GT2017-64407

HEEDS OPTIMIZED HYCHEM MECHANISMS Graham Goldin Siemens CD adapco Lebanon NH USA Zhuyin Ren Tsinghua Univ Beijing China Yang Gao Tianfeng Lu Univ of Connecticut Storrs CT USA Hai Wang Rui Xu Stanford Univ Palo Alto CA USA ABSTRACT Transportation fuels consist of a large number of hydrocarbon components and combust through an even larger number of intermediates Detailed chemical kinetic models of these fuels typically consist of hundreds of species and are computationally expensive to include directly in 3D CFD simulations HyChem Hybrid Chemistry is a recently proposed modeling approach for high temperature fuel oxidation based on the assumptions that fuel pyrolysis is fast compared to the subsequent oxidation of the small fragments and that although their proportions may differ all fuels pyrolyse to similar sets of these fragment species Fuel pyrolysis is hence modeled with a small set of lumped reactions and oxidation is described by a compact C0 4 foundation chemistry core The stoichiometric coefficients of the global pyrolysis reactions are determined to match experimental or detailed mechanism computational data such as shock tube pyrolysis products ignition delays and laminar flame speeds The model is then validated against key combustion properties including ignition delays laminar flame speeds and extinction strain rates The resulting HyChem model is relatively small and computationally tractable for 3D CFD simulations in complex geometries This paper applies the HEEDS optimization tool to find optimal pyrolysis reaction stoichiometric coefficients for high temperature combustion of two fuels namely Jet A and n heptane using a 47 species mechanism It was found that optimizing on experimental ignition delay and laminar flame speed targets yield better agreement for ignition delay times and flame speeds than optimizing on pyrolysis yield targets alone For Jet A good agreement for ignition delays and flame speeds were obtained by using both ignition delay and flame speeds as targets For n heptane a trade off between ignition delay and flame speed was found where increased target weights for ignition delay resulted in worse flame speed predictions and visa versa INTRODUCTION Liquid transportation fuels such as gasoline diesel and jet fuels are composed of thousands of different hydrocarbon species The composition of a given fuel say diesel varies from location to location and day to day It is difficult to characterize these fuel compositions which are often modeled as a surrogate blend of several neat fuels The resulting chemical mechanism to pyrolyse the fuel components and oxidize the numerous pyrolysis fragments can consist of hundreds or even thousands of species 1 While such mechanisms can be used in 0D and 1D flame calculations it is computationally expensive to use them in 3D CFD simulations of complex geometries such as gas turbines and In Cylinder Engines ICE with millions of grid cells where all species are transported and chemistry is computed on the fly A contemporary approach called HyChem Hybrid Chemistry 2 3 produces mechanisms for complex hydro carbon fuels with tens of species These mechanisms are general and have demonstrated good predictions of chemical kinetic phenomena such as ignition delay times premixed laminar flame speeds non premixed flame extinction strain rates etc over a wide range of operating conditions Mechanisms with tens of species can be affordably included in complex geometry 3D CFD simulations HyChem is based on two physical insights The first is that the large hydrocarbon species in various real fuels pyrolyse to similar sets of small hydrocarbon species fragments although the proportion of these small species fragments may differ from Proceedings of ASME Turbo Expo 2017 Turbomachinery Technical Conference and Exposition GT2017 June 26 30 2017 Charlotte NC USA GT2017 64407 1Copyright 2017 ASME fuel to fuel The second is that pyrolysis occurs fast relative to fuel fragment oxidation with the large hydrocarbons breaking down in a transient period say tens of micro seconds while subsequent oxidation takes a significantly longer time Based on these two assumptions the complex processes of fuel pyrolysis with its myriad of associated species is modeled with a single fuel species and a very small set of semi global oxidative pyrolysis reactions The stoichiometric coefficients of the global pyrolysis reactions are specific to each fuel The global pyrolysis reactions are added to an oxidation mechanism of the pyrolysis products which in general are better understood and more universal than fuel pyrolysis models There are several approaches to determine the stoichiometric coefficients of the semi global fuel pyrolysis reactions in HyChem One approach is to experimentally measure the proportion of the small hydrocarbon fragments resulting from fuel pyrolysis typically in shock tube and flow reactor pyrolysis experiments and fit these to the lumped HyChem pyrolysis reactions A similar approach is to computationally model these experiments with a comprehensive mechanism and calculate the stoichiometric proportions Once these coefficients are determined the performance of the HyChem mechanism can be assessed by comparing with measured or computed combustion tests such as ignition delays pyrolysis yields laminar flame speeds extinction strain rates and so on An alternative approach is to use an optimization algorithm to determine the stoichiometric coefficients that best match some set of target data such as pyrolysis yields ignition delays flame speeds and so on This methodology is applied in this paper In particular an appropriate set of targets is investigated The three target sets investigated are 1 Experimental pyrolysis yields 2 Experimental ignition delays 3 Experimental ignition delays and flame speeds The HyChem pyrolysis stoichiometric coefficient optimization is performed for two fuels namely Jet A and n heptane HYCHEM FORMULATION The original HyChem model 2 3 has nine global pyrolysis species of H CH3 CH4 C2H4 C3H6 i C4H8 1 C4H8 C6H6 and C7H8 Pyrolysis experiments of Jet A JP8 and JP10 3 show that about 90 of pyrolysis mole fraction yields are composed of these nine species The global pyrolysis reactions in HyChem are then formulated as 1 1 2 1 and 1 1 1 2 where R represents species H CH3 O OH O2 and HO2 The fuel is modeled by a single species CnHm with average numbers of carbon n and hydrogen m atoms Equations 1 and 2 represent seven lumped pyrolysis reactions Ensuring element balances results in the following constraints 4 3 13 3 1 4 4 3 10 1 5 1 6 where 2 3 4 4 Hence the global pyrolysis equations 1 and 2 have seven independent stoichiometric parameters which can be adjusted namely and The kinetic rate parameters namely pre exponential factors temperature exponents and activation energies for the seven semi global pyrolysis reactions are taken from 2 Note that a sub set of these parameters such as the pre exponential factors or all of them can be added to the independent variables in the optimization routine However this exercise is beyond the scope of the current work and is left for future studies The global pyrolysis steps can be added to a C0 4 foundation chemistry core for oxidation of the nine pyrolysis species In this work the oxidation core is taken from USC Mech II which has 111 species among 784 reactions 4 The HyChem models were reduced using directed relation graph DRG and DRG aided sensitivity analysis DRGASA 5 and unified to 47 species and 263 reactions OPTIMIZATION The commercial software package HEEDS MDO 6 was used to optimize the seven independent pyrolysis variables The commercial chemical kinetic software package DARS 7 was used to calculate pyrolysis constant pressure reactor ignition delay constant volume reactor and freely propagating laminar flame speed calculations with mixture averaged transport properties 2Copyright 2017 ASME The search algorithm used in HEEDS MDO is named SHERPA and is a single objective constrained optimization problem and a hybrid combination of Nelder Mead Simplex 8 simulated annealing 9 quadratic programming 10 and a genetic algorithm 11 HEEDS MDO works through text files where variables are tagged in input files the pyrolysis reaction stoichiometric coefficients in the chemical mechanism in Chemkin format and output files pyrolysis yields ignition delays and laminar flame speeds written by DARS The corresponding target curves which are the experimentally measured pyrolysis yields ignition delays and laminar flame speeds are read into HEEDS MDO which minimizes the least squares deviation between the DARS results and experimental target curves HEEDS MDO runs the DARS executable and the only HEEDS MDO input is the number of evaluations which is set to 1000 in this work It is possible that a better set of coefficients could be found by running more evaluations which would result in predicted curves closer to the experimental data The HEEDS cost function C is calculated as the weighted root mean square RMS of the deviation of the predicted and target curves 7 where T is the number of target curves e g ignition delay flame speed etc Nt is the number of computed points for each target curve t yi t is the value of the computed point in target curve t Yi t is the interpolated value of the experimental target curve point and Wt is the weight assigned to the t th target RESULTS 1 JET A Jet A is modeled as C11H22 2 so that m 11 and n 22 in the lumped pyrolysis reactions in equations 1 through 6 Three optimizations of the stoichiometric coefficients in the HyChem Jet A model are performed with experimental 2 target cases of Case 1 Pyrolysis yields Case 2 Ignition delays Case 3 Ignition delays and flame speeds For case 1 the HEEDS targets were the experimentally measured CH4 and C2H4 yields at two times hence four HEEDS targets For case 2 HyChem stoichiometric coefficients were optimized to match four ignition delay curves four HEEDS targets And for case 3 the same four targets were used as in case 2 plus an additional target of laminar flame speed five HEEDS targets The weights of each target Wt in Eq 7 were set to unity for cases 1 and 2 giving equal weight to each pyrolysis curve case 1 and each ignition delay curve case 2 For case 3 which targets both ignition delays and flame speeds Wt was set to 1 0 for ignition delays and 0 2 for the flame speeds The reason for this is that ignition delay times were of order 1 units of ms and flame speeds of order 40 units of cm s so that with unity weights ignition delay solutions would be preferred as these have lower cost function in Eq 7 These weighting factors for case 3 were obtained manually by trial and error to obtain some compromise in accuracy for both ignition delay and flame speed For case 1 the experimental pyrolysis is obtained from shock tube measurements at a pressure of 12 4 atm with mole fraction of Jet A of 0 73 and Ar as the balance gas Pyrolysis species CH4 and C2H4 were measured at times of 0 5ms 1ms and 1 5ms for temperatures ranging from 1100K to 1300K The experimentally measured CH4 and C2H4 at 0 5ms and 1 5ms are used as HEEDS targets Pyrolysis is modeled in a constant pressure Yield is calculated as the CH4 or C2H4 species mole fraction divided by the initial fuel mole fraction 0 0073 Figures 1 and 2 show the experimentally measured pyrolysis yields and the results of the HyChem HEEDS optimized mechanism calculations at times of 0 5ms and 1 5ms respectively The optimized mechanism reasonably matches the experimental data 2 Fig 1 Experimental symbols 2 and HyChem optimized lines case 1 pyrolysis yields versus temperature around 12 atm at time 0 5 ms 3Copyright 2017 ASME Fig 2 Experimental symbols 2 and HyChem optimized lines case 1 pyrolysis yields versus temperature around 12 atm at time 1 5 ms For cases 2 and 3 experimentally measured ignition delay times are used as the HEEDS optimization targets instead of the pyrolysis yield targets used in case 1 In addition to the measured ignition delays case 3 also targets the measured freely propagating laminar flame speeds Figures 3 through 6 compare computed ignition delays with HEEDS HyChem optimized mechanisms with experimental data at various initial compositions temperatures and pressures Three mechanisms are compared corresponding to the three target cases namely pyrolysis yields case 1 ignition delays case 2 and ignition delays as well as laminar flame speed case 3 The experimental ignition delays are measured from shock tube data 2 Observations are corrected for small deviations in the experimental pressure and equivalence ratio using the scaling formula 8 Ignition delays are modeled with constant volume reactors The ignition delay time is calculated as the time of maximum temperature gradient Fig 3 shows base 10 logarithm of ignition delays ig in ms versus reciprocal temperature for a mixture of Jet A and air at equivalence ratio of 1 1 and pressure of 10 9 atm Fig 4 similarly presents ignition delays for a mixture of Jet A with 4 O2 in Ar at a pressure of 13 6 atm and a of 1 0 Fig 5 shows ignition delays for a mixture of Jet A with 4 O2 in Ar at a pressure of 1 1 atm and a of 0 9 And finally Fig 6 shows ignition delays for a mixture of Jet A with 21 O2 in Ar at a pressure of 16 4 atm and a of 1 0 Fig 3 Experimental symbols 2 and HyChem optimized lines cases 1 3 ignition delay time versus inverse temperature for Jet A air 1 1 p 10 9 atm Fig 4 Experimental symbols 2 and HyChem optimized lines cases 1 3 ignition delay time versus temperature inverse for Jet A with 4 O2 in Ar 1 0 p 13 6 atm 4Copyright 2017 ASME Fig 5 Experimental symbols 2 and HyChem optimized lines cases 1 3 ignition delay time versus temperature inverse for Jet A with 4 O2 in Ar 0 9 p 1 1 atm Fig 6 Experimental symbols 2 and HyChem optimized lines ignition delay time versus temperature inverse for Jet A with 21 O2 in Ar 1 0 p 16 4 atm From Figs 3 6 it is clear that optimizing on pyrolysis yields alone case 1 gives inaccurate ignition delay predictions It appears that optimizing on ignition delay and flame speed case 3 gives similar accuracy in ignition delay prediction as optimizing only on ignition delay case 2 Since cases 2 and 3 were not targeted to pyrolysis data to give an indication of the accuracy of ignition delay optimized mechanisms for pyrolysis predictions Figs 7 and 8 show pyrolysis simulations using the optimized mechanisms of cases 1 and 2 at 0 5ms and 1 5ms respectively The optimized mechanism based on ignition delay and flame speed for case 3 is very close to that of case 2 and is not included in the plot to reduce clutter Pyrolysis is not well predicted for the ignition delay targets However since it is far more common in CFD to simulate ignition delay and laminar flame speed rather than pyrolysis yields optimizing ignition delay and flame speed alone or in addition to pyrolysis yield is preferable to optimizing on pyrolysis yield alone Fig 7 Experimental symbols 2 and HyChem optimized lines cases 1 2 pyrolysis yields versus temperature at time 0 5ms Fig 8 Experimental symbols 2 and HyChem optimized lines cases 1 2 pyrolysis yields versus temperature at time 1 5ms Lastly Fig 9 shows the unstrained laminar flame speed predictions for cases 1 through 3 compared with the experimental measurements for a pressure of 1 bar and unburned temperature of 403K Interestingly although the pyrolysis optimized mechanism case 1 predicted ignition delay poorly it predicts flame speed quite well As expected case 3 which targets flame speed in addition to ignition delay predicts flame speed better than case 2 which targets ignition delay only Note that flame speed calculations are an order of 5Copyright 2017 ASME magnitude more computationally expensive than ignition delay and the run time for case 3 was nine times that for case 2 Fig 9 Experimental symbols 2 and HyChem optimized lines cases 1 3 laminar flame speeds versus equivalence ratio The results for Jet A optimized HyChem coefficients in this section were performed on a limited set of experimental data In order to assess the HyChem approach for another fuel and with a wider range of experimental data the method is applied to n heptane RESULTS 2 N HEPTANE The same HyChem mechanism used for Jet A in the previous section is applied to n heptane The oxidation sub mechanism is identical and the only difference is the fuel composition for n heptane C7H16 with m 7 and n 16 in the seven lumped pyrolysis reactions in equations 1 through 6 as well as the HyChem optimized stoichiometric coefficients of these reactions Following the procedure for Jet A in the previous section optimization is performed with ignition delay targets labelled Case 4 as well as ignition delay plus flame speed targets labelled Case 5 Note that only high temperature 1000K ignition is computed in this work and Negative Temperature Coefficient NTC effects are not considered It is possible to model NTC behavior with the HyChem model although other species such as C7H15O2 C7H4OOH O2C7H14OOH and OC7H13OOH etc and their associated reactions would need to be considered which is out of the scope of the present work The experimental ignition delay data is from 12 15 and the experimental flame speed data is from 16 17 Fig 10 shows the experimental and HEEDS HyChem optimized ignition delay Case 4 for five different conditions of equivalence ratios and pressures p Case a 0 25 p 12 atm Case b 0 25 p 45 atm Case c 1 0 p 6 5 atm Case d 1 0 p 42 atm Case e 2 0 p 13 5 atm Fig 10 Experimental symbols and HyChem optimized ignition delay time lines conditions a e versus temperature inverse for n heptane Case 4 ignition delay time targeted The five cases represent lean stoichiometric and rich mixtures at low and high pressures Reasonable agreement with experiment is demonstrated in Fig 10 In order to assess the performance of the HyChem mechanism for ignition conditions that are not optimi