L}}}} & {\dfrac{{\partial {E_{q6}}}}{{\partial {\pi _F}}}} & {\dfrac{{\partial {E_{q6}}}}{{\partial {\pi _C}}}} & {\dfrac{{\partial {E_{q6}}}}{{\partial {\pi _{HT}}}}} & {\dfrac{{\partial {E_{q6}}}}{{\partial {\pi _{LT}}}}}\end{array}} \right]\end{equation}

The aerodynamic and thermodynamic parameters of each section and the overall performance parameters of the engine can be further obtained when the equations are solved. The formula of the engine thrust is:

(15) \begin{equation}F = {W_9}({V_9} - {V_0}) + ({P_{s9}} - {P_{s0}}){A_9}\end{equation}

where W ₉ is the flow rate at the nozzle exit, V ₉ and V ₀ are the gas velocity at the nozzle exit and the atmosphere; P _s9 and P _s0 are the gas static pressure at the nozzle exit and the atmosphere.

The specific fuel consumption rate is:

(16) \begin{equation}sfc = \left({W_f} + {W_{fAB}}\right)/F\end{equation}

where W _f and W _fAB are the fuel flow rate of the main burner and the afterburner.

2.2 Calculation of backward infrared radiation intensity of exhaust system

After applying the infrared suppression measures described above, the high-temperature components that can be directly observed by the infrared detector in the backward direction of the turbofan engine exhaust system includes the IFSGS, the inner surface of the expansion section of the nozzle, and the part inner surface of bypass duct may also be observed. The infrared radiation of the exhaust system includes the infrared radiation of the high-temperature solid wall and the gas flow inside and outside the nozzle. The calculation method of the backward infrared radiation intensity of the exhaust system is as the function in reference Reference Wang6:

(17) \begin{equation}IR = \dfrac{{{A_c}{\varepsilon _{I,c}}}}{\pi }\int\limits_\lambda {{\sigma _\lambda }{M_{\lambda bb}}\!\left( {{T_c}} \right)d\lambda } + \dfrac{{{A_n}{\varepsilon _{I,n}}}}{\pi }\int\limits_\lambda {{\sigma _\lambda }{M_{\lambda bb}}\!\left( {{T_n}} \right)d\lambda } + \dfrac{{{A_{16}}{\varepsilon _{I,16}}}}{\pi }\int\limits_\lambda {{\sigma _\lambda }{M_{\lambda bb}}\!\left( {{T_{16}}} \right)d\lambda } + {I_{gas}}\end{equation}

where, A _c , $\varepsilon$ _I,c , T _c are the backward projected area, material emissivity, and surface temperature of the IFSGS respectively; A _n , $\varepsilon$ _I,n , T _n are the backward projected area, material emissivity, and surface temperature of the expansion section of the nozzle respectively; A ₁₆, $\varepsilon$ _I,16, T ₁₆ are the backward projected area, material emissivity, and surface temperature of the visible inner surface of bypass duct respectively; M _λbb is the monochromatic radiance of blackbody; I _gas is the contribution value of gas radiation, and it is given as 8% of the total value of infrared radiation contribution of the solid wall according to experience; and σ _λ is the gas transmittance.

The infrared radiation energy of the exhaust system is mainly concentrated in the medium wave band, so the integral range of the wavelength is 3–5 $\mu$ m in the formula (17). At wavelength λ, the relationship between M _λbb and temperature T is determined by Planck’s law, as shown in formula ((18)):

(18) \begin{equation}{M_{\lambda bb}}\!\left( T \right) = \frac{{{t_1}}}{{{\lambda ^5}}} \cdot \frac{1}{{{e^{{t_2}/\lambda T}} - 1}}\end{equation}

where t ₁ and t ₂ are constants. t ₁ = (3.7415 ± 0.0003)×10^–16 (W· $\mu$ m⁴/m²), t ₂ = (1.43879 ± 0.00019)×10^–2 ( $\mu$ m·K).

The formula of gas transmittance σ _λ is:

(19) \begin{equation}{\sigma _\lambda } = \mathop \prod \limits_{1\;\;\;\;i} \!\left( {1 - {\alpha _{\lambda ,i}}} \right)\end{equation}

where the calculation formula of gas absorptivity σ _λ,i (where i represents the microelement section on the centre line of the exhaust jet) is:

(20) \begin{equation}{\alpha _{\lambda ,i}} = 1 - {e^{{\rm{ - }}{\kappa _{\lambda ,i}} \cdot {\rm{d}}{x_i}}}\end{equation}

where dx _i represents the length of the microelement. The calculation formula of absorption coefficient $\kappa_{\lambda,i}$ is:

(21) \begin{equation}{\kappa _{\lambda ,i}} = {F_{C{O_2},i}} \cdot \frac{{{P_i} \cdot 273}}{{1.01325 \times {{10}^5} \cdot {T_i}}}\kappa _{\lambda ,C{O_2}}^{STP}({T_i}) + {F_{{H_2}O,i}} \cdot \frac{{{P_i} \cdot 273}}{{1.01325 \times {{10}^5} \cdot {T_i}}}\kappa _{\lambda ,{H_2}O}^{STP}({T_i})\end{equation}

where F _CO2,i and F _H2O,i are mole fractions of carbon dioxide and water vapour in gas, respectively. P _i and T _i are pressure and temperature at section i, respectively. $\kappa^{STP}_{\lambda,CO_{2}}$ and $\kappa^{STP}_{\lambda,H_{2}O}$ are absorption coefficients of carbon dioxide and water vapour at standard temperature and pressure, respectively.

The empirical formula is applied to the temperature and component concentration change of the exhaust jet:

In the jet core area (0 ≤ x ≤ x _core ):

(22) \begin{equation}\left\{ {\begin{array}{l}{T = {T_9}}\\[4pt]{F = {F_9}}\end{array}} \right.\end{equation}

In the jet main area (x ≥ x _core ):

(23) \begin{equation}\left\{ {\begin{array}{l}{\dfrac{{T - {T_0}}}{{{T_9} - {T_0}}} = 1 - \exp \!\left[ { - 1/\left(\left(0.25 - 0.04{M_9}\right){{\left(\dfrac{{{\rho _0}}}{{{\rho _9}}}\right)}^{ - 0.22}}\dfrac{x}{{{R_9}}}{{\left(\dfrac{{{\rho _0}}}{{{\rho _9}}}\right)}^{0.5}} - 2.3\right)} \right]}\\[19pt]{\dfrac{F}{{{F_9}}} = 1 - \exp \!\left[ { - 1/\left(\left(0.25 - 0.04{M_9}\right){{\left(\dfrac{{{\rho _0}}}{{{\rho _9}}}\right)}^{ - 0.22}}\dfrac{x}{{{R_9}}}{{\left(\dfrac{{{\rho _0}}}{{{\rho _9}}}\right)}^{0.5}} - 2.3\right)} \right]}\end{array}} \right.\end{equation}

where, T is the local gas temperature; T ₉ and T ₀ represent the gas temperature at nozzle exit and ambient, respectively; x is the distance from the nozzle exit section; R ₉ represents the radius of nozzle exit; $\rho$ represents the gas density; M ₉ represents the Mach number of gas at the nozzle exit; x _core represents the length of the jet core area, and its calculation formula is:

(24) \begin{equation}{x_{core}} = \frac{{9.2}}{{(1 - 0.16{M_9}){{({\rho _0}/{\rho _9})}^{0.28}}}} \cdot {R_9}\end{equation}

The calculation flow of engine performance parameters is shown in Fig. 4.

Figure 4. Calculation flow of engine performance parameters.

Table 2. Performance requirements and design variable range under various operating conditions

4.1 The reference engine refitted with infrared radiation suppression module

The design parameters of the reference engine at the aerodynamic design point had been determined, so there were five design variables to be optimised in the cruise state, namely, the total temperature T _t4,CR at the burner exit, the cooling air fraction $\varepsilon$ _c,CR for the IFSGS, the cooling air fraction $\varepsilon$ _w,CR for the nozzle expansion section, the area ratio C _8,CR of the nozzle throat and the area ratio C _9,CR of the nozzle exit. Nozzle throat area A _8,CR , and exit area A _9,CR could be adjusted. The calculation formula of nozzle throat area A _8,CR in cruise state is:

(27) \begin{equation}{A_{8,CR}} = {A_{8,TO}} \cdot {C_{8,CR}}\end{equation}

where, A _8,TO is the nozzle throat area in the ground state, which is determined by the ground state design parameters. The calculation formula of nozzle exit area A _9,CR in cruise state is:

(28) \begin{equation}{A_{9,CR}} = {A_{8,CR}} + {C_{9,CR}} \cdot ({A_{9ideal,CR}} - {A_{8,CR}})\end{equation}

where, A _9ideal,CR is the ideal nozzle exit area in the cruise state, which means the gas expands completely in the nozzle, and the static pressure at the nozzle exit is equal to atmospheric pressure. The nozzle throat area A _8,CR , and nozzle exit area A _9,CR determine the backward visible area of high-temperature components such as IFSGS and nozzle expansion section, which has an important impact on the infrared radiation intensity of the exhaust system.

The change in engine performance with a single design variable is shown in Fig. 5. It can be seen that increasing the cooling airflow fraction or shrinking the area of the nozzle throat and exit can inhibit the infrared radiation intensity of the engine. Among them, increasing the cooling airflow ratio $\varepsilon$ _c,CR of the IFSGS has the best infrared suppression effect, while shrinking the area of nozzle outlet A _9,CR not only reduces the infrared radiation intensity but also leads to a significant decrease in thrust and a significant increase in fuel consumption. In addition, reducing the total temperature T _t4,CR at the burner exit plays a positive role in both reducing the intensity of infrared radiation and the specific fuel consumption rate. It can be noticed that when $\varepsilon$ _c,CR and $\varepsilon$ _w,CR are equal, the sfc _CR in Fig. 5(a) is smaller than that in Fig. 5(b). The cooling air for the IFSGS is introduced from the bypass duct, which is equivalent to mixing part of the bypass flow with the core flow before the mixer, and the impact on the engine performance only comes from the flow loss in the air entrainment pipeline, while the cooling air for the nozzle expansion section is not rectified and accelerated in the contraction section of the nozzle, and most of its kinetic energy will be lost after mixing with the gas in the expansion section of the nozzle.

Figure 5. The change of engine performance parameters with a single design variable.

Taking the specific fuel consumption rate sfc _CR and infrared radiation intensity IR _CR as the optimisation objectives, the performance optimisation solutions at the subsonic and supersonic cruise state of the reference engine refitted with infrared suppression module were obtained respectively, as shown in the Figs 6 and 7. When the specific fuel consumption rate sfc _CR1 of the engine refitted with infrared suppression module was equal to that of the reference engine without infrared stealth capability, the infrared radiation intensity IR _CR1 of the refitted engine decreased by 39.0% (column II in Table 7). Under the condition of meeting the minimum thrust requirements in the subsonic cruise state, the maximum reduction of infrared radiation intensity IR _CR1 could reach 47.7% (column III in Table 7).

Figure 6. Performance optimisation of the reference engine refitted with infrared suppression module in subsonic cruise state.

Figure 7. Performance optimisation of the reference engine refitted with infrared suppression module in supersonic cruise state.

When the specific fuel consumption rate sfc _CR2 of the engine refitted with infrared suppression module was equal to that of the reference engine without infrared stealth capability, the infrared radiation intensity IR _CR2 of the refitted engine decreased by 30.8% (column IV in Table 7). Under the condition of meeting the minimum thrust requirements in the supersonic cruise state, the maximum reduction of infrared radiation intensity IR _CR2 could reach 39.9% (column V in Table 7).

In the solution set, the nozzle throat area ratio C _8,CR has a strong positive correlation with the infrared radiation intensity IR _CR , while there is a strong negative correlation between the cooling air fraction $\varepsilon$ _c,CR for the IFSGS and IR _CR . The nozzle exit area ratio C _9,CR is close to the upper limit value of 1, and the cooling air fraction $\varepsilon$ _w,CR for the nozzle expansion section is close to the lower limit value of 0.01. In the solution set with lower infrared radiation intensity IR _CR , the burner exit total temperature T _t4,CR is slightly higher than that with higher infrared radiation intensity. In general, the reference engine refitted with an infrared suppression module can reduce the infrared radiation intensity by shrinking the nozzle throat area ratio and increasing the cooling air fraction for the IFSGS, while shrinking the nozzle exit area or increasing the cooling air fraction for the nozzle expansion section is not the best choice.

4.2 Cycle optimisation design through MDPs concept

The engine refitted with the infrared suppression module described above had certain cycle parameters, which limited the infrared stealth performance of the engine. To obtain a more ideal infrared stealth effect, the cycle optimisation design of the turbofan engine was carried out. In the cycle optimisation design using the MOPSO method, both the ground state and cruise state were set as the engine design points through the MDPs concept. The cycle parameters of the ground state and the adjustable parameters of the cruise state could be mixed into a set of optimisation variables, and the performance parameters of the two states could also be mixed into a set of optimisation targets. The performance constraints of each design point in Table 2 must be ensured to be met. Two sets of optimisation design schemes were given in this paper. Scheme 1 took the specific fuel consumption rate sfc _CR1, backward infrared radiation intensity IR _CR1 in subsonic cruise state and thrust F _TO in ground state as the optimisation objectives, and scheme 2 took the specific fuel consumption rate sfc _CR2, backward infrared radiation intensity IR _CR2 in supersonic cruise state and thrust F _TO in ground state as the optimisation objectives. The design variables to be optimised include the air intake W _TO , fan pressure ratio $\pi$ _F,TO , compressor pressure ratio $\pi$ _C,TO , burner exit total temperature T _t4,TO and T _t4,CR , mixer entry Mach number M _6,TO , bypass ratio α _TO , the cooling air fraction $\varepsilon$ _c,CR for the IFSGS, the cooling air fraction $\varepsilon$ _w,CR for the nozzle expansion section, area ratio C _8,CR of the nozzle throat and area ratio C _9,CR of the nozzle exit.

Figure 8 shows the design domain optimised by schemes 1 and 2. In the three-dimensional target space, the optimised Pareto solution set constitutes an irregular surface. Pareto solution sets can be divided into four design domains: ground state high thrust design domain A, cruise state low fuel consumption design domain B, cruise state low infrared characteristic design domain C and performance balance design domain D. The performance parameters corresponding to the design domains are shown in Tables 3 and 4.

Table 3. Performance parameter intervals corresponding to design domains of scheme 1

Table 4. Performance parameter intervals corresponding to design domains of scheme 2

Figure 8. Design domain partition.

Table 5. Design variables corresponding to design domains of scheme 1

Table 6. Design variables corresponding to design domains of scheme 2

Table 7. Comparison of optimisation design results

According to scheme 1 in Fig. 8(a), when F _TO and sfc _CR1 of cycle optimised design engine is equal to that of the reference engine without infrared stealth capability, IR _CR1 of the cycle optimised design engine decreases by 67.9% (column VI in Table 7), and the maximum reduction of IR _CR1 can reach 82.2% (column VII in Table 7) when meeting the minimum thrust requirements in the subsonic cruise state.

According to scheme 2 in Fig. 8(b), when F _TO and sfc _CR2 of cycle optimised design engine is equal to that of the reference engine without infrared stealth capability, IR _CR2 of the cycle optimised design engine decreases by 52.1% (column VIII in Table 7), and the maximum reduction of IR _CR2 can reach 70.3% (column IX in Table 7) when meeting the minimum thrust requirements in the supersonic cruise state. Therefore, the infrared stealth performance of the cycle optimised engine was better than that of the reference engine refitted with infrared suppression module.

Figures 9 and 10 respectively show the performance optimal solution and corresponding design variables after the cycle optimisation design of schemes 1 and 2. Tables 5 and 6 lists the design variable intervals corresponding to the design domains of schemes 1 and 2 respectively.

Figure 9. Optimal performance solution and corresponding design variables of scheme 1.

Figure 10. Optimal performance solution and corresponding design variables of scheme 2.

The optimised ground state air intake W _TO is close to the upper limit, and a larger air intake means a larger engine size and larger infrared radiation area. However, for two engines with similar geometry, the one with a larger size can work at lower throttle under the set thrust demand. Therefore, in general, the design of a larger air intake is conducive to reducing the infrared radiation characteristics of the engine.

In the solution sets, the bypass ratio α _TO has a strong negative correlation with specific fuel consumption rate sfc _CR and a strong positive correlation with infrared radiation intensity IR _CR . Because the surface temperature of the components in the core stream duct is much higher than that in the bypass duct, the strong infrared radiation surface area of the engine with a smaller bypass ratio is also smaller when the total air intake is the same. Another clear trend is: In the low infrared characteristic design domain, when the corresponding burner exit total temperature in the ground state and cruise state are both close to the lower limit, the cooling air fraction for the IFSGS is close to the upper limit of 0.1.

Similar to the results in Figs 6 and 7, C9_,CR is close to the upper limit value of 1 in most design domains, $\varepsilon$ _w,CR is close to the lower limit of 0.01. This shows that it is not the best choice to reduce the infrared radiation characteristics for an engine with cycle optimisation design by shrinking the exit area of the nozzle or increasing the cooling air fraction for the expansion section of the nozzle.