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Purpose A higher-order implicit shock-capturing scheme is presented for the Euler equations based on time linearization of the implicit flux vector rather than the residual vector. Design/methodology/approach The flux vector is linearized through a truncated Taylor-series expansion whose leading-order implicit term is an inner product of the flux Jacobian and the vector of differences between the current and previous time step values of conserved variables. The implicit conserved-variable difference vector is evaluated at cell faces by using the reconstructed states at the left and right sides of a cell face and projecting the difference between the left and right states onto the right eigenvectors. Flux linearization also facilitates the construction of implicit schemes with higher-order spatial accuracy (up to third order in the present study). To enhance the diagonal dominance of the coefficient matrix and thereby increase the implicitness of the scheme, wave strengths at cell faces are expressed as the inner product of the inverse of the right eigenvector matrix and the difference in the right and left reconstructed states at a cell face. Findings The accuracy of the implicit algorithm at Courant–Friedrichs–Lewy (CFL) numbers greater than unity is demonstrated for a number of test cases comprising one-dimensional (1-D) Sod’s shock tube, quasi 1-D steady flow through a converging-diverging nozzle, and two-dimensional (2-D) supersonic flow over a compression corner and an expansion corner. Practical implications The algorithm has the advantage that it does not entail spatial derivatives of flux Jacobian so that the implicit flux can be readily evaluated using Roe’s approximate Jacobian. As a result, this approach readily facilitates the construction of implicit schemes with high-order spatial accuracy such as Roe-MUSCL. Originality/value A novel finite-volume-based higher-order implicit shock-capturing scheme was developed that uses time linearization of fluxes at cell interfaces.

Liquid vaporization under thermodynamic phase non-equilibrium condition at the gas-liquid interface is investigated over a wide range of fluid state typical of many liquid-fueled energy conversion systems. The validity of the phase-equilibrium assumption commonly used in the existing study of liquid vaporization is examined using molecular dynamics theories. The interfacial mass flow rates on both sides of the liquid surface are compared to the net vaporization rate through an order-of-magnitude analysis Results indicated that the phase-equilibrium assumption holds valid at relatively high pressures and low temperatures, and for droplets with relatively large initial diameters (for example, larger than 10 µm for vaporizing oxygen droplets in gaseous hydrogen in the pressure range from 10 atm to the oxygen critical state). Droplet vaporization under superheated conditions is also explored using classical binary homogeneous nucleation theory, in conjunction with a real-fluid equation of state. It is found that the bubble nucleation rate is very sensitive to changes in saturation ratio and pressure; it increases by several orders of magnitude when either the saturation ratio or the pressure is slightly increased. The kinetic limit of saturation ratio decreases with increasing pressure, leading to reduced difference between saturation and superheat conditions. As a result, the influence of non-equilibrium conditions on droplet vaporization is lower at a higher pressure.

Molecular dynamics simulations are conducted to investigate the effect of melting on energy accommodation coefficient (EAC) of Al-noble gas systems. The accommodation coefficients are computed for a gas temperature of 3000 K and slab temperatures in the range of 600-1500 K. Three different noble gases: helium, argon and xenon, are considered. Density functional theory (DFT) derived gas-metal interatomic potentials are used to obtain accurate predictions of accommodation coefficients. An abrupt jump in the accommodation coefficient upon melting is observed for argon and xenon, whereas the accommodation coefficient is negligibly affected for helium gas. The effects of gas-metal potential and gas atom mass are probed separately and it is found that the gas-metal potential has a negligible effect on the magnitude of EAC jumps. The gas atom mass, on the other hand, exerted a strong effect; heavier gases exhibited greater EAC jumps than lighter gases. The underlying physics is then unraveled by studying the effects of surface roughness and lattice dynamics on accommodation coefficient. Surface roughness increases the tangential EACs significantly for all gases, but the normal EACs are not as strongly amplified. Analysis of vibrational density of states of solid and liquid slabs suggests the activation of low frequency vibrational modes upon melting. This coupled with the roughening of surface upon melting results in an abrupt jump in the accommodation coefficient, especially for heavier gases.

First principles informed atomistic-scale simulations are conducted to compute equilibrium energy accommodation coefficients of aluminum-noble gas systems for a temperature range of 25-800 K. Densi...

Molecular dynamics (MD) simulations and thermodynamic analysis are conducted to investigate size effect on melting point of alumina nanocrystals. Different geometries including spherical and cubic particles, planar thin films, and spherical shells are considered. The atomic interactions in MD simulations are captured using Vashishta et al.’s potential function. Thermophysical properties of concern such as the bulk melting point, latent heat, density, and surface free energy are calculated using MD simulations and fed as inputs to the thermodynamic models. Predictions of MD simulations are compared with those of thermodynamic melting models. For all cases, heterogeneous melting is observed, where nucleation of the melt phase occurred at the free surface and the melting front propagated into the interior regions of the crystal. Results suggest that the melting point drops sharply below a threshold particle size, which is a function of the geometry. The threshold particle size of spherical particles is greater than that of planar films. Melting point predictions are quite sensitive to the choice of thermodynamic model and thermophysical property values. To ascertain the effects of curvature and core size on shell melting point, melting points of planar semi-infinite films and spherical shells are calculated and compared. For particle sizes of concern to practical applications (∼100 nm or greater), shell melting point is nearly independent of core size and the semi-infinite planar film approximation is reasonable to estimate the melting point of alumina shells. In this size regime, melting points of 2–4 nm thick spherical oxide shells vary roughly in the range of 1800–2350 K, which is relatively close to the bulk melting point. Results of the present study do not indicate an enormous depression in the melting point, as the previous works suggest. This implies that the melting point depression of the oxide layer cannot fully describe the scatter in the measured ignition temperature of aluminum particles., by Nikhil Joshi, Nilkumar Mathur, Tejas Mane and Dilip Sundaram

Multiscale modeling and simulation of heat transfer between alumina nanoparticles and helium gas is conducted. Density functional theory (DFT) simulations are first performed to calculate adsorption energies and derive pair potentials for alumina-helium system. The obtained well depths are 2.794 meV and 0.921 meV for Al-He and O-He interactions, substantially lower than the values obtained using the Lorentz-Berthelot mixing rules. Subsequently, DFT derived potentials are used to conduct molecular dynamics (MD) simulations and calculate accommodation coefficients for solid temperatures in the range of 1700-2100 K and gas temperature of 300 K. The calculated accommodation coefficients are of the order of 0.1 and are weakly dependent on the solid temperature. Predictions are within the upper bound of 0.4 obtained using Altman's model for materials and conditions considered in the present study. MD derived accommodation coefficients are then fed as inputs to a macroscopic heat transfer model to predict temporal evolution of temperature of an alumina nanoparticle placed in helium gas. The proposed model captures the temporal decay of particle temperature reasonably well until about 200 ns. The disparity between predictions and experimental data is primarily attributed to different reasons such as heating up of the gas in a confined environment and sintering and aggregation of particles.

Nano aluminum particles have received considerable attention in the combustion community; their physicochemical properties are quite favorable as compared with those of their micron-sized counterparts. The present work provides a comprehensive review of recent advances in the field of combustion of nano aluminum particles. The effect of the Knudsen number on heat and mass transfer properties of particles is first examined. Deficiencies of the currently available continuum models for combustion of nano aluminum particles are highlighted. Key physicochemical processes of particle combustion are identified and their respective time scales are compared to determine the combustion mechanisms for different particle sizes and pressures. Experimental data from several sources are gathered to elucidate the effect of the particle size on the flame temperature of aluminum particles. The flame structure and the combustion modes of aluminum particles are examined for wide ranges of pressures, particle sizes, and oxidizers. Key mechanisms that dictate the combustion behaviors are discussed. Measured burning times of nano aluminum particles are surveyed. The effects of the pressure, temperature, particle size, and type and concentration of the oxidizer on the burning time are discussed. A new correlation for the burning time of nano aluminum particles is established. Major outstanding issues to be addressed in the future work are identified.

Metal particles are attractive candidate fuels for various propulsion and energy-conversion applications, primarily due to their high energy densities. Micron-sized particles present several drawbacks, such as high ignition temperatures and particle agglomeration, resulting in low energy-release rates. Nanoparticles, on the other hand, are quite attractive due to their unique and favorable properties, which are attributed to their high specific surface area and excess energy of surface atoms. As a result, there is a growing interest in employing metal nanoparticles in propulsion and energy-conversion systems. The present work provides a comprehensive review of the advances made over the past few decades in the areas of synthesis, properties, and applications of metal-based energetic nanomaterials. An overview of existing methods to synthesize nanomaterials is first provided. Novel approaches to passivate metal nanoparticles are also discussed. The physicochemical properties of metal nanoparticles are then examined in detail. Low-temperature oxidation processes, and ignition and combustion of metal nanoparticles are investigated. The burning behaviors of different energetic material formulations with metal nanoparticles such as particle-laden dust clouds, solid propellants, liquid fuels and propellants, thermite materials, and inter-metallic systems are reviewed. Finally, deficiencies and uncertainties in our understanding of the field are identified, and directions for future work are suggested., by Dilip Sundaram, Vigor Yang and Richard A. Yetter

The presence of artificial correlations associated with Green-Kubo (GK) thermal conductivity calculations is investigated. The thermal conductivity of nano-suspensions is calculated by equilibrium molecular dynamics (EMD) simulations using GK relations. Calculations are first performed for a single alumina (Al2O3) nanoparticle dispersed in a water medium. For a particle size of 1 nm and volume fraction of 9%, results show enhancements as high as 235%, which is much higher than the Maxwell model predictions. When calculations are done with multiple suspended particles, no such anomalous enhancement is observed. This is because the vibrations in alumina crystal can act as low frequency perturbations, which can travel long distances through the surrounding water medium, characterized by higher vibration frequencies. As a result of the periodic boundaries, they re-enter the system resulting in a circular resonance of thermal fluctuations between the alumina particle and its own image, eventually leading to artificial correlations in the heat current autocorrelation function (HCACF), which when integrated yields abnormally high thermal conductivities. Adding more particles presents 'obstacles' with which the fluctuations interact and get dissipated, before they get fed back to the periodic image. A systematic study of the temporal evolution of HCACF indicates that the magnitude and oscillations of artificial correlations decrease substantially with increase in the number of suspended nanoparticles., by Murali Gopal Muraleedharan, Dilip Sundaram, Asegun Henry and Vigor Yang

The combustion-wave propagation of nickel-coated aluminum particles is studied theoretically for packing densities in the range of 10–100% of the theoretical maximum density. Emphasis is placed on the effect of packing density on the burning properties. The energy conservation equation is solved numerically and the burning rate is determined by tracking the position of the flame front. Atomic diffusion coefficients and reaction rate of isolated nickel-coated aluminum particles are input parameters to the model. The burning behaviors and combustion wave structures are dictated by the heat transfer from the flame zone to the unburned region. Five different models for the effective thermal conductivity of the mixture are employed. The impact of radiation heat transfer is also assessed. As a specific example, the case with a particle size of 79 μm is considered in detail. The burning rate remains nearly constant (

The combustion of aluminum particle, liquid water, and hydrogen peroxide (H2O2) mixtures is studied theoretically for a pressure range of 1–20 MPa and particle sizes between 3 and 70 μm. The oxidizer-to-fuel (O/F) weight ratio is varied in the range of 1.00–1.67, and four different H2O2 concentrations of 0%, 30%, 60%, and 90% are considered. A multi-zone flame model is developed to determine the burning behaviors and combustion-wave structures by solving the energy equation in each zone and enforcing the temperature and heat-flux continuities at the interfacial boundaries. The entrainment of particles is taken into account. Key parameters that dictate the burning properties of mixtures are found to be the thermal diffusivity, flame temperature, particle burning time, ignition temperature, and entrainment index of particles. When the pressure increases from 1 to 20 MPa, the flame thickness decreases by a factor of two. The ensuing enhancement of conductive heat flux to the unburned mixture thus increases the burning rate, which exhibits a pressure dependence of the form rb = apm. The exponent, m, depends on reaction kinetics and convective motion of particles. Transition from diffusion to kinetically-controlled conditions causes the pressure exponent to increase from 0.35 at 70 μm to 1.04 at 3 μm. The addition of hydrogen peroxide has a positive effect on the burning properties. The burning rate is nearly doubled when the concentration of hydrogen peroxide increases from 0 to 90%. For the conditions encountered in this study, the following correlation for the burning rate is developed: r b [ cm / s ] = 4.97 ( p [ MPa ] ) 0.37 ( d p [ μ m ] ) - 0.85 ( O / F ) - 0.54 exp ( 0.0066 C H 2 O 2 ) .

mixtureexhibitedalinearburningrateof4. 8c m∕satapressureof10.7MPaandapressureexponentof0.79.Three motors of internal diameters in the range of 1.91–7.62 cm were studied. Grain configuration, nozzle throat diameter, and igniter strength were varied. The propellants were successfully ignited and combusted in each laboratory-scale motor, generating thrust levels above 992 N in the 7.62-cm-diam motor with a center-perforated grain configuration (7.62 cm length) and an expansion ratio of 10. For the 7.62 cm motor, combustion efficiency was 69%, whereas the specific impulse efficiency was 64%.Increased combustionefficiency and improvedease of ignitionwere observedat higher chamber pressures (greater than 8 MPa).

The combustion wave propagation of nanoaluminum–water mixtures is studied theoretically and experimentally for particles in the size range of 38–130 nm and over a pressure range of 1–10 MPa. A multi-zone framework is established to predict the burning properties and flame structure by solving the conservation equations in each zone and enforcing the mass and energy continuities at the interfacial boundaries. The flame properties are measured by burning nanoaluminum–water strands in a constant-volume vessel. The present study deals with the downward propagating flame. Emphasis is placed on the effects of particle size and pressure. An analytical expression for the burning rate is derived, and physicochemical parameters that dictate the flame behavior are identified. For conditions present in the study, the burning rate shows pressure and particle size dependencies of the form r b [ cm / s ] = 98.8 × ( p [ MPa ] ) 0.32 ( d p [ nm ] ) - 1.0 . The flame thickness increases with increasing particle size and decreasing pressure. Results support the hypothesis that the combustion of aluminum–water mixtures is controlled by mass diffusion across the oxide layers of the particles.

Pyrophoricity of nascent and passivated nano-aluminum particles in air is studied theoretically using energy balance analyses. The work incorporates size-dependence of physicochemical properties of particles at nano-scales, and considers free-molecular and radiation heat exchange with the surrounding environment. The heterogeneous oxidation process is modeled using the Mott–Cabrera mechanism. Nascent aluminum particles with diameters lower than 32 nm are predicted to be pyrophoric. The critical diameter for particles passivated with 0.3-nm thick oxide layer is calculated as 3.8 nm. Particles with oxide layers thicker than 0.3 nm are found to be non-pyrophoric. The sensitivity analysis suggests that the model results are significantly affected by the choice of physicochemical properties, polymorphic state of the oxide layer, parameters of the Mott–Cabrera oxidation kinetics, and heat-transfer correlation. The critical particle size increases by 40%, when bulk material properties calculated at room temperature are used and the oxide layer is assumed to be in a crystalline form. It decreases by 43%, when free-molecular effects are neglected.

Thermochemical behavior of nickel-coated aluminum particles in the size range of 4–18 nm is studied using molecular dynamics simulations. The analysis is carried out in isothermal–isobaric and isochoric-isoenergetic ensembles using an embedded atom method. Emphasis is placed on analyzing the melting points of the core and shell, diffusion of atoms, and intermetallic reactions. The aluminum core melts at a temperature greater than the melting point of a nascent aluminum particle due to the cage-like mechanical constraint imposed by the nickel shell. The melting point of the aluminum core increases from 775 to 1000 K when the core diameter increases from 3 to 12 nm. The melting point of the core is not significantly affected by variations in the shell thickness in the range of 1–3 nm, although the melting point of the shell increases with increasing thickness from a value as low as 1100 K at 1 nm to 1580 K at 3 nm. Melting is followed by diffusion of atoms and energy release due to intermetallic reactions, ...

Flame propagation of aluminum–ice (ALICE) mixtures is studied theoretically and experimentally. Both a mono distribution of nano aluminum particles and a bimodal distribution of nano- and micron-sized aluminum particles are considered over a pressure range of 1–10 MPa. A multi-zone theoretical framework is established to predict the burning rate and temperature distribution by solving the energy equation in each zone and matching the temperature and heat flux at the interfacial boundaries. The burning rates are measured experimentally by burning aluminum–ice strands in a constant-volume vessel. For stoichiometric ALICE mixtures with 80 nm particles, the burning rate shows a pressure dependence of r b = aP n , with an exponent of 0.33. If a portion of 80 nm particles is replaced with 5 and 20 μm particles, the burning rate is not significantly affected for a loading density up to 15–25% and decreases significantly beyond this value. The flame thickness of a bimodal-particle mixture is greater than its counterpart of a mono-dispersed particle mixture. The theoretical and experimental results support the hypothesis that the combustion of aluminum–ice mixtures is controlled by diffusion processes across the oxide layers of particles.

Equilibrium molecular dynamics simulations are conducted to investigate heat transport in aqueous suspensions of alumina nanoparticles. The thermal conductivity of the suspension, calculated by the Green-Kubo relations, is studied for a wide range of volume fractions, particle sizes, and temperatures. The particle volume fraction is varied in the range of 1-9% and the particle size range of concern is 1-9 nm. The temperature varies between 300 and 370 K. The radial distribution function and the radial density profiles are utilized to estimate the thickness of the ordered base-fluid nanolayer adsorbed on the particle surface. Emphasis is placed on elucidating the relationship between the thermal conductivity enhancement and the nanolayer thickness. Results show that the effective thermal conductivity increases near-linearly as a function of volume fraction, whereas the slope of this function decreases with an increase in particle size. The nanolayer thickness is independent of the particle volume fraction. The effect of particle size on thermal conductivity is studied for a volume fraction of 5%, temperature of 300 K, and pressure of 1 atm. The nanolayer thickness remains almost constant with an increase in particle size. However, both effective thermal conductivity, and nanolayer thickness normalized with particle diameter decreases sharply with increasing particle size and attains an asymptotic value at particle diameter ~ 150 nm. The effect of temperature on the effective thermal conductivity is studied for a particle size of 3 nm and volume fraction of 5%. The thermal conductivity decreases steadily with increasing temperature, whereas the nanolayer thickness remains nearly constant. For particle sizes less than 10 nm, the enhancement in thermal conductivity is significantly greater than the predictions of existing theoretical models. A strong correlation between nanolayer properties and enhanced thermal conductivity of fully dispersed nanoparticle suspensions can be deduced from the results.

The combustion of alane and aluminum with water in its frozen state has been studied experimentally and theoretically. Both nano and micron-sized particles are considered over a broad range of pressure. The linear burning rate and chemical efficiency are obtained using a constant-pressure strand burner and constant-volume cell, respectively. The effect of replacing nano-Al particles by micron-sized Al and alane particles are examined systematically with the additive mass fraction up to 25%. The equivalence ratio is fixed at 0.943. The pressure dependence of the burning rate follows the power law, r b = aP n , with n ranging from 0.41 to 0.51 for all the materials considered. The burning rate decreases with increasing alane concentration, whereas it remains approximately constant with cases containing only Al particles. The chemical efficiency ranged from 32% to 83%, depending on the mixture composition and pressure. Thermo-chemical analyses are conducted to provide insight into underlying causes of the decreased burning rate of the alanized compositions. A theoretical model is also developed to explore the detailed flame structure and burning properties. Reasonably good agreement is achieved with experimental observations.

The combustion of nano-aluminum and water mixtures is studied theoretically for a particle size of 80 nm and over a pressure range of 1–10 MPa. Emphasis is placed on the effects of entrainment and agglomeration of particles on the burning rate and its dependence on pressure. The flame thickness increases by a factor of ∼10, when particle entrainment is considered. This lowers the conductive heat flux at the ignition front, thereby reducing the burning rate. The pressure dependence of the burning rate is attributed to the changes in the burning time and velocity of particles with pressure. In the diffusion limit, the pressure exponent increases from 0 to 0.5, when the entrainment index increases from 0 to 1.0. A similar trend is observed in the kinetics-controlled regime, although the corresponding value exceeds the diffusion counterpart by 0.5. The kinetics-controlled model significantly over-predicts the burning rate and its pressure exponent, depending on the entrainment index. The present analysis suggests that nano-particles formed closely-packed agglomerates of diameter 3–5 μm, which may burn under diffusion-controlled conditions at high pressures.

The metal-water system is attractive for propulsion and energy-conversion applications. Of all metals, aluminum is attractive due to its high energy density, relative safety, and low cost. Experimental studies provide new insight on the combustion and propulsive behaviors. The burning rate is found to be a strong function of both pressure and particle size. Furthermore, there is a wide scatter in the measured pressure exponents due to differences in particle size, pressure, pH, and equivalence ratio. A major problem with Al/H2O mixtures is incomplete combustion and poor impulses, thereby rendering Al/H2O mixtures unsuitable for practical applications. Efforts to improve the performance of Al/H2O mixtures have only met with moderate success. Although experiments have revealed these new trends, not much is offered in terms of the underlying physics and mechanisms. To explore the combustion mechanisms, theoretical models based on energy balance analysis have been developed. These models involve numerous assumptions and many complexities were either ignored or treated simplistically. The model also relies on empirical inputs, which makes it more a useful guide than a predictive tool. Future works must endeavor to conduct a more rigorous analysis of metal-water combustion. Empirical inputs should be avoided and complexities must be properly treated to capture the essential physics of the problem. The model should help us properly understand the experimental trends, offer realistic predictions for unexplored conditions, and suggest guidelines and solutions in order to realize the full potential of metal-water mixtures., by Dilip Sundaram

Molecular dynamics simulations are performed to investigate the thermochemical behavior of aluminum-coated nickel particles in the size range of 4–13 nm, beyond which asymptotic behavior is observed. The atomic interactions are captured using an embedded atom model. Emphasis is placed on the particle melting behavior, diffusion characteristics, and inter-metallic reactions. Results are compared with the corresponding properties of nickel-coated nano-aluminum particles. Melting of the shell, which is a heterogeneous process beginning at the outer surface of the particle, is followed by diffusion of aluminum and nickel atoms and inter-metallic reactions. The ensuing chemical energy heats up the particle under adiabatic conditions. The alloying reactions progressively transform the core–shell structured particle into a homogeneous alloy. The melting temperature of the shell is weakly dependent on the core size, but increases significantly with increasing shell thickness, from 750 K at 1 nm to 1,000 K at 3 nm. The core melts at a temperature comparable to the melting point of a nascent particle, contrary to the phenomenon of superheating observed for nickel-coated aluminum particles. The melting temperature of the core decreases from 1,730 to 1,500 K, when its diameter decreases from 10 to 7 nm. For smaller cores, the majority of nickel atoms participate in reactions before melting. The diffusion coefficient of nickel atoms in aluminum shell exhibits a temperature dependence of the form D = D 0 exp(−E A/RT), with an activation energy of 43.65 kJ/mol and a pre-exponential factor of 1.77 × 10−7 m2/s. The adiabatic reaction temperature, also a size-dependent quantity, increases with increasing core diameter, attains a maximum value of 2,050 K at 5 nm, and decreases with further increase in the core diameter. The calculated values agree reasonably with those obtained via chemical equilibrium analysis. The burning time exhibits strong dependence of particle core size and shell thickness of the form τ b = a d c δ s , where the exponents n and m are 1.70 and 1.38, respectively. The finding further corroborates the fact that the reaction rate is controlled by diffusion process.

Thermo-mechanical behavior of nickel coated nano-aluminum particles, in the size range of 4-16 nm, is studied using molecular dynamics simulations. The analysis is carried out in isothermal-isobaric and isochoric-isoenergetic ensembles using an embedded atom method. Emphasis is laid on analyzing the melting of Al core, diffusion of Al and Ni atoms, and intermetallic reactions for different core sizes and shell thicknesses. The melting point of the Al core is found to exceed the heterogeneous melting point of pure nAl particle and approach the homogenous melting point of Al, irrespective of the shell thickness. The diffusion of Al atoms, after melting, is accompanied by self-sustaining inter-metallic reactions between Al and Ni atoms. The advent of these reactions is, to some extent, delayed for a thicker shell and expedited for a larger core. The amount of heat release due to the reactions increases as the Al or Ni atomic fraction increases to 0.5. Adiabatic reaction temperatures close to 2300 K are predicted for near-equiatomic particles with a 1 nm thick Ni shell. The simulation results indicate the possibility of ignition of these particles in an inert environment and also help in explaining their reduced ignition temperatures.

The combustion of nano-aluminum, alane, and ice mixtures is theoretically studied. A multi-zone theoretical framework is established by solving the energy equation in each zone and matching the temperature distribution and the heat flux at the interfacial boundaries. The effect of replacing a portion of nano-aluminum particles with micron-sized aluminum and alane particles is examined in the pressure range of 1-10 MPa and for an additive mass fraction of 25%. The addition of micron-sized alane particles results in lower flame temperatures due to the dehydrogenation reaction of alane particles prior to their ignition. The lower flame temperatures and the longer burning times of micron-sized alane particles is responsible for lower flame speeds of these mixtures. For bimodal aluminum-ice mixtures, the lower mass fraction of alumina causes an increase in the flame temperatures. However, the mixtures exhibit mildly lower flame speeds, in view of the longer burning times of micron-sized aluminum particles. The flame thickness of a bimodal mixture of aluminum particle mixtures is higher than that of mono-dispersed mixtures due to the prevalence of two distinct reaction zones. The model results are well supported by experimentally measured burning rates.

A theoretical investigation on the combustion behavior of nano-aluminum (nAl) and liquid water is conducted. Linear burning rates of nAl and liquid water as a function of pressure and equivalence ratio are reported. A 38-nm diameter aluminum particle with a 3.1-nm thick oxide layer has been chosen for the present study. The simulation is carried out for a pressure range of 0.1 - 3.65 MPa. The equivalence ratio considered in the present study varies from 0.5 to 1.25. The model predicts an increase in linear burning rate from 0.7 to 8.1 cm/s at a pressure of 3.65 MPa, as the equivalence ratio is increased from 0.5 to 1.25. The predicted burning rates are in good agreement with the experimentally measured values. The flame thickness predicted by the model is 108 microns.