Experimental Investigation on Temperature Effects of Cryogenic Pressure-Sensitive Paint

Abstract

Pressure-sensitive paint (PSP) is an important wind tunnel testing technology. Compared with conventional PSP, the performance and test accuracy of cryogenic PSP are still immature. Therefore, investigating how to improve the pressure sensitivity of cryogenic PSP and reduce the interference of temperature effect is of great significance. By studying the PSP luminescence characteristics at different time points, temperatures, and pressures, some interesting phenomena have been discovered. When the temperature reaches 323 K, PSP can accelerate aging, leading to significant and irreversible changes in coating performance. Additionally, the effect of temperature on the luminescence characteristics of PSP shows significant differences over time. This unusual phenomenon may be related to the microstructure change in PTMSP (PtTFPP) coatings over time. In the beginning, PTMSP coating has high activity and spacing between PtTFPP luminescence centers, which change significantly with the microstructure as the temperature decreases. This might result in a stronger concentration quenching of PtTFPP, which counteracts the expected enhancement of luminescence efficiency typically caused by the temperature decrease. After 72 h, the microstructure of the coating tends to be stable, and the effect of temperature on the fluorescence characteristics of PSP becomes a thermal quenching law similar to that of traditional PSP. This discovery can provide a more precise basis for correcting the temperature effect for cryogenic PSP coatings with varying service lives.

1. Introduction

Pressure-sensitive paint (PSP) is a crucial tool for evaluating boundary layer and excursion interference characteristics, as well as the aerodynamic load characteristics of large aircraft under flight Reynolds number conditions in cryogenic wind tunnels. Additionally, it is capable of providing full-domain, high-resolution continuous pressure distribution mapping of the flight vehicle surface [1,2,3,4,5]. Since the 1990s, the National Aeronautics and Space Administration (NASA), the German Aerospace Center (DLR), and the Japan Aerospace Exploration Agency (JAXA) have consistently conducted research on the fundamental scientific challenges and experimental applications of cryogenic PSP [6,7,8,9,10,11]. However, in deep cryogenic environments, cryogenic PSPs suffer from limited oxygen molecule diffusion kinetics, leading to a significant reduction in the oxygen penetration rate compared to conventional PSP coatings. This results in a synergistic decay of both pressure sensitivity and light-emitting quantum efficiency. Additionally, in wind tunnel experiments using PSP, there is a need not only for high-pressure sensitivity to measure small pressure changes on the model’s surface but also for lower temperature sensitivity to minimize the temperature effects that could interfere with the accuracy of the pressure measurement data. Therefore, an in-depth study of the influence of temperature on the paint properties such as the pressure sensitivity, luminous intensity, and photodegradation rate of PSP coatings and their mechanism is essential to enhance the characteristics of cryogenic PSP coatings and measurement accuracy in large-scale cryogenic wind tunnel engineering applications.

The core principle of the PSP technique is based on photoluminescence and oxygen-quenching effects. A luminescent molecule absorbs photons of a specific radiation frequency, exciting electrons from the ground state to an excited state. These excited electrons return to the ground state either through radiative or non-radiative processes. The radiative transition, known as luminescence, includes both fluorescence and phosphorescence. In non-radiative deactivation, the excited state energy can be transferred to oxygen molecules through a process known as oxygen quenching, which reduces luminescence intensity. According to Henry’s law, the oxygen concentration within a PSP polymer is proportional to the partial pressure of oxygen at the polymer surface. In air, the total pressure is proportional to the partial pressure of oxygen. As the air pressure increases, more oxygen molecules diffuse into the PSP polymer layer, leading to a greater quenching of the luminescent molecules. Consequently, the luminescence intensity decreases as air pressure increases.

The relationship between luminous intensity and oxygen concentration can be described by the Stern–Volmer relationship. In experimental aerodynamics, the quantitative relationship between luminous intensity I and air pressure P is defined by the Stern–Volmer equation:

$${\displaystyle \frac{I_{ref}}{I}}=A(T)+B(T){\displaystyle \frac{P}{P_{ref}}}$$

(1)

where $I_{ref}$ is the luminous intensity under reference conditions, and $A\left(T\right)$ and $B\left(T\right)$ are the Stern–Volmer constant, also known as the PSP-coated luminous intensity-to-pressure conversion coefficient, which is determined by the static calibration of the PSP, and which is temperature-dependent due to thermal quenching.

Pressure sensitivity is a key performance indicator of PSP, which reflects the sensitivity of the coating to changes in surface pressure. It refers to the relative change in the luminous intensity of PSP caused by the pressure change under the given conditions of reference pressure $P_{ref}$ and temperature T. It can be obtained by the derivation of Equation (1) at the reference pressure $P_{ref}$.

$$S_p\left(T\right)={\displaystyle \frac{d\left(\frac{I_{ref}}{I}\right)}{dP}}$$

(2)

The temperature sensitivity $S_T$ describes the degree of sensitivity of the PSP to changes in temperature, and a lower temperature sensitivity indicates that the PSP is less affected by temperature. The normalized luminescent intensity, $I\left(T\right)$/$I\left(T_{ref}\right)$, can be described with empirically based polynomial functions. The first-order polynomial fit is [12]

$${\displaystyle \frac{I\left(T\right)}{I\left(T_{ref}\right)}}=A+B{\displaystyle \frac{T}{T_{ref}}}$$

(3)

where A and B are calibration constants under the first-order polynomial fit. In the same manner as with pressure sensitivity, the luminescent intensity change, δ, for the first-order polynomial fit was defined as the slope of the normalized intensity, $I\left(T\right)/I\left(T_{ref}\right)$, at the reference temperature.

$$S_T={\displaystyle \frac{d\left(\frac{I\left(T\right)}{I\left(T_{ref}\right)}\right)}{dT}}$$

(4)

In recent years, many studies on the temperature effects of PSP have made stage-by-stage progress [13,14,15,16,17,18,19,20]. Hayashi and Sakane et al. [12] quantified the linear increase in the pressure sensitivity of PC-PSP with increasing temperature (1.06%/K) in terms of static and dynamic characteristics, while the dynamic time response fluctuates < 10.5% within 283–363 K, using PC-PSP as a research object. Temperature control or localized temperature compensation strategies are proposed. Liu et al. [21] summarized the two primary sources of temperature effects from the perspectives of physical mechanisms and material design. They highlighted that temperature induces a shift in the calibration curve by affecting the activation energy and the oxygen diffusion coefficient of the non-radiative decay rate of luminescent molecules. Additionally, they emphasized that developing low-activation-energy polymer matrices is key to reducing temperature sensitivity. To correct temperature-induced errors, they proposed using dual-luminophore PSP and Fluorescence Lifetime Imaging (FLIM) techniques based on light intensity ratios. Bencic et al. [22] proposed a polynomial correction method for non-uniform temperature surfaces, allowing multiple temperature calibration curves to be combined into a single one. Their experimental results demonstrated that this method reduced the root mean square (RMS) error from 5.51 kPa to 2.13 kPa in supersonic mixing jets (acrylic materials) and from 1.78 kPa to 0.86 kPa in jet-cavity interactions (aluminum materials), validating its applicability to both high- and low-thermal-conductivity materials. The study also highlighted that temperature correction improves accuracy even more than in situ calibration, emphasizing the necessity of temperature compensation.

In this paper, based on the research of Yorita et al. [4], we optimized some spraying and preparation conditions and finally obtained a cryogenic PSP coating. The pressure sensitivity, aging rate, and temperature effect were tested at the oxygen concentration of 2000 ppm. The thermal quenching effect of PSP has significant changes over time. In the initial stage, both fluorescence emission thermal quenching and anti-thermal quenching phenomena coexist, and after 72 h, the overall appearance is a single thermal quenching phenomenon. Sensitivity and aging tests show that the change in the overall pressure sensitivity of the PSP was less than 16% at 72 h and less than 22% at 144 h. In addition, the pressure sensitivity of the PSP after 144 h at 123 K was 0.244%/kPa, which represents a 15.8% change in the overall pressure sensitivity compared to 24 h after spraying. These data can provide a more precise basis for correcting the temperature effect for cryogenic PSP coatings with varying service lives.

2. Experimental Methods and Calibration System

2.1. Cryogenic PSP Coating Spraying

In this paper, pressure-sensitive paint suitable for cryogenic conditions was prepared using the highly oxygen-permeable polymer PTMSP as a binder and the long luminescence lifetime luminescent molecule PtTFPP as a probe. These PSP samples were utilized to study the laws and mechanisms of the influence of temperature on pressure sensitivity and luminescence intensity.

The steps for preparing the PSP are as follows: (1) Grinding and cleaning the test sample. (2) Preparing and spraying the polymer solution: Dissolve 0.1 g of PTMSP in 20 mL of toluene, stir for more than 12 h, and then spray the mixed PTMSP solution with optimized spraying parameters onto the surface of the sample to control the coating thickness within the range of 5–10 μm. (3) Configuring and spraying probe solution: Dissolve 0.1 g of PtTFPP in 100 mL toluene, stir thoroughly until well mixed, and then spray it onto the surface of the sample. Place the static calibration sample in a relatively dark, dry environment at room temperature and pressure for a period of time until the toluene has completely evaporated. The ratio of polymer, probe, and organic solvent, as well as the thickness of the coating, have a great influence on the coating properties, which need to be finely controlled during the configuration process.

2.2. The Calibration System

In this study, a cryogenic PSP static calibration system, independently developed by the High-Speed Institute of China Aerodynamic Research and Development Center, is used to investigate the temperature effects of cryogenic PSP experimentally. The system primarily consists of a calibration chamber, a pressure measurement and control system, a temperature measurement and control system, an oxygen content measurement and control system, and an image acquisition system. The temperature measurement and control system is mainly based on the adjustment of the electric heating power and refrigerant flow rate so as to achieve continuous adjustment in the range of 110 K to 373 K, with a control accuracy of 0.1 K. The oxygen measurement and control system is primarily controlled by N₂ and O₂ mass flow and provides adjustable oxygen concentration standard gases from 100 ppm to 520,000 ppm in mixed gas chambers for paint calibration, with an oxygen concentration control error of less than 0.5% of the actual oxygen concentration. The pressure measurement and control system adopts a high-precision pressure controller, which can continuously regulate the pressure in the range of 0 to 450 kPa with a pressure control accuracy of 0.001% FS. In addition, the image acquisition system mainly consists of an excitation light source and a CCD camera. The excitation light source is a specific band light source with a center wavelength of 395 nm, which is used to excite the static calibration sample to produce a fluorescence signal with a center wavelength of 650 nm; The CCD camera is a B4020 series high-performance device owned by Imperx, a manufacturer based at Boca Raton, Florida, USA.This article has a 560 nm high pass filter in front of its optical lens to capture the fluorescence signal of the sample.The schematic diagram of the cryogenic PSP calibration system is shown in Figure 1.

Before evaluating the paint properties, the mixing gas chamber and calibration chamber need to be first purged with dry nitrogen and vacuumed to prevent frost formation on the coating samples under cryogenic conditions. Then, the calibration system was controlled to the target test sample temperature and oxygen concentration. Finally, the pressure was rapidly adjusted by the pressure controller, and calibration images were acquired at intervals under different pressures. This operation was repeated to obtain the pressure response curves of the cryogenic PSP at various temperatures and oxygen concentrations. Similarly, by keeping the oxygen concentration and pressure in the calibration chamber constant and varying the surface temperature of the calibration sample, the temperature response curves of the cryogenic PSP coating were obtained.

Prior to the calibration experiments, we conducted a systematic evaluation of the combined error of the calibration system. The calibration samples on the sixth day after spraying were placed in the calibration chamber with the oxygen concentration set at 2000 ppm and the temperature at 298 K. Seven sets of pressure response curves were obtained by repeatedly adjusting the pressure from 5 kPa to 200 kPa for seven cycles. The integrated error of the calibration system was systematically evaluated by solving the twofold standard deviation of the repeatable pressure response curves and plotting the corresponding error bars. The repeatability curves for the seven cycles are shown in Figure 2. The error of the system is within 0.5% in all the regions except 0.68% at 5 kPa, and the fluctuation is small.

3. Results and Discussion

3.1. Effect of High Temperature on Paint Properties

In cryogenic wind tunnel tests, PSP is typically used in a broad temperature range, with the total temperature of the free stream ranging from lower than 120 K to approximately 323 K. To verify the applicability of the self-developed PSP coating in cryogenic wind tunnels and determine whether the paint undergoes irreversible changes in coating properties at extreme temperatures, this paper proposes a PSP stable temperature range based on the cryogenic PSP static calibration system. The evaluation procedure is as follows: (1) Prepare a static calibration sample using the paint formulation and spraying process mentioned in Section 2.1. (2) Obtain the pressure response curve using the static calibration system at room temperature or a moderate temperature. After an interval of five minutes, obtain the curves again at this temperature with the same procedure and compare them to ensure stability at the current temperature. (3) Adjust the sample temperature from the moderate temperature to the target extreme temperature and hold for five minutes. The sample temperature is then lowered and returned to a moderate temperature. (4) Recalibrate the pressure curve under moderate temperature. (5) Compare the pressure response curves before and after extreme temperature impingement to determine whether the paint undergoes irreversible changes in coating properties. If a significant change is observed, it indicates that the target extreme temperature causes structural damage to the cryogenic PSP coating, demonstrating that the designed cryogenic PSP is not suitable for this target temperature. The flowchart of this determination method is shown in Figure 3.

In this paper, three groups of samples from the same batch of spraying were selected and put into the calibration chamber together to carry out the calibration experiments at the same time. It can be seen that the three groups of samples at 260 K all show good repeatability; the detailed results are shown in

Table 1. Overall pressure sensitivity comparison tables.

Calibration Sample	260 K Before Heating	260 K Repeatability Before Heating	260 K After Heating
Sample 1	0.497%/kPa	0.498%/kPa	0.499%/kPa (303 K Heating)
Sample 2	0.503%/kPa	0.504%/kPa	0.497%/kPa (313 K Heating)
Sample 3	0.498%/kPa	0.498%/kPa	0.452%/kPa (323 K Heating)

. After that, the three groups of samples were heated at 303 K, 313 K, and 323 K for 5 min and then put into the calibration chamber at the same time to set the target temperature of 260 K for calibration experiments. As can be seen from Figure 4, for the two groups of samples before and after heating at 303 K and 313 K, there is no obvious change in the pressure response curve, and the overall pressure sensitivity change is less than 1.3%. After 323 K heating, the overall pressure sensitivity of the coating decreased by 9.2%.

To investigate the cause, scanning electron microscope (SEM) observations were conducted on the cross-sectional morphology of the coating before and after extreme temperature impingement, as shown in Figure 5. It is worth noting that the samples we used for SEM characterization were pure PTMSP coatings and not surface-sprayed PtTFPP. The results indicate that the coating cross-section exhibits signs of thermal deformation to some extent after heating [23]. The experimental findings suggest that the microstructure of the coating undergoes changes at this temperature. This phenomenon may be attributed to the accelerated aging of the polymer’s porous structure of the cryogenic PSP coating at 323 K, which reduces the oxygen permeability rate and leads to a significant decrease in pressure sensitivity. Using the aforementioned PSP applicability temperature evaluation method, the self-developed cryogenic PSP is verified as suitable for temperatures from room temperature down to 123 K.

3.2. Effect of Temperature on Luminous Intensity

In order to better evaluate and reduce pressure measurement errors caused by temperature effects, we measured the luminescence characteristics of coatings at different temperatures and pressures and analyzed their patterns. This provides a reference for interpreting cryogenic PSP pressure measurement results and developing temperature effect correction methods. Figure 6 shows the variation in luminescence intensity with temperature at different sample storage times and under different pressure conditions. As the temperature decreases from 298 K to 123 K, the thermal quenching effect weakens, and the luminescence intensity of the coating gradually increases. This trend is consistent with that of conventional PSP. As the temperature decreases below 248 K, the luminescence intensity of the coating exhibits an inverse relationship with conventional PSP behavior. As the temperature decreases during a certain cryogenic temperature range, the luminescence intensity of the coating gradually weakens. Repeated calibration experiments confirmed this anomalous trend.

The observed phenomenon may be attributed to the unique molecular configuration developed during the spray-coating process: The high molecular weight of PTMSP promotes extended molecular chain crosslinking, resulting in a metastable microstructure characterized by loosely interconnected molecular networks and an enlarged free volume fraction immediately post-deposition. This transient structural state enhances the coating’s sensitivity to both temperature fluctuations and pressure variations during the initial stabilization period.

The possible cause of this phenomenon may be related to the molecular structure and curing process of PTMSP. After spraying, due to the high molecular weight of PTMSP, the crosslinking between molecular chains requires a prolonged period to fully complete. As a result, within a short time after application, the crosslinking reaction between PTMSP molecular chains remains incomplete. At this stage, the polymer structure is relatively loose, with a high free volume fraction. In this state, the microstructure of the coating becomes more sensitive to changes in surface pressure and temperature. During the temperature decrease, volume contraction causes significant changes in the spacing between PtTFPP fluorescent probes embedded in PTMSP. This, in turn, affects the aggregation state of the probes and the distribution of luminescence energy levels, leading to an anomalous anti-thermal quenching phenomenon in PtTFPP luminescence intensity. Over time, the polymer structure within the coating gradually stabilizes, and the anti-thermal quenching effect diminishes. At this stage, only the normal thermal quenching behavior can be observed. This finding provides valuable insights for temperature effect correction in the engineering application of cryogenic PSP, helping to minimize measurement errors caused by temperature effects.

3.3. Effect of Temperature on Pressure Sensitivity

Pressure sensitivity is a key parameter in evaluating the characteristics of cryogenic PSP coatings. Figure 4 presents the pressure response curves of the self-developed cryogenic PSP coating at different temperatures. The data are plotted with 223 K and 110 kPa as the reference state. As shown in Figure 7a, on the first day after spraying, as the temperature decreases from 298 K to 123 K, the oxygen permeability rate of the polymer gradually decreases, leading to a gradual reduction in overall pressure sensitivity. However, in general, the changes in oxygen permeability rate and pressure sensitivity remain relatively small. Notably, an abnormal increase in pressure sensitivity is observed in the low-pressure region at 148 K and 123 K. This phenomenon may be attributed to the prolonged fluorescence lifetime of PtTFPP at low temperatures, which extends the oxygen quenching time window. Additionally, the increase in free volume fraction at low pressures counteracts the material contraction caused by temperature reduction, resulting in an unexpectedly high sensitivity in the low-pressure region. Over time, crosslinking between molecular chains within the coating becomes more complete, leading to a gradual attenuation of this abnormal sensitivity effect, which stabilizes by the 144 h, as shown in Figure 7b,c. This discovery provides valuable insights for enhancing the pressure sensitivity of the cryogenic PSP, offering potential strategies for further optimization.

The results in Figure 8 show the pattern of change in pressure sensitivity over time in a calibration environment of 2000 ppm oxygen concentration and different temperatures. As shown in Figure 8, the PSP shows a more decreased sensitivity at low pressures compared to high pressure over time. The change in the overall pressure sensitivity of the PSP was less than 16% at 72 h and less than 22% at 144 h. In addition, the pressure sensitivity of the PSP after 144 h at 123 K was 0.244%/kPa, which represents a 15.8% change in the overall pressure sensitivity compared to 24 h after spraying.

4. Conclusions

The temperature effects on luminescence intensity and pressure sensitivity, along with their underlying mechanisms of a self-developed cryogenic PSP employing high-oxygen-permeable polymer PTMSP as a binder and long-lifetime luminescent molecule PtTFPP as a probe, were investigated in this study. The research results indicate the following:

• When the temperature reaches 323 K, coatings can accelerate aging, leading to significant and irreversible changes in coating performance.
• The thermal quenching effect of PSP has significant changes over time. In the initial stage, both fluorescence emission thermal quenching and anti-thermal quenching phenomena coexist, and after 72 h, the overall appearance is a single thermal quenching phenomenon. As time passes, the PSP structure tends to stabilize and eventually exhibits a similar thermal quenching trend as conventional PSP. In addition, the temperature quenching effect increases from 72 to 144 h.
• As the temperature decreases, the overall pressure sensitivity of PSP decreases. After 144 h at a temperature of 123 K, the pressure sensitivity of the PSP was 0.244%/kPa, and the overall pressure sensitivity changed by 15.8% compared to 24 h after spraying.

The results provide valuable insights for improving their measurement accuracy in cryogenic, high-Reynolds-number wind tunnel applications. In the future, more efforts will be made to optimize the present cryogenic PSP formulation to further reduce its temperature effects, expand its applicable temperature range, and enhance its pressure sensitivity under deep, low-temperature conditions.