A central issue in the design of aircraft is improving the lift of aircraft wings. To assist in the design of more efficient wings, wind-tunnel tests are performed in which the pressures at various parts of the wing are measured generally using only a few localized pressure sensors. Recently, pressure-sensitive paints have been developed to provide a more detailed view of wing pressure. In these paints, a luminescent molecule is dispersed into an oxygen-permeable paint and the aircraft wing is painted. The wing is placed into an airfoil, and luminescence from the paint is measured. The variation in O₂pressure is measured by monitoring the luminescence intensity, with lower intensity demonstrating areas of higher O₂pressure due to quenching. 

a. The use of platinum octaethylporphyrin (PtOEP) as an oxygen sensor in pressure-sensitive paints was described by Gouterman and coworkers [Review of Scientific Instruments 61 (1990): 3340]. In this work, the following relationship between luminescence intensity and pressure was derived: l₀/l = A + B(P/P₀), where I₀ is the fluorescence intensity at ambient pressure P₀, and I is the fluorescence intensity at an arbitrary pressure P. Determine coefficients A and B in the preceding expression using the Stern€“Volmer equation: k _total = 1/t _f = k _f + k_q[Q]. In this equation Ï„ _l is the luminescence lifetime, k _f is the luminescent rate constant, and k _q is the quenching rate constant. In addition, the luminescent intensity ratio is equal to the ratio of luminescence quantum yields at ambient pressure, Φ₀, and an arbitrary pressure, Φ: Φ₀/Φ = l₀/l.

b. Using the following calibration data of the intensity ratio versus pressure observed for PtOEP, determine A and B:

c. At an ambient pressure of 1atm, I₀ = 50,000 (arbitrary units) and 40,000 at the front and back of the wing. The wind tunnel is turned on to a speed of Mach 0.36 and the measured luminescence intensity is 65,000 and 45,000 at the respective locations. What is the pressure differential between the front and back of the wing?

Transcribed Image Text:

I/I P/P I/I P/P, 0.46 1.0 1.0 0.65 0.61 0.9 0.86 0.40 0.87 0.80 0.55 0.34 0.83 0.75 0.50 0.28 0.65 0.77 0.46 0.20 0.70 0.53 0.35 0.10