Session: 10-04-01: Fluid Measurements and Instrumentation

Paper Number: 113535

113535 - Spatially Resolved Ion Current Density Measurements With a Transient Insertion Langmuir Probe 

This work presents a novel technique for constructing spatially resolved ion densities from spinning disc Langmuir probe (SDLP) measurements in a flame.  By measuring electrical currents from the probe when a bias voltage is applied, the Langmuir probe famously allows researchers to infer the charge density at the probe surface.  For decades, by limiting the residence time in the plasma, wires on spinning discs have extended this technique to flames that threaten to melt or damage the probe.  However, in flames of industrial relevance, the ion density is strongly non-uniform, and the current measurement is an integral of the current density along the probe's length, so spatial information is lost in a single measurement.  In the present work, a two-dimensional Fourier expansion of current density in a flame cross-section is constructed using least square regression from many individual wire measurements in the flame.  In principle, the approach resembles the tomographic transformations used in medical scanners, but it is distinct because the integration does not fully penetrate the domain.  Unfortunately, the typical numerical advantages that arise from the orthogonality of Fourier basis functions is lost when integrals are not evaluated over an integer number of periods, but the Fourier expansion still provides an intuitive interpolation scheme, where the maximum wavenumber in the expansion provides a natural spatial filter.  Presented here are (1) a formulation for the current density, (2) a brief derivation of the least-square model from the wire measurements, (3) criteria for the highest wavenumber allowed in the expansion, (4) solution of a prototype problem generated from a false probe current data set, (5) description of an experiment used to measure probe currents in an oxyfuel cutting torch preheat flame, (6) solution for spatially resolved current density in the oxyfuel flame.  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.  It is found that the Fourier expansion is vulnerable to artifacts when current density gradients are parallel to the wire trajectory, but otherwise the analysis faithfully recreates the ``truth'' data set.  Images constructed from the oxyfuel flame show small rings with intense current density in the inner cones and a quasi-uniform background current in the outer cone. 

Presenting Author: Christopher Martin Pennsylvania State University - Altoona

Presenting Author Biography: Dr. Martin is an Associate Professor of Mechanical Engineering at Penn State's Altoona College. Before returning to academe, he was a plasma torch R&D engineer with ESAB Welding and Cutting. His research focuses on ion currents in high temperature flames, and industrial sensing and control.

Authors:

Christopher Martin Pennsylvania State University - Altoona
Jacob Orr Penn State Altoona
S. M. Mahbobur Rahman Virginia Tech
Alexandrina Untaroiu Virginia Tech