1

COMBUSTION EFFICIENCY AND THE θ-PARAMETER IN THE DESIGN AND DEVELOPMENT OF GAS TURBINE COMBUSTORS

David G. Lilley*

School of Mechanical and Aerospace Engineering Oklahoma State University

Stillwater, OK 74078

and

Ashwani K. Gupta* Department of Mechanical Engineering

University of Maryland College Park, MD 20742

ABSTRACT

The aerodynamics benefits of lateral jet injection into swirling crossflow have long been recognized and used by combustion engineers. Studies are reported here on research related to the correlation of data, for swirling flowfields with lateral jet injection and combustion. Combustion efficiency and the θ-parameter are found to correlate well aerodynamic influences for combustor design.

INTRODUCTION

In the design and development of gas turbine combustors, research encompasses steady turbulent flow with combustion in round and rectangular cross-sectioned main flow regions, with lateral jet injection. The value of this configuration, for mixing improvement and enhancement of combustion, has long been recognized by combustion engineers. A useful correlation of the results is provided by the well-known and now famous θ-parameter, developed by Lefebvre (1980, 1983, 1989, and 1999). It correlates well the aerodynamic influences for combustor design. *Professor, Fellow AIAA

COMBUSTION MIXING ZONES The methods employed to determine the diameter or

height of the combustor liner are discussed in Lefebvre (1980, 1983, 1989, and 1999). After assessing this dimension by considering combustion efficiency and pressure loss, the designer has to determine the length of the primary zone. In general, a satisfactory recirculation flow path can be achieved by the use of opposed jets flowing radially inward from the liner wall, as shown in Fig. 1a, or by the use of an air swirler, as shown in Fig. 1b. A highly successful configuration, and one that is widely used, is a combined swirler-opposed jet arrangement, as illustrated in Fig. 1c. In all cases, the primary-zone airflow path is roughly circular, and thus it is easier to fit short-length patterns into chambers of short dimensions. Because of this, there is a tendency for combustors to have similar L/D ratios, and for small combustors to exhibit high heat-release rates if the latter are defined in the conventional manner.

If high heat-release rates are needed from a large

combustor, it is necessary to create a large number of small air-recirculation zones within it, and this requires a correspondingly large number of fuel-injection points. The “double-banked” annular chamber is a good example of this type of approach, which can yield significant reductions in overall liner length at the expense of a considerable increase in the number of fuel injectors.

40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit11 - 14 July 2004, Fort Lauderdale, Florida

AIAA 2004-3543

Copyright © 2004 by Copyright 2004 by the authors. All rights reserved. . Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

2

JET TRAJECTORIES

To establish a flow field within a liner and ensure the proper distribution of air to all zones, some knowledge is needed of the factors that govern the trajectory and penetration of air jets in crossflow. Of prime importance is the jet mixing that occurs in the dilution zone in which relatively cold air jets penetrate and mix with hot combustion products to achieve an outlet temperature distribution acceptable to the turbine. As each air jet penetrates into the main stream, it creates a blockage, which produces an increase in pressure on the upstream side of the jet and a reduction in pressure on the downstream side. This pressure difference provides the force that deforms the jet and contributes to the development of the “kidney-shaped” profile, as illustrated in Fig. 2. The flow field downstream of the dilution holes is dominated by vortex systems which control the entrainment and mixing of dilution air and mainstream gas. Single Jets

Many workers have attempted to trace the paths of round jets injected at various angles (usually 90°) into flowing airstreams. Temperature traverses in line with the jet at various distances downstream of its origin may be used to characterize the jet location. The point of lowest temperature in the traverse was used to define the center of the jet, and the maximum penetration was equated to the depth at which the centerline of the jet became asymptotic to the mainstream flow.

Data especially relevant to gas turbine combustors,

because of test conditions, may be taken to simulate those in an actual dilution zone. This leads to the trajectory of a jet in crossflow, as illustrated in Fig. 2, which is adequately described by the expression

Y/dj = 0.82J0.5(X/dj)

0.33

where

J = (ρjUj2)/(ρgUg

2)

If a single jet is injected into a crossflow at an angle θ, where θ is less than 90°, its trajectory is readily obtained by multiplying the value of Y/dj for 90° by sinθ. Here the angle θ = 0° corresponds to parallel injection in the direction of the mainstream, while θ = 90° represents perpendicular injection.

The equation implies that jet penetration increases

continually with increase in downstream distance. In practice, the jet may attain its maximum penetration within a fairly short distance downstream of its origin. Thus, this and other similar equations to be found in the literature are useful only for describing the initial portion

of the jet trajectory and lose their validity as the jet centerline becomes asymptotic to the crossflow.

Of more practical interest is the maximum

penetration achieved by the jet. For a single round jet injected into a circular duct, it is found that the maximum penetration is given by

Ymax = 1.15djJ0.5sinθ

The data on which this equation is based are shown in Fig. 3. Multiple jets

Multiple jets entering a circular duct have been found to penetrate lower than that for a single jet. This is attributed to the blockage effect of the jets in producing a local increase in mainstream velocity. From analysis of these data, the following equation is recommended for estimating the maximum penetration of round air jets into a tubular liner:

( )jgg5.0

jmax mmmJd25.1Y +=

The level of agreement between the predictions of this equation and measured values of Ymax/dj is shown in Fig. 4.

These investigations are for injection into circular

ducts, but a considerable amount of numerical and experimental work on the penetration of multiple jets has been carried out using rectangular ducts to simulate flow conditions in annular combustors. Most annular combustors feature two rows of dilution holes in the same axial plane, one row on the inner liner and the other on the outer liner. Usually, the number of holes in each row is the same. In most designs, the opposing holes are arranged to be “in-line” so that the jets impinge on each other, but in other designs, the holes are staggered circumferentially to allow the jets to penetrate past each other.

In almost all annular combustors, the aerodynamic

quality of the air approaching the outer row of dilution holes is impaired by the presence of various obstacles in the outer annulus, such as fuel-nozzle feed arms, liner support pins, and igniters, with the result that the flow approaching the outer dilution holes contains numerous small eddies and other flow perturbations that have an adverse effect on the uniformity of the flow entering the dilution holes. For this and other reasons, several studies have been carried out on the penetration and mixing of “single-sided” jets, that is, jets of air entering the crossflow through a single row of holes located in one wall of a rectangular duct.

3

SWIRLER AERODYNAMICS

The primary-zone airflow pattern is of prime importance to flame stability. Many different types of airflow patterns are employed, but one feature common to all is the creation of a toroidal flow reversal that entrains and recirculates a portion of the hot combustion products to mix with the incoming air and fuel. These vortices are continually refreshed by air admitted through holes pierced in the liner walls, supplemented in most cases by air flowing through swirlers and flare-cooling slots, and by air employed in atomization.

One of the most effective ways of inducing flow

recirculation in the primary zone is to fit a swirler in the dome around the fuel injector. Vortex breakdown is a well-known phenomenon in swirling flows; it causes recirculation in the core region when the amount of rotation imparted to the flow is high, as illustrated in Fig. 5. This type of recirculation provides better mixing than is normally obtained by other means, such as bluff bodies, because swirl components produce strong shear regions, high turbulence, and rapid mixing rates. These characteristics of swirling flows have long been recognized and have been used in many practical combustion devices to control the stability and intensity of combustion and the size and shape of the flame region.

Air swirlers are widely used in both tubular and

annular combustors. The two main types of swirlers are axial and radial. They are often fitted as single swirlers, but sometimes as double swirlers that are mounted concentrically and arranged to supply either co-rotating or counter-rotating airflows. Examples of modern combustors fitted with axial, radial, and double swirlers may be found in Lefebvre (1999).

Swirl Number

Gupta et al (1984) have discussed at length swirling flows. The following nondimensional criterion, called the swirl number, is used to characterize the amount of rotation imparted to the flow in a duct:

SN = 2Gm/(DswGt)

where

Gm = axial flux of angular momentum Gt = axial thrust For the values of swirl number less than around 0.4,

no flow recirculation is obtained, and the swirl is described as weak. Most swirlers of practical interest operate under conditions of strong swirl (that is, SN > 0.6).

Expressions for calculating swirl numbers for various

types of swirl generators have been derived. For an

annular swirler with constant vane angle θ, the expression recommended is

( )( )

θ⎥⎥⎦

⎤

⎢⎢⎣

⎡

−

−= tan

DD1

DD132S

2swhub

3swhub

N

Thus, for a simple axial swirler, the minimum vane

angle required to obtain strong recirculation (SN > 0.6) for a typical swirler having Dhub/Dsw = 0.5 is calculated from this equation as 38° vane angle.

Recirculation Zone

The recirculation region in a free swirling flow is shown in Fig. 6. Because the flow is assumed to be axisymmetric, only half the flow pattern is considered. The recirculation region is contained within the curve ACB. The point B is called the stagnation point. The flow outside ACB is the main flow which drives the recirculation along the solid curve AB. Conditions of zero axial velocity are represented by the dashed curve AB.

Typical axial and swirl velocity profiles are shown in

Fig. 7. All the velocity components decay in the downstream direction. After the stagnation point, the reverse axial velocities disappear, and further downstream, the peak of the axial velocity profile shifts toward the centerline as the effect of swirl diminishes.

Several workers have studied factors governing the

size of the recirculation zone. It has been shown that variations in vane type (flat or curved), vane angle, vane aspect ratio, and space/chord ratio are particularly effective. Experimental data show that the size of the recirculation zone is increased by:

1. An increase in vane angle. 2. An increase in the number of vanes. 3. A decrease in vane aspect ratio. 4. Changing from flat to curved vanes. Flow Reversal

One of the primary functions of the swirler is to induce combustion products to flow upstream to meet and merge with the incoming fuel and air. For weak swirl, there is little or no flow recirculation, but when the swirl number is increased and reaches a critical value (SN > 0.4), the static pressure in the central core just downstream of the swirler becomes low enough to create flow recirculation, as indicated in Fig. 5. From velocity measurements carried out along the swirler axis for several swirler designs, it was ascertained what degree of influence the key geometric parameters have on the reverse mass flow rate. Results showed that curved-vane swirlers induce larger reverse mass flows than the corresponding flat-vane swirlers, and that the reverse

4

flow is increased by an increase in swirl number. The effect of swirl number on the maximum reverse mass flow rate is illustrated in Fig. 8. It is of interest to note that under conditions of very strong swirl, corresponding to vane angles of around 65°, the reverse mass flow created by the swirler can actually exceed the mass flow passing through the swirler.

THE θ-PARAMETER

Here the combustion zone is envisioned as being similar in structure to the flame brush produced on a Bunsen burner under turbulent flow conditions. Combustion performance is then described as a function of the ratio of turbulent burning velocity to the velocity of the fresh mixture entering the combustion zone. It is assumed that evaporation rates and mixing rates are both infinitely fast, and that all of the fuel that burns does so completely. Combustion inefficiency arises when some of the mixture succeeds in passing through the combustion zone without being entrained by a turbulent flame front, Fig. 9.

This model developed by Lefebvre and colleagues

resulted in deriving a parameter that was shown to correlate experimental data on combustion efficiency obtained over wide ranges of pressure, temperature, and air flow rate for various designs of combustion chamber. The model is described only briefly below; for further details reference should be made to the original paper, see Lefebvre (1983 and 1999).

Combustion efficiency is defined as:

( )HmqTcSAfuel)in available(heat

)/combustionin released(heat

ApTfg

c

∆ρ=

=η

The equation simplifies to

ηc α ST/Uref

If one expresses Uref in terms of Am , P3, and Aref and

then describe ST in terms of laminar burning velocity and turbulence intensity (which, in turn, is related to the liner pressure loss factor), this becomes

( ) ( )[ ] [ ] m5.0refLA3

mref3ref3c qPmbTexpDPAP ∆=η

It has been demonstrated that combustion efficiency

data obtained during low pressure tests on several types of combustion chambers could be satisfactorily correlated by assigning values to m and b of 0.75 and 300, respectively. Substitution of these values, and neglecting the pressure loss term which varies little between one combustor and another, leads to the well-known θ parameter

( ) ( )[ ]A375.0

refref75.1

3 m300TexpDAPff =θ=ηθ

This famous equation, see Lefebvre (1983 and 1999), has been applied with considerable success to the correlation of experimental data on combustion efficiency, and has proved very useful in reducing the amount of rig testing required to evaluate new combustor designs. As shown in Fig. 10, only a few test points are needed to establish the complete performance curve for a chamber. Furthermore, it is possible to predict, with reasonable accuracy, combustion efficiencies at flow conditions that lie outside the capacity of the test facility – provided, of course, that at these extrapolated conditions, the combustion performance is not limited by fuel evaporation or by any factor other than chemical reaction rates.

The main advantage of the θ-equation is that it

provides a method of scaling combustor dimensions and operating conditions to common values so that any differences in performance that remain can be attributed directly to differences in design. This is a tremendous asset when one is attempting to select a design for a new combustion chamber from several existing designs, none of which is of the required size or has been tested at the relevant operating conditions.

The manner in which the θ-parameter is used can be

demonstrated by reference to Fig. 11, which shows performance curves for two different combustor designs. Clearly, design A is superior to design B, because for any given value of combustion efficiency the θ- parameter has a lower value. This means that under any given operating conditions of Am , P3, and T3, design A can equal the combustion efficiency of design B, and yet be made smaller in size.

Any new chamber design must be based to a large

extent on previous experience. A most useful way in which past experience can be summarized is by the use of charts where combustion efficiency data from all known systems are correlated against all the relevant variables. Such a chart is shown in Fig. 12, in which the hatched areas include experimental data obtained from a large number of multican, can-annular, and annular chambers. This figure may be used to determine the size of chamber needed to meet any stipulated performance requirement. For all types of engines, the most arduous operating conditions are those at which the inlet pressure P3 is a minimum. For aircraft engines, this usually corresponds to the engine windmilling after a flameout at high altitude.

When flameout occurs in flight, the engine rotational

speed falls rapidly to its windmilling value. The relight sequence is first to use the ignition system to relight the combustor. When this has been accomplished, the next step is to accelerate the engine up to its normal rotational speed. This normally calls for a minimum combustion

5

efficiency of around 80 percent. As previously discussed, a lower level of combustion efficiency could result in a rich extinction of the flame, whereas a higher level would lead to an unnecessarily large combustor.

Appropriate values of Aref and Dref may be obtained

from Fig. 12 by reading off a value of θ at a point along a horizontal line within the hatched area at 80 percent combustion efficiency, and then substituting into it the values of P3, T3, and Am corresponding to the engine windmilling at the maximum guaranteed relight altitude. The actual point chosen within the hatched area will represent a balance between the conflicting needs of high performance, small combustor size, and low development cost.

A notable feature of the θ-parameter is that it ignores

the influence of drop size on combustion efficiency. The fact that it has been shown to work successfully over wide ranges of combustor types and operating conditions tends to confirm that drop sizes are indeed irrelevant to combustion efficiency. However, for fuels heavier than Jet A (JP5), the effects of atomization and evaporation cannot be ignored, see Lefebvre (1989). FLOW VISUALIZATION Gupta and Lilley (1985) discuss at length the flowfield modeling and diagnostics problems, methods and solutions. One useful flowfield examination technique is the multi-spark visualization method, described and used by Lilley (1986 and 1988). The technique uses a low-resistance ionized path between two electrodes. This path moves with the airflow, and is sequentially lit up by successive sparks caused from a high voltage source. By placing electrodes in the wall boundary layer, where there is essentially zero velocity (next to the wall), several discharges can follow the ionized path as it moves with the fluid. The test section materials must have low electrical conductivity, such as acrylic, so as not to interfere with spark paths. The spark itself provides sufficient lighting for photographs. One camera (side view) is used for photographs with zero swirl. Two cameras (side and end view) are used simultaneously in the swirl crossflow cases to give added perspective to the three-dimensional features of the resulting flowfield. Extensive flow visualization experiments have been conducted to characterize the time-mean flowfield of a single and double (two opposed) deflected turbulent jet(s) in a confining cylindrical crossflow, see Lilley (1988). Jet-to-crossflow velocity ratios of R = 2, 4, and 6 were investigated, under crossflow inlet swirler vane angles of 0 (swirler removed), 45, and 70 degrees. Here R is equal to the lateral jet velocity divided by the average crossflow velocity. Smoke, neutrally buoyant helium-filled soap bubbles, and multi-spark flow visualization techniques were employed to highlight interesting features of the deflected jet, as well as the

trajectory and spread pattern of the jet. Gross flowfield characterization was obtained for a range of lateral jet-to-crossflow velocity ratios and a range of inlet swirl strengths in the main flow. The flow visualization results are particularly useful for identifying regions of the flow in need of further detailed study. Figure 13 presents multi-spark photographs for the case R = 4 with one lateral jet entering the crossflow under nonswirling, moderate and strongly conditions. These particular photographs were taken with the electrodes positioned at x/D = 1.5 where the jet enters at x/D = 1. In Part a of the figure, the camera is positioned to the side of the facility and a vertical rx-plane is observed. In the swirl flow case of Parts b and c, a second camera was simultaneously operated from a downstream location to illustrate the rθ-plane behavior of the sparks. In these swirl cases, both photographs were combined to form a common picture. In the R = 2 case without swirl (not shown) the flowfield is merely deflected upward by the entering jet. The case of R = 4 shows flow acceleration above and around the jet, which has its centerline nearly corresponding with the centerline of the tube. The ‘fold-over’ just above the jet centerline probably corresponds to the downflow around the jet as the jet displaces the crossflow in the upper half of the test section. With moderate swirl (φ = 45 degrees) the case of R = 4 has little effect on the swirl pattern. With strong swirl (φ = 70 degrees), the injected jet seems to slightly inhibit the swirl strength. Figure 14, Parts a, b, and c, presents multi-spark flow visualization pictures for the R = 4 case with two opposed jets entering different crossflow swirl conditions with φ = (swirler removed), 45, and 70 degrees of swirl, respectively. Electrodes are positioned at x/D = 1.5, but three other downstream locations have also been used. The two opposed jets are located at x/D = 1. In Part a, the influence of the opposed jets is clearly visible. Near the center of the test section, the flow is accelerated as indicated by the larger spacing between the sparks near the center of the section. Near the top and bottom of the test section, the presence of the opposed jets is indicated by the sparks wrapping around the boundaries of the jets. With distance downstream, the opposed jets were found to amalgamate with the crossflow to exhibit the characteristic flat velocity profile of turbulent flow in round tubes. Figure 14b is for the case of swirl vane angle φ = 45 degrees and little variation in the swirl pattern is distinguishable up to x/D = 2.5. At x/D = 2.5 however, there appears to be an elongation of successive sparks, and a strengthening of the centrally located precessing vortex core. Part c of the figure presents multi-spark photography for the case of φ = 70 degrees. Interpreting the flowfield is difficult because of the spark pattern. It does not exhibit the symmetric swirl pattern of locations further downstream, where the symmetrical spark shows

6

no direct influence from the opposed jets such as being deflected around the jets. The flow visualization techniques enabled gross flowfield characterization to be obtained for a range of lateral jet-to-crossflow velocity ratios, a range of inlet swirl strengths in the main flow and the use of zero, one, and two lateral jets. The swirl in the confined crossflow was found to deflect the lateral jet(s) from its (their) vertical course in a spiral fashion. However, the jet still gets absorbed finally into the precessing vortex core of the crossflow. Evidence was also found that the jet can deflect the axis and hinder the upstream propagation of this vortex/core region toward the swirler. FLOWFIELD MANIFESTATION

Quantitative information on time-mean and rms components of axial, tangential and radial components of velocity in swirl flows, both without and with combustion, has been carried out using 3-D Particle Image Velocimetry (PIV) diagnostics. Details on the diagnostics are provided in Gupta et al (2004). Archer and Gupta (2004) used a double concentric swirl burner to determine the flowfield that simulated a single swirl cup in a gas turbine combustor. The swirl angle as well as the direction of the flow in each annulus of the burner could be adjusted to provide control on the radial distribution of swirl in the burner. Both co- and counter-swirl arrangements have been examined using the 3-D PIV diagnostics. This technique can provide information on mean and rms components velocity as well as strain rates and vorticity. This provides information on the local residence time distribution in the combustor. These parameters influence the emission of pollutants, including NOx. The NOx reduction can be enhanced by proper utilization of swirl, as it induces a phenomenon known as vortex breakdown, where a central recirculation zone is formed. The central recirculation zone is the region in the flame that recirculates and burns hot volatile gases released from the fuel, in a low oxygen concentration regime, thus enabling the suppression of NOx. Data on the mean axial and tangential components of velocity under burning conditions are shown in Figs. 15 through 18 for the cases of co-swirl 45°/50° and counter-swirl 45°/-50° (distribution of swirl in the inner and outer swirl annulus of the burner). The data clearly identify the inner recirculation region, shear layer region between the flows from the inner and outer swirler as well as the plug flow region downstream of the central toroidal recirculation zone. The axial velocity vector plots, shown in Figs. 15 and 16, clearly show the recirculation regions. Corresponding swirl vector plots are given in Figs. 17 and 18. Results show that for the non-burning case the size of the central recirculation region varies with the radial distribution of swirl. The central recirculation zone is attributed to a

highly non-steady phenomenon, called the vortex breakdown. The recirculation zone and the phenomenon of vortex breakdown can substantially influence distribution of the velocity components. This recirculation region is found to be larger under combustion conditions than its counterpart non-burning case under unconfined conditions (see Archer and Gupta, 2004). However, under confined flame conditions the size and strength of the recirculation zone is much smaller as compared to the unconfined case. The effect of combustion is to radially expand the flow field. This increased radial distribution is an effect of thermal expansion caused by the heat release involved in the combustion process. The co-swirl case (45°/50°) still has a longer and stronger recirculation region. The magnitude of the axial velocity decreases due to the flame expansion effects. This decrease in velocity is only seen in the co-swirl case. The counter-swirl case showed an increase in velocity due to stronger entrainment and probably greater heat release. The increased mixing strength of the counter-swirl case accounts for this difference. In the counter-swirl case the exothermic reactions cause the hot gases created in the flame environment to travel faster than the corresponding fluid under non-combustion conditions. This is because the hotter gases have a lower density and thus the higher momentum gained at the reaction zone results in greater velocity of the flow. The counter-swirl flame has a smaller residence time due to its smaller recirculation region. These data have been used to determine the actual swirl number associated with the flow under both isothermal and combustion conditions. Combustion significantly modifies the flow field and swirl number. These results indicate the significant role of swirl distribution in the burner on swirl strength and distribution from the combustor. CLOSURE Combustion flowfields are affected by the number of lateral jets, the jet velocity ratio, and the crossflow swirl strength, as well as the injection angle of the injected jets. The study included the investigation of the trajectory, penetration, and mixing efficiency of the lateral injection, and potential combustion improvement. Studies are reported here on research related to the correlation of data, for swirling flowfields with lateral jet injection and combustion. Combustion efficiency and the θ parameter are found to correlate well aerodynamic influences for combustor design. The present review highlighted some of the findings, summarizing the activities, describing the facilities and techniques, and discussing major results obtained. Finally, experiments, theory and calculations can effectively contribute toward understanding and utilization of the enhanced combustion intensity from injected jets into swirling flow fields. Recent developments in flowfield diagnostics allow one to determine 3-D information on the flow field. Particle image velocimetry has been