The main focus of this section is to investigate the temperature distribution of the optical window and analyze the impact of flow field on optical transport phenomena in the presence of jet flow, MVGs, and suction. Additionally, it discusses measures for correcting aero-optical effects through integrated flow control.
4.1. Aero-Optical Effect Correction with Jet Flow
This section focuses on investigating the impact of different jet modes on the aerodynamic heating effect of the seeker’s optical window and analyzing the disparities in aero-optical effects caused by two nozzle modes with varying orientations.
The thermal radiation of the infrared window is a crucial factor that limits infrared imaging. Therefore, the primary issue addressed by the cooling jet is the degradation of imaging quality caused by aerodynamic heat, resulting in a decrease in window temperature.
Figure 13 illustrates the distribution of window temperature under four different operating conditions.
Figure 13a represents the temperature distribution without jet cooling. As velocity increases, the flow field experiences stronger compression, leading to higher peak pressure and density on the optical window. Simultaneously, the shock layer at the front end of the hood becomes thinner, with a smaller shock angle. Due to this compression effect, as well as an increased flow-field temperature and heat flux on the optical window, the friction between the air medium and the wall intensifies, while imposing higher material requirements for optical windows with elevated wall temperatures. Consequently, higher speeds necessitate greater reliance on jet cooling to mitigate aerodynamic effects and safeguard optical windows from damage. It can be observed that at 5 Ma, aerodynamic heating causes an increase in window temperature up to 900 K. When the airflow encounters a step in its direction of flow, its velocity decreases, causing the conversion of kinetic energy into internal energy and a subsequent rise in temperature occurs. Upon leaving the optical window surface, encountering a compression corner further reduces the airflow speed while generating additional heat energy. Henceforth, this results in a high-low-high trend within the surface temperature distribution; however, these variations are minimal, with an approximate difference of only 30 K.
The temperature distribution of the window during jet cooling parallel to the window at a speed of 5 Ma is illustrated in
Figure 13b. It is evident that an effective reduction in window temperature can be achieved when the jet flow rate is 0.05 kg/s, resulting in an average temperature decrease to 150 K. However, as the cooling gas gradually dissipates along the direction of flow due to its parallel nature with respect to the window, the cooling effect diminishes and consequently leads to a gradual increase in window temperature.
In
Figure 13c, we observe the window temperature distribution when employing a perpendicular jet relative to the seeker axis under identical flight Mach number conditions. It becomes apparent that direct exposure of the cooling gas on the window surface is absent compared to the Case3 (
θ = 15°) mode, resulting in a weaker reduction in window temperature. This discrepancy primarily arises from significant changes in incoming flow velocity, caused by expansion waves formed upon encountering vertical jets, leading to substantial reflux near the nozzle and dissipation of gas kinetic energy. Consequently, this results in inferior temperature drop effects compared to those observed with parallel jets.
Figure 13d primarily investigates whether reducing jet flow has a notable impact on window cooling performance. As depicted in this figure, even when utilizing a reduced jet flow rate of 0.01 kg/s, there remains some degree of reduction in window temperature; however, due to limited amounts of cooling gas available at such low rates, rapid consumption occurs, along with diminishing effectiveness along the direction of flow.
Subsequently, the impact of different jet angles and flow rates on the reduction of window temperature is compared under decreased inlet pressure conditions, as depicted in
Figure 14 below.
Figure 14a illustrates the temperature distribution across the window when a jet flow rate of 0.05 kg/s is employed at Mach 5 flight speed and an altitude of 30 km. The figure clearly demonstrates a significant cooling effect on the window, with minimal temperature fluctuations, which can be attributed to reduced total pressure resulting in diminished external interference from cooling gas and facilitating efficient heat absorption near the window surface. In
Figure 14b, where a perpendicular jet mode is utilized, it becomes evident that temperatures near the rear step are higher, due to vertical jets disrupting the normal free flow and causing increased separation zones, along with larger return regions at the back step, consequently leading to elevated temperatures. Excessive cooling gas carried downstream by free flow enhances cooling effectiveness for downstream windows compared to upstream positions. The temperature distribution of the window gradually increases in
Figure 14c,d as the jet flows decrease, while still maintaining directionality towards flow progression. In summary, both jet modes improve the wall temperatures of windows compared to back-step flow fields without jets. Among them, tangentially parallel window jet cooling exhibits superior performance over vertical axis jet cooling.
The objective of this section is to investigate the correction method for mitigating the aero-optical effect, which arises from the combined influence of temperature variations in the optical window wall and flow field development. Essentially, the aero-optical-induced optical transport effect is caused by density fluctuations in the flow field. In theory, suppressing density fluctuations in the flow field can effectively suppress the aero-optical effect.
Figure 15 presents density pulsation information along the symmetric surface of the optical hood for different flow conditions. Based on our analysis, jet cooling proves effective in reducing aerodynamic heat radiation through windows. However, as shown in
Figure 15a, under the Case0 and the Case1(without jet) conditions, there is minimal density pulsation, along with negligible additional disturbance effects. Conversely, after introducing jet flow (Case2 and Case3), due to disturbances induced by jet flow, density pulsations increase noticeably upstream within the flow mixing zone but rapidly decrease downstream, along with fluid motion directionality. Comparing Case4 (
P = 5529) and Case6 (
P = 1197) reveals that increasing flight altitude significantly reduces density fluctuation at identical Mach numbers.
Figure 15b compares how decreasing jet flow affects density pulsation levels; it becomes evident that only reducing jet flow leads to significant reductions in density pulsation under similar jet patterns—thus indicating an expected weakening of aero-optical transmission effects as well. Further comparison between Case8 (
θ = 15°) and Case9 (
θ = 90°) demonstrates that changes in jet angle also result in reduced impact on fluid field densities owing to the cooling gas reduction.
The density pulsation information in the flow field is directly associated with the aero-optical effect problem.
Figure 16 illustrates the RMS density distribution in the lateral direction of the optical window at
y/
δ = 6.25. Based on the aforementioned analysis, jet cooling proves effective in mitigating the aerodynamic heat radiation phenomena on the window surface. However, as depicted in
Figure 16a, under the Case0 and Case1 (without jet) conditions, there is relatively uniform
ρrms distribution in the lateral direction, with minimal influence from additional disturbances. Nevertheless, upon introducing jet flow (Case2 condition), significant density fluctuations are observed upstream of the flow mixing zone due to the disturbance caused by jet flow interaction.
Figure 16b compares how reduced jet flow impacts density pulsation.
It can be observed that when comparing Case5 (jet flow = 0.05 kg/s) with Case8 (jet flow = 0.01 kg/s) under similar jet modes, reduced jet flow significantly diminishes density pulsation while also weakening aero-optical transmission effects accordingly. Furthermore, compared to Case8 (θ = 15°) and Case9 (θ = 15°), decreased gas injection leads to a reduction in ρrms, influenced by different jet modes.
It can be seen from
Figure 17 that the RMS of optical window density varies greatly along the longitudinal direction, mainly in the vicinity of the near-wall turbulent boundary layer and shock wave in the flow field. The parameters of the flow field in the turbulent boundary layer near the wall of the (high) supersonic flow field have a large gradient due to the influence of turbulence, so there will be a large deflection phenomenon when the ray passes through the flow field of the turbulent boundary layer. Since the density field of the (hypersonic) supersonic flow field has a great gradient when passing through the shock wave, the refractive index field determined by the density field will naturally have a large gradient near the shock wave, so the ray will also have a large deflection when passing through the shock wave.
The comparison of Case1 (without jet) and Case3 (jet flow = 0.05 kg/s) in
Figure 17a shows that, due to the difference between the two conditions, only with or without jet flow, it can be seen that when the jet flow is tangent parallel to the window, a great gradient value appears near the window wall, and the root mean square of density rises sharply, reaching a maximum value of
ρrms(max) = 0.7 kg/m
3. It can be concluded that the light will have a large deflection here. However, after
z/
δ = 5, the
ρrms values under the two conditions tend to be consistent due to the weakening of the near-wall flow field interference. Case4 (jet flow = 0.05 kg/s,
θ = 90°) is the case of jet flow perpendicular to the axis, and the root mean square of density near the wall also has an extreme value of
ρrms ≈ 0.27, but because it is upstream of the window, it is close to the shock wave. In
Figure 17a, the dimensionless distance along the longitudinal direction is denoted as
z/
δ. Here,
z/
δ = 0 corresponds to the window surface, while
z/
δ ≈ 7 is in close proximity to the shock layer of the seeker’s outflow field. It can be observed that
ρrms exhibits an extreme state under all working conditions at this location. Due to the perpendicular orientation of Case4 jet with respect to the seeker axis, the emitted cooling gas encounters and interacts with the shock layer of the seeker’s flow field, resulting in the formation of an interference structure. Consequently, the
ρrms near the shock wave tends to be slightly larger compared to its state without jet.
4.2. Aero-Optical Effect Correction with Micro Vortex Generators (MVGs)
The temperature distribution of the optical window under
Ma = 3 without jet cooling is compared in
Figure 18 below. It can be observed that the temperature at the upstream position of the optical window is slightly higher with MVGs than without MVGs.
Overall, there is little difference in the surface temperature between the two windows, which also indicates that MVGs will not play a role in cooling the windows without jet cooling measures.
In order to directly compare the flow field with and without MVGs,
Figure 19 illustrates the refractive index distribution near the optical window at
Ma = 3 without jet cooling. Similarly,
Figure 20 depicts the refractive index distribution near the optical window at
Ma = 5 without jet flow. During high-speed flight, the flow field near the seeker undergoes compression into layers, resulting in air flow adherence to the seeker wall and the formation of a shock layer. The flow in the shock layer exhibits a narrow front and wide rear distribution. Considering the overall shape depicted in
Figure 1a and the installation position shown in
Figure 3 for MVGs, it can be concluded that their presence does not affect the bow shock wave present on the outer layer of the seeker. Additionally, due to turbulent boundary layer effects and associated low density, there is also a decrease in the refractive index near walls. However, regardless of whether
Ma = 3 or
Ma = 5, both cases exhibit similar distribution patterns for refractive indices without significant gradients.
The temperature distribution in the optical window with jet cooling (
Ma = 3, flow jet = 0.05 kg/s) is compared in
Figure 21, where (a) is without MVGs and (b) is with MVGs.
Due to the concave structure of the optical window, resistance is encountered when high-speed air flows through the vortex generator, resulting in a reduction in air velocity and transfer of heat from “extra” kinetic energy into the turbulent boundary layer, leading to a diminished cooling effect. The average surface temperature of the window with MVGs is approximately 30 K higher compared to that without MVGs, yet it generally satisfies the requirement for window cooling. However, the addition of MVGs results in a gradual increase in the window temperature distribution along the flow direction (Y-axis).
The introduction of the cooling jet leads to a highly non-uniform refractive index distribution within the investigate area, primarily characterized by slight variations along the flow direction parallel to the wall (
y-axis). Along the direction perpendicular to the window surface (
z-axis), there is an initial increase, followed by a decrease in refractive index distribution, as illustrated in
Figure 22. The addition of jet gas significantly enhances the complexity of flow field structure, resulting in distinct shear layer, mixing layer, and turbulent boundary layer structures near the window. Furthermore, both density and density gradient experience substantial increments within the flow field. A comparison between
Figure 22a,b reveals that after incorporating micro-vortex generators, the pulsations in proximity to the window are considerably reduced, as indicated by the red dashed circle in the figure below.
The comparison of temperature distribution in the optical window at
Ma = 5 for jet cooling is illustrated in
Figure 23 below. It can be observed that the addition of MVGs leads to a more uniform temperature distribution across the entire window, reducing the temperature difference between the highest and lowest points to only 4.5 K. In contrast, without MVGs, temperatures gradually increase along the flow direction, resulting in a significant difference of 42.8 K. This non-uniform temperature distribution induces stress-induced deformation in the window material, exacerbating both the elastic and aero-optical effects. Thus, it can be concluded that micro-vortex generators effectively enhance temperature uniformity within cooled jets.
The turbulent boundary layer plays a crucial role in generating the aero-optics effect. In flow fields with higher Mach numbers, the stratification of the flow field becomes more pronounced due to increased compressibility. As shown in
Figure 24, the addition of MVGs can still inhibit the formation of large-scale vortex structures.
The comparison of wavefront aberration with and without MVGs is depicted in
Figure 25 below. It can be observed from Case10 (
Ma = 3, without jet, with MVGs) that MVGs do not modify the amplitude of wavefront distortion. This can be attributed to the fact that the overall density gradient in the shock layer remains unchanged during downstream airflow development, transitioning solely from a large-scale vortex structure to a small-scale one. Moreover, it demonstrates that passive flow control fails to effectively mitigate aero-optical-induced wavefront aberration.
After cooling with jet flow, it is evident that wavefront aberration increases uniformly along the flow direction, as depicted in Case2 (without MVGs). However, when MVGs are added, a series of “gullies” appear on the distorted surface due to their arrangement upstream of the window, as an array. The small vortices generated after airflow passes through MVGs affect optical transmission in the downstream flow field, leading to this phenomenon observed in Case11 (Ma = 3, jet flow = 0.05 kg/s, with MVGs). It is noteworthy that comparing Case0 (Ma = 3, without jet) and Case2 (Ma = 3, jet flow = 0.05 kg/s) reveals an overall improvement in wavefront distortion values after incorporating the jet flow. This finding further supports the notion that a significant portion of imaging distortion arises from contributions by mixed layers and turbulent boundary layers.
When investigating higher Mach numbers’ impact on wavefront distortion with added MVGs, it was found that the aforementioned “gully” phenomenon occurs due to their inclusion—resulting in waveform distortions seen under Case12 (Ma = 5, without jet, with MVGs) conditions. As Ma increases, relative to the results obtained under Case1 (Ma = 5, without jet, without MVGs) conditions, there is approximately a 21.7% decrease observed at peak distortions.
4.3. With Suction-Controlled Aero-Optical Effect Correction
According to the prediction, the implementation of inspiratory control will further suppress the development of large-scale vortex structures, resulting in a more flattened disturbed flow field near the window. The stratification along the
z-axis will become more pronounced, and density fluctuations will be further reduced. In high Mach number flight, one of the primary challenges for optical detection is mitigating aerodynamic thermal radiation effects on optical windows.
Figure 26 illustrates the temperature distribution across the window, with suction control applied. It can be observed that with or without MVGs, adding suction control to the compression corner downstream effectively maintains a low window temperature gradient. Compared to
Figure 21b, there is an enhanced uniformity in the window temperature distribution achieved through this approach.
The spatial distribution of the density field in the vicinity of the hypersonic/supersonic optical window directly influences its optical detection performance. However, when employing jet cooling and inspiratory rectification in the optical window, it not only introduces complex flow field structures such as shock waves and expansion waves but also experiences influences from mixed layers and turbulent boundary layers, resulting in a more pronounced spatial non-uniformity in the density field. Therefore, studying the refractive index field derived from the density field becomes crucial.
Figure 27 illustrates the distribution of refractive index near the optical window under blowing–suction refrigeration control. In this figure, due to inspiratory control at the downstream compression corner of the window, there is an absence of observed complex flow field structures. Comparing with
Figure 22a and
Figure 24a, the fluctuations in refractive index within the flow field are reduced while exhibiting a more distinct longitudinal distribution.
The disturbance of the flow field at the compression corner downstream of the window is clearly evident in
Figure 28 below. However, it can be observed that the inspiratory control in other regions of the window at
Ma = 3 does not significantly enhance the refractive index fluctuation results of the flow field.
The flow results at higher Mach numbers reveal the significant impact of the inspiratory disturbance downstream of the window on the density distribution throughout the boundary layer.
Figure 29b demonstrates a high-density region extending from upstream to the tail of the window near its wall, providing evidence for how this inspiratory disturbance contributes to stratification within the flow field and facilitates a reduction in phase inequality during ray transmission.
The following three comparison diagrams depict the wavefront distortion results under three conditions: only the jet without any inspiratory disturbance at 3 Ma, the addition of inspiratory disturbance, and the inclusion of MVGs and inspiratory disturbance, as illustrated in
Figure 30. It is observed that incorporating an inspiratory disturbance can effectively reduce both the average and maximum values of wavefront distortion by 14.7%. A careful analysis reveals that although the mean value of wavefront distortion can be reduced, there remains an increasing trend in distortion along the flow direction. This phenomenon arises due to a larger distance between the shock layer and downstream window caused by outer shock waves. Consequently, this issue cannot be resolved solely through wall-based flow control measures; alternative flow strategies need to be explored to mitigate aero-optical interference resulting from this problem.
The following three comparison figures depict the wavefront distortion results after introducing inspiratory disturbance and with MVGs at 5 Ma, as illustrated in
Figure 31. Incorporating inspiratory disturbance at high Mach numbers still effectively reduces the average wavefront distortion value. Furthermore, it can be observed from the comparative analysis that the inclusion of MVGs does not significantly mitigate aero-optics effects in the presence of inspiratory disturbance.