Two-dimensional laser-induced fluorescence thermometry in a medium- to high-enthalpy CO₂ flow

Abstract

Ground-based experimental facilities are needed to qualify materials subjected to aerothermodynamic loads during an entry into the Martian atmosphere. In the present work, the focus is on quantifying the temperature field in a medium- to high-enthalpy CO$_{2}$ flow (from 4.5 to ${10.5}\, \hbox {MJ}/\hbox {kg}$) of a plasma wind tunnel using one- and two-dimensional two-photon absorption laser-induced fluorescence (CO-TALIF) thermometry at a CO number density in the range of 1–2 $\times$ 10$^{17}$ cm$^{-3}$. However, the measurement method developed here can also be used to study satellite propulsion systems. Due to absorption by air, a two-photon excitation scheme of the CO molecule at 115 nm (VUV) was used. Experimental and simulated excitation spectra are compared for temperature determination. For spectrum simulation in the B$^1\varSigma ^+$ $\leftarrow$ X$^1\varSigma ^+$ system, an existing program was extended and a polynomial regression correlation was developed for signals with low signal-to-noise ratios. After the first one-dimensional temperature measurements using CO-TALIF in the free-stream to quantify the radial temperature profile for three conditions in the medium- to high- enthalpy range, respectively, two-dimensional measurements in a steady state test chamber at room temperature were carried out. For the two-dimensional investigations, a light sheet optic was designed to generate a light sheet free of divergence in width and thickness. The results of the one- and two-dimensional temperature measurements performed at medium- to high-enthalpy conditions provided plausible results concerning both the values and the course in radial and axial direction, the latter being, to the authors’ knowledge, the first two-dimensional temperature measurements under such conditions using CO-TALIF.

1 Introduction

The current focus for studying entry maneuvers is not limited to the Earth’s atmosphere, but also includes landings on other planets in the solar system, such as Mars, whose atmosphere consists predominantly of CO$_{2}$ [1]. During entry maneuvers of (re-)entry bodies into planetary atmospheres, their structure is stressed by high aerothermodynamic loads and effects from vibrational excitation and relaxation of gas molecules to their dissociation and ionization (plasma) occur [2].

On the one hand, the measurement development carried out in the present work is motivated by future Mars missions and shall contribute to an extension of the application range of optical measurement methods in medium- to high-enthalpy CO$_{2}$ flows to real flow conditions in order to obtain robust measurement data for numerical simulation. On the other hand, the findings from this will be used in the development of a measurement system for satellite propulsion systems as well as evaluation algorithms for different species to be studied spectroscopically.

Experimental investigations, supported by CFD simulations, are necessary to qualify materials which are exposed to the high aerothermodynamic loads occurring during entry maneuvers. The problem here is that very few experimental data are available that reflect the stresses during actual entry maneuvers, such as the data from the ExoMars Schiaparelli module [3]. Such tests to capture real-world conditions involve very high costs as well as large amounts of time. Accordingly, the study of the loads relies on ground-based test facilities that can replicate these conditions. For this purpose, among others, plasma wind tunnels are used, which allow the generation of high-enthalpy flows in a continuous operation. The investigations within the scope of the present work were carried out at the plasma wind tunnel (PWT) of the Institut für Thermodynamik at the Universität der Bundeswehr München [4], which can be operated with CO$_{2}$ as test gas.

It is essential for the use of such test facilities to quantify the inflow conditions as precisely as possible in order to obtain reliable data for the simulation. Optical methods are very well suited for measurements in high-enthalpy flows in the supersonic regime, since they do not affect the flow field and since their use is not restricted by thermal load limits as is the case with probes. In particular, the temperature field of the  free-stream, to which the objects to be examined are exposed, is relevant here. Different methods exist for non-intrusive temperature determination, of which LIF is characterized by high signal intensity, even at low particle densities of the species studied spectroscopically and, in principle, even when the laser beam is expanded to a light sheet (planar LIF or PLIF). This allows a two-dimensional measurement of the temperature field with a corresponding increased gain of information.

LIF requires the presence of an excitable species in the measurement volume. The dissociation product CO comes into question as a species occurring already in low-enthalpy CO$_{2}$ flows. In particular, the electronic system B$^1\varSigma ^+$ $\leftarrow$ X$^1\varSigma ^+$ has been extensively characterized in the literature and studied using numerous LIF measurements each with a different focus. We refer representatively to the publications [1, 5,6,7,8,9]. The B-X electronic system was also used for laser-induced excitation of the CO molecule for the studies in the present work. Since the excitation wavelength required for this ($\lambda \approx {115}\,\hbox {nm}$) is in the vacuum UV (VUV) range, which is absorbed to a large extent by the ambient oxygen, it was necessary to realize the excitation via two-photon absorption, which, however, significantly reduces the achievable signal intensity [10]. The resulting quadratic dependence of the TALIF signal on the excitation energy should be emphasized, which considerably increases the difficulty of planar measurements on CO [2]. In addition, low particle densities occur in supersonic flows due to the expansion of the test gas via a Laval nozzle, which additionally reduces the detectable signal.

With regard to one-dimensional TALIF spectroscopy of CO$_{2}$ plasma jets, measurements have been carried out at various experimental facilities, in some cases also with thermometry. For a presentation of relevant work in this regard, the reader is referred to the review by [2]. So far, PLIF studies of CO were focused on the determination of CO concentration. Zhou et al. [11] determined the CO concentration by two-photon absorption PLIF (TAPLIF) measurements close to the surface of a heated catalyst placed within a CO$_2$ environment. Voigt et al. [5] describe the planar determination of CO particle density in flames at different pressure levels while Richardson et al. [12] used TAPLIF to determine the CO concentration in an inverted diffusion flame. Instead of determining the temperature of the flame by TAPLIF of the CO molecule, Richardson et al. complement their research by investigating the flame temperature with single-photon absorption PLIF of the hydroxyl radical (OH). Regarding CO-TAPLIF thermometry, no investigations could be found in the literature.

In previous own investigations at the PWT, both PLIF thermometry of NO [13] and TALIF thermometry of CO [8] have already been successfully performed, in each case on a steady state test chamber, a flat flame burner, and in the free-stream of the PWT at a stagnation enthalpy $h_0$ of ${3.6}\, \hbox {MJ}/\hbox {kg}$ (NO) and ${2.1}\, \hbox {MJ}/\hbox {kg}$ (CO, low-enthalpy).

The work presented here first describes the results of CO-TALIF thermometry in the free-stream of the PWT at stagnation enthalpies between 4.5 and ${10.5}\, \hbox {MJ}/\hbox {kg}$, including a unique evaluation method, the polynomial regression correlation (PRC), to evaluate the signal even at high noise levels. Then, preparatory investigations using CO-TAPLIF on a steady state test chamber are presented to define optimal experimental parameters for the following measurements and to establish the data reduction. Finally, the authors show the first results, to their knowledge, of thermometry using CO-TAPLIF in a medium- to high-enthalpy free-stream at stagnation enthalpies of 4.5 and ${9.0}\, \hbox {MJ}/\hbox {kg}$.

2 Measurement technique

2.1 Theoretical background

2.1.1 General principle

In this study, laser-induced fluorescence is detected while tuning the laser across a spectral region (excitation scan) which contains transition energies of the CO molecule. The resulting excitation spectrum allows the determination of the temperature by correlating it to simulated excitation spectra that are calculated with varied temperatures.

2.1.2 Energy levels and transitions

The energy levels of a diatomic molecule can be calculated using the approach of an anharmonically oscillating rotator. This approach determines the energy levels for the vibrational $\overline{E}_\mathrm {v}(v)$ and rotational $\overline{E}_{\mathrm {r},v}(J)$ modes taking coupling effects into account. The energy $\overline{E}_\mathrm {e}(n)$ stored in the electronic mode can be determined from the relevant electronic molecular quantum numbers, summarized in this case by the variable n, or taken from the literature [14]. The overline indicates that the energy levels are given in the unit of a wavenumber [1/m]. Especially for the two energy levels $\text {B}^1\varSigma ^+$ and $\text {X}^1\varSigma ^+,$ the calculation can be simplified to Eq. (1), since the angular momentum caused by orbiting electrons and their spin is zero and a coupling with the atom cores’ rotation can be omitted [10].

$$\begin{aligned} \begin{aligned} \overline{E}_\mathrm {i}(J,v,n) =&\ \overline{E}_\mathrm {e}(n) + \overline{E}_{\mathrm {r},v}(J) + \overline{E}_\mathrm {v}(v) \\ =&\ \overline{E}_\mathrm {e}(n) + B_{\mathrm {r},v}J(J+1)\\ {}&-D_{\mathrm {r},v}J^2(J+1)^2+\omega _e\left( v+\frac{1}{2}\right) \\ {}&-\omega _e x_e\left( v+\frac{1}{2}\right) ^2+\omega _e y_e\left( v+\frac{1}{2}\right) ^3. \end{aligned} \end{aligned}$$

(1)

All molecular specific constants, including the constants $\omega _e x_e$ and $\omega _e y_e$, modeling the quadratic and cubic anharmonic oscillation as well as the constants that are required to calculate the vibration-dependent rotational constant $B_{\mathrm {r},v}$ and the vibration-dependent centrifugal distortion constant $D_{\mathrm {r},v}$ in accordance with [10] must be taken from literature.

The ground state $\text {X}^1\varSigma ^+$, the excited state $\text {B}^1\varSigma ^+$ and three further electronic states relevant within this study are displayed as Morse potential functions in Fig. 1. The values for the molecular constants used for the calculation were taken from the literature [14, 15].

Fig. 1

Potential energy according to the Morse Potential of the CO electronic states relevant for this study

For electronic transitions, the change of the rotational quantum number is restricted to $\varDelta J= 0,~\pm 2$, according to the selection rule for a two-photon absorption process by linear polarized light. The resulting three transitions are generally referred to as O-, Q- and S-branch with $\varDelta J \in \{-2, 0, +2\}$. A transition between vibrational states is not limited by a selection rule [10, 16].

In addition to the spectral position of a transition given by the energy levels and following the selection rules, it is necessary to determine transition probabilities to be able to derive thermal properties from a LIF excitation scan. The transition probability between two vibrational levels in two different electronic states is given by the Franck–Condon factors which were taken from [17] for this study. The probability of a transition between two electronically and vibrationally defined states is defined by the Hönl-London factors for the O-, Q- and S-branch according to [16] and simplified according to [7] for the Q-branch as given by Eqs. (2a-c).

$$\begin{aligned}&S^\mathrm {O}_{J',J''}=\frac{J''(J''-1)}{30(2J''-1)}, \end{aligned}$$

(2a)

$$\begin{aligned}&S^\mathrm {Q}_{J',J''}=\frac{2J''+1}{9}\mu ^2_\mathrm {I}, \end{aligned}$$

(2b)

$$\begin{aligned}&S^\mathrm {S}_{J',J''} = \frac{(J''+1)(J''+2)}{30(2J''+3)}. \end{aligned}$$

(2c)

A further decisive parameter that influences the fluorescence signal and that is required for its evaluation is the population of molecules within the relevant energy levels. This population distribution is temperature dependent and, assuming a thermal equilibrium, given by a Boltzmann distribution. The distribution is calculated in two steps. At first the population distribution of vibrational levels over the electronic ground state is calculated with Eq. (3), followed by the determination of the population distribution over the rotational levels within each vibrational state using Eq. (4) [10].

$$\begin{aligned}&f_{\mathrm {B},v}(T)=\exp \left( -v\frac{\omega _e c_0 h}{kT}\right) \left[ 1-\exp \left( -\frac{\omega _e c_0 h}{kT}\right) \right] . \end{aligned}$$

(3)

$$\begin{aligned}&f_{\mathrm {B},J}(T)=(2J+1)\exp \left[ -J(J+1)\frac{h c_0 B_\mathrm {r}}{kT}\right] \frac{h c_0 B_\mathrm {r}}{kT}. \end{aligned}$$

(4)

Both equations use a simplified molecular model. Equation (3) assumes the molecule to be a harmonic oscillator and Eq. (4) assumes that the molecule is represented by a rigid rotator in accordance with [10]. The distributions are defined by the physical constants: the speed of light $c_0$, Planck’s constant h, Boltzmann’s constant k, the molecular constants $\omega _e$ and $B_\mathrm {r}$ and are functions of the molecules’ temperature T. Multiplying the population distributions $f_{\mathrm {B},v}$ and $f_{\mathrm {B},J}$ results in the population distribution over the rotational, vibrational (rovibrational) levels within an electronic state of the CO molecule.

2.1.3 Two-photon laser-induced fluorescence

Due to the large difference in energy between the ground state $\text {X}^1\varSigma ^+$ and excited state $\text {B}^1\varSigma ^+$ of the CO molecule, an excitation energy in the VUV spectral region is required. However, radiation at such wavelengths is almost entirely absorbed by molecular oxygen within the atmosphere. Therefore, a common approach is the two-photon absorption laser-induced fluorescence (TALIF) method [10]. A multi-level scheme describing the TALIF excitation and de-excitation processes is shown in Fig. 2. A molecule is excited by two photons from the electronic energy level $\text {X}^1 \varSigma ^+$ to a virtual intermediate energy level $\overline{E}_\mathrm {i,intm}$ and from there to level $\text {B}^1 \varSigma ^+$ at the absorption rate constant $W_{12}$ which is given in Eq. (5).

$$\begin{aligned} W_{12}=\frac{\alpha _{12}I^2}{h\nu _\mathrm {dye}}. \end{aligned}$$

(5)

Compared to the absorption rate constant in a single-photon process, the absorption rate constant in the two-photon process is quadratically proportional to the laser irradiance I rather than linearly proportional. Furthermore, the absorption cross sections $\alpha _{12}$ is generally low for two-photon processes so that stimulated emission is expected to be neglectable in comparison to other depopulation processes. For the same reason, the absorption rate is low compared to a single-photon processes so that saturation effects could also be neglected [10].

The fluorescence can occur according to two de-excitation branches including the energy levels shown in Fig. 1. In the first one, fluorescence lowers the CO molecules’ energy level from $\text {B}^1 \varSigma ^+$ to a rovibrational energy level of the $\text {A}^1 \varPi$ state with a spontaneous emission rate constant $A_{\mathrm {BA}}$. In the second branch, the energy level drops by a collisional process (quenching) at a rate defined by the quenching rate constant $Q_{\mathrm {Bb}}$ to the $\text {b}^3 \varSigma ^+$ state from where the molecules radiate photons at a different wavelength with the spontaneous emission rate constant $A_\mathrm {ba}$. Further depopulation of the upper level may take place due to photoionization or predissociation with rate constants $W_{2\mathrm {i}}$ and P.

Fig. 2

Multi-level scheme of the electronic transitions of the CO molecule between the states in Fig. 1 (dashed: state change with photon absorption or emission)

Since only relative intensities are viewed in this study and assuming a stationary plasma flow where the number density distribution of CO in the flow stays constant, the excitation spectrum can be simulated regarding only the excitation and de-population processes. In this study, it is assumed that quenching can be neglected since the pressure is low in all test conditions. This simplifies the measurements and postprocessing since only the $\text {B}^1\varSigma ^+ \rightarrow \text {A}^1\varSigma ^+$ fluorescence must be detected. Furthermore, photoionization and predissociation are assumed to be neglectable. The relative intensity is then directly proportional to the excitation rate, which can be evaluated sufficiently by the transition probability given by the Hönl–London and Franck–Condon factors, by the population distribution of the ground states expressed by the Boltzmann factors and line broadening mechanisms that are described in Sect. 2.3.1. During the measurement of an excitation spectrum, laser shot-to-shot energy deviations can have a large impact on the fluorescence signal. Therefore, the fluorescence signal must be normalized for every point of measurement according to the following proportionality:

$$\begin{aligned} P_\mathrm {F}\propto W_{12}\propto I^2. \end{aligned}$$

(6)

2.2 Experimental setup

2.2.1 Laser-optical test setup

The laser system used to excite CO consists of a flashlamp-pumped, frequency-tripled Nd:YAG laser (Spectra-Physics, Quanta-Ray PRO, wavelength: ${355}\,\hbox {nm}$, maximum pulse energy: ${550}\,\hbox {mJ}$, pulse duration: 8–12 ns, repetition rate: ${10}\,\hbox {Hz}$) and a dye laser (Radiant Dyes, NarrowScan) filled with Coumarin 47. The fundamental wavelength of this dye in the range of 446–478 nm is halved to the required wavelength in the range from 223 to ${239}\,\hbox {nm}$ using a beta-barium-borate crystal with a spectral linewidth of ${0.06}\,{\hbox {cm}^{-1}}$. To correct the detected laser-induced fluorescence for the energy of the individual laser pulses, a portion of about ${9}\%$ of the laser beam is reflected from a fused silica glass and recorded with a pyroelectric energy sensor (Coherent, EnergyMax). The laser beam is guided into the measurement volume via three mirrors. Two lens systems are used to generate a focused beam (one-dimensional measurement) or a light sheet (two-dimensional measurement), which is described below. The fluorescence signal is recorded using an intensified ${16}\,\hbox {bit}$ CCD camera (Andor, USB iStar) with a resolution of ${1024}\,\hbox {Px} \times {1024}\,\hbox {Px}$ via an UV lens (${105}\,\hbox {mm}$, f/4.5) and a transmission filter (425– ${760}\,\hbox {nm}$) to reduce the influence of the Rayleigh scattering. The selected gate width was 78 ns for the one-dimensional free-stream measurements, 200 ns for the steady state test chamber measurements and 55 ns for the two- dimensional free-stream measurements. The readout time can be reduced by restricting the observation window of the CCD sensor (region of interest, ROI) and the signal-to-noise ratio (SNR) can be increased by combining the charge of several neighbouring pixels into one superpixel (SPx, hardware binning). The camera used also offers the option of accumulating several individual images before readout, which leads to a further increase in SNR due to the readout noise then being recorded only once. To synchronize the components, the Q-switch pulse of the pump laser is used as a start signal to expose the sensors. Via an output channel of the camera’s internal digital delay generator (DDG), the energy sensor is controlled to record the energy of each individual laser pulse. To realize the time sequence for the accumulation of a certain number of frames on the sensor at one wavelength and the subsequent adjustment (excitation scan), the dye laser is controlled via another channel of the DDG. Its software counts the incoming pulses and changes the wavelength according to the number of images to be accumulated. In Fig. 3, the schematic of the used optical setup without the laser system is shown.

Fig. 3

Schematic of the optical setup used for CO-TAPLIF

2.2.2 Light sheet optic

For the first realization of CO-TAPLIF measurements at the PWT, a light sheet optic was designed within the scope of this work, which allows a signal strength sufficient for a quantitative evaluation despite the quadratic dependence of the signal strength on the excitation energy. To ensure a high and constant energy density of the light sheet, it must not diverge in width or thickness.

In addition, the space required by the optical system must not exceed the available space between mirror 3 and the entrance window of ${500}\,\hbox {mm}$ to be able to arrange the components outside the measurement chamber. This avoids their contamination and damage during operation of the PWT and allows better accessibility for adjustment purposes.

Figure 4 shows the focal lengths of the lenses and their distances from each other. The focal length ratio of the spherical lens SL2 ($f_2 = {300}\,\hbox {mm}$) to the first cylindrical lens CL1 ($f_1 = {-30}\,\hbox {mm}$) $f_2/\vert f_1 \vert = 10$ determines the ratio of the width of the light sheet $h_2 = {30}\,\hbox {mm}$ to the diameter of the laser beam $d_1 = {3}\,\hbox {mm}$, where $h_2$ must not exceed the diameter of the entrance window to the measuring chamber of $d = {35}\,\hbox {mm}$. Furthermore, the focal length ratio of the spherical lens SL2 to the second cylindrical lens CL3 ($f_3 = {-100}\,\hbox {mm}$) $\vert f_3 \vert /f_2 = 1/3$ determines the thickness of the light sheet $h_3 = {1}\,\hbox {mm}$, which must be minimized, in order to maximize the energy density, and kept constant. It should be mentioned that CL1 does not affect the thickness of the laser beam perpendicular to the flow direction $d_1$ (downstream view in Fig. 4) and CL3 does not affect its width in the flow direction $h_2$ (side view in Fig. 4). In addition, the use of two cylindrical lenses arranged perpendicular to each other allows independent displacement of the light sheet along the flow axis and perpendicular to it, which greatly simplifies the adjustment of the optic. The dimensions of the lenses were selected in such a way that no parts of the laser beam are cut off.

Fig. 4

Schematic of the light sheet optic, left half: downstream view, right half: side view

For the one-dimensional measurements, the light sheet optic is replaced by a converging lens ($f = {1000}\,\hbox {mm}$). As a result of the large focal length of the lens, a high energy density is ensured above and below the focal point at the level of the nozzle center axis.

2.2.3 Test chamber

To determine the optimal experimental parameters for the following measurements and to prepare the data reduction, preliminary investigations were carried out on a steady state test chamber, with which spatially homogeneous, stationary and easily quantifiable conditions can be set in the measurement volume. The temperature within the chamber was kept at room temperature and the pressure could easily be varied and monitored by a sensor. The test chamber was positioned in such a way that the measurement volume excited by the laser and detected by the optic is in the same position as for the free-stream measurements. This ensures unchanged signal propagation times and the same imaging scale when switching between measurements, and avoids readjustment of the light sheet optic.

The stainless steel test chamber has a volume of ${0.004}\,{\hbox {m}^3}$ and four optical ports made of fused silica glass, each of which is offset from the other by ${90}^{\circ }$ in circumferential direction. This results in an observation angle of the excited measurement volume of ${90}^{\circ }$ to the laser beam direction. For evacuation by means of a vacuum pump and for filling with the test gas, the test chamber has two further connections.

2.2.4 Arc heated plasma wind tunnel (PWT)

Figure 5 shows the schematic structure of the PWT. The test gas is introduced into the arc chamber via two branches. Gas 1 is used to supply the arc, while gas 2 stabilizes the arc and cools the inner walls. The type of gas used in these experiments (gas 1 and gas 2) and the corresponding mass flows ($\dot{m}_1$ and $\dot{m}_2$) are given in Table 2 ($\dot{m}_3 = {0}\,\hbox {g/s}$ for all conditions). It should be noted that the designations gas 1 to gas 3 do not refer to the type of gas but to the position of its injection into the test setup as shown in Fig. 5. In the arc chamber, the arc is formed between the two Y-shaped DC electrodes. Partial ionization of the test gas occurs, so that the ionized gas and the electrons act as charge carriers. Heating of the test gas occurs by kinematic interaction of the charge carriers with the gas.

Fig. 5

Schematic structure of the PWT

After heating, the test gas enters the reservoir of the Laval nozzle via the settling chamber and is expanded into the measurement chamber. The nozzle used in this work has a diameter ratio between nozzle exit and narrowest cross section of $d_\mathrm {e}/d^* = {20.6}\,\hbox {mm} / {6.5}\,\hbox {mm}$ and a Mach number of $M = {3.7}$. The nozzle is movable along the main flow direction so that LIF measurements can be realized at different positions downstream of the nozzle exit without readjustment of the beam path. Between the arc chamber and the settling chamber, the test gas can be cooled and the mass-specific stagnation enthalpy reduced by supplying gas 3.

Three optical access points made of fused silica glass are available on the PWT for optical measurement techniques: one access point in the base plate of the measurement chamber for coupling the laser beam into the measurement volume and two windows on the lateral flanges of the measurement chamber for signal detection. The exhaust gas is conveyed out of the measuring chamber via a heat exchanger by means of a vacuum pump and an axial fan.

For the TALIF measurements carried out in CO$_2$ mode as part of this work, the aim is to achieve the lowest possible pressure in the measuring chamber, against which the test gas is expanded via the Laval nozzle. The pumping capacity of the vacuum pump connected to the measuring chamber allows a chamber pressure $p_\mathrm {C}$ in the range of 2–${10}\,\hbox {mbar}$, depending on the mass flow. All gases are supplied via gas bottles, which are connected to the individual gas branches via plug-in couplings. In CO$_2$ operation with a CO number density in the range of 1–2 $\times$ 10$^{17}$cm$^{-3}$, the test gas flow in the measuring chamber is diluted with N$_2$ in order not to exceed the explosion limit of CO in the exhaust gas.

Table 1 shows the experimental parameters pulse energy of the dye laser $E_\mathrm {p, dye}$, wavelength increment during excitation scan $\varDelta \lambda _\mathrm {dye}$, scale related to the single pixel $scale_1$ and related to the superpixel $scale_2$ of the one- and two-dimensional optical measurements in the test chamber and in the free-stream of the PWT. $Scale_2$ results from the binning applied in the respective experiments.

Table 1 Parameters of the one- and two-dimensional optical measurements in the test chamber and in the PWT free-stream

2.3 Methodology

The approach for temperature determination followed in the present work is based on the comparison of experimental excitation spectra with those simulated for different temperature levels.

2.3.1 Spectrum simulation

To simulate the temperature dependent excitation spectrum of the CO molecule for two-photon excitation in the electronic B–X system, the CO Excitation Spectrum Calculation (COESC) program was created based on the existing in-house tool NOCO-Spectra [18]. The main progress of the revision of the existing program is the possibility to account for instrumental broadening by using a numerical approximation of the Voigt line shape function rather than a Gaussian line shape function, which only accounts for Doppler broadening. COESC only takes into account Q-branch transitions ($\varDelta J = 0$), dominating the excitation spectrum for two-photon excitation of CO in the B–X system [16, 19]. The validity of the approximation neglecting O- and S- branch transitions is supported by usage in other spectrum simulations of CO described in literature [5, 6]. Spectra were simulated for temperature and spectral ranges of ${200}\hbox { K} \le T \le {2500}\,\hbox {K}$ and ${114.925}\hbox { nm} \le \lambda \le {115.075}\hbox { nm}$ with resolutions of $\varDelta T = {10}\hbox { K}$ and $\varDelta \lambda = {0.1}\hbox { pm}$, respectively. The molecular constants of the electronic states X$^1\varSigma ^+$ and B$^1\varSigma ^+$ were taken from [14, 20]. The constants $\omega _ey_e$ and $\beta _e$ of the B$^1\varSigma ^+$ state were assumed as zero as no data could be found in literature.

The functionality of COESC is based on three core components of both atomic and molecular spectrum simulation: (1) spectral positions of transitions, (2) strengths of the individual transitions relative to each other ((1) + (2) gives line spectrum), (3) spectrum shape. The transitions’ spectral positions equal the energy differences between the corresponding quantum mechanical states and are calculated using Eq. (1). The relative line strengths $\mathcal {S}$ combine Boltzmann fractions and transition probabilities [6]:

$$\begin{aligned} \mathcal {S} = f_\mathrm {B}(T;J'',v'')\cdot \frac{S_{J',J''}}{2J''+1}\cdot S_{v',v''}~. \end{aligned}$$

(7)

According to Eq. (7), the relative line strength $\mathcal {S}$ represents the modified Einstein coefficient for absorption $B_{12}$ neglecting the factors specifying the change in electronic state (excitation only in one electronic system $\text {B}^1\varSigma ^+ \leftarrow \text {X}^1\varSigma ^+$) and scaled by a constant factor as only relative, not absolute line strengths are required [10]. Furthermore, $B_{12}$ is complemented by the Boltzmann fraction of the transition’s lower energy level $f_\mathrm {B}(T;J'',v'') = f_{\mathrm {B},J''}(T)f_{\mathrm {B},v''}(T)$ defined by Eqs. (3) and (4), also neglecting the electronic fraction. The Boltzmann fraction in Eq. (7) accounts for the proportionality $P_\mathrm {LIF} \propto f_\mathrm {B}$ as well as the temperature dependency of the excitation spectrum. For calculating the Q-branch Hönl-London factor in Eq. (2b), the invariant of the two-photon polarizability tensor $\mu _\mathrm {I}^2$ was arbitrarily set to one, as only relative line strengths are required and COESC just takes Q-branch transitions into account. An accurate value of $\mu _\mathrm {I}^2$ has to be used, if O- and S-branch transitions are taken into account as well to get correct relative line strengths of Q- with O- and S-branch transitions.

Physical and instrumental broadening mechanisms cause a continuous spectrum from the discrete line spectrum taken into account by various line shape functions and thus defining the spectrum shape. The mechanisms considered in COESC are the temperature dependent Doppler broadening (Gaussian line shape function $\mathcal {L}_\mathrm {D}(\nu )$) and the instrumental broadening caused by the finite spectral linewidth of the dye laser, for which a Lorentzian line shape function $\mathcal {L}_\mathrm {L}(\nu )$ is assumed [21, 22]. The resulting line shape function of the excitation spectrum $\mathcal {L}_\mathrm {abs}(\nu )$ can be expressed as [22]

$$\begin{aligned} \begin{aligned} \mathcal {L}_\mathrm {abs}(\nu )&= \mathcal {L}_\mathrm {D}(\nu )*\mathcal {L}_\mathrm {L}(\nu ;\varDelta \nu _L)*\mathcal {L}_\mathrm {L}(\nu ;\varDelta \nu _L)\\&= \mathcal {L}_\mathrm {D}(\nu )*\mathcal {L}_\mathrm {L}(\nu ;2\varDelta \nu _L)~, \end{aligned} \end{aligned}$$

(8)

$(*)$ representing the convolution operator. In particular, the two-photon excitation is considered by twofold convolution of the Doppler broadened line spectrum with the line shape function of the dye laser, so that its effective FWHM $\varDelta \nu _\mathrm {L}$ equals the doubled real FWHM, caused by the mathematical properties of the Lorentz function [23]. The implementation of COESC considers the Gaussian and Lorentzian portions of the overall excitation spectrum line shape function by usage of a Voigt profile as convolution of Gaussian and Lorentzian function [10]. For reasons of minimizing computational effort, a numerical approximation of the Voigt profile is used rather than the analytical expression which requires the calculation of an improper integral [15, 24].

2.3.2 Experimental data preparation

In the following description, the term pixel means hardware-binned superpixels, software binning was not used. The data gathered in each experimental excitation scan were the LIF signal from the ICCD camera in grayscale values and the temporal energy evolution of the exciting dye laser. The raw data postprocessing represents the preprocessing for the temperature determination methods described in Sect. 2.3.3 and mainly includes background correction and signal normalization.

The objective of background correction is the reduction of the signal portion, not caused by fluorescence but e.g. noise, ambient light or free-stream self-illumination. For this purpose, the signal was averaged over a region of pixels where no fluorescence signal was detected in for each accumulated image—to consider temporal fluctuations—and subtracted from the signal in each pixel in the image. That way a reduction of influence is accomplished for ICCD noise (readout noise, dark current) as well as uniform ambient radiation. However, this kind of background correction is sometimes insufficient (i.e. the pixel individual noise is still significant versus the LIF signal) for measurements with low SNR as this is the case for CO-TAPLIF measurements, especially at the edges of the light sheet. As a solution, a pixel-individual background correction was performed if necessary. Therefore the signal intensity, spectrally averaged over a range of a few picometers at higher wavelength after the characteristic intensity drop in the B–X(0,0) band at low J, thus following the Q(0)-transition, was subtracted from the raw data. For this, taking advantage of the fact that no transitions of the CO molecule cause radiation in this spectral region of the excitation spectrum for the relevant temperature range, signal zeroing is predestinated. Neglecting this pixel-individual background correction causes the tendency of determining too high temperatures for signals with low SNR, as noise at lower wavelength (higher J) is interpreted as LIF signal by mistake and the signal of these transitions increases with temperature because of rising ground state populations.

The background-corrected signal was normalized with the quadratic exciting laser energy with the objective of compensating the influence of temporal fluctuations of the laser pulse energy during an excitation scan (duration: $\mathcal {O}$(min)) on the detected fluorescence signal. This quadratic normalization occurs because of the quadratic proportionality of the LIF signal power to the irradiance and thus equally of the detected signal to the laser pulse energy, see Eq. (6). In general, this proportionality holds for each pixel individually with the corresponding portion of the exciting laser pulse energy causing the detected signal. For the performed measurements, the assumption was made that the spatial energy profile over the light sheet’s width as well as over the distance travelled through the measurement volume remains invariant for consecutive dye laser pulses. Under this assumption, the normalization of the individual pixel’s signals with the whole laser pulse energy is valid. The laser pulse energy used for normalization was averaged over all pulses for which an image was accumulated. As only a very small spectral range was scanned for gathering the excitation scans in the B–X(0,0) band of the CO molecule, the spectral dependency of the laser pulse energy loss caused by lenses, mirrors and the fused silica, to consider the actual portion of the whole laser pulse energy that reaches the measurement volume, was neglected [18].

Because of the described corrections of the raw experimental data, an arbitrary unit [a.u.] is used for the LIF signal for further analysis in the present work. The spatial resolution of the measurements is achieved by the fact that for each pixel, a separate excitation spectrum could be evaluated for the temperature determination.

2.3.3 Temperature determination methods

The LIF thermometry performed is based on the temperature dependency of the excitation spectra of the investigated species, due to temperature-dependent populations of rovibrational levels of the electronic ground state and thus relative line strengths of different transitions. Conventional methods for temperature determination using LIF compare fluorescence intensities of two (two-line technique) or multiple (multiline technique) excitation transitions [18]. In the present work, a direct comparison of experimental with simulated excitation spectra was performed, so that not only the fluorescence intensities of two or more excitation transitions were taken into account, but the spectrum shape in a defined spectral range as a whole. The focus of both temperature determination methods described hereafter is on the laser-induced excitation of the B–X(0,0) vibrational band of the CO molecule.

The first method used for temperature determination is the so-called correlation automated rotational fitting (CARF), also used in the CO-LIF thermometry investigations preceding the present work [8]. The former implementation of the method was revised and its functionality extended. Two datasets serve as inputs: (1) postprocessed experimental excitation spectra, (2) database of temperature-dependently simulated excitation spectra (COESC). The first step of the CARF method is a compensation of the spectral offset between experimental and simulated excitation spectra, i.e. the alignment of the experimental wavelength axis relative to the simulated axis (fixed reference, absolute position of transitions irrelevant), using cross correlation. Most important for an accurate spectral correlation is the significant intensity drop at low J. After proper alignment, the simulated spectra are cut to the spectral range of the experimental ones. Hereafter, the pixel individual zeroing of the experimental excitation spectra is performed if necessary. Furthermore, the experimental and simulated spectra are cut to the spectral range that should be used for temperature correlation (intensity abnormalities that may distort temperature determination are avoided). In the last step of the CARF algorithm, the actual temperature correlation, i.e. the normalized cross correlations $\mathcal {K}(T)$ between the experimental spectra and those of all simulated temperature levels are calculated for each pixel. Normalized means that $\mathcal {K}(T) = 1$ for correlation of two identical spectra. Each pixel is assigned the temperature, for whose corresponding simulated spectrum the highest correlation value $\mathcal {K}(T)$ is reached.

The second method used for temperature determination is called polynomial regression correlation (PRC) and was developed in the course of the present work. The development of this method was motivated by the generally significantly lower SNR of the CO-TAPLIF measurements realized at the PWT for the first time for temperature determination, compared to one-dimensional measurements. It is extremely difficult to acquire detailed spectrum characteristics, especially the intensity peaks of the single transitions by CO-TAPLIF in such challenging environments as within the free-stream of the PWT. What the experimental spectra do accurately depict, however, is the mean trend of an increasing signal intensity with increasing wavelength for excitation in the B–X(0,0) vibrational band. It was observed that the CARF algorithm often has poor uniqueness in temperature correlation, i.e. $\mathcal {K}(T)$, for signals with such low SNR. Based on this, the objective of the PRC method is, to reach a more unique temperature correlation for signals with bad SNR by taking advantage of the temperature sensitivity of the mean signal trend instead of the specific spectrum shape. For this, the simulated spectra are simplified to their trend of an intensity increase with increasing wavelength by a least squares polynomial regression (integrated in COESC). The best results with PRC were obtained using a polynomial degree of 15 for regression. Such a low degree is sufficient to just fit the signal trend, not the single peaks. The spectral range used for the regression ends before the intensity drop at low J.

Fig. 6

Polynomial regression of the CO B–X(0,0) band for different temperatures

Figure 6 visualizes the temperature sensitivity of the polynomial regression. The implementation and the principle of the PRC is based on the CARF method, but with the main difference in temperature correlation. While the spectral correlation for compensating the wavelength offset between experimental and simulated spectra is also performed with the simulated spectra, not their regressions, as described above, for temperature correlation, the normalized cross correlations of the experimental spectra and the regression polynomials are computed.

The CARF method is flexibly usable for other species as well. The PRC algorithm was developed for this specific spectral range of CO, but the main principle is also adaptable for other species with suitable characteristics in their excitation spectra.

No quantitative uncertainty analysis for temperature determination was performed in the present work, but a qualitative inspection by two criteria: (1) maximum absolute value of $\mathcal {K}(T)$, (2) uniqueness, i.e. unambiguous expression of the maximum, of $\mathcal {K}(T)$.

3 Results and discussion

In the present work, one- and two-dimensional CO-TALIF measurements were conducted in a steadystate test chamber and the PWT free-stream. The conditions for the free-stream measurements are summarized in Table 2. $\dot{m}_1$ and $\dot{m}_2$ denote the mass flow rates of the first and second gas inlet ($\dot{m}_3 = {0}\hbox { g/s}$ for all conditions), $h_0$ and $T_0$ the free-stream total enthalpy and temperature, respectively, $p_0$ the nozzle reservoir pressure and $p_\mathrm {C}$ the pressure in the measurement chamber of the PWT against which the test gas is expanded. The steady state test chamber was filled with pure CO at the temperature $T = {295}\,\hbox {K}$ (room temperature) and pressure $p = {10}\,\hbox {mbar}$.

Table 2 Experimental conditions of one- and two-dimensional PWT free-stream measurements (*CO₂, ^†N$_{2}$)

3.1 PWT  free-stream: one-dimensional

As the first step, following up on the work of Kirschner et al. [8], one-dimensional CO-TALIF measurements in the PWT free-stream were performed for the determination of radial temperature distributions at $x = {7}\hbox { mm}$ downstream the nozzle outlet.

Fig. 7

One-dimensional radial temperature distributions

Figure 7 shows the measured radial temperature profiles of the three conditions 1D-I, -II and -III, with successively increasing total enthalpy, respectively, comparing the results using CARF (upper subplot) and PRC (lower subplot) for temperature determination with a spatial resolution of 0.575 mm/SPx in radial and main flow direction, compare Table 1. For the purpose of best comparability, the upper and lower subplot both show the temperature distributions determined for the lower free-stream half (below the nozzle centerline), mirrored upward for the CARF temperature profiles. Under the assumption of a rotationally symmetric nozzle and subsequent free-stream flow, the whole free-stream temperature profile in the measurement plane at $x = {7} \hbox { mm}$ is determined by only using the data gathered for one free-stream half. The temperature profiles determined with both methods for the upper free-stream half support the assumption of a rotationally symmetric flow field, being very similar to those determined for the lower half, so that a presentation of these data is omitted. For both evaluation methods, CARF and PRC, the successively higher temperature level in the free-stream, which is expected at increased total enthalpy $h_0$, can be clearly seen with the larger increase of the temperature level at the stronger increase of $h_0$ between conditions 1D-II and 1D-III ($|\varDelta _\mathrm {II,III}h_0| = {3.5}\,\hbox {MJ/kg}$ compared to $|\varDelta _\mathrm {I,II}h_0| = {2}\hbox { MJ/kg}$). Using CARF, the average temperature levels in the free-stream core are approximately 1175 K, 1325 K and 1625 K, using PRC 1275 K, 1325 K and 1675 K for conditions 1D-I, -II and -III, respectively. This shows the trend that higher temperature levels tend to be determined with PRC than with CARF, with a maximum deviation of $\varDelta T = {100}\hbox { K}$ for condition 1D-I.

For conditions 1D-II and -III, a similar agreement between the experimental and simulated spectra is reached for CARF and PRC evaluation. For condition 1D-I, the CARF evaluation results in a better agreement of the experimental with the simulated excitation spectrum than using PRC. For PRC, the intensity before the characteristic intensity drop turns out to be too low, i.e. the correlation is done with a regression polynomial which shows a lower relative signal increase towards higher wavelengths in the correlated region, which is associated with a higher temperature, see Fig. 6.

Fig. 8

1D-III excitation spectrum (PRC, centerline)

As representative example of the one-dimensional free-stream measurements, Fig. 8 shows the comparison of simulated and experimental spectra for condition 1D-III and PRC evaluation for the superpixel at centerline. For best comparison, the experimental spectrum is scaled relative to the simulated one, normalized to unity maximum intensity, by its mean value (i.e. after scaling, both spectra have an equal mean value for the plotted spectral range). This scaling is only relevant for visualization and has no influence on temperature determination using the normalized cross correlation. The intensity is plotted against the effective wavelength of the two-photon excitation, i.e. the half dye laser wavelength. Pixel individual zeroing was performed using the average signal detected in the range $\lambda \in [{115.056}, {115.058}]\,\hbox { nm}$. In the following descriptions, $\lambda$ refers to the spectral axis, i.e. the spectral positions, determined using COESC, which is used as reference for all measurements.

In the experimental excitation spectrum, a signal drop is observed between the transitions Q(8)@${115.051}\hbox { nm}$ and Q(13)@${115.0473}\hbox { nm}$, which is not reproduced by COESC. This signal drop was also observed by Kirschner [18] for one-dimensional CO-TALIF measurements in the PWT free-stream. The relative signal drop for this range of the rotational quantum number $J'' = J'$ (Q-branch) correlates with the descriptions of Voigt et al. [5], wherein the relative signal decrease at high exciting laser intensity is attributed to a higher rate of photoionization $W_\mathrm {2i}$ for levels $J' \in [8, 12]$–which correspond to excitation transitions Q(8) to Q(12)–compared to the remaining excited rotational levels, which is accompanied by a lower rate of spontaneous emission $A_{21}$ and thus a lower fluorescence signal. Since the excitation laser beam is focused with a converging lens in the measurement volume to perform the one-dimensional CO-TALIF measurements, very high excitation intensities result there, so that the conditions for the increased depopulation of the excited rotational levels $J' \in [8, 13]$ as a result of photoionization are given for the observed signal drop and this is consequently assumed to be the case. For the measurements performed, the signal drop is observed including $J' = 13$, whereas in [5] it is described only including $J' = 12$. The reproducibility of this signal decrease is observed in the experimental excitation spectra of the conditions 1D-I, -II and -III, respectively. To avoid falsification of the temperature correlation due to the signal drop not present in the simulated spectra, for all one-dimensional conditions only the spectral range $\lambda _\mathrm {COESC} \in [{115.01}, {115.046}]\,\hbox { nm} \rightarrow \varDelta \lambda _\mathrm {COESC} = {36}\hbox { pm}$was used in CARF and PRC to perform this correlation, indicated by dashed vertical lines in Fig. 8.

With increasing rotational quantum number J, i.e. from and including Q(21)@${115.038}\hbox { nm}$, small deviations appear between the experimental and simulated spectral positions of the individual transitions. Accordingly, a larger increase in spectral spacing between experimentally recorded transitions towards smaller wavelengths is observed than is represented by COESC. The reason for this spectral shift cannot be conclusively identified in the present work. Possible factors influencing this effect include the molecular constants of the two electronic states X$^1\varSigma ^+$ and B$^1\varSigma ^+$ of the CO molecule stored in COESC, since the molecular constants are each determined only on the basis of experimental data spanning a certain range of quantum mechanical rotational levels, and uncertainties in the experimental data, especially towards higher rotational quantum numbers, may occur [20]. The observed spectral offset for transitions of higher rotational quantum number was also noticed in the investigations of Kirschner [18] using the spectral simulation program NOCO-Spectra. Another possible cause for these deviations is an inaccurately tuned wavelength of the dye laser in the form of an actually performed spectral step size that does not exactly match the one specified in the software for the excitation scan. Such inaccuracy in the operation of the dye laser could spectrally distort the experimentally recorded excitation spectra compared to the simulated ones (here: stretched $\rightarrow$ would correspond to an actual smaller step size than the one specified in the software), as also observed in [6]. However, this argument is weakened by the fact that the spectral offset occurs only towards smaller wavelengths and, when aligned with the characteristic intensity drop, does not occur already at transitions with small rotational quantum number ($J < 21$). Nevertheless, a variable uncertainty in the step size of the dye laser over the scanned spectral range cannot be excluded as a cause.

The spatial resolution of the one-dimensional CO-TALIF temperature measurements in the free-stream of the PWT was significantly improved in the present work, compared to the measurements of Kirschner et al. [8] that preceded this work, by almost a factor of four from ${2.27}\hbox { mm/SPx}$ to a value of ${0.575}\hbox { mm/SPx}$ in radial and main flow direction. This spatial resolution is much higher than for the PLIF measurements described in the following sections, because focusing the laser beam with the converging lens instead of the light sheet optic gives a higher irradiance and thus—due to its quadratic proportionality to the TALIF fluorescence signal—allows less hardware binning for reaching a sufficiently high SNR, i.e. that the detected fluorescence signal is only hardly disturbed by the influence of free-stream intrinsic lights and PWT condition fluctuations.

Comparing condition 1D-I with $h_0 = {5.0}\hbox { MJ/kg}$ to the condition investigated from Kirschner et al. [8] at the PWT with $h_0 = {2.1}\hbox { MJ/kg}$, the trend of an increasing average temperature in the free-stream core caused by the higher stagnation enthalpy is mapped correctly by our measurements. For the lower enthalpy condition in [8], average temperature levels of $T = {1100}\hbox { K}$ and $T = {1000}\hbox { K}$ were determined at positions $x = {2}\hbox { mm}$ and $x = {22}\hbox { mm}$ downstream the nozzle outlet, respectively, slightly overestimating the corresponding levels of CFD calculations of the nozzle flow and the subsequent free-stream used for validation purposes. In contrast, we determined $T = {1175}\hbox { K}$ and $T = {1275}\hbox { K}$ at $x = {7}\hbox { mm}$ for condition 1D-I using CARF and PRC evaluation, respectively.

3.2 Steady state test chamber: two-dimensional

In the next step, to expand the CO-TALIF to planar temperature measurements, experiments were conducted in a steady state test chamber filled with pure CO. The measurements in the steady state test chamber served on the one hand to study different detection settings of the ICCD camera with regard to an optimization of the SNR of the recorded fluorescence signal and on the other hand to validate the temperature determination methods on the basis of the known test gas temperature.

With regard to an optimization of the SNR, the hardware binning in particular has turned out to be the most important setting of the ICCD camera. The goal is a trade-off between spatial resolution (lowest possible binning) and SNR (highest necessary binning). To take this trade-off into account, the hardware binning for all measurements was set in such a way that software binning in post-processing could be omitted, since hardware binning generally allows a higher SNR at the same spatial resolution.

Fig. 9

Steady state test chamber temperature fields, test gas temperature $T = {295} \hbox { K}$, data gathered in the framed superpixel used for PRC data evaluation shown in Fig. 10

Figure 9 shows the temperature fields with a spatial resolution of ${2.3}\hbox { mm/SPx}$, see Table 1, determined in the steady state test chamber using CARF and PRC for temperature determination. For both methods, valid temperature values were calculated over a width of ${10}\, \hbox{SPx} \;\widehat{=} \; {23}\,\hbox {mm}$, where temperatures were labeled as valid under the conditions of a normalized cross correlation value greater than $\mathcal {K}_\mathrm {min}(T) = {0.9}$ and values in the range $T = {300} \pm {100}\hbox { K}$. A comparison of the two temperature fields shows that a much more homogeneous temperature field (that better corresponds to the actual conditions) is calculated with PRC, which at the same time has smaller deviations from the test gas temperature of $T = {295}\hbox { K}$ than that calculated with CARF.

Fig. 10

Test chamber excitation spectrum (PRC, framed SPx of Fig. 9)

As representative example, Fig. 10 visualizes the comparison of the experimental (scaled by the mean value, as described in Sect. 3.1) and simulated excitation spectra along with the corresponding regression polynomial—for which the maximum value of $\mathcal {K}(T)$ is reached—for PRC evaluation of the data gathered in the framed superpixel of Fig. 9. For the CARF method, the spectra of the whole shown spectral range were used and for PRC the full range of the plotted regression polynomial. Pixel individual zeroing does not show significant influence on the calculated temperatures for the measurements in the steady state test chamber due to a high SNR.

Figure 10 shows good consistency between experimental and simulated spectrum, especially regarding the spectral positions of individual transitions as well as relative signal intensities. As discussed in Sect. 3.1, small deviations in the spectral positions occur for the transitions towards higher rotational quantum number from and including Q(21). Furthermore, in the region of transitions of small quantum numbers $J''$ (towards longer wavelengths), deviations of the experimental spectrum from the simulated spectrum are observed close to the characteristic intensity drop. The experimental intensity fluctuations occurring there are not reproduced by COESC with such relative strength. The influence of these fluctuations not reproduced by the simulation with regard to the evaluation on the basis of the PRC method is estimated as small, because the trend of the excitation spectrum of an intensity increasing to larger wavelengths is reproduced by the experimental spectrum. Using CARF, a larger influence could result from this deviation, because for the temperature correlation not only the trend of the signal is used on the basis of the regression polynomial, but instead the simulated spectrum is used for the temperature correlation directly, so that inaccuracies in the actual shape of the excitation spectrum could affect the correlation more significantly and cause inaccuracies. This assessment is reinforced by the more accurate temperature field determined using PRC compared to that determined using CARF, as can be seen in Fig. 9. Although the steady state test chamber measurements are primarily representative of low temperature levels only, this reasoning can be applied to compare the CARF and PRC methods regardless of temperature level. For a precise application of CARF, due to the consideration of the entire spectrum shape, both a very well-resolved experimental excitation spectrum (low fluctuations, high SNR, high spectral resolution) is required and this shape must be reproduced very accurately by the simulation over the entire spectral range investigated. In contrast, the PRC evaluation is estimated in such a way that, as a result of the simplified temperature correlation for which the temperature sensitivity of the excitation spectrum is broken down to the regression polynomial, a not exact shape of both the experimental and the simulated spectrum has a smaller impact on the temperature calculation, as long as the trend of the signal is mapped appropriately. This fact is considered to be a major advantage of PRC over CARF.

The measurements in the steady state test chamber demonstrate the feasibility of CO-TAPLIF thermometry with high accuracy for low test gas temperatures with a spatial resolution that corresponds quite closely to that in the previous one-dimensional measurements in the PWT free-stream of Kirschner et al. [8]. Similar results were reached for both temperature determination methods (slightly more accurate for PRC) because of a high SNR. An advanced performance of PRC compared to CARF is expected for the CO-TAPLIF free-stream measurements with lower SNR.

3.3 PWT  free-stream: two-dimensional

After successful demonstration of the feasibility of planar CO-TALIF temperature measurements and studying the influences of different parameters in data generation, the technique was extended to measurements in the PWT free-stream.

Fig. 11

Temperature fields for condition 2D-I ($\dot{m}_1=1.0\, \hbox {g/s}\, \hbox {N}_{2}$, $\dot{m}_2=2.4\, \hbox {g/s}\,\hbox {CO}_{2}$, $h_0=4.5\,\hbox {MJ}/\hbox {kg}, T_0=3400\hbox {K}, \hbox {p}_0=1\,\hbox { bar}, \hbox {p}_\mathrm {C}=2\,\hbox {mbar}$), data gathered in the framed superpixel used for PRC data evaluation shown in Fig. 12

Figure 11 shows the temperature fields obtained for condition 2D-I using both CARF and PRC evaluation methods with a spatial resolution of ${2.3}\,\hbox {mm/SPx}$, see Table 1. The spatial coordinate x denotes the distance from the nozzle outlet, r the radial distance to the nozzle centerline. Under the specification $\mathcal {K}_\mathrm {min}(T) = {0.85}$, both for CARF and PRC plausible temperature values were determined over a width of three to four superpixel columns in the free-stream ($\widehat{=}\ {6.9}$ to ${9.2}\hbox { mm}$) as well as five superpixel columns outside the free-stream ($\widehat{=}\ {11.5}\hbox { mm}$). While temperatures tend to be higher with PRC in the one-dimensional measurements shown in Fig. 7 and Fig. 11 shows an opposite trend. However, using PRC the temperature field tends to be more symmetrical with respect to the nozzle centerline, which is confirmed as a qualitative characteristic of the temperature field in the free-stream by the one-dimensional investigations at the position $x = {7}\hbox { mm}$ downstream of the nozzle outlet. For both evaluation methods, Fig. 11 shows that only in the core section of the light sheet width a signal quantitatively evaluable by thermometry is obtained. This is due to the spatial energy profile over the light sheet width, decreasing towards the edges. In addition, for both evaluation methods, there is a tendency for the temperature to reduce in main flow direction across the three fully evaluable superpixel columns.

Fig. 12

2D-I excitation spectrum (PRC, framed SPx of Fig. 11)

As representative example, Fig. 12 shows the comparison of experimental and simulated excitation spectra for the superpixel at centerline framed in Fig. 11 after PRC evaluation. The experimental spectrum shows significant intensity increases in the spectral ranges $\lambda _\mathrm {COESC} = {115.037}\hbox { nm}$ to ${115.040}\hbox { nm}$ as well as $\lambda _\mathrm {COESC} > {115.055}\hbox { nm}$ not covered by the simulation. These types of signal increases are not observed for the other free-stream conditions measurements (one- and two-dimensional). Since for all these conditions according to Table 2 only CO$_{2}$ is used as test gas, but for condition 2D-I N$_{2}$ is added to the CO$_{2}$, the signal increases in the two spectral regions are presumably attributed to the laser-induced excitation of a species other than CO, which is present in the heated mixture of CO$_{2}$ and N$_{2}$ and whose fluorescence signal passes the transmission filter in front of the ICCD camera. The excitation of this species does not have to be caused by two-photon absorption as in the case of CO, but is also possible due to single-photon absorption of the exciting laser beam at $\lambda _\mathrm {dye} \approx {230}\,\hbox { nm}$. As species with transitions in this spectral range of slightly above ${230}\,\hbox { nm}$, which do not occur in the pure CO$_{2}$ flow, but can occur in the in the CO$_{2}$-N$_{2}$ mixture, N$_{2}$ in the so-called first Kaplan system and NO in the $\gamma$-system are possible candidates [25, 26]. In particular, it should be noted that these signal increases are only detected in the free-stream, not in the light sheet section outside the free-stream. An explanation for this could be that these species do not accumulate in sufficient quantity in the measuring chamber over the duration of the experiment, which seems rather implausible after a sufficient amount of CO for thermometry accumulates in the measuring chamber, or instead, that the lower energy level of the excited transition is only enough populated at the temperatures in the free-stream to cause such a fluorescence signal.

The signal enhances in the two spectral ranges of the experimental excitation spectrum have two negative influences on the evaluation for temperature determination. On the one hand, only the spectral ranges $\lambda _\mathrm {COESC} = {115.040}\,\hbox { nm}$ to ${115.055}\,\hbox { nm} \rightarrow \varDelta \lambda _\mathrm {COESC} = {15}\,\hbox { pm}$ for CARF and up to the end of the regression polynomial for PRC (marked with dashed lines in Fig. 12) can be used to avoid falsification. Furthermore, due to increasing signal at $\lambda _\mathrm {COESC} > {115.055}\,\hbox { nm}$, only the spectral range between $\lambda _\mathrm {COESC} = {115.054}\,\hbox { nm}$ and ${115.0545}\,\hbox { nm}$ can be used for pixel-individual zeroing of the experimental excitation spectra. However, especially in the case of the planar free-stream measurements, this pixel-individual zeroing proves to be necessary for plausible quantitative temperature determination. Besides the described partial deviations, the experimental excitation spectrum shows good agreement with the simulated spectra for both evaluation methods.

After only a narrow spatial temperature field could be determined for the test condition 2D-I with CO-TAPLIF thermometry, the aim of the test condition 2D-II is to specify the temperature field for a larger area in the main flow direction. For this purpose, it is necessary to achieve a higher absolute fluorescence signal with a SNR sufficient for a plausible temperature correlation over a larger width of the light sheet. One possibility to realize this is to reduce the light sheet thickness, so that a sufficiently high fluorescence signal can also be achieved in the edge regions of the light sheet. Since a further reduction of the light sheet thickness could not be realized with the light sheet optic designed within the present work aligned as shown in Fig. 4, the light sheet optic—to demonstrate the influence of a lower light sheet thickness—was placed inside the measuring chamber below the free-stream for measuring the condition 2D-II. The uppermost cylindrical lens CL3 was removed from the beam path and the two-lens system consisting of CL1 and SL2 was aligned in such a way that, on the one hand, the light sheet is parallelized in width and, on the other hand, the spherical lens SL2 focuses the light sheet in thickness at the height of the nozzle centerline. Above and below the nozzle centerline, due to the absence of CL3 a varying energy density results due to the convergence and divergence of the light sheet thickness, respectively, whereby a sufficient energy density over the entire free-stream was expected due to the small free-stream diameter. A further increase of the energy density of the exciting laser light results from the removal of the lens CL3 from the beam path, after this lens only transmits approximately ${90}\%$ of the incoming laser light. This arrangement of the light sheet optic within the measurement chamber was for demonstration purposes only and, due to the aspects discussed in Sect. 2.2.2, it should not be aimed at in the long term.

Fig. 13

Temperature fields for condition 2D-II ($\dot{m}_1=2.4\,\hbox {g/s} \, \hbox {CO}_{2}$, $h_0=9.0 \, \hbox {MJ}/\hbox {kg}, T_0=6300\,\hbox {K}, \hbox {p}_0=0.9\,\hbox {bar}, \hbox {p}_\mathrm {C}=3\,\hbox {mbar}$), data gathered in the framed superpixel used for PRC data evaluation shown in Fig. 14

Figure 13 shows the temperature fields determined for condition 2D-II using CARF and PRC, respectively, again with a spatial resolution of ${2.3}\,\hbox { mm/SPx}$. The area for which the temperature correlation yields plausible values under the specification $\mathcal {K}_\mathrm {min}(T) = {0.6}$ is mainly located in the core and above the free-stream. This can be justified by a focal point of SL2 located slightly above the nozzle centerline. For this measurement a temperature field could be determined for both evaluation methods over a width of twelve superpixel columns ($\widehat{=}\ {27.6}\,\hbox { mm}$). This allows to more comprehensively map the effects of the flow field in main flow direction with a single measurement. Thus, in Fig. 13, the growth of the shear layer in the main flow direction can be seen, causing the area influenced by the high temperature core flow to extend to larger distances r from the nozzle centerline. This is accompanied by a decreasing temperature level in the main flow direction in the core region of the free-stream. The temperature field determined using PRC is more symmetrical with respect to the nozzle centerline, which seems more plausible assuming an approximately rotationally symmetric flow field.

Comparing condition 2D-II with $h_0 = {9.0}\,\hbox { MJ/kg}$ to condition 1D-III with $h_0 = {10.5}\,\hbox { MJ/kg}$, because of the lower stagnation enthalpy also lower temperatures are expected in the free-stream. This trend is mapped correctly in Fig. 13 considering both evaluation methods after a temperature level of approximately 1600–1700 K is determined in the free-stream core region for condition 1D-III at $x = {7}\hbox { mm}$, whereas for the two-dimensional measurements at this position a temperature level in the range 1150–1500 K is determined.

Fig. 14

2D-II excitation spectrum (PRC, framed SPx of Fig. 13)

As representative example, Fig. 14 compares the experimental with the simulated spectrum of highest temperature correlation value $\mathcal {K}(T)$ for PRC evaluation of the framed superpixel in Fig. 13. The experimental spectrum has a poor SNR, especially compared to the planar measurement of condition 2D-I in Fig. 12. As a result of this low SNR, in particular the pixel individual zeroing is very important for a plausible temperature determination and is performed using the spectral range $\lambda _\mathrm {COESC} = {115.055}\hbox { nm}$ to ${115.057}\hbox { nm}$. The intensity variations caused by the different excitation transitions are superimposed by significant arbitrary signal fluctuations (noise) in such a way that the trend but not the actual shape of the excitation spectrum can be recognized. This circumstance characterizes the motivation for the innovation and application of the PRC evaluation method.

Fig. 15

2D-I, -II temperature correlation value

Figure 15 shows the curves of the temperature correlation value $\mathcal {K}(T)$ for the two conditions 2D-I and -II for the framed superpixels of Figs. 11 and 13, respectively. While in Fig. 15a for the exemplary superpixel of the condition 2D-I at good SNR of the experimental spectrum, distinct maxima result for the CARF as well as the PRC evaluation, Fig. 15b demonstrates the advantage of the PRC method at a poor SNR for the selected superpixel of the condition 2D-II. While there is no clear temperature correlation for CARF, but a further increase of the correlation value after a first local maximum, there is a distinct maximum for PRC. Although this is only an isolated case and distinct correlation curves are also obtained with CARF for most of the superpixels in Fig. 13, this exemplary observation demonstrates that the PRC method tends to be better suited for the evaluation of signals with poor SNR, since a more reliable temperature correlation seems to be obtained.

Compared with the experimental excitation spectra of the one-dimensional measurements in Sect. 3.1, Figs. 12 and 14 clearly show the influence of the fluctuations of the experimental conditions as signal fluctuations that are significant compared with the intensity variations of the individual transitions. Furthermore, as a result of the lower intensity of the exciting laser light, no signal collapse before the characteristic intensity drop at low J occurs in the two-dimensional measurements which supports the above mentioned assumption of increased photoionization of certain excited rotational levels.

Performing two-dimensional thermometry measurements, the temperature in several superpixel columns can be determined in a single measurement, whereas with one-dimensional measurements only in one. Thus, not only radial but also effects in main flow direction can be mapped within one measurement, for which otherwise several one-dimensional measurements would be necessary, requiring a high reproducibility of the test conditions. However, for the planar measurements, a much higher hardware binning in and orthogonal to the main flow direction is necessary compared to the one-dimensional measurements in order to obtain a SNR acceptable for temperature evaluation. Strong temperature gradients can occur in both of these directions, which cannot be mapped as accurately as with the one-dimensional measurements due to the lower spatial resolution and decreased derived temperature accuracy because of intensity smoothing due to pixel binning with accompanying averaging of retrieved temperatures. Thus, using the one-dimensional configuration, measurements could only be made along one line, but with a much higher resolution of 0.575 mm/ SPx compared to 2.3 mm/ SPx in and orthogonal to the main flow direction. With the current status of the CO-TAPLIF thermometry realized for the first time at the PWT, the one-dimensional configuration is thus still to be considered as the method of choice for accurate quantitative measurements with high spatial radial resolution. The two-dimensional measurements, on the other hand, are already suitable for qualitative representations of the temperature field under the conditions in the free-stream.

4 Conclusion

A plasma wind tunnel is operated at the Institut für Thermodynamik at the Universität der Bundeswehr München to qualify materials that are exposed to high aerothermodynamic loads when entering the Martian atmosphere. For the use of such test facilities, it is essential to quantify the flow conditions as precisely as possible in order to obtain reliable data for the numerical simulation.

The non-intrusive optical measurement method laser-induced fluorescence (LIF) is characterized by high signal intensity even at low particle densities and, in principle, also when the laser beam is expanded to form a light sheet. To measure the temperature field present in the CO$_{2}$ flow, one- and two-dimensional two-photon absorption laser-induced fluorescence (CO-TALIF) thermometry was used in the present work at a CO number density in the range of 1—$2\,\times \,10^{17}\,\hbox {cm}^{-3}$. To perform these measurements, a light sheet optic consisting of three lenses was designed to generate a light sheet free of divergence in width and thickness and with a energy density sufficient for a quantitative evaluation despite the quadratic dependence of the signal strength on the excitation energy.

Instead of two- or multiline thermometry, a direct comparison of experimental with simulated excitation spectra was performed, so that the shape of the entire spectrum in a defined spectral region was considered. To simulate the temperature dependent excitation spectrum of the B–X(0,0) vibrational band of the CO molecule for two-photon excitation, an existing in-house tool was extended and the CO Excitation Spectrum Calculation (COESC) program was created. COESC provides the ability to account for instrumental broadening by using a numerical approximation of the Voigt line shape function instead of a Gaussian line shape function. Spectra were obtained for temperature and spectral ranges of ${200}\hbox { K} \le T \le {2500}\hbox { K}$ and ${114.925}\hbox { nm} \le \lambda \le {115.075}\hbox { nm}$ with resolutions of $\varDelta T = {10}\hbox { K}$ and $\varDelta \lambda = {0.1}\hbox { pm}$, respectively.

Two different temperature determination methods were used. In the so-called correlation automated rotational fitting (CARF), a normalized cross correlation between the post-processed experimental excitation spectra and the temperature dependent simulated excitation spectra from a database generated using the spectrum simulation program COESC takes place. Each pixel is assigned the temperature for whose corresponding simulated spectrum the highest correlation value is obtained.

However, it turned out to be extremely difficult to capture the intensity peaks of the individual transitions under the unfavorable measurement conditions as in the free-stream of the PWT with CO-TAPLIF. Therefore, the CARF algorithm exhibited only moderate uniqueness in temperature correlation for signals with low SNR. In contrast, however, the experimental spectra accurately reproduced the average trend of increasing signal intensity with increasing wavelength for excitation in the B–X(0,0) vibrational band. Therefore, in the polynomial regression correlation (PRC) method developed in this work, the simulated spectra are reduced to their trend of increasing intensity with increasing wavelength by a polynomial least squares regression. With a polynomial degree of 15, only the trend of the spectrum, but not the individual peaks, is mapped and, accordingly, a more distinct temperature correlation was achieved for signals with low SNR.

One-dimensional temperature measurements were performed using CO-TALIF in the free-stream of the PWT for three conditions in the medium- to high-enthalpy range (${5.0}\, \hbox {MJ}/\hbox {kg}$ to ${10.5}\, \hbox {MJ}/\hbox {kg}$), respectively. In order to define optimal experimental parameters for the following CO- TAPLIF measurements in the free-stream and to establish the data reduction, two-dimensional measurements were then carried out in a steadystate test chamber at room temperature. Finally, CO-TAPLIF temperature measurements were performed in a medium- to high-enthalpy free-stream of the PWT at stagnation enthalpies of ${4.5}\, \hbox {MJ}/\hbox {kg}$ and ${9.0}\, \hbox {MJ}/\hbox {kg}$.

The results of the one- and two-dimensional temperature measurements provided plausible results concerning both the values and the course in radial and axial direction, the latter being, to the authors’ knowledge, the first two-dimensional temperature measurements under such experimental conditions using CO-TALIF.

The experience gained from this study is currently being applied to investigate a newly developed magnetic nozzle plasma thruster at the Institut für Thermodynamik. A similar laser setup, combined with light sheet optic, is used here to measure atom and ion temperatures.

To realize a more accurate temperature determination at the PWT with higher spatial resolution also for the planar measurements, the focus will primarily be on a further optimization of the SNR, for which initial investigations have already been carried out as part of this work and which will be continued in future studies.