# Category Pressure and Temperature Sensitive Paints

## Collision-Controlled Model

When the rate constant kq for the oxygen quenching and the oxygen concentration

[O2] are considered in a collision-controlled reaction, the Stern-Volmer relation is called the collision-controlled model to distinguish from the diffusion-controlled relation (or adsorption-controlled model). The rate of collision of the oxygen molecules on a porous surface is [O2]c /4, where c* is the average speed of the molecules. According to the theory of ideal gas, one knows

where pOq is the partial pressure of oxygen, T is the absolute temperature in

Kelvin, Mm is the molar mass, R is the universal gas constant, and N0 is the Avogadro’s number.

The rate of the oxygen quenching is modeled by a product of an effective contact area and the collision rate

Hence, the rate of the oxygen quenching is proportional to the partial pressure of oxygen or air pressure, but is inversely proportional to the square root of temperature. The Stern-Volmer relation for the luminescent lifetime then becomes

1 Geff No Фо2

-_ ka + , =P

T pKMmRT

For aerodynamic applications, the Stern-Volmer relation for the collision – controlled quenching process can be written as

where the coefficients at the reference conditions are defined as

Acollision, ref 1 /(1 + Z) , Bcollision, ref Z /(1 + Z) ,

OeffN 0Фо2Р ref

karef-l2nMmR Tref

Although Eq. (2.33) has the same form as that for a conventional polymer binder, the Stern-Volmer coefficients AcoUiion and Bcoliisinn have different physical meanings. The coefficient Bmllso>n has weaker temperature dependency that is inversely proportional to the square root of temperature. In contrast, the temperature dependency of Acoliiiion has the same form as that for a conventional polymer binder; linearization of Eq. (2.34) at T = Tref leads to

## Models for Porous Pressure Sensitive Paint

In the preceding section, the photophysical models for a conventional polymer PSP are discussed. Nevertheless, according to the work of Sakaue (1999), the photophysical models for a porous PSP or open PSP system are different. In general, pores in a porous PSP are macroscopic, which are much larger than the size of an oxygen molecule. Figure 2.2 shows schematically a comparison of a conventional polymer PSP with a porous PSP. In a conventional polymer PSP, as shown in Fig. 2.2(a), the oxygen molecules in the working gas permeate into a polymer binder layer and quench the luminescence. In contrast, as illustrated in Fig. 2.2(b), a porous PSP has a much larger open surface to which the luminophore molecules are directly applied; the oxygen molecules can directly quench the luminescence without having to permeate into a binder layer. Therefore, the use of a porous material as a binder for PSP offers two advantages. First, a porous PSP can achieve a very fast time response (in the order of microseconds) for unsteady PSP measurements; secondly, it makes PSP measurements possible at cryogenic temperatures at which oxygen diffusion is prevented through a conventional homogeneous polymer.

(a)

(b)

The oxygen quenching process in a porous PSP is different from that in a conventional polymer PSP. Figures 2.3(a) and (b) illustrate two scenarios of the oxygen quenching in a porous PSP; in both cases, a luminophore molecule is adsorbed on a porous surface opened to the working gas. In Fig. 2.3(a), a gaseous oxygen molecule collides to a luminophore molecule, resulting in the oxygen quenching; in this case, the oxygen quenching process is controlled by a collision between the gaseous oxygen molecule and luminophore molecule adsorbed on the surface. In other case, as illustrated in Fig. 2.3(b), an adsorbed oxygen molecule can cause quenching by diffusing to a luminophore molecule and hence the oxygen quenching process is related to adsorption and diffusion of the oxygen molecule into the luminophore molecule. Wolfgang and Gafney (1983) studied the oxygen quenching of tris(2,2′-bipyridyl)ruthenium (Ru(bpy)) on a porous Vycor glass and reported that Ru(bpy) was quenched by either a gaseous oxygen molecule colliding to the adsorbed Ru(bpy) or an adsorbed oxygen molecule.

Fig. 2.3. Oxygen quenching mechanisms for porous PSP: (a) Collision controlled model; (b) Adsorption controlled model. From Sakaue (1999)

Two photophysical models were developed by Sakaue (1999) to describe the oxygen quenching on a porous surface by considering the Eley-Rideal (ER) mechanism and Langmuir-Hinshelwood (LH) mechanism. The ER mechanism is a target annihilation reaction between a gaseous oxygen molecule and an adsorbed luminophore molecule; it is a collision-controlled reaction (Samuel et al. 1992). The LH mechanism, which is adsorption/surface-diffusion-controlled, is a reaction between an adsorbed oxygen molecule and an adsorbed luminophore molecule (Hinshelwood 1940). Samuel et al. (1992) studied the oxygen quenching of Ru(bpy) on a porous silica surface over a temperature range of 88-353 K and reported that at low temperatures the oxygen quenching was diffusion-controlled (the LH type). As temperature increased, the reaction remained the LH type in nature, but it was increasingly influenced by the target annihilation reaction (the

ER type). At higher temperatures, the reaction was no longer the LH type, which was dominated by the ER type reaction. In these cases, the rate constant kq for the oxygen quenching and the oxygen concentration [O2] were described in a different manner from that for a conventional polymer binder.

## Models for Conventional Pressure Sensitive Paint

From a standpoint of engineering application, it is unnecessary to analyze all the intermediate photophysical processes and their interactions. Therefore, a lumped model for luminescence (fluorescence and phosphorescence) is given here by considering the main processes: excitation, luminescent radiation, non-radiative deactivation, and quenching. The luminophore is excited by a photon from a ground state L0 to an excited state L, i. e., L0 + hv — L. The excited state L returns to the ground state L0 by either a radiative process (emission) or a radiationless process (deactivation). In the radiative process, the luminescent

* k

emission releases energy of hv,, that is L*——- -——L0 + hv,, where kr is the rate

constant for the radiation process and v, is the frequency of the luminescent emission. In the deactivation process, L* returns to L0 by releasing heat, which

* к

is expressed as L —— -—— L0 + A, where knr is the rate constant for the combined

effect of all the non-radiative processes. If temperature around a luminophore molecule increases, the deactivation rate increases, reducing the radiative process from L*. Thus, the rate constant knr for the non-radiative processes is

temperature-dependent. The quenching process by a quencher Q is expressed as к

L* + Q——- —>L0 + Q*, where kq is the rate constant of the quenching process
and Q* denotes the excited quencher. The molecular oxygen O2 in the ground state is an efficient quencher for both the excited singlet and triplet states. The molecular oxygen is excited to O* once it quenches luminescence, i. e., L + O2 ^ L0 + O*. By combining the rates of emission, deactivation and quenching processes, the rate of change of the population of the excited state [L* ] is given by the first-order equation

= I a – (kr + knr + kq[Q])[L*] . (2.3)

dt

The rate of excitation is Ia = ks1[L0], where [L0] is the population in the ground state and ks1 is the rate constant for excitation. At a steady state d[L* ] / dt = 0, without quenching ([Q] = 0 ), we have

I a = {kr + knr )[L*] . (2.4)

The amount of luminophore molecules in a given excited state is described by the quantum yield of luminescence defined by

^ rate of luminescence

Ф =—————————— . (2.5)

rate of excitation

The quantum yield Ф for the luminescent emission from L* with the quencher Q is expressed by

ф= kr[L ] =————— hr——— = J_, (2.6)

Ia kr + knr + kq[Q] Ia

where I is the luminescent intensity. The quantum yield without quenching is

where I0 is the luminescent intensity without quenching. Dividing Ф0 by Ф , we obtain the well-known Stern-Volmer relation

where T0 = 1/(kr + k^) is the luminescent lifetime without quenching. The luminescent lifetime with the quencher is

1

T =———————–

kr + knr + kq[ Q]

Thus, Eq. (2.8) can be written as

ф0/ Ф = т0/т. (2.10)

When the quencher is oxygen, the Stern-Volmer equation is

I т

-f =-0- = 1 + kqT0[O2]. (2.11)

I т

In general, the rate constants knr and kq for the non-radiative and quenching processes are temperature-dependent. The temperature dependency of knr can be decomposed into a temperature-independent term and a temperature-dependent term modeled by the Arrhenius relation (Bennett and McCartin 1966; Song and Fayer 1991), i. e.,

E

knr = knro + knriexp(—£~) , (2.12)

where krr0 = knr(T = 0) and knr1 are the rate constants for the temperature – independent and temperature-dependent processes, respectively, Enr is the activation energy for the non-radiative process, R is the universal gas constant, and T is the absolute temperature in Kelvin. The temperature dependency of the rate constant kq for the quenching process is related to oxygen diffusion in a

homogenous polymer layer used for a conventional PSP. According to the Smoluchowski relation, the rate constant kq for the oxygen quenching can be

described by

kq = 4nRABN0D (2.13)

where Rab is an interaction distance between the luminophore and oxygen molecules, and N0 is the Avogadro’s number. The diffusivity D has the temperature dependency modeled by the Arrhenius relation

E

D = D0 exp(—– —) , (2.14)

where ED is the activation energy for the oxygen diffusion process. Therefore, from Eq. (2.9), the reciprocal of the luminescent lifetime is

According to Henry’s law, the oxygen population [O2]polymer in a polymer binder is proportional to the partial pressure of oxygen pO or air pressure p, i. e.,

[ O 2] polymer = spo2 = s0o2p (2.16)

where S is the oxygen solubility in a polymer binder layer and ф02 is the mole fraction of oxygen in the testing gas. The mole fraction of oxygen ф02 is 21% in the atmosphere, but it varies depending on testing facilities. For example, ф0і is only a few ppm (1ppm = 10-4%) in a cryogenic wind tunnel where the working gas is nitrogen. Defining the permeability P0 = SD0, from Eq. (2.15), we have

– = ka + Kp, (2.17)

T

where the coefficients ka and K are defined as

E E

ka = kr + knro + k„riexp(–E-) and K = 4nRABNoPoexp(–^)фо Rl Rl

In aerodynamic applications, it is difficult to obtain the zero-oxygen condition since the working gas in most wind tunnels is air containing 21% oxygen. Thus, instead of using the zero-oxygen condition, we usually utilize the zero-speed (wind-off) condition as a reference. Taking a luminescent intensity ratio between the wind-off and wind-on conditions, we obtain the Stern-Volmer equation suitable to aerodynamic applications

The Stern-Volmer coefficients in Eq. (2.19) are

ka K

Apolymer Apolymer, ref, and Bpolymer Bpolymer, ref

karef Kref

where the reference coefficients are defined as

The subscript ‘polymer’ specifically denotes a conventional polymer-based PSP; it will be seen that porous PSPs have somewhat different forms of the Stern- Volmer coefficients. Eq. (2.19) indicates that a ratio between the luminescent intensities in the wind-on and wind-off conditions is required to determine air pressure. This intensity-ratio method is commonly employed in PSP and TSP measurements.

Using the expressions for ka and K, we can write Apolymer and Bpolymer as a

function of temperature

Apolymer Apolymer ,ref

1 + £exp( – Enr/RT) [1]

 ET

 (2.22)

 B polymer B polymer, ref exp

 RTr

where the factor £ is defined as £ = knr1 /(kr + knr0) . For (T – Tref ) / Tref << 1, the linearized expressions for Apolymer and Bpolymer are

where the factor n is

£eXp(- E„rlRTref)

n =—————— – —- – —

1 + £ exp( – Enr/RTref)

Clearly, the Stern-Volmer coefficients Apolymer and Bpolymer satisfy the following

constraint

Apolymer (Tref ) + Bpolymer (Tref ) 1 ‘

Eq. (2.23) indicates that the Stern-Volmer coefficient B polymer depends on the activity energy ED for the oxygen diffusion process; this implies that the temperature sensitivity of PSP is mainly related to the oxygen diffusion. Indeed, experiments conducted by Gewehr and Delpy (1993) and Schanze et al. (1997) for two different oxygen sensors showed that the temperature dependency of the oxygen diffusivity in a polymer dominated the temperature effect of PSP. This finding has an important implication in the design of low-temperature-sensitive PSP formulations; the low-temperature-sensitive PSP should have a polymer binder with the low activation energy for oxygen diffusion. In another special case where ED ~ Enr and n ~ 1 over a certain range of temperature, the coefficients Apoiymer(T) and Bpolymer(T) have the same temperature dependency; thus a ratio between Apolymer(T) and Bpolymer(T) becomes temperature

independent. PSP satisfying the above conditions is so-called ‘ideal’ PSP (see Section 3.6). This paint is advantageous for correcting the temperature effect since the Stern-Volmer relation becomes temperature independent when the intensity ratio scaled by a single temperature-dependent factor is used as a similarity variable.

In many PSP measurements, the linear Stern-Volmer relation Eq. (2.19) is sufficiently accurate in a certain range of pressure. However, over an extended range of the partial pressure of oxygen or air pressure, the non-linear Stern-

Volmer behavior becomes appreciable for microheterogeneous PSPs (Carraway et al. 1991a; Xu et al. 1994; Hartmann et al. 1995). The main physical mechanisms behind the non-linear Stern-Volmer characteristics are associated with microheterogeneity of the environment of a probe molecule and deviation from Henry’s law. Solid-state matrices like polymers may provide numerous different kinds of environments for a probe molecule, resulting in the non-exponential decay or multiple-exponential decay of luminescence. In some cases, a double exponential model is sufficient for the decay; thus the oxygen quenching of luminescence in microheterogeneous systems is described by a two-component model

where f01 and f02 are the fractional intensity contributions of the two

components in the absence of oxygen (f01 + f02 = 1), KSV1 and KSV2 are the

where C is the Langmuir gas capacity due to adsorption and b is the Langumir affinity coefficient. Based on the dual sorption model Eq. (2.27), Hubner and Carroll (1997) suggested an extended form of the Stern-Volmer relation

Eq. (2.28) was able to give a good fit to experimental data for some PSPs. From a standpoint of aerodynamic applications, an empirical form of the non-linear Stern – Volmer relation is usually given by a polynomial

## Basic Photophysics

1.1. Kinetics of Luminescence

Pressure sensitive paint (PSP) and temperature sensitive paint (TSP) are, respectively, based on the oxygen and thermal quenching processes of luminescence which are reversible processes in molecular photoluminescence. The general principles of luminescence are described in detail by Rebek (1987), Becker (1969) and Parker (1968). The different energy levels and photophysical processes of luminescence for a simple luminophore can be clearly described by the Jablonski energy-level diagram shown in Fig. 2.1. The lowest horizontal line represents the ground-state energy of the molecule, which is normally a singlet state denoted by S0. The upper lines are energy levels for the vibrational states of excited electronic states. The successive excited singlet and triplet states are denoted by S1 and Sz and T1, respectively. As is normally the case, the energy of the first excited triplet state T1 is lower than the energy of the corresponding singlet state S1.

A photon of radiation is absorbed to excite the luminophore from the ground electronic state to excited electronic states (S0 ^ Sj and S0 ^ S2). The excitation process is symbolically expressed as S0 + hv ^ Sj, where h is the Plank constant and v is the frequency of the excitation light. Each electronic state has different vibrational states, and each vibrational state has different rotational states. The excited electron returns to the unexcited ground state by a combination of radiative and radiationless processes. Emission occurs through the radiative processes called luminescence. The radiation transition from the lowest excited singlet state to the ground state is called fluorescence, which is expressed as Sj ^ S0 + hvf. Fluorescence is a spin-allowed radiative transition between two states of the same multiplicity. The radiative transition from the triplet state to the ground state is called phosphorescence (Tj ^ S0 + hvp ), which is a spin-

forbidden radiative transition between two states of different multiplicity. The lowest excited triplet state, T1, is formed through a radiationless transition from S1 by intersystem crossing (Sj ^ Tj). Since phosphorescence is a forbidden transition, the phosphorescent lifetime is typically longer than the fluorescent lifetime. Luminescence is a general term for both fluorescence and phosphorescence.

 Singlet Excited States Fig. 2.1. Jablonsky energy-level diagram

Radiationless deactivation processes mainly include internal conversion (IC), intersystem crossing (ISC) and external conversion (EC). The internal conversion (IC) is a spin-allowed radiationless transition between two states of the same multiplicity (S2 ^ Sj, Sj ^ S0). Typically, this process is expressed as Sj ^ S0 + A, where A denotes heat released. IC appears to be particularly efficient when two electronic energy levels are sufficiently close. The intersystem crossing (ISC) is a spin-forbidden radiationless transition between two states of the different multiplicity, which are expressed as Sj ^ Tj + A and Tj ^ S0 + A. Phosphorescence depends to a large extent on the population of the triplet state (Tj) from the excited singlet state (Sj) by the intersystem crossing. In addition, deactivation of an excited electronic state may involve interaction and energy transfer between the excited molecules and the environment like solutes, which are called external conversion (EC).

The excited singlet and triplet states can be deactivated by interaction of the excited molecules with the components of a system. These bimolecular processes are quenching processes, including collisional quenching (diffusion or non­diffusion controlled), concentration quenching, oxygen quenching, and energy transfer quenching. The oxygen quenching of luminescence is the major photophysical mechanism for PSP. Due to the oxygen quenching, air pressure on
an aerodynamic model surface is related to the luminescent intensity by the Stern – Volmer equation that will be further discussed. The quantum efficiency of luminescence in most molecules decreases with increasing temperature because the increased frequency of collisions at elevated temperatures improves the possibility for deactivation by the external conversion. This effect associated with temperature is the thermal quenching, which is the major photophysical mechanism for TSP.

The population of the excited singlet states (SI) and triplet states (TI) at any given time depends on the competition among different photophysical processes listed in Table 2.1. The singlet state population [SI] and triplet state population [TI] are described by the following first-order kinetic model

йЫ. = I a – (kf + kic + + kq(s)[Q])[Sj]

where Ia is the light absorption rate of generating the excited singlet states, [Q] is the population of the quencher Q, kf and kp are, respectively, the rate constants for fluorescence and phosphorescence, kisc(si } and kisc(ti } are, respectively, the rate constants for the intersystem crossings SI ^ TI and TI ^ S0, kcc is the rate constant for the internal conversion, and kq(s) and kq(t) are the rate constants for the quenching in the singlet states and triplet states, respectively. The light absorption rate Ia = ksI[S0] is proportional to the population [S0] in the ground state and the rate constant of excitation ks1. After a pulse excitation, the times required for the populations in the excited singlet state and triplet state to decay to 1/e of the initial value are, respectively,

Tf = (kf + kic + kisc(sI-tI) + kq(s)[Q])

Tp = I/(kp + kisc(ti-So) + kq(t) [Q]). (2.2)

The time constants Tf and Tp are defined as the fluorescent and phosphorescent

lifetimes, respectively. Usually, the lifetime of a specific photophysical process is defined as the reciprocal of the corresponding rate constant. Typical values of the lifetimes for different photophysical processes are listed in Table 2.1. When the intersystem crossing from T1 back to Sq (T1 ^ S1 + A ) is included in the kinetic

m°deb extra terms kisc(tl-Sl)[Tj] and – kisc(,I-Sl)[Ti] should be adde^

respectively, to the right-hand sides of Eq. (2.1) for [SI] and [TI], where ksx( ) is the rate constant for the intersystem crossing Tq ^ Sq. In this case,

the kinetic model becomes a coupled system of equations (Mosharov et al. 1997; Bell et al. 2001). Since S1 is a higher energy state than T:, this intersystem crossing is thermally activated and therefore the rate constant for the process T1 — S: is temperature-dependent.

Table 2.1. Photophysical processes involving electronically excited states

 Step Process Rate Lifetime (s) Excitation S0 + hv —^ S1 kJSJ 10-15 Fluorescence (F) Sj —— S0 + hv f kf[S, J 10-11 -10-6 Internal Conversion (IC) S1 — S0 +A к ic[S]J 10-14 -10-11 Intersystem Crossing (ISC) S1 — T1 +A к isc( S1 – t1) [ S1 J 10-11 -10-8 Phosphorescence (P) Ti — S0 + ^vp kp[T2J 10-3 -102 Intersystem Crossing (ISC) T1 — S0 + A kisc(t1 – Sg ) [,T1 J

## Historical Remarks

The working principles of PSP are based on the oxygen quenching of luminescence that was first discovered by H. Kautsky and H. Hirsch (1935). The quenching effect of luminescence by oxygen was used to detect small quantities of oxygen in medical applications (Gewehr and Delpy 1993) and analytical chemistry (Lakowicz 1991, 1999) before experimental aerodynamicists realized its utility as an optical sensor for measuring air pressure on a surface. J. Peterson and V. Fitzgerald (1980) demonstrated a surface flow visualization technique based on the oxygen quenching of dye fluorescence and revealed the possibility of using oxygen sensors for surface pressure measurements. Pioneering studies of applying oxygen sensors to aerodynamic experiments were initiated independently by scientists at the Central Aero-Hydrodynamic Institute (TsAGI) in Russia and the University of Washington in collaboration with the Boeing Company and the NASA Ames Research Center in the United States. The conceptual transformation from oxygen concentration measurement to surface pressure measurement was really a critical step for aerodynamic applications of PSP, signifying a paradigm shift from conventional point-based pressure measurement to global pressure mapping.

G. Pervushin and L. Nevsky (1981) of TsAGI, inspired by the work of I. Zakharov et al. (1964, 1974) on oxygen measurement, suggested the use of the oxygen quenching phenomenon for pressure measurements in aerodynamic experiments. The first PSP measurements at TsAGI were conducted at Mach 3 on a sphere, a half-cone and a flat plate with an upright block that were coated with a long-lifetime luminescent paint excited by a flash lamp. Their PSP was acriflavine or beta-aminoanthraquinone in a matrix consisting of silichrome, starch, sugar and polyvinylpyrrolidone. A photographic film camera was used for imaging the luminescent intensity field. The results obtained in these tests were in reasonable agreement with the known theoretical solution and pressure tap data (Ardasheva et al. 1982, 1985). Another TsAGI group consisting of A. Orlov, V.

PSP was independently developed by a group of chemists led by M. Gouterman and J. Callis at the University of Washington (UW) in the late 1980s (Gouterman et al. 1990; Kavandi et al. 1990). The chemists at UW were initially interested in use of porphyrin compounds as an oxygen sensor for biomedical applications. After stimulating discussions with experimental aerodynamicists J. Crowder of the Boeing Company and B. McLachlan of NASA Ames, Gouterman and Callis understood the important implication of oxygen sensors in aerodynamic testing and started to develop a luminescent coating applied to surface for pressure measurements. Their classical PSP used platinum-octaethylporphorin (PtOEP) as a luminescent probe molecule in a proprietary commercial polymer mixture called GP-197 made by the Genesee Company. In 1989, using PtOEP in GP-197, M. Gouterman and J. Kavandi conducted PSP measurements on a NACA 0012 airfoil model (3-in chord and 9-in span) in the 25×25 cm wind tunnel at NASA Ames Fluid Dynamics Laboratory. The model was spray coated with a commercial white epoxy Krylon base-coat and then sprayed with PtOEP in GP-197. An UV lamp was used for excitation, and an analog camera interfaced to an IBM-AT computer with an 8-bit frame grabber for image acquisition. The model was set at the angle-of-attack of 5o and the Mach numbers ranged from 0.3 to 0.66. Their data showed very favorable agreement with pressure tap data, clearly indicating the formation of a shock on the upper surface of the model as the Mach number increases (Kavandi et al. 1990; McLachlan et al. 1993a). More importantly, this work established the basic procedures for intensity-based PSP measurements such as image ratioing and in-situ calibration. Following the tests at NASA Ames, Kavandi demonstrated the same PSP system in the Boeing Transonic Wind

Tunnel on various commercial airplane models, which was briefly discussed by Crowder (1990). Several proprietary paint formulations have been developed at UW, and successfully applied to wind tunnel testing at the Boeing Company and NASA Ames (McLachlan et al. 1993a, 1993b, 1995; McLachlan and Bell 1995; Bell and McLachlan 1993, 1996; Gouterman 1997).

Excellent work on PSP was also made at the former McDonnell Douglas (MD, now the Boeing Company at St. Louis) (Morris et al. 1993a, 1993b; Morris 1995; Morris and Donovan 1994; Donovan et al. 1993; Dowgwillo et al. 1994, 1996; Crites 1993; Crites and Benne 1995). MD PSPs were mainly based on Ruthenium compounds that were successfully used in subsonic, transonic and supersonic flows for a generic wing-body model, a full-span ramp, F-15 model, and a converging-diverging nozzle. Other major PSP research groups in the United States include NASA Langley, NASA Glenn, Arnold Engineering Development Center (AEDC), United States Air Force Wright-Patterson Laboratory, Purdue University, and University of Florida. European researchers in DLR (Germany), British Aerospace (BAe, UK), British Defense Evaluation and Research Agency (DERA, UK), and Office National d’Etudes et de Recherches Aerospatiales (ONERA, France) have been active in the field of PSP (Engler et al. 1991, 1992; Engler and Klein 1997a, 1997b; Engler 1995; Davies et al. 1995; Lyonnet et al. 1997). In Japan, the National Aerospace Laboratory (NAL), in collaboration with Purdue and a number of Japanese universities, developed cryogenic and fast – responding PSPs (Asai 1999; Asai et al. 2001, 2003). More and more research institutions all over the world are becoming interested in developing PSP technology because of its obvious advantages over conventional techniques. Brown (2000) gave a historical review with personal notes and recollections from some pioneers on early PSP development.

Before the advent of polymer-based luminescent TSPs, thermographic phosphors and thermochromic liquid crystals have been used for measuring the surface temperature distributions in heat transfer and aerothermodynamic experiments. Thermographic phosphors are usually applied to a surface in the form of insoluble powder or crystal in contrast to polymer-based luminescent TSPs although both techniques utilize the temperature dependence of luminescence. A family of thermographic phosphors can cover a temperature range from room temperature (293 K) to 1600 K, which overlaps with the temperature range of polymer-based TSPs from cryogenic temperature (about 100 K) to 423 K. In this sense, thermographic phosphors and polymer-based luminescent TSPs are complementary to cover a broader range from cryogenic to high temperatures. L. Bradley (1953) explored aerodynamic application of thermographic phosphors mixed with binders and ceramic materials to measure surface temperature. Then, thermographic phosphors were used for temperature measurements in high-speed wind tunnels (Czysz and Dixon 1969; Buck 1988, 1989, 1991; Merski 1998, 1999), gas turbine engines (Noel et al. 1985, 1986, 1987; Tobin et al. 1990; Alaruri et al. 1995), and fiber-optic thermometry systems (Wickersheim and Sun 1985). Allison and Gillies (1997) gave a comprehensive review on thermographic phosphors. Thermochromic liquid crystals applied to a black surface selectively reflect light and hue varies depending on the temperature of the surface, which allows measurement of the surface temperature in a relatively narrow range from 25 to 45oC. After E. Klein (1968) used liquid crystals in aerodynamic testing, this technique for global temperature measurement has been used in turbine machinery (Jones and Hippensteele 1988; Hippensteele and Russell 1988; Ireland and Jones 1986), hypersonic tunnels (Babinsky and Edwards 1996), and turbulent flows (Smith et al. 2000).

Polymer-based TSPs are relatively new compared to thermographic phosphors and thermochromic liquid crystals. P. Kolodner and A. Tyson (1982, 1983a, 1983b) of the Bell Laboratory used a Europium-based TSP in a polymer binder to measure the surface temperature distribution of an operating integrated circuit. A family of TSPs have been developed at Purdue University and used in low-speed, supersonic and hypersonic aerodynamic experiments (Campbell et al. 1992, 1994; Campbell 1994; Liu et al. 1992b, 1994a, 1994b, 1995a, 1995b, 1996, 1997a, 1997b). Two typical TSPs are EuTTA in model airplane dope (-20 to 100oC) and Ru(bpy) in Shellac (0 to 90oC). Several cryogenic TSPs (-175 to 0oC) were first discovered at Purdue University (Campbell et al. 1994) and used for transition detection in cryogenic flows (Asai et al. 1997c; Popernack et al. 1997). Further development of cryogenic TSPs was made at Purdue (Eransquin 1998a, 1998b), NAL in Japan (Asai et al. 1997c; Asai and Sullivan 1998) and NASA Langley. TSP formulations were also studied at the University of Washington (Gallery 1993) and one of the paints was used for boundary-layer transition detection at NASA Ames (McLachlan et al. 1993b).

PSP and TSP have become an active and growing interdisciplinary research area, offering the promise of quantitative pressure and temperature mapping on the one hand and giving new technical challenges on the other hand. Useful reviews were given by Crites (1993), McLachlan and Bell (1995a), Crites and Benne (1995), Liu et al. (1997b), Mosharov et al. (1997), Bell et al. (2001), and Sullivan (2001). This book provides a systematic and detailed description of all the technical aspects of PSP and TSP, including basic photophysics, paint formulations and their physical properties, radiative energy transport, measurement methods and systems, uncertainty, time response, image and data analysis techniques, and various applications in aerodynamics and fluid mechanics.

## Temperature Sensitive Paint

Temperature sensitive paint (TSP) is a polymer-based paint in which the temperature-sensitive luminescent molecules are immobilized. The quantum efficiency of luminescence decreases with increasing temperature; this effect associated with temperature is thermal quenching that serves as the major working mechanism for TSP. Over a certain temperature range, a relation between the luminescent intensity I and absolute temperature T can be written in the Arrhenius form

where Enr is the activation energy for the non-radiative process, R is the universal gas constant, and Tref is a reference temperature in Kelvin. Figures 1.7 and 1.8

show, respectively, the temperature dependencies of the luminescent intensity and the Arrhenius plots for three TSPs: Ru(bpy) in Shellac, Rodamine-B in dope and EuTTA in dope. The procedure for applying TSP to a surface is basically the same as that for PSP. Not only does TSP use the same measurement systems shown in Figs. 1.4 and 1.5, but also most data processing methods for TSP are similar to those for PSP. Ideally, TSP can be used in tandem with PSP to correct

the temperature effect of PSP and simultaneously obtain the temperature and pressure distributions. Compared to conventional temperature sensors, TSP is a global measurement technique that is able to obtain the surface temperature distribution with reasonable accuracy at a much higher spatial resolution.

A family of TSPs has been developed, covering a temperature range of -196oC to 200oC. The accuracy of TSP is typically 0.2-0.8oC. TSP has been used in various aerodynamic experiments to measure the temperature and heat transfer distributions. In hypersonic wind tunnel tests, TSP not only visualized flow transition patterns, but also provided quantitative heat transfer data calculated based on quasi-steady and transient heat transfer models. Figure 1.9 shows a windward-side heat transfer image of the lower half of the waverider model at Mach 10 at 0.57 s after the wind tunnel started to run (Liu et al. 1995b), where the gray intensity bar denotes heat flux in kW/m2. TSP is an effective technique for visualizing boundary-layer transition from laminar to turbulent flow. Due to a significant difference in convection heat transfer between the laminar and turbulent flow regimes, TSP can visualize a surface temperature change across the transition line. In low-speed wind tunnel tests, a model is typically heated or cooled to increase the temperature difference. However, in high-speed flows, friction heating often produces a sufficient temperature difference for TSP transition visualization. Cryogenic TSPs have been used to detect boundary-layer transition on airfoils in cryogenic wind tunnels over a range of the total temperatures from 90 K to 150 K. Complemented with other techniques, TSP has been used to study the relationship between heat transfer and flow structures in an acoustically excited impinging jet. The mapping capability of TSP allows quantitative visualization of the impingement heat transfer fields controlled (enhanced or suppressed) by acoustical excitation. The heat transfer fields in complex separated flows induced by shock/boundary-layer interactions have also been studied using TSP. A novel heat transfer measurement technique has been developed, which combines a laser scanning TSP and a laser spot heating units into a single non-intrusive system. An infrared laser was used to generate local heat flux and convection heat transfer was determined based on a transient heat transfer model from the surface temperature response measured using TSP. This system was applied to quantitative heat transfer measurements in complex flows on a 75-degree swept delta wing and around an intersection of a strut and a wall. Through an optical magnification system, TSP can achieve a very high spatial resolution over the surface of a small object like MEMS devices. TSP has been used to measure the surface temperature field of a miniature flush-mounted hot – film sensor in a flat-plate turbulent boundary layer.

 Fig. 1.8. The Arrhenius plots for three TSPs

 Fig. 1.9. Heat transfer image obtained using TSP on the windward side of the waverider at Mach 10. From Liu et al. (1995b)

## Pressure Sensitive Paint

The basic concepts of pressure sensitive paint (PSP) are simple. After a photon of radiation with a certain frequency is absorbed to excite the luminophore from the ground electronic state to the excited electronic state, the excited electron returns to the unexcited ground state through radiative and radiationless processes. The radiative emission is called luminescence (a general term for both fluorescence and phosphorescence). The excited state can be deactivated by interaction of the excited luminophore molecules with oxygen molecules in a radiationless process; that is, oxygen molecules quench the luminescent emission. According to Henry’s law, the concentration of oxygen in a PSP polymer is proportional to the partial pressure of oxygen in gas above the polymer. For air, pressure is proportional to the oxygen partial pressure. So, for higher air pressure, more oxygen molecules exist in the PSP layer and as a result more luminescent molecules are quenched. Hence, the luminescent intensity is a decreasing function of air pressure.

The relationship between the luminescent intensity and oxygen concentration can be described by the Stern-Volmer relation. For experimental aerodynamicists, a convenient form of the Stern-Volmer relation between the luminescent intensity I and air pressure p is

— = A + B-^-, (1.1)

1 Pref

where Iref and pref are the luminescent intensity and air pressure at a reference

condition, respectively. The Stern-Volmer coefficients A and B, which are temperature-dependent due to the thermal quenching, are experimentally determined by calibration. Theoretically speaking, the intensity ratio Iref/I can

eliminate the effects of non-uniform illumination, uneven coating and non­homogenous luminophore concentration in PSP. In typical tests in a wind tunnel, I ref is taken when the tunnel is turned off and hence it is often called the wind-off

intensity (or image); likewise, I is called the wind-on intensity (or image). Figures 1.2 and 1.3 show, respectively, the luminescent intensity as a function of pressure at the ambient temperature and the corresponding Stern-Volmer plots for three PSPs: Ru(ph2-phen) in GE RTV 118, Pyrene in GE RTV 118 and PtOEP in GP 197.

A measurement system for PSP or TSP is generally composed of paint, illumination light, photodetector, and data acquisition/processing unit. Figure 1.4 shows a generic CCD camera system for both PSP and TSP. Many light sources are available for illuminating PSP/TSP, including lasers, ultraviolet (UV) lamps, xenon lamps, and light-emitting-diode (LED) arrays. Scientific-grade charge – coupled device (CCD) cameras are often used as detectors because of their good linear response, high dynamic range and low noise. Other commonly-used photodetectors are photomultiplier tubes (PMT) and photodiodes (PD). A generic laser-scanning system, as shown in Fig. 1.5, typically uses a laser with a computer-controlled scanning mirror as an illumination source and a PMT as a detector along with a lock-in amplifier for both intensity and phase measurements. Optical filters are used in both systems to separate the luminescent emission from the excitation light.

 Fig. 1.2. The luminescent intensity as a function of pressure for three PSPs at the ambient temperature, where pref is the ambient pressure and Iref is the luminescence intensity at the ambient conditions.

 Fig. 1.3. The Stern-Volmer plots for three PSPs at the ambient temperature, where prf is the ambient pressure and Iref is the luminescence intensity at the ambient conditions.

 Computer

 CCD camera

 Lummophore molecule

 Fi ter

 Polymer

 Illumination light

Basecoat

Mode surface

Painted mode

Target

Fig. 1.4. Generic CCD camera system for PSP and TSP

Once PSP is calibrated, in principle, pressure can be directly calculated from the luminescent intensity using the Stern-Volmer relation. Nevertheless, practical data processing is more elaborate in order to suppress the error sources and improve the measurement accuracy of PSP. For an intensity-based CCD camera system, the wind-on image often does not align with the wind-off reference image due to aeroelastic deformation of a model in wind tunnel testing. Therefore, the image registration technique must be used to re-align the wind-on image to the wind-off image before taking a ratio between those images. Also, since the Stern – Volmer coefficients A and B are temperature-dependent, temperature correction is certainly required since the temperature effect of PSP is the most dominant error source in PSP measurements. In wind tunnel testing, the temperature effect of PSP is to a great extent compensated by the in-situ calibration procedure that directly correlates the luminescent intensity to pressure tap data obtained at well – distributed locations on a model during tests. To further reduce the measurement uncertainty, additional data processing procedures are applied, including image
summation, dark-current correction, flat-field correction, illumination compensation, and self-illumination correction. After a pressure image is obtained, to make pressure data more useful to aircraft design engineers, data in the image plane should be mapped onto a model surface grid in the 3D object space. Therefore, geometric camera calibration and image resection are necessary to establish the relationship between the image plane and the 3D object space.

Besides the intensity-ratio method for a single-luminophore PSP, lifetime measurement systems and multi-luminophore PSP systems have also been developed. Theoretically speaking, the luminescent lifetime is independent of the luminophore concentration, illumination level and coating thickness. Hence, the lifetime method does not require the reference intensity (or image) and it is ideally immune from the troublesome ratioing process in the intensity-ratio method for a deformed model. Similarly, one of the purposes of developing the multiple – luminophore PSP system is to eliminate the need of the wind-off reference image and reduce the error associated with model deformation. Another goal of using the multiple-luminophore PSP system is to compensate the temperature effect of PSP.

 Fig. 1.5. Generic laser scanning lifetime system for PSP and TSP

Most PSP measurements have been conducted in high subsonic, transonic and supersonic flows on various aerodynamic models in both large production wind tunnels and small research wind tunnels. PSP is particularly effective in a range of Mach numbers from 0.3 to 3.0. Figure 1.6 shows a typical PSP-derived pressure field on the F-16C model at Mach 0.9 and the angle-of-attack of 4 degrees, which was obtained by Sellers and his colleagues (Sellers 1998a, 1998b, 2000; Sellers and Brill 1994) at the Arnold Engineering Development Center (AEDC). For PSP measurements in large wind tunnels, the accuracy of PSP is typically 0.02-0.03 in the pressure coefficient, while in well-controlled experiments the absolute pressure accuracy of 1 mbar (0.0145 psi) can be achieved. In short-duration hypersonic tunnels (Mach 6-10), measurements require very fast time response of PSP and minimization of the temperature effect of PSP. Binder-free, porous anodized aluminum (AA) PSP has been used in hypersonic flows and rotating machinery since it has a very short response time of 30-100 in comparison with a timescale of about 0.5 s for a conventional polymer-based PSP. Furthermore, because AA-PSP is a part of an aluminum model, an increase of the surface temperature in a short duration is relatively small due to the high thermal conductivity of aluminum. Since a porous PSP usually exhibits the pressure sensitivity at cryogenic temperatures, AA-PSP and polymer – based porous PSP have been used for pressure measurements in cryogenic wind tunnels where the oxygen concentration is extremely low and the total temperature is as low as 90 K.

 Fig. 1.6. PSP image for the F-16C model at Mach 0.9 and the angle-of-attack of 4 degrees. From Sellers (2000)

PSP measurements in low-speed flows are difficult since a very small change in pressure must be resolved and the major error sources must be minimized to obtain acceptable quantitative pressure results. Some low-speed PSP measurements were conducted on delta wings where upper surface pressure exhibited a relatively large change induced by the leading-edge vortices. In addition, experiments were conducted on airfoils, car models and impinging jets at speeds as low as 20 m/s. The pressure resolution of PSP in low-speed flows is ultimately limited by the photon shot noise of a CCD camera. Instead of pushing PSP instrumentation to the limit in low-speed flows, the pressure-correction method was proposed to recover the incompressible pressure coefficient from PSP results obtained in subsonic flows at suitably higher Mach numbers by removing the compressibility effect.

Since PSP is a non-contact technique, it is particularly suitable to pressure measurements on high-speed rotating blades in rotating machinery where conventional techniques are difficult to use. Both CCD camera and laser scanning systems have been used for PSP measurements on rotating blades in turbine engines and helicopters. Impinging jets were used in some studies as a canonical flow for testing the performance of PSP systems. Flight test is a challenging area where PSP has showed its advantages as a non-contact, optical pressure measurement technique. The pressure distributions on wings and parts of aircrafts have been measured using film-based camera systems in early in-flight experiments and a laser scanning system in recent flight tests.

## Pressure and Temperature Sensitive Paints

The aim of this book is to provide a systematic description of pressure and temperature sensitive paints (PSP and TSP) developed since the 1980s for aerodynamics/fluid mechanics and heat transfer experiments. PSP is the first global optical technique that is able to give non-contact, quantitative surface pressure visualization for complex aerodynamic flows and provide tremendous information on flow structures that cannot be easily obtained using conventional pressure sensors. TSP is a valuable addition to other global temperature measurement techniques such as thermographic phosphors, thermochromic liquid crystals and infrared thermography. This book mainly covers research made in the United States, Japan, Germany, France, Great Britain and Canada. Excellent work on PSP in Russia has been described in the book “Luminescent Pressure Sensors in Aerodynamic Experiments” by V. E. Mosharov, V. N. Radchenko and

S. D. Fonov of the Central Aerohydrodynamic Institute (TsAGI).

We are truly grateful to our colleagues in the field of PSP and TSP for kindly providing their paper drafts, offering comments, and allowing us to use their published results. Without their helps, this book cannot be completed. Especially, we would like to thank the following individuals and organizations:

T. Amer, K. Asai, J. H. Bell, T. J. Bencic, O. C. Brown, G. Buck, A. W. Burner, S. Burns, B. Campbell, B. F. Carroll, L. N. Cattafesta, J. Crafton, R. C. Crites, G. Dale, R. H. Engler, R. G. Erausquin, W. Goad, L. G. Goss, J. W. Gregory, M. Gounterman, M. Guille, M. Hamner, J. M. Holmes, C. Y. Huang, J. P. Hubner, J. Ingram, H. Ji, R. Johnston, J. D. Jordan, M. Kameda, M. Kammeyer, J. T. Kegelman, N. Lachendro, J. Lepicovsky, Y. Le Sant, X. Lu, Y. Mebarki, R. D. Mehta, K. Nakakita, C. Obara, D. M. Oglesby, T. G. Popernack, W. M. Ruyten, H. Sakaue, E. T. Schairer, K. S. Schanze, M. E. Sellers, Y. Shimbo, K. Teduka, S. D. Torgerson, B. T. Upchurch, A. N. Watkins.

NASA, ONR, AFOSR, Boeing, Raytheon, Japanese NAL.

Quantitative measurements of surface pressure and temperature in wind tunnel and flight testing are essential to understanding of the aerodynamic performance and heat transfer characteristics of flight vehicles. Pressure data are required to determine the distribution of aerodynamic loads for the design of a flight vehicle, while temperature data are used to estimate heat transfer on the surface of the vehicle. Pressure and temperature measurements provide critical information on important flow phenomena such as shock, flow separation and boundary-layer transition. In addition, accurate pressure and temperature data play a key role in validation and verification of computational fluid dynamics (CFD) codes. Traditionally, surface pressure is measured by utilizing a pressure tap or orifice at a location of interest connected through a small tube to a pressure transducer (Barlow et al. 1999). Hundreds of pressure taps are needed to obtain an acceptable pressure field on a complex aircraft model. Manufacturing, tubing and preparing such a model for wind tunnel testing is very labor-intensive and costly. For thin models such as supersonic transports, military aircraft and small fan blades, installation of a large number of pressure taps is impossible. Furthermore, pressure measurements at discrete taps ultimately limit the spatial resolution of measurements such that some details of a complex flow field cannot be revealed. Similarly, a surface temperature field is traditionally measured using temperature sensors such as thermocouples and resistance thermometers distributed at discrete locations (Moffat 1990).

Since the 1980s, new optical sensors for measuring surface pressure and temperature have been developed based on the quenching mechanisms of luminescence. These luminescent molecule sensors are called pressure sensitive paint (PSP) and temperature sensitive paint (TSP). Compared with conventional techniques, they offer a unique capability for non-contact, full-field measurements of surface pressure and temperature on a complex aerodynamic model with a much higher spatial resolution and a lower cost. Therefore, they provide a powerful tool for experimental aerodynamicists to gain a deeper understanding of rich physical phenomena in complex flows around flight vehicles.

Both PSP and TSP use luminescent molecules as probes that are incorporated into a suitable polymer coating on an aerodynamic model surface. In general, the luminophore and polymer binder in PSP and TSP can be dissolved in a solvent; the resulting paint can be applied to a surface using a sprayer or brush. After the solvent evaporates, a solid polymer coating in which the luminescent molecules are immobilized remains on the surface. When a light of a proper wavelength illuminates the paint, the luminescent molecules are excited and the luminescent

light of a longer wavelength is emitted from the excited molecules. Figure 1.1 shows a schematic of a generic luminescent paint layer emitting radiation under excitation by an incident light.

 Fig. 1.1. Schematic of a luminescent paint (PSP or TSP) on a surface

The luminescent emission from a paint layer can be affected by certain physical processes. The main photophysical process in PSP is oxygen quenching that causes a decrease of the luminescent intensity as the partial pressure of oxygen or air pressure increases. The polymer binder for PSP is oxygen permeable, which allows oxygen molecules to interact with the luminescent molecules in the binder. For certain fast-responding PSP, a mixture of the luminophore and solvent is directly applied to a porous solid surface. In fact, PSP is an oxygen-sensitive sensor. By contrast, the major mechanism in TSP is thermal quenching that reduces the luminescent intensity as temperature increases. TSP is not sensitive to air pressure since the polymer binder used for TSP is oxygen impermeable, while due to the thermal quenching PSP is intrinsically temperature-sensitive. After PSP and TSP are appropriately calibrated, pressure and temperature can be remotely measured by detecting the luminescent emission. PSP and TSP are companion techniques because they not only utilize luminescent molecules as probes, but also use the same measurement systems and similar data processing methods.