Measurement of temperature PDFS in turbulent flames by the CARS technique

Twenty-Fnurth Symposium (International) on Combustion/The Combustion Institute, 1992/pp. 527-535

M E A S U R E M E N T O F T E M P E R A T U R E P D F S I N T U R B U L E N T F L A M E S

B Y T H E C A R S T E C H N I Q U E

DEREK BRADLEY, MALCOLM LAWES, MICHAEL J. SCOTI" AND CHRISTOPHER G. W. SHEPPARD

Departnuent of Mechanical Engineering, University of Leeds, Leeds, LS2 9JT, UK

DOUGLAS A. GREENHALGH

School of Mechanical Engineering, Cranfield Institute of Technology, Cranfield, Bedford, MK43 OAL, UK

AND

FIONA M. PORTER

AEA Technology, Building 551, llarwell Laboratory, Oxfordshire, 0 X l l ORA, UK

Accurate temperature measurement with the CARS technique is difficult when appreciable temperature gradients occur within the measurement volume. The problem is aggravated by the non-linearity of the spectral intensity with temperature. The paper reports on the results of steps taken partially to ameliorate the problem, in the context of attempts to measure temperature pdfs in turbulent combustion. These involve a two beam system for the emitted nitrogen spectra, one beam of which is attenuated to reduce the intensity. By this means the full range of intensities that arise in combustion can be accommodated by the diode array camera and accuracy is preserved over a wide range. Furthermore, the intensity of the spectrum is measured and a calibration relates this to the proFs~rtion of hot gas in the control volume, although this strategy is only partially successful because of the variation of laser intensity from shot to shot. Within the spectrum a "hot' band and a "cold' band are used separately for theoretical spectral matching and consequent temperature measurement. This is relevant to the case where a thin flame lies across the measurement volume. Further refinements make some allowance for flame thickness, but even with these measures some ambiguities remain. The refinements are discussed in relation to measurements of temperature probability density fimctions through a prcmixed methane-air turbulent flame of rela- tively low Karlovitz number on a V burner. Expected bimodal distributions are confirmed.

Introduction

A knowledge of the temperature fluctuations at a point is vital to the successful mathematical mod- elling of turbulent combustion.t Measurements with thermocouples are impossible because of their in- ertia, electronic noise and perturbation of the flow. 2 These problems can be overcome by laser diagnos- tics, but the length of the measuring volume can be approximately 3 mm in the direction of the beams, more than the thickness of many flames, and this creates problems of spatial resolution.

Coherent anti-Stokes Raman spectroscopy, gives a signal which varies non-linearly with temperature and this exacerbates the problem. Magre et al. ~ and Shepherd et al. 4 varied the proportions of hot and cold gas within the measurement w~lume and computed the single temperatures that gave the best spectral fits to nitrogen spectra. Only when the hot

and cold temperatures were close was the spectral best fit single temperature close to that of ~ e adiabatically mixed temperature for the volume.

When they differed by 1700 K, or more, the best fit single temperature was close to that of the cold gas, unless the volume of hot gas was more than 90%. The paper reports steps that partially can ameliorate such problems. Within the N2 spectra 'hut' and 'cold' bands are interpreted separately to yield two temperatures, which may be different. The intensities of spectra are measured and a calibration relates these to the proportion of hot gas in the measurement volume.

Numerical Simulation of Two Temperature CARS Measurements

The effects of hot and cold gas within the measurement volume, both at uniform temperature,

527

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FIG. l. VaTiation of calculated temperature with proportion of hot and cold gas in the measurement vohlme. T~,~, = 2000 K, T~!~ = 500 K.

upon the spectra were simulated numerically. The- oretical spectra from the No molecule in the two gases were computed with a modified version of the colnmercial computer code s'~ CARP-PC, namely, CARP-2T. This calculates the coherently generated CARS spectrum for different proportions of hot and cold gas. The two spatial regions give rise to two sets of degenerate transitions, each set of which populates the various spectral lines according to the appropriate Boltzmann distribution. The separate sets nf transitions contribute to the CARS spectrum shape in the same way as do separate vibrational bands. This procedure generated composite spectra for various hot and cold temperatures and proper- tions of each. These were analysed as if they were experimental ones, but from uniform temperature gas within the measurement voh, me, and the temperature was found for each best fit spectrum. This two temperature model assumes that only oue flame front crosses the measurement w)lume and neglects the flame thickness.

Curve A in Fig. 1 shows the temperature for the best cnmputed single temperatt, re spectrum match to the two temperature spectrum for various proportions of hot gas at 2000 K and cold gas at 500 K in the measurement volume. Curve B shows the adiabatically mixed temperature for the two temperature volume. There are large differences in these temperatures, and the differences between the composite and best match single temperature spectra were, for many mixtures, small. This suggested a close scrutiny of spectra and their intensities is imperative.

The full line curve in Fig. 2 is a computed com-

to 'hot ~ ~ cot_~d

8 ~ i band

-g

5

i 2 I 2000 K ./.'*J I

_ .~.!g i /

2280 2500 2520 Roman shift (cm -1)

I

I

2540

FIG. 2. Composite spectrum with 10% by volume of gas at 500 K and 90% at 2000 K. Broken curves show single temperature spectra.

posite spectrum with 10% by volume of gas at 500 K and 90% at 2000 K. Here, 'intensity' is proportional to the sum of the squares of the amplitudes for both the hot and the cold gases. There is a large narrow peak due to the v = 0--+ v = 1 fimda- mental vibrational 'cold band', indicative of cold gas, together with individual Q-branch transitions which appear at about 1000 K. There is also a significant contribution in the v = 1 --+ v = 2 'hot band' tran- sition. Visual inspection of the spectrum suggests it is a composite one with no single temperature fit to it. The broken curves are cold and hot spectra at 500 and 2000 K, normalized to have the same cold and hot peak intensities as the composite spectrum. Most of the composite spectrum for the cold gas lies in a narrow band around 2330 em -1, while that for hot gas extends from a lower wavenumber into this 'cold band'.

This suggests that the spectrum might be analysed in two parts and yield two temperatures. Comparison of the composite spectrum with the broken curves shows that within the waveband 2286 to 2310 cm t the composite spectrum is almost identical with the hut single temperature one, just as within the band 2328 to 2338 cm-I it is close to the cold one. Spectral division into hot and cold wavebands yielded two temperatures. In practice, in few mixtures are the characteristics as differen- tiated as in Fig. 2. Because the peak spectral intensity varies approximately inversely with the cube of temperature, but a small proportion of low tem-

CARS TEMPERATURE PDFS IN TURBULENT FLAMES 529

perature gas can dominate a composite spectrum. In addition, when the difference between the hot and cold temperatures is small, so, also, is the difference in their spectral contributions.

Shown in Fig. 2 is the division into spectral ranges: the full spectrum, band S, a narrow 'cold band', C, a hot range which contains the 'hot band' and part of the 'cold band', H, and an intermediate range, I. Curve C in Fig. 1 shows the single best fit temperatures that arise when only the narrow cold range, C, is analysed with CARP-PC. These temperatures are close to the true cold gas temperature when the proportion of hot gas is less than 50%, and are within 100 K for proportions below 80%. Curve H, derived from band H in Fig. 2, shows this can almost reproduce the initial hot temperature only when the proportion of hot gas is above 80%. Below this value, the derived values of hot temperature become very unreliable. Curve I is derived from band I and yields temperatures between the actual hot and cold temperatures.

In the analysis of the burner experimental spectra a library of curves, similar to those in Fig. 1, was generated for different frequency bands, hot and cold temperatures and proportions. These were used to select the most appropriate frequency band for a given measurement and to assess its accuracy.

Apparatus

V Burner:

An unconfined premixed, methane-air V flame, of equivalence ratio 1.1 (adiabatic temperature, 2207 K), was stabilized on a 1 mm diameter rod, mounted in the exit plane of a 50 mm diameter cylindrical burner. Turbulence was generated by a wire mesh grid with a wire diameter of 1 mm and a wire spac- ing of 3 mm, mounted 50 mm upstream of the rod. Mean and turbulent velocities were characterised both in cold and in reacting flows by laser doppler velocimetery. In the region of the flame the cold flow r.m.s, turbulent velocity was 0.25 m s -1 and the integral length scale was about 3 mm. The value of the product of Karlovitz stretch factor and Lewis number was approximately 0.01. This and sheet photographs suggested the flame was in the contin- uous wrinkled laminar flame sheet regime. 7

CARS System:

The Spectron Laser Systems integrated CARS source comprised a Q-switched frequency doubled Nd:YAG laser with an energy of 350 mJ in 15 ns pulses at 10 Hz and a 35 mJ broad band dye laser, pumped by part of the Nd:YAG beam. The dye wavelength was about 600-610 nm, The length of the measurement volume was measured by travers-

ing a jet of N2 from a hypodermic tube along it in an atmosphere of CO2. The length was 3 mm and the estimated diameter 100 I~m. No allowance was made for the non-uniform laser intensity distribution within the volume.

Data collection was via a B & M Spectronik BM100 Spectrograph, SIT 512 channel diode array camera, AK500/12 intensifier and STH500-1000 controller. Data were analysed on a Dell system 325 PC. The interface between the camera controller and the computer was supplied by UKAEA., Har- well, as was the data collection software. Pre-pro- cessing of the signal removed the background noise, ratioed the signal to that from the dye laser, and corrected for the well known non-linear response of the diode array camera, s Nitrogen spectra were analyzed with computer codes CARP-PC and QUICK, to produce single shot temperatures. The QUICK code decreased analysis times by interpo- lating between a library of spectra generated by CARP-PC to find the best theoretical fit to experimental spectra. Utilizing the full spectrum, it was estimated that the accuracy of temperature measurements in isothermal flows, in the range 1500 to 2000 K, was -+ 30 K averaged over many shotsl s The r.m.s, value of single shot measurements was 50 K. Utilizing the hot waveband measurements in isothermal hot gas gave mean values within 5 K of those obtained from the full spectrum. The r.m.s. value of single shot measurements was 135 K. The comparable values for the cold waveband were 20 and 135 K, respectively. Errors due to stimulated Raman pumping are likely to be small.

Dual Beam Technique:

Shot to shot temperature variations can be as much as 1900 K. Shown in Fig. 3(a) is the theoretical variation of peak spectral intensity of the CARS signal with temperature, after including the effects of the finite resolution of the camera and spectrograph, obtained with CARP-PC. The intensity is normalized by the value at 293 K. Because the peak intensity varies approximately inversely as the cube of the temperature between 300 and 2000 K the signal intensity varies by nearly three orders of magnitude. This creates measurement difficulties due to the limited dynamic range (32:1) of the de- tector. 9 This has led to the use of multi signal beam techniques. 1~ Figure 4 describes the present technique, in which the CARS signal was divided into two beams with intensity ratios of 97: 3 with a wedge and projected on to different regions of the diode array. This increased the dynamic range of the data collection system so that the full range of signal strengths could be measured simultaneously. Both the 3% and 97% intensity signals were recorded, but, depending upon their intensities, only one was

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FIG. 3. Theoretical variations of signal intensity with (a) temperature and (b) percentage of hot gas. Normalized by value at 293 K.

analyzed. The laser power was maintained constant, except for shot to shot variations. The signal intensity, in conjunction with hot and cold band temperature measurements, was used to estimate the proportions of hot and cold gas in the measurement volume. To calibrate the system the average value of peak signal intensity from atmospheric air was measured. If the temperature in the measurement volume were uniform this measurement, in conjunction with Fig. 3(a), could provide an estimate of the temperature from the measured signal intensity. But, more importantly, the value of the signal intensity provides an estimate of the hot and cold gas proportions when the temperature in the measurement.volume is not uniform. For example, Fig. 3(b) shows the computed effect on the intensity of an increasing percentage of hot gas. The curves are for different cold gas temperatures, obtained from the CARP-2T code, for a hot gas temperature of 2200 K. Figure 3(a) and the appropriate equivalent of Fig. 3(b), constructed from a knowledge of hot and cold gas temperatures, provided some estimate

FIG. 4. Dual signal beam optical arrangement.

of the proportions of hot and cold gas in the measurement volume.

Temperature Measurements:

To minimise the simultaneous presence of hot and cold gas in the measurement volume, the CARS beams were aligned tangential to the turbulent flame front. Shown in Fig. 5(a) is an experimental spectrum and the computed best fit single temperature spectra. Also shown is the difference between the two. An indication of the closeness of matching can be obtained by summing, over all wavenumbers, the square of their difference. On this basis the differences between the spectral pairs might be at- tributed to noise. However, the measured spectrum exhibits a steep gradient at the higher wavenumbers, suggestive of a low temperature contribution. Yet it also shows evidence of a 'hot band'. Clearly, the spectrum is mixed and a single temperature theoretical fit is erroneous. It would appear unwise to reject or accept spectra solely on the bases of either noise, or some simple 'sum of squares' parameter and prudent not to reject a


measured spectrum without careful scrutiny, since to do so would be to discard information and gen- erate bias.

Classification of Spectra

A preliminary comparison of measured and theoretical single temperature spectra enabled the for- mer to be categorised as predominantly cold or mixed. An apparently hot category was not neces- sary, because the strength of any cold signal made it advisable to categorise such signals as mixed�9

Predominantly Cold Spectra (0-80% Hot Gas):

Because hot gas spectra are only manifest with a hot gas volumetric fraction greater than 80%, this category covers proportions of 0-80% of hot gas. The proportions of hot and cold gas in the measurement volume were estimated from the measured spectral intensity, Fig. 3(a) and such curves as those in Fig. 3(b). There is but slight depen- dence of intensity on cold gas temperature and, for less than 80% hot gas, a square law is a good ap- proximation to the variation of intensity in Fig. 309). For this category, it was assumed that the temperature of the hot gas was much greater than that of the cold gas and that the hot gas contribution to signal intensity was small. This assumption probably is not unduly restrictive because, if the hot and cold temperatures were close, the CARS spectrum would yield a close and acceptable average of the two. Also, since the spectral intensity from close temperatures is similar, the procedure discussed below would yield a volume of cold gas close to 100%.

The CARP-PC and QUICK codes yielded the cold gas temperature. Because of the weakness of the hot gas contribution no temperature could be at- tributed to it and such missing data were assigned to an unknown hot box in the temperature distribution�9

Mixed Spectra (80-100% Hot Gas):

This category arises because only with 80% or more hot gas in the measurement volume is the signal component in the 'hot band' strong enough to yield a hot temperature. Shown in Fig. 5(b) is a typical theoretical best fit, obtained with CARP- PC, to the measured separate hot and cold wavebands of the mixed spectrum in Fig. 5(a). The strong narrow peak in the cold band in Fig. 5(a), com- bined with the strong hot band, suggests the presence of both cold and hot gas, yet the best theoretical isothermal fit suggests a temperature of 1246 K. On the other hand, the two band matching to

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be seen in Fig. 5(b) gives hot and cold temperatures of 1931 and 628 K.

Curve C in Fig. 1 suggests that in the presence of more than 80% of hot gas, cold band temperature measurements are unreliable. To find the volumetric fractions of the two gases the computed curves equivalent to those in Fig. 3(b) therefore assumed a cold gas temperature of 400 K. The un- measurable cold temperatures were assigned to an unknown cold box in the temperature distribution.

Derivation of Temperature PDFs

Illustrated in Fig. 6 are four temperature pdfs derived from the same set of measurements at a given position in the reaction zone of the turbulent flame�9 That in Fig. 6(a) results from the best computed isothermal fits to the measured spectra. Fig-


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Fie. 6. Comparison of pdf generation methods from the same signals. Position = 11.3 mm from burner axis.

ure 6(b) results from the spectral categorisation approach, just described. Where there are two temperatures the area weightings are proportional to the estimated fractions. Where the percentage of hot or cold gas is known, but not the temperature, with the same area weighting, there is an attribu- tion to the unknown cold or hot box. Such boxes are shown horizontally over the full range of distributed cold and hot temperatures. Figure 6(c) is derived from (b). In doing this the areas of the un-

known cold and hot boxes were distributed in proportion to the distributions of temperature under- neath the boxes in Fig. 6(b).

Figure 6(d) recognises that, in practice, there is no discontinuity in temperature and that where cold and hot temperatures are measured they must be joined by a region of high temperature gradient. The worst case assumption was made that the flame was aligned normal to the major axis of the measurement volume. The volumetric proportions of hot


T = 2229 K = 158 K

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FIG. 7. Normalized temperature PDFs through the V flame.

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and cold gas were known, but, typically, only one temperature. This was taken to be the mean value within the appropriate volume. The temperature distribution across the remaining volume was that computed for a laminar flame by Dixon-Lewis. This procedure gave some small weighting to the intermediate temperatures and this can be seen from the pdfs.

In Fig. 7 are shown measured pdfs, processed according to the same principles as Fig. 6(d), at seven different positions through the flame. As was the case for the data in Fig. 6, the number of spectral measurements at each given position was 250.

Discussion and Conclusions

The two temperature composite theoretical spectra obtained by CARP-2T fitted well with experimental spectra, except for a small spectral band near 2325 nm. Experimental spectra have a narrower cold band than those computed, and are more closely

represented by the outline around the hot and cold spectra, shown by the broken curves in Fig. 2. This suggests that there might be a phase shift in the CARS signal at the boundary between the hot and cold portions of the measurement volume.

The differences between the raw pdf of Fig. 6(a) and the 'best processed' one of Fig. 6(d) show the probable effects of temperature gradients within the measurement volume. The cold and hot boxes in Fig. 6(b) indicate the degree of uncertainty in both cold and hot temperature measurement, while the difference between Figs 6(c) and (d) shows the possible minor influence of the high flame temperature gradients. Figure 7 confirms the expectation of bimodal pdfs at low Karlovitz stretch factor.

A c k n o w l e d g m e n t s

Collaboration of AEA Technology is gratefully ac- knowledged, in particular the help of Mr D. R. Williams.


REFERENCES

1. ARD AL-MASSEErt, W. A., BRADLEY, D., GAS- KELL, P. H. AND IAU, A. K. C.: Twenty-Third Symposium (International) on Combustion, p. 825, The Combustion Institute, (1991).

2. BRADLEY, D., IAU, A. K. C. AND MISSAGHI, M.: Combust. Sci. Tech. 64:119 (1989).

3. MAGRE, P., MOREAU, G., COLLIN, BORGHI, R. AND PEALAT, M.: Combust. Flame 71:147 (1988).

4. SHEPHERD, I. G., PORTER, F. M. AND GREEN- HALGrt, D. A.: Combust. Flame 82:106 (1990).

5. GREENHALGH, D. A.: In Advances in non-linear

spectroscopy, (Clarke, R. J. H., Hester, R. E. eds.) p. 193, J Wiley, Chichester, UK, (1988).

6. CARP-PC and QUICK are commercially avail- able computer codes developed by AEA Tech- nology, Harwell and supplied by Epsilon Re- search Ltd.

7. ABDEL-GAYED, R. (]., BRADLEY, D. AND LUNG, F. K-K.: Combust. Flame 76,213 (1989).

8. SNELLING, D. R., SMALLWOOD, G. J. AND SAW- CHOK, R. A.: Applied Optics 28:3226 (1989).

9. ECKBRETH, A. C.: Applied Optics 22:2118 (1989). 10. Goss, L. P., SwIxzEa, G. L. TRvMP, D. D. AND

SCHREIBER, P. W.: AIAA Publ. No. 82-0240 (1982).

COMMENTS

G. M. Dobbs, United Technologies Research Cen- ter, USA. What precautions did you take to elimi- nate stimulated Raman pumping, since it could lead to spectra with a hot/cold appearance? Your model ignores the complex physics of signal generation in the focal volume and how the strength of the hot and cold signals may depend on the local optical intensities and hot/cold proportions. Making this simplifying assumption, couldn't one calculate an entirely synthetic dataset of spectra having an assumed distribution of hot and cold temperatures and volume fractions? One could then analyze the dataset using the four methods you present in Fig. 6 to assess the self-consistency without the additional complications in experimental data being present. Experimentally, could you change your beam crossing angle and see the effect of a change in the focal volume, if any, on your histograms?

Dieter Briiggemann, Aachen University of Tech- nology, Germany. Have you investigated the influence of experimental volume variation on the re- sulting pdf's?

Author's Reply. We examined room temperature spectra at the same laser energy as that used in the present work and there was no evidence of stimulated Raman pumping.~ However, if there was any effect, this would result in a small systematic error in our measurements which would not alter our conclusions.

Synthetic data sets can be valuable but the only ones we used are those described in the text.

A change in the beam crossing angle would be useful in assessing the effect of measurement volume length on the histograms, but this was not done during the present study.

REFERENCE

1. SNELLING, D. R., SMALLWOOO, G. J, ANO PARA- ~ESWARAN, T.: Applied Optics 28, 3233 (1989).

Marcus Alden, Lund Institute of Technology, Sweden. 1) How relevant is it to divide the probe volume into only two parts? What error will this cause compared to using a multi-temperature (from cold to hot) approach?

2) When you divide the probe volume into two parts, these regions will probably have different composition and thus different XNa. What errors will this introduce if you are only using one value for XNR?

Author's Reply. 1) It is, of course, an approxi- mation. Our attempts to allow for the flame thickness suggest the error is not too large (c.f. Figs 6c and d).

2) The two temperature code we used took the signal as being built up across two zones of different temperature and different medium composi- tions, as specified by nitrogen concentration and non resonant susceptibility. Different non resonant sus- ceptibilities were used for burnt and unburnt com- positions and there was no need to approximate to a uniform one.

Dr. E. Hassel, Technische Hochschule Darm- stadt, Germany. What applications for your new CARS spectra evaluation scheme do you have in mind? Do you think it is possible to improve data evaluation with your method in turbulent flames


where the spatial gradient of the temperature is not infinite. Please comment.

Author's Reply. We intend to derive temperature pdfs in flames with various Karlovitz numbers for the validation of mathematical models. The present burner and others will be used for this purpose.

Our methodology is. most suited to either small or very high temperature gradients. The present two temperature analysis is applicable where the spatial temperature gradient is very high as in the V flame. However, in very highly stretched flames, temperature gradients may not be so high and accuracy might be improved.

Junyung Zhu, Aerometrics, USA. What is the corrected CARS Mean Temperature? Is it volume weighted? or density weighted? Which weighed mean temperature is more useful? If you do density weighted, the result will be close to thermocouple data.

Author's Reply. The values are volume weighted. Transformation from one basis to another is made easily. We do not readily accept that thermocou- pies give a density weighting.

Documents

Measurement of temperature PDFS in turbulent flames by the CARS technique