1. Introduction

The future development of combustion devices with improved efficiency and pollutant emissions will strongly rely on a better understanding of the underlying chemical and physical processes in the flame. In particular, for premixed combustion, which is of great interest for industrial applications with the potential of low pollutant emissions, a detailed investigation of the fundamental mechanisms is still required. In this field, the interactions of the turbulent flow field and the chemical reactions are especially important. Besides the aim to gain a deeper understanding, experiments are also performed to validate computational models, which are used for the numerical simulation of premixed combustion within the framework of computational fluid dynamics CFD. Here, experimental data have to be acquired which can be directly compared to results from CFD studies whereby the ‘language’ of the experimental results should be as similar as possible to that one of numerical results.

Of special interest are laser techniques for the simultaneous measurement of several quantities. Such investigations can give direct insight into the most important correlations between these quantities which have to be modeled within the numerical simulations as well as into fundamentals of molecular transport in reacting and non-reacting flows. In this context, a number of studies have been published in which by the simultaneous application of different laser techniques certain combinations of velocity, temperature, density, species concentration and their local gradients have been determined [1–6]. For premixed combustion, the so called flamelet regime characterizes a combustion regime, where the chemistry can be described independently of the flow field in the form of small flamelets which govern the instantaneous flame front. In this regime, the flame can be regarded to behave similar to the laminar case and thus as a good approximation, the status of the gas-phase in a particular position can be described as either burnt or unburnt. Here, a large number of quantities are accessible by the measurement of the position of the instantaneous flame front in combination with the flow field.

Typically, the velocity field is measured by particle image velocimetry (PIV) in a planar domain or point wise by laser Doppler velocimetry (LDV). For the simultaneous investigation of the flame structure the most straight-forward approach is to measure the temperature field, e.g., by planar laser Rayleigh scattering thermometry (PLRS) [7], which is, however, restricted to particle-free flames preventing the simultaneous application with PIV and LDV. One possible solution is filtered Rayleigh scattering (FRS) [8, 9], in which a very narrowband molecular filter is used in order to suppress the elastically scattered light from the particles while the spectrally broadened Rayleigh signal from the molecules is transmitted. Then, this part of the signal is used for the temperature determination and the transition from unburnt to burnt gas is deduced by identifying the position of the steepest gradient in the local temperature distribution. However, the technique is associated with high experimental complexity.

Hence, for flame front tracking many researchers make use of the laser-induced fluorescence (LIF) signal from radicals which are generated in the flame front and partly persist in the product zone. Most frequently, the super-equilibrium of the concentration of the hydroxyl radical (OH) close to the main reaction zone is used as an accepted flame front marker, however with a known slight shift towards the product region. Also laser-induced fluorescence imaging of other radicals like C₂ and CH, and the CH₂O molecule has been used by different groups to identify the reaction zone of hydrocarbon flames (e.g. [10–13]).

All of the described techniques have in common that, beyond the equipment used for PIV, additional complex and expensive devices like tunable laser systems, intensified cameras and/or a molecular filter cell in the detection path are necessary. Moreover, for the investigation of temporal correlations, flame front displacement speeds or phenomena like thermo-acoustic instabilities, the described laser-detector systems must be able to work with several kHz sampling rate. Such laser systems are rarely commercially available and if this is the case often connected with great expenditure [3].

In this contribution, we present the validation of an experimental approach which can provide a drastic reduction in terms of experimental complexity, the conditioned particle image velocimetry (CPIV) technique. Basic ideas for the technique have already been proposed by Armstrong and Bray in 1992 with the aim to measure conditioned velocities simultaneously in reactant and product mixtures [14], however, at that time, with photographic PIV which did not allow a statistical evaluation at high confidence levels. Stevens et al. [15] showed in 1998 correlated vector-scalar measurements for a one-dimensional flame with a similar technique. In Ref. [16] our group has successfully applied the technique to characterize a turbulent swirl flame, however, a proof of the principle was only performed based on a non-simultaneous detection of the average flame position by a separate planar laser Rayleigh scattering experiment. The term conditioned PIV is derived from the possibility to evaluate turbulence parameters of turbulent flames conditioned to the unburnt and burnt part via threshold setting on the particle density. In this context, for each region of interest (ROI) an operator is generated based on particle density which identifies the referring ROI either as unburnt or burnt area. We follow basically the same principle with the difference that we assign instantaneous values of the reaction progress variable to each ROI. Besides the simultaneous measurement of the two-dimensional flow field and the position of the instantaneous flame front, CPIV also enables the comparatively simple determination of the flame front displacement speed from a series of images taken with a kHz-sampling rate, which otherwise would require the simultaneous application of a kHz-OH-LIF system.

In order to assess the ability of the CPIV-approach to reproduce the flame front on a single-shot basis, we simultaneously apply the heat release imaging technique which reveals the “true” position of the flame front. By this comparison the influence of possible interferences from both thermophoretic effects on the seeding particles and an undesirable slip velocity of the particles when passing the strong temperature gradient inside the reaction zone shall be investigated. For the heat release imaging, OH radical and formaldehyde (CH₂O) concentrations are simultaneously measured using planar laser-induced fluorescence techniques. It has been shown in previous investigations that the product of OH and CH₂O concentration (which are the reactants for the formyl radical (CHO) generation in hydrocarbon flames) is directly proportional to the actual heat release [17]. More details about this concept are given in the experimental section. Furthermore, we will compare several derived quantities like the turbulent flux of the reaction progress variable, the flame surface density and flame front curvatures obtained from the different techniques.

2. Experimental

2.1 Burner set-up

The burner we have used in this study is a wire stabilized Bunsen burner with a resulting V-shaped flame (Fig. 1), centered at the burner geometry axis (d_wire=1.6 mm). The inner diameter of the burner at the rim is 48 mm, with a surrounding co-flow of 150 mm. The wire position is 10 mm above the outlet. Further details of the inner burner geometry can be taken from [18].

 

Fig. 1. Burner set-up.

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2.2 Conditioned particle image velocimetry

For standard particle image velocimetry in reacting or non-reacting flows, sub-micrometer particles are seeded to the flow, which are assumed as chemically inert and to follow the flow without significant slip. Then, the flow is illuminated twice with a laser light-sheet and two successive images are taken. The local flow velocity is computed from the movement of the particles between the two images, typically by applying a cross-correlation algorithm. In non-reacting flows the gas density and with that the particle number density remains largely constant (despite local statistical fluctuations about the mean density from one region of interest to another). In contrast, there is a strong gas density change in flames owing to the heat release from the chemical reactions which in turn leads to a strong particle number density change. This change is rather gradual in non-premixed flames but well defined in premixed flames. When the seeding concentration is properly adjusted, the step in the gas density is reflected very clearly in the particle images, see Fig. 2.

 

Fig. 2. PIV raw image with intensity histogram after spatial filtering (the plotted line shows the flame front position).

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Hence, these images can also be used to determine the flame front position and shape in premixed flames.

Besides the flow velocity determination from adaptive cross-correlations of the subsequent images (dt=40 μs) for the vector calculation (in the presented case over 16 × 16 pixels with an overlap of 50 % of adjacent ROIs), two additional steps are applied [19]. First, the intensity of the Mie scattered light detected on the CCD-chip is averaged over each interrogation area which was chosen for the final vector calculation. Subsequently, an automatic histogram-based threshold setting procedure is performed on these spatially filtered intensity data. With the assumption of a thin reaction zone a nearly bimodal density distribution with two distinct maxima can be expected. To distinguish between unburnt and burnt density a threshold is determined for each image, being located between the two maxima. For this purpose, a histogram function is created over the raw histogram data, where after smoothing a cubic spline interpolation is applied (see histogram in Fig. 2). The values of the two maxima are determined from the first derivative of the histogram function, and the threshold is set to be the arithmetic mean value. Binarization is performed for each averaged intensity data in the different ROI. Following the thin flame assumption the locations with intensities higher than the threshold are described as unburnt, i.e. the reaction progress variable is set to zero. Locations with intensities lower than the threshold are assigned to the burnt part of the flame with reaction progress equal to one. In order to account for fluctuations of laser power and seeding density the threshold finding procedure is applied individually to each image.

Knowing the stoichiometry of the mixture, all acquired quantities φ, can also be expressed in a Favre averaged (density weighted) way ρφ̄/ρ̄. This is very interesting for comparisons with numerical simulations since the conservation equations for reactive flows are usually solved in a density weighted manner in CFD.

2.3. Measurement of the heat release distribution simultaneous with CPIV

With the aim to provide validation for the flame front detection strategy within the CPIV approach, we have chosen to perform a simultaneous experiment for the local heat release determination. This is achieved by acquiring the laser-induced fluorescence signal from the hydroxyl radical OH and formaldehyde CH₂O. This technique has proven to be a good approach for the imaging of the flame heat release rates in hydrocarbon flames, whereby the pixelwise multiplication of both single-shot images results in an closely related image of the instantaneous heat release rate distribution [12, 17, 20]. The idea is that the heat release has been shown to be well correlated with the concentration of the formyl radical CHO [21]. However, owing to spectroscopic reasons, the signal-to-noise ratio (SNR) for CHO-LIF is not sufficient for planar measurements on a single-shot basis. Therefore, an indirect measurement of the heat release is performed, where the product of the simultaneously recorded CH₂O and OH-LIF signals is proportional to the reaction rate of the formyl radical generation CH₂O + OH → HCO + H₂O, given that the temperature dependency of the detectable signal g(T) is known and proportional to the forward reaction rate constant k_f(T) [17].

Recent improvements in camera and filter technologies have now enabled a simultaneous measurement of the heat release via the combination of CH₂O- and OH-LIF even in lean premixed methane flames with peak SNR greater than 10 in the single-shot. The fuel/air-ratio ϕ of the investigated flame is 0.77, with a total mass-flow rate of the methane/air mixture of 9 kg/h. The set-up is shown in Fig. 3.

 

Fig. 3. Experimental set-up.

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In our study we have applied a 3^rd generation ICCD-camera with a quantum efficiency of more than 30 % at around 400 nm. The signal of the image plane is collected via a Soligor 90 mm f/2.5 lens on the camera chip (1024×1024 pixel). We used a dye laser system with Pyridine 1 solved in ethanol with subsequent frequency doubling in a BBO-crystal to excite rotational transitions of the ù A₂-X̃¹ A₁4₀ ¹ vibronic band near 353 nm [22] which have shown to give a good signal to noise ratio in combination with a numerically validated proportionality between the temperature dependency of the detectable signal g(T) and the forward reaction rate constant k_f(T) over a limited temperature range from 900 to 1500 K [20]. The laser energy in the object plane was 10 mJ. A long-wave-pass very sharp interference filter provided large transmission ratios (<90%) above the excitation wavelength in combination with an optical density of 6 below 355 nm, resulting in suppression of elastically scattered light. The connection in series of two of the mentioned filters allowed a simultaneous measurement with good signal-to-noise ratio of the low CH₂O-concentrations within the flame front in combination with additionally seeded particles for the velocity field measurement via PIV. Possible interferences from methane or nitrogen Raman transitions (see spectra in [12, 22]), were below the detection limit. This was tested by the application of a polarizing filter which was rotated by 90° without a change in signal (which is expected for the unpolarized fluorescence but not for the largely polarized vibrational Raman transitions).

The locations of the OH-radical downstream the reaction zone was imaged by a fiber coupled, 2nd generation ICCD-camera (quantum efficiency @ 400 nm: 12 %, 1024×1024 pixel) after passing through a filter combination of two Schott WG295 and a UG11 filters. The camera is mounted on the other side of the light sheet whereby the signal is collected via a UV-transmittive 105 mm f/4.5 Nikon Nikkor objective on the CCD chip. For excitation of the OH-radicals we tuned the frequency-doubled output of a second dye laser (using Rhodamine 6G solved in ethanol) to the Q1(9) transition near 283 nm in the (1,0) band of the OH A-X system. The laser energy for excitation of the OH-radical was 12 mJ/pulse. Here, the directly emitted non-ideal laser profile was homogenized by a micro-lens array based beam homogenizer (BH), which is described in detail in [23]. The laser profile for the excitation of the CH₂O molecule was adjusted to be quasi-homogeneous by placing an aperture behind the light-sheet generating optics. With the aim to minimize interferences from flame luminescence, the exposure times for both cameras was reduced to 30 ns, which was limited by the jitter of the laser systems.

For the simultaneously acquired images a mapping function was created, using an 8 parameter bilinear geometric warping algorithm, providing sub-pixel accurate superposition. Before the images were multiplied pixelwise, some image processing steps were performed. Subsequent to a dark-noise and non-resonant background subtraction, the images were corrected with respect to vignetting effects by the generation of a correction matrix which was derived from the imaging of a homogeneously emitting luminescent foil. Finally, both the OH as well as the CH₂O images were convoluted by a 3×3 averaging kernel in order to reduce influences from the detector noise. The resulting spatial resolution per pixel for all cameras in this study is 30.46 μm.

2.4. Simultaneous planar measurement of the temperature field and the heat release

Besides the direct comparison of the heat release technique with the conditioned particle image velocimetry, we have performed a simultaneous measurement of the heat release and the temperature field by simultaneously applying planar laser Rayleigh scattering.

The possibility to measure simultaneously temperature and heat release distribution in turbulent combustion was already demonstrated by Böckle et al. [24], however, an extra validation for our set-up with differences in resolution and applied laser-detector systems seemed to be indispensable. Therefore, we applied the double-pulsed PIV laser in the single-shot modus, whereby a maximum output energy of 200 mJ/pulse was achieved. The Rayleigh signal was recorded by a double-intensified CCD-camera (1024×1024 pixels) equipped with a 105 mm f/2.5 Nikon Nikkor lens. The Rayleigh signal was captured via a short pass dichroic mirror (HR 532 nm) being placed under 45° in front of the OH-LIF camera. Due to the fact that the burner for the simultaneous HR-CPIV measurements was contaminated with seeding particles, we have performed the validation experiment in a separate wire-stabilized methane-air flame using a 13 mm diameter, 820 mm long tube, covered by a coaxial, slow air flow (fuel/air-ratio ϕ=0.91, total mass-flow rate: 3 kg/h).

3. Results

The results of the first validation experiment comparing the local heat release measurements (via OH and CH₂O-LIF signals) with the position of the steepest temperature gradient for lean methane-air flames is shown in Figs. 4–7. The height of the images is 19.5 mm.

Figures 4 and 5 are normalized single-shot images from the OH radical and the CH₂O molecule, respectively, whereby the pixelwise product which correlates with the heat release rate is illustrated in Fig. 6. The image of the OH radical shows the well-known super-equilibrium close to the actual reaction zone. The CH₂O is detectable only within a small region close to the reaction zone, shifted towards the unburnt side. The dots in Figs. 5 and 6 are artifacts resulting from the adjusted high gain factor for the CH₂O camera. The actual heat release according to Fig. 6 is located only within a very sharp zone which corresponds nicely to the temperature image in Fig. 7.

 

Fig. 4: OH-LIF.

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Fig. 5. CH₂O-LIF.

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Fig. 6: Position of the heat release.

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Fig. 7. Normalized temperature distribution.

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The reason for the noise in the Rayleigh image compared to the LIF images is the fact that the applied camera system was equipped with a two-staged intensifier, showing a rather limited image quality. A quantitative comparison of Figs. 4–7 is given in the left-hand diagram of Fig. 8, where 20 flame normal profiles have been extracted at different positions intersecting the flame front, averaged and plotted against the flame normal position. Each extracted profile was adjusted along the flame front normal direction so that the maximum values of the heat release were matched. It can be seen, that the position of the steepest temperature gradient is well correlated with the position of the heat release. The detected length of the temperature increase seems to be smeared by the two-staged intensifier of the CCD camera for the Rayleigh imaging, which, however, should not influence the detectable position.

The direct comparison between CPIV and the heat release detection technique with respect to the flame front identification was performed in another wire-stabilized Bunsen-type which has shown to be more suitable for combustion experiments with seeded particles.

For one exemplary chosen single-shot distribution of the OH, CH₂O and heat release, flame normal profiles have been extracted. Additionally, the averaged flame position derived from the binarization algorithm within the CPIV-approach was included in the right-hand diagram shown in Fig. 8.

 

Fig. 8. Flame normal profiles (left: extracted from simultaneous Rayleigh-LIF experiment, right: extracted from simultaneous LIF-CPIV experiment).

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The OH radical concentration increases within 1 mm from background-level until the superequilibrium concentration is reached decreasing further downstream. The maximum of the CH₂O concentration with a FWHM-width of 710 μm lies about 0.4 mm towards the unburnt mixture compared to the determined position of the strongest heat release. The heat-release distribution features a width of 300 μm. The position of the instantaneous flame front derived from the CPIV-approach is shifted by only 80 μm towards the unburnt mixture while the 50-% level of the OH-distribution is displaced by the same length towards the burnt gas.

We can conclude that the flame front detection strategies using OH-LIF or CPIV are both very well correlated with the position of the maximum heat release. From the relative distances of the concentration curves in Fig. 8 we can derive recommendations for histogram based flame front detection approaches to achieve highest accuracy. Here, the threshold for the OH-LIF technique should be shifted slightly from the mean distance between educt and product peak towards the unburnt side with the aim to directly detect the position of the maximum heat generation. On the other side, an adjustment of the threshold level towards the product side is advisable for the CPIV-technique.

However, in the following we will show that the observed fine scale differences do not significantly affect quantities derivable from the instantaneous flame fronts detected by OH-LIF or CPIV. We have chosen a direct comparison of the planar flame surface density ∑ derived from both techniques which describes the convolution of the flame front per unit volume. This quantity is usually used for the determination of the reaction rate $\dot{\omega }¯$ in premixed combustion. For flames with negligible influence of the out-of-plane component as it is the case in the V-flame investigated here, the mean flame surface density can be derived from the length of the flame front within a certain two-dimensional region of interest (ROI) [25].

If the instantaneous flame front is located within such a ROI, the length of the intersection is calculated from the path integral along the flame front, otherwise set to zero. The mean flame surface density is then evaluated by the generation of the arithmetic mean value of the path length within the ROI based on 512 single-shot images. The comparison is shown in Figs. 9 and 10, whereby only one branch of the V-shaped flame is analyzed. The planar distribution shows very good agreement with slight differences at the bottom. The absolute values are almost identical, however for the flame front density derived from the CPIV-approach, little more noise can be seen.

With the aim to access more precisely possible deficiencies in the capability to resolve geometrical structures, we have evaluated flame front curvature statistics derived from OH-LIF and CPIV comparatively. For that, the Cartesian coordinates of the ROIs which are located at the flame front are first identified, a path-length parameter s is introduced and a parameterization of the instantaneous flame front in form of two functions (x(s), y(s)) is performed. This enables the representation of the contour by a cubic spline interpolation. From that, the referring derivatives included in the definition of 2D curvature in the formulation following Mokhtarian and Mackworth ([26], see Eq. 1) can be calculated.

 

Fig. 9. Flame surface density ∑ derived from OH-LIF with radial profile views taken 20 and 30 mm downstream the stabilizing wire.

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Fig. 10. Flame surface density ∑ derived from CPIV with radial profile views taken 20 and 30 mm downstream the stabilizing wire.

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For an exemplary single-shot image the characteristic curvature values along the flame front are determined and plotted in Fig. 11 as a function of the normalized path-length parameter s, starting from the right-top corner of the binarized image. In addition to the comparison of results from both measurement techniques, we have varied the step-size for the cubic spline interpolation (top: every 4^th node, bottom: full resolution).

 

Fig. 11. Flame front curvature along the flame surface for a single shot binarized image (segments with constant positive or negative curvature are labeled with capitals).

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Both experimental strategies are able to resolve the characteristic flame front curvatures of the single-shot image. Also, the curvature values which have been derived from the cubic spline interpolation between every fourth node seem to be less affected by discretization noise.

Finally, a statistical evaluation of the data-set was performed, resulting in more than 50000 sampling points for the curvature analysis. In Fig. 12 both curvature distributions are shown in a pdf-diagram. Here, the width as well as the center of the distributions show almost similar behavior, whereas the distribution from CPIV is slightly wider, meaning that more strong curvatures (i.e., smaller radii) are present in the CPIV-images. This may be attributed to the noisier images compared to the rather smooth OH-radical distribution.

 

Fig. 12. Flame front curvature statistics derived from OH-LIF and CPIV.

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Therefore, we can deduce that the shift introduced from OH-LIF and CPIV in different directions relative to the position of the true position does not significantly affect the analysis of geometrical structures.

A final comparison has been done by analyzing simultaneous correlations of the flow and reaction field which is expressed within the density weighted turbulent flux of the reaction progress variable $\bar{\rho }\widetilde{u_{\mathrm{rad}}^{″}c″}$ (only the radial component is shown here).

 

Fig.13. Favre averaged radial turbulent flux $\bar{\rho }\widetilde{u_{\mathrm{rad}}^{″}c″}$ derived from OH-LIF with radial profile views taken 20 and 30 mm downstream the stabilizing wire.

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Fig. 14. Favre averaged radial turbulent flux $\bar{\rho }\widetilde{u_{\mathrm{rad}}^{″}c″}$ derived from CPIV with radial profile views taken 20 and 30 mm downstream the stabilizing wire.

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This term appears when the balance equations which are used for the numerical modeling of turbulent combustion are expressed in a temporally averaged way, whereby the Tilde-symbol and the double prime denote Favre averaging (density weighting).

Obviously the turbulent flux features the same spatial distribution when deduced from the LIF and CPIV data sets (Figs. 13 and 14). Moreover, there is no evidence that the absolute values differ in so far that a difference with respect to measurement accuracy and precision would be noticeable. Furthermore, the noise level for both measurement strategies is similar.

Besides the direct comparison of different planar measurement techniques for the analysis of flame front structure and the resulting validation of the CPIV technique, we have the opportunity, to present the first simultaneous measurement of the planar heat release distribution and the flow field of a premixed flame (see Fig. 15).

 

Fig. 15. Single-shot image of the simultaneous measurement of flow and heat release field in a turbulent premixed V-shaped methane-air flame.

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This offers the chance to analyze flow field related influences on the heat release distribution like the effect of tangential strain rate on the chemical reaction rate simultaneously with curvature effects. Such experimental correlations, measured at high spatial resolution are of special importance at the moment for an improvement of models for closure of the reaction rate in the governing equations used for Large-eddy simulations (LES).

4. Conclusion

In summary, the flame front detection capability of the conditioned particle image velocimetry technique (CPIV) was validated on a single-shot basis via simultaneous measurements of the heat release distribution. CPIV offers the possibility to measure simultaneously the flow and reaction field of turbulent premixed flames in the thin flame regime using only moderate experimental complexity.

We have demonstrated that there is a strong correlation between the position where the maximum heat release, measured by simultaneously applying OH- and CH₂O-LIF, is located and the position of the flame front derived from CPIV measurements. By a preceding experiment we could evaluate our heat release detection scheme via an observable correlation of the steepest temperature gradient with the position of the maximum heat release production. Furthermore, we have compared flame characterizing quantities being separately derived from the CPIV approach and the commonly used OH-LIF technique for flame front characterization. Both the planar distribution of the flame surface density and the radial component of the turbulent flux of the reaction progress variable separately derived from a series of CPIV and LIF images show almost perfect agreement. The CPIV technique has also proven to be an adequate technique for the analysis of the flame structure in the form of flame front curvature statistics. The comparison of curvature values derived from OH-LIF images is virtually identical to the curvature distribution measured with CPIV, however, if a statistical evaluation is performed, the curvature characteristics derived from CPIV tends to show a slightly wider distribution.