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Syngas Combustion in a Round-Jet Burner
Introduction
This model simulates turbulent combustion of syngas (synthesis gas) in a simple round jet burner. Syngas is a gas mixture, primarily composed of hydrogen, carbon monoxide and carbon dioxide. The name syngas relates to its use in creating synthetic natural gas.
The model setup corresponds to the one studied by Couci and others in Ref. 1. The temperature and composition resulting from the nonpremixed combustion in the burner setup have also been experimentally investigated by Barlow and coworkers (Ref. 2 and Ref. 3) as a part of the International Workshop on Measurement and Computation of Turbulent Nonpremixed Flames (Ref. 4). The model is solved in COMSOL Multiphysics by combining a Reacting Flow and a Heat Transfer in Fluids interface.
Model Definition
The burner studied in this model consists of a straight pipe placed in a slight coflow. The gas phase fuel is fed through the pipe using an inlet velocity of 76 m/s, while the coflow velocity outside of pipe is 0.7 m/s. At the pipe exit, the fuel gas mixes with the coflow, creating an unconfined circular jet. The gas fed through the tube consists of three compounds typical of syngas: carbon monoxide (CO), hydrogen (H2), and nitrogen (N2). The coflow gas consists of air. At the pipe exit, the fuel is ignited. Since the fuel and oxidizer enter the reaction zone separately, the resulting combustion is of the nonpremixed type. A continuous reaction requires that the reactants and the oxidizer are mixed to stoichiometric conditions. In this setup, the turbulent flow of the jet effectively mixes the fuel from the pipe with the coflowing oxygen. Furthermore, the mixture needs to be continuously ignited. In this burner the small recirculation zones generated by the pipe wall thickness provide the means to decelerate hot product gas. The recirculation zones hereby promote continuous ignition of the oncoming mixture and stabilizes the flame at the pipe orifice. In experiments (Ref. 4), no lift-off or localized extinction of the flame has been observed.
In the current model, the syngas combustion is modeled using two irreversible reactions:
(1)
This assumption of a complete oxidation of the fuel corresponds to one of the approaches used in Ref. 1. The mass transport in the reacting jet is modeled by solving for the mass fractions of six species: the five species participating in the reactions and nitrogen N2 originating in the coflowing air.
The Reynolds number for the jet, based on the inlet velocity and the inner diameter of the pipe, is approximately 16,700, indicating that the jet is fully turbulent. Under these circumstances, both the mixing and the reactions processes in the jet are significantly influenced by the turbulent nature of the flow. To account for the turbulence when solving for the flow field, the k-ω turbulence model is applied.
Taking advantage of the symmetry, a two-dimensional model using a cylindrical coordinate system is solved.
Turbulent reaction rate
When using a turbulence model in a Reacting Flow interface, the production rate (SI unit: kg/(m3·s)) of species i resulting from reaction j is modeled as the minimum of the mean-value-closure reaction rate and the eddy-dissipation-model rate:
The mean-value-closure rate is the kinetic reaction rate expressed using the mean mass fractions. This corresponds to the characteristic reaction rate for reactions that are slow compared to the turbulent mixing, or the reaction rate in regions with negligible turbulence levels. This can be quantified through the Damköhler number, which compares the turbulent time scale (τT) to the chemical time scale (τc). The mean-value-closure is appropriate for low Damköhler numbers:
The reaction rate defined by the eddy-dissipation model (Ref. 5) is
(2)
where τT (SI unit: s) is the mixing time scale of the turbulence, ρ is the mixture density (SI unit: kg/m3), ω is the species mass fraction, ν denotes the stoichiometric coefficients, and M is the molar mass (SI unit: kg/mol). Properties of reactants of the reaction are indicated using a subscript “r,” while product properties are denoted by a subscript “p”.
The eddy-dissipation model assumes that both the Reynolds and Damköhler numbers are sufficiently high for the reaction rate to be limited by the turbulent mixing time scale τT. A global reaction can then at most progress at the rate at which fresh reactants are mixed, at the molecular level, by the turbulence present. The reaction rate is also assumed to be limited by the deficient reactant; the reactant with the lowest local concentration. The model parameter β specifies that product species is required for reaction, modeling the activation energy. For gaseous nonpremixed combustion the model parameters have been found to be (Ref. 5):
,
In the current model the molecular reaction rate of the reactions is assumed to be infinitely fast. This is achieved in the model by prescribing unrealistically high rate constants for the reactions. This implies that the production rate is given solely by the turbulent mixing in Equation 2.
It should be noted that the eddy-dissipation model is a robust but simple model for turbulent reactions. The reaction rate is governed by a single time scale, the turbulent mixing time-scale. For this reason, the reactions studied should be limited to global one-step (as in Equation 1) or two-step reactions.
thermal properties — heat of reaction and heat capacity
In this model, a thermodynamic system including all present species is set up. The system is used to define species as well as mixture properties dependent on temperature and composition. When coupling the Chemistry interface to the Thermodynamic system, all thermodynamic and transport properties needed are automatically defined.
Two of the thermal properties needed are the heat of reaction and the heat capacity of the mixture. Figure 1 shows the variation of enthalpy of formation with temperature for all individual species. The enthalpy of formation is seen to increase with temperature for all species, and accurate results will be obtained by taking the temperature-dependence into consideration.
Figure 1: Enthalpy of formation for all individual species.
The heat capacities for all species in the system plotted against temperature are seen in Figure 2. As for the enthalpy of formation, all species’ heat capacities increase with temperature, making it relevant to also take the temperature-dependence on heat capacity into consideration.
Figure 2: Heat capacity for all individual species.
The heat of formations for each species at T = 298 K are given in Table 1 and the heat capacities at T = 300 K and T = 2000 K are given in Table 2. Both tables compare data based on Ref. 6 and Ref. 7 to calculated values from COMSOL. By using these values in Equation 3, the heat of formation at T = 298 K can be calculated. Since the heat of formation of the products is lower than that of the reactants, both reactions are exothermic and release heat:
(3)
 
Table 1: Species enthalpy of formation at 298.15 K from both reference data and comsol.
Species
ΔHf (kJ/mol)
T = 298.15 K (Ref. 6)
ΔHf (kJ/mol)
T = 298.15 K (COMSOL)
N2
0
0
H2
0
0
O2
0
0
H2O
-241.84
-241.82
CO
-110.54
-110.53
CO2
-393.55
-393.98
Table 2: Species heat capacity at 300 K and 2000 K from both reference data and comsol.
Species
Cp (J/mol/K)
T = 300 K
(Ref. 6, Ref. 7 for CO and CO2)
Cp (J/mol/K)
T = 300 K (COMSOL)
Cp (J/mol/K)
T = 2000 K
(Ref. 6)
Cp (J/mol/K)
T = 2000 K
(COMSOL)
N2
29.075
29.142
35.987
36.368
H2
28.878
28.857
34.238
34.528
O2
29.330
29.395
37.790
37.882
H2O
33.468
33.602
51.145
51.193
CO
29.035
29.136
33.254
36.591
CO2
37.101
37.225
54.363
61.078
Results and Discussion
The resulting velocity field in the nonisothermal reacting jet is visualized in Figure 3. The expansion and development of the hot free jet is clearly seen. The turbulent mixing in the outer parts of the jet acts to accelerate fluid originating in the co-flow, and incorporate it in the jet. This is commonly referred to as entrainment and can be observed in the co-flow streamlines which bend toward the jet downstream of the orifice.
Figure 3: The velocity magnitude and flow paths (streamlines) of the reacting jet.
The temperature in the jet is shown in Figure 4 where a revolved dataset has been used to emphasize the structure of the round jet. The maximum temperature in the jet is seen to be approximately 2150 K. The carbon dioxide mass fraction in the reacting jet is plotted in Figure 5. The formation of CO2 takes place in the outer shear layer of the jet. This is where the fuel from the pipe encounters oxygen in the coflow and reacts. The reactions are promoted by the turbulent mixing in the jet shear layer. It is also seen that the CO2 formation starts just outside of the pipe. This is also the case for the temperature increase in Figure 4. This implies that there is no lift-off and the flame is attached to the pipe.
In Figure 6, Figure 7, and Figure 8 the results reached in the model are compared with the experimental results of Barlow and coworkers (Ref. 2, Ref. 3, and Ref. 4). In Figure 6 the jet temperature is further examined and compared with the experiments. In the left panel the temperature along the centerline is plotted. It is seen that the maximum temperature predicted in the model is close to that in the experiment. However in the model the temperature profile is shifted in the downstream direction. This is most likely due to the fact that radiation has not been included in the model.
In the right panel of Figure 6 temperature profiles at 20 and 50 pipe diameters downstream of the pipe exit are compared with the experiments. The axial velocity of the jet is compared with the experimental results in Figure 7, using the same down stream positions. The axial velocity is found to compare well with the experimental values at both positions.
In Figure 8 the species concentration along the jet centerline is analyzed and compared with the experimental results. For some species, N2, and CO2, the axial mass fraction development agrees well with the experimental results. For the fuel species CO and H2 a fair agreement is observed. For the remaining species, O2 and H2O, the trend appears correct but the profiles are shifted downstream, as was the case with the temperature. The reason for the discrepancy in the mass fractions can in part be attributed to the fact that radiation is not included, but the accuracy is probably also significantly influenced by the simplified reaction scheme and the eddy-dissipation model.
Figure 4: Jet temperature shown using a revolved dataset.
Figure 5: CO2 mass fraction in the reacting jet.
Figure 6: Jet temperature along the centerline (left), and radially at two different positions downstream of the pipe exit (right) scaled by the inlet temperature. The centerline and radial distance is scaled by the inner diameter of the pipe. Model results are plotted using lines, while experimental results are indicated using symbols. The downstream positions are defined in terms of the inner diameter of the pipe (d).
Figure 7: Axial velocity at two different positions downstream of the pipe exit, scaled by the inlet velocity. The radial distance is scaled by the inner diameter of the pipe. Model results are plotted using lines, while experimental results are indicated using symbols.
Figure 8: Species mass fractions along the jet centerline. The centerline distance is scaled by the inner diameter of the pipe. Model results are plotted using lines, while experimental results are indicated using symbols.
References
1. A. Cuoci, A. Frassoldati, G. Buzzi Ferraris, T. Faravelli, and E. Ranzi, “The ignition, combustion and flame structure of carbon monoxide/hydrogen mixtures. Note 2: Fluid dynamics and kinetic aspects of syngas combustion,” Int. J. Hydrogen Energy, vol. 32, pp. 3486–3500, 2007.
2. R.S. Barlow, G.J. Fiechtner, C.D. Carter, and J.-Y. Chen, “Experiments on the Scalar Structure of Turbulent CO/H2/N2 Jet Flames,” Comb. and Flame, vol. 120, pp. 549–569, 2000.
3. M. Flury, Experimentelle Analyse der Mischungsstruktur in turbulenten nicht vorgemischten Flammen, Ph.D. Thesis, ETH Zurich, 1998.
4. R.S. Barlow and others, “Sandia/ETH-Zurich CO/H2/N2 Flame Data - Release 1.1,” http://www.sandia.gov/TNF/DataArch/SANDchnWeb/SANDchnDoc11.pdf, 2002.
5. B.F. Magnussen and B.H. Hjertager, “On Mathematical Modeling of Turbulent Combustion with Special Emphasis on Soot Formation and Combustion,” 16th Symp. (Int.) on Combustion. Comb. Inst., Pittsburgh, Pennsylvania, pp. 719–729, 1976.
6. A. Frassoldati, T. Faravelli, and E. Ranzi, “The Ignition, Combustion and Flame Structure of Carbon Monoxide/Hydrogen Mixtures. Note 1: Detailed Kinetic Modeling of Syngas Combustion Also in Presence of Nitrogen Compounds,” Int. J. Hydrog. Energy, vol. 32, pp. 3471–3485, 2007.
7. B.E. Poling, J.M. Prausnitz, and J.P. O’Connell, The Properties of Gases and Liquids, McGraw-Hill, 2001.
Application Library path: Chemical_Reaction_Engineering_Module/Reactors_with_Mass_and_Heat_Transfer/round_jet_burner
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  2D Axisymmetric.
2
In the Select Physics tree, select Chemical Species Transport>Nonisothermal Reacting Flow>Turbulent Flow>Turbulent Flow, k-ω.
3
Click Add.
4
In the Added physics interfaces tree, select Transport of Concentrated Species (tcs).
5
In the Number of species text field, type 6.
6
In the Mass fractions table, enter the following settings:
wCO
wO2
wCO2
wH2
wH2O
wN2
7
Click  Study.
8
In the Select Study tree, select General Studies>Stationary.
9
Click  Done.
Global Definitions
Parameters 1
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file round_jet_burner_parameters.txt.
Geometry 1
Rectangle 1 (r1)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type GeomW.
4
In the Height text field, type GeomH.
5
Click  Build Selected.
Rectangle 2 (r2)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type Pth.
4
In the Height text field, type Pl.
5
Locate the Position section. In the r text field, type Di/2.
6
Click  Build Selected.
Chamfer 1 (cha1)
1
In the Geometry toolbar, click  Chamfer.
2
On the object r2, select Points 3 and 4 only.
It might be easier to select the points by using the Selection List window. To open this window, in the Home toolbar click Windows and choose Selection List. (If you are running the cross-platform desktop, you find Windows in the main menu.)
3
In the Settings window for Chamfer, locate the Distance section.
4
In the Distance from vertex text field, type Pth*0.15.
5
Click  Build Selected.
6
Click the  Zoom Extents button in the Graphics toolbar.
Polygon 1 (pol1)
1
In the Geometry toolbar, click  Polygon.
2
In the Settings window for Polygon, locate the Coordinates section.
3
From the Data source list, choose Vectors.
4
In the r text field, type GeomW GeomW*1.5 GeomW*1.5 GeomW.
5
In the z text field, type 0 GeomH GeomH GeomH.
6
Click  Build Selected.
Union 1 (uni1)
1
In the Geometry toolbar, click  Booleans and Partitions and choose Union.
2
Select the objects pol1 and r1 only.
3
In the Settings window for Union, locate the Union section.
4
Clear the Keep interior boundaries check box.
5
Click  Build Selected.
Difference 1 (dif1)
1
In the Geometry toolbar, click  Booleans and Partitions and choose Difference.
2
Select the object uni1 only.
3
In the Settings window for Difference, locate the Difference section.
4
Find the Objects to subtract subsection. Click to select the  Activate Selection toggle button.
5
Select the object cha1 only.
6
Click  Build Selected.
Line Segment 1 (ls1)
1
In the Geometry toolbar, click  More Primitives and choose Line Segment.
2
In the Settings window for Line Segment, locate the Starting Point section.
3
From the Specify list, choose Coordinates.
4
In the z text field, type Pl-0.15*Pth.
5
Locate the Endpoint section. From the Specify list, choose Coordinates.
6
In the r text field, type Di/2.
7
In the z text field, type Pl-0.15*Pth.
8
Click  Build Selected.
Line Segment 2 (ls2)
1
In the Geometry toolbar, click  More Primitives and choose Line Segment.
2
In the Settings window for Line Segment, locate the Starting Point section.
3
From the Specify list, choose Coordinates.
4
In the r text field, type Di/2+Pth.
5
In the z text field, type Pl-0.15*Pth.
6
Locate the Endpoint section. From the Specify list, choose Coordinates.
7
In the r text field, type GeomW+0.5*(Pl-0.15*Pth)*GeomW/GeomH.
8
In the z text field, type Pl-0.15*Pth.
9
Click  Build Selected.
Line Segment 3 (ls3)
1
In the Geometry toolbar, click  More Primitives and choose Line Segment.
2
In the Settings window for Line Segment, locate the Starting Point section.
3
From the Specify list, choose Coordinates.
4
In the r text field, type Di/2.
5
In the z text field, type Pl-0.15*Pth.
6
Locate the Endpoint section. From the Specify list, choose Coordinates.
7
In the r text field, type Di/2+(GeomH-Pl+Pth*0.15)*tan(pi/180).
8
In the z text field, type GeomH.
9
Click  Build Selected.
Line Segment 4 (ls4)
1
In the Geometry toolbar, click  More Primitives and choose Line Segment.
2
In the Settings window for Line Segment, locate the Starting Point section.
3
From the Specify list, choose Coordinates.
4
In the r text field, type Di/2+Pth.
5
In the z text field, type Pl-0.15*Pth.
6
Locate the Endpoint section. From the Specify list, choose Coordinates.
7
In the r text field, type Di/2+Pth+(GeomH-Pl+Pth*0.15)*tan(5*pi/180).
8
In the z text field, type GeomH.
9
Click  Build Selected.
Form Union (fin)
1
In the Model Builder window, click Form Union (fin).
2
In the Settings window for Form Union/Assembly, click  Build Selected.
Mesh Control Edges 1 (mce1)
1
In the Geometry toolbar, click  Virtual Operations and choose Mesh Control Edges.
2
On the object fin, select Boundaries 4, 8, 13, and 14 only.
3
In the Settings window for Mesh Control Edges, click  Build Selected.
4
Click the  Zoom Extents button in the Graphics toolbar.
Form Composite Edges 1 (cme1)
1
In the Geometry toolbar, click  Virtual Operations and choose Form Composite Edges.
2
On the object mce1, select Boundaries 3 and 11 only.
3
In the Settings window for Form Composite Edges, click  Build Selected.
Define a Thermodynamic System that can be used for several physical properties in the model. The system is in gas phase and consists of water, hydrogen, oxygen, nitrogen, carbon monoxide and carbon dioxide.
Global Definitions
In the Physics toolbar, click  Thermodynamics and choose Thermodynamic System.
Select System
1
Go to the Select System window.
2
Click Next in the window toolbar.
Select Species
1
Go to the Select Species window.
2
In the Species list, select water (7732-18-5, H2O).
3
Click  Add Selected.
4
In the Species list, select carbon monoxide (630-08-0, CO).
5
Click  Add Selected.
6
In the Species list, select carbon dioxide (124-38-9, CO2).
7
Click  Add Selected.
8
In the Species list, select nitrogen (7727-37-9, N2).
9
Click  Add Selected.
10
In the Species list, select oxygen (7782-44-7, O2).
11
Click  Add Selected.
12
In the Species list, select hydrogen (1333-74-0, H2).
13
Click  Add Selected.
14
Click Next in the window toolbar.
Select Thermodynamic Model
1
Go to the Select Thermodynamic Model window.
2
Click Finish in the window toolbar.
Global Definitions
Gas System 1 (pp1)
As stated in the Model Definition section, the heat of reaction and heat capacity of the mixture are dependent on temperature and composition. To display their dependence, plots where the enthalpy of formation and heat capacity are plotted against a temperature span between 298.15 and 2000 K are later created. The functions necessary for these plots will now be obtained.
1
In the Model Builder window, under Global Definitions>Thermodynamics right-click Gas System 1 (pp1) and choose Species Property.
Select Properties
1
Go to the Select Properties window.
2
In the list, select Heat capacity (Cp) (J/(K*mol)).
3
Click  Add Selected.
4
In the list, select Enthalpy of formation (J/mol).
5
Click  Add Selected.
6
Click Next in the window toolbar.
Select Phase
1
Go to the Select Phase window.
2
Click Next in the window toolbar.
Select Species
1
Go to the Select Species window.
2
Click  Add All.
3
Click Next in the window toolbar.
Species Property Overview
1
Go to the Species Property Overview window.
2
Click Finish in the window toolbar.
Chemistry (chem)
Reaction 1
1
In the Model Builder window, under Component 1 (comp1) right-click Chemistry (chem) and choose Reaction.
2
In the Settings window for Reaction, locate the Reaction Formula section.
3
In the Formula text field, type CO+O2=>CO2.
4
Click Apply.
Since all species in the reaction are written using their chemical formulas, their molar masses are pre-defined to come from thermodynamics. Moreover, the reaction can also be balanced using the Balance button.
Click Balance in the upper-right corner of the Reaction Formula section.
Reaction 2
1
In the Physics toolbar, click  Domains and choose Reaction.
2
In the Settings window for Reaction, locate the Reaction Formula section.
3
In the Formula text field, type H2+O2=>H2O.
4
Click Apply.
5
Click Balance in the upper-right corner of the Reaction Formula section.
Species 1
1
In the Physics toolbar, click  Domains and choose Species.
2
In the Settings window for Species, locate the Name section.
3
In the text field, type N2.
Since a Thermodynamic system is defined earlier, the Thermodynamics check box can be selected that uses the values for density and heat capacity from the system.
1
In the Model Builder window, click Chemistry (chem).
2
In the Settings window for Chemistry, locate the Mixture Properties section.
3
Select the Thermodynamics check box.
4
Locate the Species Matching section. From the Species solved for list, choose Transport of Concentrated Species.
5
Find the Bulk species subsection. In the table, enter the following settings:
Species
Type
Mass fraction
Value (1)
From Thermodynamics
CO
Variable
wCO
Solved for
CO
CO2
Variable
wCO2
Solved for
CO2
H2
Variable
wH2
Solved for
H2
H2O
Variable
wH2O
Solved for
H2O
N2
Free species
wN2
Solved for
N2
O2
Variable
wO2
Solved for
O2
6
Click to expand the Calculate Transport Properties section. From the Thermal conductivity list, choose User defined.
7
In the k text field, type k_mix.
8
From the Dynamic viscosity list, choose User defined.
9
In the μ text field, type mu_mix.
Transport of Concentrated Species (tcs)
In the Model Builder window, under Component 1 (comp1) click Transport of Concentrated Species (tcs).
Reaction 1
1
In the Physics toolbar, click  Domains and choose Reaction.
Thanks to the balanced reactions, the stoichiometric coefficients are known.
2
Select Domain 1 only.
3
In the Settings window for Reaction, locate the Reaction Rate section.
4
In the νwCO text field, type -2.
5
In the νwO2 text field, type -1.
6
In the νwCO2 text field, type 2.
7
Locate the Rate Constants section. In the kf text field, type 1e100.
8
Locate the Turbulent Flow section. From the Turbulent-reaction model list, choose Eddy-dissipation.
9
Click to expand the Regularization section. Select the Rate expressions check box.
Reaction 2
1
Right-click Reaction 1 and choose Duplicate.
2
In the Settings window for Reaction, locate the Reaction Rate section.
3
In the νwCO text field, type 0.
4
In the νwCO2 text field, type 0.
5
In the νwH2 text field, type -2.
6
In the νwH2O text field, type 2.
The reaction rates are now decided and can be used for each reaction.
Chemistry (chem)
1: 2 CO + O2 =2 CO2
1
In the Model Builder window, under Component 1 (comp1)>Chemistry (chem) click 1: 2 CO + O2 =2 CO2.
2
In the Settings window for Reaction, locate the Reaction Rate section.
3
From the list, choose User defined.
4
In the rj text field, type tcs.treac1.r.
5
Find the Volumetric overall reaction order subsection. In the Forward text field, type 0.
2: 2 H2 + O2 =2 H2O
1
In the Model Builder window, click 2: 2 H2 + O2 =2 H2O.
2
In the Settings window for Reaction, locate the Reaction Rate section.
3
From the list, choose User defined.
4
In the rj text field, type tcs.treac2.r.
5
Find the Volumetric overall reaction order subsection. In the Forward text field, type 0.
Transport of Concentrated Species (tcs)
1
In the Model Builder window, under Component 1 (comp1) click Transport of Concentrated Species (tcs).
2
In the Settings window for Transport of Concentrated Species, locate the Transport Mechanisms section.
3
From the Diffusion model list, choose Fick’s law.
4
Locate the Species section. From the From mass constraint list, choose wN2.
Initial Values 1
1
In the Model Builder window, under Component 1 (comp1)>Transport of Concentrated Species (tcs) click Initial Values 1.
2
In the Settings window for Initial Values, locate the Initial Values section.
3
In the ω0,wCO text field, type 0.
4
In the ω0,wO2 text field, type wcf_O2.
5
In the ω0,wCO2 text field, type 0.
6
In the ω0,wH2 text field, type 0.
7
In the ω0,wH2O text field, type 0.
Inflow 1
1
In the Physics toolbar, click  Boundaries and choose Inflow.
2
Select Boundary 2 only.
3
In the Settings window for Inflow, locate the Inflow section.
4
From the Mixture specification list, choose Mole fractions.
5
In the x0,wCO text field, type x0_CO.
6
In the x0,wO2 text field, type x0_O2.
7
In the x0,wCO2 text field, type x0_CO2.
8
In the x0,wH2 text field, type x0_H2.
9
In the x0,wH2O text field, type x0_H2O.
Inflow 2
1
In the Physics toolbar, click  Boundaries and choose Inflow.
2
In the Settings window for Inflow, locate the Inflow section.
3
In the ω0,wCO text field, type 1e-5.
4
In the ω0,wO2 text field, type wcf_O2.
5
In the ω0,wCO2 text field, type 1e-5.
6
In the ω0,wH2 text field, type 1e-5.
7
In the ω0,wH2O text field, type 1e-5.
8
Select Boundaries 9 and 10 only.
Outflow 1
1
In the Physics toolbar, click  Boundaries and choose Outflow.
2
Select Boundary 3 only.
Turbulent Flow, k-ω (spf)
Fluid Properties 1
1
In the Model Builder window, under Component 1 (comp1)>Turbulent Flow, k-ω (spf) click Fluid Properties 1.
2
In the Settings window for Fluid Properties, locate the Model Input section.
3
Click Make All Model Inputs Editable in the upper-right corner of the section.
4
Locate the Fluid Properties section. From the ρ list, choose Density (chem).
5
From the μ list, choose User defined. In the associated text field, type mu_mix.
Inlet 1
1
In the Physics toolbar, click  Boundaries and choose Inlet.
2
Select Boundary 2 only.
3
In the Settings window for Inlet, locate the Boundary Condition section.
4
From the list, choose Fully developed flow.
5
Locate the Fully Developed Flow section. In the Uav text field, type Ujet.
Inlet 2
1
In the Physics toolbar, click  Boundaries and choose Inlet.
2
Select Boundaries 9 and 10 only.
3
In the Settings window for Inlet, locate the Velocity section.
4
Click the Velocity field button.
5
Specify the u0 vector as
0
r
Ucf
z
6
Locate the Turbulence Conditions section. From the IT list, choose Low (0.01).
7
From the LT list, choose User defined.
8
In the text field, type 0.1*Di.
Outlet 1
1
In the Physics toolbar, click  Boundaries and choose Outlet.
2
Select Boundary 3 only.
3
In the Settings window for Outlet, locate the Pressure Conditions section.
4
Select the Normal flow check box.
Heat Transfer in Fluids (ht)
Initial Values 1
1
In the Model Builder window, under Component 1 (comp1)>Heat Transfer in Fluids (ht) click Initial Values 1.
2
In the Settings window for Initial Values, locate the Initial Values section.
3
In the T text field, type T0.
Fluid 1
1
In the Model Builder window, click Fluid 1.
2
In the Settings window for Fluid, locate the Model Input section.
3
Click Make All Model Inputs Editable in the upper-right corner of the section.
4
Locate the Heat Convection section. From the u list, choose Velocity field (spf).
5
Locate the Heat Conduction, Fluid section. From the k list, choose User defined. In the associated text field, type k_mix.
6
Locate the Thermodynamics, Fluid section. From the ρ list, choose Density (chem).
7
From the Cp list, choose Heat capacity at constant pressure (chem).
Inflow 1
1
In the Physics toolbar, click  Boundaries and choose Inflow.
2
Select Boundaries 2, 9, and 10 only.
3
In the Settings window for Inflow, locate the Upstream Properties section.
4
In the Tustr text field, type T0.
Outflow 1
1
In the Physics toolbar, click  Boundaries and choose Outflow.
2
Select Boundary 3 only.
Mesh 1
Mapped 1
1
In the Mesh toolbar, click  Mapped.
2
In the Settings window for Mapped, click to expand the Control Entities section.
3
Clear the Smooth across removed control entities check box.
Distribution 1
1
Right-click Mapped 1 and choose Distribution.
2
Select Boundaries 2 and 15 only.
3
In the Settings window for Distribution, locate the Distribution section.
4
From the Distribution type list, choose Predefined.
5
In the Number of elements text field, type 20.
6
In the Element ratio text field, type 4.
7
From the Growth rate list, choose Exponential.
Distribution 2
1
In the Model Builder window, right-click Mapped 1 and choose Distribution.
2
Select Boundaries 11, 16, and 17 only.
3
In the Settings window for Distribution, locate the Distribution section.
4
From the Distribution type list, choose Predefined.
5
In the Number of elements text field, type 200.
6
In the Element ratio text field, type 250.
7
From the Growth rate list, choose Exponential.
Distribution 3
1
Right-click Mapped 1 and choose Distribution.
2
Select Boundaries 9 and 18 only.
3
In the Settings window for Distribution, locate the Distribution section.
4
From the Distribution type list, choose Predefined.
5
In the Number of elements text field, type 20.
6
In the Element ratio text field, type 400.
7
From the Growth rate list, choose Exponential.
8
Select the Reverse direction check box.
Distribution 4
1
Right-click Mapped 1 and choose Distribution.
2
Select Boundaries 1, 4, and 8 only.
3
In the Settings window for Distribution, locate the Distribution section.
4
From the Distribution type list, choose Predefined.
5
In the Number of elements text field, type 20.
6
In the Element ratio text field, type 200.
7
From the Growth rate list, choose Exponential.
8
Select the Reverse direction check box.
Distribution 5
1
Right-click Mapped 1 and choose Distribution.
2
Select Boundary 12 only.
3
In the Settings window for Distribution, locate the Distribution section.
4
From the Distribution type list, choose Predefined.
5
In the Number of elements text field, type 20.
6
In the Element ratio text field, type 8.
7
From the Growth rate list, choose Exponential.
Distribution 6
1
Right-click Mapped 1 and choose Distribution.
2
Select Boundaries 3 and 13 only.
3
In the Settings window for Distribution, locate the Distribution section.
4
From the Distribution type list, choose Predefined.
5
In the Number of elements text field, type 20.
6
In the Element ratio text field, type 4.
7
From the Growth rate list, choose Exponential.
8
Click  Build All.
9
In the Study toolbar, click  Show Default Solver.
Study 1
Solution 1 (sol1)
1
In the Model Builder window, expand the Study 1>Solver Configurations>Solution 1 (sol1)>Stationary Solver 1 node, then click Segregated 1.
2
In the Settings window for Segregated, locate the General section.
3
In the PID controller - proportional text field, type 0.65.
4
In the PID controller - derivative text field, type 0.025.
5
In the Target error estimate text field, type 0.1.
6
In the Model Builder window, expand the Study 1>Solver Configurations>Solution 1 (sol1)>Stationary Solver 1>Segregated 1 node, then click Velocity u, Pressure p.
7
In the Settings window for Segregated Step, locate the General section.
8
Under Variables, click  Add.
9
In the Add dialog box, in the Variables list, choose Wall temperature, downside (comp1.nirf1.TWall_d), Wall temperature, upside (comp1.nirf1.TWall_u), and Temperature (comp1.T).
10
Click OK.
11
In the Model Builder window, under Study 1>Solver Configurations>Solution 1 (sol1)>Stationary Solver 1>Segregated 1 click Turbulence variables.
12
In the Settings window for Segregated Step, click to expand the Method and Termination section.
13
In the Damping factor text field, type 0.4.
14
In the Number of iterations text field, type 2.
15
In the Model Builder window, under Study 1>Solver Configurations>Solution 1 (sol1)>Stationary Solver 1>Segregated 1 right-click Temperature and choose Disable.
Global Definitions
The enthalpy of formation and heat capacity plots will now be created (Figure 1 and Figure 2).
Gas System 1 (pp1)
In the Model Builder window, expand the Global Definitions>Thermodynamics>Gas System 1 (pp1)>Mixture node.
Enthalpy of formation 1 (EnthalpyF_carbon_dioxide_Gas12, EnthalpyF_carbon_dioxide_Gas12_Dtemperature, EnthalpyF_carbon_dioxide_Gas12_Dpressure)
1
In the Model Builder window, expand the Global Definitions>Thermodynamics>Gas System 1 (pp1)>Mixture>Vapor node, then click Global Definitions>Thermodynamics>Gas System 1 (pp1)>carbon dioxide>Vapor>Enthalpy of formation 1 (EnthalpyF_carbon_dioxide_Gas12, EnthalpyF_carbon_dioxide_Gas12_Dtemperature, EnthalpyF_carbon_dioxide_Gas12_Dpressure).
2
In the Settings window for Species Property, click to expand the Plot Parameters section.
3
In the table, enter the following settings:
Argument
Lower limit
Upper limit
temperature
298.15
2000
4
Click  Create Plot.
Results
When working with the functions, they tend to load for a while. By choosing to manually save data in the model under Results, it will be possible to enable Save plot data under each plot group and therefore shorten the loading time.
1
In the Settings window for Results, locate the Save Data in the Model section.
2
From the Save plot data list, choose Manual.
Enthalpy of Formation
1
In the Model Builder window, under Results click 1D Plot Group 1.
2
In the Settings window for 1D Plot Group, type Enthalpy of Formation in the Label text field.
3
Locate the Save Data in the Model section. Select the Save plot data check box.
4
In a similar fashion, repeat the steps above, to create plots with the same temperature limits for the rest of the species.
1D Plot Group 2
In the Model Builder window, expand the Results>1D Plot Group 2 node.
Function 1
In the Model Builder window, expand the Results>Enthalpy of Formation node, then click Function 1.
Function 2
1
Drag and drop below Enthalpy of Formation
Function 1.
2
Drag-drop all functions into the same plot group to plot them in the same graph.
Since 1D Plot Group 2 - 1D Plot Group 6 are empty now, delete them.
1D Plot Group 2, 1D Plot Group 3, 1D Plot Group 4, 1D Plot Group 5, 1D Plot Group 6
1
In the Model Builder window, under Results, Ctrl-click to select 1D Plot Group 2, 1D Plot Group 3, 1D Plot Group 4, 1D Plot Group 5, and 1D Plot Group 6.
2
Right-click and choose Delete.
The same procedure will now be performed for the heat capacity functions. As before, start by creating plots for each of the heat capacity functions.
Global Definitions
Heat capacity (Cp) 1 (HeatCapacityCp_carbon_dioxide_Gas11, HeatCapacityCp_carbon_dioxide_Gas11_Dtemperature, HeatCapacityCp_carbon_dioxide_Gas11_Dpressure)
1
In the Model Builder window, under Global Definitions>Thermodynamics>Gas System 1 (pp1)>carbon dioxide>Vapor click Heat capacity (Cp) 1 (HeatCapacityCp_carbon_dioxide_Gas11, HeatCapacityCp_carbon_dioxide_Gas11_Dtemperature, HeatCapacityCp_carbon_dioxide_Gas11_Dpressure).
2
In the Settings window for Species Property, locate the Plot Parameters section.
3
In the table, enter the following settings:
Argument
Lower limit
Upper limit
temperature
298.15
2000
4
Click  Create Plot.
Results
Heat Capacity
1
In the Settings window for 1D Plot Group, type Heat Capacity in the Label text field.
2
Locate the Save Data in the Model section. Select the Save plot data check box.
3
Repeat creating plots for the functions Heat capacity (Cp) 2 - Heat capacity (Cp) 6 using the same temperature limits.
1D Plot Group 3
In the Model Builder window, expand the Results>1D Plot Group 3 node.
Function 1
In the Model Builder window, expand the Results>Heat Capacity node, then click Function 1.
Function 2
1
Drag and drop below Heat Capacity
Function 1.
2
Repeat the drag-dropping of functions 3-6 into the Heat Capacity plot group.
1D Plot Group 3, 1D Plot Group 4, 1D Plot Group 5, 1D Plot Group 6, 1D Plot Group 7
Since 1D Plot Group 3 - 1D Plot Group 7 are empty now, delete them.
1
In the Model Builder window, under Results, Ctrl-click to select 1D Plot Group 3, 1D Plot Group 4, 1D Plot Group 5, 1D Plot Group 6, and 1D Plot Group 7.
2
Right-click and choose Delete.
Now we have two plots: one contains all enthalpy of formation functions, one contains all heat capacity functions.
Enthalpy of Formation
1
In the Model Builder window, under Results click Enthalpy of Formation.
2
In the Settings window for 1D Plot Group, click to expand the Title section.
3
From the Title type list, choose None.
4
Locate the Plot Settings section.
5
Select the x-axis label check box. In the associated text field, type Temperature (K).
6
Select the y-axis label check box. In the associated text field, type Enthalpy of Formation (J/mol).
7
Locate the Legend section. From the Layout list, choose Outside graph axis area.
Function 1
1
In the Model Builder window, click Function 1.
2
In the Settings window for Function, click to expand the Legends section.
3
Select the Show legends check box.
4
From the Legends list, choose Manual.
5
In the table, enter the following settings:
Legends
CO2
Function 2
1
In the Model Builder window, click Function 2.
2
In the Settings window for Function, locate the Legends section.
3
Select the Show legends check box.
4
From the Legends list, choose Manual.
5
In the table, enter the following settings:
Legends
CO
Function 3
1
In the Model Builder window, click Function 3.
2
In the Settings window for Function, locate the Legends section.
3
Select the Show legends check box.
4
From the Legends list, choose Manual.
5
In the table, enter the following settings:
Legends
H2
Function 4
1
In the Model Builder window, click Function 4.
2
In the Settings window for Function, locate the Legends section.
3
Select the Show legends check box.
4
From the Legends list, choose Manual.
5
In the table, enter the following settings:
Legends
N2
Function 5
1
In the Model Builder window, click Function 5.
2
In the Settings window for Function, locate the Legends section.
3
Select the Show legends check box.
4
From the Legends list, choose Manual.
5
In the table, enter the following settings:
Legends
O2
Function 6
1
In the Model Builder window, click Function 6.
2
In the Settings window for Function, locate the Legends section.
3
Select the Show legends check box.
4
From the Legends list, choose Manual.
5
In the table, enter the following settings:
Legends
H2O
6
In the Enthalpy of Formation toolbar, click  Plot.
Heat Capacity
All datasets Grid 1D 1 - Grid 1D 1k contain the same information. Therefore, change the dataset to be the same as for the Enthalpy of Formation plot group.
1
In the Model Builder window, under Results click Heat Capacity.
2
In the Settings window for 1D Plot Group, locate the Data section.
3
From the Dataset list, choose Grid 1D 1.
4
Locate the Title section. From the Title type list, choose None.
5
Locate the Plot Settings section.
6
Select the x-axis label check box. In the associated text field, type Temperature (K).
7
Select the y-axis label check box. In the associated text field, type Heat Capacity (J/mol/K).
8
Locate the Legend section. From the Layout list, choose Outside graph axis area.
Function 1
1
In the Model Builder window, click Function 1.
2
In the Settings window for Function, locate the Legends section.
3
Select the Show legends check box.
4
From the Legends list, choose Manual.
5
In the table, enter the following settings:
Legends
CO2
Function 2
1
In the Model Builder window, click Function 2.
2
In the Settings window for Function, locate the Legends section.
3
Select the Show legends check box.
4
From the Legends list, choose Manual.
5
In the table, enter the following settings:
Legends
CO
Function 3
1
In the Model Builder window, click Function 3.
2
In the Settings window for Function, locate the Legends section.
3
Select the Show legends check box.
4
From the Legends list, choose Manual.
5
In the table, enter the following settings:
Legends
H2
Function 4
1
In the Model Builder window, click Function 4.
2
In the Settings window for Function, locate the Legends section.
3
Select the Show legends check box.
4
From the Legends list, choose Manual.
5
In the table, enter the following settings:
Legends
N2
Function 5
1
In the Model Builder window, click Function 5.
2
In the Settings window for Function, locate the Legends section.
3
Select the Show legends check box.
4
From the Legends list, choose Manual.
5
In the table, enter the following settings:
Legends
O2
Function 6
1
In the Model Builder window, click Function 6.
2
In the Settings window for Function, locate the Legends section.
3
Select the Show legends check box.
4
From the Legends list, choose Manual.
5
In the table, enter the following settings:
Legends
H2O
6
In the Heat Capacity toolbar, click  Plot.
The datasets that are not used can now be deleted.
1
Delete all datasets Grid 1D 1a to Grid 1D 1k.
Now are the graphs for enthalpy of formation and heat capacity finished and are presented as Figure 1 and Figure 2 in the Model Definition section. To obtain the values presented in Table 1 and Table 2, Evaluation Groups are used, which gives the values for each function at the specific temperature.
Evaluation Group 1
1
In the Results toolbar, click  Evaluation Group.
2
In the Settings window for Evaluation Group, locate the Transformation section.
3
Select the Transpose check box.
Enthalpy of Formation, 298 K
1
Right-click Evaluation Group 1 and choose Global Evaluation.
2
In the Settings window for Global Evaluation, type Enthalpy of Formation, 298 K in the Label text field.
3
Locate the Expressions section. In the table, enter the following settings:
Expression
Unit
Description
EnthalpyF_carbon_dioxide_Gas12(298.15[K],1.0133E5[Pa])
J/mol
Enthalpy of formation 1
EnthalpyF_carbon_monoxide_Gas14(298.15[K],1.0133E5[Pa])
J/mol
Enthalpy of formation 2
EnthalpyF_hydrogen_Gas16(298.15[K],1.0133E5[Pa])
J/mol
Enthalpy of formation 3
EnthalpyF_nitrogen_Gas18(298.15[K],1.0133E5[Pa])
J/mol
Enthalpy of formation 4
EnthalpyF_oxygen_Gas110(298.15[K],1.0133E5[Pa])
J/mol
Enthalpy of formation 5
EnthalpyF_water_Gas112(298.15[K],1.0133E5[Pa])
J/mol
Enthalpy of formation 6
If clicking the Evaluate button now, no values will be given. This is because the datasets are empty. Using the feature Get initial values under Study 1 enables evaluation of the function values in Enthalpy of Formation, 298 K.
Study 1
In the Study toolbar, click  Get Initial Value.
Results
Enthalpy of Formation, 298 K
1
In the Model Builder window, under Results>Evaluation Group 1 click Enthalpy of Formation, 298 K.
2
In the Evaluation Group 1 toolbar, click  Evaluate.
Heat Capacity, 300 K
1
In the Model Builder window, right-click Evaluation Group 1 and choose Global Evaluation.
2
In the Settings window for Global Evaluation, type Heat Capacity, 300 K in the Label text field.
3
Locate the Expressions section. In the table, enter the following settings:
Expression
Unit
Description
HeatCapacityCp_carbon_dioxide_Gas11(300[K],1.0133E5[Pa])
J/(mol*K)
Heat capacity (Cp) 1
HeatCapacityCp_carbon_monoxide_Gas13(300[K],1.0133E5[Pa])
J/(mol*K)
Heat capacity (Cp) 2
HeatCapacityCp_hydrogen_Gas15(300[K],1.0133E5[Pa])
J/(mol*K)
Heat capacity (Cp) 3
HeatCapacityCp_nitrogen_Gas17(300[K],1.0133E5[Pa])
J/(mol*K)
Heat capacity (Cp) 4
HeatCapacityCp_oxygen_Gas19(300[K],1.0133E5[Pa])
J/(mol*K)
Heat capacity (Cp) 5
HeatCapacityCp_water_Gas111(300[K],1.0133E5[Pa])
J/(mol*K)
Heat capacity (Cp) 6
4
In the Evaluation Group 1 toolbar, click  Evaluate.
Heat Capacity, 2000 K
1
Right-click Evaluation Group 1 and choose Global Evaluation.
2
In the Settings window for Global Evaluation, type Heat Capacity, 2000 K in the Label text field.
3
Locate the Expressions section. In the table, enter the following settings:
Expression
Unit
Description
HeatCapacityCp_carbon_dioxide_Gas11(2000[K],1.0133E5[Pa])
J/(mol*K)
Heat capacity (Cp) 1
HeatCapacityCp_carbon_monoxide_Gas13(2000[K],1.0133E5[Pa])
J/(mol*K)
Heat capacity (Cp) 2
HeatCapacityCp_hydrogen_Gas15(2000[K],1.0133E5[Pa])
J/(mol*K)
Heat capacity (Cp) 3
HeatCapacityCp_nitrogen_Gas17(2000[K],1.0133E5[Pa])
J/(mol*K)
Heat capacity (Cp) 4
HeatCapacityCp_oxygen_Gas19(2000[K],1.0133E5[Pa])
J/(mol*K)
Heat capacity (Cp) 5
HeatCapacityCp_water_Gas111(2000[K],1.0133E5[Pa])
J/(mol*K)
Heat capacity (Cp) 6
4
In the Evaluation Group 1 toolbar, click  Evaluate.
The values in rows 7-12 in the table from Evaluation Group 1 are for 300 K, while the values for rows 13-18 are for 2000 K. Together with the values in rows 1-6, these are presented in Table 1 and Table 2.
Study 1
Solution 1 (sol1)
1
In the Model Builder window, under Study 1>Solver Configurations right-click Solution 1 (sol1) and choose Compute.
The default plots that are supposed to be generated when clicking Compute were not generated this time because they had already been generated when performing the Get initial values step. Therefore, they need to be reset.
2
In the Study toolbar, click  Reset Default Plots.
Now move on to postprocess the result from the nonisothermal jet. Start by creating a Mirror 2D dataset as well as a revolved 3D dataset.
Results
Mirror 2D 1
In the Results toolbar, click  More Datasets and choose Mirror 2D.
Cut Line 2D 1
1
In the Results toolbar, click  Cut Line 2D.
2
In the Settings window for Cut Line 2D, locate the Data section.
3
From the Dataset list, choose Mirror 2D 1.
4
Locate the Line Data section. From the Line entry method list, choose Point and direction.
5
Find the Point subsection. In the y text field, type Pl+20*Di.
6
Click to expand the Advanced section. Find the Space variable subsection. In the x text field, type r_mirr20.
Cut Line 2D 2
1
In the Results toolbar, click  Cut Line 2D.
2
In the Settings window for Cut Line 2D, locate the Data section.
3
From the Dataset list, choose Mirror 2D 1.
4
Locate the Line Data section. From the Line entry method list, choose Point and direction.
5
Find the Point subsection. In the y text field, type Pl+50*Di.
6
Locate the Advanced section. Find the Space variable subsection. In the x text field, type r_mirr50.
Now apply the mirror dataset to the relevant plot groups.
Velocity (spf)
1
In the Model Builder window, under Results click Velocity (spf).
2
In the Settings window for 2D Plot Group, locate the Data section.
3
From the Dataset list, choose Mirror 2D 1.
4
In the Velocity (spf) toolbar, click  Plot.
Streamline 1
Right-click Velocity (spf) and choose Streamline.
Streamline 1
1
In the Model Builder window, expand the Results>Velocity (spf) node, then click Streamline 1.
2
In the Settings window for Streamline, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1)>Heat Transfer in Fluids>Velocity and pressure>ht.ur,ht.uz - Velocity field.
3
Locate the Streamline Positioning section. From the Positioning list, choose Uniform density.
4
In the Separating distance text field, type 0.035.
5
Locate the Coloring and Style section. Find the Point style subsection. From the Color list, choose Gray.
6
In the Velocity (spf) toolbar, click  Plot.
7
Click the  Zoom Extents button in the Graphics toolbar.
Pressure (spf)
1
In the Model Builder window, under Results click Pressure (spf).
2
In the Settings window for 2D Plot Group, locate the Data section.
3
From the Dataset list, choose Mirror 2D 1.
4
In the Pressure (spf) toolbar, click  Plot.
Wall Resolution (spf)
1
In the Model Builder window, click Wall Resolution (spf).
2
In the Settings window for 2D Plot Group, locate the Data section.
3
From the Dataset list, choose Mirror 2D 1.
4
In the Wall Resolution (spf) toolbar, click  Plot.
Mass fraction, CO2
1
In the Model Builder window, right-click Concentration, CO2 (tcs) and choose Duplicate.
2
In the Settings window for 2D Plot Group, type Mass fraction, CO2 in the Label text field.
3
Locate the Data section. From the Dataset list, choose Mirror 2D 1.
4
Locate the Plot Settings section. From the Color list, choose White.
Surface 1
1
In the Model Builder window, expand the Mass fraction, CO2 node, then click Surface 1.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type wCO2.
4
In the Mass fraction, CO2 toolbar, click  Plot.
5
Click the  Zoom Extents button in the Graphics toolbar.
Temperature, 3D (ht)
1
In the Model Builder window, under Results click Temperature, 3D (ht).
2
In the Settings window for 3D Plot Group, locate the Plot Settings section.
3
Clear the Plot dataset edges check box.
Import the experimental data files. The files correspond to the ones published online (Ref. 2) by R. Barlow and coworkers. The name of the model, round_jet_burner, has been prepended to the filenames.
Centerline data
1
In the Results toolbar, click  Table.
2
In the Settings window for Table, type Centerline data in the Label text field.
3
Locate the Data section. Click Import.
4
Browse to the model’s Application Libraries folder and double-click the file round_jet_burner_chnAclY.fav.
z/Di = 20, Radial Data
1
In the Results toolbar, click  Table.
2
In the Settings window for Table, type z/Di = 20, Radial Data in the Label text field.
3
Locate the Data section. Click Import.
4
Browse to the model’s Application Libraries folder and double-click the file round_jet_burner_chnAd20Y.fav.
z/Di = 50, Radial Data
1
In the Results toolbar, click  Table.
2
In the Settings window for Table, type z/Di = 50, Radial Data in the Label text field.
3
Locate the Data section. Click Import.
4
Browse to the model’s Application Libraries folder and double-click the file round_jet_burner_chnAd50Y.fav.
z/Di = 20, Radial Velocity Data
1
In the Results toolbar, click  Table.
2
In the Settings window for Table, type z/Di = 20, Radial Velocity Data in the Label text field.
3
Locate the Data section. Click Import.
4
Browse to the model’s Application Libraries folder and double-click the file round_jet_burner_seq1420.dat.
z/Di = 50, Radial Velocity Data
1
In the Results toolbar, click  Table.
2
In the Settings window for Table, type z/Di = 50, Radial Velocity Data in the Label text field.
3
Locate the Data section. Click Import.
4
Browse to the model’s Application Libraries folder and double-click the file round_jet_burner_seq1450.dat.
1D Plot Group 22
In the Results toolbar, click  1D Plot Group.
Line Graph 1
1
Right-click 1D Plot Group 22 and choose Line Graph.
2
Select Boundary 1 only.
3
In the Settings window for Line Graph, locate the y-Axis Data section.
4
In the Expression text field, type T/T0.
5
Locate the x-Axis Data section. From the Parameter list, choose Expression.
6
In the Expression text field, type (z-Pl)/Di.
7
Click to expand the Coloring and Style section. From the Color list, choose Black.
8
Click to expand the Legends section. Select the Show legends check box.
9
From the Legends list, choose Manual.
10
In the table, enter the following settings:
Legends
Model
Table Graph 1
1
In the Model Builder window, right-click 1D Plot Group 22 and choose Table Graph.
2
In the Settings window for Table Graph, locate the Data section.
3
From the x-axis data list, choose r(mm).
4
From the Plot columns list, choose Manual.
5
In the Columns list, select T(K).
6
Click to expand the Preprocessing section. Find the x-axis column subsection. From the Preprocessing list, choose Linear.
7
In the Scaling text field, type 1/(Di*1000).
8
Find the y-axis columns subsection. From the Preprocessing list, choose Linear.
9
In the Scaling text field, type 1/T0.
10
Locate the Coloring and Style section. Find the Line style subsection. From the Line list, choose None.
11
From the Color list, choose Black.
12
Find the Line markers subsection. From the Marker list, choose Square.
13
Click to expand the Legends section. Select the Show legends check box.
14
From the Legends list, choose Manual.
15
In the table, enter the following settings:
Legends
Exp.
T @ centerline
1
In the Model Builder window, under Results click 1D Plot Group 22.
2
In the Settings window for 1D Plot Group, type T @ centerline in the Label text field.
3
Locate the Plot Settings section.
4
Select the x-axis label check box. In the associated text field, type (z-Pl)/Di.
5
Select the y-axis label check box. In the associated text field, type T/T0.
6
Locate the Axis section. Select the Manual axis limits check box.
7
In the x minimum text field, type -10.
8
In the x maximum text field, type 120.
9
In the y minimum text field, type 0.5.
10
In the y maximum text field, type 8.
11
Locate the Legend section. From the Layout list, choose Outside graph axis area.
12
Click to expand the Title section. From the Title type list, choose Manual.
13
In the Title text area, type Temperature Along the Centerline.
14
In the T @ centerline toolbar, click  Plot.
1D Plot Group 23
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, locate the Data section.
3
From the Dataset list, choose None.
Line Graph 1
1
Right-click 1D Plot Group 23 and choose Line Graph.
2
In the Settings window for Line Graph, locate the Data section.
3
From the Dataset list, choose Cut Line 2D 1.
4
Locate the y-Axis Data section. In the Expression text field, type T/T0.
5
Locate the x-Axis Data section. From the Parameter list, choose Expression.
6
In the Expression text field, type r_mirr20/Di.
7
Locate the Coloring and Style section. From the Color list, choose Black.
8
Locate the Legends section. Select the Show legends check box.
9
From the Legends list, choose Manual.
10
In the table, enter the following settings:
Legends
z/Di = 20, Model
Line Graph 2
1
Right-click Line Graph 1 and choose Duplicate.
2
In the Settings window for Line Graph, locate the Data section.
3
From the Dataset list, choose Cut Line 2D 2.
4
Locate the x-Axis Data section. In the Expression text field, type r_mirr50/Di.
5
Locate the Coloring and Style section. Find the Line style subsection. From the Line list, choose Dashed.
6
Locate the Legends section. In the table, enter the following settings:
Legends
z/Di = 50, Model
7
In the 1D Plot Group 23 toolbar, click  Plot.
Table Graph 1
1
In the Model Builder window, right-click 1D Plot Group 23 and choose Table Graph.
2
In the Settings window for Table Graph, locate the Data section.
3
From the Table list, choose z/Di = 20, Radial Data.
4
From the x-axis data list, choose r(mm).
5
From the Plot columns list, choose Manual.
6
In the Columns list, select T(K).
7
Locate the Preprocessing section. Find the x-axis column subsection. From the Preprocessing list, choose Linear.
8
In the Scaling text field, type 1/(Di*1000).
9
Find the y-axis columns subsection. From the Preprocessing list, choose Linear.
10
In the Scaling text field, type 1/T0.
11
Locate the Coloring and Style section. Find the Line style subsection. From the Line list, choose None.
12
From the Color list, choose Black.
13
Find the Line markers subsection. From the Marker list, choose Square.
14
Locate the Legends section. Select the Show legends check box.
15
From the Legends list, choose Manual.
16
In the table, enter the following settings:
Legends
z/Di = 20, Exp
Table Graph 2
1
Right-click Table Graph 1 and choose Duplicate.
2
In the Settings window for Table Graph, locate the Data section.
3
From the Table list, choose z/Di = 50, Radial Data.
4
Locate the Coloring and Style section. Find the Line markers subsection. From the Marker list, choose Triangle.
5
From the Positioning list, choose Interpolated.
6
Locate the Legends section. In the table, enter the following settings:
Legends
z/Di = 50, Exp
T @ z/Di = 20, 50
1
In the Model Builder window, under Results click 1D Plot Group 23.
2
In the Settings window for 1D Plot Group, type T @ z/Di = 20, 50 in the Label text field.
3
Locate the Title section. From the Title type list, choose Manual.
4
In the Title text area, type Temperature Downstream of the Pipe Exit.
5
Locate the Plot Settings section.
6
Select the x-axis label check box. In the associated text field, type r/Di.
7
Select the y-axis label check box. In the associated text field, type T/T0.
8
Locate the Axis section. Select the Manual axis limits check box.
9
In the x minimum text field, type -10.
10
In the x maximum text field, type 10.
11
In the y minimum text field, type 0.5.
12
In the y maximum text field, type 8.
13
Locate the Legend section. From the Layout list, choose Outside graph axis area.
14
In the T @ z/Di = 20, 50 toolbar, click  Plot.
uz @ z/Di = 20, 50
1
In the Model Builder window, right-click T @ z/Di = 20, 50 and choose Duplicate.
2
In the Settings window for 1D Plot Group, type uz @ z/Di = 20, 50 in the Label text field.
Line Graph 1
1
In the Model Builder window, expand the uz @ z/Di = 20, 50 node, then click Line Graph 1.
2
In the Settings window for Line Graph, locate the y-Axis Data section.
3
In the Expression text field, type w/Ujet.
Line Graph 2
1
In the Model Builder window, click Line Graph 2.
2
In the Settings window for Line Graph, locate the y-Axis Data section.
3
In the Expression text field, type w/Ujet.
Table Graph 1
1
In the Model Builder window, click Table Graph 1.
2
In the Settings window for Table Graph, locate the Data section.
3
From the x-axis data list, choose Fblgr.
4
From the Table list, choose z/Di = 20, Radial Velocity Data.
5
In the Columns list, select uz.
6
Locate the Preprocessing section. Find the y-axis columns subsection. In the Scaling text field, type 1/Ujet.
Table Graph 2
1
In the Model Builder window, click Table Graph 2.
2
In the Settings window for Table Graph, locate the Data section.
3
From the x-axis data list, choose Fblgr.
4
From the Table list, choose z/Di = 50, Radial Velocity Data.
5
In the Columns list, select uz.
6
Locate the Preprocessing section. Find the y-axis columns subsection. In the Scaling text field, type 1/Ujet.
uz @ z/Di = 20, 50
1
In the Model Builder window, click uz @ z/Di = 20, 50.
2
In the Settings window for 1D Plot Group, locate the Title section.
3
From the Title type list, choose Manual.
4
In the Title text area, type Axial Velocity Downstream of the Pipe Exit.
5
Locate the Plot Settings section. In the y-axis label text field, type uz/Ujet.
6
Locate the Axis section. In the y minimum text field, type -0.25.
7
In the y maximum text field, type 1.25.
8
In the uz @ z/Di = 20, 50 toolbar, click  Plot.
CO, N2 @ centerline
1
In the Model Builder window, right-click T @ centerline and choose Duplicate.
2
In the Settings window for 1D Plot Group, type CO, N2 @ centerline in the Label text field.
3
Locate the Title section. In the Title text area, type Mass Fraction Along the Centerline.
4
Locate the Plot Settings section. In the y-axis label text field, type wCO, wN2.
5
Locate the Axis section. In the y minimum text field, type -0.05.
6
In the y maximum text field, type 1.
7
In the CO, N2 @ centerline toolbar, click  Plot.
Line Graph 1
1
In the Model Builder window, expand the CO, N2 @ centerline node, then click Line Graph 1.
2
In the Settings window for Line Graph, locate the y-Axis Data section.
3
In the Expression text field, type wCO.
4
Locate the Legends section. In the table, enter the following settings:
Legends
CO, Model
Table Graph 1
1
In the Model Builder window, click Table Graph 1.
2
In the Settings window for Table Graph, locate the Data section.
3
In the Columns list, select YCO.
4
Locate the Preprocessing section. Find the y-axis columns subsection. In the Scaling text field, type 1.
5
Locate the Legends section. In the table, enter the following settings:
Legends
CO, Exp.
6
In the CO, N2 @ centerline toolbar, click  Plot.
Line Graph 2
1
In the Model Builder window, under Results>CO, N2 @ centerline right-click Line Graph 1 and choose Duplicate.
2
In the Settings window for Line Graph, locate the y-Axis Data section.
3
In the Expression text field, type wN2.
4
Locate the Coloring and Style section. Find the Line style subsection. From the Line list, choose Dashed.
5
Locate the Legends section. In the table, enter the following settings:
Legends
N2, Model
Table Graph 2
1
In the Model Builder window, under Results>CO, N2 @ centerline right-click Table Graph 1 and choose Duplicate.
2
In the Settings window for Table Graph, locate the Data section.
3
In the Columns list, select YN2.
4
Locate the Coloring and Style section. Find the Line markers subsection. From the Marker list, choose Triangle.
5
From the Positioning list, choose Interpolated.
6
Locate the Legends section. In the table, enter the following settings:
Legends
N2, Exp
7
In the CO, N2 @ centerline toolbar, click  Plot.
H2, H2O @ centerline
1
In the Model Builder window, right-click CO, N2 @ centerline and choose Duplicate.
2
In the Settings window for 1D Plot Group, type H2, H2O @ centerline in the Label text field.
3
Locate the Title section. From the Title type list, choose Manual.
4
In the Title text area, type Mass Fraction Along the Centerline.
Line Graph 1
1
In the Model Builder window, expand the H2, H2O @ centerline node, then click Line Graph 1.
2
In the Settings window for Line Graph, locate the y-Axis Data section.
3
In the Expression text field, type wH2.
4
Locate the Legends section. In the table, enter the following settings:
Legends
H2, Model
Table Graph 1
1
In the Model Builder window, click Table Graph 1.
2
In the Settings window for Table Graph, locate the Data section.
3
In the Columns list, select YH2.
4
Locate the Legends section. In the table, enter the following settings:
Legends
H2, Exp.
Line Graph 2
1
In the Model Builder window, click Line Graph 2.
2
In the Settings window for Line Graph, locate the y-Axis Data section.
3
In the Expression text field, type wH2O.
4
Locate the Legends section. In the table, enter the following settings:
Legends
H2O, Model
Table Graph 2
1
In the Model Builder window, click Table Graph 2.
2
In the Settings window for Table Graph, locate the Data section.
3
In the Columns list, select YH2O.
4
Locate the Legends section. In the table, enter the following settings:
Legends
H2O, Exp
H2, H2O @ centerline
1
In the Model Builder window, click H2, H2O @ centerline.
2
In the Settings window for 1D Plot Group, locate the Plot Settings section.
3
In the y-axis label text field, type wH2, wH2O.
4
Locate the Axis section. In the y maximum text field, type 0.15.
5
In the y minimum text field, type -0.02.
6
In the H2, H2O @ centerline toolbar, click  Plot.
O2, CO2 @ centerline
1
In the Model Builder window, right-click H2, H2O @ centerline and choose Duplicate.
2
In the Settings window for 1D Plot Group, type O2, CO2 @ centerline in the Label text field.
3
Locate the Title section. From the Title type list, choose Manual.
4
In the Title text area, type Mass Fraction Along the Centerline.
Line Graph 1
1
In the Model Builder window, expand the O2, CO2 @ centerline node, then click Line Graph 1.
2
In the Settings window for Line Graph, locate the y-Axis Data section.
3
In the Expression text field, type wO2.
4
Locate the Legends section. In the table, enter the following settings:
Legends
O2, Model
Table Graph 1
1
In the Model Builder window, click Table Graph 1.
2
In the Settings window for Table Graph, locate the Data section.
3
In the Columns list, select YO2.
4
Locate the Legends section. In the table, enter the following settings:
Legends
O2, Exp.
Line Graph 2
1
In the Model Builder window, click Line Graph 2.
2
In the Settings window for Line Graph, locate the y-Axis Data section.
3
In the Expression text field, type wCO2.
4
Locate the Legends section. In the table, enter the following settings:
Legends
CO2, Model
Table Graph 2
1
In the Model Builder window, click Table Graph 2.
2
In the Settings window for Table Graph, locate the Data section.
3
In the Columns list, select YCO2.
4
Locate the Legends section. In the table, enter the following settings:
Legends
CO2, Exp
O2, CO2 @ centerline
1
In the Model Builder window, click O2, CO2 @ centerline.
2
In the Settings window for 1D Plot Group, locate the Plot Settings section.
3
In the y-axis label text field, type wO2, wCO2.
4
Locate the Axis section. In the y minimum text field, type -0.05.
5
In the y maximum text field, type 0.4.
6
In the O2, CO2 @ centerline toolbar, click  Plot.