Experimental and numerical detonation cell in H2-N2O-Ar mixtures

More documents

Recommendations

Info

NH + NO = N2O + H (6) NH + NH = N2 + H + H (7) By analyzing the reduced model, it is found that the role of the reverse reaction R6 and forward reaction R7 consists to limit the consumption of H radical by the forward reaction R5. Further reduction could be achieved by eliminating the two last reactions and reducing the rate constant of reaction R5. The reduction of the preexponenial factor of reaction R5 by 45 % allows to compensate the effect of reactions R6 and R7 and to delete 2 species, NH and NO, among the 10 remaining species. Finally, the partially globalized version of the reduced model, noted as globalized model, includes reactions R1-R5. More details on the reduction procedure can be found in [19] Several tests have been performed to validate the reduced kinetic schemes. Their applicability to detonation simulations is tested using the constantpressure reactor model. The initial conditions are determined behind a shock wave propagating in a fresh mixture at P1 = 10 kPa and T1 = 297 K. The shock velocity, D, is varied within the range (0.8-1.2) DCJ, whereDCJ = 1897 m/s, yielding the following variations of the post-shock conditions: P2 = 241-546 kPa and T2 = 1316-2465 K. Figure 5 presents a comparison of the maximum thermicity and of time to maximum thermicity, predicted with the three kinetic schemes: detailed, reduced R1-R7, globalized R1-R5. From Figure 5, one can see that the results given by the three reaction mechanisms are in good agreement. The predictions provided by the last one are as accurate as those given by the reduced scheme R1-R7. Maximum thermicity (s -1 ) 1x10 7 1x10 6 Time to maximum Thermicity Maximum Thermicity Detailed scheme Reduced scheme Globalized scheme 0.8 0.9 1 1.1 1.2 D/DCJ Figure 5: Maximum thermicity and time to maximum thermicity in a H2-N2O-Ar mixture as a function of D/DCJ: comparison between the detailed, the reduced and the globalized chemical schemes. Initial conditions: Φ=1;XAr =0.4;P1 = 10.1 kPa; T1 = 297 K. 1x10 -4 1x10 -5 1x10 -6 1x10 -7 Time to maximum thermicity (s) 4 Other tests were conducted using the ZND model. Figure 6 shows spatial profiles of temperature and thermicity computed with the detailed and globalized kinetic schemes for D = DCJ. The latter gives a slightly higher detonation velocity DCJ = 1908 m/s. This example proves that the reduced scheme provides correct profiles of macroscopic quantities during the entire oxidation process. 2D detonation simulations discussed below have been conducted with the globalized kinetic scheme. Temperature (K) 3200 2800 2400 2000 1600 Detailled scheme Globalized scheme Temperature 0.0004 0.0008 0.0012 Distance (m) Thermicity 1E+006 8E+005 4E+005 0E+000 Figure 6: Temperature and thermicity profiles in a H2- N2O-Ar mixture: comparison between the detailed and the globalized chemical scheme. Initial conditions: Φ = 1; XAr =0.4;P1 = 10.1 kPa; T1 = 297 K. For the cell size prediction, first, the correlation of Ng has been tested against the experimental data from the present study. Figure 7 shows an example of the results obtained. λ (mm) 100 10 0.2 T 1 = 295 K X Ar = 0.2 0.3 P 1 = 7 kPa P 1 = 10 kPa P 1 = 35 kPa 0.4 0.5 0.6 0.7 0.8 0.9 Equivalence ratio 1 Thermicity (s-1) 2 3 Figure 7: Comparison between Ng’s cell size correlation and the experimental detonation cell size of H2-N2O-Ar mixture. Initial conditions: Φ = 0.3-2.5; XAr =0.2;P1 =7-35kPa;T1 = 297 K. It can be seen that the correlation allows a good quantitative prediction of the cell size with a mean error around 40 %. The evolution of cell size as
a function of the equivalence ratio, initial pressure and dilution is well reproduced by the correlation. As important parameters of the correlation (the induction distance and the reaction zone length) are derived from the detailed scheme, it can be concluded that the accuracy of the predicted cell size is directly related to the quality of the kinetic scheme. Thus, the correlation of Ng can be used as a reliable tool as long as a carefully validated detailed chemical model is used. Further, 2-D numerical simulations have been performed. Figure 8 and Figure 9 show a Schlieren picture of the detonation front and a numerical soot record, respectively. Figure 8: Numerical Schlieren picture of a simulated detonation in a H2-N2O-Ar mixture. Initial conditions: Φ = 1; XAr =0.4;P1 = 10.1 kPa; T1 = 297 K. The numerical soot foils are used to estimate the cell size. The mean cell size in the simulations presented in Figure 8 and Figure 9 is 9 mm, that is almost two times smaller than the experimental one. As the velocity of the simulated detonation is 50 m/s higher than in the experiment, it was decided to adjust the propagation velocity in the simulation. The desired effect can be achieved by modifying the enthalpy of formation of H2O, the most important oxidation product. Based on computational tests, the modified enthalpy of formation must be -221.1 kJ/mol instead of the standard value of -241.8 kJ/mol. Additionnal simulations have been performed and a mean cell size of 18 mm was derived, perfectly matching the experimental data. Figure 10 sums up the results of the different numerical simulations and compares them with the experimental results and Ng’s correlation. 5 Figure 9: Example of numerical soot foil obtained in a H2-N2O-Ar mixture. Initial conditions: Φ = 1; XAr = 0.4; P1 = 10.1 kPa; T1 = 297 K. λ (mm) 100 10 Experimental data λnum-adjusted λnum λNg 1 Equivalence ratio Figure 10: Dependence of the cell size on the equivalence ratio in H2-N2O-Ar mixtures: comparison between experimental data and different predictions. Initial conditions: Φ = 0.3-2.5; XAr =0.4;P1 =10kPa;T1 = 295 K. Theoretically, the most reliable method for cell size prediction would consist in deriving the detonation cell size from numerical simulation. In practice, such simulations are very costly and require a drastic reduction of the chemical kinetics so that it is often taken into account as a single irreversible step. In detonation waves, instabilities result from the coupling between chemistry and gasdynamics. Consequently, it is not surprising that the use of a single reaction results in poor cell size prediction. In the present study, although the detailed scheme has been strongly reduced, the chemical mechanism consists of 5 reversible reactions. The cell size predicted using this approach is within the experimental range of measurement. However, the obtained value is
Page 1 and 2: Experimental and numerical detonati
Page 3: ecomes effective inducing a large j

Experimental and numerical detonation cell in H2-N2O-Ar mixtures

Create successful ePaper yourself

Delete template?

Save as template?