Estimation of soot absorption function via the two separated pulses laser-induced incandescence technique

Abstract

An original in situ experimental approach is proposed to estimate the absorption function of soot particles in flames: the two separated pulses laser-induced incandescence technique (SP-LII). The SP-LII technique is based on measuring the peak temperature of soot particles heated by laser pulses at two different fluences. From these two temperature measurements, the absorption function is estimated by solving the energy equation applied to soot particles during laser energy absorption once the product of soot density and specific heat is known. In order to solve the energy equation, two methods are considered here. The first method, called the “absorption model” (AM), solves the energy equation when all loss terms are neglected during absorption. The second method uses a look-up table (LUT) generated with an LII code in which the main loss terms are modelled. Both methods also provide information on the gas temperature $T_0$, assuming that gas and solid phases are at equilibrium. First, the SP-LII technique’s accuracy and limits are theoretically explored using peak temperatures from simulations done with an LII code. Overall, the AM method is efficient but is restricted to soot primary particles diameter $> \sim 10$ nm and low fluences. By contrast, the LUT method has an extended operational range, but it requires more information than the AM method, and its accuracy depends on the validity of the power loss models used to generate the look-up table. It is then concluded that the AM method represents the best compromise between the complexity of the methods and the expected accuracy of the results. Then, the feasibility of the SP-LII technique is proven by performing measurements in a laminar diffusion methane/air sooting flame and post-processing them with the AM method. Results for the absolute value and for the spatial evolution of ${E(m_{\lambda} )}$ are coherent with the literature. Finally, a possible extension of the SP-LII technique to turbulent flames is discussed.

A Estimation of \({E(m_{\lambda} )}\) along the flame’s axis with the LUT method

In order to test the LUT method with the experimental data of the $CH_4$/air flame, a new look-up table adapted to the test case and with refinement in the fluence direction was created. The parameters $d_p$, $\rho$, $\alpha$ and $\beta$ are selected as follows:

• $d_p$ is set to 10 nm.

• With the AM method, $\rho c$ = 4.6e6 J/K/m$^3$ was selected. However, the LII code used for the look-up table generation does not allow the change of the specific heat, which is hardcoded as a temperature-dependent function. Thus, To be consistent with the value selected with the AM method, it was decided to set the density to $\rho$ = $\frac{4.6e6}{c(T=3300K)}$ = 2067 kg/m$^{3}$.

• $\alpha$ is set to 0.3.

• For $\beta$, three cases were considered. The first one is $\beta$ = 0. It allows confronting the AM and the LUT methods with the same assumptions regarding the sublimation losses. The second case is $\beta = 0.2$. This case was considered to verify if the LUT allows exploiting the data where the soot peak temperature exceeds the limit of 4000 K. The value $\beta$ = 0.2 was selected following the conclusion about the mass accommodation coefficient of Sect. 5.3. The last case is $\beta$ = 0.13, the value for which the best agreement in ${E(m_{\lambda} )}$ estimations is seen for the three couples of laser fluences.

Figure 19a compares the estimation of ${E(m_{\lambda} )}$ of the AM and LUT methods when sublimation is neglected ($\beta = 0$). The LUT estimations are almost always above the ones of the AM, with a maximum of + 14%. This difference can be explained by the conduction losses that are accounted for with the LUT.

Figure 19b is identical to Fig. 19a, but with $\beta$ = 0.2 instead of $\beta$ = 0. In this case, the estimations of ${E(m_{\lambda} )}$ are plotted even when the peak temperature exceeds the limit of 4000 K. For the couple 64/106 mJ/cm$^2$, ${E(m_{\lambda} )}$ is 3 to 20% higher than the ones for $\beta$ = 0 up to HAB = 35 mm. Above that, ${E(m_{\lambda} )}$ reaches the table limit (0.6) at HAB = 37 mm. For the two other couples, ${E(m_{\lambda} )}$ reaches the table’s upper limit at HAB = 33 and 34 mm for 64/149 mJ/cm$^2$ and 106/149 mJ/cm$^2$, respectively. Such high values for ${E(m_{\lambda} )}$ show that the sublimation process is over-predicted.

The HABs for which the estimations of the LUT are close to the one of the AM method correspond to the ones for which the peak temperatures are the lowest ($< \sim$3500 K).

The best agreement for the three couples of laser fluence is found for $\beta$ = 0.13. This case is plotted in Fig. 19c. In this case, estimations of ${E(m_{\lambda} )}$ with the LUT method are close to the AM method for HAB < 31 mm. Above that, differences slightly increase, and ${E(m_{\lambda} )}$ reaches $\sim$0.5 at HAB = 36 mm before sharply increasing at the flame’s extremity. The results of Fig. 19c should be interpreted with care and do not legitimise the usage of high fluences for the SP-LII if one sets $\beta$ = 0.13. The authors believe that the strong variations in the estimation of ${E(m_{\lambda} )}$ with the hypothesis made on $\beta$ confirm the necessity to avoid high laser fluences even when using the LUT method.

Fig. 19

Evolution of ${E(m_{\lambda} )}$ as a function of HAB for three couple of laser fluences: 64/106 mJ/cm$^2$ (blue $\circ$), 64/149 mJ/cm$^2$ (red $\times$) and 106/149 mJ/cm$^2$ (black $*$). The solid lines represent the estimations obtained using the AM method, while the dotted lines are for the LUT method for a $\beta$ = 0, b $\beta$ = 0.2, and c $\beta$ = 0.13