Nomenclature
-
$a$
-
plug cone front angle/
$^\circ $
-
$\beta $
-
plug cone rear angle/
$^\circ $
- R
-
gas constant
- k
-
specific heat capacity ratio
- R
-
radius of the leading edge and trailing edge connection section of plug/mm
- h
-
plug height/mm
- A axis
-
outlet area of axisymmetric nozzle
- A plug
-
outlet area of plug nozzle
- C D
-
discharge coefficient
- m ac
-
actual mass flow of nozzle
- m id
-
ideal mass flow of nozzle
- p t7
-
total pressure at nozzle inlet
- T t7
-
total temperature at nozzle inlet
- A 9
-
outlet area of nozzle
- C Fg
-
thrust coefficient
- F ac
-
actual thrust
- F id
-
ideal thrust
- c 9
-
outlet mean velocity of nozzle
- c 9i
-
outlet velocity when the mainstream is gully expanded
- P 0
-
ambient pressure
- P 9
-
pressure at nozzle outlet
- k
-
specific heat ratio
- R
-
gas constant
-
$\sigma $
-
total pressure recovery coefficient
- p t9
-
total pressure at nozzle outlet
-
${I_\lambda }$
-
spectral radiation intensity
-
${L_{b\lambda }}\!\left( i \right)$
-
blackbody radiance at the absorption point of the i-th random ray
- A d
-
projection area
- I
-
integrated radiation intensity
- MFR
-
mass flow rate
1.0 Introduction
Infrared radiation characteristics and suppression technologies are crucial considerations in the infrared stealth design of aircraft. The exhaust system of an aircraft engine, as the primary infrared radiation source in the 3–5 μm band, contributes more than 90% of the infrared radiation characteristics in this band [Reference Mahulikar, Sonawane and Arvind Rao1]. Therefore, it is essential to implement measures to suppress its infrared radiation characteristics to ensure the aircraft’s survivability and combat capability. Exhaust system suppression measures include enhancing the mixing of the core jet, cooling designs for high-temperature surfaces [Reference Shan, Zhang and Pan2, Reference Chen and Zhang3], applying low-emissivity coatings [Reference Liu and Ji4] and modifying the nozzle or using shielding designs [Reference Gao, Yang, Zhou and He5]. The underlying logic is to minimise the infrared radiation signals from high-temperature components inside the exhaust system received by detectors. This has led to the development of non-conventional nozzles with low radiation characteristics, such as dual-mode nozzles and S-shaped nozzles.
As a modified nozzle design, the plug nozzle has been paid increasing attention due to its potential advantages for aerodynamic performance [Reference Maiden and Petit6]. Researchers have conducted several studies on aerodynamic aspects. Zebbiche [Reference Zebbiche7] developed a design method for a supersonic plug nozzle. Chutkey et al. [Reference Chutkey, Vasudevan and Balakrishnan8–Reference Chutkey, Vasudevan and Balakrishnan10] carried out a study on the truncated plug nozzle, analysed the flow field in detail and discussed the relationship of shock wave and curvature. Later, Dumitrescu et al. [Reference Dumitrescu, Gherman and Dragan11] studied the three truncated plug nozzles (40%, 50% and 60%, see Fig. 1(a)) and pointed out the 40% truncation plug performed best. In recent years, Resta et al. [Reference Resta, Di Cicca, Ferlauto and Marsilio12] investigated the flow field of axisymmetric plug nozzle with differential throttling technique (the nozzle flow passage was divided into different parts with the mainstream condition set appropriately in each part to achieve the required vector deflection – Fig. 1(b)). Their results suggested satisfactory performance on thrust vectoring under the various pressure ratio. Zhang et al. [Reference Zhang, Cheng, Liu, Rong, Sheng, Shen, Wu and Wang13] compared the plug nozzle and Laval nozzle (convergent-divergent nozzle, refer to the profile of axisymmetric nozzle in Fig. 1(c)), two commonly used nozzles in rotating detonation engines, aiming to maximise the propulsion performance. Zaman and Fagan [Reference Zaman and Fagan14] extend the investigation to noise of the supersonic plug nozzles. The plug they designed was based on the method of characteristics and with multiple geometry for the truncated cone. Their results demonstrated that the position of the plug cone, relative to nozzle exit, has a significant impact on the nozzle performance. Note that these researches indicate that the plug nozzle presents good aerodynamic characteristics. This is probably because the plug cone in their research model extends beyond the nozzle outlet, meaning that the mainstream will continue to expand along the end of plug cone after flowing out of the nozzle.
Schematic of nozzle model. (a) Truncated plug by [Reference Dumitrescu, Gherman and Dragan11]. (b) Schematic of differential throttling technique [Reference Resta, Di Cicca, Ferlauto and Marsilio12]. (c) Axisymmetric nozzle and binary plug nozzle [Reference Chen, Yang, Chen and Shi15, Reference Song, Yang, Gao, Shi and He16].
The large amount of mainstream gas with high temperature produced by the aeroengine combustion/operation will not only lead to significant changes in the aircraft plume [Reference Cheng17], but also transfer plenty of significant heat to the internal components. These processes contribute to infrared radiation of solid and gas. Thus, to improve the stealth performance of the nozzle, one important approach is to shield the internal high temperature components [Reference Shi, Zhou, Xu, Shi and Wang18]. Wang et al. [Reference Wang, Duan, Jin and Hu19] pointed out that the plug cone has the ability to shield and thus has the potential to improve stealth characteristics. Due to the plug cone extending beyond the nozzle exit, many researcher also apply cooling design on the plug to suppress its infrared signal. Some typical parameters of film cooling, such as blowing ratio, hole inclination angle of holes [Reference Ma, Zhang and Bai20–Reference Wang, Ji and Lu22], are also applied to the plug nozzle to further improve its potential for infrared shielding. Another design of plug nozzle, involving the plug cone being embedded inside the nozzle, allows shielding of the high temperature components [Reference Chen and Ji23]. In addition, some researchers have also studied radar scattering characteristics (RCS), and compared the main contributions of RCS for both asymmetric and binary plug nozzle [Reference Chen, Yang, Chen and Shi15, Reference Song, Yang, Gao, Shi and He16].
To sum up, most previous cooling proposals for the infrared suppression of plug nozzle have applied film cooling holes to the plug cone. Designers need to include build cooling flow channel for each hole and thus improve costs in design and manufacture. This paper proposes a method of cooling via introduction of slots in the plug cone walls to reduce the infrared radiation intensity of plug nozzles and simplify manufacture. The work reported here first designed an axisymmetric baseline nozzle and a binary plug nozzle based on the mass flow matching principle enforcing equal mass flow for both nozzles, as described in Section 2.2; a comparative analysis of their aerodynamic and infrared characteristics was then carried out. Finally, the impact of different cooling air combinations of the leading-edge and trailing-edge cooling slots on the plug nozzle’s infrared characteristics was investigated and discussed.
2.0 Physical model
2.1 Nozzle model
Due to the nozzle symmetry, a half model of nozzle is adopted to improve calculation efficiency, as shown in Fig. 2. There are several main components inside the nozzle, including an annular mixer, central cone and plug cone. Due to the plug cone being located at the outlet of the binary nozzle, a circular-to-square transition section is introduced in the middle of the nozzle. This transition section geometry is generated using a curvature control method, with the implementation process described in detail in Zhou et al. [Reference Zhou, Tan and Li24]. This method is able to create a transition from a circular to an arbitrary cross-sectional shape, inhibiting risk of flow separation as far as possible by maintaining a smooth transition at all times. The nozzle geometry is shown in Table 1.
Nozzle geometry
Schematic of binary plug convergent nozzle.
Figure 3 shows the control parameters for plug cone geometry. The plug length (L) is 951.9 mm, with a front angle (
$\alpha $
) of 30
$^\circ $
and a rear angle (
$\beta $
) of 20
$^\circ $
. The radius of the leading and trailing edge plug connection section of plug (R) is 400 mm, with a plug height (h) of 191 mm. This result is a height-to-core radius ratio of 0.5. The leading edge and trailing edge of the plug cone are completed by fillets with radii of 50 mm and 2 mm.
Schematic of plug cone dimensions.
Figure 4 represents the slot cooling positions; slots on leading edge are labelled as ‘Slot 1–2’ and slots on the trailing edge as ‘Slot 3–6’. The cooling air and bypass gas have the same temperature.
Schematic of slot cooling position on the plug.
2.2 Establishment of the baseline nozzle
An axisymmetric nozzle is adopted as the baseline nozzle for comparison with the binary plug nozzle. Since the binary plug nozzle differs from the baseline nozzle only in the convergent section and in the vicinity of nozzle exit, it is necessary to ensure that the geometry before the convergent section of the plug nozzle matches that of the baseline nozzle. According to the principle of matching nozzle mass flow, both plug and baseline nozzle must have equal outlet mass flow. Thus, during the geometry set-up process, the outlet size of the baseline nozzle was continually adjusted in CFD predictions until the CFD-calculated mass flow in both nozzles was approximately equal, thereby completing the establishment of an equivalent baseline nozzle geometry. Table 2 illustrates this establishment process for the baseline nozzle. The outlet area of the plug nozzle is held constant in all calculations and the cross-sectional area of the baseline nozzle kept unchanged along with the plug nozzle in the axial direction until the end position of circular-to-square section. Then, after prescribing an initial outlet radius for baseline nozzle, a CFD calculation is performed. Finally, repeat the above steps by adjusting the radius for the baseline nozzle exit according to the results. After several iterations, when area ratio at nozzle outlet between axisymmetric and binary plug nozzle (A axis/A plug) was 0.9297, their mass flow matches with each other. The axisymmetric nozzle with this area ratio was then chosen as the equivalent baseline nozzle for comparative analysis.
Mass flow ratio of axisymmetric nozzle to binary plug nozzle (Aaxis/Aplug)
2.3 The definition of nozzle performance parameters
The flow capacity of a nozzle is generally expressed using discharge coefficient. The discharge coefficient (C
D) is the ratio of the actual mass flow (
${m_{ac}}$
) to ideal mass flow (
${m_{id}}$
), where
${m_{ac}}$
is obtained by CFD calculation and
${m_{id}}$
is calculated using Equation (1):
\begin{align}{m_{id}} = \sqrt {\frac{{\rm{k}}}{{\rm{R}}}{{\left( {\frac{2}{{{\rm{k}} + 1}}} \right)}^{\frac{{{\rm{k}} + 1}}{{{\rm{k}} - 1}}}}} *\frac{{{p_{t7}}}}{{\sqrt {{T_{t7}}} }}{A_9} = {\rm{K}}\frac{{{p_{t7}}}}{{\sqrt {{T_{t7}}} }}{A_9}\end{align}
where
${p_7}$
and
${T_{t7}}$
are total parameters given to the boundary conditions at the nozzle inlet;
${A_9}$
is the area at nozzle outlet. Specific heat capacity ratio (k) and gas constant (R) are constant. Therefore,
${\rm{K\;}}$
is also a constant, which is
$0.0404\sqrt {\frac{{{\rm{kg}}\cdot{\rm{K}}}}{{{\rm{N}}\cdot{\rm{m}}}}} $
for air (k = 1.4, R = 287.06 J/(kg
$ \cdot $
K)) and
$0.0397\sqrt {\frac{{{\rm{kg}}\cdot{\rm{K}}}}{{{\rm{N}}\cdot{\rm{m}}}}} $
for gas (k = 1.33, R = 287.4 J/(kg
$ \cdot $
K)) [Reference Hill, Philip and Peterson25].
The thrust coefficient is defined as the ratio of the actual nozzle thrust to the thrust under one-dimensional isentropic fully expanded flow conditions:
\begin{align}{C_{Fg}} = \frac{{{F_{ac}}}}{{{F_{id}}}}\end{align}
where
${F_{ac}}$
is actual thrust,
${F_{id}}$
is one-dimensional isentropic fully expanded total thrust.
The actual thrust can be calculated through the Equation (3):
\begin{align}{F_{ac}} = {m_{ac}}{c_9} + \left( {{P_9} - {P_0}} \right){A_9}\end{align}
where
${c_9}$
is the mass-averaged velocity at nozzle outlet,
${P_9}$
and
${P_0}$
are static pressures at the nozzle outlet and ambient pressure,
${A_9}$
is the area of nozzle outlet.
The calculation formula for
${F_{id}}$
is given by Equation (4):
\begin{align}{F_{id}} = {m_{ac}}{c_{9i}}\end{align}
where
${c_{9i}}$
is the outlet velocity when the mainstream is fully expanded, which can be calculated by Equation (5):
\begin{align}{c_{9i}} = \sqrt {\frac{{2{\rm{k}}}}{{{\rm{k}} - 1}}{\rm{R}}{T_{t7}}\left[ {1 - {{\left( {\frac{{{p_9}}}{{{p_{t7}}}}} \right)}^{\frac{{k - 1}}{k}}}} \right]} \end{align}
where k and R are the specific heat ratio and the gas constant, respectively.
The total pressure recovery coefficient is defined as the ratio of the total pressure at the nozzle outlet to the total pressure at the nozzle inlet. It is primarily used to assess the energy loss caused by the mixing of gas and air from core duct and bypass duct within the nozzle. The calculation formula is given by Equation (6):
\begin{align}{\rm{\sigma }} = \frac{{{p_{t9}}}}{{{p_{t7}}}}\end{align}
where
${p_{t9}}$
is the total pressure at the nozzle outlet and is obtained by mass-averaged integration of CFD results.
3.0 Numerical method
3.1 Fluid domain and mesh partitioning
To get better mesh quality and reduce the cell number, a hexahedral structured mesh is adopted to discretise the nozzle domain. Mesh refinement was applied to areas with significant pressure or velocity gradient changes, such as in the vicinity of the mixer, the slots, the plug cone, the nozzle outlet and the interaction region of plume and freestream. These are all zones which feature strong mixing and fluid shearing. Finally, to allow for sufficient development of the nozzle wake, the farfield length and diameter of the solution domain are set to 12 times the nozzle length and the nozzle outer diameter, respectively, as shown in Fig. 5.
Schematic of fluid domain grid. (a) Nozzle mesh. (b) Farfield mesh.
3.2 Boundary conditions and mesh independence assessment
All solid surfaces within the nozzle are set as adiabatic no-slip walls. The discretisation method chosen is the second-order upwind scheme, with convergence residuals for all equations set to 1 × 10−4. The datum state chosen to evaluate the nozzle flow field, was an incoming Mach number of 0.06, an ambient temperature of 15 °C, and an ambient pressure of 101,325 Pa. Due to the high Re flow inside the nozzle, a turbulence model suitable for such conditions is required for numerical calculations.
Zheng [Reference Zheng26] indicates that the RNG k-ε and Realizable k-ε models simulated the surface pressure on the plug nozzle walls quite accurately compared to experimental results, making these potential options for the turbulence model in the current study. Unlike flow conditions considered in most previous film cooling studies, the flow field near the plug after preliminary calculations in this paper is high subsonic, approximately 0.6–0.7 Ma. Therefore, turbulence models commonly used in film cooling, such as the SST k-ω model, may have significant prediction errors under high turbulence and high Reynolds number conditions. Silieti et al. and Xu et al. [Reference Silieti, Kassab and Divo27, Reference Xu, Wang and Wang28] demonstrated that for mainstream Mach numbers > 0.6 Ma (including supersonic conditions), the Realizable k-ε model not only predicts film cooling characteristics with higher accuracy but also has a faster computation speed compared to models like Reynolds Stress Models (RSM). Therefore, after comprehensive consideration, the Realizable k-ε turbulence model with standard wall functions was chosen for all calculations in this study.
The ASME-recommended Grid Convergence Index (GCI) method [Reference Celik, Ghia and Roache29] was chosen to conduct grid independence verification and numerical discretisation error uncertainty analysis. Three levels of grids uniformly refined in each direction (Coarse, Moderate, Fine) were designed to determine the discretisation error range for the nozzle model. Specific details of the verification process are outlined in Table 3. Although the fine grid is closer to the extrapolated value, the error between the moderate grid and the extrapolated value is only 0.16%, and the overall GCI is less than 5%, meeting the computational requirements. Therefore, considering factors such as the number of grids, the selected 1/2 nozzle model, and time efficiency, a structured grid of approximately 2.75 million cells was chosen for the flow field calculations.
The error of the nozzle mass flow between grids and the extrapolated value
3.3 Infrared calculation method
The essence of the numerical calculation of the infrared radiation characteristics for an aircraft engine exhaust system is to solve the radiation transfer equation, which is the fundamental equation for studying the infrared radiation characteristics of a chosen target object. The radiation transfer equation also needs satisfy the energy balance along the direction of each chosen ray. In this paper, the Reverse Monte Carlo Method (RMCM) is used to calculate the infrared radiation intensity. The principle of RMCM involves emitting a characteristic ray from the detection point and tracking its path in reverse to determine whether it is absorbed or continues to propagate forward. This process continues until the ray either exits the boundary of the computational domain or is absorbed. The absorption point then serves as the starting point for forward tracking its incident path back to the detection point. Finally, the contribution of this absorption point to the infrared radiation at the detection point is calculated. Figure 6 shows a schematic diagram of the random ray backward tracking using the RMCM method. It illustrates that the problem of infrared radiation from the nozzle is essentially an analysis of the infrared radiation distribution of the entire exhaust system at various azimuth angles. It also involves studying the total radiation intensity received by a detection point in a particular direction from the exhaust system.
Schematic of random ray backtracking.
This method first randomly emits N detection rays within the stereo angle space. The spectral radiation intensity (
${I_\lambda }$
) at the detection point is obtained from Equation (7):
\begin{align}{I_\lambda } = {{\rm{A}}_d}\mathop \sum \limits_{i = 1}^N {L_{b\lambda }}\left( i \right)/N\end{align}
where
${{\rm{A}}_{d}}$
is the projected area of the target region on the plane that is perpendicular to the detection direction;
${L_{b\lambda }}\left( i \right)$
is the blackbody radiance at the absorption point of the i-th random ray, which is calculated based on the local temperature using Planck’s formula.
The integrated radiation intensity (I) of the target within a certain wavelength band is obtained from Equation (8):
\begin{align}I = \mathop \smallint \nolimits_{{\lambda _1}}^{{\lambda _2}} {{\rm{A}}_d}\mathop \sum \limits_{i = 1}^N {L_{b\lambda }}\left( i \right)/Nd\lambda \end{align}
In Equation (8), the absorption coefficient of the infrared-active gas is approximated using the narrow band model. When solving for the integrated radiation intensity, the wavelength band of interest needs to be discretised. The total radiation intensity for the current band is then obtained by integrating the radiation intensities at each spectral discretisation point.
The infrared radiation intensity of the exhaust system is composed of solid radiation and gas radiation. For solid surfaces, the calculation of infrared radiation is mainly influenced by factors such as the size of the surface geometry, its position relative to the detection point, and its temperature. For gases, when solving the radiative transfer equation, the emissivity and transmissivity of the gas need to be considered. These parameters are affected by local pressure, temperature and wavelength. Therefore, to solve the infrared radiation characteristics of the exhaust system, it is first necessary to calculate the steady-state flow field of the nozzle. The core gas composition of the nozzle includes H2O, CO2 and CO, with the gas contents shown in Table 4. This paper uses Ansys Fluent to obtain the flow field data of the nozzle and employs a self-developed RMCM programme of our research team to calculate the infrared radiation intensity. This programme was demonstrated to deliver good calculation accuracy for the disk model test case, with errors for different angles being less than 1% [Reference Gao30] (see Fig. 7).
Gas composition
Calculation method validation results on a circular disk(30). (a)3–5 μm. (b)8–14 μm.
The detection wavelength bands for the infrared radiation calculation are 3–5 μm and 8–14 μm, with each band discretised into 41 spectral points. The solid surface reflection is modeled using a diffuse reflection model, with a surface emissivity of 0.85. The inlets of the inner and outer nozzle are assumed to be equivalent grey surfaces, with an emissivity of 0.85. The detection point is located 5 km from the nozzle. The definitions of the yaw detection plane and pitch detection plane are shown in Fig. 8. Due to the symmetry of the two nozzles in both yaw and pitch directions, only the detection range from 0° to 90° is analysed in this paper.
Schematic of detection plane.
Comparison of nozzle temperature distribution in nozzle duct cross section.
4.0 Results and discussion
4.1 Comparison of plug nozzle and baseline nozzle
To illustrate the flow pattern differences between baseline and plug nozzles, Fig. 9 shows a comparison of temperature distributions at various cross sections within the nozzle. Due to the circle-to-square transition in the plug nozzle, the temperature distribution at plane 3 gradually begins to be different from that the in the axisymmetric nozzle. At plane 4, the mainstream reaches the leading edge of the plug cone, where the flow is deflected by the plug cone’s wall, and a wall-induced compression in the Y-direction of increasing strength begins. The temperature distribution at planes 5 and 6 show that, influenced by this compression, the mainstream develops cross-stream (X-direction) motions, causing the high-temperature gas to gradually reach the nozzle’s sidewall. Planes 7 and 8 indicate that the high-temperature gas flow continues to be influenced by these lateral motions, affecting the sidewall area more than at planes 5 and 6. However, due to continued mainstream acceleration and the mixing of bypass air and core duct gas, the temperature decreases slightly.
Figure 10 compares the aerodynamic performance of the axisymmetric baseline nozzle and binary plug nozzle based on the ‘flow matching’ principle. When the actual mass flow of both nozzles is the same, the exit area of the plug nozzle is slightly larger than that of the axisymmetric nozzle, indicating a reduction in flow capacity of the plug nozzle, due to the blocking effect of the plug cone.
Comparison of nozzle performance.
Near the nozzle exit, the introduction of the plug cone not only introduces new boundary layer growth over upper and lower walls of the plug cone, but also affects the boundary layer development over the nozzle exit walls. Thus, the effective area of the plug nozzle decreases, affecting nozzle flow capacity. To keep the mass flow unchanged, the exit area of plug nozzle must inevitably be relatively larger to compensate for increased boundary layer growth. In terms of the total pressure recovery coefficient, the plug nozzle is lower than the axisymmetric nozzle, again due to the blocking effect of the plug cone and increased flow losses around the plug cone, especially near the trailing edge. The impact of these greater flow losses also affects the thrust coefficient, resulting in a noticeably lower thrust coefficient for the plug nozzle compared to the baseline nozzle.
Figure 11 shows the distribution of total pressure recovery coefficient at the nozzle outlet. Figure 12 shows the plug surface streamlines and the 3D streamlines in the immediate vicinity of the nozzle exit trailing edge. The fluid inside the boundary layer over the plug cone is affected by the viscous forces, creating losses and decreasing the fluid velocity near the plug cone. The fluid eventually separates from the top of trailing edge. Meanwhile, the mainstream flow from upper and lower passages merges after the cone trailing edge. These flow aspects are the principal cause of greater loss for the plug nozzle.
Distribution of total pressure recovery coefficient on the outlet.
Streamlines near the trailing edge.
To mitigate these shortcomings, future improvements can be made by optimising the plug cone shape, for example via computational investigation of improved aerodynamic shaping of the plug cone.
In terms of infrared radiation characteristics, the baseline nozzle, the plug nozzle and the plug nozzle with cooling measures are compared for the same nozzle inlet boundary conditions. For the plug nozzle with cooling measures, the mass flow through each of the rear row slots of plug cone is the same and the total mass flow ratio (MFR) of cooling air through all four slots to mainstream flow is 0.75%. Figure 13 presents the infrared brightness images at a 90° detection angle on the yaw detection plane (side view of the nozzle) in the 3–5 μm band for the three nozzles. At this direction, the narrow edge of the plug nozzle exit corresponds to the axisymmetric nozzle exit. The mainstream of the plug nozzle, after compression by the nozzle exit wall, expands more laterally. As a result, the infrared brightness profile of the axisymmetric nozzle appears longer and wider.
Integral brightness of nozzle at a 90
$^\circ $
angle on the yaw detection plane.
Note that, for the plug nozzle with cooling, the cooling air from the upper and lower nozzle channels of the nozzle merges at the trailing edge of the plug cone, forming a low-temperature wake in the core region of the jet plume that develops downstream. This effectively separates the high-temperature jet streams from the upper and lower flow channels, resulting in a noticeable ‘layering’ appearance in the infrared brightness image of the exhaust jet.
Figure 14 shows the infrared brightness image of the plug nozzle at a 90° detection angle on the vertical detection plane in the 3–5 μm band. Unlike the situation on the yaw detection plane, the high-temperature exhaust plume of the nozzle in this projection direction obscures the trailing edge cooling film. As a result, almost no difference can be observed in the infrared brightness image.
Integral brightness of plug nozzle at a 90° angle on the vertical detection plane.
Figure 15 shows the infrared brightness image of the plug nozzle at a 0° detection angle (nozzle rear view of nozzle) in the 3–5 μm band. From this brightness image, it can be seen that the rearward infrared brightness of the plug nozzle with cooling significantly decreases, indicating that the cooling measures have had a substantial effect on infrared suppression. Even without cooling measures, the rearward brightness of the plug nozzle is slightly lower compared to the axisymmetric nozzle. Two factors contribute to this, one is the geometry changes of circular-to-square section and the second is that the plug cone enhances the mixing of high-temperature gas and bypass air, leading to temperature decrease of the mainstream flow. This causes the plug cone wall temperature to be lower than the central cone, core duct and the mixer. Another reason is that the plug cone shields the high-temperature core duct and mixer. Note that the infrared radiation contribution mainly comes from the plug cone, leading to the lower integral brightness of the plug nozzle.
Integral brightness of nozzle at a 0° angle (nozzle rear view).
Figure 16 (a) and (b) present the total radiation intensity curves of the baseline nozzle and the plug nozzle in the 3–5 μm and 8–14 μm bands. The infrared radiation intensity of the plug nozzle without cooling measures is only slightly reduced in the nozzle rearward direction (0° detection angle). This is due to the mixing of inner and outer flow streams, which lowers the surface temperature of the plug cone. However, when cooling air with an MFR of 0.75% is introduced on the surface of the plug cone, the plug nozzle shows substantial infrared suppression benefits across the entire detection plane. These benefits stem from two factors: effective cooling of the plug cone surface and the shielding effect of the plug cone, which together significantly reduces the infrared characteristics received by the detector from the central cone and the core duct. Considering that the axisymmetric nozzle, even with cooling measures applied to the centre cone, will still receive some infrared characteristics from the core duct, this highlights the advantages of the plug nozzle in infrared signal suppression.
Total radiation intensity on the vertical detection plane. (a) 3–5 μm. (b) 8–14 μm. (c) Schematic of radiation composition from three representative detection angle.
Figure 16(c) explains the shape of the total radiation intensity curve for the plug cone. In general, the magnitude of infrared radiation is directly related to the projection area of the high-temperature medium. As the detection angle changes from 0° to 90° in the vertical plane, the view transitions from the rear of the nozzle to above the nozzle. The projected area shifts from including the plug cone and the gas jet directed toward the viewing angle to only the projection of the high-temperature gas. At this point, the total radiation composition shifts from being dominated by solid radiation to being primarily gas radiation. When the detection angle reaches around +/- 20°, the projection area of the plug cone is minimised, and the view of the plug cone is limited to the area near the trailing edge. At this angle, solid radiation significantly decreases. However, the projection area of the mainstream gas increases, and gas radiation also increases, but the increase is much smaller than the decrease in solid radiation. Therefore, at around 20°, the total radiation is at its lowest. As the viewing angle continues to increase, the projection area of the plug cone remains almost unchanged, causing the total radiation to become dominated by gas radiation. The projection area of the high-temperature tail plume continuously increases, leading to an increase in both gas radiation and total radiation, resulting in a shape characterised by the wings on both sides in Fig. 16(a).
4.2 The effect of slot length
In a plug nozzle, the plug cone extends across the entire width of the nozzle exit and thus is exposed to both the high-temperature gases from the core duct and the cooler air from the bypass duct. Most of the plug cone surface is subjected to high temperature, with the low-temperature regions mainly located near the sidewalls and adjacent to the nozzle exit. Cooling of this small low-temperature region is unnecessary, potentially leading to a waste of cooling air if full-length slots are used. This section primarily investigates the effects of varying spanwise slot lengths on the infrared radiation characteristics of the nozzle under constant cooling air flow conditions.
The cooling air inlet is set as a mass flow inlet, with a total MFR of 1% for the slots (slot 3–6) used in this section. Each slot is fed by identical cooling air with a mass flow of 0.08 kg/s and a temperature of 424 K. The gas composition and temperature are the same as those of the bypass air. The dimensionless length of the slot is defined as the ratio of the slot length (L c) to plug cone width. The dimensionless length parameters for the slots in each model discussed in this section are shown in Table 5.
Dimensionless length of slot for each case
Figure 17 shows the wall temperature distribution on the plug at various slot dimensionless lengths. The situation of Case 0 has been shown in Section 4.1 (the case of plug with no cooling) and thus is not repeated here. Case 1 represents a whole width slot. Due to the slot dimensionless length in Case 2 being reduced by 0.04 (which is 17 mm) compared to Case 1, the cooling effect on the downstream wall surface of the slot is better for the same inlet cooling air MFR. At the location indicated by the arrow upstream of Slot 2 in Case 1, the wall temperature differences between Case 1, Case 2 and Case 3 are 6.1 K and 13.1 K, respectively. When the slot length is reduced to the length of Case 2, some regions downstream of the front row slot near the nozzle sidewall begin to revert to a high-temperature state (partially covered by isothermal lines in Fig. 17). When the slot length is further reduced to that in Case 3, both the front and rear row slot downstream regions near the sidewall revert to high-temperature states.
Wall temperature distribution on the plug.
Since the cooler air flow from the bypass duct will also provide some degree of cooling to the nozzle sidewalls from nearby plug cone surface regions as it flows through the nozzle sidewall, when the slot length equals the width of the plug cone (as in Case 1), cooling is affected by both the outer mainstream flow and the slot cooling air, resulting in double cooling and thus potentially inefficient use of cooling air. With the same total amount of cooling air, a shorter slot length allows more cooling air to cool the downstream edge of the plug cone, thus avoiding cooling air waste. However, since Case 3 shows local high-temperature regions downstream of both the front and rear row slots, which is not favourable to thermal protection, it also indicates that the slot length should not be too short.
Figure 18 shows the integral brightness of the nozzle at a 0° angle (nozzle rear view) with the 3–5 μm and 8–14 μm bands. For Cases 1 to 3, the relative locations of the slots can be clearly observed, indicated by the missing parts in the continuous infrared brightness distribution. Comparing Cases 1 to 3 and considering the wall temperature distribution maps of the plug cone, it is evident that since the slot length is shorter than the plug cone width, a small area near the nozzle exit wall of the plug cone returns to a high-temperature state. Therefore Cases 2 and 3 exhibit a continuous distribution of higher infrared brightness around the exit periphery. Among them, Case 3 shows the most apparent continuous distribution of infrared brightness due to the shortest slot length. Thus, the above discussion implies it is best to maintain a small distance from the nozzle sidewall when designing the slots. In this paper, slot non-dimensional length of 0.96 is the most probable optimum value, since for this slot width no local high-temperature regions appearing compared to other cases.
Integral brightness of nozzle at a 0° angle (nozzle rear view). (a) 3–5 μm. (b) 8–14 μm.
Figure 19 shows the infrared radiation intensity curves of a nozzle with various slot lengths for the 3–5 μm band on the vertical detection plane. By comparing Case 0 intensity values with those of other models, it is evident that since Case 0 employs no cooling measures, the plug cone wall remains at a high temperature, generating significant solid radiation. At −90° detection angle, corresponding to the nozzle’s lateral direction, the total radiation intensity value is primarily determined by gas radiation intensity, as high-temperature components are not visible.
Infrared radiation intensity curve of plug nozzle in 3–5 μm band with various slot length on the vertical detection plane. (a) Total radiation intensity, (b) Solid radiation intensity, (c) Gas radiation intensity, (d) Solid radiation intensity originated by plug.
In the nozzle rear view of the nozzle (0° detection angle), the total infrared radiation intensity for Case 0 is approximately 1,265 W/Sr, while for Cases 1 to 3, it is around 320 W/Sr. Thus, compared to the baseline uncooled nozzle, cooling measures reduce the total radiation intensity of the nozzle by about 74%. The slot length also affects the infrared radiation intensity, but its impact is sufficiently small that the curves only deviate slightly. The effect of slot length mainly affects the temperature distribution and integral brightness.
Finally, the infrared radiation intensity curves of the nozzles with various slot length for the 8–14 μm band on the vertical detection plane indicate that changing the slot length has almost no effect on the intensity in this band width (see Fig. 20).
4.3 The effect of slot cooling configuration
To further investigate the effect of plug cooling features on the infrared characteristics, this section explores the impact of various cooling slot combinations on the infrared radiation intensity of a plug nozzle with slot dimensionless length of 0.96. The mass flows of cooling air through the slot gaps are shown in Table 6. Case 0 represents a plug without leading edge slots cooling and with the MFR of cooling air in the trailing edge slots the same for Case 0 and Case 2 is the same, aiming to isolate the effect of leading-edge slot cooling. As a further example, the total MFR of cooling air for Cases 0, 1 and 3 are set the same to study the effect of mass flow configuration on plug cone cooling. The contribution of leading/trailing edge slots on the infrared radiation can be identified via comparison of Cases 1 and 3.
Figure 21 shows the plug cone surface temperature distribution with different cooling air mass flows from the front and rear slots. From Cases 1–3, it can be seen that the introduction of cooling air at the leading edge of the plug cone significantly lowers the temperature of the surface downstream of the front slot gap. The flow of the mainstream is affected by not only the convergent wall of exit section wall, but also the flow deflection caused by the plug wall with its varying curvature near the leading edge and at the leading/trailing edge connection section (see Fig. 9). Note the change in mainstream flowing after the circle-to-square transition (seen by comparing Cases 0 and 2).
To further evaluate the impact of these cooling air combinations, Fig. 22 illustrates the average surface temperatures for Cases 0–3. Since Case 2 has the highest total mass flow of cooling air, it provided the lowest area-averaged plug wall temperature of 667 K on the plug. Using Case 0 (no leading-edge cooling) as a reference, the area-averaged wall temperature of Case 1 drops from 844 K to 740 K, a 12.3% reduction. In Case 3, the area-averaged wall temperature drops to 798 K, a reduction of 5.5%. By comparing Cases 1 and Case 3, it is evident that the leading-edge cooling has a more significant impact on the area-averaged wall temperature of the plug.
Mass flow configuration for slot cooling
Infrared radiation intensity curve of plug nozzle in 8–14 μm band with various slot length on the vertical detection plane. (a) Total radiation intensity, (b) Solid radiation intensity, (c) Gas radiation intensity, (d) Solid radiation intensity originated by plug.
For solid surfaces, infrared radiation intensity is mainly influenced by factors such as emissivity and surface temperature. Figure 23 shows the variation of plug cone infrared radiation intensity with detection angle on the vertical detection plane for plug cone. Case 2 exhibits the lowest infrared radiation characteristics in the 3–5 μm and 8–14 μm bands, indicating that the introduction of leading-edge cooling exerts a noticeable influence on plug cone radiation. By comparing Cases 0, 1 and Case 3, it is evident that with the same cooling air mass flow, although the area-averaged wall temperatures of Case 1 and Case 3 are lower, their radiation intensities at various detection angles on the detection plane are higher than those of Case 0 (no leading-edge cooling). Therefore, together with the wall temperature distribution at the rear edge of the plug cone seen in Fig. 21, it can be concluded that the detectable radiation intensity of the cone is not significantly related to its area-averaged wall temperature but is more influenced by the wall temperature at the rear edge of the plug cone.
Wall temperature distribution on the plug.
Area-averaged wall temperature of plug.
Infrared radiation intensity curve of plug on the vertical detection plane. (a) 3–5 μm, (b) 8–14 μm.
Figure 24 shows the variation of infrared radiation intensity on the vertical detection plane in the 3–5 μm and 8–14 μm bands for different cooling configurations of the plug nozzle. From Fig. 24(a), it can be seen that Case 2 (the highest total cooling air mass flow as well as the trailing edge slot cooling) exhibits the lowest total radiation intensity across the entire detection range. Comparing this with Case 0, whilst the addition of leading-edge cooling reduces the radiation intensity, this is attributed to leading-edge cooling air affecting trailing edge wall temperature. The relationship between solid radiation signatures for the four-slot cooling configurations is: Case 1 > Case 3 > Case 0 > Case 2. This indicates that, whilst maintaining the total mass flow of cooling air remaining constant, the mass flow at the trailing edge cooling air should be maximised as it significantly lowers plug trailing edge wall temperature, resulting in reduced solid radiation from the plug. For gas radiation, the relationship is: Case 2 has the least, followed by Case 3, with Cases 0 and Case 1 showing little difference. For gas radiation, differences between the four configurations are minimal and, since gas radiation intensity is influenced by multiple factors, it is difficult to qualitatively analyse its relationship in different cooling configurations. In the 8–14 μm band, the curves (Fig. 24 (b)) generally follow the same variation pattern as in the 3–5 μm band with only minor changes observed.
Infrared radiation intensity curve of plug nozzle in 3–5 μm and 8–14 μm band with various cooling configuration on the vertical detection plane. (a)3–5 μm. (b)8–14 μm.
Combining information from Figs 22 and 24, the cooling air configuration of Case 3 is recommended, since this configuration scheme has better performance on radiation reduction whilst maintaining adequate thermal protection of the plug cone.
5.0 Conclusions
Numerical calculations have been reported and analysed to compare and contrast the temperature field and infrared radiation characteristics of a binary plug nozzle under the influence of several cooling air plug cone slot configurations. The primary conclusions are as follows:
-
1. The plug cone affects the nozzle’s flow capacity. The increase in fluid affected by boundary layer growth over the plug cone as well as flow separation from the top of the plug trailing edge introduce extra losses. Compared to a baseline axisymmetric nozzle, the discharge coefficient, thrust coefficient and total pressure recovery coefficient decrease by 1.1%, 2.1%, and 0.7%, respectively.
-
2. For small detection angles, the cooling measures provide significant infrared suppression benefits for a plug nozzle. Simultaneously, however, the outflow of cooling air from the slots results in a distinct ‘layered’ feature in the exhaust jet. In addition, the effect of slot length primarily influences sidewall wall temperature distribution and integral brightness, while its impact on radiation intensity curves is small.
-
3. Leading edge slot cooling is effective in decreasing the area-averaged wall temperature but has only a slight benefit for infrared radiation reduction. The essence of radiation reduction due to leading-edge cooling is its influence on the trailing edge wall temperature.
-
4. ‘Leading-edge + trailing-edge’ cooling scheme reduces the area-averaged plug cone wall temperature by 5.5% – 12.3% (depending on cooling configuration) compared to the ‘trailing-edge cooling’ scheme.
-
5. The infrared radiation intensity of the plug nozzle is more significantly influenced by the trailing-edge slot cooling. The cooling configuration of Case 3 in Section 4.3 is recommended, since this scheme has better performance for the infrared radiation reduction, whilst providing adequate thermal protection for the plug cone.
This study has aimed to contribute to available knowledge on the infrared suppression/thermal protection for binary plug nozzles. Future research should explore optimisation of the cooling flow from each slot to meet the combined design objectives of adequate thermal protection, efficient use of cooling air, and the optimum radiation suppression. In addition, to mitigate the negative impact of plug cone on the flow, future improvements can be made by optimising the shape of the plug cone.
Acknowledgements
The authors would like to express their gratitude for the financial support of the National Natural Science Foundation of China (No. 12102356) and the infrared radiation calculation code used in this paper, which is developed by Prof. Yang’s group. Additionally, the author also would like to express deep gratitude to the advisor (Prof. Yang) for the support provided and the reviewers’ valuable modifications suggestions on this paper.
Competing interests
We declared that there is no conflict of interest.
