Assessment of a Gas Turbine NOx Reduction Potential Based on a Spatiotemporal Unmixedness Parameter

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
Stefan Dederichs ◽  
Nikolaos Zarzalis ◽  
Peter Habisreuther ◽  
Christian Beck ◽  
Bernd Prade ◽  
...  
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Flame Front ◽  
Gas Turbine ◽  
Equivalence Ratio ◽  
Reduction Potential ◽  
Nox Emissions ◽  
Reaction Progress ◽  
One Dimensional ◽  
Mixing Quality

The paper presents a one-dimensional approach to assess the reduction potential of NOx emissions for lean premixed gas turbine combustion systems. NOx emissions from these systems are known to be mainly caused by high temperatures, not only from an averaged perspective but especially related to poor mixing quality of fuel and air. The method separates the NOx chemistry in the flame front zone and the postflame zone (slow reaction). A one-dimensional treatment enables the use of detailed chemistry. A lookup table parameterized by reaction progress and equivalence ratio is used to improve the computational efficiency. The influence of mixing quality is taken into account by a probability density function of the fuel element–based equivalence ratio, which itself translates into a temperature distribution. Hence, the NOx source terms are a function of reaction progress and equivalence ratio. The reaction progress is considered by means of the two-zone approach. Based on unsteady computational fluid dynamics (CFD) data, the evolution of the probability density function with residence time has been analyzed. Two types of definitions of an unmixedness quantity are considered. One definition accounts for spatial as well as temporal fluctuations, and the other is based on the mean spatial distribution. They are determined at the location of the flame front. The paper presents a comparison of the modeled results with experimental data. A validation and application have shown very good quantitative and qualitative agreement with the measurements. The comparison of the unmixedness definitions has proven the necessity of unsteady simulations. A general emissions-unmixedness correlation can be derived for a given combustion system.

Assessment of a Gas Turbine NOx Reduction Potential Based on a Spatiotemporal Unmixedness Parameter

2013 ◽  
Author(s):  
Stefan Dederichs ◽  
Peter Habisreuther ◽  
Nikolaos Zarzalis ◽  
Christian Beck ◽  
Werner Krebs ◽  
...  
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Flame Front ◽  
Gas Turbine ◽  
Equivalence Ratio ◽  
Reduction Potential ◽  
Nox Emissions ◽  
Reaction Progress ◽  
One Dimensional ◽  
Mixing Quality

The paper presents a one-dimensional approach to assess the reduction potential of NOx emissions for lean premixed gas turbine combustion systems. NOx emissions from these systems are known to be mainly caused by high temperatures; not only from an averaged perspective but especially related to poor mixing quality of fuel and air. The method separates the NOx chemistry in the flame front zone and the post flame zone (slow reaction). A one-dimensional treatment enables the use of detailed chemistry. A look up table parameterized by reaction progress and equivalence ratio is used to improve the computational efficiency. The influence of mixing quality is taken into account by a probability density function of the fuel element based equivalence ratio, which itself translates into a temperature distribution. Hence, the NOx source terms are a function of reaction progress and equivalence ratio. The reaction progress is considered by means of the two-zone approach. Based on unsteady CFD data, the evolution of the probability density function with residence time has been analyzed. Two types of definitions of an unmixedness quantity are considered. One definition accounts for spatial as well as temporal fluctuations and the other is based on the mean spatial distribution. They are determined at the location of the flame front. The paper presents a comparison of the modeled results with experimental data. A validation and application have shown very good quantitative and qualitative agreement with the measurements. The comparison of the unmixedness definitions has proven the necessity of unsteady simulations. A general emissions - unmixedness correlation can be derived for a given combustion system.

NOx-Formation and CO-Burnout in Water Injected, Premixed Natural Gas Flames at Typical Gas Turbine Combustor Residence Times

2017 ◽  
Author(s):  
Stephan Lellek ◽  
Thomas Sattelmayer
Keyword(s):  
Gas Turbine ◽  
Water Droplet ◽  
Equivalence Ratio ◽  
Water Injection ◽  
Power Production ◽  
Nox Emissions ◽  
Residence Times ◽  
Gas Turbine Combustor ◽  
Reaction Progress ◽  
Progress Variable

With the transition of the power production markets towards renewable energy sources an increased demand for flexible, fossil based power production systems arises. Steep load gradients and a high range of flexibility make gas turbines a core technology in this ongoing change. In order to further increase this flexibility research on power augmentation of premixed gas turbine combustors is conducted at the Lehrstuhl für Thermodynamik, TU München. Water injection in gas turbine combustors allows for the simultaneous control of NOx emissions as well as the increase of the power output of the engine and has therefore been transferred to a premixed combustor at lab scale. So far stable operation of the system has been obtained for water-to-fuel ratios up to 2.25 at constant adiabatic flame temperatures. This paper focuses on the effects of water injection on pollutant formation in premixed gas turbine flames. In order to guarantee for high practical relevance experimental measurements are conducted at typical preheating temperatures and common gas turbine combustor residence times of about 20 ms. Spatially resolved and global species measurements are performed in an atmospheric single burner test rig for typical adiabatic flame temperatures between 1740 and 2086 K. Global measurements of NOx and CO emissions are shown for a wide range of equivalence ratios and variable water-to-fuel ratios. Cantera calculations are used to identify non-equilibrium processes in the measured data. To get a close insight into the emission formation processes in water injected flames local concentration measurements are used to calculate distributions of the reaction progress variable. Finally, to clarify the influence of spray quality on the composition of the exhaust gas a variation of the water droplet diameters is done. For rising water content at constant adiabatic flame temperature the NOx emissions can be held constant, whereas CO concentrations increase. On the contrary, both values decrease for measurements at constant equivalence ratio and reduced flame temperatures. Further analysis of the data shows the close dependency of CO concentration on the equivalence ratio, however, due to the water addition a shift of the CO curves can be detected. In the local measurements changes in the distribution of the reaction progress variable and an increase of the flame length were detected for water injected flames along with changes of the maximum as well as the averaged CO values. Finally, a strong influence of water droplet size on NOx and CO formation is shown for constant operating conditions.

NOx-Formation and CO-Burnout in Water-Injected, Premixed Natural Gas Flames at Typical Gas Turbine Combustor Residence Times

2017 ◽  
Vol 140 (5) ◽  
Author(s):  
Stephan Lellek ◽  
Thomas Sattelmayer
Keyword(s):  
Gas Turbine ◽  
Water Droplet ◽  
Equivalence Ratio ◽  
Water Injection ◽  
Power Production ◽  
Nox Emissions ◽  
Residence Times ◽  
Gas Turbine Combustor ◽  
Reaction Progress ◽  
Progress Variable

With the transition of the power production markets toward renewable energy sources, an increased demand for flexible, fossil-based power production systems arises. Steep load gradients and a high range of flexibility make gas turbines a core technology in this ongoing change. In order to further increase this flexibility research on power augmentation of premixed gas turbine combustors is conducted at the Lehrstuhl für Thermodynamik, TU München. Water injection in gas turbine combustors allows for the simultaneous control of NOx emissions as well as the increase of the power output of the engine and has therefore been transferred to a premixed combustor at lab scale. So far stable operation of the system has been obtained for water-to-fuel ratios up to 2.25 at constant adiabatic flame temperatures. This paper focuses on the effects of water injection on pollutant formation in premixed gas turbine flames. In order to guarantee for high practical relevance, experimental measurements are conducted at typical preheating temperatures and common gas turbine combustor residence times of about 20 ms. Spatially resolved and global species measurements are performed in an atmospheric single burner test rig for typical adiabatic flame temperatures between 1740 and 2086 K. Global measurements of NOx and CO emissions are shown for a wide range of equivalence ratios and variable water-to-fuel ratios. Cantera calculations are used to identify nonequilibrium processes in the measured data. To get a close insight into the emission formation processes in water-injected flames, local concentration measurements are used to calculate distributions of the reaction progress variable. Finally, to clarify the influence of spray quality on the composition of the exhaust gas, a variation of the water droplet diameters is done. For rising water content at constant adiabatic flame temperature, the NOx emissions can be held constant, whereas CO concentrations increase. On the contrary, both values decrease for measurements at constant equivalence ratio and reduced flame temperatures. Further analysis of the data shows the close dependency of CO concentration on the equivalence ratio; however, due to the water addition, a shift of the CO curves can be detected. In the local measurements, changes in the distribution of the reaction progress variable and an increase of the flame length were detected for water-injected flames along with changes of the maximum as well as the averaged CO values. Finally, a strong influence of water droplet size on NOx and CO formation is shown for constant operating conditions.

scholarly journals A fractional generalization of the dirichlet distribution and related distributions

2021 ◽  
Vol 24 (1) ◽  
pp. 112-136
Author(s):  
Elvira Di Nardo ◽  
Federico Polito ◽  
Enrico Scalas
Keyword(s):  
Monte Carlo ◽  
Probability Density Function ◽  
Monte Carlo Simulations ◽  
Probability Density ◽  
Dirichlet Distribution ◽  
One Dimensional ◽  
Reasonable Approximation ◽  
Generalized Dirichlet Distribution ◽  
The One ◽  
Generalized Dirichlet

Abstract This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the n partitions of the interval [0, Wn ] are independent and identically distributed random variables following the generalized Mittag-Leffler distribution. The expected value and variance of the one-dimensional marginal are derived as well as the form of its probability density function. A related generalized Dirichlet distribution is studied that provides a reasonable approximation for some values of the parameters. The relation between this distribution and other generalizations of the Dirichlet distribution is discussed. Monte Carlo simulations of the one-dimensional marginals for both distributions are presented.

Monte Carlo Probability Density Function Method for Gas Turbine Combustor Flowfield Predictions

1997 ◽  
Vol 13 (2) ◽  
pp. 218-225 ◽  
Author(s):  
Anil K. Tolpadi ◽  
Sanjay M. Correa ◽  
David L. Burrus ◽  
Hukam C. Mongia
Keyword(s):  
Monte Carlo ◽  
Probability Density Function ◽  
Probability Density ◽  
Gas Turbine ◽  
Density Function ◽  
Function Method ◽  
Gas Turbine Combustor

The nature of the electronic states in disordered one-dimensional systems

1963 ◽  
Vol 274 (1359) ◽  
pp. 529-545 ◽  
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Analytical Calculation ◽  
Homogeneous Boundary Condition ◽  
High Electron ◽  
One Dimensional ◽  
Computer Calculations ◽  
A Chain ◽  
Zero Potential

We consider an electron moving in the field of a one-dimensional infinite chain of identical potentials separated by regions of zero potential, the lengths s of these regions being distributed according to a probability density function p(8) . If we define the reduced phase of a real solution of the wave equation as the principal value of arctan ( — ψ'/kψ ) and є i as the reduced phase at the point x i immediately to the left of the i th atomic potential, it is shown for all bounded p(s) and sufficiently high electron energies that the є i are distributed according to a probability density function which depends on the direction of integration from a specified homogeneous boundary condition. This result is shown to imply that the eigenfunctions for such systems are localized in the sense that the envelope of such a function decays on average in an exponential manner on either side of some region. An analytical calculation for a random chain of δ-functions gives the decay of the nodes explicitly for high energies, and numerical calculations of the decay for a liquid model are presented. Further support for the theory is provided by computer calculations of some of the eigenfunctions of a chain of 1000 randomly placed δ-functions.

Impact of Cooling Air Injection on the Combustion Stability of a Premixed Swirl Burner Near Lean Blowout

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
A. Marosky ◽  
V. Seidel ◽  
T. Sattelmayer ◽  
F. Magni ◽  
W. Geng
Keyword(s):  
Flame Front ◽  
Equivalence Ratio ◽  
Flame Stabilization ◽  
Air Injection ◽  
Combustion Stability ◽  
Nox Emissions ◽  
Test Rig ◽  
Lean Blowout ◽  
Burner Exit ◽  
Cooling Air

In most dry, low-NOx combustor designs of stationary gas turbines, the front panel impingement cooling air is directly injected into the combustor primary zone. This air partially mixes with the swirling flow of premixed reactants from the burner and reduces the effective equivalence ratio in the flame. However, local unmixedness and the lean equivalence ratio are supposed to have a major impact on combustion performance. The overall goal of this investigation is to answer the question of whether the cooling air injection into the primary combustor zone has a beneficial effect on combustion stability and NOx emissions or not. The flame stabilization of a typical swirl burner with and without front panel cooling air injection is studied in detail under atmospheric conditions close to the lean blowout limit (LBO) in a full-scale, single-burner combustion test rig. Based on previous isothermal investigations, a typical injection configuration is implemented for the combustion tests. Isothermal results of experimental studies in a water test rig adopting high-speed planar laser-induced fluorescence (HSPLIF) reveal the spatial and temporal mixing characteristics for the experimental setup studied under atmospheric combustion. This paper focuses on the effects of cooling air injection on both flame dynamics and emissions in the reacting case. To reveal dependencies of cooling air injection on combustion stability and NOx emissions, the amount of injected cooling air is varied. OH*-chemiluminescence measurements are applied to characterize the impact of cooling air injection on the flame front. Emissions are collected for different cooling air concentrations, both global measurements at the chamber exit, and local measurements in the region of the flame front close to the burner exit. The effect of cooling air injection on pulsation level is investigated by evaluating the dynamic pressure in the combustor. The flame stabilization at the burner exit changes with an increasing degree of dilution with cooling air. Depending on the amount of cooling, only a specific share of the additional air participates in the combustion process.

Characteristic Time Model Correlation of NOx Emissions From Lean Premixed Combustors

1995 ◽  
Author(s):  
Donald M. Newburry ◽  
Arthur M. Mellor
Keyword(s):  
Gas Turbine ◽  
Diffusion Flame ◽  
Characteristic Time ◽  
Equivalence Ratio ◽  
Nox Emissions ◽  
Time Model ◽  
New Model ◽  
Gas Turbine Combustors ◽  
Ratio Data ◽  
Lean Premixed

The semi–empirical characteristic time model (CTM) has been used previously to correlate and predict emissions data from conventional diffusion flame, gas turbine combustors. The form of the model equation was derived for NOx emissions from laboratory flameholders and then extended to conventional gas turbine combustors. The model relates emissions to the characteristic times of distinct combustion subprocesses, with empirically determined model constants. In this paper, a new model is developed for lean premixed (LP) NOx emissions from a perforated plate flameholder combustor burning propane fuel. Several modifications to the diffusion flame CTM were required, including a new activation energy and a more complicated dependence on combustor pressure. Appropriate model constants were determined from the data, and the correlation results are reasonable. An attempt was made to validate the new model with LP NOx data for a different but geometrically similar flameholder operating at lower pressures. The predictions are good for the low equivalence ratio data. However, a systematic error in the reported equivalence ratios may be adversely affecting the predictions of the higher equivalence ratio data through the calculated adiabatic flame temperature.

Implication of Different Fuel Injector Configurations for Hydrogen Fuelled Micromix Combustors

2011 ◽  
Author(s):  
Bhupendra Khandelwal ◽  
Yingchun Li ◽  
Priyadarshini Murthy ◽  
Vishal Sethi ◽  
Riti Singh
Keyword(s):  
Gas Turbine ◽  
Thermal Energy ◽  
Combustion Zone ◽  
Equivalence Ratio ◽  
Nox Emissions ◽  
Fuel Injector ◽  
Gas Turbine Combustors ◽  
The Impact

A design of a hydrogen fuelled micromix concept based combustor is proposed in this paper. The proposed micromix concept based combustor yields improved mixing, which leads to wider flammability range of the hydrogen-air flames compared to conventional kerosene and micromix concept based combustors. This improved mixing allows the combustion zone to operate at a much lower equivalence ratio than the conventional kerosene based and micromix concept based combustors considered in this study. Furthermore, when burning hydrogen the thermal energy radiated to the surroundings is lower (as the result of using lower equivalence ratio) than that of kerosene, consequently resulting in an increased liner life and lower cooling requirement. The aim of this paper is to highlight the impact of using hydrogen as a fuel in gas turbine combustors. It is perceived that this new micromix concept based combustor would also help in achieving low emissions and better performance. Possibilities for lowering NOx emissions when using hydrogen as a fuel in new designs of micromix combustor are also discussed.

Model Based Control of Emissions and Pulsations in a Premixed Combustor Using Fuel Staging

2009 ◽  
Author(s):  
Arnaud Lacarelle ◽  
Jonas P. Moeck ◽  
Christian O. Paschereit ◽  
Gregor Gelbert ◽  
Rudibert King
Keyword(s):  
Time Delays ◽  
Mixing Model ◽  
Extremum Seeking ◽  
Step Response ◽  
Nox Emissions ◽  
Pressure Pulsations ◽  
Model Based Control ◽  
One Dimensional ◽  
Mixing Quality ◽  
Fuel Staging

A mixing model of a swirl inducing premixed burner is derived from non-reacting investigation and used to control the fuel staging of the burner to ensure stability and low NOx emissions. The convective time delays, critical for the combustor stability, are obtained after identification of a step response of the outlet concentration with a one dimensional mixing model. The steady mixing is used to evaluate quantitatively the mixing quality which correlates with NOx emissions. Time delays as well as scalar unmixedness criteria derived from those measurements are used to predict the combustor stability and NOx emissions maps for different injection configurations at one operating point. The resulting model is used to extend an Extremum Seeking Controller, which adjusts the fuel repartition to reduce the pressure pulsations and NOx emissions.

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