**Abstract**

The current chapter presents the use of computational fluid dynamics (CFD) for simulating the combustion process taking place in gas turbines. The chapter is based on examples and results from a series of applications developed as part of the research performed by the authors in national and European projects. There are envisaged topics like flame stability, pollutant emission prediction, and alternative fuels in the context of aviation and industrial gas turbines, growing demands for lower fuel consumption, lower emissions, and overall sustainability of such energetic machines. Details on the available numerical models and computational tools are given along with the expectation for further developing CFD techniques in the field. The chapter includes also some comparison between theoretical, numerical, and experimental results.

**Keywords:** combustion, gas turbine, numerical simulations, models, alternative fuels, experiments

## **1. Introduction**

Gas turbines are energetic machines based on Brayton thermodynamic cycle [1] (**Figure 1**) meaning, among others, temperature rise using combustion at quasi-constant pressure.

In **Figure 1**, evolution (1–2) represents the real compression evolution of the working fluid into the compressor, (2–3) represents combustion at constant pressure, (3–4) represents real expansion of the working fluid into the turbine, and (4–1) represents the cooling down of the working fluid at constant pressure, usually the atmospheric one. Evolutions (1–2is) and (3–4is) are the isentropic compression and isentropic expansion, respectively, and they are shown on the graphic in order to emphasize the difference between real and ideal (isentropic).

Unlike compressors and turbines in which only pure gas-dynamic processes develop, combustion involves also chemical reactions between air and fuel, resulting in flue gases driving the turbine. Since combustion is known from ages, the overall efficiency of it is very high [2] and enhanced by the high pressure provided by the compressor. Still, many current studies are directed on this subject willing to reduce pollutant emissions or to accommodate alternative fuels such as biogas or both.

In general, the combustion process is organized into the gas turbine as shown in **Figure 2** [3].

In **Figure 2** the red arrows represent the burning working fluid (realizing close to stoichiometric mixture ratio with the injected fuel and very high temperature in the flame presented in orange), and the blue arrows represent the fluid which cools down the burning one down to the required temperature of the thermodynamic cycle (which is limited by the materials used to realize the combustion chamber and the turbine).

from stoichiometric reaction, while the blue zone (L) is lean in fuel, meaning less fuel than the calculated from stoichiometric reaction. The Clean Sky research project aims at demonstrating that by realizing such an arrangement of the combustion

The thermodynamics of combustion is relatively simple and is based on the heat

ProductsjTinitial þ HEAT or ProductsjTcombustion

(1)

process, the maximum flame temperature can be lowered reducing thus the dissociation reactions that create NOx, at the same final temperature reaching

> 8 ><

> >:

Computational fluid dynamics (CFD) has been intensively used in the aerospace domain mainly for predicting the performances of the studied object which can be the entire aircraft or some particular part of it. For the gas turbines, all the main components can be studied using CFD: in the case of the compressor,

the aerodynamic part is the most important seeking for high efficiency of transforming the available mechanical work into total pressure of the air; in the case of the turbine, the things are reversed, the study being focused on reducing the losses of transforming the potential energy of the fluid in the form of pressure and temperature, into mechanical work; in the case of the combustion chamber, aerodynamics plays a big role in the injection of fuel and mixing, but

it must be coupled with chemical reactions and heat release within the

a result of energy exchanges that occur due to intermolecular collisions.

cient amount of energy to trigger a chemical transformation.

The combustion process is the result of a strong exothermic chemical reaction as

Generally, at ambient temperature, a chemical reaction occurs very slowly, because, although collisions at molecular level occur, they do not generate a suffi-

According to the chemical kinetic theory, only "active" collisions, collisions involving molecules having an initial energy greater than or equal to an energy called activation energy, lead to a chemical reaction. This energy is needed to destroy or weaken existing intermolecular connections. The activation energy is

*<sup>k</sup>* <sup>¼</sup> <sup>A</sup> � *<sup>T</sup>*<sup>β</sup> � exp �Ea

where *k* is the reaction rate coefficient, A is the pre-exponential factor, Ea is the activation energy, R is the universal gas constant, β is the temperature exponent,

The combustion process can be expressed in a simplified way through the global

R � *T*

� � (2)

Still, the use of this equation gives good results only for the temperature at the end of the combustion process and not so accurate results on the resulting composition. Thus, the chemical reaction must be carefully studied and implemented in

Tinitial !

the study concerning the combustion chamber of a gas turbine.

the turbine.

transforming fluid.

**2. Combustion and chemistry in CFD**

given by Arrhenius equation [5, 6]:

and *T* is the temperature.

**217**

reaction mechanism, Eq. (3):

of reaction as shown in Eq. (1):

Reactantsj

*CFD Application for Gas Turbine Combustion Simulations*

*DOI: http://dx.doi.org/10.5772/intechopen.89759*

The arrangement of the combustion chamber is the subject of many research projects, some of the latest being lean burn program [4] where the reduction of NOx through the reduction of combustion temperature by multiple combustion is sought.

In **Figure 3**, depicted is a type of combustion which may lead to lower NOx production: the red zone (R) is rich in fuels, meaning more fuel than the calculated

**Figure 1.** *Brayton cycle in temperature vs. entropy coordinates.*

**Figure 2.** *Combustion chamber.*

**Figure 3.** *Clean Sky research project [4].*

*CFD Application for Gas Turbine Combustion Simulations DOI: http://dx.doi.org/10.5772/intechopen.89759*

In **Figure 2** the red arrows represent the burning working fluid (realizing close to stoichiometric mixture ratio with the injected fuel and very high temperature in the flame presented in orange), and the blue arrows represent the fluid which cools down the burning one down to the required temperature of the thermodynamic cycle (which is limited by the materials used to realize the combustion chamber and

The arrangement of the combustion chamber is the subject of many research projects, some of the latest being lean burn program [4] where the reduction of NOx through the reduction of combustion temperature by multiple combustion is

In **Figure 3**, depicted is a type of combustion which may lead to lower NOx production: the red zone (R) is rich in fuels, meaning more fuel than the calculated

the turbine).

sought.

**Figure 1.**

**Figure 2.**

**Figure 3.**

**216**

*Clean Sky research project [4].*

*Combustion chamber.*

*Brayton cycle in temperature vs. entropy coordinates.*

*Computational Fluid Dynamics Simulations*

from stoichiometric reaction, while the blue zone (L) is lean in fuel, meaning less fuel than the calculated from stoichiometric reaction. The Clean Sky research project aims at demonstrating that by realizing such an arrangement of the combustion process, the maximum flame temperature can be lowered reducing thus the dissociation reactions that create NOx, at the same final temperature reaching the turbine.

The thermodynamics of combustion is relatively simple and is based on the heat of reaction as shown in Eq. (1):

$$\text{Reactants}|\_{\text{Tinital}} \rightarrow \begin{cases} \text{Products}|\_{\text{Tinital}} + \text{HEAT} \\ \text{or} \\ \text{Products}|\_{\text{Tomustion}} \end{cases} \tag{1}$$

Still, the use of this equation gives good results only for the temperature at the end of the combustion process and not so accurate results on the resulting composition. Thus, the chemical reaction must be carefully studied and implemented in the study concerning the combustion chamber of a gas turbine.

Computational fluid dynamics (CFD) has been intensively used in the aerospace domain mainly for predicting the performances of the studied object which can be the entire aircraft or some particular part of it. For the gas turbines, all the main components can be studied using CFD: in the case of the compressor, the aerodynamic part is the most important seeking for high efficiency of transforming the available mechanical work into total pressure of the air; in the case of the turbine, the things are reversed, the study being focused on reducing the losses of transforming the potential energy of the fluid in the form of pressure and temperature, into mechanical work; in the case of the combustion chamber, aerodynamics plays a big role in the injection of fuel and mixing, but it must be coupled with chemical reactions and heat release within the transforming fluid.

## **2. Combustion and chemistry in CFD**

The combustion process is the result of a strong exothermic chemical reaction as a result of energy exchanges that occur due to intermolecular collisions.

Generally, at ambient temperature, a chemical reaction occurs very slowly, because, although collisions at molecular level occur, they do not generate a sufficient amount of energy to trigger a chemical transformation.

According to the chemical kinetic theory, only "active" collisions, collisions involving molecules having an initial energy greater than or equal to an energy called activation energy, lead to a chemical reaction. This energy is needed to destroy or weaken existing intermolecular connections. The activation energy is given by Arrhenius equation [5, 6]:

$$k = \mathbf{A} \cdot T^{\theta} \cdot \exp\left(\frac{-\mathbf{E\_a}}{\mathbf{R} \cdot T}\right) \tag{2}$$

where *k* is the reaction rate coefficient, A is the pre-exponential factor, Ea is the activation energy, R is the universal gas constant, β is the temperature exponent, and *T* is the temperature.

The combustion process can be expressed in a simplified way through the global reaction mechanism, Eq. (3):

$$\text{Fuel} + \text{Oxidizer} \to \text{CO}\_2 + \text{H}\_2\text{O} + \text{Heat} \tag{3}$$

Information of laminar model flames are pre-calculated and stored in a library to reduce computational time (PDF table). On the other hand, the model is still restricted by assumptions like fast chemistry or the neglecting of different Lewis

The coupling of laminar chemistry with the fluctuating turbulent flow field is done by a statistical method. The PDF used can in principle be calculated at every

The most often mentioned advantage of this method is that the nonlinear chemical source term needs no modeling. Even though the method avoids some modeling which is necessary if using moment closure, it still requires modeling of some of the most important terms, in particular, the fluctuating pressure gradient term and the molecular diffusion term. If combustion occurs in thin layers as assumed here, the molecular diffusion term is closely coupled to the reaction term, and the problem of modeling the chemical source term is then shifted towards modeling the diffusion

**2.4 Burning velocity model (BVM) and extended coherent flame model**

The burning velocity model (BVM) and the extended coherent flame model (ECFM) model the propagation of a premixed or partially premixed flame by solving a scalar transport equation for the reaction progress. The BVM uses an algebraic correlation for modeling the turbulent burning velocity (propagation speed of the flame in turbulent flow). When using the ECFM, the turbulent burning velocity is closed by solving an additional transport equation for the flame surface

• A model for the progress of the global reaction: burning velocity model (BVM),

• A model for the progress of the global reaction: extended coherent flame model (ECFM), which is a member of the class of flame surface density models.

• Aa model for the composition of the reacted and nonreacted fractions of the

The model solves the unfiltered Navier-Stokes equations for a global chemical reaction mechanism. The method uses no sub-grid closure models but employs the inherent numerical scheme dissipation to account for the energy transferred to the

LEM is a stochastic approach aimed at stimulating the turbulent mixing, molecular diffusion, and the chemical reaction in a one-dimensional domain embedded in the LES cells of the computational domain (LEMLES). LEM is the only known

• A model for the composition of the reacted and nonreacted fractions of the

point in the flow field by solving a PDF transport equation.

*CFD Application for Gas Turbine Combustion Simulations*

*DOI: http://dx.doi.org/10.5772/intechopen.89759*

numbers of the chemical species.

The BVM is a combined model using:

fluid: laminar flamelet with PDF.

fluid: laminar flamelet with PDF.

**2.5 The monotone integrated LES (MILES)**

**2.6 The linear eddy mixing (LEM) model**

also called turbulent flame closure (TFC).

The ECFM is a combined model employing:

term.

density.

sub-grid scales.

**219**

**(ECFM)**

In CFD modeling more complex reaction mechanisms (e.g., mechanisms which take into consideration the formation of NO) are also available. Using a more complex reaction mechanism is more time-consuming and requires higher computational power. Thus, depending on the purpose of the conducted numerical simulation, a simpler or more complex reaction mechanism should be chosen.

In CFD modeling several combustion models are available [7–9].

#### **2.1 Eddy dissipation model (EDM)**

The eddy dissipation model is based on the concept that chemical reaction is fast relative to the transport processes in the flow. When reactants mix at the molecular level, they instantaneously form products. The model assumes that the reaction rate may be related directly to the time required to mix reactants at the molecular level.

By default, for the eddy dissipation model, it is sufficient that fuel and oxidant be available in the control volume for combustion to occur.

Because of the assumption of complete combustion, the eddy dissipation model may overpredict temperature under certain conditions (e.g., for hydrocarbon fuels in regions with fuel-rich mixture).

The eddy dissipation model was developed for use in a wide range of turbulent reacting flows covering premixed and diffusion flames. Because of its simplicity and robust performance in predicting turbulent reacting flows, this model has been widely applied in the prediction of industrial flames.

#### **2.2 The finite-rate chemistry (FRC) model**

The finite-rate chemistry model allows the computation of reaction rates described by the molecular interaction between the components in the fluid. It can be combined with the eddy dissipation model for flames where chemical reaction rates might be slow compared with the reactant mixing rates. The finite-rate chemistry model is best applied to situations where the chemical time scale is rate-limiting. This model can be used in conjunction with both laminar and turbulent flow.

#### **2.3 The flamelet model**

The flamelet model can provide information on minor species and radicals, such as CO and OH, and accounts for turbulent fluctuations in temperature and local extinction at high scalar dissipation rates, for the cost of solving only two transport equations. The model is only applicable for two-feed systems (fuel and oxidizer) and requires a chemistry library as input. The model can be used only for nonpremixed systems.

The flamelet concept for non-premixed combustion describes the interaction of chemistry with turbulence in the limit of fast reactions (large Damköhler number). The combustion is assumed to occur in thin sheets with inner structure called flamelets. The turbulent flame itself is treated as an ensemble of laminar flamelets which are embedded into the flow field.

The main advantage of the flamelet model is that even though detailed information of molecular transport processes and elementary kinetic reactions are included, the numerical resolution of small length and time scales is not necessary. This avoids the well-known problems of solving highly nonlinear kinetics in fluctuating flow fields and makes the method very robust. Only two scalar equations have to be solved independent of the number of chemical species involved in the simulation.

*CFD Application for Gas Turbine Combustion Simulations DOI: http://dx.doi.org/10.5772/intechopen.89759*

Fuel þ Oxidizer ! CO2 þ H2O þ Heat (3)

In CFD modeling more complex reaction mechanisms (e.g., mechanisms which

The eddy dissipation model is based on the concept that chemical reaction is fast relative to the transport processes in the flow. When reactants mix at the molecular level, they instantaneously form products. The model assumes that the reaction rate may be related directly to the time required to mix reactants at the molecular level. By default, for the eddy dissipation model, it is sufficient that fuel and oxidant

Because of the assumption of complete combustion, the eddy dissipation model may overpredict temperature under certain conditions (e.g., for hydrocarbon fuels

The eddy dissipation model was developed for use in a wide range of turbulent reacting flows covering premixed and diffusion flames. Because of its simplicity and robust performance in predicting turbulent reacting flows, this model has been

The finite-rate chemistry model allows the computation of reaction rates described by the molecular interaction between the components in the fluid. It can be combined with the eddy dissipation model for flames where chemical reaction rates might be slow compared with the reactant mixing rates. The finite-rate chem-

The flamelet model can provide information on minor species and radicals, such as CO and OH, and accounts for turbulent fluctuations in temperature and local extinction at high scalar dissipation rates, for the cost of solving only two transport equations. The model is only applicable for two-feed systems (fuel and oxidizer) and requires a chemistry library as input. The model can be used only for non-

The flamelet concept for non-premixed combustion describes the interaction of chemistry with turbulence in the limit of fast reactions (large Damköhler number). The combustion is assumed to occur in thin sheets with inner structure called flamelets. The turbulent flame itself is treated as an ensemble of laminar flamelets

The main advantage of the flamelet model is that even though detailed information of molecular transport processes and elementary kinetic reactions are included, the numerical resolution of small length and time scales is not necessary. This avoids the well-known problems of solving highly nonlinear kinetics in fluctuating flow fields and makes the method very robust. Only two scalar equations have to be solved independent of the number of chemical species involved in the simulation.

istry model is best applied to situations where the chemical time scale is rate-limiting. This model can be used in conjunction with both laminar and

take into consideration the formation of NO) are also available. Using a more complex reaction mechanism is more time-consuming and requires higher computational power. Thus, depending on the purpose of the conducted numerical simu-

lation, a simpler or more complex reaction mechanism should be chosen. In CFD modeling several combustion models are available [7–9].

be available in the control volume for combustion to occur.

widely applied in the prediction of industrial flames.

**2.2 The finite-rate chemistry (FRC) model**

**2.1 Eddy dissipation model (EDM)**

*Computational Fluid Dynamics Simulations*

in regions with fuel-rich mixture).

turbulent flow.

**2.3 The flamelet model**

premixed systems.

**218**

which are embedded into the flow field.

Information of laminar model flames are pre-calculated and stored in a library to reduce computational time (PDF table). On the other hand, the model is still restricted by assumptions like fast chemistry or the neglecting of different Lewis numbers of the chemical species.

The coupling of laminar chemistry with the fluctuating turbulent flow field is done by a statistical method. The PDF used can in principle be calculated at every point in the flow field by solving a PDF transport equation.

The most often mentioned advantage of this method is that the nonlinear chemical source term needs no modeling. Even though the method avoids some modeling which is necessary if using moment closure, it still requires modeling of some of the most important terms, in particular, the fluctuating pressure gradient term and the molecular diffusion term. If combustion occurs in thin layers as assumed here, the molecular diffusion term is closely coupled to the reaction term, and the problem of modeling the chemical source term is then shifted towards modeling the diffusion term.

## **2.4 Burning velocity model (BVM) and extended coherent flame model (ECFM)**

The burning velocity model (BVM) and the extended coherent flame model (ECFM) model the propagation of a premixed or partially premixed flame by solving a scalar transport equation for the reaction progress. The BVM uses an algebraic correlation for modeling the turbulent burning velocity (propagation speed of the flame in turbulent flow). When using the ECFM, the turbulent burning velocity is closed by solving an additional transport equation for the flame surface density.

The BVM is a combined model using:


The ECFM is a combined model employing:


#### **2.5 The monotone integrated LES (MILES)**

The model solves the unfiltered Navier-Stokes equations for a global chemical reaction mechanism. The method uses no sub-grid closure models but employs the inherent numerical scheme dissipation to account for the energy transferred to the sub-grid scales.

#### **2.6 The linear eddy mixing (LEM) model**

LEM is a stochastic approach aimed at stimulating the turbulent mixing, molecular diffusion, and the chemical reaction in a one-dimensional domain embedded in the LES cells of the computational domain (LEMLES). LEM is the only known

combustion model that does not use the scale separation hypothesis and is, therefore, valid even in regimes where the hypothesis fails. Also, the model is highly compatible with the large eddy simulation (LES) technique and very flexible in terms of the chemical reaction mechanism used to describe the chemical reactions. Nevertheless, the approach has some limitations. Most importantly, LEMLES is relatively much more expensive than conventional LES models, such as EBULES. However, it is highly scalable, so the overall computation time can be decreased by increasing the number of processors. Laminar molecular diffusion across LES cells is not included, but this limitation is significant only in laminar regions, whereas LEMLES is designed for high Reynolds number turbulent flow applications. Also, the viscous work is neglected in the sub-grid temperature equation but is explicitly included in the LES energy equation, which is used to ensure total energy conservation. Finally, the flame curvature effect is not explicitly present in the sub-grid.

combustion of these fuels has allowed to determine the parameters to be used as input data in numerical simulations of the combustion process in the gas turbine's

*CFD Application for Gas Turbine Combustion Simulations*

*DOI: http://dx.doi.org/10.5772/intechopen.89759*

The numerical grid and boundary conditions are shown in **Figure 5**.

the reaction products, while the NO formation is controlled by two reaction

tion in the combustion chamber are displayed in **Figures 6** and **7**.

**Air mass flow rate**

*Computational grid with defined regions for the boundary conditions [10].*

The numerical simulations, starting from data provided by either the producer, theoretical computations or experimental, include four cases, for the two mentioned alternative fuels, at two different operating regimes of the gas turbine: nominal and idle. The working fluids are defined as ideal gases: air as bicomponent mixture with 21% oxygen and 79% nitrogen; methane from the software library and biogas, as reacting mixture with 50% methane and 50% carbon dioxide. The cases

The eddy dissipation model, within ANSYS CFX [11], controls the formation of

Using the 17 double thermocouples mounted on the engine, **Figure 8** containing a comparison between numerical and experimental results was obtained. It can be seen that the numerical results predict that two areas of maximum temperature exist at the end of the combustion chamber, and it was confirmed by the experi-

> **O2 mass fraction**

760,000 0.825 0.233 0.010683 1 0

232,500 0.314 0.233 0.003212 1 0

760,000 0.825 0.233 0.0419 0.267 0.733

**[Pa] [kg/s] [kg/s]**

C4 Biogas, idle 232,500 0.314 0.233 0.0118 0.267 0.733

**Fuel mass flow rate**

**CH4 mass fraction**

**CO2 mass fraction**

schemes, WD1 and WDS. The advantage of the WDS scheme is that it also contains the CO creation model, through water-gas shift mechanism, allowing for higher accuracy, a fact also confirmed by the comparison with the experimental results, while the disadvantage consists in the necessity for higher computational resources and up to 50% more computing time. Some images with the temperature distribu-

combustor.

are summarized in **Table 1**.

ments on the entire engine.

**Reference pressure**

**Case/ parameter**

C1 Methane, nominal

C2 Methane, idle

C3 Biogas, nominal

*Input data for numerical cases.*

**Table 1.**

**Figure 5.**

**221**
