Hypotheses-Driven Combustion Technology and Design Development Approach Pursued Since Early 1970s

Abstract

The empirical/analytical combustion design methodology practiced since middle 1970s comprises continuously evolving conventional design practice with significantly increased roles played by hypotheses formulation, its direct or indirect verification, semi-analytical models and multidimensional computational tools. Rapid advances in “applicable CFD” and turbulent combustion modeling during the early 1970s with remarkable contributions made by the team led by Prof. Spalding combined with resources (dollars, people, and facilities) provided by industry (Garrett, Allison, GE Aviation, Goodrich, Parker, and Woodward), government (NASA, the US Air Force, Army and Navy) and numerous universities led to formulation and successful applications of empirical/analytical design methodology in several gas turbine combustion technology and design programs. These programs included NASA staged combustion Concept 3 (in 1977), two Army combustor concepts for small engines (1978), 2100, 2400, and 2900 °F temperature rise combustors (1981–1983), the two first product combustors (1986), two near-stoichiometric temperature high-performance combustors (1993), entitlements for ultralow NO_x premix/pre-vaporized and partially premixed mixers (1993, 2008), an RQL combustor for the largest turbofan engine (1996), the second-generation lean-dome combustion technology TAPS demonstration (2003) and its product introduction in GEnx (2009), NASA LDI-2 and LDI-3 technology demonstrations in 2014 and 2018, respectively. An overview of these activities along with the most recent CFD simulation and diagnostics activities are described in this chapter as a recognition of 50 Years of CFD in Engineering Sciences that has provided useful insight for advancing combustion technologies and products while simultaneously improving design process efficiency.

1 Introduction

It is appropriate to start this chapter by reminiscing the state of the gas turbine combustion design process in 1972, the year Mongia joined AiResearch Manufacturing Company in Phoenix, a division of Garrett Corporation. He had to rely on simple design tools for combustion system design and development process including (1) Airflow and pressure distributions around the combustor and hot-side gas temperatures; (2) Liner wall temperature levels and gradients that his on the job teacher Jack Haasis told him that he can guess better than the state-of-the-art one-dimensional heat transfer analysis; (3) Highly empirical correlations for Sauter mean diameter (SMD) of pressure atomizing sprays, combustion efficiency, lean blowout, and ignition fuel/air ratio; and (4) Very limited poor quality design database. But thanks to the CFD revolution that occurred in the late 1960s and early 1970s for which a lot of credit should be given to Professor Spalding, his team, and the three key Garrett management team members (Dr. Monte Steel, Carl Paul and Dr. John Mason) who were willing to provide resources that made possible the first successful demonstration of the effectiveness of an empirical/analytical design methodology as summarized in [1, 2].

Both the NASA Lewis Research Center under its Pollution Reduction Technology Program (PRTP) and the US Army AVRADCOM of Fort Eustis under its Combustor Design Criteria (ACDC) Program as summarized in [3,4,5] facilitated the first two platforms for formulating and validation of Empirical Analytical Design Methodology (EADM) as expressed by the following key sentences duplicated from the abstract sections of [3, 4]:

CFD “when used in the proper context in conjunction with empirical methodology will reduce the design and development time and cost associated with gas turbine combustion systems.”

“The baseline, Concept I, configuration met all design objectives with no hardware modifications. Concept II met the design objectives after only one major hardware modification. — The combustor development (process) was significantly reduced, meeting the main objective of the (ACDC) program.”

It is perhaps an appropriate time to reflect on the gems of “empirical/analytical design methodology” pursued by Mongia and his coworkers during his 37-year period in industry (1972–2009), as summarized in Sect. 2. Here, we summarize that the success of EADM depended strongly on the process of (1) Defining and pursuing verification of key hypotheses germane to advancing technology consistent with program milestones; (2) Calibration of semi-analytical and CFD combustion models with engineering data on element test rigs that simulate “real” combustors’ operation (in Sect. 3); and (3) The art of design supported by models qualitatively (in Sect. 4). The resulting empirical/analytical design methodology was used for advancing combustion technology by relying on CFD simulations to provide qualitative guidance continued through the end of 1995.

The anchored design methodology [6] formulated in 1994 with models’ refinements pursued through 1998 [7, 8], which allowed computational control volumes approaching one million, was considered mostly applicable for scaling and advancing rich-dome combustion products. It offered significant advantage over semi-analytical models even when they both have comparable accuracy levels, as summarized in Sect. 5. We expected that use of the anchored design tools will reduce dependence on hypotheses and the art of design, but that was not the case for the development of the GE90-110/115 engine combustion system.

The first-generation lean-dome combustion products did not fully measure up to expectations leading to intensive lean technology development effort starting in 1995. Realizing the limitations of the in-house codes for handling comprehensive combustion system modeling approach, we switched to a commercial code in 2001 without fully realizing the level of effort required to get useful Phase I computational tool which finally happened in June 2007, as summarized in Sect. 6 in regard to its accuracy levels. But even with comprehensive combustion system analysis capable of handling 20 million mesh size or more, the dependence on hypotheses and art of design continues.

In spite of all the effort we have put in since the early 1970s for improving the accuracy of models’ predictions in regard to critical design requirements (but excluding pattern factor and radial profile factor), the model accuracy is approximately three times the experimental standard deviation (σ_exp) in regard to gaseous emissions, operability, and liner hot spots. Consequently, the spirit of empirical/analytical modeling concept continues to play key role in making critical design-related decisions which is consistent with reality, namely, CFD can complement and shorten significantly the gas turbine combustion design and substantiation process but it will continue to depend on the ingenuity of the designers in regard to hypotheses motivated by lessons learned from their empirical design database.

As required contractually by sponsored technology programs, gas turbine original equipment manufacturers OEM’s publish technical papers honestly while simultaneously minimizing details considered critical for maintaining competitive edge. However, after his retirement from GE in February 2009, Mongia got involved in fundamentals of technology development, application of CFD and diagnostics in association with his coauthors leading to “share everything openly” including application of the NASA National Combustion Code (NCC) in the lean-direct injection (LDI) technology development. Therefore, we summarize most recent modeling and diagnostics activities for gaseous emissions and operability relevant to both rich- and lean-dome combustors in Sect. 7 followed by summary in Sect. 8.

2 Hypotheses-Driven Combustion Technology and Design Development Process

The Army Combustor Design Criteria (ACDC) Program’s use of empirical/analytical design methodology [2] needs to be further explained as illustrated in Fig. 1. Fundamental and applied combustion research as well as OEM’s combustion technology and product development activities went through transformational changes in the early 1970s perhaps caused primarily by the Clean Air Act. However, the intensity with which the boxes 5 and 6 were allowed to interact with the so-called conventional approach, namely, boxes 1 through 4 shown in Fig. 1, varied enormously in the early 1970s through 2009, the year Mongia retired. After successful demonstration of the empirical/analytical design methodology in ACDC, NASA T1 Concept 3 and several other technology programs described briefly in this chapter, application of CFD in combustion technology and product development programs was claimed by almost all the engine OEM’s. However, the extent of success or failures of CFD in accomplishing the critical design metrics cannot be quantified accurately because of the complexity of the circumstances as evident from Fig. 1.

Fig. 1

Conventional combustion technology or product development process comprised of boxes 1 through 4 has been complemented by boxes 5 and 6 starting early 1970s

Mongia considers himself to be blessed for having interacted personally with dozens of combustion fundamental research scientists including Professor Spalding; they were or are awesome that he used to call some of them as “gods of combustion”. But nobody knew this list for obvious reasons. Similarly, Mongia has interacted with equally “street smart” dozens of senior and peer combustion technologists and designers and promising next-generation combustion engineers that have contributed to advancing combustion technologies and products since the early 1970s. For example, the swirl cup, a term coined by GE, in various shapes, forms and designs started appearing in GE gas turbine engines in the late 1960s and became an essential entity in all its modern engines starting early 1970s. Mongia came to know about the use of swirl cup in GE’s Dual-Annular Combustion (DAC) technology program in 1975, see [9]. Mongia was a test engineer working for his first-team leader Mike Wood who also designed his version of dual radial swirler design in 1973. But his approach called NASA T1 Concept 3 [10,11,12] for staged combustion technology program was distinctly different from DAC for obvious reasons.

Mongia calls combustion engineers as “mortals” in contrast to “gods of combustion” because the former struggle throughout their careers for meeting conflicting design requirements, see [13]. They try to make best use of combustion fundamentals, work hard to meet technology and product design requirements, and continue to discover new applicable combustion science in “real” hardware. Let us illustrate this point by sharing the development of TAPS technology and products described later in this chapter. The first 3 years of the TAPS technology development effort costing approximately $10 million entailed conceptual design and single-cup testing of the various configurations illustrated through Fig. 2 reproduced from US Patent 6,367,262, April 9, 2002.

Fig. 2

TAPS1 Mod1 conceptual configurations involving different arrangements of swirlers and fuel insertion devices, axial, radial, and combination as claimed in US Patent 6,367,262, April 9, 2002

It followed through several inventions in the ensuing years that can be broadly divided into the following categories:

• TAPS1 Mod2: US Patents 6,381,964, May 7, 2002; and 6,389,815, May 21, 2002.

• Improving Low-Power Emissions and/or fuel nozzle: US Patents 6,405,523, June 18, 2002; 6,865,889, March 15, 2005; 7,010,923, March 14, 2006; 7,878,000, February 1, 2011; 8,171,735, May 8, 2012; and 8,555,645, October 15, 2013.

• Improving Operability: US Patents 6,453,660, Sep 24, 2002; 8,001,761, August 23, 2011; and 8,607,575, December 17, 2013.

• TAPS2 and TAPS3 for 50% and 75% further reduction in high-power NO_x compared to TAPS1: US patents 6,418,726, June 16, 2002; 6,484,489, November 26, 2002; 7,464,553, December 16, 2008; 7,565,803, July 28, 2009; 7,581,396, September 1, 2009; and 7,762,073, July 27, 2010.

• Multi-Injection Concept, an alternate to TAPS: US patents 6,363,726, April 2, 2002; 6,474,071, November 5, 2002; and 6,609,377, August 26, 2003.

For the benefit of readers not familiar with the US Patent Office (USPO) process for awarding patents, both OEM and USPO conduct meticulous investigation for application and award of patents, especially when it comes to their use in commercial products because of its financial ramifications. OEM’s are very careful in regard to patent infringement violations; see for example, the New York Times article by Don Clark and Daisuke Wakabayashi dated April 16, 2019 on Apple and Qualcomm patent violation dispute settlement.

It is a strange coincidence that we included in this chapter that fuel nozzle and wall carboning and resulting hot-section distress were serious issues in the engine products of the 1970s to come across nozzle carbon buildup issue encountered in one of the LEAP-1B engines. This carboning issue could be responsible for creating hot-spot in the high-pressure turbine leading to blade failure as reported in the Aviation Daily article of April 18, 2019 by Sean Broderick and Guy Norris.

As to the extent of level of effort required for the development of CFD tools and combustion technology, especially to educate young readers involved in fundamental and applied combustion research, we share a few examples from Mongia’s experience since early 1970s. There is no hesitation in stating that Mongia would not have ventured into including boxes 5 and 6 in his design process shown schematically in Fig. 1 without direct and indirect help he received from the dozens of fundamental combustion researchers since the early 1970s through the end of 2008. It obviously includes Professor Spalding and his team and many more; there are too many people to mention (and they know who they are), and manuscript page limitation does not allow us to do full justice in describing qualitative contributions of their important publications in all the hypotheses Mongia used since early 1970s. A generic description of these hypotheses (rich-quick quench-lean combustion for rich-dome, and equivalent extended list for lean-dome combustion) leaves out “all of the trade secrets” from the general-purpose publications. Mongia had high regards for all of his competitors; they were equally competent if not more. He did not consider “wise” to second-guess one’s competitor and try to copy their works, especially if one wants to become a leader in one’s chosen field of expertise.

As to application of CFD in the design process, Mongia’s views expressed openly in February 1979 have not changed as of now. Namely, assign at least two Ph.D.’s with expertise in CFD and combustion modeling as part of the technology team; and hope, (1) Code will be “ready” to provide the guidance; (2) Provide “qualitative” guidance; and (3) Set quantitative guidance goal as long-term prospects. In all the programs that Mongia was involved personally as team leader, first or second line manager, CFD was never “fully ready” for providing “qualitative” guidance. Mongia kept on increasing CFD and combustion modeling manpower over the years in his department in addition to seeking more collaboration with the research community in order to achieve the abovementioned objectives (1) and (2). These were the “best” CFD and combustion modeling people and they worked hard. Mongia had more than 4 CFD and combustion modeling people by end of 1983, 10 by end of 1993, and 30 by end of 2007. In all these programs, Mongia thought he got the design guidance qualitatively, but with a reservation expressed by one of his peers at the end of the four concepts selected by Mongia for full-annular pizza pie rig testing. He said, “I see that you used CFD in selecting these concepts but I don’t understand how you made the decision.” Mongia shrugged his shoulders; got hardware fabricated and test results met his expectations.

Looking back, Mongia feels that he was always using composite of boxes 5 and 6 (in Fig. 1) coupled with continuously evolving conventional combustion technology and product design development process. He was fortunate enough to have help from a highly competent dedicated professionals throughout his 37-year industry career. When Mongia asked one of his right-hand persons how many people have been involved in the development of TAPS technology during 1998 and 2003, he counted more than 100. Of course, we used applicable combustion fundamentals; sought help from more than four universities together with very esteemed professors who have provided us with highly valuable insight which along with “street smart” combustion engineers have made possible to make progress from lean-dome DAC’s summarized in Fig. 3a to GEnx shown in Fig. 3b. But the “same” TAPS technology when applied to LEAP-X products produced mixed results, namely, comparable takeoff NO_xEI at 33.4 takeoff pressure ratio (PR), but worse than DAC’s for the higher pressure ratios. In spite of the best comprehensive CFD modeling capability developed since 2001, more than 10 years of fundamental research on TAPS, the best combustion team that Mongia was proud of pulling together, his own experience in developing TAPS technology and its scale-up to GEnx proven through TG6, he can only second-guess the circumstances that led to the results summarized in Fig. 3b. It should be mentioned that Mongia thought he knew the reasons why DAC did not get lower NO_x at nominal 40 pressure ratio conditions before marching on TAPS technology development path. He would not dare to conclude that something went wrong with LEAP-X product for lack of on-hand experience. It is for this reason, Mongia never felt comfortable in assessing other OEM’s technology and/or modeling capabilities.

Fig. 3

Evolution of three combustion technology products, namely, GE Rich-Quench-Lean (RQL), lean-domes’ DAC and TAPS technologies. a Lean Dual-Annular Combustion products (CFM DAC’s tested in 1995, 1996 and 1997) and GE90DAC tested in 1995 compared with GE RQL products, CFM56-Tech Insertion, CF34-10, GE90-110/115 and CF6-80C2. RQL’s takeoff ${\text{NO}}_{\text{x}} {\text{EI}} = 0.0544{\text{PR}}^{1.806}$ whereas that of the lean DAC’s ${\text{NO}}_{\text{x}} {\text{EI}} = 0.00111{\text{PR}}^{2.9502}$. b GE Twin Annular Premixing Swirl stabilized (TAPS) products GEnx (tested during 2009 and 2012) and LEAP-X models compared with GE RQL; GEnx takeoff ${\text{NO}}_{\text{x}} {\text{EI}} = 3.52 \times 10^{ - 5} {\text{PR}}^{3.6535}$

Therefore, the main objective of this chapter is to summarize examples of hypotheses-based combustion technology programs that Mongia was personally involved, see [1, 2, 4, 10,11,12, 14,15,16,17,18,19,20,21,22,23,24,25,26,27], models formulation, calibration/validation, and application of CFD. The second objective is to show typical comparison between predictions (for consistently formulated approach applicable during design process) and data from “real” combustors, as summarized in Sects. 5 and 6; references for the most relevant publications have been provided for the readers interested in details. There are thousands of outstanding benchmark quality diagnostics and model validation publications reported by “gods” of combustion which we chose not to include in our list of publications because of page limitations.

3 Combustors Internal Flow Field Data and CFD Models’ Calibration

The ACDC Program and Concept III of the NASA Pollution Reduction Technology Program (PRTP) were the first two programs that conducted several engineering benchmark quality experiments in order to calibrate the first-generation of CFD-based combustion models that could afford only very coarse mesh simulations as summarized in this section. As summarized in [3], a systematic set of engineering experiments were undertaken to calibrate six analytical models, namely, (1) quasi-one-dimensional model for correlating with pressure and airflow distributions around the combustor, (2) fuel insertion model, (3) liner cooling model, (4) emissions model, (5) transition mixing model, and (6) three-dimensional combustor performance model, as described in [5]. We will illustrate the extent of these experiments by picking two examples, starting with jet mixing investigation that included the following dilution jet orifice configurations and operating conditions:

Single row of two, four and six orifices, and two rows of six orifices, inline and staggered arrangement were investigated in order to provide thermocouple-based jet mixing characteristics that were used for calibrating three-dimensional turbulent mixing model. The jet air supply pressure was varied in order to investigate mixing of dilution jet air (at ~300 K) in a 12.6 cm diameter cylindrical test section placed downstream of a can combustor that provided hot-side nominal air temperature, pressure and velocity of 1200 K, 10 atm and 40 m/s, respectively. The orifice pressure drop was varied between 1 and 10% with the corresponding jet velocity variation between 40 and 150 m/s and resulting jet momentum ratios of $J = 4 {-} 60$, and jet Reynolds numbers of $Re_{j} = 1.4 \times 10^{5} {-} 6.8 \times 10^{5}$.

Since relative circumferential location of the primary and dilution jet orifices is an important design variable for controlling mixing in the dilution zone with attendant impact on combustor exit temperature quality, we have summarized only one experimental data expressed in terms of isothermal temperature contours in Figs. 4, 5, 6, and 7 for both inline and staggered orifice configurations. For the staggered configuration: hot-side axial velocity, density, jet velocity, and density were $U_{\text{hot}} = 39\,{\text{m}}/{\text{s}}$, $\rho_{\text{hot}} = 2.93\,{\text{kg}}/{\text{m}}^{3}$, $V_{j} = 72\,{\text{m}}/{\text{s}}$, and $\rho_{j} = 11.73\,{\text{kg}}/{\text{m}}^{3}$ giving $J = 13.5$ and $Re_{j} = 2.65 \times 10^{5}$. For the inline configuration: $U_{\text{hot}} = 39\,{\text{m}}/{\text{s}}$, $\rho_{\text{hot}} = 2.95\,{\text{kg}}/{\text{m}}^{3}$, $V_{j} = 66.7\,{\text{m}}/{\text{s}}$, and $\rho_{j} = 11.75\,{\text{kg}}/{\text{m}}^{3}$ giving $J = 11.6$ and $Re_{j} = 2.48 \times 10^{5}$. The center of the first-row jets is at x/D_j = 0.0 whereas that of the second row is x/D_j = 5.9 implying that the downstream edge of the first-row jet is at x/D_j = 0.5 whereas upstream edge of the second row jet is at x/D_j = 5.4.

Fig. 4

Mixing characteristics of inline and staggered dilution jets configurations in a nonreacting can combustor test section upstream of the second row of orifices. Source [3]

Fig. 5

Mixing characteristics immediately downstream of the second row located at $x/D_{j} = 5.9$; dilution jet orifice diameter $D_{j} = 7.19\,{\text{mm}}$ can radius = 8.8$D_{j}$. Source [3]

Fig. 6

Mixing characteristics further downstream of the second row located at $x/D_{j} = 5.9$. Source [3]

Fig. 7

Comparison between data (symbols) and predicted profiles of fuel/air ratio inline (θ = 30°) and in-between (θ = 0°) primary jets of a can combustor at simulated idle condition, P3 = 2.02 atm., T3 = 371 K, FAR = 0.0104, ΔP = 3.1%. Source [3]

Figure 4 shows measured contours at x/D_j = 0.71 (namely, 0.21D_j downstream of the edge of the orifice) and x/D_j = 4.95 and 5.3, respectively, for the staggered and inline configurations, with the corresponding axial locations being 0.45D_j and 0.1D_j upstream of the edge of the second row orifice. As evident from the data slightly upstream of the second row orifice, the effect of staggered versus inline dilution orifice configuration continues downstream as summarized in Fig. 5 with further corroboration by Fig. 6. Therefore, what has been known empirically for controlling hot-streaks in gas turbine combustors by both inline and staggered two rows of primary/dilution orifices can be explained by this simple experiment. What was interesting to observe that three-dimensional jet mixing CFD models could reproduce this qualitatively with less than 40,000 nodes providing impetus for using three-dimensional combustor CFD modeling techniques for optimizing combustor exit temperature quality; now a standard practice among all OEM’s albeit with several million mesh sizes.

The second example is on reacting flow in a “real” can combustor shown in Fig. 7: A 5-in. (12.7 cm) can combustor with six equispaced primary orifices (1.12 cm diameter) at x = 9.09 cm, followed by inline six dilution orifices (1.42 cm diameter) at x = 17.21 cm cooled by “English” louver cooling slots with the corresponding metering cooling holes placed at x = 4.37, 11.52, 19.90, and 28.98 cm; here, x denotes axial distance downstream of the face of the fuel nozzle.

Two types of fuel nozzles (natural gas nozzle and air-assisted airblast nozzle) were used for making gaseous emissions measurements within the combustor covering up to eight axial stations (ranging between x = 6 and 26.2 cm) and five circumferential stations for each of the preselected ten radial stations, namely, y = 0, 0.60, 1.07, 1.80, 2.42, 3.02, 3.63, 4.23, 4.84, and 5.44 cm. A total of 13 data sets were taken covering combustor overall pressure drop between 2 and 6%, inlet pressure P3 between 2 and 10 atm., inlet temperatures T3 between 366 and 623 K, overall fuel/air ratio FAR between 0.006 and 0.015 and resulting combustor exit adiabatic temperature T4 between 643 and 1170 K. The nominal test conditions and detailed emissions (unburned fuel, CO, NO_x, and CO₂) data are reported in [3] including mesh for three-dimensional model simulations shown in Fig. 8 and comparison between model predictions and data for all of the 13 data sets. Here, we have summarized key findings for the two cases, both for Jet-A fuel; the simulated idle in somewhat more details shown in Figs. 7, 9 and 10, and the simulated maximum power shown in Fig. 11.

Fig. 8

32 × 16 × 14 grids (5040 control volumes) were used for the simulations presented in Figs. 7 and 9, 10 and11. Source [3]

Fig. 9

Comparison between data (symbols) and predicted profiles of combustion efficiency along the three planes θ = 0°, 15° and 30° at two axial stations in the intermediate combustion zone. Primary jets are along θ = 30° and in-between primary jets along θ = 0°. Refer to Fig. 7 for operating conditions and Fig. 8 for mesh description. Source [3]

Fig. 10

Comparison between data (symbols) and predicted profiles of combustion efficiency along the three planes θ = 0°, 15° and 30° at three axial stations, ~2 cm upstream and downstream of dilution jets located at x = 17.2 cm, and further downstream by additional 2 cm. Refer to Fig. 7 for operating conditions. Source [3]

Fig. 11

Comparison between data (symbols) and predicted profiles of fuel/air ratio and combustion efficiency for the θ-plane in-between the primary jets (namely θ = 0°) in a can combustor burning Jet-A fuel at simulated max power operating condition, P3 = 9.99 atm., T3 = 623 K, FAR = 0.0148, ΔP = 3.2%. Refer to hardware and the corresponding mesh in Figs. 7 and 8, respectively. Source [3]

No one would dare to show now a comparison between data and simulations for 32 × 16 × 14 mesh size; but that is all we could afford to do in the 1970s. It is perhaps appropriate here to remind the readers that Professor Spalding’s publication in 1979, see [28], used 33 × 22 × 12 nodes for three-dimensional CFD simulation of a research combustor. The only difference is that we were dealing with a “real” can combustor. While a modified eddy break-up model for a two-step kinetic scheme along with five-discrete size spray deterministic Lagrangian formulation was used for a practical can combustor, that is where we started from in the application of CFD in the development of combustion technology and product in the late 1970s. Readers may want to refer to [1, 2, 4, 14,15,16,17,18,19,20, 29] for details. We started RANS simulations of “real” combustors with ~7,000 nodes in the middle 1970s and increased continually to ~75,000 by early 1990s. Starting 1995, the mesh size increased from 200,000 to 600,000 until 2001 when we decided to increase steadily from one million to 10–20 million mesh size. It is a true statement to make that we made use of “applicable CFD simulations along with hypotheses” (see boxes 5 and 6 in Fig. 1) in all the combustion technology and product development activities starting with the Army ACDC and NASA PRTP in the middle 1970s through 2007 in which Mongia was involved personally as team leader or hands-on manager, a long period of more than 30 years.

No one will disagree with the statement: multielement emissions probe inserted in practical combustors (can or annular) cannot provide profiles of fuel/air ratio, NO_x, CO, and unburned fuel and resulting combustion efficiency accurate enough for calibrating or validating turbulent combustion models. But what was the alternative for young combustion engineers in the middle 1970s or is in 2019 who want to apply CFD in the development of combustion technology or more challenging combustion products? Combustion technology and product development was our primary job responsibility. All industry and sponsored technology and product development activities are schedule and resource driven. Formulation, calibration, and validation of CFD-based combustion models tried to follow both short-term and long-term goals, namely, use hypotheses-based CFD models to support ongoing hardware programs while keeping in mind the ultimate objective: a hardware consistent modeling methodology that reproduces aerothermal performance, emissions, and operability of product combustors with accuracy comparable with data expressed in terms of standard deviation σ_exp as summarized in [13]. After putting in considerable resources in this area since 1975, the models have not reached this goal in spite of increasing mesh size to 20 million or more, use of unstructured grids, URANS, LES and its equivalent time-filtered Navier–Stokes (TFNS) simulations perhaps due to our inability to reproduce accurately spray characteristics and resulting fuel/air mixing and turbulent combustion with attendant impact on accurately predicting aerothermal design, performance, operability, and emissions characteristics relevant to meeting design requirements. Tens of thousands of research articles have been published in the last 50 years covering these topics with attendant advances in turbulent spray combustion sciences relevant to gas turbine combustors, and CFD has become an integral part of the design process. We will share examples from the formative years and how they have helped us address technology and product development challenges as explained in Sect. 4.

Due to page limitation, we will make summary statements for the figures covered in Sect. 3. Although we have not presented CFD simulations for the jet mixing data summarized in Figs. 4, 5, 6 and 7, we can say that predicted temperature contours were in qualitative agreement with the data.

It is hard to make good quality emissions measurements 0.9 cm downstream of the primary jet (at x = 10 cm, Fig. 7); but CFD gave us qualitatively good agreement with fuel/air ratio profiles data in addition to combustion efficiency data at idle summarized in Figs. 9 and 10. Similar summary statement can be made for the maximum power condition summarized in Fig. 11.

Similar level of comprehensive internal emissions mapping was conducted, albeit at one atmosphere only but for different T3 and FAR conditions, for two product annular combustors and a staged combustion annular combustor [1]. Schematic description of two of these combustors (Fig. 12) along with typical data and predictions (namely, radial profiles of fuel/air ratio in Fig. 13 and axial variations of total fuel, unburned fuel and CO mass fractions in Figs. 14 and 15) gave us confidence in making qualitative use of CFD in the combustion technology and development process. It is perhaps CFD “when used in the proper context in conjunction with empirical methodology” gave us the insight for expeditiously developing combustion technologies summarized in next section. Details on the models’ calibrations are given in [1, 3, 6,7,8, 11,12,13, 18, 29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45].

Fig. 12

Internal emissions mapping of a staged Concept III annular combustor, left part from [1] and its counterpart conventional diffusion flame annular combustor shown on right

Fig. 13

Comparison between measured and predicted radial profile of fuel/air ratio at axial station #4 of the staged combustor’s two planes lying inline and in-between premix/prevaporating jets. Source [1]

Fig. 14

Comparison between measured and predicted circumferentially and radially averaged axial profiles of total fuel, unburned fuel and CO (all in mass fractions) for the staged combustor shown in Fig. 12

Fig. 15

Comparison between measured and predicted radially and circumferentially averaged axial profiles of total fuel, unburned fuel and CO (all in mass fractions) for the conventional diffusion flame combustor shown in Fig. 12

4 Addressing Technology Challenges During 1970–1990s

Empirical/analytical design methodology [31, 32] helped develop several combustion technologies as described in [1, 2, 4, 14,15,16,17,18,19,20, 29, 30]. The first application included two ACDC combustion concepts for small engines (in 1978) and subsequently increasing its temperature rise ΔT from 1635 to 2100 °F. We will give an overview of how CFD was used to provide insight for these combustors. In parallel was the development of NASA PRTP Concept 3 (in 1977), two high ΔT (2400 and 2900 °F) combustors, the two first product combustors (1986), two near-stoichiometric temperature high-performance combustors (1993), and entitlements for ultralow NO_x premix/pre-vaporized mixer (1993). To be covered in next three sections are RQL combustor for the largest turbofan engine (1996), the second-generation lean-dome combustion technology TAPS demonstration (2003) and its product introduction in GEnx (2009), entitlement ultralow NO_x partially premixed mixer, and NASA LDI-2 and LDI-3 technology demonstrations in 2014 and 2018, respectively.

Internal flow mapping (for example, jet mixing summarized in Figs. 4, 5 and 6) of can combustor emissions and three-dimensional CFD simulations (Figs. 7, 8, 9, 10 and 11), three annular combustors (two of these shown in Fig. 12 and overview of comparison between data and CFD simulations summarized in Figs. 13, 14 and 15) led to a comfortable conclusion: CFD can be used to reliably predict qualitatively internal flow field characteristics of technology and product gas turbine combustors leading to expeditious development of combustion technologies for addressing the challenges commonly encountered in the 1975–1993 period. These included product combustors with high NO_x, CO, HC and smoke emissions, pattern factor, local liner hot spots, liner and fuel nozzle carboning with attendant frequent interruptions caused by unscheduled repair and overhaul shop visits. Qualitative applications of CFD-based combustion models helped us rapidly develop low-emissions, high-performance combustion technologies as summarized in several publications; [31, 32] provide good summary of these CFD-based design tools which do not need to be discussed here. However, we provide some examples in this section to illustrate how CFD predictions were used to facilitate technology development during the early period of empirical/analytical design methodology evolution starting with the Army ACDC Concepts I and II leading to the first high-ΔT (2200 °F) small annular combustor compared to 1635 °F ΔT Concept I without adversely impacting other design requirements.

The left part of Fig. 16 shows schematic layout of the ACDC Concept I and Concept II Mod 1, indicating that both combustors’ outer liner wall diameter is 9.65 in. (24.5 cm) and channel height is 1.73 in. (4.39 cm). They also used the same set of ten air-assisted airblast nozzles inserted through the outer liner wall with the identical axial and circumferential location. However, since these combustors’ lengths are different (being 3.8 in. and 4.27 in., respectively), the x-location of the spray origin from the respective domes is different for these combustors, as will be described shortly. Consistent with the practice of the 1970s, Concept I has three rows of orifices identified as 2, 4, and 6 for the outer wall but only two rows for the inner wall identified as 11 and 13 in Fig. 16. The spray origin is located at x = 1.9 cm, y = 2.9 cm from the inner wall at θ = 9° compared to the center of the dome swirler being x = 0, y = 2.2 cm and θ = 18°. The spray with 90° included angle is injected towards the dome with specified back and down angles. Both combustors’ sea-level design point is identical, namely, combustor airflow rate Wa3.1 = 2.7 lb/s, inlet pressure P3 = 147 psi, inlet air temperature T3 = 665 °F, fuel/air ratio F/A = 0.0268, and the corresponding combustor exit temperature T4 = 2300 °F. When a technology program for higher temperature rise demonstration was called for, this small combustor with corrected airflow rate W_C = 0.397 lb/s was able to increase its exit temperature T4 to 2850 °F by simply adding a row of primary orifices through the inner liner resulting in three rows of orifices for the inner wall also, as illustrated in the right part of Fig. 16. Amazingly, this 2200 °F ΔT combustor had pattern factor (PF) less than 0.2 along with its sea-level idle lean blowout fuel/air ratio (LBO F/A) less than 0.005. It also had relatively uniform liner wall temperature characteristics and attendant acceptable liner hot spots.

Fig. 16

Army Combustor Design Criteria (ACDC) Concepts I and II met all design objectives; later followed by Concept I potential higher temperature rise capability demonstration [4]

Concept I was designed by using an empirical/analytical design methodology as described in [2, 4]. It included analytical investigations of ten modifications by making use of the three-dimensional Combustor Performance Model that had been calibrated by using an extensive engineering database described in [3] with some examples shown previously in Figs. 7, 8, 9, 10 and 11. We show Figs. 17 and 18 as an illustration for augmenting empirical design know-how of a typical experienced combustor designer’s perspective.

Fig. 17

Predicted fuel/air contours (at two axial stations in the primary zone) expressed as equivalence ratio ϕ of the Army Combustor Design Criteria Concept I at its design point; see Fig. 16 for design conditions and legends [4]

Fig. 18

Predicted ϕ contours at the intermediate and dilution orifices axial planes #4–11 and #6–13; see Fig. 16 for design conditions and legends [4]

One nozzle sector of 36° of Concept I with dome swirler center located at θ = 18° was simulated by 13 θ-nodes, combustor length of 12.6 cm divided into 30 x-nodes, channel height of 4.4 cm covered by 19 y-nodes. Recall, Serag-Eldin and Spalding [28] used 33 × 22 × 12 nodes for three-dimensional CFD simulation of a research combustor, not much different from 30 × 19 × 13 used here. The main difference is that we used it for developing an advanced technology reverse-flow annular combustor shown in Fig. 17. The radius of the inner wall is 7.85 cm. The two outer wall (OD) primary jets are located at x = 3.2 cm and θ = 18° and 30°. The six impinging intermediate jets (three each through OD and inner wall ID, respectively) are located at x = 5.1 cm, and six impinging dilution jets are located at x = 7.6 cm with circumferential locations of θ = 6°, 18°, and 30°, respectively. The three OD cooling slot lips are located at x = 1.4, 4.3 and 6.6 cm, respectively; and the four ID cooling slot lips are located at x = 1.4, 4.3, 6.6 and 9.8 cm, respectively. The centerline of the nozzle shroud is located at x = 2.7 cm whereas its spray exits at x = 1.9 cm, y = 2.92 cm from the inner wall and θ = 9° which may be compared with the center of the dome swirler being x = 0, y = 2.2 cm and θ = 18°. All these combustor details were considered adequately represented by 30 × 19 × 13 nodes resulting in 5236 control volumes; no one will accept this statement in 2019.

The predicted fuel/air distribution expressed as equivalence ratio ϕ is shown in Figs. 17 and 18 for the selected four axial stations, namely the spray origin located at x = 1.9 cm, primary orifices located at x = 3.2 cm, intermediate orifices at x = 5.1 cm, and dilution orifices at x = 7.6 cm. These locations have been identified as stations 2, 4, 6, 11, and 13, respectively in Fig. 16. It should be made clear that here as well through the early 1990s our objective was to make qualitative assessment of the predicted flow field characteristics including mean velocity components, turbulence kinetic energy k, turbulent mixing times k/ε (here ε is dissipation rate of k), spray transport and evaporation and attendant fuel/air distribution, concentration of unburned fuel and CO (as determined by two-step kinetic scheme and modified eddy break-up time approach calibrated with the extensive data sets described in [3]), temperature distribution, combustor exit temperature quality and adiabatic wall temperature levels and gradients.

Due to page limitations, we have not shown predicted contours of velocity components, unburned fuel, CO and temperature here. Suffices to say that from these predictions along with empirical correlating parameters including combustor reference velocity (V_R), heat release rate (HRR), loading parameter (LP), cold and hot residence times τ_C and τ_H, summarized in Table 1, we expected to have low PF for both Concepts I and II, lower values of LBO FAR, NO_x, smoke and idle HCEI for Concept I compared to Concept II, also summarized in Table 1.

Table 1 Design, performance and emissions characteristics of Army Combustor Design Criteria ACDC Concept I and Concept II Mod 1

It is hard to make direct comparison of the Concept I and II (CI and CII) combustors’ emissions with the modern low-emissions rich-dome combustion products developed during 1995–2009 timeframe. We can, however, summarize these results by comparing takeoff NO_xEI with idle COEI and the latter with idle HCEI by selecting one of the smallest product engine combustors identified as 2.8 in Fig. 19. Product combustor 2.8 belongs to a group of low-emissions combustors (LEC) of modern propulsion engines covering takeoff pressure ratio between 20 and 40 with the corresponding takeoff thrust ranging between 60 and 500 kN. We got both CI and CII combustors showing better emissions characteristics than the best LEC technology products developed between 1995 and 2009; the credit goes to the proper use of the empirical/analytical methodology or “Good Karma”.

Fig. 19

Emissions characteristics of Concept I and Concept II Mod 1 compared with the best modern low-emissions combustion product

Let us illustrate one more example on how CFD was used in the Army program in regard to eliminating liner and dome wall carboning problems that were very common in combustors during the 1970s; a typical case is illustrated in Fig. 20a. This product combustor exhibited excessive amount of dome and liner wall carboning, which when built in chunks big enough will lead to breaking of the carbon clinkers and passing through turbine hot-section leading to blades’ erosion and attendant loss in power up to 10%. Based on experience, we related its occurrence to the extent of fuel rich pockets and separating flow regions near the wall. We tried indirect verification of this hypothesis in Concept I design process.

Fig. 20

Application of empirical/analytical design methodology for reducing carbon formation in a product combustor

Figure 21 shows predicted contours of fuel/air ratio (expressed as equivalence ratio ϕ) at the Concept I dome as affected by the spray cone angle α and spray Sauter mean diameter D₃₂. When a spray with α = 90° and D₃₂ = 50 μm was replaced with α = 60° and D₃₂ = 50 μm, we see increased degree of fuel rich pockets. On the other hand, decreasing D₃₂ from 50 to 15 μm, we do not see any fuel rich pockets as shown in Fig. 21. The main inference from these CFD simulations is that when we use the injector with “right” combination of spray cone angle and D₃₂, we should not see any dome carboning.

Fig. 21

Three-dimensional CFD predicted profiles of unburned fuel (expressed as equivalence ratio) on the Concept I showing effect of spray angle (α) and Sauter mean diameter (D₃₂) on unburned fuel distribution at the dome [4]

Figure 22a shows typical hardware condition of the ACDC Concept I after a rig shutdown, indicating very small sooting which is generally consistent in combustors having no carbon deposition problems. This combustor also went through 600 simulated takeoff-idle power thermal cycles; each cycle comprised of 2-min steady-state operation at takeoff conditions followed by snapped reduction (in less than 1 s) to a reduced level of fuel flow rate in order to simulate idle fuel/air ratio, followed by 2-min steady-state operation at idle FAR; and then snap back to takeoff fuel flow rate. Figure 22b shows typical dome condition after completing 600 thermal cycles, indicating an acceptable level of sooting and no carboning. It is interesting to note that PF of this combustor at the start of thermal cycling was 0.219 compared to 0.178 measured after completing 600 thermal cycles.

Fig. 22

Indirect qualitative substantiation of three-dimensional CFD predicted contours of unburned fuel and flow field characteristics near the ACDC Concept I at design point by comparing sooting after one rig testing with 90-deg spray, Part (a), compared to slightly more sooting observed after 600-4 min simulated takeoff-idle cycles shown in Part (b). Source [4]

When a proper set of hypotheses as summarized in Fig. 20b was used along with the empirical/analytical design methodology, we were able to get rid of dome and liner wall carboning problem of the product combustor (Fig. 20a) as illustrated in Fig. 20c. This was not the last time we encountered carboning problem. We encountered one in the late 1980s and another one in the middle 1990s. All of these problems got eventually resolved with conventional or hypotheses-based design approach. It is, therefore, not surprising to discover nozzle carboning problem in the LEAP-1B engines where 1% of the engines in field operation are under close observation for avoiding turbine blade failure.

5 On Predictability of Rich-Dome Combustors

None of the CFD simulations conducted before 1994 exceeded 100,000 computational control volumes, and the complex combustors’ configurations were simulated by stairstep Cartesian/cylindrical coordinate system. Therefore, CFD simulations were used to provide qualitative guidance which along with combustor design experience know-how facilitated significant advances in both technology and combustor products. Mongia and his team continued to meet or exceed management expectations and enjoyed 20-year streak of continuing success of empirical/analytical design methodology for which credit should duly be given to the insight provided by CFD simulations.

However, starting 1994, our focus shifted to higher resolution simulations but still limited to less than one million control volumes that used curvilinear orthogonal coordinate system which allowed better representation of product combustors. With improved spray and turbulent combustion modeling capabilities as described in [6], we wanted to set our CFD simulation accuracy goals comparable with state-of-the-art semi-empirical gaseous emissions models as described in [46]. Here, the emphasis was on developing low-emissions rich-dome combustion products; although limitations were established on how much this approach can be extended for application in lean-domes’ development, as summarized in [7, 8]. This methodology, known popularly as “anchored CFD”, became the workhorse for developing rich-dome low-emissions combustion products as described in [21, 22]. Until the comprehensive combustion system analysis approach was developed [13, 33,34,35,36], the anchored CFD was used cautiously for providing guidance in the design and development activities of lean-domes described in [23,24,25]. Readers may want to go through these publications, namely [6,7,8, 13, 21,22,23,24,25, 33,34,35,36, 46], in order to get details on the modeling and resulting technology and combustion products. In Figs. 23, 24, 25, 26, 27 and 28, we will illustrate capability of the anchored models (Figs. 23, 25 and 27) compared to their counterparts’ semi-empirical models (Figs. 24, 26 and 28) for NO_x, CO and HC emissions for several product combustors operating from idle to maximum power.

Fig. 23

NO_xEI data from five product combustors compared with anchored CFD predictions; adopted from [6]

Fig. 24

NO_xEI data from four rich-dome product combustors compared with semi-empirical correlation; adopted from [46]

Fig. 25

COEI data from five product combustors compared with anchored CFD predictions; adopted from [6]

Fig. 26

COEI data from four rich-dome product combustors compared with semi-empirical correlation; adopted from [46]

Fig. 27

HCEI data from five product combustors compared with anchored CFD predictions; adopted from [6]

Fig. 28

HCEI data from four rich-dome product combustors compared with semi-empirical correlation; adopted from [46]

Since majority of NO_x emissions contribution comes from high-power operation, accuracy of the model predictions is generally considered relevant for high-power. On the other hand, model accuracy for CO and HC is generally based on idle emissions. For the selected five product combustors summarized in Figs. 23, 25 and 27, CFD predictions for NO_x are within ±10% whereas those of COEI and HCEI are approximately ±50% and ±60%, respectively. The corresponding semi-empirical emissions prediction accuracy levels are ±10%, ±35% and ±35%, respectively. Some from the old school of combustion designers may come to wrong conclusion, namely, why do we need CFD simulations when they are not more accurate than the semi-empirical correlations? For obvious reasons, middle of the road, empirical/analytical design methodology is the right approach which has been practiced by Mongia and his coworkers since 1975.

6 On Predictability of Lean-Dome Combustors

A comprehensive combustion system analysis methodology was kicked off in 2001 while simultaneously successfully adopting partially premixed laminar flamelet modeling considered critical for providing radical concentrations required to solve turbulent transport equations to compute “accurately” HC, CO, NO_x emissions for the four types of combustors, namely, dry low NO_x combustors [37], modern rich-dome aviation combustors [38], industrial diffusion flame combustors with water injection [39], and second-generation lean-dome propulsion engine combustors [24, 25]. These emissions-related publications based on composite laminar flamelet modeling approach did not use comprehensive combustion system analysis as described in [13]. Only two publications, [35] and [36], have shared comprehensive analysis based composite laminar flamelet predictions; the former for the second-generation lean-domes and the latter for rich-domes known popularly as RQL. In [36], only NO_xEI emissions results for a product combustor were published, getting high-power NO_x prediction capability comparable with the anchored CFD shown in Fig. 23.

While the overview level details of the comprehensive system analysis were provided in [13], suffices to say here that this approach does not require user to provide pressure and airflow distribution around the combustor, inlet conditions for the various holes and swirlers including profiles of the mean and turbulence quantity of the dependent variables. The user can conduct simulations for any engine operating conditions of interest, namely, compressor discharge pressure P3 and temperature T3, airflow rate and combustor fuel flow rate. The combustor diffuser inlet profiles of the total and static pressure distributions are provided by compression system design tools. Validated injector comprehensive models are used to compute spray conditions required for combustion system analysis (CSA) simulation. Combustion system hardware is simulated to the accuracy consistent with manufacturing tolerances by using unstructured mesh requiring 15–25 million size as described in [13].

Even though most of the simulations have been reported by using RANS, the advantage of LES is well established as described in [40,41,42]; the latter produces better agreement with data on average exit temperature (θ_avg) profiles without having to use turbulent Schmidt number (Sc_t) as a variable in RANS simulations; a practice commonly used by most of the OEM’s for both θ_avg and maximum exit temperature (θ_max) profiles. Figure 29 shows a typical comparison for a selected combustor. In spite of the obvious advantage of LES over RANS, the former is used by OEM’s only as a last resort to sort through critical design challenges because it requires at least an order of magnitude bigger computer resources and a need for thoroughly anchoring the LES modeling strategy before it can be used as part of combustor design toolkit. A recent example described in next section is the use of a time-filtered Navier–Stokes (TFNS) for the lean-direct injection (LDI) technology development effort.

Fig. 29

Typical comparison between data and simulations with combustor exit plane normalized average and maximum temperature, θ_avg and θ_max, radial profiles showing effect of turbulent Schmidt number Sc_t. All calculations except one are with RANS simulations

There were many reasons that motivated us to develop and validate comprehensive CSA approach; perhaps the most important one being technology and product development of the second-generation lean-domes [24, 25]. Here, we wanted more accurate description of the combustor internal flow field and temperature contours (see Figs. 30 and 31) in order to relate these more reliably in regard to NO_x and CO emissions (see Figs. 32 and 33) and tradeoff for combustor exit temperature profiles shown in Fig. 34 for one of the two combustors covered in these figures. Even though Figs. 32 and 33 appear to show better agreement with data compared to anchored CFD (see Figs. 23 and 25), there is a lot more to be done before the job is completed; the least is to get equally good agreement with other second-generation lean-domes’ engine data which takes us to introductory part of the next section.

Fig. 30

Reacting flow mean axial-velocity contours (m/s) predicted by comprehensive combustion system analytical modeling approach [35]

Fig. 31

Mean gas temperature contours (°F) predicted by comprehensive combustion system analytical modeling approach [35]

Fig. 32

NO_xEI data from two lean-dome combustors compared with predictions of comprehensive combustion system analytical modeling approach [34]

Fig. 33

COEI data from two lean-dome combustors compared with predictions of comprehensive combustion system analytical modeling approach [35]

Fig. 34

Typical comparison between data and predicted average combustor exit temperature profile [35]

7 Recent Lean and Rich-Dome Combustors’ Fundamental Investigations

While the second-generation lean-domes show the potential of further reducing emissions [24], it also raises concerns about challenges in regard to operability, autoignition, and flashback. It is remarkable to see these lean-domes operating reliably at takeoff pressure ratio of 47.5 in the GEnx-1B engine while simultaneously achieving 27% reduction in LTO NO_x compared to its counterpart rich-dome Trent1000; see Table 2. However, at lower takeoff pressure ratio of 37.5, it demonstrated 43% NO_x reduction, a 16 point competitive loss as it went to its highest operating pressure. Can CFD help in recovering this loss? Yes, it can as evident qualitatively for the predicted contours of two lean-dome Combustors 1 and 2 shown previously in Figs. 30 and 31. The TALON X rich-dome technology-based combustion products emissions certified in 2017 have achieved another significant step in reducing NO_x compared to its counterpart RQL combustors. While its competing lean-dome LEAP has 13% lower NO_x compared to TALON X at 33 pressure ratio, its NO_x at 41.5 pressure ratio does not show any advantage over RQL; another opportunity for CFD tools to help.

Table 2 Design and technology evolution of propulsion engines during last 40 years in regard to rich or lean-dome technology (RD/LD), takeoff fan bypass ratio (BPR) and pressure ratio (PR), rated thrust and landing-takeoff NO_x emissions of the selected 8 engines emissions certified during 1976 and 2017

The next generation of very large engines GE90-X is expected to operate above 50 pressure ratio which provides impetus for looking into more robust lean-dome technologies as described in [47]. One of these approaches called swirl venturi lean-direct injection first-generation technology (LDI-1) was described in [48]. Its second-generation technology, LDI-2, described in [26] relied on high-resolution CFD simulations reported in several publications [e.g., 27, 49,50,51,52]. Both RANS and TFNS simulations have been used; here, we will give an overview of back to back comparison between RANS and TFNS results reported in [52] where 21.34 million all-tetrahedral elements were used to resolve details of a three-cup third-generation LDI-3 flametube configuration shown schematically in Fig. 35.

Fig. 35

Dome-layout with main- and pilot-injector elements for a 3-cup LDI-3 flametube simulated by 21.34 million all-tetrahedral elements. Source [52]

CFD computations with OpenNCC were reported for a generic NASA N+3 ICAO engine cycle for single-aisle, mid-range aircraft of 25,000 lb. Thrust class at an operating takeoff pressure ratio of 40. OpenNCC CFD results reported include flow field predictions and emissions comparisons for the idle and approach conditions. While the details of the hardware, models, mesh generation strategy, numerical scheme, and convergence criteria were reported in [27, 49,50,51,52], here we will focus on the key results as summarized in Table 3 and Figs. 36, 37, 38 and 39.

Table 3 Comparison between data and predictions; adopted from [52]

Fig. 36

Axial-velocity (m/s) contours in three axial cross sections through centerline of two main injectors and the pilot injector. Left: RANS solution. Right: TFNS solution from [52]

Fig. 37

a Temperature (K) contours in three axial cross sections through centerline of two main injectors and the pilot injector. Left: RANS solution. Right: TFNS solution from [52]. b NO mass fraction contours in three axial cross sections through centerline of two main injectors and the pilot injector. Left: RANS solution. Right: TFNS solution from [52]

Fig. 38

a Isometric contours of NO (ppm) at idle predicted by TFNS. Left: horizontal center plane including Mains and Pilots. Right: vertical plane with composite of three pilot injectors. b Isometric contours of CO (ppm) at idle predicted by TFNS. Left: horizontal center plane including Mains and Pilots. Right: vertical plane with composite of three pilot injectors

Fig. 39

a Isometric contours of NO (ppm) at approach predicted by TFNS. Left: horizontal center plane including Mains and Pilots. Right: vertical plane with composite of three pilot injectors. b Isometric contours of CO (ppm) at approach predicted by TFNS. Left: horizontal center plane including Mains and Pilots. Right: vertical plane with composite of three pilot injectors

An initial evaluation of OpenNCC was performed for the central, five-injector cup of the three-cup, nineteen-element geometry. Figure 36 shows axial-velocity contours of the OpenNCC results at various cross sections for this five-injector cup. A strong, prominent central recirculation zone (CTRZ) behind the pilot was predicted by both RANS and TFNS methods. One major difference was that TFNS predicts a relatively symmetric and uniform flow pattern behind each of the four main injectors. The RANS predictions showed relatively large variations in the flow patterns behind the four main injectors. The corresponding reacting flow solutions for temperature and NO mass fraction, as predicted by RANS and TFNS, are shown and compared in Fig. 37a and b, respectively. Based on the single-cup geometry evaluation with OpenNCC, the TFNS methodology was chosen for further study of the full three-cup, nineteen-element geometry.

Table 3 summarizes the OpenNCC TFNS results, as compared with measured experimental data [52]. The predicted effective area, as computed from nonreacting computations, compares very well with experimental data (2.5% error). Figures 38 and 39 show the contours of predicted NO and CO, for the idle and approach conditions, respectively. For the idle case, only the pilot injector of each of the three cups is fueled. For the approach case, all five injectors of the central cup and the pilot injectors of each seven-element module are fueled.

The predicted NO_xEI for the idle case provides the best comparison with data (6.5% error), followed by NO_xEI prediction of the approach case (35% error). However, the prediction of emissions for COEI for both cases is in large error when compared to experimental data. The current results suggest that considerably more effort needs to be invested in improving modeling capabilities (chemical kinetic models, spray modeling, turbulence-chemistry interaction, etc.), particularly for CO predictions at low-power cycle conditions (idle, approach).

In order to meet continuing stringent regulatory requirements, the rich-dome combustion products have recently encountered smoke emissions challenges as summarized in Fig. 40 for 13 propulsion engine models ranging in takeoff thrust from 30 to 514 kN whereas the corresponding takeoff pressure ratio varies between 15.8 and 49.4. Small and medium-size engines with takeoff pressure ratio less than 35 fall along Group 1 engines for both landing-takeoff (LTO) NO_x and smoke emissions expressed as % of regulatory standards, with the former as %CAEP8. OEMs prefer to have 20–30% margin from the regulatory standards. All large engines used to meet LTO NO_x standards, namely % of CAEP4 or CAEP6. In regard to smoke they fell in Group 2 during 1995–2011 timeframe. However, after 2011 Group 2 NO_x group led to Group 3 and Group 4 for smoke emissions which are considered uncomfortably too close to the regulatory levels. TALON X technology created further reduction in NO_x leading to Group 3 NO_x engines; but one of these engine models belongs to Group 4 smoke engines. This clearly makes tradeoff between NO_x and smoke emissions more intense while simultaneously ensuring high-altitude ignition capability more difficult to maintain.

Fig. 40

NO_x and smoke emissions tradeoffs encountered in recently certified combustion products

One OEM has decided to go with lean-dome propulsion engines and has already in revenue service two engines (namely, LEAP and GEnx), and plans to introduce GE90-X. These three engines cover takeoff thrust and operating pressure ratio ranges of 120–500 kN and 33 to 50+, respectively. While lean-domes produce considerably lower NO_x and smoke emissions compared to rich-domes, they are accompanied by more challenging operability issues. Therefore, long-term accuracy objectives of the phenomenological combustion models and CFD simulations need to be comparable with data measurement capabilities expressed in terms of standard deviation σ summarized in Table 4. From here, we can set our long-term CFD accuracy goals comparable with experimental error, namely, 5% for LTO NOx, and 20% for LTO HC, LTO CO, and maximum SAE smoke number.

Table 4 Current status of engine emissions measurement standard deviation σ for HC, CO, NO_x and smoke number (SN)

Accurate high-resolution CFD simulations for applying fundamentals learned in regard to operability experiments conducted under controlled laboratory environment for both rich and lean-dome concepts need to be extended for providing guidance during the engine development process. For example, as reported in [53], rich-dome combustor rig experiments were conducted parametrically including ignition/lean blowout testing at ambient pressure/temperature, high-altitude (simulated combustor pressures of 35, 55, 80 kPa, and pressure drop of 1–5%) ignition testing, and ignition process visualization with a high-speed camera providing 6750 frames/s, shutter speed of 1/51,000 s with resolution of 768 pixels × 768 pixels. The high-speed camera was used for studying sequence of ignition kernel (shown in Fig. 41 to appear at time τ = 0.15 ms) followed by its growth and propagation and eventually sustained combustion in the primary zone at fuel/air ratio (FAR) above ignition (here 0.024) at τ = 8.88 ms. On the other hand, when below ignition FAR, here 0.021 FAR, the ignition kernel does not grow and we found no flame in the primary zone at τ = 3.55 ms. CFD simulations are planned to be undertaken to model the entire process starting with ignition kernel, its growth and propagation to achieving self-sustaining combustion or extinction. Validated models will be used for studying tradeoff between NO_x, smoke and operability for a typical gas turbine combustor.

Fig. 41

An illustration of high-speed flow visualization showing successful ignition at 0.0173 FAR and ignition failure at 0.014 FAR; from [53]

A very extensive operability related fundamental investigation is currently ongoing as described in [54,55,56,57] with several more planned to be published including CFD simulations relevant to swirl venturi LDI mixers, as well as the same set of configurations without flare that resembles modern airblast injectors. Advanced diagnostics used include two-dimensional time-resolved particle image velocimetry (PIV) system, OH*, CH*, and NO₂* chemiluminescence signals with an intensified charge-coupled device camera with species-specific bandpass filters for each radical, namely 310 ± 2 nm with 10 nm full width half maximum (FWHM) for OH*, 430 ± 2 nm with 10 nm FWHM for CH*, and 750 ± 10 nm with 70 nm FWHM for NO₂*.

We want to summarize key findings on the weak and strong swirling flow field established by LDI and airblast configurations with 45° and 60° (also called baseline) outer swirler vane angles; inner swirler vane angle is 60° for all the four configurations summarized in Figs. 42, 43, 44 and 45. Direct flame images overlaid with velocity vector maps for the baseline LDI configurations with and without the venturi flare section are shown in Fig. 42 for a pressure drop of 3% and ϕ = 0.65. Without the venturi flare, both the Airblast-60°cw and Airblast-45°cw configurations exhibit lifted flames, although the Airblast-60°cw appears to have a stronger flame than Airblast-45°cw, with the primary flame zone of Airblast-60˚cw located several throat diameter (D_t) lower than for the Airblast-45°cw case. Comparing the LDI-45°cw with its airblast counterpart, while overall flame structure is similar, the flame sits closer to the dump plane for the LDI configuration. However, for the LDI-60°cw configuration with and without the venturi flare, the flame is either anchored to the dump plane or lifted solely due to the flare.

Fig. 42

Flame structure variations at 3% pressure drop and ϕ = 0.65 for the LDI-60°cw, Airblast-60°cw, LDI-45°cw, and Airblast-45°cw configurations, represented by mean direct flame images overlaid with mean velocity vectors

Fig. 43

Mean reacting axial-velocity fields at ϕ = 0.65 for the Airblast-60°cw, LDI-60°cw, Airblast-45°cw, and LDI-45°cw configurations

Fig. 44

Lean blowout limits of the four selected configurations

Fig. 45

NO₂* chemiluminescence contours at ϕ = 0.65 for the Airblast-60°cw, LDI-60°cw, Airblast-45°cw, and LDI-45°cw configurations

The source of this change in flame behavior is apparent from the velocity field results, as shown in Fig. 43. The minor differences in flame structure between the two 45°-vane angle cases can be explained by the swirling jet structure; whereas for the LDI-45°cw case the jet is radially larger and axially shorter, removal of the venturi flare results in a thinner and dramatically longer jet. This behavior suggests that for a given flame propagation, the flame will not be able to stabilize until further downstream due to slower expansion of the swirling jet. More interesting, however, are the 60°cw cases. Removal of the venturi flare from the LDI-60°cw configuration results in a flow field much more akin to that found in the LDI-45°cw configuration, namely, a swirling jet flow in lieu of a strong center recirculation zone. Clearly, the removal of the flare section significantly weakens overall swirl strength to the point that vortex breakdown no longer occurs. Considering the above in terms of swirl number, the results are somewhat intuitive. For a given vane configuration, tangential velocities are essentially fixed; the addition or removal of a flare section will alter this motion very little. However, due to the Coanda effect—that fluid streamlines tend to follow solid boundaries—flow passing through the venturi flare will tend to expand, in the process reducing axial velocity. This in turn effectively increases the swirl number by decreasing the flux of axial momentum. One interesting implication is that the Coanda effect is typically influenced by the immersion depth of the mixer relative to the dome; a future study will explore the extent to which apparent swirl strength is influenced by swirl assembly insertion depth.

In terms of operability, the aforementioned alterations to the flow field greatly impact LBO limit. As shown in Fig. 44, across the pressure drop range tested, the LBO limits for the three configurations not exhibiting a center recirculation zone are roughly similar, while the LDI-60°cw configuration exhibits LBO limits consistently 5–10% lower. Also shown in Fig. 45, NO₂* emissions are strongly tied to the presence of the center recirculation zone. For each of the configurations resulting in a lifted flame, including Airblast-45°cw, Airblast-60°cw, and LDI-45°cw, NO₂* emissions are relatively low. Some correlation with swirl strength exists; the Airblast-45°cw configuration exhibits the lowest emissions, followed by the LDI-45°cw, and then the Airblast-60°cw case. However, when a center recirculation zone is present, as for the LDI-60°cw case, high NO₂* signal is observed from just after the dump plane to 11–12 D_t downstream. This provides further evidence that for a single swirl injector, a design tradeoff exists between operability, stability, and NO_x emissions.

Even though we would like to have modern CFD tools’ capabilities better than what is summarized in Table 3 for LDI or their predecessors for TAPS summarized in Figs. 32, 33 and 34, it is important to recognize that these tools have been used successfully for developing lean-dome technologies (LDI-3 and TAPS3) and products (GEnx) and will play important role for creating next-generation TAP3 based potential products identified as TAPS3PP in Fig. 46. It is interesting to notice that the first-generation dual-annular combustion know-how led to GE90 DACI product for large 40 pressure ratio engines. As is generally the case, its NO_x technology as measured in terms of takeoff NO_xEI versus takeoff pressure ratio was not better than low-pressure ratio rich-dome technology, the CFM56 identified as CFM PLEC. As expected, the GE90 DAC I emissions results provided impetus for developing the second-generation lean-dome technology and products (e.g., GEnx), known popularly as TAPS as described in [24, 25]. Compared to GE90 DAC I at 40.4 pressure ratio, GEnx achieved 68% reduction in takeoff NO_xEI. As leading combustion designers have experienced several times before, the GEnx scale-up for the CFM56 application (known as LEAP-X) did not turn out good. Its takeoff NO_xEI at 41.5 pressure ratio turned out to be 2.1 times GEnx value for the same pressure ratio. On the other hand, for the lower pressure ratio of 33.4, its NO_xEI was only 1.37 times GEnx value. When and if the competitive marketing situation arises, we are sure that the TAPS-based LEAP-X will be followed by further reduction in NO_x emissions comparable with GEnx or beyond by applying TAPS3 technology and producing potential TAPS3 based product, TAP3PP.

Fig. 46

Takeoff NO_x emissions index versus takeoff pressure ratio of several propulsion engine combustion products including rich-dome pre-low-emissions CFM56 products certified in early 1990s (CFM PLEC), the first dual-annular 40-pressure ratio lean-dome combustor (GE90DAC I) which provided impetus to develop second-generation lean-dome GEnx based on TAPS1 technology

It is equally interesting to note that LDI-3 technology (see Fig. 35) was developed by using CFD showing it slightly lower than GEnx takeoff NO_xEI, namely, 22% lower at 37.5 pressure ratio, even though we need to further improve its prediction capability, as summarized in Table 3. What we are trying to convey is CFD when used properly will always provide good guidance even when its accuracy levels are significantly off compared to measurement uncertainties.

8 Summary

The empirical/analytical design methodology (EADM) reported by Mongia and his coworkers in 1977–1978 [1, 2] perhaps provided impetus for other gas turbine OEM’s to pursue variants of theirs consistent with their vision. Figure 1 gives a schematic representation of EADM which comprises of mutually interacting five elements. Can we include elements 1 through 5 as part of continuously evolving conventional design process that is uniquely different for each major OEM’s? How closely coupled are elements 5 and 6? It is, therefore, fair assumption to make that EADM’s of all major OEM’s are uniquely different; moreover, they include trade secrets critical for maintaining competitive edge. Mongia did not feel qualified enough to make assessment calls for EADM’s pursued by others. This chapter’s focus is only on EADM used in programs where Mongia was personally involved as team leader. We used CFD simulations in conjunction with applicable hypotheses supported by subcomponent engineering tests or not in order to seek qualitative guidance during continuously evolving design process even for a given project. This approach has been used successfully in several programs as recognized by customers as described in [1, 2, 4, 6, 9,10,11, 14,15,16,17,18,19,20,21,22,23,24,25, 29]. These programs included NASA staged combustion Concept 3 (in 1977), two Army combustor concepts for small engines (1978), 2100, 2400 and 2900 °F temperature rise combustors (1981–1983), the two first product combustors (1986), two near-stoichiometric temperature high-performance combustors (1993), entitlements for ultralow NO_x premix/pre-vaporized and partially premixed mixers (1993, 2008), an RQL combustor for the largest turbofan engine (1996), the second-generation lean-dome combustion technology TAPS demonstration (2003) and its product introduction in GEnx (2009), NASA LDI-2 and LDI-3 technology demonstrations in 2014 and 2018, respectively. Mongia agrees with the statement made by one of his peers in 2005, “I see that you use CFD in selecting designs. But I don’t understand your decision process.”

The key to success of EADM includes (1) Proper use of the methodology (Fig. 1), customers’ trust, freedom to define and pursue evolving technical approach; (2) Combustion hypotheses driven by test results, see Fig. 20b as an example for addressing dome and liner wall carboning; (3) Element test configurations tested under relevant initial and boundary conditions, cf. Sect. 3; (4) Establishing limits of models’ capabilities, cf. Sects. 5 and 6; (5) Optimum use of resources, team members, time, test facilities, design experience driven by test results backed by semi-analytical and CFD design tools; and (6) Art of design and application of tools. CFD has become an integral part of combustion design practice; but its usefulness will be influenced greatly by how well these six elements are integrated. Section 7 summarizes vision of the authors on how CFD can be helpful in developing technology; and ongoing applicable fundamental research effort for both rich- and lean-dome combustion concepts. Even though the scope of the effort required for the abovementioned (3) and (4) has exceeded the original estimate by a factor of up to 5; and we do not see clearly how models’ accuracy levels can become comparable with experimental data scatter, “genuine” CFD design tools development will be pursued by enlightened combustion designers.