Merrill W. Beckstead

A REVIEW OF RIJKE TUBES, RIJKE BURNERS AND RELATED DEVICES

Abstract Thermoacoustic devices related to the Rijke tube are reviewed. Most modern thermoacoustic devices use as a heat source a heated wire or ribbon or a premixed gas flame anchored to a metal gauze, metal tube matrix or porous ceramic frit. Numerous experiments have confirmed that combustion-driven oscillations in tube devices are ‘Rijke tube’ or ‘organ pipe’ oscillations, i.e. frequencies are the same as those in a Rijke tube or organ pipe of the same length and with the same gas temperature distribution. Experiments have also established the validity of Rayleighs stability criterion for the development of heat-driven acoustic oscillations. Modern mathematical analyses of acoustic oscillations in Rijke-type devices begin with a common basis: equations for mass, momentum and energy conservation. Almost all analyses assume constant hot section temperature. The main difference between analyses is the manner in which the oscillating response of the heat source is modeled. Frequency of oscillation is governed primarily by the acoustic speed of gases in a chamber. Thus, the flame or heater response model used does not significantly effect frequency predictions. However, the flame or heater response model can have a dramatic effect on predicted growth rates. Since flame models influence predicted response of Rijke burners, some work with vibrating flames is also reviewed. Flame response models vary widely, from simple phenomenological models to sophisticated models based on large activation energy asymptotic theory.

The Simulation of the Combustion of Micrometer-Sized Aluminum Particles with Steam

The Liang and Beckstead aluminum-particle combustion model has been successfully joined with a detailed chemical-kinetic mechanism. The model has been used to investigate the effect of oxidizer concentration, initial temperature, and pressure on the combustion of steam and micrometer-sized aluminum particles. The results compare well with experimental data investigating the effects of initial temperature and oxidizer concentration on burn time. The simulations and experimental data have opposite trends for the change in burn time as the pressure increased. The calculated flame temperature increases with increasing pressure, initial temperature, and oxidizer concentration. The effects of particle diameter, initial temperature, and pressure on the calculated flame temperature, flame structure, and species profiles were also investigated.

A numerical model for temperature gradient and particle effects on Rijke burner oscillations

Abstract Equations that describe acoustic oscillations in a Rijke burner have been developed. Eigenvalues giving frequencies and growth rates of acoustic modes can be calculated from these equations. In their most general form, these acoustic equations include the effects of nonuniform gas temperature and entrained, burning particles. In general, analytical solution of the equations is not possible. A computer program has been developed that uses numerical methods to calculate eigenvalues from the general equations. For some limiting cases, analytical solution of the equations is possible. Analytical solutions are presented for three such cases. Eigenvalues predicted by the numerical model compare well to the analytical solutions. The Bailey and McIntosh flame-acoustic interaction models were tested with the computer program. Predicted frequencies and growth rates agreed well with experimental data when heat loss was taken into account. The program matched one experimental frequency and growth rate exactly when a time lag was added to the Bailey model. The McIntosh model did nearly as well without any adjustments. A particle combustion-acoustic interaction model for burning aluminum particles has been developed. This model was also tested in the Rijke burner model. The predictions show qualitative but not quantitative agreement with experimental measurements of particle combustion effects. A mechanism is suggested that may explain the discrepancy.

COMBUSTION MODELING OF GLYCIDYL AZIDE POLYMER WITH DETAILED KINETICS

ABSTRACT The steady-state combustion of the monopropellant glycidyl azide polymer (GAP) has been modeled using a one-dimensional, three-phase numerical model. Combustion characteristics of four formulations of cured GAP with varying amounts of the curing agent hexamethylene diisocyanate (HMDI) have been modeled. A two-step global decomposition condensed-phase kinetic mechanism has been developed, based on experimental data. A detailed gas-phase kinetic mechanism, with 460 reactions and 74 species, has been assembled and used. The combustion has been modeled over pressures of 5–100 atm and initial temperatures of 298 ± 50 K. The calculated combustion characteristics include the burning rate, pressure exponent, temperature sensitivity, surface and flame temperatures, temperature and species profiles, and condensed- and gas-phase heat released. The model calculations have been compared with various experimental data, and most of the calculations and their trends seem to be consistent with experimental data. The GAP content of the GAP-HMDI formulation has been predicted to have a significant influence on the burning rate. The calculated GAP-HMDI burning rates were ∼1.05–1.93 cm/s at 70 atm, increasing with the GAP content of the formulation. The calculated pressure exponents were ∼0.4 and the calculated temperature sensitivities were ∼0.01–0.014 K−1. The condensed phase plays a significant role for GAP combustion. Parametric studies have been performed to study the effect of varying the values of reaction parameters and thermophysical properties such as specific heat and thermal conductivity.

Modeling and Simulation of Combustion of Solid Propellant Ingredients Using Detailed Chemical Kinetics

Over the past several years, the capability of modeling premixed combustion using detailed kinetic mechanisms has been evolving and successfully applied to solid propellant ingredients. The approach utilizes a one-dimensional description of both the gas and condensed phases of a homogeneous ingredient. Emphasis has been placed on steady state combustion, but there has also been limited applications describing both ignition and oscillatory combustion. Initially, a significant effort was placed on modeling RDX combustion over a wide range of ambient conditions, resulting in burning rates and flame structures that agree closely with experimental measurements. As part of the analysis, a gas phase mechanism based on 45 species and 232 reaction steps was developed, which has subsequently provided a basis for application to other propellant ingredients. The approach not only allows calculating burning rate as a function of pressure, but also temperature sensitivity and spatial distributions of temperature and species concentrations. Models have also been adapted for HMX, GAP, GAP/RDX, GAP/HMX, NG, BTTN, GAP/BTTN, ADN, AP, AP/HTPB, etc. The principle challenge is determining a reaction mechanism for the condensed phase.

Combustion Instability Additive Investigation

Combustion stability additives like zirconium carbide (ZrC), aluminum oxide (AO o is the angular frequency, ro is the particle relaxation time:

Modeling multiphase effects in the combustion of HMX and RDX

RDX and HMX have similar structures and bur ning rates. However, the burning -rate temperature sensitivity ( �p) is significantly different between RDX and HMX at low pressures. Recent efforts to mathematically model the steady -state combustion of RDX and HMX with detailed chemical kinetics in the gas phase and distributed decomposition in the condensed phase hav e succeeded in modeling burning rates at a specific initial temperature. However, all have failed to calculate thep trends of HMX at low pressure and differentiate thep of RDX and HMX. RDX and HMX both burn with a thin multi -phase surface of bubbles i n liquid. A liquid -bubble submodel was developed to improvep calculations. Calculations including the liquid -bubble submodel produced the desired trends in both the HMX and RDXp values. To predict the observed HMXp values with the model, first, evapo ration in the sub -surface was limited near the gas -liquid surface. Second, the difference in surface temperature at different initial temperatures was adjusted to follow trends in experimental data. Third, the Marangoni effect was added to the calculation of the bubble velocities. At low pressures, the Marangoni effect was found to be greater in the higher initial temperature calculations because the temperature gradient was steeper. For RDX, there was little change in the calculatedp values with the addition of the liquid - bubble submodel. This is the first combustion model with detailed gas phase kinetics to predict the properp trends for both HMX and RDX.

RDX/GAP Pseudo-Propellant Combustion Modeling

The steady-state combustion of mixtures of RDX/GAP has been modeled using a 1dimensional, three-phase numerical model, with detailed chemical kinetics. Several compositions have been modeled, from 100% RDX/0% GAP to 0% RDX/100% GAP. The approach used in this work has been to first model and validate monopropellant RDX and GAP. These monopropellant kinetic models were then combined to get the pseudopropellant model, thus limiting the uncertainties in model inputs. Based on experimental decomposition studies of RDX and GAP in the literature, a condensed-phase kinetic model consisting of four global reactions has been assembled. The evaporation of RDX is also included. A detailed gas-phase kinetic mechanism has been assembled based on several mechanisms reported in the literature. The gas-phase mechanism consists of 83 species and 534 reactions and has been used previously in modeling several monopropellants and pseudo-propellants. The improvement and validation of this universal gas phase mechanism is one of the main goals of this work. The combustion has been modeled over a pressure range of 1 atm-136 atm (2000 psia), and initial temperatures of 298 ± 50 K. The calculated combustion characteristics include the burning rate, pressure exponent, temperature sensitivity, surface and flame temperatures, temperature and species profiles, and condensed and gas-phase heat releases.

Multi-Phase Combustion Modeling of Ammonium Dinitramide Using Detailed Chemical Kinetics 1

*† ‡ § A multi-phase model for the combustion of ammonium dinitramide (ADN) monopropellant is presented. As part of the work, an in depth study concerning ADN combustion has been undertaken. An extensive literature review has been conducted to extract both experimental data and qualitative theories concerning ADN combustion. Analyses and reviews are presented pertaining to some of the major theories. Based on the literature review a numerical model has also been developed for ADN using the BYU PHASE3 combustion code. The model accurately predicts burning rates, temperature and species profiles, and other combustion characteristics of ADN at pressures preceding the unstable region (20 to 100 atm) of combustion. Burning rates are also predicted in the unstable zone and at higher pressures. Results are discussed and proposed modifications to the present condensed phase model are presented. Nomenclature b = constant in burning rate correlation P = pressure n = pressure exponent