7.5.1 Ignition and Relight Envelope

As noted earlier, the pressure dependence of the reaction rate coefficient may cause a relight problem at high altitude. A relight zone is plotted in Figure 7.8 in an altitude–Mach number plot (i.e., flight envelope) for the combustion of a typical hydrocarbon fuel in air (Henderson and Blazowski, 1989). We note that below 0.2 atm pressure, combustor relight is not possible at standard temperature, due to low reaction rate.

7.5.2 Reaction Timescale

The reaction timescale and its relation to the residence timescale of the air–fuel vapor mixture control the combustion efficiency. We require that the two timescales to be equal, to establish a minimum length requirement of the combustor. A typical variation of reaction timescale with equivalence ratio for gasoline–air combustion is shown in Figure 7.9 (from Kerrebrock, 1992). This shows that near stoichiometric combustion, ∼ 1, the reaction time reaches a minimum of ∼0.3 ms. The minimum reaction timescale is one of the indicators of the desirability of stoichiometric combustion. We shall see in the next section that the flammability limit of most fuels is a narrow band centered on the stoichiometric mixture ratio of = 1.

The reaction timescale is inversely proportional to reaction rate (Equation 7.67), which may be written as

(7.68)

There are no universal rules for the pressure and temperature exponents, n and m, in a gas turbine combustor, but typical value of n is ∼1–2 and m is ∼1.5–2.5 (Zukoski, 1985). The aircraft gas turbine combustor or afterburner is designed for a residence timescale in the primary zone or the flameholder recirculation zone-mixing layer to be long compared with the reaction timescale. Hence, we are not reaction-time-limited in a conventional combustor or afterburner. However, in a scramjet combustor with a Mach 3 combustor inlet flow, we are residence-time-limited, hence reaction timescale becomes especially critical. Fortunately, the fuel of choice, hydrogen, offers not only a regenerative cooling option for the engine inlet, combustor, and nozzle but also ∼1/10 of the chemical reaction timescale of hydrocarbon fuels. The pollutant formations and their dependence on the combustor characteristic timescales will be discussed in section 7.7 in this chapter.

7.5.3 Flammability Limits

A practical aspect of combustor design examines the issues of flammability limits of various fuel–air mixture ratios as a function of temperature and pressure in a quiescent environment. It is learned that a fuel–air mixture of equivalence ratio leaner than 0.6 and richer than 3.0 will not react (i.e., sustain combustion) in room temperature and pressure, as shown in Figure 7.10 (Blazowski, 1985). In reality, a narrow band around a stoichiometric fuel–air mixture ratio is our open window for a sustained combustion. With the increase in temperature, the flammability limit boundary widens to 0.3 < < 4.0 in the spontaneous ignition temperature range (T 225°C) for a kerosene-air mixture. The flammability limits of different fuel–air mixtures, in percentage stoichiometric, are shown in Table 7.5 at the temperature of 25 °C and 1 atm pressure. The most remarkable is the wide flammability limits of hydrogen. Also hydrogen, methane, and propane enjoy very large heating capacity making them suitable coolants for active cooling of the engine and airframe structure of a hypersonic aircraft.

The effect of low ambient pressure (corresponding to high altitude) on flammability limit of gasoline–air mixtures is shown in Figure 7.11 (from Olson, Childs, and Jonash, 1955). We note that the lean flammability limit at altitude approaches the stoichiometric ratio, that is, ≈ 1. We also observe that the rich flammability limit becomes much wider with the increase in pressure.

As noted earlier, the flammability limits are defined for a fuel–air (gas phase) mixture as a function of temperature and pressure in a quiescent environment. In the presence of flow, combustion instabilities may set in to cause a flame blowout. Hence, the presence of a flow may drive an otherwise stable combustion (in the flammable zone) into an unstable reaction where the combustion efficiency goes to zero at the point of flame blowout. In order to sustain combustion in the presence of flow, that is, to avoid blowout, we need to employ flame stabilization schemes, which are suitable for the primary combustors and the afterburners. We will address several stabilization schemes in this chapter.

A need for an external source of energy release, as provided by an electric spark discharge, is (implicitly) demonstrated in the flammability limit diagram of kerosene–air mixture in Figure 7.10. Note that below the spontaneous ignition temperature (SIT) of the fuel–air mixture (of ∼225°C), the mixture that is defined as flammable will not self-ignite. Hence, an ignition source that is an intense localized heat source is needed to initiate the reaction. The intense localized energy release will raise the temperature of a pocket of the vaporized fuel–air mixture to a temperature above the SIT. A flame front signifying the chemical reaction zone is then formed, which propagates in the flammable mixture at a finite speed S_T. Table 7.6 contains the spontaneous ignition temperature of some common fuels for reference (from Gouldin, 1973). A high spontaneous ignition temperature is desirable for a fuel that is to be used for its cooling capacity. For example, propane in Table 7.6 has the highest SIT at 767 K, which makes it a good candidate for cooling purposes. Since the spontaneous ignition temperature of fuel–air mixtures is a strong function of mixture pressure, the SIT information contained in Table 7.6 needs to be viewed with caution and not to be used for the “general purpose” fuel system safety calculation. The minimum external energy (stimulus) needed to initiate a reaction is a function of the equivalence ratio as well as the type of fuel for vaporized fuel–air mixtures. Figure 7.12 (from Lewis and von Elbe, 1961) shows the level of ignition energy of various vaporized fuel–air mixtures as a function of equivalence ratio. The ignition energies are in the form of ”bucket” shapes with the minimum ignition energy corresponding to a particular equivalence ratio.

Note that in Figure 7.11, the minimum ignition energy points on the ”buckets” shifts to the right, that is, toward higher equivalence ratios, with higher molecular weight fuels. Methane, CH₄, has a molecular weight of 16 and the minimum ignition energy around the stoichiometric ratio, whereas n-heptane, C₇H₁₆, has a molecular weight of 100 and the minimum ignition energy occurring around an equivalence ratio of ∼2. We may express this observation in terms of the specific gravity of these fuels as well where methane’s specific gravity is 0.466 (a light fuel) and n-heptane’s specific gravity is 0.684 (a relatively heavier fuel).

7.5.4 Flame Speed

There are two types of flames, premixed flames and diffusion flames. When the fuel and oxidizer are in gaseous form and premixed into a (stoichiometric) flammable mixture prior to combustion initiation, the resulting flame is called a premixed flame (e.g., Bunsen burner). When the fuel and oxidizer are initially separated, as in a candle burning in air, the combustion takes place within a diffusion flame zone where the vaporized fuel diffuses outward and meets an inwardly diffusing oxidizer. For an aircraft application where space is at a premium, a premixed flame combustor with a high level of turbulence intensity is the desirable choice. The effect of turbulence intensity is to promote mixing enhancement. It is the rapid and efficient mixing of the vaporized fuel–air mixture in a combustion chamber that is a performance limiting parameter, that is, limiting the energy release rate, rather than the chemical reaction timescale or flame propagation speed in conventional burners. The flame zone in a premixed combustor starts propagating initially as a laminar flame and later develops into a turbulent flame. A schematic drawing of a laminar premixed flame and its typical characteristic parameters (thickness, propagation speed, temperature range, pressure drop, and wave angle, α) are shown in Figure 7.13. The laminar flame parameters in Figure 7.13 are extracted from Borman and Ragland (1998). S_L is the laminar flame speed, δ_L is the flame thickness, and α is the relative flow angle.

The initial mixture temperature has the most pronounced effect on laminar flame speed. The burning velocity of the laminar flame zone increases nearly fourfold when the initial mixture temperature is raised from 200 to 600 K, as reported by Dugger and Heimel (1952) for methane (CH₄), propane (C₃H₈), and ethylene (C₂H₄) combustion in air. The mixture pressure has a minor effect on the laminar flame speed as discussed by Lefebvre (1983). The experimental results of Jost (1946), shown in Figure 7.14, demonstrate the equivalence ratio of the laminar flame speed. Moreover, they confirm the typical speed of ∼0.5 m/s for a hydrocarbon fuel, as in propane. They also show nearly an order of magnitude increase in laminar flame speed for hydrogen, which reconfirms the status of hydrogen as an ideal fuel.

The effect of turbulence on premixed flame speed is to enhance momentum transfer between the burning front and the unburned reactants. In addition, turbulence increases the total surface area of the flame and hence increases the heat transfer between the reaction zone and the unburned gas. To visualize the surface area of a flame front under the influence of turbulence, a wrinkled flame front is proposed. Under this scenario, large (energetic) turbulent eddies strike the flame front and wrinkle the surface, while small-scale turbulence changes the transport properties within the flame zone. Figure 7.15 shows a representative drawing of a wrinkled flame front with a range of turbulent eddy sizes within the flame (adapted from Ballal and Lefebvre, 1975). Consequently, the flame propagation speed is increased from the laminar flame speed S_L to the turbulent flame speed S_T. The first model, due to Damkohler (1947), proposes enhancing the laminar flame speed by adding the root mean square of the turbulent fluctuation speed. The increase in flame surface area due to turbulence is proportional to

(7.69)

The laminar flame speed is S_L ∼ 0.5–2 m/s (depending on the initial mixture temperature), which is now enhanced by turbulent fluctuations. A low turbulence intensity environment, of say 5%, in a (fuel–air mixture) flow of ∼50–100 m/s results in a root mean square of the turbulent fluctuation speed of 2.5–5 m/s. Now, in a high turbulence intensity environment, of say 15–30%, in a flow with a mean speed of ∼100 m/s, the turbulence contribution to flame propagation speed may be as high as 30 m/s. Although the simple model of Damkohler in Equation 7.69 does not account for turbulence scale, the thickness of the reaction zone and other effects such as flame stretching, it serves the purpose of demonstrating the attractiveness of turbulence-enhanced mixing and its impact on the reaction timescale. A review of more elaborate models is beyond the scope and intention of the present treatment. Excellent books on combustion, such as those authored by Lefebvre (1983), Kuo (1986), Glassman (1987), Borman and Ragland (1998), among others, are recommended for further reading in this fascinating field.

7.5.5 Flame Stability

Does a Bunsen burner or a candle in a laboratory produce a stable flame? The obvious answer is yes, but the correct answer should be a conditional yes or a maybe. Since we did not specify any source or intensity of airflow in the room, we could not rule out the possibility of flame extinction caused by the airflow. If we place a Bunsen burner or a candle in a duct (for measurement purposes) connected to a fan on one side, we may experimentally establish the wind speed in the duct that causes the candle flame to blowout. Similar experiments may be conducted in a premixed combustible mixture where a flame front is established and propagates in the mixture at the flame speed S. Now, if we set the premixed gas into motion at speed U in the opposite direction to S and equal to it in magnitude, we shall achieve a stationary flame front. Simply adding the velocity vectors demonstrates the principle. For a given mixture fuel–air ratio, we may repeat the experiment for different flow speeds until we achieve an extinction of the flame (i.e., at the blowout speed). We may subsequently vary the fuel–air mixture ratio from a lean limit where extinction occurs to a rich limit at a given flow speed. The result of this experiment may be plotted in terms of the fuel–air mixture (or equivalence ratio) and the flow speed (or air mass flow rate, which is proportional to flow speed) in what is known as a stability plot or the stability loop, due to its shape. Figure 7.16 shows the combustion system stability loop for a constant pressure (from Lefebvre, 1983).

The lower branch of the stability loop is the lean extinction limit and the upper branch is the rich extinction limit of combustion chamber. The maximum blowout speed occurs at the maximum flame speed, which is usually near the stoichiometric mixture ratio. The effect of pressure on the lean stability limit is negligible and widens the rich stability limit with the increase in pressure.

A recirculation zone in the burner (with a backward flow) is needed to stabilize a premixed flame. In studying swirling jets, we learn that when the ratio of jet angular momentum to jet axial thrust times jet diameter exceeds ∼0.5, a recirculatory flow in the core of the swirling jet is established. This is known as a vortex breakdown. A schematic drawing of a swirling jet with vortex breakdown is shown in Figure 7.17.

Flow visualization (via dye injection in water) of a bubble-type vortex breakdown is shown in Figure 7.18 (from Sarpkaya, 1971). The complex network of vortex filaments winding in and out of the bubble and a spiraling wake formation indicates filling and emptying of the bubble. This environment, that is, the recirculation and intense mixing of a vortex breakdown, comes close to a model of a perfectly stirred reactor that is often used in combustion studies.

To help stabilize the flame in the primary zone of a main burner, air is introduced through single or double rows of swirl vanes. Also, to create a perfectly stirred reaction zone in the main burner, part of the excess air is injected into the burner through the primary air holes as radial jets. When opposing radial jets collide, a stagnation point is created with the resultant streams directed along the axis in the upstream and downstream directions. The opposing flows of the axial jet moving upstream and the spiraling air–fuel mixture create a recirculation zone with intense mixing. The combustor primary zone may also be modeled as a perfectly stirred reactor. A schematic drawing of radial jets and subsequent axial jet formations are shown in Figure 7.19.

In an afterburner, the necessary recirculation zone to stabilize the premixed flame is created by the massively separated wakes of bluff bodies. Some geometric examples of bluff bodies that create massively separated wakes are produced in Figure 7.20.

The flameholding, that is, creating a reversed flow environment, in a high-speed scramjet combustor may be achieved by a direct fuel injection in the supersonic air stream, or via a backward-facing step. The former involves a bow shock, and the latter involves the corner flow separation. These flowfields are of interest in high-speed propulsion and are shown in Figure 7.21.

The primary zone of a burner and the wake of a bluff body in the afterburner are modeled as a perfectly stirred reactor where the reactants and products are mixed infinitely fast. Such an environment produces the maximum energy release (due to infinitely fast chemical reaction rates) for the given volume of the reactor and at a fixed reactor pressure. The theory of perfectly stirred reactor has many applications, among which the stability of premixed turbulent flames in a flow environment. The perfectly stirred reactor theory predicts

(7.70)

where the mass flow rate in the reactor is , volume of the reactor is V, pressure of the reactor is p, the exponent of pressure represents the order of reaction, which is close to 2, and is the equivalence ratio of the fuel–air mixture. The parameter on the right-hand side of Equation 7.70 is called the combustor loading parameter (CLP). A graph of Equation 7.70 is shown in Figure 7.22 (from Spalding, 1979). A lean and a rich extinction limit (i.e., when flame instability causes extinction) are observed in Figure 7.22, similar to the stability loop of Figure 7.16. The pressure exponent “n” is taken as 1.8 in Figure 7.22, and the dimensions of the combustor loading parameter are lbm/(s · atm^1.8 · ft³) in English units.

Fundamental contributions to understanding flame stability are due to the works of Longwell, Chenevey, and Frost (1949), Haddock (1951), and Zukoski–Marble (1955). Although, we will briefly address the afterburner stability in this chapter, these references are recommended for further reading.

7.5.6 Spontaneous Ignition Delay Time

In continuing with our studies of combustion timescales and the role of chemical kinetics, we enter a new characteristic timescale, namely, the spontaneous ignition delay time. Spontaneous ignition delay time is defined as the time elapsed between the injection of a high-temperature fuel–air mixture and the appearance of a flame in the absence of an ignition source. There are two factors that contribute to an autoignition delay time. First is the rate of evaporation of fuel droplets, and the second is the chemical reaction time of the vaporized fuel and air. To promote the rate of evaporation, a liquid fuel has to be efficiently atomized to a fine spray mist. Modern aircraft engine combustors utilize spray injectors that produce an atomized fuel drop size distribution in the range of 10–400 m. Rao and Lefebvre (1981) express the ignition delay time as

(7.71)

The subscript “i” stands for ignition delay, and “e” stands for evaporation timescale in Equation 7.71. Evaporation timescale in a stagnant mixture is proportional to the surface area of the liquid fuel droplet, as the heat transfer rate to the liquid is proportional to the surface area, i.e.,

(7.72)

where D is the liquid fuel droplet diameter, and Re_D is the fuel droplet Reynolds number based on diameter of the droplet, turbulent fluctuation velocity u′ (rms), and the kinematic viscosity of the gas ν_g. In the presence of a highly turbulent mixture, the evaporation time is proportional to the droplet diameter to the power three halves, that is,

(7.73)

according to Ballal and Lefebvre (1980). The effect of turbulence is hence to increase the heat transfer and reduce the evaporation timescale. The reaction time is expressed in terms of the mixture temperature (in K), by Rao and Lefebvre (1981), as

(7.74)

From the chemical kinetic rate Equation 7.67, we may also deduce the reaction timescale as the inverse of the rate constant based on initial temperature T₁, namely,

(7.75)

The ignition delay time for a range of initial temperatures between 600 and 1000 K and a range of pressures between 1 and 30 atm is shown in Figure 7.23 (adapted from Rao and Lefebvre, 1981).

Figure 7.23 is a log–log plot. It shows an exponential drop in ignition delay time with initial temperature, as expected from Equation 7.75. The ignition delay time is also reduced with the increase in combustion pressure. This pressure dependence becomes weaker for a high inlet temperature (1000 K) and at a high pressure (30 atm). Interestingly, the conditions of 1000 K inlet temperature and 30 atm combustion pressure are representative of a typical gas turbine engine combustor inlet conditions. Based on these, the ignition delay time is ∼1–2 ms. From the reaction timescale given by Kerrebrock in Equation 7.78, we may express the pressure dependence of the ignition delay time with an inverse relation, such as

(7.76)

The results of autoignition delay time studies of Spadaccini (1977) for typical hydrocarbon fuels at elevated temperatures and at the pressure of 10 atm are shown in Figure 7.24 (a log–linear plot). We again observe an exponential drop in ignition time delay with temperature. The pressure dependence follows Equation 7.76, or the trends shown by Rao and Lefebvre in Figure 7.23.

7.5.7 Combustion-Generated Pollutants

The subject of pollution is an integral part of the current section, that is, chemical kinetics. However, due to its importance, this subject is presented, in more detail, after the discussion of combustion chambers and afterburners in section 7.7.

7.6.1 Combustion Chamber Total Pressure Loss

The total pressure loss in a combustor is predominantly due to two sources. The first is due to the frictional loss in the viscous layers where we can lump in the mixing loss of the fuel and air streams prior to chemical interaction. The second source is due to heat release in an exothermic chemical reaction in the burner. The first is usually modeled as the “cold” flow loss and the second is the “hot” flow loss. We recognize, however, that the subdivision of the losses into “cold” and “hot” is artificial and the two forms of total pressure loss occur simultaneously and interact in a complex way. But throughout the ages, engineering is practiced through the art of simplification, that is, engineers have broken down a complex problem into a series of elementary and solvable problems and then tried to predict the solution of the complex problem by devising a correlation between the elementary solutions and the observation or measurement. We intend to stay our engineering course on the topic of combustion chamber total pressure loss. There are several methods of quantifying the total pressure loss in a combustor, namely,

(7.77)

(7.78)

(7.79)

The first expression is the overall total pressure loss ratio, the second expression is a measure of the total pressure loss in terms of the inlet dynamic pressure, and the last expression uses a reference velocity for the dynamic pressure and measures the total pressure loss in terms of the reference dynamic pressure. The reference velocity is the mass averaged gas speed at the largest cross-section of the burner, based on the combustor inlet pressure and temperature. The reference Mach number is the ratio of the reference speed to the speed of sound at the prediffuser inlet a₃. All the aerodynamic losses scale with reference dynamic pressure, as shown in Figure 7.29 (from Henderson and Blazowski, 1989).

A parabolic dependence of the total pressure loss on the reference Mach number is shown in Figure 7.29. Kerrebrock suggests an empirical rule for the combustor total pressure ratio, as a fraction of reference dynamic pressure. In terms of the average Mach number of the gases in the burner, M_b, Kerrebrock’s empirical rule is stated as

(7.80)

where .

This equation states that the total pressure loss is proportional to an “average” dynamic pressure of the gases in the combustor, with the proportionality constant . We note that the total pressure loss grows as the mean flow speed increases. Now, we appreciate the role of prediffuser in a combustion chamber. The total pressure loss due to combustion that is, heat release, in the burner may be modeled by a Rayleigh flow analysis. The conservation of mass and momentum for a constant-area frictionless duct are

(7.81)

(7.82)

Now, instead of the compressible equation for the total pressure involving Mach number, we may use the low-speed version in an approximation, that is, the Bernoulli equation, namely,

(7.83)

Canceling the first two parentheses via momentum Equation 7.82, and using the continuity equation we may simplify Equation 7.83 as

(7.84)

Now, using the perfect gas law for the density ratio and neglecting static pressure changes between the inlet and exit of the burner in favor of the large temperature rise across the combustor, we may write the following simple expression for the total pressure loss due to heating in a constant-area burner as

(7.85)

In deriving the above expression, we made a series of approximations and simplifications. Consequently, we may use Equation 7.85 in relative terms, for example, in describing the effect of the throttle setting (T₄) on the variation of (hot) total pressure loss in a burner. Lefebvre (1983) suggests a correlation based on the Equation 7.85 that involves two unknown coefficients, K₁ and K₂, as

(7.86)

The correlation coefficients K₁ and K₂ need to be established experimentally. This is another example of a simple model (Equation 7.85) that is the basis of an engineering correlation for a complex problem. The total pressure loss due to combustion is small compared with aerodynamic losses, namely,

The cold total pressure loss is in the range of ∼4–7%, that is,

In an afterburner, the process of flame stabilization is achieved via flameholders, as described earlier, that creates massively separated wakes and is responsible for the bulk of the total pressure loss. We model an afterburner as a constant-area duct with a series of bluff bodies in the stream with a known drag coefficient. The diagram that describes the problem is shown in Figure 7.30.

We may account for the wall friction in the momentum balance equation either directly or we may combine its overall drag contribution with the flameholder drag. The effect of combustion on total pressure loss is important and will be investigated later in this section.

First, we model the afterburner-off condition, which is known as the “dry” analysis of the engine. The “wet” mode analysis follows the “dry” mode in this section.

From continuity equation we have

(7.87)

The fluid momentum equation in the streamwise direction gives

(7.88)

We define the flameholder drag in terms of the duct cross-sectional area A as

(7.89)

Rearranging the terms of the momentum equation, we get

(7.90)

Therefore, the static pressure ratio is expressed in terms of the inlet and exit Mach numbers and the flameholder drag coefficient C_D as

(7.91)

From the continuity equation, we express the density ratio in terms of the velocity ratio and then we replace the gas speed by the product of Mach number and the speed of sound to get

(7.92)

We use the energy equation for an adiabatic process, which is a statement of the conservation of total enthalpy, to get the static temperature ratio, namely,

(7.93)

By invoking the perfect gas law, we link the static pressure, density, and temperature ratios of the gas at the inlet and exit of the duct as

(7.94)

Now, all the ratios in Equation 7.94 are expressed in terms of the inlet and exit Mach numbers and gas properties. Hence, for a known inlet condition, we may use this equation to establish the exit Mach number M_e. Let us substitute expressions 7.91, 7.92, and 7.93 in Equation 7.94 to get the desired equation involving one unknown M_e,

(7.95)

We may simplify the above equation by combining the gas properties and the last two brackets, to get

(7.96)

Fortunately, Equation 7.96 is aquadratic equation for Me with a closed form solution, that is, no iteration is needed. Therefore the exit Mach number is

(7.97)

where

(7.98)

With exit Mach number known, we may substitute it in Equation 7.91 to get the static pressure ratio, and the total pressure ratio is then calculated by

(7.99)

Now we may graph the total pressure loss, due to flameholder drag, across the afterburner, as a function of inlet Mach number and gas properties at the inlet and exit.

Figure 7.31 shows the aerodynamic impact of flameholder drag on afterburner total pressure loss. The importance of low inlet Mach number to the afterburner may also be discerned from this figure. The penalty for a high inlet Mach number (of say ∼0.5) is severe and thus the necessity of a prediffuser becomes evident. The presence of aerodynamic drag in the afterburner causes the exit Mach number to increase and approach a choked, that is, M_e = 1, state. Frictional choking in the afterburner is to be avoided since combustion also tends to increase the Mach number, as in Rayleigh flow. A graph of the exit Mach number as a function of inlet Mach number and the flameholder drag coefficient is shown in Figure 7.32.

The flameholder drag coefficient in our analysis was defined based on the afterburner cross-sectional area. However, the drag coefficient of bluff bodies is defined based on the maximum cross-sectional area of the bluff body. Therefore,

(7.100)

where the A_max is the base area of an individual bluff body and N is the number of bluff bodies used in the flameholder arrangement, typically in the form V-gutter rings and radial V-gutter connectors. We may define a flameholder blockage area ratio as

(7.101)

Therefore, the drag coefficient used in our afterburner total pressure loss calculation is related to the individual drag coefficients via the blockage factor, that is,

(7.102)

Figure 7.33 serves as a definition sketch for the afterburner duct, and the flameholder rings that contribute to the blockage parameter B. Here the radial gutters that connect the V-gutter rings to the turbine exit diffuser cone or the casing are not shown. The EJ200 of Eurojet Consortium uses radial gutters (instead of rings) for flame holding (Figure 7.47).

To account for higher flow velocities in the plane of the flameholder, due to flameholder blockage, the drag coefficient needs to be scaled by the dynamic pressure ratio, that is,

(7.103)

where subscript “fh” identifies the plane of the flameholder and the bluff body drag coefficient (e.g., a V-gutter) was assumed to be ∼1. Note that a flat plate, in broadside, creates a drag coefficient of 2 and a cylinder in cross flow ∼1.2 (both flows at a Reynolds number based on plate height or cylinder diameter of 100, 000).

The analysis of an afterburner in the “wet” mode differs from the “dry” mode only in its energy balance equation, namely,

(7.104)

By neglecting the fuel-to-air ratio in the afterburner in favor of 1 on the left-hand side of the energy equation and renaming the product term on the RHS as “q, ” we get

(7.105)

We may relate the static enthalpy ratio to the stagnation enthalpy and Mach number as

(7.106)

By replacing Equation 7.93 with the above equation, and proceeding with the substitution of the static pressure ratio and density ratio in the perfect gas law, we obtain

(7.107)

Again, the above expression involves one unknown, that is, M_e, and is fortunately a quadratic equation with the following closed form solution:

(7.108)

where

(7.109)

Now, let us graph the total pressure loss in an afterburner in the wet mode (sometimes referred to as the reheat mode), using the above solution for the exit Mach number. Figure 7.34 shows the afterburner total pressure loss increases with heat release in the combustor. We also note that the choked exit condition is reached at a relatively low inlet Mach number of <0.4. Higher heating levels and flameholder drag coefficients will result in earlier choking than shown in Figure 7.34. Thus, the necessity of decelerating the flow entering an afterburner is again evident from Figure 7.34.

We produce Figure 7.35 to demonstrate the effect of higher flameholder drag coefficient on the afterburner wet mode total pressure loss, and the inlet Mach number range that leads to exit choking. Based on these results, an inlet’s Mach number range of ∼0.2–0.25 is desirable for an afterburner.

7.6.2 Combustor Flow Pattern and Temperature Profile

A typical flow pattern in a primary burner is demonstrated in Figure 7.36a (from Tacina, 2000), which shows the burner primary zone, intermediate zone, and the dilution zone in an annular combustor. We have already discussed the primary zone in the context of flammability, flame stability, and stoichiometry. The primary air jets in opposing radial directions are also introduced to stabilize the flame and increase combustor efficiency/heat release rate. The role of intermediate zone is seen as an extension of the primary zone in achieving a complete combustion/controlling pollutant formations, and the dilution zone is seen as producing a desired turbine inlet temperature profile, as shown in Figure 7.36a. Airflow distribution in a modern combustor is shown in Figure 7.36b.

The temperature profile at the turbine inlet exhibits nonuniformity due to the number of fuel injectors used in the circumferential direction, the nonuniformity in dilution air cooling and mixing characteristics as well as other secondary flow patterns and instabilities that are set up in the burner. These spatial nonuniformities at combustor exit are described by two nondimensional parameters, the pattern factor and the profile factor.

Pattern factor

(7.110)

where T_t-max is the absolute maximum exit temperature in the circumferential and radial directions, T_t-avg is the average of the exit temperature, and T_t-in is the average inlet total temperature. Since the nonuniformity parameter in the numerator of Equation 7.110 is the absolute maximum of the exit temperature (i.e., the absolute peak), this parameter is also known as the peak temperature factor. Turbine nozzle is exposed to this nonuniformity. The desired range of this parameter is between 0.15 and 0.25 in modern high-temperature rise combustors.

Profile factor

(7.111)

where T_t-max-avg is the circumferential average of the maximum temperature, that is, the average of all the local peaks in the circumferential direction. Since the flow acceleration in the turbine nozzle reduces the temperature distortion levels, the turbine rotor that follows the nozzle is exposed to this nonuniformity. The range of this parameter is between 1.04 and 1.08.

REMARKS     Flow acceleration dampens nonuniformity in the flow, whereas flow deceleration amplifies distortion. Therefore, the temperature distortion at the turbine inlet is reduced after the nozzle. By the same token, the flow distortion in the inlet diffuser or in the compressor blades is amplified. All engineers dealing with fluid flow problems should know this principle. The proof of this principle is very simple using a parallel flow model (see Problem 7.22).

7.6.3 Combustor Liner and Its Cooling Methods

Combustion takes place inside a combustor liner. It consists of a dome in the primary zone, primary air holes for the primary (radial) jets, air holes for the intermediate zone (radial jets), and the cooling holes/slots in the dilution zone. The combustion temperature may exceed 2500 K (in the primary zone), whereas the liner temperature needs to be kept at ∼1200 K. The heat transfer to the liner from the combustion side is in the form of radiation and convective heating by the hot combustion gases. The conventional cooling techniques used in gas turbine engines are

1. Convective cooling
2. Impingement cooling
3. Film cooling
4. Transpiration cooling
5. Radiation cooling
6. Some combination of the above.

The convective cooling method is primarily used in cooled turbine blades with the philosophy of maximizing the heat transfer rate from a hot wall (gas side) to the coolant inside the blade. The coolant may also impinge on a hot surface to create a stagnation point and hence enhance the heat transfer to the coolant through the wall. The impingement cooling method is often used in the leading-edge cooling of turbine blades. The film cooling method operates on the principle of minimizing heat transfer to the wall from the hot gases by providing a protective cool layer on the hot surface. The cool layer acts like a “blanket” that protects the surface from the hot gases. In film cooling, the coolant is injected through a series of discrete fine film holes, at a slanted angle to the flow direction, and emerges on the hot side to provide the protective cooling layer. Note that the philosophy of film cooling to minimize heat transfer to a wall is different from that of convective cooling, which maximizes the heat transfer through a wall. The transpiration cooling calls for a porous surface where the coolant emerges on the hot gas side through the pores. The cooling protection that it provides is similar to the film cooling technique, that is, by blanketing the surface with a coolant layer. Transpiration cooling may be viewed as the ultimate film cooling in the limit of infinitely many and continuously distributed film holes on a surface. Finally, the radiation cooling accompanies all surfaces above the absolute zero temperature. The radiation cooling of the liner to the outer casing, however, represents only a small fraction of the overall heat transfer of the liner. We shall discuss these in the context of cooled turbine blades and shrouds in more detail in Chapter 10.

The availability of excess air at the burner inlet dominates the application of these heat transfer techniques to a combustor liner. The primary and the intermediate zone air holes are designed to provide combustion stability and maximizing the chemical reaction heat release. The remaining air, which may be about 15–30% of the combustor inlet flow, is used to provide a reliable and uniform cooling protection to the liner. A successively more sophisticated technique of liner cooling is shown in Figures 7.37 and 7.38 (from Henderson and Blazowski, 1989). Starting from the louver cooling with the problems of uniform coolant distribution and control that marked the early combustor development to the most sophisticated transpiration cooling are schematically shown in Figure 7.37.

The coolant mass flow requirement is diminished with cooling effectiveness. Simple film cooling, convection/film, impingement/film, and the transpiration cooling are ranked from the highest to the lowest coolant requirement, respectively. The film cooling method eliminates the problem of coolant injection uniformity and control that was shown by louver technique. The combination convection/film and impingement/film cooling techniques offer a further enhancement of cooling effectiveness of the combustor liner. The transpiration cooling through a porous liner minimizes the coolant flow requirement and offers the most uniform wall temperature distribution (Figure 7.38). The problem of pore clogging, however, poses a challenge in transpiration cooling.

To quantify the coolant mass flow requirement, we define a cooling effectiveness parameter Φ according to

(7.112)

The cooling effectiveness is the ratio of two temperature differentials. The numerator is the difference between the hot gas T_g and the desired (average) wall temperature T_w. The denominator represents the absolute maximum potential for wall cooling. Therefore, the cooling effectiveness Φ is the fraction of the absolute maximum cooling potential that is realized in the wall cooling process. The hot gas in this application is the combustion temperature (T_g) or sometimes referred to as the flame temperature, and the coolant is the compressor discharge temperature (T_c). The desired wall temperature T_w is dictated by the wall material properties and durability requirements (e.g., 18, 000 or 20, 000-hr life). The variation of cooling effectiveness with coolant flow is shown in Figure 7.39 (data from Nealy and Reider, 1980).

In future advanced gas turbine engines, the combustor temperature may reach ∼2500 K (near the maximum adiabatic flame temperature of hydrocarbon fuels), with a desired liner temperature of ∼1200 K and a compressor discharge temperature of 900 K, the cooling effectiveness is then 0.8125. In examining Figure 7.39, we note that a film-cooled liner may not reach this desired level of cooling effectiveness, regardless of percentage coolant available. On the contrary, this level of cooling effectiveness represents the maximum possible limit of the transpiration cooling at close to 18% coolant availability/usage. Application of a thin layer of refractory material such as a ceramic coating lowers the heat transfer to the wall and thus allows a higher operating temperature in the combustor. To tolerate a higher heat release level in an advanced combustor, the liner material needs to tolerate higher operating temperatures and require less (to no) cooling percentage. In addition to operating at high temperatures, the liner material has to be oxidation resistant. Refractory metals such as molybdenum and tungsten suffer in this regard. A promising new liner material is the ceramic matrix composite (CMC). Development of prototype CMC combustor liner has been approached in industry by using silicon carbide fiber reinforced silicon carbide (SiC/SiC). The use of advanced composite materials as combustor liners represents a challenge in manufacturing, scaling up, life prediction, damage tolerance, reparability characteristics and cost.

7.6.4 Combustion Efficiency

Combustion efficiency measures the actual rate of heat release in a burner and compares it with the theoretical heat release rate possible. The theoretical heat of reaction of the fuel assumes a complete combustion with no unburned hydrocarbon fuel and no dissociation of the products of combustion. The actual heat release is affected by the quality of fuel atomization, vaporization, mixing, ignition, chemical kinetics, flame stabilization, intermediate air flow, liner cooling, and, in general, the aerodynamics of the combustor. Here a variety of timescales as in residence time, chemical reaction/reaction rate timescales, spontaneous ignition delay time that includes vaporization timescale, among other time constants enter the real combustion problem. The unburned hydrocarbon (UHC) and carbon monoxide (CO) that contribute to combustor inefficiency are also among the combustion-generated pollutants. The allowable levels of these pollutants in aircraft gas turbine engine emissions, regulated by the U.S. Environmental Protection Agency (EPA), place a 99% combustion efficiency demand on the combustor.

For a gas turbine combustor, when chemical kinetics is the limiting factor in combustor performance, Lefebvre (1959, 1966) introduces a combustor loading parameter (CLP) θ, which correlates well with combustion efficiency. θ parameter is defined as

(7.113)

The combustor inlet pressure, temperature, and mass flow rate are p_t3, T_t3, and ₃, respectively, maximum cross-sectional area of the burner is defined as A_ref, the combustor height is H and b is a reaction rate parameter. The dependence of the reaction rate parameter b on the primary zone equivalence ratio is estimated by Herbert (1957) to be

(7.114)

These expressions are plotted in Figure 7.40 (from Henderson and Blazowski, 1989). Note that dimensions of the parameters used in Figure 7.40 a are in English units, as described in the definition box in the graph.

The lowest combustion efficiency is, of course, zero in the flameout limit. This could happen at a high altitude when the low combustor pressure in essence slows the reaction rate to a halt (τ_residenceτ_reaction). The graphical correlations used in the combustion efficiency Figure 7.40 are then used to size the combustor in conditions corresponding to high altitude (for a relight requirement) assuming a combustor efficiency of 80%.

7.6.5 Some Combustor Sizing and Scaling Laws

The engine size, that is, the core (air) mass flow rate, and the compressor pressure ratio, by and large, determine the combustor inlet flow area. The flow area takes the form of an annulus, and its size is A₃. We may calculate the flow area A₃ by a one-dimensional continuity equation such as

(7.115)

At design point, the engine (core) mass flow rate, the compressor discharge parameters p_t3 and T_t3 (which are a function of π_c and e_c), and our design choice for M₃ size the flow area A₃ according to Equation 7.115. A typical compressor exit Mach number is ∼0.4–0.5. However, a combustor requires a prediffuser to decelerate the air from the compressor to improve combustion total pressure (loss) and combustion efficiency. A desired combustor inlet Mach number is ∼0.2. A conventional diffuser may be designed by using the design charts that were presented in the inlet and nozzle chapter. Diffusion is a slow and patient process, which normally takes place in a long duct of shallow wall divergence angles of ∼3–5° inclination with respect to a straight centerline. To shorten the axial length of a combustor prediffuser, one may employ a

• Diffuser with splitter vanes
• Dump diffuser
• Vortex-controlled diffuser.

The subject of a wide-angle diffuser that employs splitter vanes was already presented in Chapter 6 (references 1 and 2 should be consulted on short and hybrid diffusers). In a dump diffuser, the flow area undergoes a sudden expansion with the attendant flow separation at the lip. Figure 7.41 shows a schematic drawing of a dump diffuser.

A curved turbulent shear layer emerges from the point of separation, which reattaches in approximately 5–7 inlet channel heights, for a two-dimensional expansion. A pair of stable vortex structures is formed (in 2D) at the separation corner. In the axisymmetric case, a stable vortex ring is formed at the separation junction. The expression used in Figure 7.41 for the static pressure ratio and velocity ratio is based on Bernoulli equation, and the last part that relates the flow speed to flow area is based on the incompressible continuity equation. The loss of total pressure between stations 1 and 2 is due to viscous/turbulent mixing and dissipation in the separated shear layer and the boundary layer formation downstream of the reattachment point. An example of an annular combustor using a dump prediffuser is shown in Figure 7.42 (from Henderson and Blazowski, 1989).

Total pressure recovery of a dump diffuser is a function of Reynolds number and the Mach number at its inlet. For Reynolds number based on the inlet diameter of ∼500, 000 to 10⁶, Barclay (1972) recommends the following correlation:

(7.116)

The exit Mach number M₂ is then established using a continuity equation, according to

(7.117)

The total pressure recovery of a dump diffuser and its exit Mach number are plotted in Figure 7.43 for an inlet Mach number of M₁ = 0.5 and γ = 1.4.

Figure 7.43 indicates that in order to decelerate a Mach 0.5 flow to an exit Mach number of 0.2 in a dump diffuser, we need to employ an area ratio of ∼2.35, and the flow in the dump diffuser will recover ∼0.935 of its inlet total pressure (i.e., it suffers ∼6.5% loss).

To establish a length for the main combustor, we relate the residence time of the fluid in the burner to the ratio of fluid mass to the flow rate in the combustor, namely,

(7.118)

where A_ref is the maximum cross-sectional area of the burner, L is the burner length, and the mass flow rate through the burner is estimated as the airflow rate at the combustor entrance. Now, expressing the fluid density in terms of compressor pressure ratio via an isentropic exponent, namely,

We may isolate combustor length L from Equation 7.118 and express it as

(7.119)

In the above expression, A₂ is the engine face area and the first parenthesis is a design parameter, which is independent of the engine size. The area ratio A₂A_ref may be related via continuity equation to the engine face axial Mach number (a design choice) and the combustor exit Mach number (i.e., taken at the exit of the turbine nozzle) M₄ and the total pressure and temperature ratios according to

(7.120)

In Equation 7.120, the burner exit Mach number (taken at the exit of the turbine nozzle) is set equal to 1, as the turbine nozzle remains choked over a wide range of operating conditions. We may approximate the total pressure ratio term in Equation 7.120 by the compressor pressure ratio and express the combustor length L as

(7.121)

The fluid residence timescale and the chemical reaction timescale may be interchanged in a combustor

(7.122)

The reaction timescale is inversely proportional to the reaction rate and attains the following general form,

(7.123)

Now, substituting Equation 7.123 for the residence timescale into Equation 7.121, we get

(7.124)

We may combine the exponents of the compressor pressure ratio in Equation 7.124 as

(7.125)

This equation relates the combustor length L to cycle parameters π_c and τ_λ, which are independent of size. Hence, a high-pressure ratio engine occupies a smaller length combustor than a comparable size engine with a lower pressure ratio. A similar argument can be made regarding the cycle thermal loading parameter τ_λ. Table 7.7 (from Henderson and Blazowski, 1989) shows some data on contemporary combustor size, weight, and cost.

7.6.6 Afterburner

So far, we have discussed the total pressure drop in an afterburner due to flameholder drag and combustion. We also alluded to the flame stability provided by abluff-body flameholder. In this section, we quantify the parameters governed by the fluid mechanics and the chemical reaction that afford flame stability in an afterburner. We also develop a scaling parameter that connects different flameholder arrangements and duct geometries to experimental results obtained in a rectangular duct with a single flameholder. We first define a bluff body and its wake in a duct by the following length and velocity scales, as shown in Figure 7.44.

The wake of a V-gutter of height “d” is shown to have a central recirculation zone of length “L, ” a wake width “W, ” a channel height “H, ” an upstream gas velocity V₁, and an accelerated gas velocity, just outside the mixing layer, V₂, known as the “edge velocity.” We had defined a blockage parameter B, which for a two-dimensional duct, as shown in Figure 7.44, is the ratio B = d/H. The blockage parameter B and the wake width establish the flow acceleration V₂. A continuous chemical reaction in the mixing layer will be supported only if the resident timescale of the fuel/air mixture in the mixing layer is longer than the reaction timescale. Hence, for flame stability, the following simple relationship should hold between the two characteristic timescales, namely,

(7.126)

This is the basis of Zukoski-Marble (1955) characteristic time model for flame stability. The resident timescale of the unburned gas is proportional to the ratio

(7.127)

where is an average gas speed in the mixing layer. Hence, a dimensionless parameter emerges that could serve as a stability criterion. Experiments are conducted that establish the flame blowout condition in a rectangular duct with a single flameholder at the center of the duct with a range of chemical reaction parameters. The blowout condition parameters are labeled with a subscript “c” and by combining the proportionality constants in the unknown time constant τ_c, the average gas speed in the mixing layer is replaced by V_2c to produce

(7.128)

as the blowout stability criterion, or the marginal stability criterion. The measurements of L and V_2c then establish the critical timescale τ_c at the blowout condition. The ratio V_2cL represents the fluid dynamic parameter in Equation 7.128, whereas τ_c represents the effect of all chemical reaction parameters lumped into a single term. The timescale τ_c, which is also referred to as ignition time, is independent of the flameholder geometry and arrangement so long as the mixing layer is turbulent. It depends, however, on a number of parameters, such as the fuel-to-air ratio, fuel type, inlet temperature, and the degree of vitiation of the afterburner gas. Experimental results of Zukoski (1985) over a range of two- and three-dimensional flame-holders indicate that the τ_c is ∼0.3 ms at stoichiometric fuel–air ratio. This is consistent with Figure 7.9 (from Kerrebrock) that shows the reaction bucket has a minimum of ∼0.3 ms near stoichiometric ratio and up to ∼1.5 ms in fuel lean and rich limits of gasoline–air mixtures (see Figure 7.9). A more convenient stability parameter may be defined using the upstream blowout velocity V_1c and the duct height H as a reference velocity and length scale,

(7.129)

The length of recirculation zone to the wake width LW is approximately four, over a wide range of bluff-body flameholder geometries. We may also approximate the ratio of edge velocity to the upstream velocity using the continuity equation for an incompressible fluid and neglecting the entrainment in the mixing layer as

(7.130)

By neglecting the entrainment in the mass flow balance of Equation 7.130; we overpredict the edge velocity V_2c, which makes our analysis more conservative. As a first-order approximation, we neglect the entrainment in the mass balance. Substituting Equation 7.130 in the stability parameter of Equation 7.129, we get

(7.131)

The emergence of WH as the nondimensional parameter in the flameholder stability criterion is of great significance. This ratio depends mainly on the flameholder blockage parameter B, which may now be generalized to include different number and arrangement of flameholders in a circular duct.

Table 7.8 is reproduced from Zukoski (1985), which relates the flameholder blockage to velocity ratio for a V-gutter wedge half-angle of 15° and 90° (flat plate in broadside) in a rectangular duct.

0.05	2.6	1.15	0.11	4.0	1.25	0.16
0.10	1.9	1.23	0.15	3.0	1.43	0.21
0.20	1.5	1.42	0.20	2.2	1.75	0.248
0.30	1.3	1.62	0.23	1.7	2.09	0.250
0.40	1.2	1.90	0.25	1.6	2.50	0.248
0.50	1.2	2.3	0.25	1.4	3.16	0.22

Source: Zukoski 1985. Reproduced with permission from AIAA

We note that stability parameter (W/H)(V₁V₂) increases with the blockage ratio and approaches a value of 0.25 for a 50% blockage. Examining the quadratic nature of Equation 7.131, we deduce that W/H of 0.5 maximizes the stability parameter, for a flameholder in a rectangular duct, which states that the optimum wake width is 50% of the duct height. Substituting these values into Equation 7.131 yields a maximum blowout velocity in the approach stream of the flameholder, V_1m

(7.132)

To demonstrate the validity of this approach, Zukoski (1985) compares the result of the theoretical predictions of Table 7.7 with experimental data of Wright (1959). Figure 7.45 shows this comparison.

These results confirm the method of approach proposed by Zukoski and support the stability criterion of Equation 7.132 for two-dimensional flameholder geometries in a rectangular duct.

For a general axisymmetric flameholder in a circular duct, the wake width is less than a two-dimensional counterpart, due to a three-dimensional relieving effect, that is,

(7.133)

Remember that a 3D drag coefficient is also less than a 2D drag coefficient (on a body with the same cross-section), hence the wake width in 3D is less than the wake width in 2D. Consequently, the edge velocity V₂ in 3D is less than the edge velocity on a two-dimensional wake. The lower edge speed increases the residence time of the fuel–air mixture in the mixing layer, therefore the velocity in the approach stream for marginal stability is higher for a 3D flameholder, that is,

(7.134)

In an axisymmetric flameholder and circular duct, the optimum wake width is ∼1/3, and the approach stream velocity for marginal stability is 50% higher in 3D than 2D, according to Zukoski (1985).

Figure 7.46 shows an afterburner with three V-gutter flameholder rings attached to the turbine exit diffuser cone via radial V-gutters (from Zukoski, 1985). There are seven fuel spray rings that are divided into five zones. The fuel spray rings are upstream of the flameholders to allow for fuel evaporation and hence reduce the ignition time in the flameholder shear layer. Zone 1 is on the shear layer of the fan and core flow. Zones 2–4 are in the fan stream and zone 5 is in the core stream. The zonal approach to fuel injection in the afterburner provides for engine thrust modulation in the reheat mode. The flow to the cooling liner is supplied by the fan stream and serves two functions. First, it protects the casing through a coolant protective layer (liner louvered) and second, the liner dampens a combustion-related acoustic instability, known as screech (liner perforated). We will examine the afterburner screech issue in more detail in a later section.

A longitudinal section of Eurojet Consortium, EJ200, turbofan engine afterburner, and nozzle is shown in Figure 7.47 (from Kurzke and Riegler, 1998). Here the fuel spray in the afterburner is divided into three stages, again for thrust modulation purposes. The fuel spray bars shown represent the primary zone, and the fuel spray to the radial gutter region (in the core stream) is the secondary zone. The fuel injection in the bypass stream is at the throat of the “colander” region. These constitute the three stages or burning zones associated with the fuel spray in this engine. The flameholder is of radial V-gutter configuration, instead of a multiring configuration, as in Figure 7.46. The perforated screech damper and the cooling liner are also shown in Figure 7.47.

7.7.1 Greenhouse Gases, CO₂ and H₂O

Carbon dioxide (CO₂) and water vapor (H₂O) constitute the products of complete combustion. The large deposition of these products in stratosphere by a fleet of commercial aircraft is feared to contribute to global warming through greenhouse effect. Both of these molecules, that is, CO₂ and H₂O, absorb infrared radiation from earth and radiate it back toward earth. Earth’s atmosphere like the glass of a greenhouse is transparent to visible light from the sun but absorbs the infrared radiation, which accounts for a warmer earth surface temperature due to a radiation absorption in its atmosphere. Now, the average temperature of the earth’s surface is 298 K, whereas without the greenhouse gases in the atmosphere it would be 255 K (i.e., 43°C colder). However, a higher concentration of these greenhouse gases in the stratosphere may tilt the balance toward global warming. The impact of the additional greenhouse gases in the atmosphere is being debated. Conflicting climatic data between the Southern hemisphere and the Northern latitudes over the past century suggest a more complex dynamics than a simple infrared radiation model proposed. Figure 7.48 (adapted from Zumdahl, 2000) shows, however, the undeniable rapid rise in atmospheric CO₂ concentration over the past 100 years with the increase in consumption of hydrocarbon fuels for electric power generation and transportation. At the present time, there is no emission regulation for carbon dioxide and water vapor and thus no FAA engine certification requirements. The unit of concentration in Figure 7.48 is parts per million in molar concentration of CO₂, that is, equal to volume fraction of CO₂ in the atmosphere. Note the rise of the atmospheric CO₂ concentration from 2000–2013, which is also shown in Figure 7.48. Data are based on the mean values of seasonal variations.

7.7.2 Carbon Monoxide, CO, and Unburned Hydrocarbons, UHC

Carbon monoxide is formed as a result of an incomplete combustion of hydrocarbon fuels. It is a source of combustion inefficiency as well as a pollutant in the engine emissions. In combustion terms, CO is a fuel with a heating value of 2267 cal/g, which is approximately 24% of the Jet A fuel specific energy, which leaves the engine in the exhaust gases without releasing its chemical energy. Partial dissociation of carbon dioxide in the hot primary zone is also responsible for carbon monoxide formation. A fuel lean operation at low engine power setting causes a slow reaction rate in the combustor and thus carbon monoxide formation. At a low power setting, combustor inlet temperature and pressure are reduced, which directly impact the reaction rate in the combustor as discussed earlier. In the case of unburned hydrocarbons, a fraction of fuel may remain unburned due to poor atomization, vaporization, and residence time or getting trapped in the coolant film of the combustor liner. The indices of carbon monoxide and unburned hydrocarbons both drop with the engine power setting. An accumulation of aircraft engine data, which is reported in Figure 7.49 (from Henderson and Blazowski, 1989), suggests the sensitivity of CO and UHC formations to engine power setting.

It is entirely plausible to relate the combustion inefficiency, that is, 1 – η_b, particularly in the idle setting, to the emission index of CO and UHC, as they are both fuels that are present in the exhaust. Blazowski (1985) expresses the combustion inefficiency in terms of emission index EI (at idle) as

(7.135)

Note that the emission index EI is the mass ratio in grams of pollutants generated per kilogram of fuel consumed. As an example, let us take emission indices of CO and UHC to be ∼100 and ∼40 g/kg, respectively, (from Figure 7.49) to represent the engine idle power setting with combustor inlet temperature ∼400 K. Substitution of these emission indices in Equation 7.135 suggests a combustor inefficiency of ∼6.3%. However, EPA standards on emissions applied to Equation 7.135 demands a combustor efficiency of 99% at idle setting.

7.7.3 Oxides of Nitrogen, NO and NO₂

Nitric oxide, NO, is formed in the high temperature region of the primary zone at temperatures above 1800 K. The chemical reaction responsible for its production is

(7.136)

Since the reaction of nitrogen is with the oxygen atom in order to create nitric oxide, the regions within the flame where dissociated oxygen exists (in equilibrium) will produce nitric oxide. This explains the high temperature requirement for NO production (in near stoichiometric mixtures). Therefore, nitric oxide is produced at high engine power settings, in direct contrast to the carbon monoxide and UHC pollutants that are generated at the low power (idle) settings. Further oxidation of NO into NO₂ takes place at the lower temperatures of the intermediate or dilution zones of the combustor. Both types of the oxides of nitrogen are referred to as NO_x in the context of engine emissions. Lipfert (1972) demonstrates the temperature sensitivity of NO_x formation through an excellent correlation with numerous gas turbine engine data. His results are shown in Figure 7.50.

We note that engine types, combustor types, and fuels had apparently no effect on the NO_x correlation presented by Lipfert (Figure 7.50). All engines correlated with the combustor inlet temperature T_t3. Combustor inlet temperature is directly related to the compressor pressure ratio π_c; thus, we expect a similar dependence on the cycle pressure ratio, as shown in Figure 7.51 (from Henderson and Blazowski, 1989).

7.7.4 Smoke

The fuel-rich regions of the primary zone in the combustor produce carbon particulates known as soot. The soot particles are then partially consumed by the high temperature gases, that is, in the intermediate and, to a lesser, extent, in the dilution zones of the combustor. Visible exhaust smoke corresponds to a threshold of soot concentration in the exhaust gases. Soot particles are primarily carbon (96% by weight), hydrogen, and some oxygen. An improved atomization of the fuel (using air-blast atomizers) and enhanced mixing intensity in the primary zone reduces the soot formation. The parameter that quantifies soot in the exhaust gases is called the smoke number, SN. Its measurement is based on passing a given volume of the exhaust gas through a filter for a specific time, then comparing the optical reflectance of the stained and the clean filter by using a photoelectric reflectometer. The procedure for aircraft gas turbine engines exhaust smoke measurements is detailed in a Society of Automotive Engineers (SAE) document – ARP 1179 (1970). The smoke number is defined as

(7.137)

where R is the absolute reflectance of the stained filter, and R₀ is the absolute reflectance of the clean filter material.

7.7.5 Engine Emission Standards

The emission standards of the U.S. EPA (1973, 1978 and 1982) and the International Civil Aviation Organization (ICAO) (1981) define the limits on CO, UHC, NO_x, and smoke production of aircraft engines near airports (Table 7.9).

In the ICAO standards, the rated cycle pressure ratio π₀₀ and the rated engine thrust F₀₀ (in kN) are incorporated in the regulated limits.

7.7.6 Low-Emission Combustors

To combat the problems of CO and UHC production at the low engine power settings, the concept of staged combustion is introduced. This concept breaks down a conventional combustor primary zone into a pair of separately controlled combustor stages, which may be stacked (as in parallel) or in series. The stages are referred to as a pilot and a main stage, with their separate fuel injection systems. The pilot stage serves as the burner for the low power setting at peak idle combustion efficiency. The main stage is for maximum power climb and cruise condition, however, operating in a leaner mixture ratio to control NO_x emissions. Complete combustion is achieved through separate fuel scheduling as well as an efficient (air-blast atomizer) fuel atomization, vaporization, and mixing in smaller volume combustors. Two concepts developed by GE-Aircraft Engines and Pratt & Whitney Aircraft are shown in Figure. 7.52.

The result of application of the double annular and Vorbix combustors to CF6–50 and JT9D-7 engines, respectively, is shown in Table 7.10 (data from Lefebvre, 1983).

The staged combustion concept is very effective in overall engine emission reduction in particular with CO and UHC, whereas NO_x continues to be a challenge. To combat NO_x, we should lower the flame temperature, which requires the combustor to operate at a lower equivalence ratio, of say ∼ 0.6. The problems of combustion stability and flameout accompany lean fuel–air mixtures. To achieve a stable lean mixture ratio to support a continuous combustion, a premixing, prevaporization approach has to be implemented. Both combustors that are shown in Figure 7.52 employ this concept. Also the positive impact of employing air-blast atomizers is incorporated in both combustors. However, Table 7.10 indicates higher levels of smoke are generated by the double annular and the Vorbix low-emission combustors. This reminds us of the conflict between single parameter and system optimization problems, in which different elements of the system often have opposing requirements for their optimization.

Water injection in the combustor effectively reduces the flame temperature and has demonstrated significant NO_x reduction. Figure 7.53 (from Blazowski and Henderson, 1974) shows the effect of water injection in the combustor on NO_x emission reduction. We note that the ratio of water to fuel flow is ∼1 for a nearly 50% NO_x reduction level. This fact eliminates the potential of using water injection at the cruise altitude to lower the NO_x emissions from an aircraft gas turbine engine.

Ultralow NO_x combustors with premixed prevaporized gases are shown to operate at low equivalence ratios (below 0.6) when the combustor inlet temperature is increased. The application of this concept to automotive gas turbines has produced a very promising ultralow NO_x emission level. The burner inlet conditions of 800 K and 5.5 atm pressures in the automotive gas turbines resemble the altitude operation (or cruise operation) of an aircraft gas turbine engine. These ultralow NO_x combustor results are shown in Figure 7.54 (from Anderson, 1974).

From Anderson’s results in Figure 7.54, we note that a reduced residence time, which is good for NO_x production, leads to a higher level of CO and UHC emissions with an attendant combustion efficiency loss. The equivalence ratio has a large impact on NO_x emissions, as seen in Figure 7.54. The NO_x emission index of 0.3 g/kg-fuel seems to be the absolute minimum possible, as indicated by Anderson. To achieve these ultralow levels of the oxides of nitrogen in the exhaust emission, an increased burner inlet temperature is required. Incorporating a solid catalytic converter in an aircraft gas turbine engine burner may enable lean combustion and ultralow NO_x emission but at the expense of more complexity, weight, cost, and durability. The premixed/prevaporized burners also exhibit problems with autoignition and flashback for advanced aircraft engines with high-pressure ratios. Another possibility for low NO_x com-bustor development takes advantage of rich burn, which results in a reduced flame temperature, and quick quench, which allows for the combustion to be completed while the temperature of the combustion gases remain very near the combustor exit temperature. This approach is called rich burn–quick quench–lean burn and has shown promising results. These approaches are summarized in Figure 7.55, from Merkur (1996). Despite these advances, we recognize that the problem of gas turbine engine emission abatement is complex and challenging. We need to improve our understanding of the physical phenomenon in the combustor and in particular in the area of autoignition and flashback in lean combustible mixtures on the boundary of lean extinction limit.

It is instructive to compare the 1992 subsonic engine technology and the high-speed civil transport (HSCT) program goals of 2005 (from Merkur, 1996). The HSCT program is inactive at the present time (Table 7.11).

	1992 Subsonic engine	2005 HSCT engine
Equivalance ratio
Gas temperature	3700
Liner temperature	<1800
Liner material	Sheet or cast superalloys	Ceramic matrix composites (CMC)
Cooling methods	Transpiration/film	Convection
Environment	oxidizing	Oxidizing or reducing
NOx	36–45 g/kg f	<5 g/kg f

Source: Merkur 1996. Reproduced with permission from ASME

7.7.7 Impact of NO on the Ozone Layer

Ozone, O₃, is toxic and a highly oxidizing agent, which is harmful to eyes, lungs, and other tissues. NO_x production in high-temperature combustion impacts the ozone in the lower as well as upper atmosphere. In this section, the chemical processes that lead to ozone creation in the lower atmosphere and to a depletion of ozone in the stratosphere are discussed.

Lower atmosphere

Combustion at high temperature (when local combustion temperature exceeds ∼1800 K) breaks the molecular bond of N₂ and O₂ and causes NO to be formed, that is,

(7.138)

Nitric oxide reacts with the oxygen in the atmosphere to form nitrous oxide, NO₂, according to

(7.139)

NO₂ absorbs light and decomposes to

(7.140)

The quantity in Equation 7.140 is radiation energy with h as Plank’s constant and ν as the frequency of the electromagnetic wave. Oxygen atom is a highly reactive substance and among other reactions, it reacts with oxygen to create ozone, that is,

(7.141)

If we sum all the reactions 7.139–7.141, we get the following net result, namely,

(7.142)

Since NO facilitated the creation of ozone, without being consumed in the process, it is serving as a catalyst. In the lower atmosphere, nitric oxide, NO, helps generate harmful ozone in a catalyst role. The impact of NO on ozone changes as we enter the ozone layer in the stratosphere.

Upper atmosphere

The role of ozone in the upper atmosphere is to protect the earth against harmful radiation from the sun, namely, to absorb the highly energetic rays known as the ultraviolet radiation (with wavelength between 100 and 4000 Å).

(7.143)

The oxygen atom is highly reactive and combines with O₂ to from ozone,

(7.144)

The photochemical cycle described by reactions 7.143 and 7.144 reactions results in no net change of the ozone concentration in stratosphere. Hence, ozone serves a stable protective role in upper atmosphere. Flight of commercial supersonic aircraft with large quantities of NO emissions (∼30 g/kg fuel) from their high-temperature engines, over extended cruise periods, and with a large fleet promises to deplete the ozone concentration levels. Again, NO appears to be a catalyst in destroying ozone in the upper atmosphere according to

(7.145)

(7.146)

(7.147)

By adding reactions 7.146 and 7.147 with twice the reaction in 7.145 (to get the right number of moles to cancel), we get the net photochemical reaction in the stratosphere as

(7.148)

Hence, ozone is depleted through a catalytic intervention of NO. The high-energy radiation absorption in stratosphere by ozone is, by and large, the source of warmth in this layer of earth’s atmosphere. Since a rise in temperature in the stratosphere with altitude is stable with respect to vertical disturbances, the ozone concentration levels should remain stable (i.e., constant) over time. A chart of ozone concentration with altitude that also depicts the best cruise altitude for the cruise Mach number of commercial aircraft is shown in Figure 7.56 (taken from Kerrebrock, 1992).

Now let us briefly summarize NO_x formation, combustor design parameters that impact its generation, and the ozone layer.

Leading to NOx:	N + O2 ↔ NO + O
Formation:	N + OH ↔ NO + H
NOx concentration:	NOx , where pt3 is combustion pressure, Tt3 compressor discharge temperature, and tp is the residence time in the primary zone.
Role of NOx in ozone depletion:	O3 + hν → O2 + O where hν is the UV radiation from the sun O + O2 → O3 O + O → O2 O + O3 → 2O2 the last two reactions tend to limit the ozone concentration in the stratosphere NO + O3 → NO2 + O2 NO2 + hν → NO + O NO2 + O → NO + O2 NO is maintained, O3 destroyed

7.10.1 Screech Damper

A Helmholtz resonator is a cavity that serves as the spring to an oscillating mass, which is contained in the neck of the cavity. The damping occurs at the natural frequency of the cavity, which is a function of the geometry of the cavity and the speed of sound. An acoustic liner composed of numerous Helmholtz resonators integrated within the liner can be designed to efficiently dampen the acoustic power near the resonant frequency of the cavity. A perforated sheet covering a honeycomb substrate is often used as an acoustic liner.