Model Development and Analysis of the Dynamics of Pressure-Sensitive Paints

Abstract

Two models for the dynamic behavior of pressure-sensitive paints are developed. The e rst of the two models is a purely empirical approach to designing a model and compensator. The second model presented encompasses the physics of the process by which an unsteady pressure e eld over the paint layer affects the layer and causes an intensity of e uorescence that is e uctuating in time. Within this second model, two different forms for the static calibration are chosen. The effect of the calibration on the system dynamics is demonstrated. Nomenclature A = amplitude a = pressure-sensitive paint thickness b = intercept of linear Stern ‐Volmer static calibration c = calibration constants D = diffusivity E = activation energy f = calibration function from pressure to intensity g = calibration function from intensity to pressure H = transfer function I = integrated intensity J = intensity per unit thickness j = the complex number, p i1 K = intensity error per unit thickness relative to surface condition M = model order m = oxygen concentration difference relative to surface condition n = oxygen concentration P = pressure T = temperature t = time x = distance from substrate ® = modal states ¸ = eigenvalues ae = solubility ? = time constant A = phase 9 = spatial eigenfunctions ! = frequency