Chapter 4 Verification
5.2 Reactive Propane-Air Mechanism
5.2.1 Reduced Chemistry
finite thickness. The viscous layer overlapped some of the finest reaction zone lengths but is distinct from the better understood induction zone. In another paper (145), they also examine the combustion modes possible behind shock waves through solu- tions of the one-dimensional, steady reactive Navier-Stokes (diffusive but nonviscous) equations with a detailed chemical reaction mechanism for stoichiometric methane-air mixtures.
Many researchers have simulated diffusion for two- and three-dimensional deto- nations, yet, almost all have neglected multi-component chemistry and/or have also neglected to resolve the diffusive scales. One work that stands out is that of the NRL group (88), which has modeled DDT (detonation to deflagration transition) in 2D and 3D. In their simulations they have used two-component chemistry. They found DDT to be very sensitive to the specific heat ratio.
The most recent and complex simulations to date that are relevant to this thesis are that of Massaet al. (116). In their two-dimensional simulations, also discussed in
§1.1.6, they neglected the shock waves (which leaves out the main source of detonation instability) and simulated with detailed chemistry the shear layer behind detonation triple points. They investigated the role of vortical structures associated with Kelvin- Helmholtz instability in the formation of localized ignition.
neglected as were many nonessential reactions. After the initial reduction, a few of the rates for the subreactions of C2H5 were tuned to rescale the induction times to match the experimental data. C2H5 is a direct product of C3H8 and therefore, tuning this reaction directly affects the induction time and only indirectly affects the exothermic energy release and long time relaxation reactions like CO2 and CO. The 22 species included in this mechanism are all essential, in that if any one species were to be removed, relatively large changes in at least one range of the overdrive solutions is affected. The species are C3H8, O2, N2, H, O, OH, H2, H2O, CO2, HO2, CO, HCO, CH2, CH3, CH2O, HCCO, C2H2, CH4, C2H3, C2H4, C2H5, NC3H7
5.2.1.1 Comparison to Detailed Chemistry
The detailed mechanism reduction was carried out by matching the induction times and the steady ZND solution profile as close as possible as shown in figures 5.1 and 5.2. The expected detonation wave speeds for the unsteady problem range from an overdrive,f =U/UCJ, of 0.8 to 1.4. Therefore, throughout the reduction process, the steady ZND solution was matched as close as possible throughout this range.
Shown in figures 5.3 and 5.4 are various properties of interest that were preserved in the reduction. The most difficult and important property to match is the thermicity, shown in figure 5.4. The location of the peak directly corresponds to the induction time/length. The shape and width of the peak directly corresponds to the exothermic pulse width. Thermicity describes the rate at which energy from chemical reactions is coupled to the fluid dynamics.
The thermicity term can be broken down into two parts, a dimensionless coefficient σi that depends on thermodynamic properties and the convective derivative of the species mass fractions,
˙ σ=
NY
X
i=1
σiDYi
Dt . (5.1)
As written, the coefficients σi in the thermicity term are difficult to compute since the necessary partial derviatives are not commonly available for a typical equation of state. Using thermodynamic identities, the following version can be obtained
σi =−1 ρ
∂ρ
∂Yi P,T,Yk6=i
− αT cP
∂h
∂Yi P,T,Yk6=i
. (5.2)
Note that this relation is completely general and is independent of any assumptions about the equation of state or the reaction mechanism. The coefficient of thermal expansion is
αT =−1 ρ
∂ρ
∂T P,Y
. (5.3)
For an ideal gas,
σi = W
Wi − hi
cPT. (5.4)
The entire coupling between the flow and the chemistry is contained with ˙σ. Ther- micity measures the rate at which chemical energy is transformed into thermal energy and vice versa. The variation of the thermicity within the flow reflects the net effect of all chemical reactions taking place: bimolecular exchanges, recombination, and dissociation. The first term in Equation 5.2 is the effective energy release associated with changing the total number of moles of species per unit mass of the reacting mix- ture. The second term in Equation 5.2 is the normalized energy release associated with chemical bond breaking and formation.
Also, note that for the overdrive greater than one cases, there is an endothermic energy deposition in the early times which is described with a negative thermicity.
For an overdrive less than one, the shape of the thermicity is very simple, it goes from practically zero to its final positive value very rapidly. In these cases the location of this rapid rise is important to match.
Figure5.1:Detonationinductiontimecomparisonsforpropane:comparingexperimentalvs.detailed(22,21)andreduced mechanisms.TheambientconditionscorrespondstoT=300K,P=20kPa.
Figure5.2:Comparingreducedanddetailedmechanism(Blanquart)(22,21)ZNDsolutionsatdifferentoverdrives.The reducedpropanemechanismneglectsN2chemistryandlargerthanC3moleculestoreduce161to22speciesand1055to53 reactions.AfewratesofsubreactionsforC2H5werehandtunedtore-scaleinductiontimes.
Figure5.3:Comparingspecificheats(gamma),Machnumber,temperature,andvelocitiesofthereduced(blue)anddetailed (red)mechanismsatoverdrivesof1.4,1.0,and0.8.
Figure5.4:Comparingdensity,thermicity,molecularweights,andtemperaturegradientsofthereduced(blue)anddetailed (red)mechanismsatoverdrivesof1.4,1.0,and0.8.Thethermicityplotonlyshowsthe1.4overdrivecaseandthetemperature gradientplotshowsthe1.0case.
5.2.1.2 Reduced Mechanism Chemistry
In figures 5.5, 5.6, and 5.7, as an example, using the CJ speed (overdrive = 1) case the change in composition through the detonation wave is shown. Note the distinct regions where the chain branching and relaxation zones begin. The relaxation involves the final formation of CO2 and CO.
Figure 5.5: Mole fractions as a function of distance for each species for the reduced mechanism at an overdrive of 1.0 (CJ speed).
In figure5.5, the species with the largest mole fractions are shown. N2is a dilutent and its mass (rather than mole) fraction is constant. All nitrogen-related reactions have been neglected in this reduction. This is a common practice for detonation hydrocarbon reductions. The rate at which N2 is made into N, NO, NO2, N2O, NO3, etc. is very slow compared to the induction time and relaxation time for CO and CO2 formation. Therefore, the dynamics of the detonation are not affected. The only difference that would be seen if these reactions were included would be a slightly different final temperature far downstream of the detonation wave.
The induction length is clearly seen in figure 5.5 by looking for the rapid con- sumption of O2 and complete consumption of C3H8. The exothermic energy release
Figure 5.6: Zoomed in view of the mole fractions as a function of distance for each species for the reduced mechanism at an overdrive of 1.0 (CJ speed).
is seen by observing the rapid formation of H2O. The chemical relaxation is mainly described by the formation of CO and CO2. HCO which is in a relatively very small concentration shown in figure 5.7, is an important intermediate in this process.
In figure 5.6, the formation of the intermediate H2 and hydrocarbons C2H2 and CH4 is observed. The formation of larger concentration radicals OH, H, and O is also observed. In the next figure, 5.7, more chain branching intermediates are viewed more closely by zooming in. The formation and depletion of CH2O, CH3, C2H3, CH2, C2H4, HCCO, is observed. There are other species of smaller concentrations such as C2H5, C3H7, and CH2O which are also essential in the chain branching process. Also, essential at early times is the HO2 radical. Shown in figure 5.8, at an early time the small concentrations of C3H7 and C2H5 are formed and then consumed as they are broken down into smaller hydrocarbons.
Our numerical simulations investigate the mechanisms involved in the diffusive processses of irregular detonations. Here, the goal is to study a highly unstable mixture for which major effects along the shear layers can be expected; e.g., unreacted pockets transported downstream or highly irregular ignition. In this case, diffusive processses can be an integral part of the detonation mechanism.
Figure 5.7: Highly zoomed in view of the mole fractions as a function of distance for each species for the reduced mechanism at an overdrive of 1.0 (CJ speed).
Figure 5.8: Zoomed in view of the mole fractions of C3H7 and C2H5 as a function of distance for each species for the reduced mechanism at an overdrive of 1.0 (CJ speed).