Walter Gill

The Frank-Kamenetskii problem revisited. Part I. Boundary conditions of first kind

Abstract The classical steady-state thermal ignition problem in the three one-dimensional geometries is considered. The well-known method of expanding the exponent first suggested by Frank-Kamenetskii is modified by performing the expansion about the unknown midplane temperature. Analytical expressions were obtained for the critical conditions that will allow the handling of more complex boundary conditions. The results are compared with the existing exact and numerical solutions.

Quantitative, three-dimensional imaging of aluminum drop combustion in solid propellant plumes via digital in-line holography

Burning aluminized propellants eject reacting molten aluminum drops with a broad size distribution. Prior to this work, in situ measurement of the drop size statistics and other quantitative flow properties was complicated by the narrow depth-of-focus of microscopic videography. Here, digital in-line holography (DIH) is demonstrated for quantitative volumetric imaging of the propellant plume. For the first time, to the best of our knowledge, in-focus features, including burning surfaces, drop morphologies, and reaction zones, are automatically measured through a depth spanning many millimeters. By quantifying all drops within the line of sight, DIH provides an order of magnitude increase in the effective data rate compared to traditional imaging. This enables rapid quantification of the drop size distribution with limited experimental repetition.

Sandia Heat Flux Gauge Thermal Response and Uncertainty Models

The San&a Heat Flux Gauge (HFG) was developed as a rugged, cost-effective technique for performing steady state heat flux measurements in the pool fire environment. The technique involves reducing the time-temperature history of a thin metal plate to an incident heat flux via a dynamic thermal model, even though the gauge is intended for use at steady state. In this report, the construction of the gauge is reviewed. The thermal model that describes the dynamic response of the gauge to the f~e environment is then advanced and it is shown how the heat flux is determined from the temperature readings. This response model is based on first principles, with no empirically adjusted constants. A validation experiment is presented where the gauge was exposed to a step input of radiant heat flux. Comparison of the incident flux, determined from the thermal response model, with the known flux input shows that the gauge exhibits an noticeable time lag. The uncertainty of the measurement is analyzed, and an uncertainty model is put forth using the data obtained from “the experiment. The uncertainty model contains contributions from seventeen separate sources loosely categorized as being either from uncontrolled variability, missing physics, or simplifying assumptions. As part of the missing physics, an empirical constant is found that compensates for the gauge time lag. Because this compensation is incorporated into the uncertainty model instead of the response model, this information can be used to advantage in analyzing pool fire data by causing large uncertainties in non-steady state situations. A short general discussion on the uncertainty of the instrument is presented along with some suggested design changes that would facilitate the determination and reduction of the measurement uncertainty.

Thermocouple Response in Fires, Part 1: Considerations in Flame Temperature Measurements by a Thermocouple

This PIRT exercise identifies a number of factors which can influence thermocouple readings made in fires. Identified factors are: (a) the fuel/oxidizer equivalence ratio and its effect on readings, (b) the influence of the state of oxidation and variation with time for the thermocouple sheath, (c) the convection coefficient models and how experimental readings are influenced by thermocouple diameter and yaw angle, (d) response time of a MIMS thermocouple, and (e) thermocouple end effects.

Problems Encountered in Fluctuating Flame Temperature Measurements by Thermocouple

Some thermocouple experiments were carried out in order to obtain sensitivity of thermocouple readings to fluctuations in flames and to determine if the average thermocouple reading was representative of the local volume temperature for fluctuating flames. The thermocouples considered were an exposed junction thermocouple and a fully sheathed thermocouple with comparable time constants. Either the voltage signal or indicated temperature for each test was recorded at sampling rates between 300-4,096 Hz. The trace was then plotted with respect to time or sample number so that time variation in voltage or temperature could be visualized and the average indicated temperature could be determined. For experiments where high sampling rates were used, the signal was analyzed using Fast Fourier Transforms (FFT) to determine the frequencies present in the thermocouple signal. This provided a basic observable as to whether or not the probe was able to follow flame oscillations. To enhance oscillations, for some experiments, the flame was forced. An analysis based on thermocouple time constant, coupled with the transfer function for a sinusoidal input was tested against the experimental results.

Estimates of the Extent and Character of the Oxygen-Starved Interior in Large Pool Fires

Based on data from large pool fire experiments and computational fire field model simulations, the size, shape, and character of the oxygen-starved interior in large pool fires is estimated. In the interior of the fire and near the pool surface, low average and low mean deviation temperatures were noted in experimental data for low wind conditions. These trends tend to indicate the presence of a non-combusting region. Using average and mean deviation temperature distributions (supplemented by heat flux measurements) from several data sets, the spatial extent of the vapor dome is estimated for a range of wind conditions. These estimates are compared with fire field model results of temperature and fuel/air concentration distributions. Predicted and measured temperature trends, supported by heat flux data, illustrate the importance of object placement within the fire during system fire survivability testing. The presence of this region also supplements conventional pool fire representations which are based on a continuous flame zone which extends to the pool surface.

A joint computational and experimental study to evaluate Inconel-sheathed thermocouple performance in flames.

A joint experimental and computational study was performed to evaluate the capability of the Sandia Fire Code VULCAN to predict thermocouple response temperature. Thermocouple temperatures recorded by an Inconel-sheathed thermocouple inserted into a near-adiabatic flat flame were predicted by companion VULCAN simulations. The predicted thermocouple temperatures were within 6% of the measured values, with the error primarily attributable to uncertainty in Inconel 600 emissivity and axial conduction losses along the length of the thermocouple assembly. Hence, it is recommended that future thermocouple models (for Inconel-sheathed designs) include a correction for axial conduction. Given the remarkable agreement between experiment and simulation, it is recommended that the analysis be repeated for thermocouples in flames with pollutants such as soot.

Thermocouple Response in Fires, Part 2: Validation of Virtual Thermocouple Model for Fire Codes

A virtual thermocouple model for high fidelity multiphysics computer simulation is introduced in this article. Detailed thermocouple and gas temperature (Coherent Anti-Stokes Raman Scattering) measurements were performed using a well-controlled, adiabatic, flat-flame Hencken burner, which provided data for validating the thermocouple model in a Sandia National Laboratories fire code. Comparison of simulation results to test data indicated a mean error of 6% between the thermocouple reading and predicted temperature.

Imaging of Flame Behavior in Flickering Methane/Air Diffusion Flames

During this study, flow visualization through the use of imaging provided visual data of the events that occurred as the flame oscillated. Imaging was performed in two different ways: 1) the first method was phase-locked imaging to capture a detailed history by simply advancing the phase angle during each image capture, 2) the second method involved high-speed imaging to gather visual image data of a natural or forced oscillating flame. For visualization, two items were considered. The first one was the shape of the flame envelope as it evolved during one oscillation cycle. From the data gathered, it was confirmed that the flame stretched in the vertical direction before quenching in the region near its center. The second consideration was imaging of the oxidizer (air) in the region immediately outside the flame. This was done by imaging the laser light reflected from particles seeded into the flow, which revealed formation of vortical structures in those regions where quenching had occurred. It was noted that quenching took place primarily by the entrainment of fresh non-reacting air into the flame. The quenching process was in turn responsible for the oscillatory behavior.

The Frank-Kamenetskii problem revisited, part III: The moving flame front

Abstract The basic flame propagation theory proposed in part by Frank-Kamenetskii was modified to show that flame behavior can be predicted in a two-zone flame structure without eliminating the ignition temperature. The ignition temperature can be retained when the inert zone maintains the reaction zone in a critical condition. By retaining the ignition temperature and by maintaining the integrity of the zone matching equations, the two step flame model we have developed predicts flame behavior in either zone.