___________________________________________________________________
| EuroCFD 1 | 0 | Computer simulation of |
| Brussels | ---- | combustion processes, by |
| 1992 | 16 | Brian Spalding, CHAM Ltd , UK |
|_____________|_______|___________________________________________|
| |
| This set of lecture panels contains the text of a lecture |
| delivered at the First European CFD Conference in Brussels. |
| The results which were displayed during the lecture were |
| PHOTON plots containing the results of KIVA and PHOENICS |
| calculations. These can be regenerated from library files |
| if they are required. |
| |
| Notes added at the date of editing (Jan '94) are marked ***** |
| |
| The lecture focusses particular attention on:- |
| 1. the important role played by small-scale phenomena |
| of the 'gas-fragment' or 'flamelet' type; and |
| 2. how these phenomena can be represented in a computer |
| code by the 'two-fluid' turbulence model. |
|_________________________________________________________________|
___________________________________________________________________
| EuroCFD 1 | 1 | Computer simulation of |
| Brussels | ---- | combustion processes, by |
| 1992 | 16 | Brian Spalding, CHAM Ltd , UK |
|_____________|_______|___________________________________________|
| |
| Contents |
| |
| * General features of the CFD of combustion |
| |
| * Pre-computer numerical approaches |
| |
| * Single-fluid computer simulations |
| |
| * Multi-fluid computer simulations |
| |
| * Conclusions |
| |
| |
|_________________________________________________________________|
___________________________________________________________________
| EuroCFD 1 | 2 | |
| Brussels | ---- | The CFD of combustion processes |
| 1992 | 16 | General features, 1 |
|_____________|_______|___________________________________________|
| Combustion processes are characterised by:- |
| ----------------------------|---------------------------------- |
| features | associated difficulties |
| ----------------------------|---------------------------------- |
| * highly non-linear sources | * tendency to divergence, to be |
| and sinks (reaction rates)| combated by under-relaxation(?) |
| | |
| * linkages between numerous | * sophisticated algorithms are |
| scalar-variable equations | needed for the efficient solving|
| (species concentrations) | of "stiff-equation" systems |
| | |
| * large variations of fluid | * fine (or highly adaptive) grids |
| properties occur, often | are needed; computer times are |
| over short distances I large |
|_________________________________________________________________|
___________________________________________________________________
| EuroCFD 1 | 3 | |
| Brussels | ---- | The CFD of combustion processes |
| 1992 | 16 | General features, 2 |
|_____________|_______|___________________________________________|
| Combustion processes are characterised by:- |
| ----------------------------|---------------------------------- |
| features | associated difficulties |
| ----------------------------|---------------------------------- |
| * presence of more than one | * at least twice single-phase no. |
| phase (gas, droplets, etc)| of equations must be solved |
| | |
| * phase-interaction laws are| * computer times are enlarged and |
| complex and ill-defined | divergence more probable |
| | |
| * sub-grid-scale features | * special techniques are needed |
| (particles, flame fronts, | for tracking particles and fronts
| flamelets, regressing | and for averaging meaningfully |
| solid-propellant surfaces)| small-wavelength fluctuations. |
|_________________________________________________________________|
___________________________________________________________________
| EuroCFD 1 | 4 | |
| Brussels | ---- | The CFD of combustion processes |
| 1992 | 16 | General features, 3 |
|_____________|_______|___________________________________________|
| Combustion processes are characterised by:- |
| ----------------------------|---------------------------------- |
| features | associated difficulties |
| ----------------------------|---------------------------------- |
| * complex and unknown | * lack of certainty impairs the |
| interactions with | reliability of computer simulat-|
| turbulent fluctuations, | ions for design purposes; |
| both: | |
| * chemical (turbulence | * only prohibitively expensive |
| influences reaction) | fine-scale (direct-simulation) |
| and | studies can (in principle) |
| * mechanical (reaction | obviate the non-linear-averaging|
| influences turbulence) | problem. |
| | |
|_________________________________________________________________|
___________________________________________________________________
| EuroCFD 1 | 5 | |
| Brussels | ---- | An example: combustion in a reciprocating|
| 1992 | 16 | engine |
|_____________|_______|___________________________________________|
| * Reciprocating-engine combustion embodies all the above- |
| mentioned features, together with time-dependence, three- |
| dimensionality, curved and moving boundaries, and complex |
| boundary conditions at walls, valves, etc. |
| |
| * Several general- and special-purpose computer codes have been
| used for engine-combustion simulation, including:- |
| PHOENICS, KIVA, FIRE, STAR-CD and PHOENICS-KIVA. |
| |
| * Although their simulations have provided helpful guidance to|
| designers, none is yet well-enough validated to be relied |
| upon for quantitative design predictions. |
| * Extracts from a PHOENICS-KIVA calculation follow, showing |
| temperature distributions in a cylinder after ignition. |
|_________________________________________________________________|
fig 1. PHOENICS-KIVA. Temperature distribution just after ignition
fig 2. PHOENICS-KIVA. A slightly-later temperature distribution
fig 3. PHOENICS-KIVA. Temperature distribution at top dead centre
fig 4. PHOENICS-KIVA. Temperature distribution during the expansion
___________________________________________________________________
| EuroCFD 1 | 10 | Numerical studies of elementary |
| Brussels | ---- | processes: |
| 1992 | 16 | ignition, propagation and extinction |
|_____________|_______|___________________________________________|
| |
| * The flame-propagation process was modelled far too crudely |
| in the engine calculation shown (as in ALL such calculations)
| |
| * In reality, sub-grid-scale phenomena of ignition, relative |
| motion, extinction and mixing between hot- and cold-gas |
| fragments control the speed at which the flame spreads. |
| |
| * These elementary processes have been studied by numerical |
| means since pre-computer times. (See the following figures |
| from "Some fundamentals of combustion" DB Spalding (1955). |
| |
| * Nowadays computer-simulation and -display techniques make it|
| easy to represent and understand the processes, as will be |
| illustrated later in the lecture. |
|_________________________________________________________________|
Stages in the development of the steady temperature profile
of a flame vortex
fig 5
Stages in the extinction of a flame vortex which is too small
to survive
fig 6
___________________________________________________________________
| EuroCFD 1 | 11 | Interactions between a hot-gas sphere |
| Brussels | ---- | and a cold combustible gas atmosphere |
| 1992 | 16 | in the presence of a body-force field |
|_____________|_______|___________________________________________|
| * The next sequences of displays present results of PHOENICS |
| calculations for the above-described problem. |
| |
| * The first sequence shows successful propagation and the |
| distortion of the flame (and increase of reaction rate) |
| brought about by the body-force effect. |
| |
| * The second sequence shows how flames can be extinguished |
| by reduced reactivity. |
| |
| * The third sequence shows how an increased body force can |
| have the same effect. |
| |
| * Innumerable variants can of course be explored once the |
| input file has been created. |
|_________________________________________________________________|
fig 7
fig 8
fig 9
fig 10
fig 11
fig 12
fig 13
fig 14
fig 15
___________________________________________________________________
| EuroCFD 1 | 12 | |
| Brussels | ---- | Elementary-process studies continued: |
| 1992 | 16 | propagation into an unburned-gas island |
|_____________|_______|___________________________________________|
| |
| * A turbulent flame in premixed combustible gas consists of |
| interspersed "islands" and "lakes" of hot and cold gas |
| fragments, interacting by reason of:- |
| |
| (1) diffusion, (2) chemical reaction, and (3) relative motion|
| |
| * The just-shown studies illustrateded propagation from a |
| hot-gas "island". |
| |
| * The next shows propagation into an unburned-gas "lake". |
| |
| * The calculation has been performed by PHOENICS in transient, |
| spherical-coordinate mode. The displays have been created by |
| PHOTON. |
|_________________________________________________________________|
fig 16
fig 17
fig 18
___________________________________________________________________
| EuroCFD 1 | 13 | The "two-fluid" model of turbulent |
| Brussels | ---- | pre-mixed combustion .. a 1983 study; |
| 1992 | 16 | flame acceleration by pressure waves |
|_____________|_______|___________________________________________|
| Consider: |
| one-dimensional transient burning of a mixture consisting of |
| "lakes" and "islands" of interspersed burned and unburned gas|
| at first WITHOUT any relative velocity. |
| |
| Suppose: |
| a shock wave impinges on this mixture, causing the hotter gas|
| to accelerate more than the colder, and so creating RELATIVE |
| MOTION. |
| |
| The consequence: |
| INCREASED MIXING between the two gases (as just seen) produces
| an increased rate of COMBUSTION, which leads to strengthening|
| of the pressure wave, and so finally to DETONATION. |
| |
|_________________________________________________________________|
click here for Appplications Album entry
___________________________________________________________________
| EuroCFD 1 | 14 | Presentation of results from the |
| Brussels | ---- | PHOENICS simulation of the process |
| 1992 | 16 | by way of line-printer plots |
|_____________|_______|___________________________________________|
| |
| Computation details: |
| |
| PHOENICS is used in its two-phase mode, solving two sets of |
| Navier-Stokes equations (one for each phase) with frictional,|
| heat- and-mass-transfer interactions, and with space and |
| pressure sharing. |
| |
| The local entrainment rate of one gas by the other is taken |
| proportional to their relative velocity. |
| |
| Simplified equations of state and reaction laws are used. |
| |
| A coarse grid (100 cells) was used, so that many parametric |
| studies could be made, only one run of which can be shown. |
|_________________________________________________________________|
*****
The following output, and of course much more, can be generated by
running the PHOENICS Library Case No W979. This also makes use of
PHOTON for displaying the development of the flame more strikingly.
PATCH(PROFIL1 ,PROFIL, 1, 100, 1, 1, 1, 1, 1, 100)
PLOT(PROFIL1 ,P1 , 0.000E+00, 0.000E+00)
PLOT(PROFIL1 ,COLD, 0.000E+00, 1.000E+00)
VARIABLE P1 COLD
MINVAL= 1.497E-07 0.000E+00
MAXVAL= 1.189E+04 1.000E+00
CELLAV= 6.969E+02 8.965E-01
1.00 +....+....+....+....+....+....+....+....+....+...PP
0.90 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC +
0.80 + CCC
0.70 + P +
0.60 + +
0.50 + P +
0.40 + +
0.30 + P +
0.20 + P +
0.10 + P +
0.00 PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP....+
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
the abscissa is X . min= 5.00E-03 max= 9.95E-01
PATCH(PROFILE ,PROFIL, 1, 100, 1, 1, 1, 1, 1, 100)
PLOT(PROFILE ,1U ,-1.000E+00,-1.000E+00)
PLOT(PROFILE ,2U ,-1.000E+00,-1.000E+00)
PLOT(PROFILE ,MDOT, 0.000E+00, 0.000E+00)
VARIABLE 1U 2U MDOT
MINVAL= -2.875E+01 -2.875E+01 -3.577E+00
MAXVAL= 1.000E+01 1.000E+01 -9.000E-12
CELLAV= 9.206E+00 7.634E+00 -2.096E-01
1.00 MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM....+
0.90 + M1 +
0.80 + M1 1+
0.70 + M 112
0.60 + +
0.50 + 2M M
0.40 + M+
0.30 + M 2+
0.20 + +
0.10 + 2MM+
0.00 +....+....+....+....+....+....+....+....+....+..M.+
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
the abscissa is X . min= 5.00E-03 max= 9.95E-01
PATCH(PROFIL1 ,PROFIL, 1, 100, 1, 1, 1, 1, 1, 100)
PLOT(PROFIL1 ,P1 , 0.000E+00, 0.000E+00)
PLOT(PROFIL1 ,COLD, 0.000E+00, 1.000E+00)
VARIABLE P1 COLD
MINVAL= 1.569E-06 0.000E+00
MAXVAL= 2.565E+04 1.000E+00
CELLAV= 2.875E+03 8.848E-01
1.00 +....+....+....+....+....+....+....+....+....PP...+
0.90 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC PP +
0.80 + CCCCCCC
0.70 + PPPP
0.60 + P +
0.50 + +
0.40 + P +
0.30 + P +
0.20 + P +
0.10 + PP +
0.00 PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP...+....+
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
the abscissa is X . min= 5.00E-03 max= 9.95E-01
PATCH(PROFILE ,PROFIL, 1, 100, 1, 1, 1, 1, 1, 100)
PLOT(PROFILE ,1U ,-1.000E+00,-1.000E+00)
PLOT(PROFILE ,2U ,-1.000E+00,-1.000E+00)
PLOT(PROFILE ,MDOT, 0.000E+00, 0.000E+00)
VARIABLE 1U 2U MDOT
MINVAL= -5.323E+01 -5.323E+01 -7.130E+00
MAXVAL= 1.000E+01 1.000E+01 -2.677E-10
CELLAV= 7.694E+00 5.088E+00 -5.030E-01
1.00 MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM1...+.22.+
0.90 + 2M1 MMMM
0.80 + 2M1 MMM22
0.70 + M 1 1 +
0.60 + 2M11 +
0.50 + 2 +
0.40 + M M +
0.30 + 2 +
0.20 + 2M +
0.10 + M +
0.00 +....+....+....+....+....+....+....+....+...MM....+
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
the abscissa is X . min= 5.00E-03 max= 9.95E-01
PATCH(PROFIL1 ,PROFIL, 1, 100, 1, 1, 1, 1, 1, 100)
PLOT(PROFIL1 ,P1 , 0.000E+00, 0.000E+00)
PLOT(PROFIL1 ,COLD, 0.000E+00, 1.000E+00)
VARIABLE P1 COLD
MINVAL= 3.727E-02 0.000E+00
MAXVAL= 4.923E+04 1.000E+00
CELLAV= 8.289E+03 8.588E-01
1.00 +....+....+....+....+....+....+....+....+PP..+....+
0.90 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC PP +
0.80 + CC PP C
0.70 + CCCCCCCCCC+
0.60 + P PPP
0.50 + +
0.40 + P +
0.30 + P +
0.20 + P +
0.10 + PP +
0.00 PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP..+....+....+
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
the abscissa is X . min= 5.00E-03 max= 9.95E-01
PATCH(PROFILE ,PROFIL, 1, 100, 1, 1, 1, 1, 1, 100)
PLOT(PROFILE ,1U ,-1.000E+00,-1.000E+00)
PLOT(PROFILE ,2U ,-1.000E+00,-1.000E+00)
PLOT(PROFILE ,MDOT, 0.000E+00, 0.000E+00)
VARIABLE 1U 2U MDOT
MINVAL= -8.731E+01 -8.731E+01 -1.338E+01
MAXVAL= 2.098E+01 2.098E+01 -1.536E-06
CELLAV= 5.365E+00 3.154E+00 -1.298E+00
1.00 MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM...+....+2222+
0.90 2222222222222222222222222222222222222M M222112M
0.80 + 22M MM1111MM2
0.70 + 2M1 1MMMM +
0.60 + 2M1 2 +
0.50 + 11M +
0.40 + 2M +
0.30 + 2 +
0.20 + MM +
0.10 + 2 2 +
0.00 +....+....+....+....+....+....+....+....MM...+....+
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
the abscissa is X . min= 5.00E-03 max= 9.95E-01
PATCH(PROFIL1 ,PROFIL, 1, 100, 1, 1, 1, 1, 1, 100)
PLOT(PROFIL1 ,P1 , 0.000E+00, 0.000E+00)
PLOT(PROFIL1 ,COLD, 0.000E+00, 1.000E+00)
VARIABLE P1 COLD
MINVAL= 1.156E-01 0.000E+00
MAXVAL= 8.923E+04 1.000E+00
CELLAV= 2.054E+04 8.111E-01
1.00 +....+....+....+....+....+....+....+.P..+....+....+
0.90 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC P P +
0.80 + CCP PP +
0.70 + CC PPPPPPP CC
0.60 + PCCCCCCCCCCCCCCP
0.50 + +
0.40 + P +
0.30 + +
0.20 + P +
0.10 + PP +
0.00 PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP.+....+....+....+
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
the abscissa is X . min= 5.00E-03 max= 9.95E-01
PATCH(PROFILE ,PROFIL, 1, 100, 1, 1, 1, 1, 1, 100)
PLOT(PROFILE ,1U ,-1.000E+00,-1.000E+00)
PLOT(PROFILE ,2U ,-1.000E+00,-1.000E+00)
PLOT(PROFILE ,MDOT, 0.000E+00, 0.000E+00)
VARIABLE 1U 2U MDOT
MINVAL= -1.355E+02 -1.355E+02 -2.446E+01
MAXVAL= 2.533E+01 2.533E+01 -8.018E-07
CELLAV= 1.051E+00 -9.770E-01 -2.659E+00
1.00 MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM..+....+....22222+
0.90 222222222222222222222222222222221M M 22221111MM
0.80 + 21M MMMMMMMMMMMM2
0.70 + 21 2211 +
0.60 + 2M1 21 +
0.50 + 211M +
0.40 + M12 +
0.30 + 2 +
0.20 + M M +
0.10 + 22 +
0.00 +....+....+....+....+....+....+....2M...+....+....+
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
the abscissa is X . min= 5.00E-03 max= 9.95E-01
PATCH(PROFIL1 ,PROFIL, 1, 100, 1, 1, 1, 1, 1, 100)
PLOT(PROFIL1 ,P1 , 0.000E+00, 0.000E+00)
PLOT(PROFIL1 ,COLD, 0.000E+00, 1.000E+00)
VARIABLE P1 COLD
MINVAL= 2.247E-01 0.000E+00
MAXVAL= 1.530E+05 1.000E+00
CELLAV= 4.533E+04 7.389E-01
1.00 +....+....+....+....+....+....+.PP.+....+....+....+
0.90 CCCCCCCCCCCCCCCCCCCCCCCCCCCCC P P +
0.80 + CC PPPP +
0.70 + CP PPPPPPPP C
0.60 + C PPPCP
0.50 + P CCCCCCCCCCCCCCCCCC+
0.40 + +
0.30 + P +
0.20 + P +
0.10 + P +
0.00 PPPPPPPPPPPPPPPPPPPPPPPPPPPPP.+....+....+....+....+
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
the abscissa is X . min= 5.00E-03 max= 9.95E-01
PATCH(PROFILE ,PROFIL, 1, 100, 1, 1, 1, 1, 1, 100)
PLOT(PROFILE ,1U ,-1.000E+00,-1.000E+00)
PLOT(PROFILE ,2U ,-1.000E+00,-1.000E+00)
PLOT(PROFILE ,MDOT, 0.000E+00, 0.000E+00)
VARIABLE 1U 2U MDOT
MINVAL= -1.972E+02 -1.972E+02 -4.229E+01
MAXVAL= 3.235E+01 3.235E+01 -2.617E-06
CELLAV= -6.035E+00 -7.290E+00 -4.855E+00
1.00 MMMMMMMMMMMMMMMMMMMMMMMMMMMMM.+....+....+..2222222+
0.90 2222222222222222222222222222MM MM 222221111MMM
0.80 + 221 MMMMMMMMMMMMMMM +
0.70 + 2M M22211 +
0.60 + 21 221 +
0.50 + M 12 +
0.40 + 2 1M +
0.30 + M 2 +
0.20 + 2 M +
0.10 + 2 2 +
0.00 +....+....+....+....+....+....+M...+....+....+....+
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
the abscissa is X . min= 5.00E-03 max= 9.95E-01
PATCH(PROFIL1 ,PROFIL, 1, 100, 1, 1, 1, 1, 1, 100)
PLOT(PROFIL1 ,P1 , 0.000E+00, 0.000E+00)
PLOT(PROFIL1 ,COLD, 0.000E+00, 1.000E+00)
VARIABLE P1 COLD
MINVAL= 3.160E-01 0.000E+00
MAXVAL= 2.418E+05 1.000E+00
CELLAV= 8.966E+04 6.463E-01
1.00 +....+....+....+....+....+.PP.+....+....+....+....+
0.90 CCCCCCCCCCCCCCCCCCCCCCCC P PP +
0.80 + C P PPPPPP +
0.70 + C PPPPPPPPPP +
0.60 + C PPPPPC
0.50 + PC C+
0.40 + CCCCCCCCCCCCCCCCCCCCCCC+
0.30 + P +
0.20 + P +
0.10 + P +
0.00 PPPPPPPPPPPPPPPPPPPPPPPP.+....+....+....+....+....+
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
the abscissa is X . min= 5.00E-03 max= 9.95E-01
PATCH(PROFILE ,PROFIL, 1, 100, 1, 1, 1, 1, 1, 100)
PLOT(PROFILE ,1U ,-1.000E+00,-1.000E+00)
PLOT(PROFILE ,2U ,-1.000E+00,-1.000E+00)
PLOT(PROFILE ,MDOT, 0.000E+00, 0.000E+00)
VARIABLE 1U 2U MDOT
MINVAL= -2.663E+02 -2.663E+02 -6.572E+01
MAXVAL= 3.944E+01 3.944E+01 -5.319E-07
CELLAV= -1.686E+01 -1.677E+01 -7.765E+00
1.00 MMMMMMMMMMMMMMMMMMMMMMMM.+....+....+....+.22222222M
0.90 22222222222222222222222MM MM 22222MMMMMMMM2
0.80 + 221 M MMMMMMMMMMMMM +
0.70 + 2M 22211 +
0.60 + 1 2211 +
0.50 + 2M M21 +
0.40 + 112 +
0.30 + 2 M +
0.20 + M 2 +
0.10 + 22 +
0.00 +....+....+....+....+....2M...+....+....+....+....+
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
the abscissa is X . min= 5.00E-03 max= 9.95E-01
PATCH(PROFIL1 ,PROFIL, 1, 100, 1, 1, 1, 1, 1, 100)
PLOT(PROFIL1 ,P1 , 0.000E+00, 0.000E+00)
PLOT(PROFIL1 ,COLD, 0.000E+00, 1.000E+00)
VARIABLE P1 COLD
MINVAL= 4.206E-01 0.000E+00
MAXVAL= 3.585E+05 1.000E+00
CELLAV= 1.598E+05 5.405E-01
1.00 +....+....+....+....+PP..+....+....+....+....+....+
0.90 CCCCCCCCCCCCCCCCCCC P P +
0.80 + CC PPPPPPPP +
0.70 + CP PPPPPPPPPPPP +
0.60 + C PPPPPPPP
0.50 + C C
0.40 + CCCCC C+
0.30 + P CCCCCCCCCCCCCCCCCCCCCCC +
0.20 + +
0.10 + P +
0.00 PPPPPPPPPPPPPPPPPPP.+....+....+....+....+....+....+
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
the abscissa is X . min= 5.00E-03 max= 9.95E-01
PATCH(PROFILE ,PROFIL, 1, 100, 1, 1, 1, 1, 1, 100)
PLOT(PROFILE ,1U ,-1.000E+00,-1.000E+00)
PLOT(PROFILE ,2U ,-1.000E+00,-1.000E+00)
PLOT(PROFILE ,MDOT, 0.000E+00, 0.000E+00)
VARIABLE 1U 2U MDOT
MINVAL= -3.377E+02 -3.377E+02 -9.302E+01
MAXVAL= 4.670E+01 4.670E+01 -9.936E-06
CELLAV= -3.200E+01 -2.997E+01 -1.112E+01
1.00 MMMMMMMMMMMMMMMMMMM.+....+....+....+....222222222MM
0.90 222222222222222222M MM MMMMMMMMMMMMMMMMMMMM2
0.80 + 21M MMMMMM2222111 +
0.70 + 21 M 2222111 +
0.60 + 21 22211 +
0.50 + M M2211 +
0.40 + 21 12 +
0.30 + 12 +
0.20 + 2MM2 +
0.10 + 2 +
0.00 +....+....+....+....MM...+....+....+....+....+....+
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
the abscissa is X . min= 5.00E-03 max= 9.95E-01
PATCH(PROFIL1 ,PROFIL, 1, 100, 1, 1, 1, 1, 1, 100)
PLOT(PROFIL1 ,P1 , 0.000E+00, 0.000E+00)
PLOT(PROFIL1 ,COLD, 0.000E+00, 1.000E+00)
VARIABLE P1 COLD
MINVAL= 5.744E-01 0.000E+00
MAXVAL= 4.923E+05 1.000E+00
CELLAV= 2.600E+05 4.274E-01
1.00 +....+....+....+PP..+....+....+....+....+....+....+
0.90 CCCCCCCCCCCCC P PP +
0.80 + C P PPPPPPPPPP +
0.70 + C PPPPPPPPPPPPP +
0.60 + PPPPPPPPPP
0.50 + C C
0.40 + CC C+
0.30 + P CCCCCCCCCC CC+
0.20 + CCCCCCCCCCCCCCCCCCCCCCC +
0.10 + P +
0.00 PPPPPPPPPPPPP..+....+....+....+....+....+....+....+
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
the abscissa is X . min= 5.00E-03 max= 9.95E-01
PATCH(PROFILE ,PROFIL, 1, 100, 1, 1, 1, 1, 1, 100)
PLOT(PROFILE ,1U ,-1.000E+00,-1.000E+00)
PLOT(PROFILE ,2U ,-1.000E+00,-1.000E+00)
PLOT(PROFILE ,MDOT, 0.000E+00, 0.000E+00)
VARIABLE 1U 2U MDOT
MINVAL= -4.045E+02 -4.045E+02 -1.249E+02
MAXVAL= 5.373E+01 5.373E+01 -5.607E-06
CELLAV= -5.154E+01 -4.696E+01 -1.462E+01
1.00 MMMMMMMMMMMMM..+....+....+....+....+..2222222222MMM
0.90 2222222222221M MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM22
0.80 + 21 M 22222111 +
0.70 + 2M 2222111 +
0.60 + 1 M 222111 +
0.50 + 2M 22211 +
0.40 + 1 221 +
0.30 + 2 1M2 +
0.20 + 2 +
0.10 + MM2 +
0.00 +....+....+...2M....+....+....+....+....+....+....+
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
the abscissa is X . min= 5.00E-03 max= 9.95E-01
PATCH(PROFIL1 ,PROFIL, 1, 100, 1, 1, 1, 1, 1, 100)
PLOT(PROFIL1 ,P1 , 0.000E+00, 0.000E+00)
PLOT(PROFIL1 ,COLD, 0.000E+00, 1.000E+00)
VARIABLE P1 COLD
MINVAL= 1.159E+00 0.000E+00
MAXVAL= 6.468E+05 1.000E+00
CELLAV= 3.922E+05 3.104E-01
1.00 +....+....PP...+....+....+....+....+....+....+....+
0.90 CCCCCCC P PPP +
0.80 + C PPPPPPPPPPPP +
0.70 + CP PPPPPPPPPPPPP +
0.60 + PPPPPPPPPPPPPPP
0.50 + C +
0.40 + C C
0.30 + P CCCCCCC C+
0.20 + CCCCCCCCCCCCC CCCCC +
0.10 + P CCCCCCCCCCCCCCCC +
0.00 PPPPPPPP..+....+....+....+....+....+....+....+....+
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
the abscissa is X . min= 5.00E-03 max= 9.95E-01
PATCH(PROFILE ,PROFIL, 1, 100, 1, 1, 1, 1, 1, 100)
PLOT(PROFILE ,1U ,-1.000E+00,-1.000E+00)
PLOT(PROFILE ,2U ,-1.000E+00,-1.000E+00)
PLOT(PROFILE ,MDOT, 0.000E+00, 0.000E+00)
VARIABLE 1U 2U MDOT
MINVAL= -4.688E+02 -4.688E+02 -1.566E+02
MAXVAL= 6.109E+01 6.109E+01 -1.975E-04
CELLAV= -7.505E+01 -6.721E+01 -1.813E+01
1.00 MMMMMMM...+.M..+....+....+....+....+22222222222MMMM
0.90 2222221M MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM1222
0.80 + 2M 222221111 +
0.70 + 1 M 2222111 +
0.60 + 2 222211 +
0.50 + M M 222211 +
0.40 + 1 2211 +
0.30 + 2 1M2 +
0.20 + M 2 +
0.10 + 2M2 +
0.00 +....+..2M+....+....+....+....+....+....+....+....+
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
the abscissa is X . min= 5.00E-03 max= 9.95E-01
PATCH(PROFIL1 ,PROFIL, 1, 100, 1, 1, 1, 1, 1, 100)
PLOT(PROFIL1 ,P1 , 0.000E+00, 0.000E+00)
PLOT(PROFIL1 ,COLD, 0.000E+00, 1.000E+00)
VARIABLE P1 COLD
MINVAL= 1.242E+04 0.000E+00
MAXVAL= 8.132E+05 1.000E+00
CELLAV= 5.572E+05 1.909E-01
1.00 +...PP....+....+....+....+....+....+....+....+....+
0.90 C P PPP +
0.80 +C PPPPPPPPPPPP +
0.70 + P PPPPPPPPPPP +
0.60 + C PPPPPPPPPPPPPPPPPPPP
0.50 + C +
0.40 + C C
0.30 + P CCCCCC C+
0.20 + CCCCCCCCCCC CCC+
0.10 +P CCCCCCCCCCCCCCCCCCCCCCCCCCCC +
0.00 PP...+....+....+....+....+....+....+....+....+....+
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
the abscissa is X . min= 5.00E-03 max= 9.95E-01
PATCH(PROFILE ,PROFIL, 1, 100, 1, 1, 1, 1, 1, 100)
PLOT(PROFILE ,1U ,-1.000E+00,-1.000E+00)
PLOT(PROFILE ,2U ,-1.000E+00,-1.000E+00)
PLOT(PROFILE ,MDOT, 0.000E+00, 0.000E+00)
VARIABLE 1U 2U MDOT
MINVAL= -5.277E+02 -5.277E+02 -1.902E+02
MAXVAL= 6.759E+01 6.759E+01 -1.094E+00
CELLAV= -1.016E+02 -8.924E+01 -2.156E+01
1.00 M....+M...+....+....+....+....+..2222MMMMMMMMMMMMMM
0.90 1M M MMMMMMMMMMMMMMMMMMMMMMMMMMMMMM1111 1222
0.80 2M 2222221111 +
0.70 + M 22222111 +
0.60 +1 2222211 +
0.50 +2M M 2222211 +
0.40 + 1 22211 +
0.30 +2 1M22 +
0.20 + 22 +
0.10 + MM2 +
0.00 +.2M.+....+....+....+....+....+....+....+....+....+
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
the abscissa is X . min= 5.00E-03 max= 9.95E-01
___________________________________________________________________
| EuroCFD 1 | 15 | Discussion of the two-fluid model |
| Brussels | ---- | of transition to detonation. |
| 1992 | 16 | |
|_____________|_______|___________________________________________|
| |
| * The results appear to be physically plausible; experimental |
| studies confirm that appropriately-directed accelerations |
| do promote mixing and chemical reaction. |
| |
| * The process is analogous to the much-studied Rayleigh-Taylor |
| instability; but it is the simultaneous energy release which |
| gives it its self-amplifying character. |
| |
| * Flames in reciprocating-engine combustion chambers are subject
| to large accelerations; so the two-fluid model of combustion |
| is probably appropriate there too. |
| |
| * The k-epsilon model is unable to represent the acceleration |
| effects. Its utility for engine calculations is doubtful. |
|_________________________________________________________________|
___________________________________________________________________
| EuroCFD 1 | 16 | Concluding remarks: |
| Brussels | ---- | How CFD can assist researchers and |
| 1992 | 16 | designers concerned with combustion |
|_____________|_______|___________________________________________|
| |
| * Researchers, including turbulence-model creators, need to |
| understand quantitatively the elementary processes of |
| heat and mass transfer, and chemical reaction, between |
| mechanically-distorted gas fragments. |
| |
| CFD simulations of the kind shown in this lecture can assist.|
| |
| * Designers need to know how chamber-shape and other changes |
| are likely to influence perfomance, at least qualitatively. |
| |
| CFD codes such as PHOENICS, KIVA etc will give correct |
| guidance only if they incorporate the augmentation-through- |
| acceleration effect. |
|_________________________________________________________________|
An additional study
-------------------
Two-fluid simulation of steady turbulent flame spread in a duct
based on the Imperial College research of Jeremy Wu, 1985.
Agreement with experiment is good.
This is PHOENICS Input Library Case no W977.
Unburned premixed gas flows in from the left where a "flame-holder"
is situated
The parabolic-flow option of PHOENICS has been used for solving
the four momentum equations and two energy equations and two
mass-conservation equations.
Contours of reactedness of the hotter fluid
Contours of reactedness of the cooler fluid
