Finite-rate Chemical Kinetics Research Articles

Numerical Simulation of the Ram Accelerator Using a New Chemical Kinetics Mechanism

Computational fluid dynamics (CFD) solutions of the full Navier-Stokes equations, including finite-rate chemical kinetics, are used to numerically simulate the reacting in-bore flowfield for a 90-mm (bore diameter) ram-accelerator projectile propulsion system. In this system a gun tube is filled with a high-pressure gaseous mixture of hydrogen, oxygen, and nitrogen. An axisymmetric projectile is launched into this tube, and rails are attached to the tube wall to ensure projectile centering. The shock system that develops around the projectile, along with boundary layers on the projectile and tube surfaces, ignites the mixture on or near the projectile afterbody. The resulting pressure imbalance on the projectile generates thrust. Numerical predictions of this pressure field can be used to evaluate the thrust efficiency of the system, i.e., the projectile design combined with the chemical composition of the propellant gas. Comparison of the predicted pressure field and the measured pressure data is used to judge the accuracy of the CFD code. The choice of chemical kinetics mechanism used in the CFD code is of critical importance in achieving an accurate numerical simulation of the ram accelerator.

Effect of confinement in high-speed reacting mixing layer

High Mach number mixing layers play an important role in the development of supersonic combustor ramjet (scramjet) engines. The mixing of air and fuel is hindered by both shorter combustor residence time and by stability of supersonic shear layer relative to subsonic counterpart. Although many experimental and computational investigations were carried out for supersonic free shear layer [1, 2, 3, 4 and 5] and confined shear layer [6, 7, 8 and 9], the effect of lateral confinement on supersonic mixing layer is not clearly brought out. The fundamental difference in the development of turbulence in the mixing layer and wall boundary layer can affect the structure of the flow and the growth rate of mixing layer significantly. Chakraborty et al. [9] have performed two-dimensional direct numerical simulation (DNS) for high-speed confined reacting shear layer with finite rate chemical kinetics with seven species and seven reactions. Arguments have been provided for treating two-dimensional calculation using the work of Lu and Wu [8], Zhuang et al. [10], Farouk et al. [7], and others who have conducted computational study of the compressibility of high-speed mixing layer and shown that two-dimensional simulation is satisfactory for confined mixing layer. Good comparison of experimental wall pressure distribution with DNS results obtained was considered the basis of further investigations.

Turbulent flame dynamics of homogeneous solid propellant in a rocket motor

A comprehensive numerical analysis has been conducted to study the combustion of a double-base homogeneous propellant in a rocket motor. Emphasis was placed on the motor internal flow development and its influence on propellant combustion. The formulation is based on the Favre-averaged, filtered equations for the conservation laws and takes into account finite-rate chemical kinetics and variable thermophysical properties. Turbulence closure is obtained using the large-eddy-simulation technique. The contribution of large energy-carrying structures to mass, momentum, and energy transfer is computed explicitly, and the effect of small scales of turbulence is modeled. The governing equations and associated boundary conditions are solved using a time-accurate, semi-implicit Runge-Kutta scheme coupled with a fourth-order central difference algorithm for spatial discretization. The motor internal flowfield is basically determined by the balance between the inertia force and the pressure gradient arising from the mass injection at the propellant surface. The temporal evolution of the vorticity field shows a laminar upstream region, a transition zone in the midsection of the chamber, and a fully developed turbulent regime further downstream. The turbulent mixing proceeds at a rate faster than chemical reactions, and the flame stretch is strong enough to regard propellant combustion as a well-stirred reactor. The combustion wave in the laminar region exhibits a two-stage structure consisting of a primary flame, a dark zone, and a secondary luminous flame. The enhanced energy and mass transport in the turbulent region partially merges the primary and secondary flames, thereby raising the temperatures in the dark zone. In the present study, the smoother axial velocity gradient and vertical flow convection prevent turbulence from deeply penetrating into the primary flame zone. The turbulence energy spectra indicate dominant harmonics in a frequency range capable of triggering combustion instabilities.

Axisymmetric Flame Spread Across Propanol Pools in Normal and Zero Gravities

Axisymmetric ignition and flame propagation across propanol pools is investigated numerically with finite-rate one-step chemical kinetics, variable properties, and an adaptive finite-difference gridding scheme without forced gas-phase flow. Propanol fuel is allowed to evaporate into the air after filling the fuel tray and before the igniter is activated. The propanol vapor profile in the gas phase is examined numerically as a function of time. At 1 -g0, a steady fuel vapor-concentration boundary layer is established in the gas phase 5 s after filling a fuel tray. Conversely, at 0-g0, the profile of fuel vapor concentration is always unsteady and keeps growing in the gas phase as time elapses. Axisymmetric flame spread over a shallow circular pool is examined as a function of oxygen concentration. The flame spread rate at \\-g0 is comparable to but lower than that at 0-g 0 for χO2,∞ ≥ 21% and T0 = 22.1°C with ΔtPI = 5s, where ΔtPI denotes the time lapse between filling the fuel tray and activating the igniter. As the oxygen concentration is reduced to 17.5% with the same ΔtPI the flame at 1-g0 pulsates whereas the flame at 0-g0 extinguishes. At 1-g0, the flame spread rate does not change for ΔtPI ≥ 5s; on the other hand, at 0-g0, the flame spread rate increases as ΔtPI is increased. Flame propagation is also examined as a function of initial pool temperature T 0 both for axisymmetric and two-dimensional configurations with pool depth 2 mm in normal gravity. For the uniform spread regime, flame spread rate in the axisymmetric configuration is nearly identical to that in the two-dimensional configuration except for a short initial time. For the nonuniform (or pulsating) spread regime, flame spread in the axisymmetric configuration is quite different from flame spread in the two-dimensional configuration. The axisymmetric flame spreads very slowly without pulsation for some initial time depending on T 0 and then either spreads with pulsations or remains stationary as long as the igniter is activated.

Numerical treatment of multi-phase flow equations with chemistry and stiff source terms

A computational model suitable for multiphase/multispecies flows has been developed. The source term containing the inter-phase interaction and species production/destruction terms can be numerically stiff, due to near-equilibrium chemistry, mass/momentum and energy exchange terms among phases. An Eulerian-Eulerian (E 2) formulation for the conservation equations has been chosen. The chemistry model is described through a multi-step, finite-rate chemical kinetics model with third body reactions. The inviscid fluxes for the right and left states are evaluated using the Total Variation Diminishing (TVD) method. Lax-Friedrichs (LF) and Steger-Warming (SW) numerical fluxes are used to calculate the full flux in the gaseous and liquid phases, respectively. The TVD-LF-SW scheme proved to be robust and suitable for liquid rocket engine applications.

Transient combustion response of homogeneous solid propellant to acoustic oscillations in a rocket motor

Interactions between acoustic waves and the transient combustion response of a double-base homogeneous propellant in a rocket motor have been analyzed numerically. The analysis extends the previous work on gas-phase flame dynamics to include the coupling with condensed-phase processes. Consequently, a more complete description of propellant combustion response to imposed acoustic oscillations can be obtained. Emphasis is placed on the near-surface flame-zone physiochemistry and its coupling with unsteady propellant burning in an oscillatory environment. The formulation treats complete conservation equations and the finite-rate chemical kinetics in both the gas-phase and subsurface regions. The instantaneous propellant burning rate is predicted as part of the solution. Various distinct features of unsteady heat release arising from propellant combustion response in a motor with forced oscillations are studied systematically. As in the pure gas-phase dynamics of the previous case, the dynamic behavior of the luminous flame plays a decisive role in determining the motor stability characteristics. However, the propellant combustion response may qualitatively modify the temporal evolution of heat-release distribution in the luminous flame and as a result exerts a significant influence on the global stability behavior. The primary flame structure adjacent to the propellant surface is usually little affected by flow oscillation. This may be attributed to the large thermal inertial of the condensed phase, which tends to restrain the temperature variation in the near-surface zone in the present study of laminar flows. The situation with a turbulent flow may be drastically different, as turbulence may penetrate directly into the, primary flame and substantially change the local flame dynamics and transport phenomena.

PDF simulation of turbulent non-premixed CH 4/H 2-air flames using automatically reduced chemical kinetics

In this paper, we present numerical simulations of a turbulent non-premixed CH4/H2-air flame based on the solution of the transport equation for the joint velocity and composition probability density function (PDF). A Monte Carlo particle-mesh approach is used to solve the modeled PDF transport equation, in which the mean pressure gradient and turbulent frequency are supplied by a finite-volume mean flow program. The finite-rate chemical kinetics of the CH4/H2-air system is simplified by the method of intrinsic low-dimensional manifolds (ILDM). Simple look-up tables guarantee an easy implementation into the turbulent PDF code. The hybrid solution algorithm is applied to calculate a recently published bluff-body stabilized turbulent non-premixed flame of CH4/H2 by Masri et al. [1]. Two different characteristic flames are presented, where one is close to chemical equilibrium and, for the other, the effects of finite-rate chemistry become significant. The mean temperature distribution and scatter plots for temperature and mass fractions of CO2 and H2O are compared with experimental data. The numerical calculations reproduce the experimentally observed phenomena, such as local extinction, quite well.

Multi-Dimensional Analysis of Turbulent Natural Gas Flames Using Detailed Chemical Kinetics

A numerical approach for predicting multi-dimensional reacting flows is presented. The various interacting processes which occur during combustion are considered: turbulent transport, chemical reaction, and radiative heat transfer. The formulation is based on time-averaged transport equations. Turbulent transport is modeled with the k-ε turbulence model, chemical reactions are considered using the eddy dissipation concept (EDC), and radiative heat transfer is modeled with the discrete ordinates method. The EDC includes influences of both local turbulence and finite-rate chemical kinetics on the reaction rates, and is applicable to general, n-step, elementary reaction mechanisms. The model is applied to two swirling natural gas flames. Predictions are presented for several detailed and reduced reaction mechanisms including the 279-step GRI-Mech. Results indicate that the use of intermediate and detailed reaction mechanisms with the EDC significantly reduces uncertainty associated with simple one- and two-step chemistry, but also that k-ε model underpredicts turbulent transport in the considered flames.

Spectroscopic investigation of the nonequilibrium excitation of NO( A) in hydrocarbon-nitrous oxide flames

A spectroscopic study of three hydrocarbon-nitrous oxide flames was undertaken to investigate the spectral character of the NO gamma band ( A− X) and NO beta band ( B− X) emission. A high-resolution (0.5 Å) 1 m spectrometer was used to record emission spectra from fuel rich atmospheric flames in bandpasses corresponding to the NO gamma and beta bands at 230 and 304 nm, respectively, as well as the OH( A− X) band at 306 nm. In addition, a finite rate chemical kinetics model (CHEMKIN) was exercised to provide a baseline for the flame characteristics. It was found that the OH( A) rotational temperature deduced from the spectra was in good agreement with the predicted flame temperature. However, the NO( A) rotational and vibrational temperature exceeded the flame temperature by over 1000 K for all three flames. Surprisingly, no emission from the NO beta system ( B− X) was detected.

Computational Analysis of Flame Spread Across Alcohol Pools

Pulsating and uniform spread across n-propanot and ethanol liquid fuel pools is simulated via a two-dimensional, transient, numerical model which incorporates finite-rate chemical kinetics, variable properties, and a partially adaptive finite-difference gridding scheme. The model is compared to detailed, independent experimental data. The explanation and characterization of the pulsating and uniform flame spread phenomena are developed Pulsating flame spread requires a gas-phase recirculation cell just forward of the flame. δ flow This cell entrains evaporating fuel vapor. The size and existence of the recirculation cell is determined by the extent of liquid motion ahead of the flame (δ flow) and by opposed flow in the gas phase, naturally induced by buoyancy. The amplitude and period of the pulsations each increase with δ flow Over the range of pool depths that were investigated (2 to 10 mm) the liquid-phase flow is primarily affected by large surface-tension variations along the liquid surface and not b...

A mixing model to improve the PDF simulation of turbulent diffusion flames

A new mixing model based on Euclidean minimum spanning trees (EMST), which has been developed by Subramaniam and Pope, is used in the PDF simulation of pilot-stabilized turbulent non-premixed flames. A model equation is solved for the joint PDF of velocity composition and turbulence frequency using a particle mesh method. Simulations using the EMST mixing model and the IEM (interaction by exchange with the mean) mixing model are compared. A simple thermochemistry equivalent to one-step reaction is used in the calculations. Comparisons are made with experimental measurements in the upstream regions of piloted H 2 /N 2 flames. This fuel is chosen because its chemistry is simple and may be adequately represented by a single-step mechanism. It is found that the EMST model gives the correct mixing pattern for the reactive scalar, as well as the conserved scalar, especially in the early parts of the jet where mixing is most difficult to represent. This result is not achieved by the IEM model. The success of the EMST mixing model is attributable to its satisfying a “localness” condition that other models violate. This is a significant advance that will enable the PDF approach to simulate complex flows with finite rate chemical kinetics.

Reacting flow simulation for a large-scale ram accelerator

Computational fluid dynamics solutions of the full Navier-Stokes equations have been used to numerically simulate the reacting in-bore flowfield for the ram accelerator projectile propulsion system. In this system a projectile and obturator are injected at supersonic velocity into a stationary tube filled with a pressurized mixture of hydrocarbon, oxidizer, and inert gases. Flow stagnation on the obturator initiates combustion of the mixture, before it is discarded. A system of shock waves on the projectile, in conjunction with viscous heating, sustains combustion. The resulting energy release, which travels with the projectile, also generates high pressures that impart thrust to the projectile. Numerical simulation utilizing finite rate chemical kinetics have been used to investigate this flowfield. Numerical results are used to visualize the flowfield, predict the effects of variation in system parameters, and predict projectile in-bore velocity.

Opposed-flow flame spread across n-propanol pools

A computational study is made of the effects of forced, opposed air flow on pulsating and uniform flame spread across n -propanol pools at either normal or zero gravity conditions. The numerical model incorporates finite-rate chemical kinetics, variable properties, and an adaptive gridding scheme in the direction of flame spread. In zero gravity, the combination of forced, opposed flow and thermocapillary-driven concurrent flow can cause a gas-phase recirculation cell to form ahead of the flame and thus lead to flame pulsations. The pulsation mechanism, in this case, is essentially the same as that previously detailed for pulsating flame spread in normal gravity without forced flow [1]. In either normal gravity or zero gravity, increasing the opposed air speed ( U opp ) causes a transition from uniform flame spread to pulsating flame spread. The value of U opp that corresponds to this transition increases with initial pool temperature ( T c ). Unlike with normal gravity flame spread, the mean flame spread rate ( Ū fl ) in zero gravity decreases significantly because of this transition for T c <21°C. As U opp is increased further, both Ū fl and the pulsation frequency increase in zero gravity but change only slightly in normal gravity. For high values of U opp , Ū fl varies little with gravity level. For low values of U opp , the flame spread rate in zero gravity is sensitive to the initial profile of fuel vapor in the gas phase.

Lower-upper scheme for chemically reacting flow with finite rate chemistry

A fourth-order shock-capturing scheme has been developed for steady-state and time-accurate simulation of chemically reacting flows with finite rate chemical kinetics. A diagonal algorithm and a local implicit technique are presented to remove the stiffness of chemical reaction and to achieve high computation efficiency. A fully implicit code is obtained by combining the present algorithm with the lower-upper scheme. The validity of this code is demonstrated by calculating the unsteady shocks in an inviscid supersonic duct and by comparing the results with the previous calculation. Then the code is used to calculate the ignition of a premixed hydrogen/air reacting flow in a ramped duct and nonpremixed hydrogen/air streams as well as nonpremixed methane/air streams in a supersonic mixing layer. The efficiency and robustness of the present scheme are shown through these numerical simulations.

Effects of acoustic oscillations on flame dynamics of homogeneous propellants in rocket motors

The interactions between acoustic waves and gas-phase flame dynamics of a double-base homogeneous propellant in a rocket motor has been studied by means of a comprehensive numerical analysis. The formulation treats the complete conservation equations of mass, momentum, energy, and species concentration, and accounts for finite rate chemical kinetics in the gas phase and subsurface reactions. The model has been implemented to examine the detailed flow structures and heat-release mechanisms in various parts of the motor, including microscale motions near the propellant surface and macroscale motions in the bulk of the chamber. Results indicate that strong interactions between exothermic reactions and acoustic waves occur in regions with steep temperature gradients due to the large activation energy of the associated chemical kinetics. The dynamic behavior of the luminous flame plays a decisive role in determining the motor stability characteristics. Distributed combustion response in the gas phase provides the energy for driving flow oscillations, and can be treated correctly as a combination of monopole and dipole sources based on acoustic theory.

Transcritical Vaporization and Combustion of LOX Droplet Arrays in a Convective Environment

Abstract The behavior of an array of liquid oxygen droplets vaporizing and burning in a gaseous mixture of hydrogen and water vapor at conditions supercritical for both propellants is investigated. The main objective is to investigate the effect of species and temperature non-uniformity (due to the presence of other droplets) on a LOX droplet transcritical behavior. Previously validated high-pressure phase equilibria computation algorithms and appropriate methods for the evaluation of thermophysical properties over wide temperature and pressure ranges are used. A simplified “parallel stream” configuration is considered. However, the contribution of the mass vaporized to the overall mass flux, is included in a quasi-steady manner. Hence the longitudinal velocity is non-uniform. Finite-rate chemical kinetics is used with a reduced four-step mechanism, three of which are assumed to be at partial equilibrium. The droplets are followed in a Lagrangian manner. The model used to predict the droplet behavior incl...

Modeling of nonequilibrium effects in a high-velocity nitrogen-hydrogen plasma jet

A numerical simulation has been performed of a high-velocity nitrogen hydrogen plasma jet in air at atmospheric pressure including finite-rate chemical kinetics. Ions, electrons, and neutral atoms and molecules are treated as separate species in the plasma mixture. The chemical reactions considered are dissociation of molecular species, ionization of atomic species, charge exchange and dissociatioe recombination of nitrogen, and hydrogen-oxygen reactions. The calculational results show that strong departures from ionization and dissociation equilibrium develop in the downstream region as the chemical reactions freeze out at lower temperatures, in spite of the assumed chemical equilibrium at the nozzle exit. The calculations also show that ionized species are over-populated throughout the flow, while dissociated species in the core of the jet are underpopulated near the nozzle exit and become over-populated farther downstream. This initial underpopulation is due to diffusive depletion of dissociated species and enrichment of molecular species in the core of the jet.

OH laser-induced fluorescence velocimetry technique for steady, high-speed, reacting flows

A high-resolution OH laser-induced fluorescence velocity measurement technique was developed for use in steady, high-speed, reacting flows. A narrow-linewidth laser source was tuned through an isolated OH absorption line to measure the Doppler-shifted line center frequency relative to an iodine reference line. A counterpropagating beam approach was used to eliminate the collisional impact shift and minimize systematic errors. Results from pointwise measurements of velocity in a unique reacting underexpanded jet facility are compared to an axisymmetric Navier-Stokes calculation with finite-rate chemical kinetics as a test of the technique over a wide range of flow conditions. The measured and calculated velocities in the supersonic jet core agree on average to within 1.3%. The uncertainty in the velocity measurement in the jet core was on average +/- 6.0% for a single measurement and +/- 3.5% for the average value of three scans. Potential errors caused by absorption effects were not detected in these measurements. 50 refs.

The Non-Equilibrium Structure of a Trichloro-ethene Methane Laminar Diffusion Flame

ABSTRACT Experimental measurements of scalar quantities in laminar counter-flow diffusion flames of mixtures of trichloroethylene (TCE) with methane have been compared with an equilibrium calculation. The data are correlated in terms of a mixture fraction. Data for stable major and minor species were obtained by using gas sampling with gas chromatography (GC) and a GC/mass spectrometer in flames with high (248 s−1) and low (175 s−1) strain rates. Calculations indicated that TCE mass fractions at equilibrium were very small, even at a relatively low temperature (600 K). However, the GC measurements showed that TCE persisted well into the flame. Strain rate was found to have a small but measurable effect on the correlation of species mass fractions and temperature with mixture fraction. The comparison of equilibrium predictions with measurements in mixture fraction space suggests that finite rate chemistry and chemical kinetics should be considered in the modeling of chlorinated hydrocarbon turbulent diffus...

Buoyant downward diffusion flame spread and extinction in partial-gravity accelerations

This paper describes experimental observations of downward, opposed-flow flame spreading made underpartial-gravity conditions aboard NASA research aircraft. Special apparatus and techniques for these tests are described, including schlieren imaging of dim near-limit flames. Flame-spreading and flammability limit behaviors of a thin cellulosic fuel, 1×10 −3 g/cm 2 tested at 1 atm of pressure in oxygen/nitrogen mixtures of 13–21% oxygen by volume, are described for effective acceleration levels ranging from 0.05 to 0.6 times normal earth gravity (1 g ). Downward-burning flammability increases in partial gravity, with the limiting oxygen fraction falling from 15.6% oxygen in 1 g to 13–14% oxygen in 0.05–0.1 g . Flame-spread rates are shown to peak in partial gravity, increasing by 20% over the 1- g value in air (21% oxygen). Partial-gravity flame-spreading results, corrected for fuel density and thickness, are consistent with results obtained at acceleration levels above 1 g in a centrifuge. The results compare qualitatively with predictions of flame spreading in buoyant flow by models that include finite-rate chemical kinetics and surface and gas-phase radiative loss mechanisms. A correlation of experimental buoyant downward flame-spread results is introduced that accounts for radiative heat losses using a dimensionless spread rate, V f o , a radiation/conduction number. S R , and the Damkohler number, Da , as parameters. The correlation includes data from 0.05 g to 4.25 g and oxygen/nitrogen mixtures from 14% to 50% oxygen.