__________________________________________________________________ | combustion | 1 | Combustion fundamentals | | lecture | ---- | by | | 1 | 20 | D.B.Spalding | |_____________|_______|___________________________________________| | | | Contents: | | | | 1. Chemical-species sources and sinks; general ideas | | | | 2. The simple chemically-reacting system (SCRS) | | Definition | | Implications | | Temperature | | Density | | Reaction rate | | Turbulence | | | | 3. Concluding remarks | |_________________________________________________________________|__________________________________________________________________ | combustion | 2 | 1.Chemical-species sources and sinks; | | lecture | ---- | general ideas,1: | | 1 | 20 | Types of chemical reactions | |_____________|_______|___________________________________________| | | | Chemical reactions are usually either:- | | | | * mono-molecular, in which molecules of one species break up,| | forming two or more other species, eg: | | | | H2 -> H + H ; H2O -> H + OH ; CO2 -> CO + O | | | | * bi-molecular, in which two molecules combine to form one | | or more other species, eg: | | | | H + H -> H2 ; H + O2 -> OH + O ; O + H -> OH | | | | * (rarely) tri-molecular, in which three molecules react. | |_________________________________________________________________|
__________________________________________________________________ | combustion | 3 | 1.Chemical-species sources and sinks; | | lecture | ---- | general ideas,2: | | 1 | 20 | Energy of reaction | |_____________|_______|___________________________________________| | | | * All chemicals reaction involve the release or absorption of| | proportionate amounts of energy. | | | | * Reactions releasing energy are called "exothermic"; those | | absorbing it are called "endothermic". | | | | * The amounts of energy involved are deducible from the | | thermodynamic properties of the reactants; they are thus | | independent of the rates at which the reactions proceed. | | | | * Thermodynamics is a well-developed subject. Quantitative | | knowledge of energy releases exists for all reactions of | | interest to combustion specialists. | |_________________________________________________________________|
__________________________________________________________________ | combustion | 4 | 1.Chemical-species sources and sinks; | | lecture | ---- | general ideas,3: | | 1 | 20 | Reversibility and equilibrium | |_____________|_______|___________________________________________| | | | | | * All chemical reactions are reversible, ie they can proceed | | in either direction. Thus: | | | | H2 -> H + H and H + H -> H2 both proceed together | | | | * "Equilibrium" is the state in which the rates of both | | "forward" and "backward" reactions are equal. | | | | * This occurs when [H2]/[H]**2 has a specific value, called | | the "equilibrium constant", dependent on temperature. | | | | Here [H2] stands for kg.moles of H2 per m**3; etc... | |_________________________________________________________________|
__________________________________________________________________ | combustion | 5 | 1.Chemical-species sources and sinks; | | lecture | ---- | general ideas,4: | | 1 | 20 | The rate of a chemical reaction | |_____________|_______|___________________________________________| | | | * The rate of a chemical reaction, measured (say) in km.moles| | of reactant consumed per unit volume and time, varies with | | concentration, temperature and pressure. | | | | * Typically, R1 + R2 -> R3 + R4 proceeds at a rate given by | | the "Arrhenius" expression: | | | | dR1/dt = - const1*[R1]*[R2]*exp(-const2/T) | | + const3*[R3]*[R4]*exp(-const4/T) | | | | where const1, const2, const3 and const4 are specific to | | the reactants in question, and T is the absolute | | temperature. | |_________________________________________________________________|
__________________________________________________________________ | combustion | 6 | 1.Chemical-species sources and sinks; | | lecture | ---- | general ideas,5: | | 1 | 20 | Chemical kinetics | |_____________|_______|___________________________________________| | | | * The science concerned with rates of reaction is called | | "chemical kinetics". | | | | * Although incomplete, in that many chemical reactions remain| | to be fully explored, chemical kinetics has collectly much | | more information than it is practicable to incorporate into| | engineering-scale combustion simulations. | | | | * For example, it is known that the burning of a hydrocarbon | | in air proceeds by way of hundreds of distinguishable | | chemical reactions, involving tens of intermediate chemical| | species. Only the initial and final states are represented | | by: fuel + oxygen -> products. | |_________________________________________________________________|
__________________________________________________________________ | combustion | 7 | 2. The "simple chemically-reacting system"| | lecture | ---- | (SCRS), 1: | | 1 | 20 | Definition | |_____________|_______|___________________________________________| | | | * The SCRS is a "model", ie a simplification of reality, | | which still represents reality in practically important | | respects, and facilitates thought and computation. | | | | * The SCRS postulates that combustion does proceed via | | fuel + oxygen -> products WITHOUT intermediates.| | | | * This reaction is taken as irreversible; ie the rate of the | | reverse reaction is presumed to be very low. | | | | * The energy released, called the "heat of combustion" ,is | | taken as independent of temperature; this implies equality | | (even constancy) of specific heats of reactants & products.| |_________________________________________________________________|
__________________________________________________________________ | combustion | 8 | 2. The "simple chemically-reacting system"| | lecture | ---- | (SCRS), 2: | | 1 | 20 | Implications | |_____________|_______|___________________________________________| | | | * The enthalpy of a mixture of fuel, oxidant and products | | can be taken as given by: | | | | h = cp*T + H*mf | | | | where cp is constant-pressure specific heat, T is absolute | | temperature, H is heat of combustion and mf is mass | | fraction of unburned fuel. | | | | * The ratios of the masses of fuel, oxidant and products | | engaging in a reaction are: 1, r and (1+r) respectively, | | where r is a constant. Typically, r = 3.5, when the fuel | | is a hydrocarbon and the oxidant is undiluted oxygen. | |_________________________________________________________________|
__________________________________________________________________ | combustion | 9 | 2. The "simple chemically-reacting system"| | lecture | ---- | (SCRS), 3: | | 1 | 20 | Equality of diffusion coefficient| |_____________|_______|___________________________________________| | | | * An often-used extension of the SCRS definition is that | | the diffusion coefficients of fuel, oxidant and product | | are all equal to each other, and to the diffusivity of | | heat; so their Prandtl/Schmidt numbers are equal. | | | | * This is not far from the truth for laminar gaseous flow; | | and it is very close to the truth for turbulent fluids. | | | | * An important consequence is that it is possible to describe| | the composition of a reacting mixture by just two variables| | for example: mf and f, where f is the "mixture fraction", | | ie the mass of material originating from fuel, per unit | | mass of mixture, regardless of whether it is burned or not.| |_________________________________________________________________|
__________________________________________________________________ | combustion | 10 | 2. The "simple chemically-reacting system"| | lecture | ---- | (SCRS), 4: | | 1 | 20 | Composition of fully-reacted gas | |_____________|_______|___________________________________________| | 1| . x | | ^ | .<--- products x | | | | . . x | | | | . x | | products| . . x | | oxygen, | . x <-- unburned fuel | | unburned| . . x | | fuel |* x . | | | *. x . . | | | *<-oxygen x . | | | . * x . | | | * x . | | |. * mixture fraction f ---> . | | 0-------*--------------------------------------1 | |_________________________________________________________________|
__________________________________________________________________ | combustion | 11 | 2. The "simple chemically-reacting system"| | lecture | ---- | (SCRS), 5: | | 1 | 20 | Reaction rate for fixed f and h | |_____________|_______|___________________________________________| | |* oxygen---> x . . | | | * x . . | | | * x . . | | | * x . . | | | * x .<--reaction | | | unburned fuel---> * . x . rate | | | * . x . | | | . * x | | | . * x. | | | . * x | | | . * . x | | | . * . | | ------------------------------------------------* | | 0 reactedness ( = (T - Tu)/(Tb - Tu) ) 1 | |_________________________________________________________________|
__________________________________________________________________ | combustion | 12 | 2. The "simple chemically-reacting system"| | lecture | ---- | (SCRS), 6: | | 1 | 20 | Features relevant to PHOENICS | |_____________|_______|___________________________________________| | | | * The f and h equations have no source terms. | | | | * Temperature can be deduced from h via: T = (h - mf*H)/cp. | | | | * mox can be deduced from mox = A + B*f + C*mf, where A,B,C | | are constants. | | | | * The mf equation has a reaction-rate source of the form: | | | | source of fuel = - const * mf * mox * function of T | | | | * When the reaction-rate constant is large, there is no need | | to solve for mf; it depends only on f (see panel 10 above).| |_________________________________________________________________|
__________________________________________________________________ | combustion | 13 | 2. The "simple chemically-reacting system"| | lecture | ---- | (SCRS), 7: | | 1 | 20 | How sources terms are calculated | |_____________|_______|___________________________________________| | | | * The equation: source = - const * mf can be created by | | PATCH(any name,VOLUME, , , , , , , , ) | | COVAL(patch name, FUEL, const, 0.0) ; | | for this makes: source = coeff * ( 0.0 - fuel ) . | | | | * The equation: source = const * ( 1 - rctd) * rctd ** expnt | | can be created by the following (library case 109): | | | | A non-linear source of RCTD is present | | PATCH(CHSOTERM,VOLUME,1,NX,1,1,1,1,1,LSTEP) | | COVAL(CHSOTERM,RCTD,GRND7,1.0) | | RSG3=1.0E8;RSG4=6.0 | | * Patch names starting CHSO activate chemical sources. | |_________________________________________________________________|
__________________________________________________________________ | combustion | 14 | 2. The "simple chemically-reacting system"| | lecture | ---- | (SCRS), 8: | | 1 | 20 | How densities may be calculated | |_____________|_______|___________________________________________| | | | * Density is calculated as p * mol wt / (gas const * T) via: | | RHO1=GRND6;RHO1A=WFU;RHO1B=WAIR;RHO1C=WPR | | which activates this section of GXRHO called from GREX2: | |C..The parameters RHOA, RHOB & RHOC are the molecular weights | |C..of these constituents of the gas. | | MOXID=INAME('OXID') | | CALL SUB2(MFUEL,INAME('FUEL'),MPROD,INAME('PROD')) | | FN12(Y,X1,X2,X3,A,B1,B2,B3) Y = A + B1*X1 + B2*X2 + B3*X3| |C.. the following call puts the reciprocal of rho in AUX(DEN) | 1 CALL FN12(AUX(DEN),MFUEL,MOXID,MPROD,0.0,1.0/RHOA,1.0/RHOB, | | 11.0/RHOC) | | FN68(Y,X1,X2,X3,A,B) Y = (A + B*X1)/(X2*X3) | | CALL FN68(AUX(DEN),P1,AUX(DEN),AUX(TEMP),PRESS0/8314.3, | 1 11.0/8314.3) | |_________________________________________________________________| __________________________________________________________________ | combustion | 15 | 2. The "simple chemically-reacting system"| | lecture | ---- | (SCRS), 9: | | 1 | 20 | How temperatures may be calculated | |_____________|_______|___________________________________________| | | | * Temperature may be calculated by way of the command: | | TMP1=GRND8;TMP1A=CPFU;TMP1B=CPPR;TMP1C=CPAIR | | | | * The first statement ensures that, provided USEGRX is TRUE, | | the subroutine GXTEMP will be called for the first-phase | | temperature, where the section represented by GRND8 will | | be visited. | | | | * The subsequent statements carry information about the | | specific heats of fuel, products and air into EARTH. | | | | * Other options are available. | | | | * The user is also free to introduce options of his own. | |_________________________________________________________________|
__________________________________________________________________ | combustion | 16 | 2. The "simple chemically-reacting system"| | lecture | ---- | (SCRS), 10:: | | 1 | 20 | Reaction rates in turbulent flows | |_____________|_______|___________________________________________| | | | * In turbulent flows, with <...> denoting time averages, | | < rate(rctd) > does NOT equal rate(
) , | | because of the non-linearity of rate; and | | | | < mf * mox > does NOT equal < mf > * < mox ) , | | because mf and mox may be finite only at different times. | | | | * Since CFD codes compute only < rctd >, < mf > and < mox > | | but need < rate > , new formulae are needed for turbulent | | flow. | | | | * No certain or universal method has yet been discovered; but| | some guesses have proved lucky. | |_________________________________________________________________| __________________________________________________________________ | combustion | 17 | 2. The "simple chemically-reacting system"| | lecture | ---- | (SCRS), 11: | | 1 | 20 | The eddy-break-up formula | |_____________|_______|___________________________________________| | | | * Experiment shows that reaction rates are often more greatly| | affected by local turbulence than by chemical-kinetic | | factors. | | | | * The eddy-break-up model (Spalding,1971) rests on the | | hypothesis that ONLY turbulence and fuel concentration | | affect the rate. | | | | * The first version was: rate =-const * rho*mf* abs.vel.grad| | | | * The second version was: rate =-const * rho*mf* epsilon/k | | | | * Both work fairly well; but they are only approximate. | |_________________________________________________________________|
__________________________________________________________________ | combustion | 18 | 2. The "simple chemically-reacting system"| | lecture | ---- | (SCRS), 12: | | 1 | 20 | The eddy-break-up model in PHOENICS | |_____________|_______|___________________________________________| | | | * The eddy-break-up model can be activated in PHOENICS by | | the SATELLITE commands: | | PATCH(CHSO,PHASEM,1,NX,1,NY,1,NZ,1,1) | | COVAL(CHSO,FUEL,GRND9,GRND9) | | | | * These activate the appropriate section of GXCHSO, called | | from GREX2. | | | | * The coding style adopted there is transparent, so that | | users may easily introduce any modifications that they | | think appropriate. | | | | | |_________________________________________________________________|
__________________________________________________________________ | combustion | 19 | 2. The "simple chemically-reacting system"| | lecture | ---- | (SCRS), 13: | | 1 | 20 | The two-fluid model of combustion | |_____________|_______|___________________________________________| | | | * PHOENICS is being used as the research vehicle for | | investigating the two-fluid model of turbulent combustion.| | | | * The central idea is that burning gases are composed of | | hotter and colder fragments of gas, intermingled, and in | | relative motion. | | | | * Mass transfer between fragments brings together hotter and| | colder (or fuel-richer and oxygen-richer) gases, and leads| | to combustion, or, if too rapid, to quenching. | | | | * The model can explain why reaction rate is turbulence- | | controlled in many conditions, but not always. | |_________________________________________________________________|
__________________________________________________________________ | combustion | 20 | | | lecture | ---- | 3. Concluding remarks | | 1 | 20 | | |_____________|_______|___________________________________________| | | | | | * Even for the idealised "simple chemical reaction", | | completely adequate means have not yet been discovered | | for predicting the rates of reaction in practical systems,| | either because: | | * the reaction zone is too thin for resolution on available | | grids; or | | * because of the unsolved turbulence problem. | | | | * For realistic chemical-kinetic schemes the task is harder.| | | | * Nevertheless, computer simulation of combustion systems | | does already assist designers and researchers. | |_________________________________________________________________|