Pressure-Sensitive and Temperature-Sensitive Paints for Measuring High Speed and Unsteady Flows

A method for estimating global heat flux from measurements of surface temperature using temperature-sensitive paint (TSP) in hypersonic wind tunnels is introduced. Exact solutions to the one-dimensional heat-conduction equation for two- and three-layer solids of finite depth are obtained using a Green's function (GF) formulation. GFs describing both the temperature change anywhere within the solid and the mean temperature across the TSP form the basis of an inverse heat-conduction problem, which is then solved using regularized deconvolution to mitigate amplification of measurement noise. The disparity between apparent and true TSP temperatures, arising from the integrated emission intensity across the paint, is minimized by means of an iterative routine considering the statistics of a virtual temperature profile. Numerical simulations of heat conduction in various scenarios are then conducted to verify the validity of the method, while its effectiveness is assessed in the analysis of exemplary wind tunnel experiments.

There are at least two direct links between the friction acting on the surface of a (slightly warmer or colder) body under the influence of an incompressible flow and the temperature distribution on the surface of the body itself. The first relies on the energy equation, which connects the evolution of the temperature distribution at the wall to the action of the skin-friction field. On the other hand, the equation of passive transport of temperature perturbations at the wall unveils a direct relationship between the celerity of propagation of thermal blobs and the friction velocity. Grounding on these relationships, this paper reports about the application of different methodologies, developed to determine skin-friction fields from surface temperature maps, to the analysis of the complex flow evolution on a lifting NACA 0015 hydrofoil immersed in a non-uniform, unsteady wake induced by a marine propeller. The adopted temperature-sensitive paint technique allows obtaining the global temperature data with the appropriate, high resolution in space and time. The approach based on the energy equation leads to an unconventional, single-snapshots optical-flow-like methodology, which allows obtaining time-resolved, relative skin-friction fields. The two approaches based on the displacement of the wall temperature perturbations enable the determination of time- and phase-averaged, quantitative skin-friction fields. One approach grounds on a classical tracking of the thermal disturbances via optical flow, the other one relies on minimizing the discrepancy between the celerity of propagation of thermal fluctuations and the behavior expected according to the Taylor hypothesis. The analysis of the skin-friction fields obtained via the three uncorrelated, complementary approaches discloses the evolution and the mutual interaction of different flow structures (manifolds) over the hydrofoil surface at lifting and zero-lift conditions: the hub and tip vortices, the blade wake, the laminar separation bubble, and the separation at trailing edge.

The feasibility of back-imaging polymer-ceramic pressure-sensitive paint (PC-PSP) was investigated, with supersonic flow over a rectangular cavity being the test subject. A PC-PSP formulation in which the luminophore was fully-integrated into the binding layer created a PSP which luminesced from the top and bottom of the layer. This PSP was applied to a clear acrylic plate serving as the cavity ceiling. Two identical high-speed cameras imaged the paint; one viewed the top of the PSP layer (front-imaging) whereas the other viewed the bottom of the layer (back-imaging). The temporal, time-averaged, and spectral response measured by each camera were functionally identical. Specifically, the two data were found to be 90% correlated in time at zero delay. The minor differences can be attributed to random noise and the fact that the cameras viewed through two different materials (one through acrylic and the other through optically-polished glass). These results illustrate that back-imaging is a promising method for overcoming the optical access constraints of conventional PSP imaging techniques.

This paper investigates the pressure sensitivity of a temperature-sensitive paint (TSP) which uses a clear coat as binder and the Ru(dpp) as luminophore, and then discusses its effect on heat flux determination. Systematic static calibrations of three TSP samples with different thicknesses (7.5 μm, 10.3 μm and 13.1 μm) are carried out in a temperature range of 298 K to 373 K and a pressure range of 3.8 kPa to 15.2 kPa. Besides, dynamic pressure response calibrations are performed from 298 K to 373 K. The static calibration results show a significant growth in the pressure sensitivity as the temperature increases. For example, the pressure sensitivity of the 10.3 μm thick TSP at 3.8 kPa grows from 0.086% kPa⁻¹ to 0.412% kPa⁻¹ as the temperature rises from 298 K to 373 K. The dynamic calibration results show that the pressure response time is in the order of seconds, which decreases significantly with both the temperature and the paint thickness. For example, the pressure response time of the 10.3 μm thick TSP decreases from 11.55 s to 0.68 s as the temperature increases from 298 K to 373 K. The calibration results suggest that the pressure sensitivity of TSP would lead to noticeable temperature and heat flux errors in high-speed, long-duration wind tunnel tests. This pressure-induced effect is evaluated for three TSP samples by the simulations with varying local pressure and heat flux. The results show that the heat flux error increases as the paint thickness reduces because of faster pressure response. The error increases with the local pressure as expected, but it shows a negative correlation to the local heat flux.

Temperature-sensitive paint (TSP) is a type of luminescent temperature sensor that can provide surface temperature measurements on the surface of a test article. These surface temperature measurements can be used to determine heat flux and visualize boundary layer transition on an aerodynamic body. This paper presents the static response characteristics of a TSP based on rhodamine B (RhB) applied on a polymer-ceramic supporting matrix. Six solvents with varying polarity indices were used to apply the RhB to the sensors, which were then evaluated in terms of luminescent signal level and temperature sensitivity. The results are presented and also compared to previous results for RhB on an anodized aluminum matrix. The temperature range was between 150 K and 365 K. The study confirms that the influence of the solvent on the sensor's final characteristics is significant, and shows temperature sensitivities as high as −4.8% K⁻¹ at 150 K when dichloromethane is used as the application solvent.

This article describes the successful implementation of a structured UV light field, generated from a modified LCD projector, to excite pressure-sensitive paint (PSP) and measure surface shape simultaneously without the need to compromise the PSP by mechanical degradation of the coating. Using commercially available hardware, results were gathered in a Mach 5 wind tunnel, showing the expected pressure distribution around a cone model with a flare and the surface geometry without any prior knowledge or information. The demonstrated methodology can be used to measure aerodynamic models exhibiting elastic deformation under load during a wind tunnel measurement campaign, providing out-of-plane motions are small. The captured deformation and pressure results can be used to support validation of structural models and correct numerical simulation meshes to the actual shape investigated in the wind tunnel.

A sprayable fast-responding pressure-sensitive paint (fast-PSP) has been developed to measure time-resolved small pressure fluctuation on model surfaces. To realize PSP with fast response, high robustness, and high luminescence intensity, we have developed a novel ruthenium complex-based fast-PSP. The binder layers of the proposed fast-PSP were prepared by mixing room-temperature-vulcanizing silicone (silicone) and titanium dioxide (TiO₂) particles with different sizes and their effects on the properties including the time response, pressure sensitivity, and luminescence intensity were investigated. The effects of the hydrophilic and hydrophobic surface treatments of TiO₂ particle on the structure and mechanical robustness of the binder layer were also studied. The developed fast-PSP was applied to the flow field measurements behind a square cylinder and was evaluated. We have succeeded in obtaining time-series data of pressure fluctuation with high accuracy even at a mean velocity of 20 m s⁻¹.

This study experimentally examined the flow phenomena and pressure distribution on the wing of Advisory Group for Aerospace Research and Development Model B (AGARD-B) at a Mach number of 0.83. For simultaneous pressure and temperature measurement, a mesoporous pressure-sensitive paint (PSP) sensor was applied to one of the wings of AGARD-B at an angle of attack (AOA) of 0°–8° and a temperature-sensitive paint sensor was applied to the other wing. The collected temperature data were used for pixel-by-pixel temperature correction in a PSP experiment. The pressure distribution obtained on the AGARD-B wing through the PSP experiment with temperature correction agreed well with that obtained through computational flow dynamics (CFD) simulation and accurately indicated the low-pressure regions introduced by the vortex generated from the leading edge at an AOA larger than 4°. The lift coefficient calculated using the PSP data agreed well with that calculated using CFD.