Diode laser absorption spectroscopy can be used for temperature measurements only in the situation where the temperature is fairly homogeneous along the beam path. Clearly, this is not typically the case in flames so this technique has significant limitations. Such diode-laser absorption thermometry has been applied (Ma et al. 2002) in a very particular type of combustion system known as a pulse detonation engine (PDE) in which a quasi-one dimensional flame front propagates very rapidly down a narrow cylinder during detonation. There are thus no significant temperature gradients normal to the cylinder axis. A DFB laser was wavelength scanned to probe the Q-branch spectrum of ethylene at around 1.62 µm, and the temperature was found from the relative intensity of two absorption lines. An attempt was made (Sanders et al. 2001) to address the situation of flows with non-uniform properties. This research exploits the possibility to scan VCSELs over a wide wavelength range to tune over sixteen separate transitions in molecular oxygen at around 760nm. Each of these transitions has a different temperature-dependence and it was possible to infer temperature distributions in the range 200K – 700K with a 30 ms time response. The authors note that other temperature ranges could be probed by
1. Introduction
selecting different sets of transitions. They consider the absorption path to be composed of n uniform temperature segments and show by a mathematical derivation that these n temperatures can be found by probing the line-strength of n+1 absorption transitions. In addition to its poor level of accuracy, this technique suffers from the difficulty that although a temperature probability distribution is found, there is no information on actual temperatures at a specific location in the beam path. A spatial temperature profile can only be inferred from prior knowledge of the situation being probed.
Temperature measurements based on absorption, therefore, have some inherent disadvantages, which will be demonstrated here by showing the results of some simple calculations. The graphs shown below give a comparison of the actual mean temperature and the temperature that would be measured by line-of-sight absorption. These take account of two separate effects that bias the measurement: 1. the density is higher in cold regions so the average will be weighted towards colder temperatures; 2. the relative population of the two levels is a non-linear function of temperature, according to Eqn. 1.7, so the average ratio does not correspond to the average temperature. Atomic indium has been chosen as the probe species for this simulation, but it is emphasised that this problem exists regardless of the probe species.
Figure 1.5 shows the result of a line-of-sight temperature measurement in a situation in which the beam path contains two regions of equal length in which the mole fraction of seeded indium is homogeneous. One of the regions is at a constant temperature of 2000 K, and the measured temperature is calculated for a range of temperatures in the second region. In Figure 1.5,
1. Introduction
the measured temperature is plotted together with the true mean of the temperatures of the two regions.
Figure 1.5. Simulation of temperature measured by absorption spectroscopy in the case of two regions of equal length and different temperature. One region is at 2000 K. The true average and measured temperature plotted against the temperature of the second region.
It is clear that the temperature is underestimated by greater amounts as the difference in temperature between the two regions increases; in this case, this is principally due to the effect of changing density with temperature. When the variable temperature region is at a temperature of 1000 K, the mean temperature along the entire beam path is 1500 K, whereas the measured temperature is 1355 K. This corresponds to an error of nearly 10 %.
A second simulation was done in which it was assumed that there is a Gaussian probability density function (PDF) in temperature, as may be the case in some engines. It should be noted, though, that the path-averaged technique gives no information about whether the PDF actually is Gaussian or not, so it is not possible to test the validity of such an assumption in a practical situation. The mean temperature was specified as 2000 K and the
1. Introduction
measured temperature was calculated for a range of standard deviations. The plot in Figure 1.6 shows that as the standard deviation is increased, a systematic underestimate of temperature is again apparent due to the biasing of the measurement toward colder regions.
Figure 1.6. The measured temperature in a system where the temperature follows a Gaussian PDF centred around a mean of 2000 K.
It has therefore been shown that diode laser absorption spectroscopy leads to measured temperatures that do not represent the true average in the system, even when a probe species is selected so that the relative population of the two levels being probed is roughly linearly proportional to temperature in the range of interest. One further influence on absorption measurements is that the effects of flame chemistry mean that the mole fraction of the probe species would probably be quite different in regions of unequal temperature. This is certainly the case in flames, where there are large spatial variations in composition, as shown in Figure 1.1. This effect is difficult to quantify but could lead to substantial unaccountable errors in the measured temperature of inhomogeneous systems. In the case of turbulent flames, this effect would mean that the use of a reactant or product of combustion as the probe species
1. Introduction
would certainly lead to a quite incorrect measurement, and it may be of little value to measure the mean temperature of a turbulent flame in any case. No previously existing diode laser technique allows the measurement of temperatures at a point in the flame, and it is the purpose of the present research to develop such a system.