implementation of law’s 19 species methane reduced ...3. create a directory and name it src in the...

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Implementation of Law’s 19 Species Methane Reduced Mechanism in

FLUENT

Mouna Lamnaouer∗

Department of Mechanical Engineering

University of Central Florida, Orlando, FL 32826

[email protected]

Sponsored by

UTSR Gas Industrial Turbine Fellowship Program

May -July 2008

Prepared for

Siemens Power Generation; Combustion Technology Orlando, Fl

Industrial Mentors

Ray Laster

Scott Martin

Managers

Mike Koenig

Anil Gulati

Abstract

A 19 species global Methane mechanism previously derived from the GRI-

Mechanism 3.0 using the method of directed relation graph (DRG) and quasi steady

state assumption (QSSA) was successfully implemented into the CFD solver

FLUENT. The precompiled mechanism was linked to the solver by the means of a

User Defined Function (UDF). The UDF communicates the chemical source terms

to the solver through the subroutine “Define Net Reaction Rates”. The subroutine

then returns the molar production rates of the species given the pressure,

temperature, and mass fractions. The global reduced mechanisms are known to be

far more accurate than the skeletal mechanisms; however the inner iterations of the

elementary reactions demand more computational time than the standard Arrhenius

mechanisms. To overcome the massive computational demands of detailed

chemistry simulation in 2D and 3D domains, FLUENT incorporates ISAT (In-Situ

Adaptive Tabulation1), which can accelerate chemistry calculations up to a

thousand- fold. The reduced mechanism was tested with two challenging cases; the

Berkeley lifted CH4/Air jet flame in a vitiated co-flow and the two-D backward

facing step expansion flow. Different turbulence-chemistry models were tested

∗ PH.D. Student and Research Assistant, Mechanical, Materials & Aerospace Engineering, P.O. Box 162450, Orlando, FL 32816-2450, UTSR Fellow.

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including the eddy dissipation, the eddy break-up and the eddy dissipation concept.

In addition to the 19 species reduced mechanism, a 16 species-46 steps skeletal

mechanism was applied to the Eddy Dissipation Concept (EDC) model for the

purpose of comparison. Overall, the 19 species reduced mechanism required

slightly higher computational time than the 16 species 46 steps mechanism. The

Berkeley flame temperature profiles exhibited fast chemistry than the experiment.

Scaling the reaction rates by the turbulent time scale constant in the EDC model

caused the reaction to slow down for the 16 species Smooke mechanism but did not

have an effect on the results obtained with the 19 species mechanism.

I. Introduction

In gas turbine applications, notably in combustion devices, the flow is very

turbulent and the interaction between the chemical kinetics and turbulence is significant.

Modeling turbulent combustion requires expensive computational resources, whose cost

increases with the number of species in the chemical kinetics mechanism. The

complexity increases even further when three dimensional full scale computational grids

are used resulting into millions of nodes. Reduced mechanisms are often used in order to

decrease the computational cost. One major concern with using reduced mechanism is

loosing accuracy and therefore making the simulations unpractical.

There are many ways by which a detailed mechanism is reduced, the two major

methods being the skeletal reduction and time scale analysis. Skeletal mechanisms are on

the same form as detailed mechanisms with the standard Arrhenius elementary reactions.

Skeletal reduction is achieved with different methods including sensitivity analysis, and

detailed reduction. Time scale reduction on the other hand is based on the quasi steady

state approximation method (QSSA) and the partial equilibrium (PE) method. QSSA

involves the identification of the QSS species through the method of direct relation graph

(DRG) where species that are not strongly coupled to the major ones are determined from

a graph search.

Based on the QSSA approach, a 19 species global methane mechanism was

derived from the GRI-Mech 3.0 using the method of directed relation (DRG) by C. K>

aw [1]. The reduced mechanism was previously validated on the base of autoignition,

premixed and non-premixed flames, with less than 10% accuracy. An algorithm was

developed to solve the large systems of sparsely coupled entities which have been

compiled into a computer code and a FORTRAN subroutine has been generated.

Execution of the code results into a reduced mechanism with only 19 species.

The mechanism was incorporated into the CFD solver FLUENT by the means of

a user defined function that uses the subroutine “Define_Net_Reaction_Rates” to

compute the species reaction rates which are then fed into to the turbulence-combustion

model.

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II. Implementation of the Reduced mechanism into FLUENT

The Implementation of the global reduced mechanism into FLUENT was accomplished

as such.

A. Set up the directory structure

1. In the working directory, create a directory and name it “libudf” for example.

2. Copy makefile.udf2 from : path/Fluent.Inc/fluent.(version)/src/makefile.udf2 ,

where path is the directory in which the release directory is installed, the correct

version of Fluent should be specified. Name the makefile.udf2 to Makefile.

3. Create a directory and name it src in the libudf directory.

4. Create the source file (.c) using the appropriate macros and copy it to the src

directory. An example of the UDF .c file used with the 19 species mechanism is

shown below (Fig. 1)

Fig. 1 The user defined function uses the “Define_Net_Reaction_Rate” Macro to

compute the net reaction rates of the species.

5. Copy makefile.udf from: path /Fluent.Inc/fluent6.(version) /src/makefile.udf ,

and name it makefile (with lower case m).

6. Identify the architecture name of the machine that you are running from by either

typing the command (fluent-arch) in the FLUENT TUI window, or running the

FLUENT utility program fluent arch at the command line of a UNIX shell.

7. Create a directory with the identified architecture name and build shared libraries

for the versions used in Fluent for e.g. lnamd64/2d or (2ddp for double precision)

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and lnamd64/3d, etc... For parallel versions, create libraries with the names

2d_node and 2d_host for single precision in 2D, or 2ddp_node and 2ddp_host for

double precision in 2d. Follow the same steps for 3d versions.

After setting up the directory structure, the next step is linking the object files from non

FLUENT sources.

B. Link precompiled object files from non-FLUENT sources

1. Compile the “Fortran code” .f file using the following command: g77 “Fortran

code” .f -c -fpic -Wall -O3. It will generate the “Fortran code” .o object file.

2. Copy the precompiled object files (.o) to all of the architecture/version directories

created in Step A (e.g., lnamd64/2d ).

3. Using a text editor, edit the file makefile in the src directory to set the following

three parameters: SOURCES, FLUENT_INC, and USER_OBJECTS.

a. Specify the name of the UDF.c file next to SOURCES.

b. Specify the path to the release directory next to FLUENT_INC

c. Specify the .o object files next to USER_OBJECTS

The makefile used for the 19 species mechanism is shown below (Fig.2)

Fig. 2 The makefile for the user defined function.

4. Cd to the libudf directory and execute the Makefile by typing the following

command: make FLUENT _arch=lnamd64

The last step is to Load the library into the FLUENT solver

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C. Load the UDF library into the Fluent Solver

1. From the Define menu, scroll down to User-Defined, Functions, precompiled and

load the UDF library. A message will be displayed on the console window

providing a status of the load process.

2. Hook the UDF to FLUENT. The name of the function supplied as a Define macro

argument in the UDF.c will become visible and selectable from the User-Defined

Function Hooks panel in FLUENT. In our case the Define_Net_Reaction_Rate

Macro was used with the name PU_19 step. Below is a snapshot of the user

defined function hook panel in Fluent (Fig. 3).

Fig. 3 The User-Defined Function Hooks Panel

UDFs may be used for the eddy dissipation concept model (EDC) and PDF Transport

models, as well as for the surface chemistry model. To demonstrate the successful

implementation of the UDF in FLUENT, simulation was performed for two combustion

models; the Berkeley flame, and the 2-D backward facing step using the eddy dissipation

concept model, where the reaction rates are computed from the 19 species FORTRAN

subroutine. It is important to understand how the turbulent reaction rates for the eddy

dissipation concept model are computed using the reaction rates from the FORTRAN

code. First, we need to understand the theory behind the EDC model.

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III. Modeling Chemistry-Turbulence Interactions

1. Eddy Dissipation Concept (EDC)

The description of the turbulence-chemistry interactions represents one of the

most difficult tasks in turbulent combustion; it is necessary to adopt a robust model that

accounts for both the chemistry and the turbulence such as the EDC model. Not to be

confused with the well known Eddy Dissipation model, the eddy-dissipation-concept

(EDC) model is an extension of the eddy-dissipation model to include detailed chemical

mechanisms in turbulent flows [2, 3]. It assumes that reaction occurs in small turbulent

structures, called the fine scales. The length fraction of the fine scales, γ is modeled as,

Where, the volume fraction constant = 2.1377, and ν is the kinematic viscosity. Species

are assumed to react in the fine structures over a time scale τ, which is proportional to the

kolmogorov time scale.

The time scale constant is equal to 0.4082. This constant can be adjusted in FLUENT

either to accelerate or slow down the reaction. Decreasing the time scale constant will

result in an acceleration of the reaction while increasing it slows down the reaction

process. FLUENT assumes that the combustion at the fine scales proceeds as a constant

pressure reactor, where * denotes fine-scale quantities.

With the initial conditions taken as the current species and temperatures in the cell. Initial

condition: Yk* = Yk. Yk* is the fine scale species mass fraction after reacting over time τ.

The source term Sk in the general conservation equation for the mean species i is

modeled as:

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2. In-Situ Adaptive Tabulation Algorithm (ISAT)

The EDC model can become computationally demanding when the chemical

mechanism used contains multiple reactions and species. Due to the nonlinearity of the

chemical kinetics mechanism, the direct integration method can become unfeasible.

FLUENT overcomes this problem and uses ISAT (In-Situ Adaptive Tabulation) to

integrate the reactions [4]. ISAT can accelerate the chemistry calculations by two to three

orders of magnitude, offering substantial reductions in run-times.

The ISAT algorithm generates on the fly look up tables of chemical reaction rates.

Simulation results using the 19 species mechanism and the EDC model indicated that

ISAT works well at least for two-D axisymmetric models. For instance, simulating a

60,000 nodes model with 16 species-46 steps mechanism on one CPU, required about 2

hours of computational time. The EDC model works best when an initial solution is

obtained from the equilibrium solution using the partially premixed combustion model.

This will accelerate convergence dramatically than attempting to initialize with the EDC

model directly.

3. Communication between the FORTRAN subroutine and The

FLUENT solver

The FORTRAN subroutine is linked to FLUENT through the “Define Net

Reaction Rate” argument macro. This macro is called by the EDC model and is used to

compute the closed turbulent species reaction rates. The EDC uses the FORTRAN

reaction rates as an input to the turbulent reaction rates. In this manner, the UDF is a

complement to the EDC model and does not bypass the EDC model.

Once the reduced mechanism is constructed and executed, the subroutine that

computes the chemical source terms is automatically generated. A coupled set of

nonlinear QSS species equations are numerically solved within the subroutine to provide

the necessary elementary reaction rates for the reduced mechanism. This subroutine

which is compatible with FLUENT is specified in the user defined function and returns

the molar production rates of the species given the pressure, temperature, and mass

fractions.

The implementation of the UDF into FLUENT was benchmarked with two

combustion models; the Berkeley flame and the two-D backward facing step.

IV. Validation Cases

1. The Berkeley flame

The Berkeley flame has been experimentally investigated by Cabra at the Berkeley lab

[5]. The mixture composition and inlet conditions are given in table 1 below.

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Table 1. Berkeley flame initial conditions

Jet Coflow

T(K) 304 1350

V (m/s) 100 5.4

YCH4 0.2132 0.0001

YO2 0.1886 0.1416

YN2 0.596 0.757

YH2O 0.0021 0.1013

The flame holder assembly is comprised of the perforated plate with a diameter

210 mm, the center jet with an internal diameter of 4.57 mm, and the exit collar. The jet

fuel velocity is 100 m/s and its temperature 304 K; the jet fuel composition is 33% CH4

and 66% Air. The co-flow air conditions are 5.4 m/s velocity and 1350 K temperature.

The products from the H2/Air flame with an equivalence ratio of 0.4 are H2O and O2.

The exit collar prevents the interference of the flame with the transient

surrounding air resulting in a uniform flame. The metal is water cooled so that radiation

effects are minimized and are not taken into account in the modeling. Also the flow is

assumed to be uniform at the jet exit with a temperature of 1350 K. A schematic of the

flame holder assembly and the lifted Methane flame is shown below. (Fig. 4)

Fig. 4 Flame holder Assembly [5]

The flame was simulated with the commercial CFD code FLUENT 6.2 as a 2-D

axisymmetric model. The computational domain included the co-flow, the jet, the

velocity inlet above the co-flow, and symmetry wall boundaries with the combustion

domain extending to 1 m downstream of jet exit. The grid provided in Fig. 5 was created

in GAMBIT using a structured and non uniform mesh.

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Fig. 5 Grid for the Berkeley flame model (1000 mm by 105 mm)

The model had a spatial resolution with the Second-Order Upwind Scheme. The

segregated implicit solver was used with the PRESTO! (Pressure Staggering Options)

algorithm for pressure interpolation. Turbulence was modeled by the RANS approach,

using the Realizable K-e model suited for rounded jets. The adiabatic heat transfer

condition was imposed at the walls and radiation effects were assumed to be negligible.

The combustion model adopted was the eddy dissipation concept model.

In addition to the 19 species global reduced mechanism, the Smooke mechanism

with 16 species and 46 reactions [6] previously derived from the GRI was also tested in

FLUENT with the Berkeley flame experiment for the purpose of comparison.

The Berkeley flame experiment was previously simulated in CFX with three

mechanisms, the Nicol 3 Step, CS&E 5 Step, and the DLR 14 Step (0.5 ms). The reported

simulations herein will include results from these three mechanisms as well for the

purpose of comparison. Provided below are the temperature contours from both the 16

species (Fig. 6) and the 19 species (Fig. 7) mechanisms.

Velocity inlet Air, 296 K, 0 m/s

Co-flow, O2, H2O 1350 K, 5.4 m/s

Jet, CH4/Air 304 K, 100 m/s Axis of symmetry

Symmetry top and bottom boundaries [zero gradient]

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Fig. 6 Temperature contours predicted by the EDC model and the 16 species

Smooke mechanism

Fig. 7 Temperature contours predicted by the EDC model and the 19 species Law

mechanism

The temperature profiles show that both the Smooke and the Law mechanisms predict

fast chemistry. With the Law mechanism, combustion is very fast and hot pockets are

formed near the jet exit as soon as the jet makes contact with the co-flow. The time

constant in the EDC model was increased in order to slow down the reaction process. As

an attempt to slow down the combustion process, the time constant from the Smooke

EDC model was increased from 0.4 to 3.5 as is shown in Fig. 8.

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Centreline profiles

0

500

1000

1500

2000

2500

0 20 40 60 80 100 120

z/D

Tem

pera

ture

(K)

Temperature (Favre mean)

14 Step, CTS = 0.50 ms DLR

Fluent Smooke tc= 0.4

Fluent Smooke tc=2.3

Fluent Smooke tc=3.4

Fluent Smooke tc= 3.5

Fluent Law 19 species

Fluent Law 19 species tc=1.4

Fig. 8 Predicted centerline temperature profiles from FLUENT using the EDC 16

species Smooke and 19 species Law models. CFX results using the DLR 14 step

mechanism are also shown.

Initially, for the Smooke model, temperature is over-predicted due to the fast chemistry

exhibited by the mechanism, however adjusting the time constant from 0.4 to 3.5 resulted

in slowing down the reaction process and the temperature profile is in better agreement

with the experiment. Increasing the time constant further caused flame extinction.

Similarly, the 19 species Law model starts of with a high temperature profile but

increasing the time constant for this model did not have an effect on the results.

The predicted species profiles from both models are shown in Fig. 9-15.

In most cases, the experimental species mass fractions are in better agreement with the

Smooke mechanism than the Law mechanism. With the 19 species Law mechanism,

kinetics were so dominant that products were already formed near the jet exit as soon as

the fuel stream made contact with co-flow.

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Centreline profiles

0.00E+00

5.00E-02

1.00E-01

1.50E-01

2.00E-01

2.50E-01

0 20 40 60 80 100 120

z/D

Y O

2

O2 Mass Fraction

5step, CTS=3.40 ms - CSE + CK4

3 Step, CTS = 3.4 ms - Nicol


Fluent Smooke 16 species tc = 3.5

Fluent Law 19 species_15 steps

Fig. 9 O2 mass fraction profile from the Law 19 species and Smooke 16 species

models. Results from CFX using the 3 step, 5 step and 14 step models are also

shown.

Centreline profiles

0.00E+00

2.00E-02

4.00E-02

6.00E-02

8.00E-02

1.00E-01

1.20E-01

1.40E-01

1.60E-01

1.80E-01

0 20 40 60 80 100 120

z/D

Y H

2O

H2O Mass Fraction




Fluent Smooke 16 species tc=3.5


Fig. 10 H2O mass fraction profile from the Law 19 species and Smooke 16 species


shown.

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Centreline profiles

0.00E+00

5.00E-02

1.00E-01

1.50E-01

2.00E-01

2.50E-01

0 20 40 60 80 100 120

z/D

Y C

H4

CH4 Mass Fraction




Fluent Smooke 16 species tc=3.5


Fig. 11 CH4 mass fraction profile from the Law 19 species and Smooke 16 species


shown.

Centreline profiles

-1.00E-02

0.00E+00

1.00E-02

2.00E-02

3.00E-02

4.00E-02

5.00E-02

6.00E-02

7.00E-02

8.00E-02

0 20 40 60 80 100 120

z/D

Y C

O

CO Mass Fraction




Fluent Smooke 16 species tc =3.5


Fig. 12 CO mass fraction profile from the Law 19 species and Smooke 16 species


shown.

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Fig. 13 CO2 mass fraction profile from the Law 19 species and Smooke 16 species


shown.

Fig. 14 H2 mass fraction profile from the Law 19 species and Smooke 16 species

models. Results from CFX using the 14 step model are also shown.

Centreline profiles

-1.00E-03

0.00E+00

1.00E-03

2.00E-03

3.00E-03

4.00E-03

5.00E-03

6.00E-03

7.00E-03

8.00E-03

9.00E-03

0 20 40 60 80 100 120

z/D

Y H

2

H2 Mass Fraction


Fluent Smooke 16 species t = 3.5


Centreline profiles

0.00E+00

1.00E-02

2.00E-02

3.00E-02

4.00E-02

5.00E-02

6.00E-02

7.00E-02

8.00E-02

9.00E-02

1.00E-01

0 20 40 60 80 100 120

z/D

Y C

O2

CO2 Mass Fraction




Fluent smooke 16 species tc=3.5


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Centreline profiles

-2.00E-03

0.00E+00

2.00E-03

4.00E-03

6.00E-03

8.00E-03

1.00E-02

1.20E-02

1.40E-02

0 20 40 60 80 100 120

z/D

Y O

H

OH Mass Fraction


Fluent Smooke 16 species t =3.5


Fig. 15 OH mass fraction profile from the Law 19 species and Smooke 16 species

models. Results from CFX using the 14 step model are also shown.

2. 2-D Backward Facing Step

Data for the two-D backward facing step were acquired from the experiment

performed by El Banhawy on turbulent combustion of a sudden expansion flow [7].

Measurements were performed in a 40 by 157 mm rectangular cross section with a step

height of 20 mm. The studied mixture is methane/air mixture with an equivalence ratio of

0.9. Initially, 94% CH4 and Air were supplied under pressure to a swirl mixer before

passing through a settling section, flow straightness, a flame trap, and into the

combustion chamber. The flow Reynolds Number is about 1.35 *10 4 and the flow rate is

125 kg/h. Table 2 provides the initial conditions applied at the inlet. The flow

configuration is described in Fig. 16

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Table 2 Backward Facing Step inlet conditions

Inflow Outflow

T (K) 300 300

V (m/s) 10.92 0

I (%) 5 5

d (m) 0.02 0.04

Y CH4 0.04994 0

Y O2 0.22137 0.23

Fig. 16 Flow configuration [7]

The computational domain modeled only the combustion chamber and consisted of a 2-D

structured grid (0.04m by 0.47 m) with 24000 cells. Initially cells were clustered near the

inlet and the walls but this did not seem to affect the results so the uniform grid was used

throughout the simulations. The 2D segregated steady model was adopted with the

PRESTO algorithm and 2nd

order upwind spatial discretization. The Realizable k-ε model

was utilized to model turbulence. A velocity and pressure boundary conditions were

imposed at the inlet and outlet respectively. 5% fluctuations were imposed on the velocity

at the inlet. The grid is displayed in Fig. 17.

0.47 m

0.04 m

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Fig. 17 Structured mesh for the 2-D backward facing step [0.47 m by 0.04 m]

The EDC combustion model was adopted with the 19 species global mechanism.

Additionally, the laminar finite rate, the eddy dissipation, and the eddy dissipation/finite

rate combustion models were used in conjunction with a one step 5 species methane

mechanism built into FLUENT. Provided first are the results obtained from the El

Banhawy experiment for mean temperature, mean axial velocity and species profiles

(Figs 18-20).

Fig. 18 Temperature contours from El Banhawy experiment [7]

Fig. 19 Mean axial velocity contours from the El Banhawy experiment [7]

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Fig. 20 Contours of volume concentrations of unburned hydrocarbons. Dashed lines

correspond to 20 mm step height [7]

From the temperature contours presented in the El Banhawy experiments, reaction is

dominant in the upper wall region up to x/h = 3.5 then spreads to the lower wall. The

maximum measured temperature was 2000 K at x/h = 12.5. The species concentration

profiles also show that the reaction is first concentrated near the upper wall then

immediately spreads toward the bottom wall. Contours of mean axial velocity capture

the recirculation region in the upper left corner. The mean attachment length was found

to be about three times the size of the step height. The flow accelerates from an average

velocity of 1 m/s at x/h = 0 to a maximum velocity of 25 m/s at x/h = 15.

To investigate whether or not the 19 species global mechanism is able to capture

the phenomena reported in the El Banhawy experiments, the 2D backward facing step

case was simulated in FLUENT. The laminar finite rate, the eddy dissipation and the

eddy dissipation/ finite rate models were adopted with the 1 step 5 species Methane

mechanism while the 19 species global mechanism was used with the EDC model.

Temperature, velocity, and density profile results from the simulations are reported below

(Fig. 20-24).

Laminar Finite Rate

a) Temperature (K)

b) X Velocity (m/s)

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c) Density (Kg/m^3)

Fig. 21 Temperature, velocity, and density profiles simulated with the 1 step-5 species Methane mechanism and laminar finite rate model

Finite/Eddy Dissipation

a) Temperature (K)

b) X Velocity (m/s)

c) Density (kg/m^3)

Fig. 22 Temperature, velocity, and density profiles simulated with the 1 step-5

species Methane mechanism and the finite/Eddy dissipation model

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Eddy Dissipation

a) Temperature (K)

b) Density (Kg/m3)

c) X Velocity (m/s)


species Methane mechanism and the eddy dissipation model

Eddy Dissipation Concept

a) Temperature (K)

21

b) Density (kg/m3)

c) X Velocity (m/s)


species Methane mechanism and the eddy dissipation concept model

All models predict a dominant reaction in the upper wall region as soon as the

fuel enters the combustion region. The reattachment length however differs from model

to model. The laminar finite rate predicts a reattachment length of 1 time the step height

while the eddy dissipation model predicts a reattachment length of 2 times the step

height. The Eddy dissipation/ Finite rate model on the other hand did not show any

reattachment and the flame is localized in the upper region throughout the combustion

process. All three models over-predict the temperature. Axial velocity results for all three

models captured the recirculation region well but failed to accurately simulate the

velocity profiles which explain the discrepancies in the temperature profile results

The 19 species mechanism was modeled with the eddy dissipation concept. The

temperature contours predict a maximum temperature of 2150 K with the reaction

concentrated in the upper wall region. However, the 19 species mechanism in

combination with the EDC model fails to predict the right reattachment length and shows

no reaction near the bottom wall (Fig. 25). Figures 26 and 27 plot the mean temperature

at locations X = 0.2 m and Y = 0.02 m for all the chemistry models discussed herein.

Fig. 25 Temperature profiles with the 19 species EDC model

22

0.00 0.01 0.02 0.03 0.040

500

1000

1500

2000

2500

3000

T

em

pera

ture

(K

)

Radial Distance (m) at X= 0.2 m

Laminar Finite Rate

Eddy Dissipation


Finite/ED

Law-19 Species EDC

Fig. 26 Temperature profile- center Line at X=0.02 m.

0.0 0.1 0.2 0.3 0.4 0.50

500

1000

1500

2000

2500

3000

Tem

pera

ture

(K

)

Center Line Distance (m) at Y= 0.02 m

Laminar Finite Rate

Eddy Dissipation


Finite/ED

Law_19 species EDC

Fig. 27 Axial Temperature profile at Y=0.02 m.

Velocity profiles provided in Fig. 28 show that the 19 species law model captures

the recirculation region at the top left corner and predicts mean velocities at x/h =15 of 23

23

m/s compared to 25 m/s as predicted from the experiment. Overall, velocity profiles from

the model are in good agreement with the experiment.

Fig. 28 Axial velocity contours with the EDC 19 species mechanism. Recirculation

zone is well captured and velocities downstream are well represented.

Species mass fractions were also plotted for all four models at a location X = 0.2 m.

Results are provided in Figs 29-34.

0.00 0.01 0.02 0.03 0.04

0.00

0.01

0.02

0.03

0.04

0.05

CH

4 M

ass F

racti

on


Laminar Finite Rate

Eddy Dissipation


Finite/ED

Law_19 species EDC

Fig. 29 CH4 mass fraction

24

0.00 0.01 0.02 0.03 0.04-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

CO

2 M

ass F

racti

on


Laminar Finite Rate

Eddy Dissipation


Finite/ED

Law_19 species EDC

Fig. 30 CO2 mass fraction

0.00 0.01 0.02 0.03 0.04

0.00

0.02

0.04

0.06

0.08

0.10

0.12

H2O

Mass F

racti

on


Laminar Finite Rate

Eddy Dissipation


Finite/ED

Law_19 species EDC

Fig. 31 H2O mass fraction

25

0.00 0.01 0.02 0.03 0.040.728

0.730

0.732

0.734

0.736

0.738

0.740

N2 M

ass F

racti

on


Laminar Finite Rate

Eddy Dissipation


Finite/ED

Law_19 species EDC

Fig. 32 N2 mass fraction

0.00 0.01 0.02 0.03 0.04-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

O2 M

ass F

racti

on


Laminar Finite Rate

Eddy Dissipation


Finite/ED

Law_19 species EDC

Fig. 33 O2 mass fraction

26

0.00 0.01 0.02 0.03 0.04

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

0.018

Radial Distance (m) at Exit

NO

x M

ass F

racti

on

at

Exit

Laminar Finite Rate

Eddy Dissipation


Law_19 species EDC

Fig. 34 NOx mass fraction

All models predict reaction occurring near the top and bottom walls except for the

eddy dissipation/ finite rate with the 1 step mechanism (eddy break-up model) and the

EDC with the 19 species mechanism. As an attempt to speed up the reaction in the 19

species EDC model, the time constant was lowered from 0.4 to 0.1, the model could not

handle the small time scale and an error generated and caused the model to crush.

At this point, it is not know the reason why the 19 species Law model did not

respond to the scaling with the time constant. It is unlikely that the discrepancies

exhibited herein are related to the model set up and the turbulence model adopted, since

different other combustion models were used and scaling with the turbulent time constant

did improve the results significantly.

Whether or not turbulence is accounted for when the Law reduced mechanism is used

in conjunction with a turbulence model is questionable, although we have explained in

details the steps undertaken to establish communication between the FORTRAN

subroutine and the FLUENT solver and how the final reaction rates are computed. Since

the 19 species Law mechanism has been validated previously with great success for

laminar studies, it would be worth looking at testing the reduced mechanism with a

laminar case and then introducing turbulence at a later time. This will prove whether or

not turbulence is bypassed when the Law mechanism is used regardless if a turbulence

model is adopted.

27

V. Conclusion

The 19 species reduced mechanism has been implemented and tested in FLUENT.

FLUENT has UDF capabilities to allow for such implementation. Validation cases

included the Berkeley flame and the 2D backward facing step experiments. The

capability of predicting temperature profiles and species concentrations using the reduced

chemical kinetic mechanism was demonstrated.

In the 2D backward facing step case, the maximum mean velocities and recirculation

zone were well captured by the EDC 19 species mechanism, however the temperature

contours showed that reattachment of the flow to the bottom wall was not exhibited and

combustion was concentrated on the upper wall region only. An attempt to decrease the

time constant in order to speed up the reaction caused the model to crush. One

explanation for the discrepancies shown with the 2D backward facing step case is the

accuracy of the turbulent model considered rather than the chemical mechanism itself

since the Law mechanism has been previously validated for ignition delay, extinction,

and flame speed with great success. Often times, tweaking the turbulent parameters is

necessary to achieve satisfying results.

For the Berkeley flame case, temperature profiles showed that both the Smooke and

the Law mechanisms predicted flame location closer to the jet exit than the experiment.

Hot pockets were observed near the jet exit for the 19 species EDC model. Increasing the

time constant in the Smooke EDC model caused the reaction to slow down and the liftoff

height of the flame to increase. However, the exit temperature was decreased. Increasing

the time constant beyond 3.5 caused flame extinction. On the other hand, the Law model

showed no effect of the time constant increase on the flame location and model crushed

when attempting to increase the time constant beyond 1.4.

As far as the computational time of the models, the 19 species global mechanism

required slightly higher computational time than the 16 species 46 steps mechanism due

to inner iterations of the elementary reaction. It is not an easy task to converge the EDC

model a UDF is involved. Helpful steps to accelerate convergence included initialization

of the model with the partially premixed solution. This allowed for convergence in

approximately 3 hours compared to 10 hours without the equilibrium solution.

One major concern that rises from testing the 19 species reduced mechanism is the

non-sensitivity of the combustion process to the turbulent time scale constant in the EDC

model, this raises the question whether or not the reaction rates computed from the

Fortran subroutine are scaled by the turbulent time scales as explained in the EDC theory.

One way to verify this hypothesis is to test the mechanism with a laminar case and

compare with CHEMKIN results. Further recommendations include the following.

1) PSR can be modeled in FLUENT by imposing a wall boundary condition at the inlet

and running unsteady with a time step of 1 microsec.

2) Since the PSR is spatially homogeneous, refinement is not necessary in the axial

direction.

3) An outlet boundary is required to account for the gas expansion.

4) CANTERA can be used to compare the results.

28

Until these steps are undertaken to achieve a conclusion regarding the discrepancies

in the results, the reduced 13 and 16 species Syngas mechanisms can then be

implemented into FLUENT following the same approach outlined herein.

VI. Acknowledgement

The author of this paper is a participant of the University Turbine Systems Research

(UTSR) program, through a fellowship grant. This report was prepared with the support

of Siemens Power Generation generally and the combustion group specifically.

VII. References

[1] Law, K., and Lu, Tianfeng, “An Efficient Reduced Mechanism for Methane

Oxidation with NO Chemistry,” 5th

US Combustion Meeting, Paper # C17, Sandiego, Ca,

March 25-28, 2007

[2] B. F. Magnussen, “On the Structure of Turbulence and a Generalized Eddy

Dissipation Concept for Chemical Reaction in Turbulent Flow,” Nineteenth AIAA

Meeting, St. Louis, 1981.

[3] I. R. Gran and B. F. Magnussen, “A numerical study of a bluff-body stabilized

diffusion flame. part 2. influence of combustion modeling and finite-rate chemistry,”

Combustion Science and Technology, 119:191, 1996.

[4] S. B. Pope, “Computationally efficient implementation of combustion chemistry

using in-situ adaptive tabulation,” Combustion Theory and Modeling, 1:41-63, 1997.

[5] http://www.me.berkeley.edu/cal/VCB/Data/VCMAData.html

[6] M.D. Smooke, I.K. Puri, K. Seshadri, Proc. Combust. Inst. 21 (1986) 1783–1792.

[7] Y. El Banhawy, S. Sivasegaram, and J. H., Whitelaw, “Premixed, Turbulent

Combustion of a Sudden-Expansion Flow,” Combustion and Flame, Vol. 50, pp 153-165,

1983.

implementation of law’s 19 species methane reduced ...3. create a directory and name it src in the...

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