2. A brief analysis of planar laser-induced fluorescence

Laser-induced fluorescence is an essentially physical process of laser resonance excitation and fluorescence generation. When the molecule is excited by laser with a specific wavelength, it will transition from a low energy state (usually ground state) to a higher energy state (the excited state). Then the molecules in the excited state will spontaneously transition from the excited energy state to the low energy state after undergoing a series of non-radiative transition energy transfer. The energy of electromagnetic radiation between the excited state and the low energy state is released in the form of fluorescence radiation.

Hydroxyl (OH radical), a very important intermediate in flames, is considered to exist in the combustion process of most hydrocarbon fuels. Quantitative measurement of OH concentration is of great significance for deep understanding, modification, and validation of reaction mechanism and chemical kinetic models. This chapter takes OH as an example to explain. Similar conclusions exist for other combustion intermediates or radicals.

The energy-level structure consists of the electronic, vibrational, and rotational energy levels. When numerous OH radicals in the flame absorb a certain wavelength laser from the ground state to the excited state, one part of molecules will shift to other vibrational or rotational energy levels due to the effect of vibrational energy transfer (VET) and rotational energy transfer (RET), one part of which will be transferred to the pre-dissociated state, and some of which will be quenched due to the collision of atoms and molecules in the surrounding environment. After above three physical processes, in fact, the OH radicals no longer involve the process of fluorescence radiation. Therefore, only a fairly small number of OH radicals can emit fluorescence from the excited state to the ground state. The physical process is shown in Figure 1.

The main purpose of the LIF technology is to determine the total number density of OH radicals by using the observable intensity of the OH fluorescence signal and then to obtain the local physical properties of the measured molecules. However, there are many physical processes difficult to observe directly in the LIF process, such as VET, RET, collisional quenching, and predissociation, which will greatly affect the intensity of the OH fluorescence signal. Therefore, if the concentration of fluorescence signal is directly obtained by observation, one will cause great deviation. Generally, the time scales of VET, RET, and collisional quenching effects are much less than the lifetime of OH fluorescence. Therefore, it is rather difficult to directly measure these physical processes on the OH fluorescence signal.

Under the linear excitation, the LIF signal intensity of the excited molecule in position x at atmospheric pressure can be expressed as follows [9]:

$$I\_{\rm LIF}(\mathbf{x}, \omega, T, N\_c) = \hbar \omega \mathbb{C}\_{\rm exp} B\_{\rm mm} N\_m^0 f\_B(\mathbf{x}, T) \frac{A\_{\rm mm}}{A\_{\rm mm} + Q(\mathbf{x}, T, N\_c)} \int\_{\omega} \frac{I(\mathbf{x}, \omega)}{c} g(\mathbf{x}, \omega, T, N\_c) d\omega \tag{1}$$

Figure 1. The LIF process of hydroxyl radical [9].

to the combustion and flow fields but also can dynamically display and image two- or threedimensional space structure of free radicals interested in combustion fields. These merits are unattainable and difficult to achieve by the traditional contact and other laser spectral diagnostic techniques, such as coherent anti-Stokes Raman scattering (CARS), degenerate four-wave mixing technology (DFWM), cavity ring down spectroscopy technology (CRDS), tunable diode

Admittedly, PLIF technology also has its own shortcomings. The biggest obstacle is that the PLIF technology is rather difficult to achieve quantitative measurement. The greatest difficulty in quantification of the PLIF lies in the fact that the electronic collisional quenching rate of the molecules to be measured is not exactly the same at the different positions of flame under the normal and high pressures. Worse still, there is a big difference for the distribution of electronic quenching rates in different types of flames. In addition, the calibration factor is also a parameter, which is easy to change with the observation conditions. In a general way, the collisional quenching rates of the molecules to be measured in flame have little effect on the fluorescence signal under the low pressure, so it can be often neglected. However, the collisional quenching rates of molecules turn out to be very sensitive to the combustion environment in flames under normal and high pressures. Therefore, the profiles of the collisional quenching rates become difficult to be measured in real time due to the diversification of the flame structure. In this case, an additional consideration is needed to accurately deduce the concentration distribution

In order to eliminate the detrimental impact of quenching effect on the quantitative measurement of species concentration, Versluis et al. [8] proposed to combine the traditional laserinduced fluorescence (LIF) with absorption spectroscopy to excite the molecules using the two opposite direction laser beams, counteracting many influencing factors, such as collisional quenching effect, pressure, and the calibration constant of the Detector and optical system, so as to deduce species concentration profiles. However, the bidirectional LIF technology is highly depending on the spatial coincidence of the beam (especially for the sheet laser beam) and the signal-to-noise ratio (SNR) of the fluorescence signal, which leads to the lack of

Laser-induced fluorescence is an essentially physical process of laser resonance excitation and fluorescence generation. When the molecule is excited by laser with a specific wavelength, it will transition from a low energy state (usually ground state) to a higher energy state (the excited state). Then the molecules in the excited state will spontaneously transition from the excited energy state to the low energy state after undergoing a series of non-radiative transition energy transfer. The energy of electromagnetic radiation between the excited state and the

Hydroxyl (OH radical), a very important intermediate in flames, is considered to exist in the combustion process of most hydrocarbon fuels. Quantitative measurement of OH concentration

laser absorption spectroscopy (TDLAS), and direct absorption spectroscopy.

information of the molecules to be measured using the fluorescence signals.

2. A brief analysis of planar laser-induced fluorescence

low energy state is released in the form of fluorescence radiation.

systematic research on this technology.

86 Laser Technology and its Applications

where ℏ is the Planck reduced constant; ω is the angular frequency related to the energy interval between the selected excited levels; Cexp is an experimental constant influenced by the quantum efficiency of detector, the filter function, and the solid angle of optical system; Bmn is the Einstein stimulated absorption coefficient from low energy state (m state) to high energy state (n state); N<sup>0</sup> <sup>m</sup> is the molecular number density in m state; f <sup>B</sup>ð Þ x; T is the Boltzmann Fraction in position x; T is the temperature; Anm is the spontaneous emission rate of excited molecules transitioning from n state to m state; Q(x,T,Nc) is the collisional quenching rate related to the temperature and the total number Nc around the collisional molecules; I(x,ω) is the intensity of excited laser in position x; and g(x, ω, T, Nc) is the molecular integrated absorption line-shape in position x. In Eq. (1), the factor of Anm=ð Þ Anm þ Q xð Þ ; T; Nc represents the fluorescence quantum efficiency used to describe the percentage of fluorescence radiation energy in the total absorbed laser energy.

The actual OH energy-level structure is fairly sophisticated, so an approximate model of two energy levels is often used. Under the two energy-level approximation, the average collisional quenching rate Q is expressed as [9]

$$Q = \sum\_{i} k\_{Q\_i} N\_i \tag{2}$$

heating collisional speed, and the number density of the collisional particles. It also can be seen from Eqs. (2)–(4) that it is rather difficult to determine the concentration, quenching section, and heating collisional speed of each collisional molecule accurately, because there are hundreds of species in the actual flame. Worse still, some colliding particles have the shorter life than OH radical, which leads to almost impossible to accurately determine the distributions of OH concentration in the observed location. In addition, the collisional environment of different flames varies also greatly. Even for only one kind of flame, the different working conditions will lead to a great change to the physical quantities affecting the rate of collisional quenching. Since there is little understanding about the non-radiative energy transfer processes of OH radical at present stage, it is almost impossible to measure the physical quantities, which can greatly affect the collisional quenching rate of OH radical by using the current experimental

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With the increasing demand for the spatial resolution of the internal structure of flame in the fields of combustion and aerodynamics, it is urgent to obtain the spatial distribution information for the combustion/flow fields, so as to further understand the basic characteristics of the chemical reaction in flames. PLIF is a laser diagnostic technique developed under this require-

The physical process of PLIF is exactly the same as the LIF technology. The difference between PLIF and LIF is that the PLIF technique uses a special sheet-forming optics to replace the "line beam" used in the LIF by a "sheet beam." And the photomultiplier tube commonly used in LIF technology is replaced by an intensified charge-coupled device (ICCD) camera, which can make two-dimensional imaging for the weak fluorescence signal. The typical PLIF measuring system consists of five parts: the laser, the sheet-forming optics, the imaging acquisition and

data storage, the digital delay control, and combustion systems, as shown in Figure 2.

ment, which is the expansion of LIF technology in two-dimensional space.

technique.

Figure 2. Typical PLIF experimental setup.

where Ni is the number density of the colliding particle ith and kQi is the quenching rate coefficient of the colliding molecule ith, which can be expressed as

$$k\_{Q\_i} = \sigma\_{Q\_i} \langle \upsilon\_i \rangle \tag{3}$$

where σQi is the collisional quenching cross section of the molecule ith and h i υ<sup>i</sup> is the average heat collisional speed of the colliding species ith, expressed as

$$
\langle \upsilon\_i \rangle = \sqrt{\frac{8k\_B T}{\pi \mu\_i}} \tag{4}
$$

where k<sup>B</sup> is the Boltzmann constant and μ<sup>i</sup> is the reduced mass of the colliding molecule ith.

As can be seen from Eq. (1), in order to determine the OH number density using observed LIF signals, it is necessary to exactly know all the factors impacting on the LIF signal, especially for the collisional quenching rate. For the premixed methane/air flame, the estimated average quantum yield is approximately 1/1000. This result shows that the effect of collisional quenching in flame is fairly strong and most of the OH radicals excited to the high energy state dissipate the absorbed laser energy in the form of non-radiative transition, such as collisional electronic quenching and VET. As a result, only a few OH radicals will release the absorbed energy to radiate fluorescence.

However, there are too many factors difficult to measure in the collisional quenching rate of OH radical in flames, including the quenching cross sections of colliding pairs, the average heating collisional speed, and the number density of the collisional particles. It also can be seen from Eqs. (2)–(4) that it is rather difficult to determine the concentration, quenching section, and heating collisional speed of each collisional molecule accurately, because there are hundreds of species in the actual flame. Worse still, some colliding particles have the shorter life than OH radical, which leads to almost impossible to accurately determine the distributions of OH concentration in the observed location. In addition, the collisional environment of different flames varies also greatly. Even for only one kind of flame, the different working conditions will lead to a great change to the physical quantities affecting the rate of collisional quenching. Since there is little understanding about the non-radiative energy transfer processes of OH radical at present stage, it is almost impossible to measure the physical quantities, which can greatly affect the collisional quenching rate of OH radical by using the current experimental technique.

With the increasing demand for the spatial resolution of the internal structure of flame in the fields of combustion and aerodynamics, it is urgent to obtain the spatial distribution information for the combustion/flow fields, so as to further understand the basic characteristics of the chemical reaction in flames. PLIF is a laser diagnostic technique developed under this requirement, which is the expansion of LIF technology in two-dimensional space.

The physical process of PLIF is exactly the same as the LIF technology. The difference between PLIF and LIF is that the PLIF technique uses a special sheet-forming optics to replace the "line beam" used in the LIF by a "sheet beam." And the photomultiplier tube commonly used in LIF technology is replaced by an intensified charge-coupled device (ICCD) camera, which can make two-dimensional imaging for the weak fluorescence signal. The typical PLIF measuring system consists of five parts: the laser, the sheet-forming optics, the imaging acquisition and data storage, the digital delay control, and combustion systems, as shown in Figure 2.

Figure 2. Typical PLIF experimental setup.

where ℏ is the Planck reduced constant; ω is the angular frequency related to the energy interval between the selected excited levels; Cexp is an experimental constant influenced by the quantum efficiency of detector, the filter function, and the solid angle of optical system; Bmn is the Einstein stimulated absorption coefficient from low energy state (m state) to high energy

Fraction in position x; T is the temperature; Anm is the spontaneous emission rate of excited molecules transitioning from n state to m state; Q(x,T,Nc) is the collisional quenching rate related to the temperature and the total number Nc around the collisional molecules; I(x,ω) is the intensity of excited laser in position x; and g(x, ω, T, Nc) is the molecular integrated absorption line-shape in position x. In Eq. (1), the factor of Anm=ð Þ Anm þ Q xð Þ ; T; Nc represents the fluorescence quantum efficiency used to describe the percentage of fluorescence radiation

The actual OH energy-level structure is fairly sophisticated, so an approximate model of two energy levels is often used. Under the two energy-level approximation, the average collisional

where Ni is the number density of the colliding particle ith and kQi is the quenching rate

where σQi is the collisional quenching cross section of the molecule ith and h i υ<sup>i</sup> is the average

s

where k<sup>B</sup> is the Boltzmann constant and μ<sup>i</sup> is the reduced mass of the colliding molecule ith. As can be seen from Eq. (1), in order to determine the OH number density using observed LIF signals, it is necessary to exactly know all the factors impacting on the LIF signal, especially for the collisional quenching rate. For the premixed methane/air flame, the estimated average quantum yield is approximately 1/1000. This result shows that the effect of collisional quenching in flame is fairly strong and most of the OH radicals excited to the high energy state dissipate the absorbed laser energy in the form of non-radiative transition, such as collisional electronic quenching and VET. As a result, only a few OH radicals will release the

However, there are too many factors difficult to measure in the collisional quenching rate of OH radical in flames, including the quenching cross sections of colliding pairs, the average

ffiffiffiffiffiffiffiffiffiffi 8kBT πμ<sup>i</sup>

kQi ¼ σQi

h i υ<sup>i</sup> ¼

<sup>Q</sup> <sup>¼</sup> <sup>X</sup> i kQi

coefficient of the colliding molecule ith, which can be expressed as

heat collisional speed of the colliding species ith, expressed as

<sup>m</sup> is the molecular number density in m state; f <sup>B</sup>ð Þ x; T is the Boltzmann

Ni (2)

h i υ<sup>i</sup> (3)

(4)

state (n state); N<sup>0</sup>

88 Laser Technology and its Applications

energy in the total absorbed laser energy.

quenching rate Q is expressed as [9]

absorbed energy to radiate fluorescence.

The laser source is usually composed of pump laser and dye laser to obtain a laser beam with different excitation wavelengths. The sheet-forming optics mainly consists of one cylindrical concave lens and other two vertical cylindrical convex lenses, achieving the transformation from line beam to sheet beam. The imaging acquisition and data storage system is mainly composed of ICCD camera and data storage module to acquire the weak fluorescence signals in a real time. The digital delay control system is used to control the synchronization between the laser and the ICCD camera. The burner is used to produce an objective flame to be researched. According to the characteristics of the actual research, the PLIF system will be slightly different, but the main assembly is still composed of the above five parts.

obtained by ultraviolet (UV) absorption spectroscopy. Jalbert [11] researched the variations of OH concentration with the flame heights in the premixed methane/air and hydrogen/air flames. And the influences of the equivalent ratio and flow rate on the OH concentration have

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Although the calibration LIF has ability to measure the species concentration profiles to a certain extent, there is more serious problem that should not be neglected: the calibration LIF ignores the fact that the collisional quenching rates vary with the spatial position in the flame. Therefore, the calibration LIF cannot be considered as a real quantitative LIF strictly. It can

When the excited energy density is higher than the threshold energy density of saturation excitation, the intensity of fluorescence signal is only related to the molecular number density, stimulated absorption, stimulated radiation, and spontaneous radiation but independent with excitation energy and the electronic quenching rate. This case is known as the saturated

In the saturated LIF, the measured fluorescence signal can directly reflect the number density of the stimulated molecules. The main drawback of the saturated LIF is that the output laser pulse is difficult to reach the required saturated excitation energy density. Therefore, it is difficult to achieve the planar concentration measurement for the species. In addition, because the laser pulse has a certain energy profile in time and space, it is easy to arise the so-called wing effect at the edge of energy profile. In other words, the laser energy density at the edge is less than the threshold energy density. Therefore, the excitation in this location still belongs to the linear excitation, leading to the fact that fluorescence signal is still affected by the collisional quenching effect. The researches on quantitative measurement of species concentration using

Carter et al. [12] used saturated LIF to measure the OH concentration distributions in C2H6/O2/N2 flames under the high pressure. The experimental results indicate that the maximum OH concentration measured by saturated LIF is 1.10 1016, 1.05 1016, 1.18 1016 and 0.98

Kohse-Höinghaus et al. [13] measured the concentrations of CH and OH radicals in a premixed C2H2/O2 flames under the low pressure using saturation LIF. The experimental results show that the concentration of CH and OH radicals in acetylene/oxygen flame is 1.1 1013 cm<sup>3</sup> (<sup>T</sup> = 1750 80 K, height at 2.6 mm) and 8.9 1014 cm<sup>3</sup> (<sup>T</sup> = 2000 100 K, height at 7.5 mm), respectively, under the pressure of 13 mbar and the equivalence ratio of 1.2.

LIPF has also been recognized a kind of quantitative LIF, which is proposed to solve the problem that the fluorescence signal is susceptible to collisional quenching effect in linear LIF.

, respectively, under the pressure of 0.98, 6.1, 9.2, and 12.3 atm.

also been investigated by using the calibration LIF.

only be regarded as a semiquantitative LIF technology.

3.3. Laser-induced pre-dissociative fluorescence (LIPF)

In the LIPF, the fluorescence quantum efficiency can be written as

3.2. Saturated LIF

saturated LIF mainly include:

10<sup>16</sup> molecules/cm<sup>3</sup>

LIF.
