Abstract

In this paper, we explore the operational map of a lean axial-staged combustor of premixed and partially premixed reacting jet-in-crossflow flames at high -pressure (5 atm). This study attempts to expand the data to relatively high pressure and could significantly aid scaling to real gas turbine engine conditions at 20–30 atm. High-speed camera, particle image velocimetry (PIV), CH* chemiluminescence, temperature, and pressure measurements were taken and processed to allow accurate reconstruction of six operating points relative to computational fluid dynamics (CFD) simulations under minimal adjustments. Variation of lean main stage (φ = 0.575 and 0.73) and rich jet (φ = 1.1, 4, and 8) equivalence ratio has been investigated for a four mm axial jet. The fully premixed flames were found to be controlled by the crossflow temperature before ignition and the crossflow oxygen content during combustion. Analysis of flame shape and position for the partially premixed operating points describes a lee stabilized as well as a more unsteady windward flame branch. Adjustment of added jet fuel and crossflow temperature along with its corresponding oxygen level is required to attain a compact flame body. The risk of delaying combustion progress is significantly increased at a richer jet φ = 8 and an overshooting, spatially divided flame was attained with a main stage φ = 0.73. Control toward a compact flame body is critical to allow combustion at reasonable reaction rate.

1 Introduction

Jet-in-crossflow is a canonical flow field that has been intensively studied for industrial application for several decades [13]. Apart from its occurrence in exhaust plumes of power plants and its use for thrust vector control of high-speed air-breathing systems and rocket vehicles [4], the main application is in the field of axial-staged gas turbine combustors for its potential to reduce NOx emissions [58]. Original equipment manufacturer patents were termed Late Lean Injection by GE [9,10] and Secondary Fuel Injection by Siemens [11,12]. Previous research in this field has significantly enhanced knowledge about short-chain fuel flames and ignition [1318], pressure [19], influence of premixing [20,21], formation of NOx [22], and detailed flow characteristics [23,24].

Closely related investigations about flame behavior determined for a premixed ethylene/air jet in their lean axial-staged combustor have been made by Refs. [2527]. An unsteady windward branch stabilized by auto-ignition was observed along with a steadily attached leeward flame, stabilized by premixed flame propagation [27]. Additional details about those windward flame stabilization behaviors, which were named complete flame attachment, unsteady lifted flame, and windward blow-off, were supplied in Ref. [25]. All average windward flames were lifted, and liftoff heights strongly correlated to the momentum flux ratio. Blending with hydrogen might aid flame stability [28].

Indication of flame stabilization mechanisms has been observed for the partially premixed flames of this study, showing the windward ignition point move in a streamwise domain of ±1.5d. Scope of this paper has thereof been defined in verifying the findings of Refs. [2527] for the fuel methane as well as extending the study to partially premixed flames.

2 Research Objective

Fuel-only flames were shown to extend far downstream [29] and would overshoot into an attached turbine section, which is not desirable for industry application. We have thus extended our lean axial-staged combustor area of application toward premixed and partially premixed operating points. This paper studies variation of jet equivalence ratio (φaxial = 1.1, 4, and 8) with its corresponding parameter methane mass (m˙axialCH4 = 0.957 g/s, 3.48 g/s, and 6.96 g/s) to account for various fuel splits as well as variation of headend equivalence ratio (φmain = 0.73, 0.575) with its corresponding parameters maximum temperature (Tmainmax = 1918 K and 1623 K) and main stage oxygen mass fraction (wmainO2 = 0.060, 0.096) to account for various gas turbine loads. Data of these six experimentally verified axial-staged combustor operating points were processed and used for description by a single 3D computational fluid dynamics (CFD) approach with minimal adjustment of models (flame propagation) and boundary conditions (temperature and headend species composition) to ensure comparability of the simulation.

3 Experiment and Diagnostics

3.1 Experimental Facility.

The experimental facility is displayed in Fig. 1. It contains a headend burner, which provides vitiated crossflow to the axial stage with quasi-uniform boundary conditions.

Fig. 1
Experimental axial-staged combustor test facility
Fig. 1
Experimental axial-staged combustor test facility
Close modal

Methane and air react in the main burner pipe at lean conditions, and bypass air is injected coaxially around the main burner pipe to further lean out the vitiated flow. The axial stage consists of an optically accessible test section with two (124 × 95.2) mm side windows, a (127 × 40.6) mm bottom window, and a top injector plate with a 4 mm wall flush injector. At the exhaust of the facility is a choke plate with a 38.0 mm choke diameter to pressurize the flow to five atmospheres [29].

3.2 Flow Control Equipment.

The main, bypass, and axial air were all metered using restriction orifice unions from Global Industries (Port Washington, NY) while the fuel flow rates were metered using O'keefe precision orifices. Pressure measurements were made by Dwyer pressure transmitters and recorded through labview to determine mass flow rates. The headend of the facility is tuned to produce temperatures and NOx levels similar to that of a real-world power generating gas turbine. Centerline temperature measurements were made using an exposed bead b-type thermocouple.

3.3 Experimental Data Processing.

High speed line of sight CH* chemiluminescence data at 200 microns per pixel spatial resolution was taken using a Photron Fastcam SA1.1 at a rate of 10,000 fps; a 430 nm filter was utilized to obtain CH* intensity. The images were processed in matlab and time-averaged images were obtained considering 4000 images per dataset. Flame boundaries were determined based on a CH* intensity gradient threshold set visually by observing where the flame lights off. This experimental CH* isolevel at certain I/Imax was compared to the similar isolevel of the normalized progress variable from the CFD. Figure 2 shows the lee-side overlay of both signals for a φaxial = 8 flame.

Fig. 2
Comparison of experimental and CFD reaction progress normalized isolevels at a φaxial= 8
Fig. 2
Comparison of experimental and CFD reaction progress normalized isolevels at a φaxial= 8
Close modal

Particle image velocimetry (PIV) was performed using a dual 532 nm Evergreen laser and an Andor camera with a delay time of 20 μs between laser pulses at 12.5 Hz. 3 μm aluminum oxide (Al2O3) particles were used to seed the flow and were tracked using PIV Lab to obtain velocity fields.

4 Computational Model

This star-ccm+ CFD model was built up in close accordance to previous numerical investigations [30,31], focused on the critical jet-in-crossflow section of the axial-staged combustor. The coordinate system origin is defined at the point of collision between the jet and crossflow, as shown in Fig. 3. Symmetry along the z axis has been utilized.

Fig. 3
Axial Stage computational domain with dimensions in (mm) and mesh grid with local refinement zones
Fig. 3
Axial Stage computational domain with dimensions in (mm) and mesh grid with local refinement zones
Close modal

4.1 Mesh grid.

A single-structured mesh grid was used with a Prism Layer Thickness of 0.4 mm and total count of 20 × 106 cells. Figure 3 depicts the computational domain with its dimensions in (mm) and local mesh refinement zones describing the fuel line, mixing and ignition domain (1) at a grid size Δs =0.125 mm as well as the counter-rotating vortex pair (CVP) dissipation domain (2) at Δs =0.25 mm. Grid convergence was shown and the highest residual levels were below 0.1% for the 20 × 106 cell mesh grid.

The simulations ran on a CentOS 7 cluster with Intel Xeon cores, ×86_64 architecture with 32 cores and 128-192 GB RAM per node. Data were connected to a Luster parallel file system with 56Gbit/s 4× FDR InfiniBand network fabric. Power demand was 5000 CPU hours per simulation.

4.2 Reactive Flow Modeling.

Reactive flow was described by the Flamelet generated manifold approach [32] at its defaults. Flamelet tables were generated in star-ccm+ from the grimech 3.0 [33], considering 15 species (CH4, CH, CO, CO2, H2, H2O, H2O2, HO2, H, N2, NO, NO2, O2, OH, and O). To obtain a reasonable estimate of the crossflow oxygen level, the headend composition was defined at equilibrium for the corresponding temperature. Data for heat loss ratio, progress variable, mixture fraction and their variances were tabulated using the 1D Premixed Reactor and adaptive gridding method. Species weights of CO, CO2, H2, and H2O ran through the star-ccm+ optimizer from defaults for a similar composition [34]. Turbulent flame closure (TFC) was applied at flame propagation rate of 1.5 to match the experimental data of partially premixed flames (φaxial = 4 and φaxial = 8). Figure 4 depicts a side-view camera image of the test facility (α) with windward and leeward ignition points highlighted by green circles as well as the adjacent CFD result at a φmain = 0.73, showing isolevels between 10% and 99% of the normalized progress variable.

Fig. 4
Experimental camera image (α) and CFD progress variable isolevels (β) at a φmain = 0.73
Fig. 4
Experimental camera image (α) and CFD progress variable isolevels (β) at a φmain = 0.73
Close modal

The premixed flames (φaxial = 1.1) were modeled using the coherent flame model (CFM) at a flame surface production coefficient increased from 1.5 to a value 2.0. All flames were locally ignited in the CFD with the corresponding pulsed progress variable (TFC) or flame area density (CFM) ignitor.

4.3 Headend Flow Profile and Turbulence.

Early imaging analysis pointed out the importance of stabilizing the headend flow to avoid acoustic instabilities and obtain a consistent boundary condition upstream of the jet-in-crossflow stage. The facility has been extended for an additional 152 mm section between the stages to a total reacting length of 1 m. Stabilized headend flow was experimentally confirmed with the PIV and the 3D field approximated by a sixth order radial fit function (Fig. 5) for the boundary condition in star-ccm+. The result is a precise overlay of experimental and CFD data, confirming the measured headend centerline properties for φmain = 0.73 (T =1918 K, v =84.4 m/s) as well as for φmain = 0.575 (T =1623 K, v =74.1 m/s). Input velocities in the near-wall domain seem to deviate from the PIV data in Fig. 5, but modeled results showed they were adequately accounted for by specification of no-slip wall condition and constant wall temperature of 400 K.

Fig. 5
Experimental PIV data and radial sixth-order CFD approximation at a φmain = 0.575
Fig. 5
Experimental PIV data and radial sixth-order CFD approximation at a φmain = 0.575
Close modal

The axial jet fuel line was modeled at adiabatic boundary condition. Influence of the boundary layer domain along the fuel line was numerically proven to increase penetration depth and could cover up to 75% of the cross-sectional area at fully developed flow condition and investigated Mach numbers between 0.6 and 0.8 for this 4 mm jet. To account for experimental nonidealities along the fuel line and at the hose fitting, inlet duct length was adjusted to result in a 40% boundary layer cross section at the point of contact with crossflow. Coupled flow model was used to account for compressible flow phenomena caused by these operating points at high subsonic Mach number. Turbulence was modeled as a steady Reynolds-averaged-Navier–Stokes field according to Ref. [35] and parameter calibration was investigated [36]. Specified turbulence intensity levels are 12% at the crossflow inlet and 5% at the jet inlet. Corrective action to match the experimental data was taken by adjusting the turbulent Schmidt and Prandtl numbers to 0.9, which is in the range defined by Ref. [37] for elevated momentum flux ratios (50–111). Further material properties were computed directly from the Flamelet table.

5 Results and Discussion

5.1 Test Matrix.

Both the CFD and experimental investigations covered two headend equivalence ratios (φmain) along with three equivalence ratios in the fuel line of the axial stage (φaxial). Test conditions and numerical results are summarized in Table 1. The temperature rise throughout the axial stage ΔT was determined by evaluating mass-weighted surface average function for cold and reacting flow at the outlet position, 40 jet diameters downstream of the jet. The momentum flux ratio J is defined in Eq. (1)
J=ρaxial*vaxial2ρmain*vmain2
(1)
Table 1

Test matrix for premixed and partially premixed operating points with a 4 mm axial jet at p =5 atm

HeadendAxial stage
m˙mainCH4 (g/s)m˙mainair(g/s)φmainTmainmax (K)wmainO2m˙axialCH4 (g/s)m˙axialair (g/s)φaxialΔTCFD (K)JCFD
20.34860.7319180.0600.95715.01.15952.1
3.48418680.5
6.968359111
17.25160.57516230.0960.95715.01.16150.7
3.48423968.7
6.96832095.7
HeadendAxial stage
m˙mainCH4 (g/s)m˙mainair(g/s)φmainTmainmax (K)wmainO2m˙axialCH4 (g/s)m˙axialair (g/s)φaxialΔTCFD (K)JCFD
20.34860.7319180.0600.95715.01.15952.1
3.48418680.5
6.968359111
17.25160.57516230.0960.95715.01.16150.7
3.48423968.7
6.96832095.7

Table 1 shows that the momentum flux ratios of the richest φaxial = 8 case are higher compared to the cases with lower axial equivalence ratios due to the excess of axial fuel. Raising the main stage equivalence ratio from a φmain = 0.575–0.73 was shown to increase the maximum headend temperature from 1623 K to 1918 K. For a φmain of 0.73, addition of a certain axial fuel amount results in a smaller axial ΔT due to the higher amount of thermodynamic irreversibility at elevated temperature level. As Table 1 further suggests, increasing the equivalence ratio of the axial stage would generally increase the total amount of axial heat release. However, the axial stage has a finite length, which is not sufficient to allow complete combustion of nonpremixed [30,31] as well as low-level partially premixed flames. Therefore, heat release of the φmain = 0.575, φaxial = 8 flame did not reach its maximum value throughout the available axial stage geometry.

5.2 Reacting Jet Penetration.

Reacting jet penetration was investigated experimentally (triangles), numerically (solid lines) and empirically with correlation from Lefebvre (circles) in Fig. 6. Particle traces of the jet trajectory have been acquired from star-ccm+. Experimental camera images were recorded at minimal ambient light pollution and provide a clear outline of the mean reacting jet trajectory. Experimental uncertainties depend on the downstream position and could be up to 6%, mainly due to combustion instabilities along the windward flame branch. The experimental trends are accurately followed by the simulation, showing maximum deviations of 2.5% from the data.

Fig. 6
Reacting jet trajectories for dJ = 4 mm, p = 5 atm, φmain = 0.73 (γ) and 0.575 (δ), J = 50.7–111
Fig. 6
Reacting jet trajectories for dJ = 4 mm, p = 5 atm, φmain = 0.73 (γ) and 0.575 (δ), J = 50.7–111
Close modal
Correlation from Lefebvre [38] is defined in Eq. (2)
ydaxial=0.82*J0.5*(xdaxial)0.33
(2)
and has been overlaid for its valid definition range up to ymax (Eq. (3)), occurring after 2.8d downstream
ymax=1.15*daxial*J0.5
(3)

The correlation is defined for nonreacting jets-in-crossflow; it describes the φaxial = 8 and φaxial = 4 graphs well but would underestimate the φaxial = 1.1 data due to proximity of the reactive domain. As shown from the CFD, a good indication of windward flame ignition is the point of wCH4 = 0.005, highlighted with a black cross in Fig. 6. Due to the low amount of methane entering the crossflow at fully premixed state, the φaxial = 1.1 cases are primarily controlled by the crossflow temperature and were shown to ignite earlier than cases at richer jet equivalence ratio. For the latter, data along the reacting jet trajectory could only capture the point of windward flame ignition. At a φaxial = 4, the opposite trend was found, showing the windward branch with a φmain = 0.575 to ignite first, which is due to the higher crossflow oxygen level. For the cases at a φaxial = 8, the windward branches did not ignite at all by the end of the viewing window. Further investigation of ignition kinetics and strength at the windward as well as the leeward flame branch has been conducted throughout the entire CFD domain (Sec. 5.3).

5.3 Windward and Leeward Flame Ignition.

Computational fluid dynamics data (gray, blue) were extracted using linearly spaced symmetry plane isolevels with minimum CH mass fraction of 1 × 10−8. Experimental CH* data (red) were processed to verify the flame shape by defining and extracting threshold intensities of the maximum chemiluminescent intensity Imax.

5.3.1 Axial Jet Equivalence Ratio of 1.1.

Analysis of two premixed flames at φaxial = 1.1 is shown as (a) and (b) in Fig. 7.

Fig. 7
CH of premixed CH4 flames at a φaxial = 1.1, dJ = 4 mm, p = 5 atm, (a) φmain = 0.73, J = 52.1 and (b) φmain = 0.575, J = 50.7
Fig. 7
CH of premixed CH4 flames at a φaxial = 1.1, dJ = 4 mm, p = 5 atm, (a) φmain = 0.73, J = 52.1 and (b) φmain = 0.575, J = 50.7
Close modal

Position of the φmain = 0.73 case has been verified by cropping the experimental CH* chemiluminescence image and filtering at levels 65% and 67% of Imax. Ignition of these lean flames is controlled by the crossflow temperature level. The φmain = 0.73 flame (a) was shown to ignite after an x/d =4 and at a liftoff height of 9d. The φmain = 0.575 (b) case needs more space to overcome the thermal delay and ignition was predicted after 8d downstream at a liftoff height of 10d. As indicated by comparison of the 1 × 10−8wCH isolevels, reaction progress after ignition is dependent on the available crossflow oxygen content, allowing flame (b) to combust at enhanced rate, once ignited.

5.3.2 Axial Jet Equivalence Ratio of 4.

Investigations of two partially premixed flames at a φaxial = 4 are denoted with (c) and (d) in Fig. 8.

Fig. 8
CH of partially premixed CH4 flames at a φaxial = 4, dJ = 4 mm, p = 5 atm, (c) φmain = 0.73, J = 68.7, and (d) φmain = 0.575, J = 80.5
Fig. 8
CH of partially premixed CH4 flames at a φaxial = 4, dJ = 4 mm, p = 5 atm, (c) φmain = 0.73, J = 68.7, and (d) φmain = 0.575, J = 80.5
Close modal

Maximum local CH mass fractions are indicated in the plots. The windward flame branch is located along the outer reacting jet trajectory (Fig. 6) and characterized by elevated levels of lift in both x/d and y/d directions. The leeward flame branch is defined as an early combustion event occurring at the inner lee-side of the jet trajectory and at lower y/d position.

For φmain = 0.73 (c), experimental CH* data were extracted using the thresholds 84% and 99% of Imax. The CFD shows CH levels at downstream positions between x/d =9 and x/d =25 and an average liftoff height of 9d. It seems to be a slightly divided flame with dominant rich ignition point (wmaxCH = 5.1 × 10−7) at the windward CVP branch after x/d =18. The leeward side ignites early due to the high lean crossflow temperature and proximity of the windward ignition point.

Operating point with a more compact partially premixed flame has been attained by reducing the mainstage equivalence ratio. For the leaner φmain = 0.575 (d), data at 65% and 92% of Imax were extracted. According to the CFD, the windward flame branch ignites 5d earlier than with flame (c) due to the increased crossflow oxygen content. CH levels are 10–20% lower than for flame (c), but local distribution of concentration is similar. Windward ignition dominates and induces an early leeward ignition after x/d =10, but due to the lower crossflow temperature, this point is slightly further downstream than in flame (c). Concluding, the flame branches are better synchronized and allow formation of a more compact flame body. CH levels in (d) are slightly below levels in (c) but net reaction progress would still be greater due to the high wmainO2 level, allowing flame (d) to be combusted by x/d =20.

5.3.3 Axial Jet Equivalence Ratio of 8.

Analysis of two partially premixed flames at a φaxial = 8 are denoted with (e) and (f) in Fig. 9. For the φmain = 0.73 case (e), experimental data at 80% of Imax were extracted. High lean crossflow temperature aids an early leeward ignition with maximum CH levels after x/d =15, yet clearly the flame is limited by low oxygen levels at φmain = 0.73, causing slow combustion progress throughout the axial stage. This visual observation was confirmed with the CFD, showing CH levels below wmaxCH = 1.6 × 10−7 at both ignition points. The high jet fuel amount (φaxial = 8) delays the rich windward ignition significantly to x/d =40. Result is a flame that is torn apart, it may not be advisable to run at this condition. Length of the flame was shown in 3D to significantly overshoot the jet-in-crossflow stage along the CVP. Applied industrially, this flame would likely extend into an attached turbine section. Liftoff height is 11d.

Fig. 9
CH of partially premixed CH4 flames at a φaxial = 8, dJ = 4 mm, p = 5 atm, (e) φmain = 0.73, J = 111, and (f) φmain = 0.575, J = 95.7
Fig. 9
CH of partially premixed CH4 flames at a φaxial = 8, dJ = 4 mm, p = 5 atm, (e) φmain = 0.73, J = 111, and (f) φmain = 0.575, J = 95.7
Close modal

A reasonable flame shape was obtained for the leaner φmain = 0.575 case (f). Experimental data were filtered at 62% of Imax. Windward and leeward flames are delayed due to the high fuel amount (ignition after 25d) and low temperature (ignition after 30d), respectively. Yet the rich windward branch ignited earlier than in (e) due to the increased oxygen level at φmain = 0.575. The ignition points seem to interact and resulting CH levels were determined to be wmaxCH = 1.9 × 10−7 (windward) and 2.3 × 10−7 (leeward), describing a 40% increase compared to flame (e). Transition zone between both flames was observed in the CFD and could be partially verified from the experimental image. Liftoff height is 13d and decreases due to diffusion, facilitated by its position being far downstream.

5.3.4 Observing Mechanism.

In a real combustor, any fixed lean headend temperature level would relate to a certain oxygen level at the headend, provided that further parameters are not varied. Two additional, partially premixed flames were simulated for definition of a valid prioritization of factors that influence windward and leeward ignition. Theoretical decrease of the O2 level for the φmain = 0.575 case with a φaxial = 8 and unaltered remaining parameters resulted in barely any ignition of the windward branch throughout the domain. Leeward ignition was delayed for another five jet diameters. 3D analysis confirmed that barely any reaction rate could be pointed out at any position inside the CVP. In contrast, artificial increase of the crossflow O2 level for the φmain = 0.73 case resulted in a slightly earlier ignition of the windward branch (2.5d early at wmainO2= 0.076), about 1d earlier ignition at the leeward side, and reaction rates in the CVP significantly increased for half an order of magnitude. These results confirm the trends observed from the data and allow formulation of an observing mechanism about parameters controlling the ignition of partially premixed, rich methane jets in a lean combustor.

  1. Along the windward branch, ignition is accelerated primarily by reducing the jet mass flow m˙axialCH4. Secondary factor promoting windward ignition is the increase of crossflow oxygen level wmainO2 and subordinate influence has the increase of crossflow temperature Tmain.

  2. At the leeward branch, ignition is facilitated by proximity of the windward ignition point, inducing an early leeward ignition. A secondary factor promoting ignition is the increase of Tmain, but its weight is an order of magnitude lower. Subordinate influence on leeward ignition has an increased wmainO2.

  3. Throughout their investigated range of variation, role of crossflow oxygen levels is to shift both flame branches along the x/d axis.

Assessment of further parameters influencing partially premixed ignition could include variation of pressure level, preheating of the fuel line, or the use of different diluents.

6 Conclusion

The present investigations of premixed and partially premixed methane flames are targeted toward industry application in a lean axial-staged gas turbine combustor at a pressure of five atmospheres and with a 4 mm axial jet. Simplicity of the premixed flame body at a φaxial = 1.1 helped isolate two major factors influencing the lean combustion regime. First, low headend temperature was shown to result in an increased thermal delay before axial ignition, and second, high headend oxygen levels accelerated the axial reaction progress after ignition. For industry application, these premixed operating points would likely not be considered due to their low axial fuel amount and poor resulting fuel splits, assuming a reasonable mass flow of main stage fuel. Future investigations with the similar facility and a 12.7 mm axial jet will be required to generate a dataset of industrially relevant premixed flames.

Promising results were attained for the partially premixed flames. The investigations at a richer φaxial = 4 resulted in stable flames with a compact flame body and high reaction rate, allowing the flame to close by the downstream end of the combustor. Plenty of margin for adjustment of headend temperature and crossflow oxygen level was proven to be available. Axial jet equivalence ratio φaxial = 4 seems to provide the best starting point for fine-tuning toward industry application in a lean axial-staged gas turbine combustor with a 4 mm methane jet.

Industrial use of the rich φaxial = 8, φmain = 0.575 flame can be considered but fine-tuning of parameters would have to take place within a narrow value range, ensuring the flame remains at an undivided, compact shape. Role of crossflow oxygen level to shift both flame branches was determined. Main influence factor on the resulting flame shape is the proximity of both local ignition points, allowing synchronized, stabilized flames at lean crossflow equivalence ratio and burning at reasonable reaction rate. In contrast, a φmain = 0.73 flame at φaxial = 8 cannot be fine-tuned to fulfill industry needs, the flame is highly divided and would significantly overshoot any reasonably dimensioned jet-in-crossflow stage.

Acknowledgment

The authors (BS, MO, TG, TW, JR, SM, and KA) acknowledge support from the Department of Energy under Award Number DE-FE0031227 and collaboration with GE Global Research.

Funding Data

  • U.S. Department of Energy (Grant No. DE-FE0031227; Funder ID: 10.13039/100000015).

Nomenclature

     
  • d =

    jet diameter, m

  •  
  • J =

    momentum flux ratio

  •  
  • m˙ =

    mass flow rate, kg/s

  •  
  • p =

    pressure, atm

  •  
  • s =

    cell dimension, m

  •  
  • T =

    temperature, K; °C

  •  
  • v =

    velocity, m/s

  •  
  • w =

    mass fraction

  •  
  • x =

    axial coordinate, downstream position, m

  •  
  • y =

    perpendicular coordinate, penetration depth, m

  •  
  • z =

    lateral coordinate, m

Greek Symbols

    Greek Symbols
     
  • Δ =

    difference

  •  
  • φ =

    equivalence ratio

Subscripts and Superscripts

    Subscripts and Superscripts
     
  • axial =

    axial stage

  •  
  • CFD =

    computational fluid dynamics

  •  
  • J =

    jet

  •  
  • main =

    main burner stage

  •  
  • max =

    maximum

Acronyms

    Acronyms
     
  • CFD =

    computational fluid dynamics

  •  
  • CFM =

    coherent flame model

  •  
  • CPU =

    central processing unit

  •  
  • CVP =

    counter-rotating vortex pair

  •  
  • fps =

    frames per second

  •  
  • PIV =

    particle image velocimetry

  •  
  • RAM =

    random access memory

  •  
  • TFC =

    turbulent flame closure

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