Chemical Source Term Research Articles

Large Eddy Simulation of a Turbulent Reacting Jet‐Flame

AbstractThe high nonlinearity of the chemical reaction terms requires a closure model for the chemical source terms occurring in the spatially filtered scalar transport equations. Based on the Conditional Moment Closure hypothesis a new model was recently proposed for LES of non‐premixed combustion. The new model was applied to an LES of a piloted jet flame to assess the model's robustness and predictive capabilities.

00/03575 Modelling of combustion of low grade lignites in fluidized beds with heat extraction

Based on the flamelet concept, a numerical model has been developed for fast predictions of NOX and CO emissions from laminar flames. The model is applied to studying NO formation in the secondary nonpremixed flame zone of fuel-rich methane Bunsen flames. By solving the steady-state flamelet equations with the detailed GRI2.1 methane–air mechanism, a flamelet library is generated containing thermochemical information for a range of scalar dissipation rates at the ambient pressure condition. Modeling of NO formation is made by solving its conservation equation with chemical source term evaluated based on flamelet library using the extended Zeldovich mechanism and “NO reburning reactions.” The optically-thin radiation heat transfer model is used to explore the potential effect of heat loss on thermal NO formation. The numerical scheme solves the two-dimensional Navier–Stokes equations as well as three additional equations: the mixture fraction, the NO mass fraction, and the enthalpy deficit due to radiative heat loss. With an established flamelet library, typical computing times are about 5 hours per calculation on a DEC-3000 300LX workstation. The predicted mixing field, radial temperature profiles, and NO distributions compare favorably with recent experimental data obtained by Nguyen et al. [2]. The dependence of NOX emission on equivalence ratio is studied numerically and the predictions are found to agree reasonably well with the measurements by Muss [3]. The computed results show a decreasing trend of NOX emission with the equivalence ratio but an increasing trend in the CO emission index. By examining this trade-off between NOX and CO, an optimal equivalence ratio of 1.4 is found to yield the lowest combined emission.

超軌道速度再突入カプセル前方衝撃波層の数値解析

The calculation code originally developed for a hypersonic nonequilibrium flow is applied to the flowfield in front of a super orbital-velocity reentry capsule. The re-entry speed is assumed to be 12km/sec. The governing equations for a chemically and thermally nonequilibrium flow consist of the full Navier-Stokes equations, including the 11 chemical species mass conservation equations and the vibrational-electronic energy conservation equation. The Park's two-temperature model is used for the chemical reaction rates. A Harten-Yee type upwind TVD scheme is used to solve the governing equations with a fractional step method. A semi-implicit scheme is introduced because of the stiffness of chemical source terms. Under a super orbital-velocity re-entry conditions, the results of numerical calculations indicate that the vibrational excitation behind a strong bow shock is prevented by nitrogen molecule dissociation. The obtained distributions of vibrational and translational temperatures and species mass fractions are essentially sufficient to yield not only the convective but also the radiative heat transfer to the capsule surface using the existing NEQAIR code.

An adaptive 3-D CFD solver for modeling explosions on large industrial environmental scales

The paper describes the computer code REACFLOW, developed at the JRC for the numerical simulation of compressible gas flows with chemical reactions, with the objective of studying large-scale chemical explosions. The code employs a finite-volume scheme on an unstructured 2-D or 3-D grid, coupled with turbulence models, and modules for either finite-rate chemistry source terms or a model for the interaction between turbulence and combustion. To overcome the problems which are related to different scales, an adaptive fully reversible CFD method is used. New grid points are temporarily inserted into the mesh to track strong disturbances in the flow (such as shocks or flame fronts) and removed when not required. The code has been tested on a number of different 2-D and 3-D problems, including fast turbulent deflagrations and detonations on medium and large scale problems

Conditional moment closure for large eddy simulation of nonpremixed turbulent reacting flows

A method for closing the chemical source terms in the filtered governing equations of motion is proposed. Conditional filtered means of quantities appearing in the chemical reaction rate expressions are approximated by assuming that these conditional filtered means are constant for some ensemble of points in the resolved flow field; for such an ensemble, integral equations can be solved for the conditional filtered means. These conditional filtered means are then used to approximate the conditional filtered mean of the chemical source term by invoking the Conditional Moment Closure hypothesis. The filtered means of the chemical source terms are obtained by integrating their conditional filtered means over the filtered density function of the conditioning variable(s). The method is applied to direct numerical simulation results to directly compare the prediction of the reaction rates with the actual filtered reaction rates. The results of this a priori test appear to show that the method is capable of predicting the filtered reaction rates with adequate accuracy—even in the presence of heat release, and local extinction phenomena. This is especially true for predictions obtained using two conditioning variables.

Modeling of NOx and Soot Formation in Diesel Combustion

N Modeling of NO x and Soot Formation in Diesel Combustion N An approach to model the formation and oxidation or reduction of soot and NO in turbulent diffusion flames is presented. The model is based on the flamelet library approach and extended to account for radiative heat losses in the flame. Due to the rather slow processes leading to soot and NO a modified flamelet library approach is used. Instead of taking the mass fractions directly from flamelet libraries the different source terms for soot and NO formation are calculated and a transport equation for the mean mass fractions is solved in the CFD calculation. The source terms are obtained from laminar counterflow-flame calculations using a detailed chemistry model for the gas phase species and the formation and oxidation of soot. Transport equations for the mean mixture fraction and the mixture fraction variance are solved and the chemical source term is closed by presuming a beta-function like distribution of mixture fraction and a log-normal distribution of the scalar dissipation rate. The model was first tested in laminar and turbulent jet flames. By applying a reduction strategy for the flamelet libraries of the source terms it was made applicable to the simulation of soot formation in a Diesel spray taking different oxidizer temperatures and pressures into account. Additionally, different formulations of the flamelet equations have been tested and their accuracy has been evaluated by comparing them to turbulent flame experiments.

The kinetic chemical equilibrium regime

We investigate reactive gas mixtures in the kinetic chemical equilibrium regime. Our starting point is a generalized Boltzmann equation with a chemical source term valid for arbitrary reaction mechanisms and yielding a positive entropy production. We first study the Enskog expansion in the kinetic chemical equilibrium regime. We derive a new set of macroscopic equations in the zeroth- and first-order regimes, expressing conservation of element densities, momentum and energy. The transport fluxes arising in the Navier–Stokes equilibrium regime are the element diffusion velocities, the heat flux vector and the pressure tensor and are written in terms of transport coefficients. Upon introducing species diffusion velocities, the kinetic equilibrium regime appears to be formally equivalent to the one obtained for gas mixtures in chemical nonequilibrium and then letting the chemical reactions approach equilibrium. The actual values of the transport coefficients are, however, different. Finally, we derive the entropy conservation equation in the Navier–Stokes equilibrium regime and show that the source term is positive and that it is compatible with Onsager’s reciprocal relations.

Detonation capturing for stiff combustion chemistry

This paper contributes to the topic of unphysical one-cell-per-time-step travelling combustion wave solutions in numerical computations of detonation waves in the presence of stiff chemical source terms. These false weak detonation solutions appear when a gas-dynamics–chemistry operator-splitting technique is used in conjunction with modern shock-capturing schemes for compressible flow simulations. A detailed analysis of piecewise constant three-state weak solutions of the Fickett–Majda detonation model equations is carried out. These structures are idealized analogues of the fake numerical solutions observed in computations. The analysis suggests that the problem can be cured by introducing a suitable ignition temperature below which the chemistry is frozen. It is found that the threshold temperatures needed to effectively suppress the undesired numerical artefacts are considerably lower than any temperature actually found in the reaction zone of a resolved detonation. This is in contrast to earlier suggestions along the same lines in the literature and it allows us to propose the introduction of such a low and otherwise irrelevant ignition temperature threshold as a routine measure for overcoming the problem of artificial weak detonations. The criterion for choosing the ignition temperature is then extended to the reactive Euler equations and extensive computational tests for both the model and the full equations demonstrate the effectiveness of our strategy. We consider the behaviour of a first-order Godunov-type scheme as well as its second-order extension in space and time using van Leer's MUSCL approach and Strang splitting.

An Efficient Multigrid Algorithm for Compressible Reactive Flows

This paper presents a parallel multigrid method for computing inviscid and viscous high speed steady-state reactive flows. The governing equations for reactive flow are solved using an explicit multigrid algorithm while treating the chemical source terms in a point implicit manner. The CUSP (Convective Upwind and Split Pressure) scheme is used to provide necessary artificial dissipation without contaminating the solution. This explicit method yields excellent parallel speedups, thus enabling the calculation of reactive flows with detailed chemical kinetics including large numbers of species and reactions. Results indicate good multigrid speedups and adequate resolution of the reaction zone in both inviscid axisymmetric and viscous two-dimensional hydrogen/oxygen and hydrogen/air test cases.

Numerical Modeling of NO Formation in Laminar Bunsen Flames—A Flamelet Approach

Based on the flamelet concept, a numerical model has been developed for fast predictions of NO X and CO emissions from laminar flames. The model is applied to studying NO formation in the secondary nonpremixed flame zone of fuel-rich methane Bunsen flames. By solving the steady-state flamelet equations with the detailed GRI2.1 methane–air mechanism, a flamelet library is generated containing thermochemical information for a range of scalar dissipation rates at the ambient pressure condition. Modeling of NO formation is made by solving its conservation equation with chemical source term evaluated based on flamelet library using the extended Zeldovich mechanism and “NO reburning reactions.” The optically-thin radiation heat transfer model is used to explore the potential effect of heat loss on thermal NO formation. The numerical scheme solves the two-dimensional Navier–Stokes equations as well as three additional equations: the mixture fraction, the NO mass fraction, and the enthalpy deficit due to radiative heat loss. With an established flamelet library, typical computing times are about 5 hours per calculation on a DEC-3000 300LX workstation. The predicted mixing field, radial temperature profiles, and NO distributions compare favorably with recent experimental data obtained by Nguyen et al. [2]. The dependence of NO X emission on equivalence ratio is studied numerically and the predictions are found to agree reasonably well with the measurements by Muss [3]. The computed results show a decreasing trend of NO X emission with the equivalence ratio but an increasing trend in the CO emission index. By examining this trade-off between NO X and CO, an optimal equivalence ratio of 1.4 is found to yield the lowest combined emission.

Simulation of Supersonic Reacting Hydrocarbon Flows with Detailed Chemistry

This paper presents a parallel multigrid method for computing inviscid and viscous high speed steady-state flows with reacting hydrocarbons. The governing equations for reactive flow are solved using an explicit multigrid algorithm while treating the chemical source terms in a point implicit manner. The CUSP (Convective Upwind and Split Pressure) scheme is used to provide necessary artificial dissipation without contaminating the solution. This explicit method yields excellent parallel speedups, thus enabling the calculation of reactive flows with detailed chemical kinetics including large numbers of species and reactions. Results indicate good multigrid speedups and adequate resolution of the reaction zone in inviscid and viscous two-dimensional hydrogen/air and methane/air test cases.

An Efficient Computational Model for Premixed Turbulent Combustion at High Reynolds Numbers Based on a Turbulent Flame Speed Closure

Theoretical background, details of implementation, and validation results for a computational model for turbulent premixed gaseous combustion at high turbulent Reynolds numbers are presented. The model describes the combustion process in terms of a single transport equation for a progress variable; turbulent closure of the progress variable’s source term is based on a model for the turbulent flame speed. The latter is identified as a parameter of prime significance in premixed turbulent combustion and determined from theoretical considerations and scaling arguments, taking into account physico-chemical properties and local turbulent parameters of the combustible mixture. Specifically, phenomena like thickening, wrinkling, and straining of the flame front by the turbulent velocity field are considered, yielding a closed form expression for the turbulent flame speed that involves, e.g., speed, thickness, and critical gradient of a laminar flame, local turbulent length scale, and fluctuation intensity. This closure approach is very efficient and elegant, as it requires only one transport equation more than the non reacting flow case, and there is no need for costly evaluation of chemical source terms or integration over probability density functions. The model was implemented in a finite-volume-based computational fluid dynamics code and validated against detailed experimental data taken from a large-scale atmospheric gas turbine burner test stand. The predictions of the model compare well with the available experimental results. It has been observed that the model is significantly more robust and computationally efficient than other combustion models. This attribute makes the model particularly interesting for applications to large three-dimensional problems in complicated geometries.

Similarity solution of mixed convection with diffusion and chemical reaction over a horizontal moving plate

The mixed convective heat and mass transfer over a horizontal plate has been investigated. A diffusion equation with a chemical reaction source term is taken into account. By applying transformation group theory to the analysis of the governing equations, we obtain a similarity solution of the problem in the case that the temperature and concentration at the wall and the moving speed of the plate are proportional to power distributions along the distance from the leading edge. Furthermore the similarity equations have been solved numerically by a fourth-order Runge-Kutta scheme. The numerical results obtained for various values of the Schmidt number, chemical reaction parameter and buoyancy parameters reveal the influence of the parameters on the flow, heat and mass transfer behavior.

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.

ASYMPTOTIC STABILITY OF EQUILIBRIUM STATES FOR MULTICOMPONENT REACTIVE FLOWS

We consider the equations governing multicomponent reactive flows derived from the kinetic theory of dilute polyatomic reactive gas mixtures. Using an entropy function, we derive a symmetric conservative form of the system. In the framework of Kawashima and Shizuta's theory, we recast the resulting system into a normal form, that is, in the form of a symmetric hyperbolic–parabolic composite system. We also characterize all normal forms for symmetric systems of conservation laws such that the null space associated with dissipation matrices is invariant. We then investigate an abstract second-order quasilinear system with a source term, around a constant equilibrium state. Assuming the existence of a generalized entropy function, the invariance of the null space naturally associated with dissipation matrices, stability conditions for the source term, and a dissipative structure for the linearized equations, we establish global existence and asymptotic stability around the constant equilibrium state in all space dimensions and we obtain decay estimates. These results are then applied to multicomponent reactive flows using a normal form and the properties of Maxwellian chemical source terms.

Second-order conditional moment closure for turbulent jet diffusion flames

The limited success in predicting nitric oxide concentrations in turbulent hydrogen-air diffusion flames using conditional first-moment closure indicates the importance of the correlations of the conditional fluctuations. Hence, a second-order closure for the chemical reaction rate term is suggested. Correction terms that account for moments of higher order are introduced. They are derived from a global one-step mechanism for hydrogen-air combustion. Assuming the radicals O, H, and OH to be in partial equilibrium and the minor radicals such as HO 2 and H 2 O 2 in steady state, chemical reaction rates can be represented by a two-variable formalism for a given enthalpy. Then, second-order moments of combined variables can be used to find more accurate solutions of the conditionally averaged chemical source terms. The model is complemented by a conditional variance transport equation. The validity of the model has been verified by comparison with experimental data, and good to excellent predictions of nitric oxide levels are achieved in undiluted and helium-diluted hydrogen jet flames.

Load Balancing and Performance Issues for Data Parallel

A data parallel program is presented that solves the reactive Euler equations for stiff chemical nonequilibrium ows on Connection Machines CM-2/200 and CM-5/5E. The program is written in CM Fortran and uses direction and time-step splitting to couple representations of the chemical and uid dynamicprocesses on a structured Cartesian grid.An explicit high-ordermonotonealgorithmwith nonlineardamping is used to integrate the convection terms, and a hybrid asymptotic/modi® ed-Euler approach is used to solve the system of ordinary differential equations from the chemical source terms. Integration of the uid dynamics was conservatively determined to be 9.4 and 12.0 G ops on a 512-node CM-5 and CM-5E, respectively. The uid dynamics solver scaled well for large problems; however, both the performance and the scaling are signi® cantly affected by the nearest-neighbor communications, which accounted for at least 24% of the execution time on the CM-5. For the integration of the chemistry source terms, poor load balancing signi® cantly affected performance of the program. Therefore, a new load-balancing algorithmwas developed that reduces the chemistry integration time by a factor of six for the test problem, a detonation propagating in a hydrogen± oxygen± argon mixture. Moreover, the chemistry integration time, with the load balancing, is slightly less than the time required to integrate the uid dynamics. As a result, an ef® cient data parallel program for solving stiff chemical nonequilibrium ows is available for problems that were too expensive to solve in the past.

Counter-gradient diffusion in a confined turbulent premixed flame

In the present study, we develop a full second order model and a new flamelet closure relation for the mean chemical source term to describe turbulent reactive flows with premixed reactants. This description ensures that non-gradient and counter-gradient diffusion which can appear in such flames, are taken into account in 2-D or 3-D geometries. 2-D calculations are performed in the case of a confined turbulent premixed flame stabilized by a backward facing step, a configuration which reveals experimentally counter-gradient diffusion and combustion induced production of turbulence. Numerical results are found to be in excellent agreement with measurements of Shepherd et al. [Nineteenth Symposium (International) on Combustion (The Combustion Institute, Pittsburgh, 1982)]. The important influence of counter-gradient diffusion on first order quantities, i.e., mean velocity and length of the recirculation zone is shown.

Load balancing and performance issues for data parallel simulation of stiff chemical nonequilibrium flows

A data parallel program is presented that solves the reactive Euler equations for stiff chemical nonequilibrium flows on Connection Machines CM-2/200 and CM-5/5E. The program is written in CM Fortran and uses direction and time-step splitting to couple representations of the chemical and fluid dynamic processes on a structured Cartesian grid. An explicit high-order monotone algorithm with nonlinear damping is used to integrate the convection terms, and a hybrid asymptotic/modified-Euler approach is used to solve the system of ordinary differential equations from the chemical source terms. Integration of the fluid dynamics was conservatively determined to be 9.4 and 12.0 Gflops on a 512-node CM-5 and CM-5E, respectively. The fluid dynamics solver scaled well for large problems. Therefore, a new load-balancing algorithm was developed that reduces the chemistry integration time by a factor of six for the test problem, a detonation propagating in a hydrogen-oxygen-argon mixture. Moreover, the chemistry integration time, with the load balancing, is slightly less than the time required to integrate the fluid dynamics.

A NOx Prediction Scheme for Lean-Premixed Gas Turbine Combustion Based on Detailed Chemical Kinetics

The lean-premixed technique has proven very efficient in reducing the emissions of oxides of nitrogen (NOx) from gas turbine combustors. The numerical prediction of NOx levels in such combustors with multidimensional CFD codes has only met with limited success so far. This is to some extent due to the complexity of the NOx formation chemistry in lean-premixed combustion, i.e., all three known NOx formation routes (Zeldovich, nitrous, and prompt) can contribute significantly. Furthermore, NOx formation occurs almost exclusively in the flame zone, where radical concentrations significantly above equilibrium values are observed. A relatively large chemical mechanism is therefore required to predict radical concentrations and NOx formation rates under such conditions. These difficulties have prompted the development of a NOx postprocessing scheme, where rate and concentration information necessary to predict NOx formation is taken from one-dimensional combustion models with detailed chemistry and provided—via look-up tables—to the multidimensional CFD code. The look-up tables are prepared beforehand in accordance with the operating conditions and are based on CO concentrations, which are indicative of free radical chemistry. Once the reacting flow field has been computed with the main CFD code, the chemical source terms of the NO transport equation, i.e., local NO formation rates, are determined from the reacting flow field and the tabulated chemical data. Then the main code is turned on again to compute the NO concentration field. This NOx submodel has no adjustable parameters and converges very quickly. Good agreement with experiment has been observed and interesting conclusions concerning superequilibrium O-atom concentrations and fluctuations of temperature could be drawn.