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A three-dimensional computational model is presented in this paper that illustrates the detailed electrical characteristics, and the current–voltage (i–v) relationship throughout the preheating process of premixed methane-oxygen oxyfuel cutting flame subject to electric bias voltages. As such, the equations describing combustion, electrochemical transport for charged species, and potential are solved through a commercially available finite volume computational fluid dynamics (CFD) code. The reactions of the methane-oxygen (CH4–O2) flame were combined with a reduced mechanism, and additional ionization reactions that generate three chemi-ions, H3O+, HCO+, and e−, to describe the chemistry of ions in flames. The electrical characteristics such as ion migrations and ion distributions are investigated for a range of electric potential, V ∈ [−5 V, +5 V]. Since the physical flame is comprised of twelve Bunsen-like conical flames, inclusion of the third dimension imparts the resolution of fluid mechanics and the interaction among the individual cones. It was concluded that charged “sheaths” are formed at both torch and workpiece surfaces, subsequently forming three distinct regimes in the i–v relationship. The i–v characteristics obtained from this study have been compared to the previous experimental and two-dimensional computational model for premixed flame. In this way, the overall model generates a better understanding of the physical behavior of the oxyfuel-cutting flames, along with more validated i–v characteristics. Such understanding might provide critical information toward achieving an autonomous oxyfuel-cutting process.

 

Recent use of ion currents as a sensing strategy in the mechanized oxyfuel cutting process motivated a series of studies which revealed that the steel work piece contributes secondary ions in addition to the primary ions classically identified in the oxyfuel flame. In this work, we present a computational model that has linked carbon-related chemi-ions as a source of secondary ions in preheating stage of oxyfuel cutting process subject to electric bias voltages. The flames' response to the electric field at different positive and negative polarities manifested a better understanding of the physical behavior of current-voltage (i-v) relationship. While copper surface exhibits stable and repeatable i-v characteristics, sporadically enhanced current was observed in positive saturation regime for steel surface, and this is believed to be due to the presence of secondary chemi-ions. To this extent, a source term of gaseous carbon has been assigned to mimic the ‘work surface’ reactions. The hypothesis is that since carbon is an important element, it will be diffusing out of the steel surface and evaporate into the flame.

 

A three-dimensional (3D) computational model is presented in this paper that illustrates the detailed electrical characteristics, and the current-voltage (i-v) relationship throughout the preheating process of premixed methane-oxygen oxyfuel cutting flame subject to electric bias voltages. As such, the equations describing combustion, electrochemical transport for charged species, and potential are solved through a commercially available finite-volume Computational Fluid Dynamics (CFD) code. The reactions of the methane-oxygen (CH4 – O2) flame were combined with a reduced mechanism, and additional ionization reactions that generate three chemi-ions, H3O+, HCO+, and e−, to describe the chemistry of ions in flames. The electrical characteristics such as ion migrations and ion distributions are investigated for a range of electric potential, V ∈ [−5V, +5V]. Since the physical flame is comprised of twelve Bunsen-like conical flame, inclusion of the third dimension imparts the resolution of fluid mechanics and the interaction among the individual cones. It was concluded that charged ‘sheaths’ are formed at both torch and workpiece surfaces, subsequently forming three distinct regimes in the i-v relationship. The i-v characteristics obtained out of the current study have been compared to the previous experimental and two-dimensional (2D) computational model for premixed flame. In this way, the overall model generates a better understanding of the physical behavior of the oxyfuel cutting flames, along with a more validated i-v characteristics. Such understanding might provide critical information towards achieving an autonomous oxyfuel cutting process.

 

This paper presents a computational model to study ion and electron transportation and current-voltage characteristics inside a methane-oxygen flame. A commercial software is used to develop the model by splitting the simulation into the combustion and electrochemical transportation parts. A laboratory experiment is used to compare the results from the model. The initial and boundary conditions represented in the model are similar to the experimental conditions in the laboratory experiment.

In the combustion part, the general GRI3.0 mechanism plus three additional ionization reactions are applied and results are then used as input into the electrochemical transportation part. A particular inspection line is created to analyze the results of the electrochemical transportation part. Ion, electron number density, and current density are studied along the interval from −40V to 40V electric potential. The ions are heavier and more difficult to move than electrons. The results show that at both torch and work surfaces charged sheaths are formed and cause three different regions of current-voltage relations.

 

This work presents a novel technique for constructing spatially resolved ion densities from Transient Insertion Langmuir Probe (TIL Probe) measurements in a flame. Similar to a tomographic transformation, this technique is used to deduce the spatial distribution of ions in a flame from many individual measurements that are integrated along a probe’s length. We demonstrate the approach in the oxyfuel cutting torch preheat flame, which presents two severe challenges for electrical measurements: (1) temperatures over 3,000K destroy most probes made from alloys with appropriate chemical stability, and (2) the relevant length scales are on the order 0.15 mm. Presented here are (1) a Fourier series formulation for the current density, (2) a least-square problem for calculating the coefficients, (3) criteria for the highest wavenumber allowed in the expansion, (4) description of an experiment used to measure probe currents in an oxyfuel cutting torch preheat flame, (5) solution for spatially resolved current density in the oxyfuel cutting torch flame. Images of ion current density are produced with a resolution of 0.15 mm (0.0059 in), exhibiting peak current densities around 14 𝜇A/mm. It is found that low-signal regions in the “shadow” of high-signal regions can suffer from signal-to-noise ratio problems due to natural fluctuations in the flame, and improvements are proposed to mitigate the effect. It is found that the numerical cost of setting up the resulting Hermitian-matrix linear problem far exceeds the numerical cost of inversion. High-level packages like Python and MATLAB are far too slow, so a multi-threaded algorithm is implemented in C, and the LAPACKE C library is used for efficient linear algebra support. 

This work presents a novel technique for constructing spatially resolved ion densities from Transient Insertion Langmuir Probe (TIL Probe) measurements in a flame. Similar to a tomographic transformation, this technique is used to deduce the spatial distribution of ions in a flame from many individual measurements that are integrated along a probe's length. We demonstrate the approach in the oxyfuel cutting torch preheat flame, which presents two severe challenges for electrical measurements: (1) temperatures over 3,000K destroy most probes made from alloys with appropriate chemical stability, and (2) the relevant length scales are on the order 0.15 mm. Presented here are (1) a Fourier series formulation for the current density, (2) a least-square problem for calculating the coefficients, (3) criteria for the highest wavenumber allowed in the expansion, (4) description of an experiment used to measure probe currents in an oxyfuel cutting torch preheat flame, (5) solution for spatially resolved current density in the oxyfuel cutting torch flame. Images of ion current density are produced with a resolution of 0.15 mm (0.0059 in), exhibiting peak current densities around 14 $\mu$A/mm. It is found that low-signal regions in the ``shadow'' of high-signal regions can suffer from signal-to-noise ratio problems due to natural fluctuations in the flame, and improvements are proposed to mitigate the effect. It is found that the numerical cost of setting up the resulting Hermitian-matrix linear problem far exceeds the numerical cost of inversion. High-level packages like Python and MATLAB are far too slow, so a multi-threaded algorithm is implemented in C, and the LAPACKE C library is used for efficient linear algebra support. 

This work presents a novel technique for constructing spatially resolved ion densities from Transient Insertion Langmuir Probe (TIL Probe) measurements in a flame. Similar to a tomographic transformation, this technique is used to deduce the spatial distribution of ions in a flame from many individual measurements that are integrated along a probe's length. We demonstrate the approach in the oxyfuel cutting torch preheat flame, which presents two severe challenges for electrical measurements: (1) temperatures over 3,000K destroy most probes made from alloys with appropriate chemical stability, and (2) the relevant length scales are on the order 0.15 mm. Presented here are (1) a Fourier series formulation for the current density, (2) a least-square problem for calculating the coefficients, (3) criteria for the highest wavenumber allowed in the expansion, (4) description of an experiment used to measure probe currents in an oxyfuel cutting torch preheat flame, (5) solution for spatially resolved current density in the oxyfuel cutting torch flame. Images of ion current density are produced with a resolution of 0.15 mm (0.0059 in), exhibiting peak current densities around 14 $\mu$A/mm. It is found that low-signal regions in the ``shadow'' of high-signal regions can suffer from signal-to-noise ratio problems due to natural fluctuations in the flame, and improvements are proposed to mitigate the effect. It is found that the numerical cost of setting up the resulting Hermitian-matrix linear problem far exceeds the numerical cost of inversion. High-level packages like Python and MATLAB are far too slow, so a multi-threaded algorithm is implemented in C, and the LAPACKE C library is used for efficient linear algebra support.