**3. Jet flame simulation and premixed flame simulation using LES**

The ASSCM sub-grid scale turbulent combustion model is applied to a partly diffusion jet flame and a premixed flame after a bluff body. The SGS turbulent combustion model is verified by the experimental data and the LES database is used to verified the RANS turbulent combustion model. The instantaneous turbulent and flame structures are studied too. The implicit box filter function and the Smagorinsky-Lilly's eddy viscosity turbulent model are used. The Smagorinsky constant is 0.1 in this chapter. The SGS mass flux and heat flux are in gradient models. Second order upwind scheme in space, second order central difference scheme for momentum equation, second order in temporal, and PISO algorithm are used. A random velocity component, satisfying Gaussian distribution is superposed at the inlet boundary. The grid size near inlet is 0.5mm around, and under 2mm in the simulation domain. The time step is 0.1ms. Each time step, it iterated 25 steps. As a comparison, the RANS model is applied for the jet flame too.

The methane-air jet flame, the 'Flame D', is measured by the Sandia Laboratory. The sketch map of this flame is shown in the figure 1. The central flow consists of 25% methane and 75% dry air, the inlet velocity is 29.7m/s, and the inlet temperature is 294K. The annular flow velocity is 6.8m/s and its temperature is 1880K. The surrounding flow velocity is 0.9m/s, and its temperature is 291K. The exit is located at a distance of 1m from the jet exit. The methane air reaction kinetics is taken from Westbrook as:

$$w\_{fu} = 2.119 \times 10^{11} Y\_{\alpha x}^{1.3} Y\_{fu}^{0.2} \exp(-2.027 \times 10^8 \text{ / RT}) \tag{7}$$

The specific heat for all the species are using subsection polynomial expression, such as the specific heat value of methane when the temperature is between 300K to 1000K:

$$C\_p = 403.58 + 9.0575T - 0.014425T^2 + 1.5805 \times 10^{-5} \stackrel{3}{T} - 6.3431 \times 10^{-9} \stackrel{4}{T} \tag{8}$$

Figure 2 is the averaged temperature comparison between the RANS unified second order moment (USM) transportation turbulent combustion model prediction results and the LES ASSCM turbulent combustion model prediction results with the experimental results. In

Turbulent Combustion Simulation

2

0

2

x=1d

0

r/d

0.00 0.03 0

RANS method.

higher stain rate regions.

0.00 0.05 0

0.00 0.05 0

Fig. 5. The RMS value of the methane concentration.

0.00 0.05 0

0.00 0.05 0

The RMS value of the LES ASSCM model and the RANS model prediction results are shown in the figure 4 and 5, as well as the comparison with the experimental data. Generally, the LES RMS predictions are worse than the LES average value predictions, especially in the regions near the methane jet area: x=1d, x=2d, and x=3d sections. These regions have great gradient value of temperature and concentration, and there are more active turbulence fluctuations. As for the prediction of the turbulent character, the LES is much better than the

Figure 6 is the instantaneous stain rate contour at the central axis section. The high velocity jet flow mixed with the low velocity co-flow air, then the mixing layer induced vortex and

Figure 7 and figure 8 are instantaneous temperature contour in different time step. From these two pictures, the temperature in the central jet flow remains low for quite long distance from the inlet. The pilot flow ignite the jet flow and the flame spread downstream.

0.00 0.05 0

0.00 0.05 0

2

0.00 0.03 0

2

0.00 0.03

YCH4 RMS

 EXP LES RANS

4

6

4

6

2

4

0 400 0

2

0 500 0

2

0 500 0

Fig. 4. The root mean square (RMS) value of the temperature.

2

0 500 0

2

0 500 0

2

2

x=2d x=3d x=7.5d x=15d x=30d x=45d x=60d x=75d

0 500 0

2

0 500 0

2

0 500 0

2

0 500

TRMS (K)

 EXP LES RANS

4

6

4

6

4

6

4

6

x=2d x=3d x=7.5d x=15d x=30d x=45d x=60d x=75d

2

4

2

2

r/d

x=1d

by Large Eddy Simulation and Direct Numerical Simulation 213

big difference between the RANS prediction results and the experimental data is mainly

from the shear layer gradient assumption and one global step reaction kinetics.

2

4

most regions the, the prediction value of the ASSCM model are very close to the experimental data. The RANS model can give the same trend of the temperature profiles.

Fig. 1. The sketch map of the jet flame and its dimension.

0.0 0.2 Fig. 3. The average oxygen concentration profiles.

0

0.0 0.2 0

0.0 0.2 0

0

0.0 0.2 0

Figure 3 shows the averaged oxygen concentration profiles comparison amongst the LES, RANS and the experimental data. In most regions, the LES ASSCM model gives good results. While the RANS predictions also are close to the experimental data in most regions. Considering RANS 1/500 computing time, it is still useful and popular in industry field. The

0.0 0.2 0 0.0 0.2 0 0.0 0.2 0

0.0 0.2

0.0 0.2 0

most regions the, the prediction value of the ASSCM model are very close to the experimental data. The RANS model can give the same trend of the temperature profiles.

Fig. 1. The sketch map of the jet flame and its dimension.

Fig. 2. The average temperature profiles.

2

0.0 0.2 0

Fig. 3. The average oxygen concentration profiles.

2

0.0 0.2 0

2

0.0 0.2 0

2

Figure 3 shows the averaged oxygen concentration profiles comparison amongst the LES, RANS and the experimental data. In most regions, the LES ASSCM model gives good results. While the RANS predictions also are close to the experimental data in most regions. Considering RANS 1/500 computing time, it is still useful and popular in industry field. The

0.0 0.2 0

2

0.0 0.2 0

2

0.0 0.2 0

2

0.0 0.2

<sup>Y</sup> <sup>O</sup> <sup>2</sup>

 EXP LES RANS

4

6

4

6

4

6

4

6

x=2d x=3d x=7.5d x=15d x=30d x=45d x=60d x=75d

4

0

0.0 0.2 0

2

0.0 0.2 0

2

r/d

x=1d

big difference between the RANS prediction results and the experimental data is mainly from the shear layer gradient assumption and one global step reaction kinetics.

Fig. 4. The root mean square (RMS) value of the temperature.

Fig. 5. The RMS value of the methane concentration.

The RMS value of the LES ASSCM model and the RANS model prediction results are shown in the figure 4 and 5, as well as the comparison with the experimental data. Generally, the LES RMS predictions are worse than the LES average value predictions, especially in the regions near the methane jet area: x=1d, x=2d, and x=3d sections. These regions have great gradient value of temperature and concentration, and there are more active turbulence fluctuations. As for the prediction of the turbulent character, the LES is much better than the RANS method.

Figure 6 is the instantaneous stain rate contour at the central axis section. The high velocity jet flow mixed with the low velocity co-flow air, then the mixing layer induced vortex and higher stain rate regions.

Figure 7 and figure 8 are instantaneous temperature contour in different time step. From these two pictures, the temperature in the central jet flow remains low for quite long distance from the inlet. The pilot flow ignite the jet flow and the flame spread downstream.

Turbulent Combustion Simulation

by Large Eddy Simulation and Direct Numerical Simulation 215

 The co-flow air was entraining to the combustion flames. The high temperature areas changed temporally. The unsteady flame is similar to the candle flickers. It also can be seen the wrinkle flame structures. Figure 9 is the instantaneous reaction rate contour. The high reaction rate

Then, a propane air premixed flame is studied. The combustion chamber is shown in the figure 10 (Giacomazzi 2004). The inlet velocity is 17m/s, temperature is 288K, and the equivalence ratio is 0.65. The final mesh section is shown in figure 11, the maximum grid

area is the low concentration area. Reaction also happens in some isolated 'islands'.

size is 0.5mm. Time step is 0.1ms, and 35 iterations during each time step.

Fig. 10. The premixed chamber with bluff body (Giacomazzi 2004).

9 1.65 0.1 <sup>4</sup> *w= Y Y ( fu* 4.836 10 exp 1.51 10 / *ox fu T)* (9)

Fig. 11. The final mesh at z=0 section.

The laminar reaction rate is:

Fig. 6. The instantaneous stain rate contour (1/s).

Fig. 8. The instantaneous temperature contour (K, t=1.1094s).

Fig. 9. The instantaneous reaction rate contour (kmol/m3s).

1.47 917 1830 2750 3660 4580 5490 6410

288 583 878 1170 1470 1760 2060 2500

288 583 878 1170 1470 1760 2060 2500

0.0 0.0796 0.159 0.239 0.318 0.398 0.478 0.597

Fig. 6. The instantaneous stain rate contour (1/s).

Fig. 7. The instantaneous temperature contour (K, t=0.8990s).

Fig. 8. The instantaneous temperature contour (K, t=1.1094s).

Fig. 9. The instantaneous reaction rate contour (kmol/m3s).

 The co-flow air was entraining to the combustion flames. The high temperature areas changed temporally. The unsteady flame is similar to the candle flickers. It also can be seen the wrinkle flame structures. Figure 9 is the instantaneous reaction rate contour. The high reaction rate area is the low concentration area. Reaction also happens in some isolated 'islands'.

Then, a propane air premixed flame is studied. The combustion chamber is shown in the figure 10 (Giacomazzi 2004). The inlet velocity is 17m/s, temperature is 288K, and the equivalence ratio is 0.65. The final mesh section is shown in figure 11, the maximum grid size is 0.5mm. Time step is 0.1ms, and 35 iterations during each time step.

Fig. 10. The premixed chamber with bluff body (Giacomazzi 2004).

Fig. 11. The final mesh at z=0 section.

The laminar reaction rate is:

$$w\_{fu} = 4.836 \times 10^9 Y\_{ox}^{1.65} Y\_{fu}^{0.1} \exp(-1.51 \times 10^4 \text{ / T}) \tag{9}$$

Turbulent Combustion Simulation

combustion flow in this premixed case.

Fig. 15. The instantaneous temperature contour (K).

Fig. 16. The averaged temperature contour (K).

generated, stretched and mixed along the combustion chamber.

by Large Eddy Simulation and Direct Numerical Simulation 217

In figure 15 and 13, the x velocity and its RMS value are compared with the experimental data generally. The predictions are close to the experimental data. Figure 14 is the averaged temperature profiles. The LES predictions are in good agreement with the experimental data. So the LES ASSCM model with the Smagorinsky-Lilly model can properly predict the

The section results are shown in figure 15 and 16: the instantaneous temperature contour and the averaged temperature contour. The bluff body in the combustion chamber works as a flame stabilizer: the premixed flame attached behind the bluff body. The high temperature regions changed a lot in pace with the time steps. The instantaneous high temperature regions are different from the averaged high temperature regions. There are wrinkled flame structures. There are vortex 'source' in the after side of the bluff body. The vortex is

Because LES method can give much better predictions on turbulent fluctuations, the LES database can be used as a preliminary test source for the RANS combustion model. In RANS USM model, the correlations are solved by transportation equations, such as the transport

*' '*

(10)

*μ K Y*

equation of the correlation of the reaction rate factor K and a species concentration:

*jj A T*

*KY a b c μ c ρ + KY x x τ τ*

*' ' ' ' <sup>e</sup> <sup>j</sup>*

 

As for the ASOM model, the expression of the the correlation of the reaction rate factor K

*ρKY + ρu KY = + tx x σ x*

*j jg j*

*' '*

g1 g2

*T*

and concentration is:

Fig. 12. The averaged x velocity with combustion.

Fig. 13. The RMS value of the x velocity with combustion.

Fig. 14. The averaged temperature profiles with combustion.

3

x=0.061 x=0.150 x=0.376 x=0.015

0.06


0 5 10 15

500 1000 1500

Fig. 14. The averaged temperature profiles with combustion.




0.00

0.02

0.04

0.06


x=0.150 x=0.350



0.00

0.02

0.04


x=0.015 x=0.061 x=0.150 x=0.376

0.06



0.00

0.02

0.04

0 20 40 60

0 5 10 15


500 1000 1500



0.00

0.02

0.04

0.06




0.00

0.02

0.04

0.06

U <sup>x</sup> (m /s)

U x,R M S (m /s)

0 5 10

 EXP LES

T(K)

20 30 40

0 20 40

Fig. 12. The averaged x velocity with combustion.

0 5 10




0.00

0.02

0.04

0.06

y


Fig. 13. The RMS value of the x velocity with combustion.



0.00

0.02

0.04

0.06




0.00

0.02

0.04

0.06





0.00

0.02

0.04

0.06

Y

3



0.00

0.02

0.04

Y

0.06

In figure 15 and 13, the x velocity and its RMS value are compared with the experimental data generally. The predictions are close to the experimental data. Figure 14 is the averaged temperature profiles. The LES predictions are in good agreement with the experimental data. So the LES ASSCM model with the Smagorinsky-Lilly model can properly predict the combustion flow in this premixed case.

Fig. 15. The instantaneous temperature contour (K).

Fig. 16. The averaged temperature contour (K).

The section results are shown in figure 15 and 16: the instantaneous temperature contour and the averaged temperature contour. The bluff body in the combustion chamber works as a flame stabilizer: the premixed flame attached behind the bluff body. The high temperature regions changed a lot in pace with the time steps. The instantaneous high temperature regions are different from the averaged high temperature regions. There are wrinkled flame structures. There are vortex 'source' in the after side of the bluff body. The vortex is generated, stretched and mixed along the combustion chamber.

Because LES method can give much better predictions on turbulent fluctuations, the LES database can be used as a preliminary test source for the RANS combustion model. In RANS USM model, the correlations are solved by transportation equations, such as the transport equation of the correlation of the reaction rate factor K and a species concentration:

$$\begin{split} \frac{\partial}{\partial t} \Big( \rho \overline{\dot{K'} \dot{Y}} \Big) + \frac{\partial}{\partial x\_j} \Big( \rho \overline{u\_j \dot{K'} \dot{Y}} \Big) &= \frac{\partial}{\partial x\_j} \Big( \frac{\mu\_e}{\sigma\_g} \frac{\partial \overline{K'} \dot{Y}}{\partial x\_j} \Big) + \\ c\_{\text{g1}} \mu\_T \frac{\partial \overline{K}}{\partial x\_j} \frac{\partial \overline{Y}}{\partial x\_j} - c\_{\text{g2}} \rho \Big( \frac{a}{\overline{\tau}\_A} + \frac{b}{\overline{\tau}\_T} \Big) \overline{K'} \dot{Y} \end{split} \tag{10}$$

As for the ASOM model, the expression of the the correlation of the reaction rate factor K and concentration is:

Turbulent Combustion Simulation


developed and the reactants mixed sufficiently.

Fig. 20. The computation domain for DNS.


**4. Direct numerical simulation for reacting flows** 

fundamental study and test sources for RANS and LES models.



0.00

0.02

0.04

0.06




0.00

0.02

0.04

0.06

by Large Eddy Simulation and Direct Numerical Simulation 219

ASOM <sup>y</sup>





0.00

0.02

0.04


K'Y'F U

0.06 LES

x=0.015 x=0.061 x=0.150 x=0.376

0.06



Fig. 19. The correlation comparison between the LES statistic and ASOM model value.

Along with the development of computational technology, direct numerical simulation becomes more and more popular in combustion simulation studies. It is a powerful tool for

In this chapter, a DNS of turbulent reacting channel flows with the consideration of the interaction between the velocity and scalars by buoyancy effect is performed using a spectral method. The instantaneous reaction rate is in Arrhenius form. The computational domain and coordinate system are shown in figure 20. x, y, z are the flow direction, normal direction, and span-wise direction separately. The height of the channel is 2H, the length in the stream-wise is 12.6H and the width in the span-wise direction is 6.28H. The flow is fully

The instantaneous continuity, momentum, species concentration and energy equations of incompressible turbulent reacting flows, with consideration of the buoyancy effect using

> 0 *<sup>i</sup> i u = x*

(12)

Boussinesq approximation and taking the Arrhenius expression of one-step kinetics.



0.00

0.02

0.04

Fig. 17. The correlation comparison between the LES statistic value and ASOM model value.

From the jet flame simulation database here, the RANS ASOM model correlation value is close to the statistic correlation value which is gotten from the LES database, which is shown in figure 17. Generally, the model value is in the same trend with the statistic value and consistent with positive and negative symbols.

The concentration correlation comparison between the model value and the statistic value is shown in figure 18. In most regions, the model values are close to the statistic values. Generally, the model value is of the same magnitude order with the statistic value. The similar statistic calculation is applied in the premixed case too, and the comparison result is shown in figure 19. The model value is close to the statistic value in all the sections.

Fig. 18. The relative correlation comparison between the LES statistic and ASOM model value.

*'*


0

value.


1


1



1


Fig. 18. The relative correlation comparison between the LES statistic and ASOM model

2


2


2

0.0 0.4 0

2


Y'Y'/YCH4/YO2

 ASOM LES

4

4

4

4

x=2d x=3d x=7.5d x=15d x=30d x=45d x=60d x=75d

2

3

1

2

2

2

1

r/d

x=1d




consistent with positive and negative symbols.




shown in figure 19. The model value is close to the statistic value in all the sections.


Fig. 17. The correlation comparison between the LES statistic value and ASOM model value. From the jet flame simulation database here, the RANS ASOM model correlation value is close to the statistic correlation value which is gotten from the LES database, which is shown in figure 17. Generally, the model value is in the same trend with the statistic value and

The concentration correlation comparison between the model value and the statistic value is shown in figure 18. In most regions, the model values are close to the statistic values. Generally, the model value is of the same magnitude order with the statistic value. The similar statistic calculation is applied in the premixed case too, and the comparison result is





K'Y'CH4

LES


0

1

2

x=15d x=30d


0

1

2


0

1

2


0

1

2


0

1

2

x=1d


0

1

2

r/d

3

2

*ε x x* 

*1 KY1 j j k KY K'Y = C*

1

x=2d x=3d x=7.5d ASOM

(11)

Fig. 19. The correlation comparison between the LES statistic and ASOM model value.
