Effect of Pressure, Environment Temperature, Jet Velocity and Nitrogen Dilution on the Liftoff Characteristics of a N 2 -in-H 2 Jet Flame in a Vitiated Co-flow

The CO 2 emission prevention advantage of generating power with high hydrogen content fuels using gas turbines motivates an improved understanding of the ignition behavior of hydrogen in premixed and partially premixed environments. Hydrogen rich fueled flame stability is sensitive to operating conditions, including environment pressure, temperature, and jet velocity. Furthermore, when premixed or partially premixed operation is needed for nitric oxide emissions reduction, a diluent, such as nitrogen, is often added in allowing fuel/air mixing prior to combustion. Thus, the concentration of the diluent added is an additional independent variable on which flame stability dependence is needed. The focus of this research is on characterizing the dependence of hydrogen jet flame stability on environment temperature, pressure, jet velocity and diluent concentration by determining the dependence of the liftoff height of lifted flames on these 4 independent parameters. Nitrogen is used as the diluent due to its availability and effectiveness in promoting liftoff. A correlation modeling the liftoff height dependence on operating conditions is developed which emphasizes the factors that bear the greatest impact on ignition behavior.


Introduction
Hydrogen (H 2 ) is an attractive stationary gas turbine fuel because its products of combustion do not contain carbon monoxide or Carbon Dioxide (CO 2 ) [1]. H 2 can be produced by reforming natural gas or by gasifying coal and when burned, the generation of power from fossil fuels in this manner is known as pre-combustion Carbon Capture and Sequestration (CCS). For gas turbine performance optimization, increased understanding of H 2 combustion stability in gas turbine environments is desired. Since the majority of stationary gas turbines are fueled by natural gas, most stationary gas turbine combustor designs operate most effectively when burning natural gas. Therefore, the knowledge base which led to the state of the art in gas turbine combustors is restricted to a single fuel. H 2 , however, differs markedly in its combustion properties from natural gas (greater energy density by mass, reduced autoignition delay times, wide flammability limits, high flame speeds [1]). A key research flame beneficial for developing knowledge which is critical for optimizing stationary gas turbine combustor performance with H 2 is the lifted flame. Additional data sets characterizing lifted H 2 jet flames in gas turbine environments are beneficial for numerical model development and in developing an improved understanding of the factors that influence partially premixed flame ignition and stability. The liftoff height (L) for lifted flames is a readily measurable quantity which serves as a challenging benchmarking parameter for numerical models.
Many explanations of the flame stabilization mechanism of turbulent lifted jet flames are available [1,2,3] which are utilized in this research in understanding lifted H 2 jet flame stability. Peters [4] explains that quenching near the nozzle due to excessive local strain rates precedes liftoff. The broad flammability limits and high diffusivity of H 2 , however, makes lifted H 2 flame generation difficult. For example, at atmospheric conditions and with a jet nozzle diameter of d jet = 2.4 mm, the flame remains attached even at the sonic velocity of H 2 (1300 m/s). Consequently, the diluent nitrogen (N 2 ) is added to H 2 which encourages liftoff for subsonic jet velocities.
The primary independent variables thought to control lifted flame stability include jet velocity (V jet ), nitrogen dilution mole fraction (y N2 ), environment temperature, and environment pressure in addition to d jet . With the exception of d jet , the impacts of each of these independent variables on L are experimentally explored in this research.
Experimental liftoff height results from prior work at atmospheric pressure motivated the development of a liftoff height correlation [1]. The correlation based on the Damköhler number, Dα, and the same correlation is applied in this research in assessing its applicability with pressure as an additional parameter. The chemical time scale, (τ chem ) in the denominator of Dα motivates the utilization of a computational model in lieu of experimental measurements for complexity reduction.

Experimental Methods
Berkeley's Vitiated Co-flow Burner (VCB) [1] has been redesigned and built in the interior of a pressure chamber in adding functionality for investigating the pressure effect on lifted N 2 -in-H 2 flames. An illustration of Berkeley's VCB is depicted in Fig. 1. Premixed H 2 and N 2 issue through a circular nozzle without taper and an inner diameter of d jet = 2.4 mm. The nozzle is placed around a co-flow composed of combustion products of premixed H 2 and air. The premixed H 2 and air flames are stabilized on a perforated plate with 348 1.6 mm diameter perforations arranged hexagonally with 4.8 mm separation between perforations. The total blockage ratio is 89%. The jet nozzle extends 25 mm above the base of the co-flow burner plate, and a 19 mm tall shroud is placed around the co-flow which reduces outside air (or vitiated air) entrainment while maintaining visibility of the jet nozzle. A blunt-edge nozzle (also known as a squared-off nozzle) is used because early scoping work indicated that changing from a blunt edge nozzle to a tapered nozzle bears no discernible impact on L. It is assumed that the insensitivity of liftoff height on nozzle geometry occurs because the liftoff heights generated with this burner configuration are sufficiently far away from the nozzle (L/d ≥ 10 in all cases) for negligible liftoff height contributions from local recirculation effects around the nozzle exit. Since a blunt-edge nozzle facilitates modeling (primarily because meshing a square nozzle is significantly less complicated), a square nozzle is used here. Thin walled tubes are avoided in reducing heat transfer from the co-flow products to the jet reactants. Simple 1D heat transfer calculations where performed [1] which show that even with the most conservative assumptions the fuel temperature would rise by only 28 K. These calculations indicated that fuel temperature increases in the jet nozzle are negligible.
The redesigned burner includes minor modifications in the design of the co-flow which were necessary for interfacing the hardware with a pressure chamber. Additionally, a spark-plug igniter is added to the co-flow as well as an additional igniter downstream for ignition of the jet. The pressurized VCB is shown in Fig. 2. The jet nozzle height is adjustable between 0 mm and 40 mm, though in this research it is held constant at 25 mm. 15 cm diameter windows allow viewing access used for schlieren imaging and direct imaging. Direct imaging was opted for L measurements due to difficulties with jet product accumulation in the stagnant regions between the co-flow and the windows which commonly obscures the schlieren images.
Typically, heat loads to the walls of the combustion chamber exceed levels at which reasonable methods for achieving steady state conditions via traditional wall cooling techniques can be employed. Instead, the burner operates in a quasi-transient mode, where the walls do not reach steady state conditions, while liftoff characteristics remain steady over the time span during which data is gathered. The co-flow burns for 6.5 seconds before jet reactant flow begins. The jet flows for 2 seconds and data is gathered for the last 500 ms of this time period. The timing sequence is determined through an iterative process achieving a workable balance between obtaining manageable combustor wall heating per experiment, eliminating flow transients at startup, and capturing a statistically significant mean value for L. The adequacy of the time span over which the mean liftoff height is determined is assessed by ensuring that a minimum number of repeating turbulence events occurs within the measurement span and that the pressure and flow rate variation over the selected time span is acceptably low. The minimum number of repeating turbulence events is estimated by counting the number of times L oscillates during the chosen time span. Typical oscillation counts vary between 10 and 20 occurrences over the chosen time span. Figure 3 shows the pressure trace for a representative experiment. Pressure variability in the final 500 ms of the test is acceptably low. Concurrently, Fig. 4 demonstrates acceptably low variability in N 2 and H 2 flow rates during the time period of data gathering.   4. y N2 and V jet traces corresponding to the pressure trace given in Fig. 3. The quasi steady-state y N2 value is 0.33 and the quasi steady-state V jet target is ~500 m/s for this example case.
All reactant flow rates are controlled via sonic flow control orifices. H 2 and N 2 timing control is accomplished with solenoid valves. The ignition system timing and valve actuation is controlled via LABVIEW. A high speed camera is triggered by illuminating a light emitting diode in the field of view and the camera's control software is set to begin capturing video data when the light is illuminated with LABVIEW. Video data is taken at 1000 Hz.
The mean value of L is determined through analysis of high speed video data using MATLAB. An example video snapshot is given in Fig. 5. The post-processing program scans the selected video still-frames starting at the bottom of the image and moving upward until the mean value of the monochromatic signal for the central 42 pixels exceeds a threshold of 60 (a value of 256 represents pixel saturation and a value of 1 represents an absence of light). The 500 ms of video is broken into 50 equally separated frames (in time), and the mean value of L determined from this set of frames is taken as L.
As described in section 1, the independent variables explored in this research include environment temperature, environment pressure (P chamb ), y N2 , and V jet . The environment temperature with the VCB is dependent on the equivalence ratio of the co-flow (φ co-flow determines T co-flow ). The impact of environment temperature is assessed in a sensitivity analysis of L to φ co-flow , while the effect of pressure is investigated more heavily. φ co-flow is held constant at φ co-flow = 0.15 for pressure investigations in keeping the data set size manageable, which corresponds to a co-flow temperature of ~664 K [1].

Numerical Simulations
The correlation utilized to model the liftoff height dependence of diluted hydrogen flames on the operating conditions is based on the Damköhler number of the flow and thus requires an adequate assessment of the characteristic chemical time scale, τ chem . In the suggested correlation the characteristic chemical time scale is represented by the quotient of flame thickness and flame speed, referred to as flame time, τ flame [1]. Flame stabilization occurs if the flame time is minimized.
In this study detailed numerical simulations using a one-dimensional combustion model are applied in computing τ flame . The model accounts for detailed chemical kinetics and detailed physical transport including differential diffusion [5]. The GRI 3.0 reaction mechanism for methane oxidation including a subset for the nitrogen chemistry [6] is used to model chemical kinetics. In order to identify the conditions at which flame time exhibits its minimum the flame speed and flame thickness of laminar flat flames [7] are determined for different jet compositions, equivalence ratios in the co-flow and pressures.

Results and Discussion
Liftoff height dependence on P chamb , φ co-flow , y N2 , and V jet , has been characterized with particular focus on pressure dependence. The sensitivity of L with respect to these parameters was characterized first for determination of the most influential variables. The sensitivity analysis was conducted for a base case with φ co-flow = 0.15, y N2 = 0.33, V jet = 400 m/s, and P chamb = 1.5 bar using the following expression.
The sensitivity analysis results are summarized in Fig. 6:   Fig. 6. Sensitivity analysis showing the sensitivity of L with respect to V jet , y N2 , φ co-flow , and P chamb with both V jet and Re jet fixed. 0.1 bar was chosen as the increment value (dy) for P chamb (both with Re jet and V jet fixed) sensitivity, 0.005 for φ co-flow sensitivity, 0.04 for y N2 sensitivity, and 100 m/s for V jet sensitivity. As expected, L exhibits negative sensitivity to P chamb , particularly when V jet is held constant because pressure increases lead to V jet decreases when Re jet is fixed causing reduced liftoff height reductions. Also as expected, a strong positive sensitivity of the liftoff height with respect to y N2 is observed. Nitrogen addition increases jet momentum which increases fluid velocity downstream of the nozzle exit and reduces the flame propagation speed. Both of these factors bear positive contributions toward V jet -L sensitivity. Surprisingly, a strongly positive sensitivity with respect to co-flow equivalence ratio is observed. The increase in coflow equivalence ratio leads to an increase in flame speed which serves to reduce the liftoff height [1]. However, since the co-flow air flow rate is held constant as equivalence ratio is varied with these experiments, the increased co-flow velocity accompanying stoichiometry increases likely effects L sensitivity more than temperature under these conditions. In short, as φ co-flow increases, the accompanied temperature increase causes an additional co-flow velocity increase (accompanied by the co-flow velocity increase contribution from the co-flow H 2 flow rate increase) because of the vitiated air density reduction. Previous research by Montgomery et al. [8] and others explores and explains liftoff height dependence on co-flow velocity.
The dependence of L on P chamb is characterized for various values of V jet and y N2 as well as cases where Re jet is held constant since it is unclear whether fixing V jet or Re jet is most appropriate. Figure 7 shows a comparison between results where L pressure dependence is characterized for V jet = 400 m/s and 500 m/s for y N2 = 0.33 and φ co-flow = 0.15. Consistent with the sensitivity analysis, L pressure trending is nearly identical for the two V jet values. L insensitivity to V jet for fully turbulent jet flames can be explained in a similar manner that flame length insensitivity to V jet is explained for attached turbulent jet flames. As jet velocity increases, turbulent diffusivity (D t ) increases, leading to faster mixing which can balance the reduction in flow time [9].
A pressure sweep where Re jet is fixed instead of V jet as pressure increases further demonstrates L insensitivity to V jet .
The value of V jet at 1.15 bar (the minimum pressure explored due to apparatus limitations) is 400 m/s and 500 m/s for Re jet = 41500 and 51150, respectively. As P chamb is increased, the reduction in V jet for Re jet = 41500 and 51150 scales by an equivalent factor, so Fig. 8 demonstrates L insensitivity to Re jet which does not diminish with velocity reductions resulting from increases in pressure up to 2 bar.
In assessing conditions for which D t does not scale linearly with V jet , an addition pressure sweep where y N2 = 0.20 demonstrates that L insensitivity to V jet occurs only when turbulence intensity is great enough to be considered "fully turbulent", or for conditions where Re jet exceeds a threshold value.
As with Fig. 8, the value of V jet at P chamb = 1.15 bar is equivalent for the two cases considered. The reduction in Re jet resulting from the reduction in y N2 , however, introduces a significant L sensitivity on V jet . As P chamb is increased, the reduction in V jet for the constant Re jet cases causes a flame stabilization location departure between the constant Re jet cases and constant V jet cases. This result suggests that for Re jet = 31000, turbulence intensity is not great enough for linear D t -V jet scaling. Scaling laws used for understanding flame length insensitivity (shown in Fig.  10) on V jet apply in a similar manner in explaining liftoff height insensitivity on V jet shown here.   The elevated pressure liftoff height data is next correlated with the Damköhler number (Dα) using a similar methodology employed by North et al. [1]. Cases with y N2 = 0.33 exhibit minimal dependence on jet velocity and the dependence on the choice of holding V jet or Re jet constant is also weak for y N2 = 0.33. A departure occurs when y N2 decreases as shown with the y N2 = 0.20 data.
The Damköhler number is formulated such that τ flow represents an estimated time which the fluid travels before reaching a 'minimum' flame time [1]. V jet is weighted by the square root of the jet density to surrounding fluid density in incorporating the momentum increase effect imparted by N 2 dilution onto τ flow . τ chem is computed as the ratio of the flame thickness (δ) to the laminar flame speed (S L ). This formulation presupposes that flame propagation effects bear a dominant role in influencing the stabilization location, which has been shown a reasonable assumption for φ co-flow < 0.20 [1]. τ chem is therefore hereafter denoted as τ flame . Prior work analyzing atmospheric (and unconfined) jet flames [1] with similar independent parameter choices indicated that the local equivalence ratio which minimizes τ flame is a consistent value of ͞ φ mr = 1.5. For the elevated pressure conditions, however, the minimum is slightly leaner as outlined in Figs. 12 and 13.  The base cases with y N2 = 0.33 exhibits a local minimum when ͞ φ mr = 1.3. Other local minimums exist, though it is reasonable to postulate that the flame most often anchors where the local minimum in τ flame is closest to the stoichiometric value because the flame propagates toward the nozzle until the steep rise observed for ͞ φ mr < 1.3. With y N2 reduced to 0.20, however, the flame time sensitivity on ͞ φ mr reduces. Furthermore, the local minimum in τ flame is a function of pressure for y N2 = 0.20. The reduced sensitivity likely increases the impact of factors other than τ flame on the liftoff height. Nonetheless, the local minimum observed for P = 1.4 is selected for implementation into the Da correlation for the y N2 = 0.20 data because this is the minimum for the atmospheric pressure cases. Consequently, this is the only flame time minimum for which the jet velocity is equivalent between the cases where V jet and Re jet are held constant with the intent of understanding the observation that fixing this independent parameter becomes important when y N2 is reduced.
The axial location (at the jet centerline) where the minimum in flame time occurs is computed from [11]: The data is first plotted together versus P chamb in understanding the level of scatter encountered as the chosen independent parameters are varied. It is assumed here that the distance between the real stabilization location (which is not in general located on the jet centerline) and the axial location where ͞ φ mr resides can be neglected [1]. The resulting dependence of the normalized liftoff heights measured and the Damköhler number is presented in Fig. 14 Generally, the L/d jet data trends surprisingly well with Da. Trending is poor for y N2 = 0.20 which is attributable to the additional effect of turbulent diffusivity scaling nonlinearly with V jet for lower Reynolds number jets -an effect which is not included with this correlation.

Conclusions
Improvements in the understanding of stability and ignition for diluted premixed and partially premixed H 2 flames are beneficial for H 2 optimized gas turbine combustor development. Lifted flames are an attractive target flame for numerical model benchmarking and flame stabilization theory improvements because the measurable liftoff height is dependent on chemical, transport, and fluid dynamic effects. Numerical models capable of accurately replicating experimentally measured liftoff heights under all relevant conditions can be used in gas turbine combustor development with increased confidence because the complexities which inherently influence the stabilization location in laboratory flames are equally applicable in gas turbine environments. This paper presents a data set characterizing the stabilization height of turbulent N 2 -in-H 2 jet flames in a vitiated co-flow versus pressure for selected values of V jet and y N2 and with φ co-flow held constant at 0.15 in keeping the independent parameter space manageable. L dependence on pressure is negative indicating that the reduction in flame time resulting from pressure increases is the dominant factor imparted by pressure effects. For high jet Reynolds numbers (Re jet ≥ 41500), L is insensitive to V jet which indicates that the rate at which turbulent diffusivity increases balances the reduction in flow time as V jet is increased for the conditions investigated. When Re jet is reduced to Re jet = 31000 by reducing the concentration of the N 2 diluent, however, L sensitivity to V jet becomes positive. A sensitivity analysis confirms L insensitivity to V jet for high turbulence intensity. The sensitivity analysis also indicates highly positive L sensitivity to φ co-flow and y N2 , whereas L sensitivity to pressure is highly negative both when V jet is held constant and Re jet is held constant as pressure is varied. A previously developed method for correlating liftoff height data in vitiated co-flows for 0.15 < φ co-flow < 0.20 with a specially formulated Damköhler number was utilized which exhibits good trending with experimental data. Consequently, the Damköhler number can be used as a means of estimating the liftoff height when experimental data is nonexistent for guiding future experimental and numerical work when pressure is parameterized.