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EXTENDED SIMPLE CHEMICALLY-REACTING SYSTEM

The PIL command SCRS activates an extension to the Simple- Chemically-Reacting-System (see PHENC entry: Combustion and the lecture on Combustion Fundamentals).

This extension indeed involves five distinct systems, each of which can be associated with one of three distinct models.

model makes provision for 5 distinct systems (ie ...), which involve either finite-rate chemistry.

The ESCRS allows for variable specific heats and heats of reaction, the data for which are taken from the CHEMKIN thermodynamic data base.

The model is currently restricted to flows in which the density does not significantly depend upon pressure.

The coding for the ESCRS model is provided in Subroutine GXSCRS and its ancillary subroutines, which are called from GREX3.

Contents

(a)Choice of model

(b)Method of activation

(c)Reaction System and Combustion Model

(d)Chemical Species

(e)Solution of the Energy Equation

(f)Inlet Boundary Conditions

(g)Thermodynamic Data

(h)Infinite-Rate Chemistry-PDF Option

(i)Finite-Rate Chemistry-Further EBU Options

(j)Finite-Rate Chemistry-Further Options

(a) Choice of model

The fast-chemistry model is appropriate for non-premixed diffusion flames only, in which the reactants enter via separate inlet streams. The model assumes:-

An option exists that allows the reactants to coexist at different times by the introduction of a double-delta probability density function (PDF) for the concentration field. (See item (h) below)

For situations in which the reactions are relatively slow, or there is premixing of the reactants, it is necessary to account for finite-rate chemistry. The ESCRS provides for this, either in terms of Arrhenius or Eddy-Break-Up (EBU) formulae.

(b) Method of activation

In order to activate the ESCRS, it is necessary to include in Group 9 of the Q1 file at least five SCRS commands, thus:
SCRS ( SYSTEM, plus four further arguments)
SCRS ( SPECIES, plus seven further arguments)
SCRS ( FUIN, plus eight further arguments)
SCRS ( OXIN, plus eight further arguments)
SCRS ( PROP, plus two further arguments)

The foregoing settings may be followed by one or more of the following optional settings:
SCRS (PDF, plus one further arguments)
SCRS (EBU, plus two further arguments)
SCRS (ARR, plus five further arguments)
SCRS (PDF,DDELTA)
SCRS (EBU,P,CEBU);
SCRS (EBU,S1,CEBU);
SCRS (EBU,S2,CEBU)
SCRS (ARR,P,PREXP,FUEXP,OXEXP,EACTP)
SCRS (ARR,S1,PREXS1,FUEXS1,OXEXS1,EACTS1)
SCRS (ARR,S2,PREXS2,FUEXS2,OXEXS2,EACTS2)
SCRS ( SYSTEM, NCSTEP, NCREAC, NELEM, MODEL)
SCRS ( SPECIES, FUEL, OXID, FP1, FP2, PROD1, PROD2, DILN)
SCRS ( FUIN, FUEL, OXID, FP1, FP2, PROD1, PROD2, DILN, TFU)
SCRS ( OXIN, FUEL, OXID, FP1, FP2, PROD1, PROD2, DILN, TOX)
SCRS ( PROP, CHEMKIN,File)

SCRS(PDF,DDELTA) activates the PDF extension to the fast- chemistry model.

SCRS(EBU,....) and SCRS(ARR,.....) are used to define the EBU and Arrhenius constants for the finite-rate chemistry model, as will be explained below.

The remaining SCRS commands will now be described in turn.

Reaction System and Combustion Model

SCRS(SYSTEM,NCSTEP,NCREAC,NELEM,Model) specifies the reaction scheme and combustion model. NCSTEP is the number of chemical steps, NCREAC is the number of chemical reactions, and NELEM is the number of chemical elements.

The argument Model selects the combustion model and it can take one of the following settings:

MODEL=INERT if no chemical reaction is required
=FASTC for infinite-rate chemistry
=FRATE for finite-rate chemistry

For MODEL=FRATE, the default is that chemical reaction proceeds by way of the Eddy Break Up (EBU) model with an EBU constant equal to 4.0. If convergence proves problematic with this model, then the user is advised to set MODEL=FRATE* which invokes a stronger linearisation of the reaction source terms.

The ESCRS allows for 5 different reaction systems by way of the following reactions:

FUEL + om1.OXID -> fpm1.FP1 + fpm2.FP2 (1)
FP1 + om12.OXID -> pm1.PROD1 (2)
FP2 + om22.OXID -> pm2.PROD2 (3)

where the reactions amongst the reactants FUEL and OXID produce the products PROD1 and PROD2 via the intermediates FP1 and FP2.

Reaction (1) is termed the primary reaction and reactions (2) and (3) are termed the secondary reactions.

The model also allows for the presence of an inert species DILN, such as nitrogen N2.

The values assigned to NCSTEP and NCREAC are used by PHOENICS to select one of the 5 systems, as follows:

System 1. NCSTEP=1 NCREAC=1 ; A single global irreversible reaction of a fuel, eg. CmHn via the primary reaction (1);

System 2. NCSTEP=1 NCREAC=-1 ; A single global irreversible reaction of a fuel, e.g. H2 or CO via the secondary reaction (2);

System 3. NCSTEP=1 NCREAC=2 ; Two competing reactions of a "binary- fuel", eg. (CO + H2), via the secondary reactions (2) and (3);

System 4. NCSTEP=2 NCREAC=2 ; A two-step reaction scheme such as the burning of CmHn with CO as an intermediate via reactions (1) and (2); and

System 5. NCSTEP=2 NCREAC=3 ; A two-step reaction scheme such as the burning of CmHn with H2 and CO as intermediates via all three reactions.

Chemical Species

SCRS(SPECIES,FUEL,OXID,FP1,FP2,PROD1,PROD2,DILN)

The arguments FUEL, OXID, FP1, FP2, PROD1, PROD2 and DILN are 4-character names which define the species variables to be stored via the SOLUTN command.

Thus, for the reaction of methane in air via reaction system (e) above, the user sets FUEL=CH4, OXID=O2, FP1=H2, FP2=CO, PROD1=H2O, PROD2=CO2 and DILN=N2, i.e. SCRS(SPECIES,CH4,O2,H2,CO,H2O,CO2,N2).

At present, the user must allocate storage for all seven species even if some are not present in the physical system. Thus, for the reaction of hydrogen in air via reaction system (b) above, the user sets SCRS(SPECIES,CH4,O2,H2,CO, H2O,CO2,N2) where CH4 and CO2 are just dummy species. For the reaction of CO in air via the same reaction system, one would set SCRS(SPECIES,CH4,O2,CO,H2,CO2,H2O,N2).

For finite-rate chemistry the SCRS(SPECIES,....) command will activate solution of the FUEL, FP1 and FP2 equations as appropriate for the selected reaction system.

Solution of the Energy Equation

The ESCRS uses a conservation equation for the total (thermal +chemical) static enthalpy of the mixture H1. The assumption of unit Lewis number and neglect of any energy sources due to radiant energy transfer, mechanical dissipation, fluid compression and/or expansion, brings the enthalpy conservation equation into the same form as the mixture fraction equation.

Under these conditions, if the system is adiabatic, the enthalpy solution will be linearly related to the mixture fraction, and so the user need only set STORE(H1) in Group 7 of the Q1 file. If thermal radiation is present and/or there is heat exchange across the system boundaries, then the user must solve for H1, i.e. SOLVE(H1);SOLUTN(H1,Y,Y,Y,P,P,P).

Inlet Boundary Conditions

The extended SCRS is applicable to two-stream problems in which identification may be made of separate entry streams termed 'fuel' and 'oxidiser'. There may be more than one entry port for each of these reactants, but properties must be uniform and the same over each port for a given reactant.

The composition and temperature of the 'fuel' and 'oxidiser' streams are defined by way of the following commands:

SCRS(FUIN,FUEL,OXID,FP1,FP2,PROD1,PROD2,DILN,TFU)
SCRS(OXIN,FUEL,OXID,FP1,FP2,PROD1,PROD2,DILN,TOX)

where FUEL, OXID, FP1, FP2, PROD1, PROD2 and DILN denote the mass fractions of these species in their respective inlet streams, and TFU and TOX are the absolute temperatures of the fuel and oxidiser streams.

The inlet conditions are specified using PATCHes with names beginning SCRS, and with the characters "F" or "O" to indicate the fuel or oxidant stream. These conditions may be applied at fixed-pressure entrainment boundaries or at fixed mass-inflow boundaries.

If the mass inflow is to be specified, then the mass flux must be specified using a density calculated from the specified inlet composition, temperature and velocity. If the enthalpy H1 is solved, then the inlet enthalpy must be calculated from the inlet composition and temperature. The ESCRS does this automatically if the user sets the VALue for P1 equal to GRND1 and the VALue for H1 equal to GRND3.

The following settings provide an example of such inlet boundary conditions for the fuel and oxidiser streams:

INLET(SCRSF,LOW,1,NX,#2,#2,1,1,#1,#NREGT)
VALUE(SCRSF,P1,GRND1);VALUE(SCRSF,W1,WINF);VALUE(SCRSF,F,1.)
VALUE(SCRSF,CH4,YCH4IN);VALUE(SCRSF,H1,GRND3)

INLET(SCRSO,LOW,1,NX,#4,#4,1,1,#1,#NREGT)
VALUE(SCRSO,P1,GRND1);VALUE(SCRSO,W1,WINO);VALUE(SCRSO,F,0.)
VALUE(SCRSO,CH4,YCH4IN);VALUE(SCRSO,H1,GRND3)

For BFC inlet PATCHes, the user sets the VALue for P1 and the velocity resolutes equal to GRND3, as for example:

INLET(SCRSF,LOW,1,NX,#2,#2,1,1,#1,#NREGT)
VALUE(SCRSF,P1,GRND3);VALUE(SCRSF,V1,GRND3)
VALUE(SCRSF,W1,GRND3);VALUE(SCRSF,F,1.)
VALUE(SCRSF,VCRT,ZERO);VALUE(SCRSF,WCRT,WINF)
VALUE(SCRSF,CH4,YCH4IN);VALUE(SCRSF,H1,GRND3)

INLET(SCRSO,LOW,1,NX,#4,#4,1,1,#1,#NREGT)
VALUE(SCRSO,P1,GRND3);VALUE(SCRSO,V1,GRND3)
VALUE(SCRSO,W1,GRND3);VALUE(SCRSO,F,0.)
VALUE(SCRSO,VCRT,ZERO);VALUE(SCRSO,WCRT,WINO)
VALUE(SCRSO,CH4,YCH4IN);VALUE(SCRSO,H1,GRND3)

Thermodynamic Data

SCRS(PROP,CHEMKIN,File) sets TMP1=GRND9, RHO1=GRND9, RHO1A= GRND9, CP1=GRND7 and instructs PHOENICS that thermodynamic data, such as the specific heats and heats of formation, are to be calculated by way of the CHEMKIN interface.

The argument File is an arbitrary 4-character name which identifies the name of the CHEMKIN mechanism file. For example, for the reaction of methane in air via the reaction system (e) above, FILE=SCRS identifies the file SCRS.CKM, which must be created by the user according to the following standard format:


ELEMENTS C O H N END
SPECIES CH4 O2 H2 CO H2O CO2 N2 END
REACTIONS
2CH4 + O2 => 2CO + 4H2 0. 0. 0.
2CO + O2 => 2CO2 0. 0. 0.
2H2 + O2 => 2H2O 0. 0. 0.
END The file SCRS.CKM must be processed by the CHEMKIN Interpreter program so as to produce the two CHEMKIN data files SCRSmcln and SCRSckln. This is done by typing CKI SCRS; a copy of the script CKI.BAT may be found in the PHOENICS directory D_CHMKIN.

Infinite-Rate Chemistry-PDF Option

The command SCRS(PDF,DDELTA) activates the double-delta PDF extension to the fast-chemistry model. It is equivalent to the following PIL commands:


SOLVE(FSQ);PRT(FSQ)=0.7
PATCH(FSQSO,PHASEM,1,NX,1,NY,1,NZ,1,LSTEP)
COVAL(FSQSO,FSQ,GRND1,GRND1)
SPEDAT(FSQ,CFSQ1,R,2.0/PRT(F))
SPEDAT(FSQ,CFSQ2,R,1.78)
SPEDAT(SCRS,IPDF,I,1)

Here FSQ is the mean square of the mixture fraction and CFSQ1 and CFSQ2 are empirical constants which determine the creation and destruction rate of FSQ.

Finite-Rate Chemistry-Further EBU Options

As was mentioned already, the default for finite-rate chemistry is that the reactions proceed by way of the EBU model, i.e.

R = -CEBU*MIN(MFU,MOX/S)*RHO*VOL*EP/KE

where R is the reaction rate of the 'fuel' species in kg/s, MFU and MO2 are the mass fractions of 'fuel' and 'oxidiser', S is the stoichometric requirement, and CEBU is the EBU constant which has a default value of 4.0. The MIN argument implies that R is dependent on the species in shortest supply.

For the case of 2 reactions competing for the same oxidiser, MOX/S is replaced with MFU*MOX/(MFU*S+MFU2*S2) where S2 is the stoichometric requirement of the 2nd reaction involving the fuel species MFU2.

The command SCRS(EBU,Reaction,CEBU) may be used to overwrite the default value of the EBU constant for the reaction specified by the second argument, namely P for the primary reaction, S1 for the 1st secondary reaction and S2 for the 2nd secondary reaction. Thus, SCRS(EBU,P,1.0) would set the EBU constant to unity for the primary reaction.

Alternatively, the SPEDAT command may be used to set the EBU constants, e.g.


SPEDAT(SCRS,CEBP,R,Value);SPEDAT(SCRS,CEBS1,R,Value)
SPEDAT(SCRS,CEBS2,R,Value)

The PIL commands SPEDAT(SCRS,IPRMOD,I,Value) and SPEDAT(SCRS, ISRMOD,I,Value) may be used to activate alternative expressions for the primary and secondary reaction rates, respectively.

If IPRMOD=1 or ISRMOD=1, the reaction rate is calculated from the Magnussen-Hjertager [1976] formula:
R = -CEBU*MIN(MFU,MO/S,0.5*MPR/[1+S])*RHO*VOL*EP/KE where MPR is the mass fraction of product species, and again CEBU is given a default value of 4.0.

If IPRMOD=2, the primary reaction rate is calculated from Spalding's recent proposal:
R = -CR*MFU*r*(1-r)**RHO*VOL*EP/KE where the reaction progress variable r=MFU/MFUu and the unburnt mass fraction MFUu=F*MFU,A+(1-F)*MFU,B. Here, MFU,A is MFU in the A stream for which the mixture fraction F=1, and MFU,B is MFU in the B stream for which F=0. This model implies that MFU=0 denotes complete combustion and r=0, while MFU=MFUu denotes zero combustion and r=1. This expression is not available for secondary reactions.

For a two-step mechanism with IPRMOD=2 for the primary reaction, ISRMOD may also be set equal to 2 so that, as proposed by Spalding, any secondary reactions are computed in proportion to the primary reaction:
Rs = (MFP/MFU)*R where Rs is the secondary reaction rate in kg/s for the intermediate species FP (=FP1 or FP2), and R is the primary reaction rate for the fuel species FU.

Finite-Rate Chemistry- Chemical-Kinetic Options

If IPRMOD=3 or ISRMOD=3 the reaction rate is calculated from an Arrhenius-type chemical-kinetic expression, as follows:
R = -1.E3*WFU*PREXP*[FU**B]*[FU**C]*EXP(-EACT/{R*T})*VOL where: R is the reaction rate in kg/s; FU and OX are the fuel and oxygen molar concentrations in g-mol/cm^3, respectively; B and C are the fuel and oxygen exponents; PREXP is the overall frequency factor in units of [(cm/g-mol)**(a+b-1)]/s; WFU is the molecular mass of the fuel; EACT is the activation energy in cal/g-mol; R= 1.987 cal/(g-mol.K) and T is the absolute temperature.

For this option, the following SCRS commands allow the User to define the Arrhenius constants in the foregoing units:


SCRS(ARR,P,PREXP,FUEXP,OXEXP,EACTP)
SCRS(ARR,S1,PREXS1,FUEXS1,OXEXS1,EACTS1)
SCRS(ARR,S2,PREXS2,FUEXS2,OXEXS2,EACTS2)

Alternatively, the SPEDAT command may be used, e.g.
SPEDAT(SCRS,PREXP,R,Value);SPEDAT(SCRS,FUEXP,R,Value)
SPEDAT(SCRS,OXEXP,R,Value);SPEDAT(SCRS,EACTP,R,Value) etc.

The default settings for the various constants are zero, and appropriate values may be found in the literature, e.g. F.L.Dryer,'The Phemonenology of Modelling Combustion Chemistry', p121, Fossil Fuel Combustion, Ed. W.Bartok & A.F.Sarofim, John Wiley & Sons, [1990].

Finite-Rate Chemistry-Further Options

The option exists for the reaction rate to be calculated from the smaller of the EBU and Arrhenius expressions, so that the reaction is controlled by the process that takes the longer time. The smaller rate of reaction corresponds to the larger of the chemical (Tc) and turbulent diffusion (Tt) time scales. In regions where Tt > Tc, the reaction is diffusion controlled, as the mixing of the reactants is slow. When Tt >Tc, the mixing is rapid so that the reaction is kinetically influenced.

The PIL command SPEDAT(SCRS,IPCHEM,I,1) may be used to activate this feature for the primary reaction, and the command SPEDAT(SCRS,ISCHEM,I,1) may be used to activate the feature for both secondary reactions.


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