Influence of emissivity on infrared radiation characteristics of the two-dimensional nozzle

In the case of the same outlet area, the two-dimensional (2-D) nozzle has a large aspect ratio compared to the axisymmetric circline nozzle, which enables it to reduce the visible area of high-temperature components such as the center cone and the flame stabilizer inside the nozzle. It can also strengthen the mixing effect of wake flow and outflow to achieve the effect of cooling. In this work, based on the calculation of the flow field of the 2-D convergent-divergent nozzle, the infrared radiation characteristics of its with different emissivity coatings and the coating under high-temperature coming off are calculated in the 3∼5um waveband. The results show that with the increase of emissivity, the mean value of infrared radiation intensity of the nozzle in the range of detection angle 0°-70° decreases to 68.80%, while the mean value of infrared radiation intensity in the range of detection angle 80°-90° rises to 136.55%. The nozzle coating coming off is caused by excessive temperature and its infrared radiation intensity even exceeds the infrared radiation intensity of the uncoated state when the coating comes off.


Introduction
Infrared radiation studies of aircraft show that when the aircraft has a low Ma number flight (e.g., Ma<1.5), the high-temperature thermal components of the exhaust system and the thermal radiation of the high-temperature gas tail jet to the infrared radiation of the aircraft in the waveband of 3~5 m accounts for about 90% of the overall radiation amount, and has become the main detection object of the infrared-guided weapon detection device [1][2][3][4].
At present, most of the homing heads of air-to-air missiles equipped with infrared homing are in the working waveband of 3~5 m.Therefore, the research on infrared stealth technology of aeroengine exhaust system and the reduction of infrared radiation characteristics of exhaust system are one of the main problems that must be solved to realize aircraft infrared stealth.If the infrared radiation intensity of the aero-engine exhaust system can be effectively suppressed, the probability of the aircraft being detected by the enemy detection system can be reduced, and the distance of the enemy to detect the aircraft can be lengthened.This is of great significance for winning modern local wars under the premise of "finding, shooting, and destroying one step ahead of the enemy" in modern wars [5] .
The influence of emissivity on the infrared radiation of exhaust system has been extensively studied in China.Ran Hongwu [6] put forward reasonable suggestions on the emissivity gradient design of infrared stealth coating and the distribution of infrared patches with different emissivity on the target surface by calculating the camouflage efficiency of camouflage stealth coating with different emissivity.Feng Xiaoxing [7] calculated the infrared radiation characteristics of fighters using low-emissivity materials through the self-developed software NUAA-IR and evaluated its stealth effect.Huang Wei[8] studied the infrared suppression effect of low emissivity coating on the center cone, the turbine, and other components by numerical simulation and experimental verification.
In this work, the infrared radiation characteristics of the 2-D nozzle with the different emissivity coatings and its coating under high-temperature coming off are calculated in the waveband of 3~5 m, and the infrared stealth effect of the exhaust system is analyzed.

Physical model
The 2-D nozzle was selected as the model, and its model was reconstructed in 3D software, including the internal duct, external duct, center cone, flame stabilizer, circline mixer, afterbody, and nozzle wall were shown in Figure 1.Because of the symmetry in the structure of the 2-D nozzle, only a quarter of the nozzle is selected in the calculation.As shown in Figure 2, the calculation domain of the far field is a quarter of the cylinder.If the nozzle length is defined as L, the length of the calculation domain is about 6L and the radius of the cylinder is about 0.8L.

Mesh division and independence verification
Figure 3 shows the mesh diagram of each component inside the nozzle.Due to the small size of each component inside the nozzle compared with the far field size, and the complex model of each component inside the nozzle, such as the flame stabilizer with the size of a few millimeters, the unstructured meshing method is used for the nozzle and far field.In order to reduce the number of meshes and increase the calculation speed, a larger mesh size is used for the far field.Meanwhile, to prevent the rapid change of the mesh size of the transition section from the nozzle outlet to the far field, the density box encryption operation is used on the back half of the nozzle.
In order to verify that the selected mesh will not affect the calculation results, five sets of meshes are generated for the nozzle model shown in Figure 4, and the number of meshes is 73W, 165W, 283W, 330W, and 625W, respectively.After the calculation of the flow field of the nozzle, the Mach number and Y + value of the nozzle outlet under the five types of meshes are analyzed.As shown in Figure 4, when the number of meshes is 73W, the nozzle outlet Mach number is 1.637Ma; when the number of meshes is 165W, the nozzle outlet Mach number increases to 1.784Ma; and when the number of meshes increases to 283W, 330W, and 625W, the corresponding Mach number of the nozzle outlet is 1.815Ma, 1.822Ma, and 1.819Ma, respectively.The Mach number is very close in the last three cases, and the error between them is less than 4%.Since the turbulence model selected is the K-SST model in this work, the Y + value should be around 1. When the number of meshes is 283W, 330W, and 625W, the corresponding Y + value tends to be stable and less than 1 slightly, so the last three sets of meshes are all acceptable.However, considering a quarter of the nozzle model, calculation efficiency, and other aspects, the number of meshes selects 283W.

Boundary conditions
The FLUENT software is used for numerical simulation of the flow field, the coupled implicit solver is used for solving, and the SST K-two-equation model is used for turbulent simulation of flow field calculation.The flow field boundary conditions are set as shown in Table 1 and the criterion for the convergence of the equations is that the residual is less than 1.0×10 -4 .
Far-field boundary Pressure far field Wall surface Wall No slip, surface emissivity =0.85

Infrared detection points setting
The calculated waveband of infrared radiation characteristics is 3~5 m, it is divided into 81 spectral points, and the detection distance is set to 1 km.The solid wall emissivity is 0.2 when the stealth coating is applied, otherwise, it is 0.85.This work focuses on the infrared radiation characteristics of the exhaust system, and the main infrared radiation of the exhaust system comes from its wake flow, so the detector distribution should be mainly in the rear hemisphere.The interval between detection angles is 5° in pitch and yaw detection plane, owing to the 2-D nozzle model being symmetrical about pitch and yaw plane, a total of 37 detection azimuth points need to be calculated.

Reverse Monte Carlo method
The infrared radiation characteristics are calculated by the Reverse Monte Carlo method (RMCM) which was developed from the Monte Carlo method (MCM).Its idea was first proposed by Nelson in 1992 and applied to solve the problem of rocket base heating [9] , and later applied to solve the problem of radiation heat transfer.RMCM emits characteristic rays from the surface of the detector, tracks its path in the opposite direction, and estimates whether the rays are absorbed or continue to advance in the process of transmission until the rays escape the boundary of the calculation domain or are absorbed.Subsequently, Taking the absorption point as the convergence point of the rays, the incident path is tracked in reverse until the detection point is encountered, and recording the radiation contribution of the convergence point to the detection point.Compared with the MCM method, RMCM is more efficient in dealing with the infrared radiation characteristics of the target of the engine exhaust system, which only concerns the received energy of the detector in a certain direction.Compared with the Discrete Transfer method (DTM), RMCM doesn't need to solve the effective radiation of solid surface elements and doesn't have the problem of discrete spatial angle, so the computational efficiency is higher than the DTM method significantly.

Calculation results of the flow field
Figure 5 is the local streamline images rendered by Mach values of gas on the narrow and wide symmetric surfaces respectively.The airflow inside the nozzle is smooth regardless of narrow or wide edge, and there are few areas where the fluid parameters change dramatically in the flow field.In Figure 5(a), there is a disturbance region in the lee region of the flame stabilizer, and the total fluid pressure in this region is also reduced.There is angular vortex flow at the red circle in Figure 5(a), but no such phenomenon at the corresponding position of the wide edge in Figure 5(b).There is a step at the narrow side and it is just in the transition section of the geometric circle turning square, so there are some angular vortex flows in the narrow side flow field, while the wide edge doesn't have such steps, so the flow field is more uniform.In addition, it clearly can be seen that the physical throat of the nozzle is consistent with the pneumatic throat basically, and the Mach number of the airflow through the throat is close to 1, satisfying the under-expanded design state.Besides, the expansion of the airflow through the throat continues to accelerate, and the maximum Mach number is 1.8.Static temperature cloud images of the narrow and wide symmetric plane are shown in Figure 6, respectively.It can be seen from the images that the length of the high-temperature core area of the wake flow of the model is about three of the nozzle lengths, and the temperature at the end of the core region of the wake flow reaches about 460K.It clearly can be found from the image that the lowtemperature airflow in the external duct and the high-temperature airflow in the internal duct are mixed more evenly after passing the mixer, and the airflow in the throat is also mixed more evenly, and the temperature of the airflow is stable at about 750K.The internal structure of the nozzle has a strong disturbance to the airflow through the nozzle, when the wake flow is just jetting out, it has a strong mixing effect with the external airflow, the wake flow temperature gradient is large and the temperature changes quickly, and the wake flow temperature gradient also decreases gradually with the motion of the airflow [10] .The static temperature distribution of the wide symmetric surface is similar to that of the narrow symmetric surface.The cloud image of static pressure distribution on the symmetrical surface of the wide edge of the nozzle shows in Figure 7 in this state.The solid red lines represent the shock wave and the dashed black lines represent the expansion wave.From the wake flow static pressure distribution can be seen that the typical expansion wave reflects on the free boundary.There is an obvious expansion wave at the nozzle outlet, indicating that the airflow in the nozzle is in an under-expanded state in this working condition.

Comparison of infrared radiation intensity of the 2-D nozzle under different emissivity coatings
The radiation heat transfer process inside the exhaust system is complicated.When the internal structure is unchanged, the radiation heat transfer between solid-solid and solid-gas will change greatly with the change of the solid surface emissivity, which will bring about great changes in the temperature field, and the surface radiant force of the object will change with the change of the emissivity and surface temperature.
Figure 8 shows the infrared radiation intensity (I) law curves of the nozzle at the different emissivity ( = 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, and 0.85) in pitch and yaw plane at 3~5 m waveband, respectively.No matter the pitch or yaw plane, the distribution law of the infrared radiation intensity curves under different emissivity conditions are similar, showing a symmetrical distribution.The infrared radiation intensity is concentrated within a small angle range, the maximum value is 90° detection angle (in the pitch plane) and 0° detection angle (in the yaw plane).As the detection angle changes from the front to the back, the high-temperature solid components inside the nozzle are gradually exposed, and the infrared radiation intensity rises sharply, especially when viewed from directly behind.Table 2 takes the pitch plane as an example to compare the mean value of infrared radiation intensity corresponding to different emissivity coatings in the range of different detection angles.As can be seen from Table 2, with the increase of emissivity, the mean value of infrared radiation intensity in the range of 0°-70° decreases to 68.80% (take Iave1 as a benchmark), while the mean value of infrared radiation intensity in the range of 80°-90° increases to 136.55% (take Iave2 as a benchmark).Since in the range of this observation angle, all high-temperature components are exposed, the influence of emissivity on the increase of radiation force is far greater than the effect of emissivity on the temperature inhibition effect.Therefore, the overall performance is that the higher the emissivity, the greater the infrared radiation intensity.

Influence of the 2-D nozzle coating coming off on infrared radiation characteristics
A kind of low-emissivity composite material is used as the stealth coating, and temperature is taken as the main factor to simulate the coming off phenomenon of the nozzle coating during the actual working process of the engine, so as to explore the influence of the stealth coating coming off on the infrared radiation characteristics of the nozzle.At present, under medium-temperature and high-temperature conditions, the most promising infrared low-emissivity coatings are metal powder, metal films, and so on [11] .In view of the working condition selected in this work, the metal micro-powder based on the resin is selected as the stealth coating.The long-term use temperature of the coating can reach 300~400 , and the short-term use temperature of the coatings can reach 500~550 .Combined with the temperature image of the nozzle wall in Figure 9 selects 550 as the critical temperature for the nozzle coating coming off.Since the coming off condition in this work is for the surface elements of the components whose temperature is greater than 550 , we can see from Figure 9 that the surface elements meeting the coming off condition are limited.The infrared calculation program developed by our research group is used to calculate the infrared radiation intensity of the nozzle under different operation conditions.Figure 10 shows the infrared radiation intensity law curves in the pitch and yaw plane under coming off, uncoated ( =0.85), and fully coated state ( =0.2) in high-temperature conditions, respectively.Taking the pitch plane as an example (figure 10(a)), compared with the fully coated state, the infrared radiation intensity in the high-temperature coming off state is much greater, and compared with the uncoated state, the infrared radiation intensity in the high-temperature coming off state is also greater when viewed from directly behind.
For high-temperature components with the coating coming off phenomenon, the infrared radiation intensity is determined by its high-temperature thermal radiation and the low-temperature components reflect the infrared radiation from high-temperature components.Due to the low-temperature components don't meet the temperature requirement of coming off, its emissivity is still 0.2.The lower its emissivity is, the higher its reflectivity is.Therefore, low-temperature surface elements will reflect a large lot of the infrared radiation from the high-temperature surface elements, resulting in the overall infrared radiation intensity even exceeding the infrared radiation intensity in the uncoated state.Figure 11 shows the infrared detection distance.Either in the pitch or yaw plane when observed from directly behind, the detection distance from long to short is coming off state, uncoated state, and fully coated state.The infrared detection distance curve is symmetrically distributed in the yaw plane, but in the range of 0°-90° is longer than 90°-180° in the pitch plane.On account of the density of water vapor in the atmosphere below the aircraft is greater than above, and the temperature and pressure below the aircraft are also greater than above.Therefore, the absorption effect of the lower atmosphere is more significant than that of the upper atmosphere, and a large amount of infrared radiation is absorbed by the atmosphere, resulting in a sharp decrease in the detection distance below the aircraft.

Conclusion
Based on the calculation of the 2-D nozzle flow field and infrared radiation field, this work calculated the overall emissivity change of the nozzle and the infrared radiation characteristics after coming off due to high temperature.The main conclusions are as follows: The (1) With the emissivity from 0.2 increase to 0.85, the average infrared radiation intensity of the 2-D nozzle in the range of 0°-70° reduces to 68.80% and in the range of 80°-90° increases to 136.55% in the waveband of 3~5 m.
(2) The infrared radiation intensity of the 2-D nozzle increases when the 2-D nozzle stealth coating comes off in the waveband of 3~5 m and exceeds the infrared radiation intensity of the uncoated state.The phenomenon in the yaw plane is similar to that in the pitch plane.

Figure 1 .
Figure 1.Cross-section of the exhaust system.Figure 2. Calculation domain of the nozzle outflow field.

Figure 2 .
Figure 1.Cross-section of the exhaust system.Figure 2. Calculation domain of the nozzle outflow field.

Figure 3 .
Figure 3. Mesh diagram of the exhaust system.Figure 4. The independence verification of mesh.

Figure 4 .
Figure 3. Mesh diagram of the exhaust system.Figure 4. The independence verification of mesh.

Figure 5 .
Figure 5. Local streamline images of (a) narrow and (b) wide symmetric surfaces.

Figure 6 .
Figure 6.Static temperature cloud images of (a) narrow symmetric and (b) wide symmetric surfaces.

Figure 7 .
Figure 7. Static pressure cloud image of symmetrical surface with wide edge.

Figure 8 .
Figure 8. Infrared radiation intensity law curves of the 2-D nozzle under different emissivity coatings (a) in the pitch and (b) yaw plane.

Figure 9 .
Figure 9. Temperature image of the 2-D nozzle wall.

Figure 10 .
Figure 10.Curves of infrared radiation intensity law under coming off, fully coated and uncoated state (a) in the pitch and (b) yaw plane.

Figure 11 .
Figure 11.Infrared detection distance under coming off, fully coated and uncoated state (a) in the pitch and (b) yaw plane.

Table 1 .
Flow field boundary setting.

Table 2 .
Comparison of the mean value of infrared radiation intensity of different emissivity coatings in the range of different detection angles.