SYSTEM AND METHODS OF GROUP COMBUSTION OF CORE-SHELL THERMITE PARTICLES

Abstract

A method and associated system of energy production, the method including providing core-shell thermite particles and combusting the core-shell thermite particles in a dispersed group to produce heat. The combustion of the core-shell thermite particles may proceed according to various core-shell thermite group combustion modes.

Claims

1. A method of energy production, the method comprising: providing core-shell thermite particles; combusting the core-shell thermite particles in a dispersed group to produce heat.

2. The method of claim 1, wherein the core-shell thermite particles comprise nano particles or micro particles.

3. The method of claim 1, wherein the core-shell thermite particles comprise nano particles and micro particles.

4. The method of any one of claims 1 to 3, wherein the particles are combusted in an environment without gaseous oxygen.

5. The method of any one of claims 1 to 4, wherein the combustion mode comprises incipient group combustion.

6. The method of any one of claims 1 to 4, wherein the combustion mode comprises partial group combustion.

7. The method of any one of claims 1 to 4, wherein the combustion mode comprises critical particle combustion.

8. The method of any one of claims 1 to 4, wherein the combustion mode comprises external particle combustion.

9. The method of any one of claims 1 to 4, wherein the combustion mode comprises sheath combustion.

10. The method of any one of claims 1 to 9, wherein the combustion occurs within a reactive solar collector.

11. The method of any one of claims 1 to 10, wherein the dispersed group is produced with a fuel injector.

12. The method of claim 11, wherein the fuel injector is a rocket injector.

13. The method of any one of claims 11 to 12, wherein the fuel injector comprises a multi-point injection system.

14. The method of any one of claims 1 to 13, wherein the heat is applied to an additive manufacturing process.

15. The method of any one of claims 1 to 14, wherein the heat is applied to a propulsion system.

16. The method of any one of claims 1 to 15, wherein the heat is applied to a power generation system.

17. The method of claim 16, wherein the power generation system comprises a combined cycle power system with heat recovery.

18. The method of any one of claims 1 to 17, wherein the heat is applied to the propulsion of a vehicle.

19. The method of claim 18, wherein the vehicle is a submarine.

20. The method of claim 18, wherein the vehicle is a spacecraft.

21. The method of claim 18, wherein the vehicle is a airplane.

22. The method of any one of claims 1 to 21, wherein the heat is applied to wireless power transmission.

23. The method of any one of claims 1 to 22, wherein the combustion products are provided as reactants to another process.

24. The method of any one of claims 1 to 22, wherein the combustion is applied to pyrotechnics.

25. A system for energy production, the system configured to: provide core-shell thermite particles; combust the core-shell thermite particles in a dispersed group to produce heat.

26. The system of claim 25, wherein the core-shell thermite particles comprise nano particles or micro particles.

27. The system of claim 25, wherein the core-shell thermite particles comprise nano particles and micro particles.

28. The system of any one of claims 25 to 27, wherein system is configured to combust the particles in an environment without gaseous oxygen.

29. The system of any one of claims 25 to 28, wherein the combustion mode comprises incipient group combustion.

30. The system of any one of claims 25 to 28, wherein the combustion mode comprises partial group combustion.

31. The system of any one of claims 25 to 28, wherein the combustion mode comprises critical particle combustion.

32. The system of any one of claims 25 to 28, wherein the combustion mode comprises external particle combustion.

33. The system of any one of claims 25 to 28, wherein the combustion mode comprises sheath combustion.

34. The system of any one of claims 25 to 33, wherein the combustion occurs within a reactive solar collector.

35. The system of any one of claims 25 to 34, wherein the dispersed group is produced with a fuel injector.

36. The system of claim 35, wherein the fuel injector is a rocket injector.

37. The system of any one of claims 35 to 36, wherein the fuel injector comprises a multi-point injection system.

38. The system of any one of claims 25 to 37, wherein the heat is applied to an additive manufacturing process.

39. The system of any one of claims 25 to 38, wherein the heat is applied to a propulsion system.

40. The system of any one of claims 25 to 39, wherein the heat is applied to a power generation system.

41. The system of claim 40, wherein the power generation system comprises a combined cycle power system with heat recovery.

42. The system of any one of claims 25 to 41, wherein the heat is applied to the propulsion of a vehicle.

43. The system of claim 42, wherein the vehicle is a submarine.

44. The system of claim 42, wherein the vehicle is a spacecraft.

45. The system of claim 42, wherein the vehicle is a airplane.

46. The system of any one of claims 25 to 45, wherein the heat is applied to wireless power transmission.

47. The system of any one of claims 25 to 46, wherein the combustion products are provided as reactants to another process.

48. The system of any one of claims 25 to 46, wherein the combustion is applied to pyrotechnics.

49. The method of claim 1, wherein the particles are combusted in an oxygenated environment.

50. The method of any one of claims 1 to 24, wherein the heat is stored as energy for further use.

51. The system of any one of claims 25-48, wherein the heat is stored as energy for further use.

52. The method of any one of claims 1 to 24, wherein the combustion occurs on Earth.

53. The system of any one of claims 25-48, wherein the combustion occurs in space.

54. The method of any one of claims 1 to 24, wherein the combustion occurs on Earth.

55. The system of any one of claims 25-48, wherein the combustion occurs in space.

56. The system of any one of claims 25-48, wherein the particles are energized using magnetic induction.

57. The method of any one of claims 1 to 24, wherein the particles are energized using magnetic induction.

58. The system of any one of claims 25-48, wherein the heat is applied to welding, sintering or joining.

59. The method of any one of claims 1 to 24, wherein the heat is applied to welding, sintering or joining.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The drawings included herewith are for illustrating various examples of articles, methods, and apparatuses of the present specification. In the drawings:

[0039] FIG. 1 is a diagram depicting core shell thermite combustion, according to an embodiment;

[0040] FIG. 2 is a diagram depicting temperature distribution of core shell thermite combustion, according to an embodiment;

[0041] FIG. 3 is a diagram depicting dispersed group core shell thermite combustion, according to an embodiment;

[0042] FIG. 4 is a graph depicting normalized mass-fraction and temperature of nanothermite group combustion, according to an embodiment;

[0043] FIG. 5 is a graph depicting the normalized radial mass flow rate against the normalized radius for different group combustion numbers (G), according to an embodiment;

[0044] FIG. 6A is a graph depicting group mass-loss rate in variation with the group number, according to an embodiment;

[0045] FIG. 6B is a graph depicting group mass-loss rate in variation with the group number, according to an embodiment;

[0046] FIG. 7A depicts a diagram illustrating the internal group combustion mode, according to an embodiment;

[0047] FIG. 7B depicts a diagram illustrating the external group combustion mode, according to an embodiment;

[0048] FIG. 8A depicts a diagram illustrating the individual particle combustion mode, according to an embodiment;

[0049] FIG. 8B depicts a diagram illustrating the incipient group combustion mode, according to an embodiment;

[0050] FIG. 8C depicts a diagram illustrating the partial group combustion mode, according to an embodiment;

[0051] FIG. 8D depicts a diagram illustrating the critical particle combustion mode, according to an embodiment;

[0052] FIG. 8E depicts a diagram illustrating the external particle combustion mode, according to an embodiment;

[0053] FIG. 8F depicts a diagram illustrating the sheath combustion mode, according to an embodiment;

[0054] FIG. 9A depicts a diagram illustrating the external sheath combustion mode, according to an embodiment;

[0055] FIG. 9B depicts a diagram showing the internal sheath combustion mode, according to an embodiment;

[0056] FIG. 10A depicts a diagram showing the required number of particles (N), for different group combustion numbers, according to an embodiment;

[0057] FIG. 10B depicts a diagram showing the fraction of cloud radius to particle radius with interparticle spacing for different group combustion numbers (G), according to an embodiment;

[0058] FIG. 11 is a diagram depicting various combustions modes of core-shell thermite group combustion, according to an embodiment;

[0059] FIG. 12 is a diagram depicting a solar collector concentrator, according to an embodiment;

[0060] FIG. 13 is a diagram depicting various rocket configurations, according to an embodiment;

[0061] FIG. 14 is a diagram depicting various fuel injector configurations, according to an embodiment;

[0062] FIG. 15 is a diagram depicting various fuel injector spray nozzle configurations, according to an embodiment;

[0063] FIG. 16 is a diagram depicting various rocket configurations, according to an embodiment;

[0064] FIG. 17 is a diagram depicting various rocket configurations, according to an embodiment;

[0065] FIG. 18 is a diagram depicting various fuel injection configurations, according to an embodiment;

[0066] FIG. 19 is a diagram depicting various rocket configurations, according to an embodiment;

[0067] FIG. 20 is a diagram depicting various fuel injection configurations, according to an embodiment;

[0068] FIG. 21 is a diagram depicting various fuel injection configurations, according to an embodiment;

[0069] FIG. 22 is a diagram depicting various fuel injection configurations, according to an embodiment;

[0070] FIG. 23 is a diagram depicting various fuel injection spray configurations, according to an embodiment;

[0071] FIG. 24 is a diagram depicting various fuel injection spray configurations, according to an embodiment;

[0072] FIG. 25 is a diagram depicting various fuel injection spray configurations, according to an embodiment;

[0073] FIG. 26A is a diagram depicting various fuel injection configurations, according to an embodiment;

[0074] FIG. 26B is a diagram depicting various fuel injection configurations, according to an embodiment;

[0075] FIG. 27 is a diagram depicting a power generation system, according to an embodiment;

[0076] FIG. 28A is a diagram depicting rocket system, according to an embodiment;

[0077] FIG. 28B is a diagram depicting rocket system, according to an embodiment;

[0078] FIG. 29 is a table comparing previous analytical models to the core-shell nanothermite combustion model, according to an embodiment;

[0079] FIG. 30 is a table classifying the intermediate models of nanothermite combustion, according to an embodiment;

[0080] FIG. 31 is a table classifying various nanothermite group combustion regimes with the lower limit and upper limit of the group combustion number (G), according to an embodiment; and

[0081] FIG. 32 is a flow chart depicting a method of energy production through dispersed group core shell thermite combustion, according to an embodiment.

DETAILED DESCRIPTION

[0082] Various apparatuses or processes will be described below to provide an example of each claimed embodiment. No embodiment described below limits any claimed embodiment and any claimed embodiment may cover processes or apparatuses that differ from those described below. The claimed embodiments are not limited to apparatuses or processes having all of the features of any one apparatus or process described below or to features common to multiple or all of the apparatuses described below.

[0083] Nanothermites are a Metastable Intermolecular Composite (MIC) which are often made of a metal and metal oxidemixed at a nanoscalethat can undergo an exothermic chemical reaction with sufficient energy input. The nanosized constituents, namely the metal fuel and solid oxidizer, are often physically mixed to promote a rapid ignition and reaction; the chemical reactions in MIC occur due to the solid-state diffusion of oxygen. Spherical core-shell nanothermites have been developed wherein a nanosized metallic core was wrapped in a thin oxidizing shell, which can be either metallic or non-metallic. As the contact area between the fuel and oxidizer was maximized, the diffusion length and timescales were minimized. Thus, the core-shell nanothermites presents many advantages, most notably that the outer shell is thermodynamically stable and therefore reactions can occur as discrete solid-state particle combustion in the absence of gaseous oxygen. This differs from classical, physically-mixed nanothermite combustion which requires physical proximity between the fuel and oxidizer particles, and thus cannot react in a dispersed phase.

[0084] Nanothermites are characterized by their high reactivity and energetic density, and can be tailored to specific applications. As they undergo highly exothermic reactions, a dispersed group of core-shell structured nanothermites can result in self-sustaining combustion due to the thermal diffusion and convection of the heated products of combustion, which ignite the neighboring particles. However, as the particle reactions are driven by solid-state oxygen diffusion, the combustion in the dispersed phase is not limited by the availability of gaseous oxygen. Instead, it is limited by the inter-particle heat and mass transfer. Furthermore, reactions can occur in vacuum, water and any other inert environment, assuming the continuum phase does not chemically impact the core-shell structure of the MIC. Additionally, heating and combustion reactions of groups of core-shell nanothermites and/or energetic particles can be used in oxygen rich environments. These characteristics make the core-shell nanothermites well suited for many novel applications, including Earth and space technologies.

[0085] A substantial amount of research has focused on the combustion of closely packed nanothermite particles. The physically mixed solid-phase fuel and oxidizer particles are often mechanically compressed, and their combustion characteristics have been investigated. The packing density, measured in terms of Theoretical Maximum Density (TMD), greatly impacts the flame propagation speed through a consolidated pellet. The flame front advances predominantly due to convective (at low TMD) or conductive (at high TMD) means, with the flame speed varying from O(10) m/s at high TMD, to O(1000) m/s at low TMD. The sensitivity of the flame propagation speed to TMD was recently assessed using numerical models. However, the combustion characteristics of dispersed core-shell nanothermites, in which the ignition and combustion of the individual particles are predicated upon the inter-particle heat and mass transfer, are not well established and represent the focus of the present work which applied a theoretical perspective to the problem.

[0086] Under sufficient heating, the combustion of a single, core-shell nanothermite particle shares many characteristics with single-particle char or droplet combustion, the primary difference being the solid-state diffusion of oxygen that occurs within a particle in the nanothermite. As the dispersed core-shell nanothermite reactions are not limited by the presence of gaseous oxygen (due to the solid-phase oxidizer transport from the shell), the combustion dynamic of multiple dispersed particles differs greatly from the classical multi-phase combustion regimes. Group combustion is the burning characteristic of the collection of particles and is helpful in modeling of dispersed particle combustion. Several different modes of group combustion have been recognized for the case of dispersed droplets and solid particles. Classically, these different modes of group combustion are governed by the availability of oxygen within the dispersed cluster. Thus, dispersed core-shell nano-energetic particles will have different group combustion characteristics.

[0087] The theory and models of metal combustion in a gaseous oxidizer have long been subject to mathematical study. Previous works examined metal particle combustion regimes and concluded that the oxidizer and pressure have a significant impact on the thermodynamics of combustion and particle combustion regimes. The metal vapours react instantly with oxygen upon contact, and vapour pressures of metals are only substantial when close to flame temperatures. It can be difficult to imagine a scenario in which a cloud of metal vapour would burn with external oxygen in a group combustion process. However, metal vapour can still burn with external oxygen caused by high-temperature plasma, laser-induced plasma, electrostatic discharge, the chemical reaction zone behind a detonation front, and other non-typical combustion applications. Emission from metal vapors (e.g., Al, B) and oxidized species (e.g., AIO, BO2) has been observed under these conditions. Other previous works investigated the scaling of the flame propagation in a particulate cloud. They adopted the following two models: a continuum model for an analytical study and a discrete source model for a numerical investigation. They discovered that the flame propagation could not be deterministically predicted in the limit of fast combustion compared to the interparticle diffusion time.

[0088] In very dense metal clouds, the reaction is more like that of metal particle agglomerate wherein the reaction rate can be restricted by the availability of oxidizer, something that does not occur in the case of nanothermites. An increase in local temperature within the particle suspension due to a reaction at multiple particle sites is referred to as the collective effect. This leads to less heat loss to its surroundings, since the particles are self-heating as they react at multiple particle sites. Compared to isolated particles, the collective effect accelerates the heating rate within a cloud, resulting in faster combustion. Previous works found that particles combust at all sizes and there is no minimum size for ignition.

[0089] Clusters of dispersed particles can emerge in turbulent flows where the discrete particles can be preferentially concentrated due to the kinematics of the turbulence. This preferential clustering of discrete particles becomes particularly important under external radiative or inductive heating. The particle heating locally heats the fluid phase and may locally generate turbulence and even further enhance clustering. The inhomogeneous particle distribution can impede the interphase heat transfer, generating hot and cold zones in the continuum phase. This is a particularly important problem in particle-laden solar collectors. If these particles are reactive, the clustering can impact the combustion dynamics of these dispersed particles, especially if the group combustion is oxygen constrained. For core-shell nanothermite particles, the implication of local clustering on the group combustion characteristics remains unclear.

[0090] Described herein is a theoretical description of the group combustion characteristics of dispersed, spherical core-shell nanothermites was proposed that built on previous analytical work. The subject matter of this disclosure differs from the classical group combustion theory in that core-shell nanothermites, as they contain both fuel and oxidizer within a discrete particle, do not undergo an oxygen-limiting group combustion behaviour. The role of group combustion theory is not limited to understanding the combustion of a group of dispersed reactive particles, but it can also help understand the ignition time, burning rates, heat release, flame structures and other combustion characteristics. For tractability, the combustion kinetics were simplified to a single-step with approximated kinetic parameters and neglected any additional forces emerging at the nanoscale. Most dispersed nanoparticles agglomerate into microsized particles containing hundreds or thousands of discrete core-shell nanosized particles. These simplifications provide a tractable framework to describe the inter-particle heat transfer of dispersed core-shell nanothermites. This framework can be extended various modes to compose and/or deploy other combustion and or heating, or a combination of two to varying degrees to support applications, processes and/or methodologies.

Single Isolated Particle Combustion

[0091] In the present disclosure, considered were spherical core-shell nanoparticles consisting of an aluminium core and a copper oxide shell. However, in other embodiments, the theory described herein is generalizable to any core-shell nanothermite material. In a dispersed phase, nanoparticles have a tendency to aggregate-due to the intermolecular and electrostatic forces-into agglomerations of particles that have a diameter on the micrometer scale. Although for most practical applications core-shell particles were used on the nanoscale, the nanoparticle aggregates were considered as isolated particles for the present disclosure. This simplification allowed the neglect of any nanoscale forces that would hinder the tractability of the analysis. It should be noted that, above the nanometer scale, the analysis is scale-independent, as shown in diagram 100 of FIG. 1. FIG. 1 shows an Illustration of the core-shell nanothermite and corresponding nanothermite agglomerate, which can disperse in the carrier phase for combustion. However, the combustion time changed with the length scales (size) of the particle agglomerate. As is seen in Equation (17), which corresponds to the particle consumption time, if the particle size (ds,0) is doubled, the consumption time (ts) of the particle quadruples.

[0092] Quasi-Steady Assumptions of Single Particle Combustionfirst considered is the simplest case of the combustion of an isolated core-shell nanothermite particle. Under sufficient heating, the oxygen from the shell undergoes solid-state diffusion and a chemical reaction with the pure metal core takes place, as shown in FIG. 1. Only the heterogeneous redox reaction near the surface involving the aluminium core with the oxygen in the copper oxide shell was considered. It is to be noted that this reaction is independent of the gaseous oxygen availability around the particle surface. To simplify the analysis, a perfectly spherical particle was considered where the solid-state reaction occurred at the edge. Depending on the composition of the nanothermites, gas is formed as a product of combustion in addition to a solid or liquid phase metal oxide. In the specific case of an aluminium core with a copper oxide shell, copper vapors are formed, as shown in diagram 200 of FIG. 2. Diagram 200 of FIG. 2 shows combustion of a single solid nanothermite; surface denotes nanothermite pellet surface. This combustion of a single-particle behaves the same as a highly concentrated group combustion event.

[0093] Thus, a concentration gradient in the gas phase is established, which results in the diffusion of copper vapors away from the particle surface. This disclosure is interested in obtaining the concentration profile of copper vapors. Under steady conditions, this profile must adjust in such a way that the combustion of nanothermite must equal the stoichiometric release of copper vapors at the particle surface. The transfer rate of copper vapors can then be evaluated using the mass conservation equations. With conservation of mass considerations, the regression rate of the particle is proportional to the vapor generation under the quasi-steady assumption. Thus, the temperature-dependent heat release, which was used in previous work, is implicitly accounted for within the gaseous formation. Furthermore, given the low thermal mass of these particles and the rapid timescale of combustion, a non-constant but uniform temperature within the particle was assumed. Similarly, the thermophysical properties of the solid, such as specific heat, were assumed to be temperature independent. Finally, using stoichiometry, the nanothermite burn rate was be evaluated.

[0094] There are some other assumptions considered in this formulation. The radiative heat release from combustion and hot particles is considered to be negligible- simplification that may not be valid in all cases. The kinetic energy of the carrier phase as well as its shear work are neglected. Finally, there was no chemical reaction with the copper vapors in the carrier phase. With these assumptions, the mass conservation, vapor product transport, and energy equation were considered. The rate of mass consumption of the solid particle (m.Math.s) is as follows:

[00001]$\begin{array}{cc}-{\stackrel{.}{m}}_s=-4r_s^2{}_s\frac{r_s}{t}=4r^{2}u=\stackrel{.}{m}={\stackrel{.}{m}}_p,& \left(1\right)\end{array}$

[0095] where rs is the radius of the particle, s is the density of the particle, is the density of the gas phase including vapor density of copper species (kg/m3), u is the velocity of the gas mixture at any spherical cross-section in the gas phase, m.Math. is the mass flux rate at any spherical cross-section in the gas phase, and m.Math. is the mass production rate of the vapor products. Here, the mass of the particle (ms) decreases with time, thus a negative value, m.Math.s<0, is obtained; similarly, the mass flux is positive. The conservation of species per unit surface area in a quiescent environment of the gas phase is as follows:

[00002]$\begin{array}{cc}\left(\mathrm{uY}\right)-\left(\frac{Y}{r}\right)=\frac{\stackrel{.}{m}}{4r^2},& \left(2\right)\end{array}$ [0096] where Y is the mass fraction of copper vapor species at a given location, D is the binary diffusion coefficient of copper vapor species in the carrier phase, is the vapor density of the copper species, and Yr is the mass fraction gradient of the copper vapor. The above equation was simplified by considering 4r2u=m.Math. from Equation (1). It is to be noted that the two ways to integrate the above equation are as follows: (1) from the particle surface (r=rs) to a radial location, r or (2) from a radial location, r, to a far away location (r=r). However, adopting any of the boundary conditions will produce the same final result. An expression of the above conservation law after integration can be written as follows:

[00003]$\begin{array}{cc}\frac{{\stackrel{.}{m}}_s}{4r}=\ln \left(\frac{1-Y}{1-Y_s}\right),\mathrm{or}\frac{{\stackrel{.}{m}}_s}{4r}=\ln \left(\frac{1-Y_{}}{1-Y}\right),& \left(3\right)\end{array}$ [0097] where Ys is the copper vapor mass fraction of the ambient gas adjacent to the particle surface and Y is the mass fraction of copper vapor at a location far from the nanothermite particle. The above equation can be rewritten by defining the mass transfer number B as follows:

[00004]$\begin{array}{cc}\frac{{\stackrel{.}{m}}_s}{4r}=\ln \left(1+B\right),\mathrm{where}B=\frac{Y_s-Y}{1-Y_s},\mathrm{or}B=\frac{Y-Y_{}}{1-Y},& \left(4\right)\end{array}$

[0098] The higher the mass combustion rate of the nanothermites, the higher the mass transfer number (B). This gives us the exact value of the constant mass flow rate (m.Math.) parameter in terms of the known boundary conditions:

[00005]$\begin{array}{cc}\stackrel{.}{m}=4r_s\ln \left(\frac{1-Y_{}}{1-Y_s}\right),& \left(5\right)\end{array}$

[0099] Above is the constant mass flow rate at any spherical cross-section of radius, r, for a given mass fraction of the vapor product in the immediate vicinity of the particle (Ys) and mass fraction of the vapor product located far from the particle (Y). The general case of the above equation is Ys>Y that leads to outwards mass flow rate (m.Math.>0) from the particle. The limiting case in which Ys=Y, which means there is no mass flow rate as m.Math.=0. Thus, the final solution of the mass fraction variation of the vapor product (Y) at any radius (r) location is obtained by substituting Equation (5) into Equation (3) to obtain:

[00006]$\begin{array}{cc}Y\left(r\right)=1-{\left(1-Y_{}\right)}^{\left(1-\frac{r_s}{r}\right)}{\left(1-Y_s\right)}^{\frac{r_s}{r}},& \left(6\right)\end{array}$

[0100] This can be further simplified as follows: Y(r)=1(1Ys)rsr if that no mass fraction of the vapor product is located far from the particle, Y=0 is considered. The conservation of energy in the domain is given by the following formula:

[00007]$\begin{array}{cc}\frac{}{r}\left(4r^2{\mathrm{uC}}_{p}T-4r^2\frac{T}{r}\right)=0,& \left(7\right)\end{array}$ [0101] where T is the thermodynamic temperature at radial location (r). Similarly, and Cp are the thermal conductivity and specific heat of the gas-mixture, respectively.

[0102] By considering the boundary condition of m.Math.=4r2, Equation (1), the solution of the above equation is given as:

[00008]$\begin{array}{cc}\frac{\stackrel{.}{m}{C}_{p}r}{}=-\ln \left(1-\stackrel{.}{m}{C}_p\left(\frac{T-T_{}}{Q_s}\right)\right),& \left(8\right)\end{array}$ [0103] where the parameter Qs is given as:

[00009]$\begin{array}{cc}{Q}_s=\frac{\stackrel{.}{m}{C}_p\left(T_s-T_{}\right)}{1-e^{-\left(\frac{\stackrel{.}{m}{r}_s{C}_p}{}\right)}},& \left(9\right)\end{array}$

[0104] Thus, the solution of the temperature is:

[00010]$\begin{array}{cc}T=T_{}+\left(T_s-T_{}\right)\frac{\left(1-e^{-\left(\frac{\stackrel{.}{m}{C}_{p}r}{}\right)}\right)}{\left(1-e^{-\left(\frac{\stackrel{.}{m}{r}_s{C}_p}{}\right)}\right)},& \left(10\right)\end{array}$

[0105] The limit cases can be verified from the above equation. For example, at the particle surface (r=rs), T=Ts, which expresses the exact boundary condition at the particle surface. A similar sanity check can be performed at a radial location far from the solid particle (r.fwdarw.). Additionally, for the limiting case when the temperature at the surface and the temperature at the freestream are equal, the solution of the above equation can be simplified to T=Ts=T.

[0106] The diffusion of the combustion products into the surrounding carrier gas is characterized by the Lewis number, Le=/D=/(DCp), which relates the mixture thermal diffusivity =\/(Cp) to the mass diffusivity (D). An assumption of the unity Lewis number was made to retain mathematical tractability. This means that the mass (mass diffusivity of the copper vapors relative to the gas mixture) and thermal diffusion were approximately equal. Considering a unity Lewis number, where the mixture thermal diffusivity is (=)/(Cp) and the species diffusivity is (D) and equal, (/(Cp=D), the above equation simplifies to:

[00011]$\begin{array}{cc}\frac{{\stackrel{.}{m}}_{s}r}{}=\ln \left(1+B_T\right),& \left(11\right)\end{array}$ [0107] where the thermal transfer number (BT) is as follows:

[00012]$\begin{array}{cc}{B}_T=\frac{{\stackrel{.}{m}}_s{C}_p\left(T_{}-T\right)}{Q_s},& \left(12\right)\end{array}$

[0108] To decipher the physical implication of the thermal transfer number (BT), let us posit that the copper vapor product leaves with an energy of m.Math.Cp(TsT). If this thermal energy is supplied to the copper vapors at Ts, the potential amount of energy that is transferred is m.Math.Cp(TsT). The higher the BT number, the higher the potential for heat transfer in the surrounding gas phase.

Comparison with Other Single-Particle Combustion Models

[0109] Previous works developed analytical models for quasi-steady single-particle combustion for a variety of fuels. Here, these models were compared to the core-shell nanothermite combustion model; the comparison is summarized in Table 2900 of FIG. 29.

Spray Combustion

[0110] The spray combustion has the following two fundamental elements: combustion of an individual fluid droplet and a collection of droplets. Intuitively, single droplet combustion generally appears in dilute sprays, whereas droplet clusters are found at higher concentration flows. It should be noted that the size of these clusters is much smaller than the integral length scale of the turbulent flow. Much research has been conducted to investigate the steady-state burning of individual drops and the two-stage ignitionparticularly in microgravity. However, the literature on group combustion is rather limited. In the case of single droplet combustion, the thermal transfer number, equivalent to Equation (12) for nanothermites, becomes:

[00013]$\begin{array}{cc}B=\frac{C_p\left(T-T_{s,b}\right)}{L_h}+\frac{Y_{O_{2,}}}{c_{O_2}}\frac{h_c}{L_h},& \left(13\right)\end{array}$

[0111] In the above equation T, Ts, b, Cp, hC, and Lh are the temperature at a distance from the fuel drop, the boiling point of the liquid fuel, the specific heat of the gas, the specific enthalpy of the combustion reaction, and the latent heat of vaporization, respectively. Likewise, YO2, represents the oxygen mass fraction at locations far from the fluid drop, and cO2 represents the oxygen stoichiometric coefficient in the reaction. Therefore, in order to elucidate the physical interpretation of B, the energy (Cp(TTs)+hcYO2,c/cO2) of the reaction products that escape from the surface was considered. By providing this thermal energy to a noncombustible liquid fuel at a temperature of Ts, the physical quantity of the fuel that can potentially be vaporized is ((Cp(TTs)+hcYO2,/cO2)/Lh). In droplet combustion, the potential of converting liquid fuel into vapors, measured in the mass of fuel per mass of the stoichiometric amount of air, is known as the transfer number B. In this sense, a greater value of B depicts a higher level of overall evaporation and consequently, a higher combustion of the fluid particles.

Coal/Char Combustion

[0112] Previous works conducted a theoretical analysis in order to decipher the combustion characteristics of char particle clusters in a quiescent flow. In their case, they determined the mass transfer number of a single coal/char particle as follows:

[00014]$\begin{array}{cc}B=\frac{\left(\frac{Y_{{\mathrm{CO}}_2}}{c_{{\mathrm{CO}}_2}}+\frac{Y_{O_2}}{c_{O_2}}\right)-\left(\frac{Y_{{\mathrm{CO}}_{2^s}}}{c_{{\mathrm{CO}}_{2^s}}}+\frac{Y_{O_{2^s}}}{c_{O_{2^s}}}\right)}{1+\left(\frac{Y_{{\mathrm{CO}}_{2^s}}}{c_{{\mathrm{CO}}_{2^s}}}+\frac{Y_{O_{2^s}}}{c_{O_{2^s}}}\right)},& \left(14\right)\end{array}$ [0113] here, YCO2, YCO2,s, YO2, YO2,s, cO2 and cCO2 represent the carbon dioxide (CO2) mass fraction, carbon dioxide (CO2) mass fraction at the char particle surface, oxygen (O2) mass fraction, oxygen (O2) mass fraction at the particle surface, oxygen and carbon dioxide stoichiometric coefficient in the reaction. In this combustion reaction, the main product is carbon dioxide, while the reaction of carbon and oxygen is trivial. Furthermore, each particle releases carbon monoxide based on the oxidation of the carbon atoms and reduction of carbon dioxide. This carbon monoxide later oxidates to create carbon dioxide provided a homogeneous gas phase. Hence, they proposed a one-step reaction scheme as follows: CO+12 O2.fwdarw.CO2. Considering this reaction, if the rate of oxidation of carbon monoxide is high, then the concentration of oxygen in the particle cloud will dwindle. Moreover, the global rate of the char cloud combustion was deemed independent of carbon monoxide oxidation, if the diffusion control is ensured for the combustion of every char particle in the group.

Particle Consumption Time and D-Square Law

[0114] Considering Equations (1) and (4) at the surface of a particle and simplifying by replacing radius of the particle with its diameters (ds):

[00015]$\begin{array}{cc}\frac{{\mathrm{dd}}_s^2}{di}=-k_q=-\frac{8))}{{}_s}\ln \left(1+B\right)=-\frac{8))}{{}_s}\ln \left(\frac{1-Y_{}}{1-Y_s}\right),& \left(15\right)\end{array}$ [0115] where kq is a constant corresponding to the linear slope of the relationship between the diameter square (d2s) and time (t). Physically, kq represents the combustion rate of the nanothermite particle. It is noteworthy that the right-hand terms of the above equation are constant in time, and the solution of the above linear differential equation is as follows:

[00016]$\begin{array}{cc}{d}_s^2=d_{s,0}^2-k_{q}t,& \left(16\right)\end{array}$ [0116] where ds, 0 is the initial size of the particle. Thus, the time taken for the particle to become completely consumed (ds=0) is (assuming that complete and idealized combustion occurs) is calculated as follows:

[00017]$\begin{array}{cc}{t}_s=d_{s,0}^2/k_q,& \left(17\right)\end{array}$

[0117] The particle diameter decays linearly with time. There is a finite time when the particle is completely consumed, given by ts=d2s,0/kq. This is an order-of-magnitude approximation given the heterogeneous makeup of the core-shell nanothermite. For other solid and liquid fuels, the scaling relation between the lifetime and diameter of the particle (tdxd2s,0) was shown previously.

[0118] Returning to the initial assumption of quasi-steady combustion, it is assumed that the particle was stationary and the gas generation and expansion were perfectly symmetrical. The above analysis does not account for the relative velocity of a nanothermite particle to the gas phase. However, it was found empirically for other fuels that even if there is a superimposed gas velocity, the scaling relationship, Equation (17), holds. Previous works that developed correlations of droplet evaporation, described the correction factor ku in the presence of a free-stream gas velocity (u). Thus, the modification ratio of ku as a correction in the presence of some flow divided by kq is as follows kukq=1+Reb, where Re is the Reynolds number, a is typically about 0.3 and b is also about 0.25 to 0.3 in droplet evaporation. With these values, there is a relatively weak dependence on kukq for various Re. Hence, the above relation can serve as a motivation for researchers to implement more detailed measurements of the variation of the nanothermite diameter with time during its combustion.

Mass Conservation and Group Combustion

[0119] This disclosure previously provided a simplified analytical framework with which to characterize the combustion of a discrete, quasi-steady, spherical core-shell nanothermite particle. Now, derived herein is an analytical approach to describe nanothermite cloud combustion. No previous disclosure exists on the thermally-driven particularities of core-shell nanothermite combustion. The theoretical approach adopted in this disclosure follows similar lines of inquiry used for spray and coal powder combustion, but adapted to the specific characteristics of nanothermites.

[0120] Distributed core-shell nanothermites are considered to be a spherical group of particles (although the results could be easily extended to cylindrical and planar clouds). Consider a group of radius RG containing nanothermite particles as shown in diagram 300 of FIG. 3. The group is essentially a two-phase region, consisting of discrete solids and a continuous gas phase. The gas phase inside the group can be divided into the film region (region C, in the particle's vicinity) and the gaseous middle region (region Bshown in FIG. 3). There is a separation of length I between the particles. Dispersed aggregates of core-=shell Al/CuO nanothermites were considered, which produce copper vapor when the aluminium core oxidizes. The copper vapor is formed at the particle surface, and it diffuses into the gaseous middle region through the film region. The rate of heat transfer and nanothermite combustion is dictated by the diffusion of copper vapor, which eventually diffuses into the outer region (region A). For the purpose of simplifying the group combustion analysis, two additional assumptions were considered. The first assumption is ds/l<<1, which translated to a continuum in the group region. Consequently, the particles are perceived as point sources. The second assumption is the presence of a uniform monodispersed cloud of nanothermite particles.

[0121] In the classical group combustion regime, an internal zone of unburnable fuel is created by the evaporation of liquid fuels or pyrolysis of solid fuels (due to lack of oxygen), which establishes a flame around a cluster of these particles. During this change, the individual particles' flames transitions to a flame around a group of particles. In the case of nanothermites, which are a type of nanoreactors that do not have limitations in terms of oxidizer availability, since it is available within each particle, each particle acts as a microreactor with the ability to ignite when it reaches above its ignition temperature. Thus, the combustion dynamics of the group are a purely heat and mass transfer problem.

[0122] It is noteworthy that heat release is a function of temperature. The temperature variation within a cloud plays an important role in group combustion, which depends on the mass transfer of copper vapor above the ignition temperature. It is reasonable to assume that combustion reactions in region B (of FIG. 3) take place uniformly since it is the domain of mean mass and mean temperature within the interstitial field. Thus, the group is considered as a homogeneous phase. It was previously demonstrated for a group interaction system that all the particles must be at the same temperature (Ts) for the thermodynamic equilibrium to occur at a steady-state. Therefore, the reaction rate in each configuration was considered constant in the model.

[0123] The group or cloud method described herein involves obtaining the statistical mean of the mass source. The conservation of mass of copper vapors of all particles for the control volume bounded within cross-sections of radiir and r+dr is given as:

[00018]$\begin{array}{cc}\frac{d}{\mathrm{dr}}\left(4\right))r^2\frac{\mathrm{dY}}{\mathrm{dr}})=\{\begin{array}{cc}4r^{2}n\left(4\right))r_s\ln \left(1+B\left(r\right)\right)),& r<R_G\\ 0,& r>R_G,\end{array}& \left(18\right)\end{array}$

[0124] Quasi-Steady Assumptions of Group CombustionThe above governing equation of group combustion holds under the following assumptions. The combustion time of each particle is sufficiently long to establish a steady state over a continuous gas field of size O(RG). The combustion and its effect of every particle can be viewed as point sources of mass and energy for the gas field. The ignition of each particle is governed by the surrounding temperature of the gas phase.

[0125] An appropriate inter-particle vapor product propagation model can determine how the steady combustion field is realized within the group combustion theory. The solution of the above governing equation was determined following the approach adopted in the literature. Here, the solution is presented for a monodispersed and uniformly distributed group. The radial variation of mass fraction and temperature is as follows:

[00019]$$\begin{gathered} \begin{array}{cc}-\frac{\ln \left(\frac{Y-Y_{}}{Y_s-1_{}}\right)}{M_{\mathrm{SC}}}=-\frac{\ln \left(\frac{T-T_{}}{T_s-T_{}}\right)}{M_{\mathrm{SC}}}=1-\frac{\sin h\left(\frac{\sqrt{G}}{\left(R_G/r\right)}\right)}{\frac{\sqrt{G}}{\{R_G/r)}\cosh \left(\sqrt{G}\right)},r<R_G, \\ & \left(19\right)\end{array} \end{gathered}$$$\begin{array}{cc}=\frac{R_G}{r}\left(1-\frac{\tan h\left(\sqrt{G}\right)}{\sqrt{G}}\right),r>R_G,& \left(20\right)\end{array}$

[0126] where MSC=In(1+B) is the non-dimensional rate of sheath combustion as is defined in Equation (30) and the group combustion number (G) can be expressed as follows:

[00020]$\begin{array}{cc}G=4{\mathrm{nr}}_s{R}_G^2=3N\left(\frac{r_s}{R_G}\right)=S_s\frac{R_G^2}{r_s}& \left(21\right)\end{array}$$\begin{array}{cc}=3{}_F{\left(\frac{R_G}{r_s}\right)}^2=\frac{9m_{s,G}}{4r_s^2{}_s{R}_G}& \left(22\right)\end{array}$$\begin{array}{cc}=\left(\frac{m_{s,G}}{\frac{4}{3}{R}_G^3}\frac{1}{{}_s}\right)\frac{3R_G^2}{r_s^2}=\left(1-\right)\frac{3R_G^2}{r_s^2},& \left(23\right)\end{array}$ [0127] where n is the density of particles (with units of m3), rs is the radius of the particle, N is the total number of particles in the group, Ss is the surface area of the particles in a unit volume, F is the ratio of fuel to air volume, ms, G is the total mass of particles in the group and =1TGD/s is the virtual porosity of the particles in the group, wherein pTGD=(ms, G43R3G) is the theoretical group density.

[0128] The G number expresses a relationship between the total number of particles (N) and normalized interparticle spacing of l/rs within a cluster. As the core-shell particles are local sources of heat and mass, the physical implication of G can also be determined as the ratio of the characteristic heat release rate of the exothermic reaction to the heat transport rate of products (as copper vapors) in the group/cloud, from Equations (19) and (20).

[0129] The normalized mass-fraction and temperature of nanothermite group combustion, determined using Equations (19) and (20), are plotted in graph 400 of FIG. 4. These normalized plots are similar to the non-dimensional temperature distribution and non-dimensional vapor mass fraction of group evaporationthis is a reasonable observation as both droplet evaporation and core-shell nanothermite combustion depend primarily on temperature, not the availability of the oxidizer. The variations of the temperature (T) and mass fraction (Y) of the nanothermite combustion products, as in Equations (19) and (20), differ from both spray and char combustion. However, the normalized Shvab-Zeldovich of variables the spray combustion (=FO2FO2, sFO2FO2,, where F2=YFcFYO2cO2) and char combustion (=1+CO221+CO22,, where CO22=YCO2cCO2+YO2cO2) are similar to that of the non-dimensional temperature (and non-dimensional mass-fraction) of the nanothermites (Equations (19) and (20)).

Group Mass-Loss Rate and Correction Factor

[0130] The outflux of copper vapors progressively increases radially (r) from the cloud center (r=0) to the cloud periphery (r=RG) because of the symmetry. The clouds mass flow rate at a radial location (r) is determined by summing up the overall particle sources (from Equation (4)) as follows:

[00021]$\begin{array}{cc}{\stackrel{.}{m}}_r={}_0^{r}4r^{2}n{\stackrel{.}{m}}_s\mathrm{dr}={}_0^{r}4r^{2}n\left(4\right))r_s\ln \left(1+B\left(r\right)\right))\mathrm{dr},& \left(24\right)\end{array}$

[0131] Further, the total mass flow rate (m.Math.G) at the boundary and outside of the cloud is as follows:

[00022]$\begin{array}{cc}{\stackrel{.}{m}}_G={\stackrel{.}{m}}_{r=R_G}={}_0^{R_G}4r^{2}n{\stackrel{.}{m}}_s\mathrm{dr}r{R}_G,& \left(25\right)\end{array}$

[0132] Thus, the normalized radial mass outflux rate of the group is given by the following formula:

[00023]$\begin{array}{cc}\frac{{\stackrel{.}{m}}_r}{{\stackrel{.}{m}}_G}={\left(\frac{R_G}{r}\right)}^{\frac{-3}{4}}\frac{\cos h\left({G^{\frac{1}{2}}\left(\frac{R_G}{r}\right)}^{\frac{-3}{2}}\right)-\frac{\sin h\left({G^{\frac{1}{2}}\left(\frac{R_G}{r}\right)}^{\frac{-3}{2}}\right)}{{G^{\frac{1}{2}}\left(\frac{R_G}{r}\right)}^{\frac{-3}{2}}}}{\cos h\left(G^{\frac{1}{2}}\right)-\frac{\sin h\left(G^{\frac{1}{2}}\right)}{G^{\frac{1}{2}}}},r<R_G& \left(26\right)\end{array}$$\begin{array}{cc}=1,r{R}_G,& \left(27\right)\end{array}$

[0133] Graph 500 of FIG. 5 plots the normalized radial mass flow rate (m.Math.r\m.Math.G) against the normalized radius (r/RG) for different group combustion numbers (G). It was observed that as the G increased, the majority of the combustion occurred near the group perimeter, for instance in sheath combustion for G>100).

[0134] Furthermore, the non-dimensional mass group rate (MG) can be obtained as follows:

[00024]$\begin{array}{cc}{M}_G=\frac{{\stackrel{.}{m}}_G}{4))R_G},& \left(28\right)\end{array}$

[0135] The mass flux in the cloud is normalized by (4RGD), analogous to the normalizing term of single particle combustion presented in Equation (5). The normalized mass flux considered in the nanothermite group combustion was described so that the conditions of the cloud versus the single particle combustion could be compared. The solution for the group mass-loss rate is provided in two forms. First, the ratio of non-dimensional nanothermite group combustion (MG) with the non-dimensional sheath combustion rate (MSC) is defined as follows:

[00025]$\begin{array}{cc}\frac{M_G}{M_{\mathrm{SC}}}=1-\left(\frac{\tan h\left(G^{1/2}\right)}{G^{1/2}}\right),& \left(29\right)\end{array}$ [0136] where the non-dimensional rate of sheath combustion (MSC) is obtained from Equation (4) as follows:

[00026]$\begin{array}{cc}{M}_{\mathrm{SC}}=\frac{{\stackrel{.}{m}}_{\mathrm{SC},G}}{4))R_G}=\ln \left(1+B\right),& \left(30\right)\end{array}$

[0137] With the increasing magnitudes of G, the above fraction (MGMSC) tends to reach a unitary value as shown by the trend of graphs 600 and 602 of FIGS. 6A and 6B. The limiting cases (e.g., G<0.1 and G>100) can be approximated as 1(tanh (G1/2) G1/2)=GG+3. Before proceeding to the next form of the group mass-loss rate, it is important to note that nanothermite group combustion was classified based on the magnitude of MGMSC, which in turn was based on the group combustion number (G). Secondly, the group mass-loss rate can be normalized by integrating the isolated group burn rate (MISO,G) as follows:

[00027]$\begin{array}{cc}=\frac{M_G}{M_{\mathrm{ISO},G}}=\frac{3}{G}\left[1-\left(\frac{\tan h\left(G^{1/2}\right)}{G^{1/2}}\right)\right]=\frac{M_G}{M_{\mathrm{SC}}}\frac{3}{G},& \left(31\right)\end{array}$ [0138] where the non-dimensional isolated group combustion is provided by considering Equation (5) of single particle combustion as follows:

[00028]$\begin{array}{cc}{M}_{\mathrm{ISO},G}=\frac{{\stackrel{.}{m}}_{\mathrm{ISO},G}}{4))R_G}=\frac{N{\stackrel{.}{m}}_{\mathrm{iso}}}{4))R_G}=N\ln \left(1+B\right)\frac{r_s}{R_G},& \left(32\right)\end{array}$

[0139] Graph 602 of FIG. 6B plots the variation of with G considering a monodispersed and uniform group of nanothermites. When the magnitude of G is approximately 0.5, equates to roughly 80% of the isolated particle combustion. The rate of particle combustion accounts for only about 10% of the isolated particle combustion rate for a group combustion number (G) of 100. As G approaches zero, the ratio tends towards one.

[0140] In this disclosure, the diffusion of species was treated as being controlled, and the problem was considered from a thermal point of view. Based on FIG. 4 for r>RG, group combustion is essentially a cloud of hot burning particles that loses heat to its surroundings. Graph 600 of FIG. 6A shows the results for group mass-loss rate in the form of MG\MSC variation with the group number (G). Graph 602 of FIG. 6B shows the group mass-loss rate in the form of variation with the group number (G).

[0141] In a group of particles where G approaches zero, each particle in the group is enclosed in a gas at the temperature of T, with MGMSC.fwdarw.0 considered for a range of MGMSC0.1. This case of isolated group combustion corresponds to group numbers of G<0.5 with .fwdarw.1 for magnitudes of M20.8. As the magnitude of G increases, each particle inside the group has the same temperature as the particle surface (TPS), and the concentration of copper vapors corresponds to the saturated condition. Therefore, a compact group of particles acts as a single, large, isolated particle placed in an ambient fluid at T and Y. Under these conditions, the group of particles is considered to combust in the sheath combustion (SC) regime. As the magnitude of G increases, the fraction MGMSC reaches one, which is considered for a range of MGMSC>0.9. This corresponds to group number of G>100 with .fwdarw.0 for a range of S0.03. This variation in does not indicate that the combustion rate of nanothermites reduces as G increases.

[0142] The above ranges of group number (G) assist in classifying the group mass loss rate to the sheath combustion mode (MG=MSC for G>100) and the isolated combustion mode (MG=MISO,G for G<0.5) as defined in Equations (29) and (31), respectively. Whilst this variation of group mass-loss rates (MG/MSC and ) with group number (G) is already established for spray and char combustion, it helps to establish that these variations are the same and consistent for nanothermite combustion as well.

Group Classification

[0143] The following part of this paper describes, in greater detail, the classification of nanothermite group combustion modes. As previously mentioned, this classification is based on the magnitude range of the group mass-loss rate MGMSC, which further depends on the group combustion number (G). G can be redefined as the ratio of mass transfer between the particles in the group (Region A, FIG. 3) to the mass transfer between the group and its surroundings (Region B, FIG. 3). This assists with the classification of different nanothermite combustion modes. When the mass transfer along the group boundary and ambient region (Region A, FIG. 3) is extremely rapid in comparison to the net transfer among the particles and surrounding gaseous phase in the group (Region B, FIG. 3), G is small and likely attributable to an isolated combustion (ISOC, Zone i) mode. When the mass transfer along the group boundary and ambient region is significantly low in comparison to the net transfer among the particles and the surrounding gaseous phase in the group, G is large and it is suitable to adopt the sheath combustion (SC, Zone iv) mode.

[0144] Other than the isolated combustion (ISOC) model and the sheath combustion (SC) model, Table 3000 of FIG. 30 also classifies the intermediate models of nanothermite combustion. Overall, nanothermite groups can be classified simply into internal group combustionrepresenting Regime I of MGMSC<0.7 with G<10and external group combustion representing Regime II of MGMSC>0.7 and with G>10 as shown in FIGS. 7A and 7B. The other modes are individual to partial group combustion in the upper limit of internal group combustion with the group combustion number in the range of 0.5<<<10 which represents Zone ii of 0.1<MGMSC<0.7 and 0.8>>0.2 in Table 3000. Further, the group combustion number in the range of 10<G<100 represents Zone iii of 0.7<MGMSC<0.9 and 0.2>>0.03. Zone iii is in the lower limit of external group combustion, depicting the modes of critical particle combustion (CPC) and external particle combustion (EPC).

Isolated Particle Combustion (ISOC)

[0145] In the case when particles are sufficiently distant from each another, they combust in an isolated mode of combustion. The existence of neighboring particles has no effect on the combustion characteristics of an individual particle.

Internal Group Combustion (IGC)

[0146] It is hard to delineate the zones of cloud combustion for nanothermite as the species in the gaseous phase do not chemically react and there is no requirement to find oxygen-deficient regions. Thus, the various minor modes of nanothermite combustion (IPG, IGC and PG, as well as CGC, EPC and SC) are placed into the same groups. Internal Group Combustion (IGC) and External Group Combustion (EGC) were also established in spray combustion. In the case of Internal Group Combustion (IGC), the highest mass fraction of copper (vapour product), Y=YMax, is located inside the group cloud (r<RG).

Individual Particle Combustion (IPC)

[0147] If the number density (n) of nanothermite increases, the burning characteristics of the constituent particles change owing to the rise in temperature within the region. However, suppose the inter-particle distance (I) is large. In such a case, each particle still maintains its own combustion characteristics, with the temperature of the cloud being higher than the temperature of isolated particle combustion. This is termed IPC, as demonstrated in diagram 800 of FIG. 8A.

Incipient Group Combustion (IGC)

[0148] The outermost nanothermites continue to combust in IPC as the magnitude of n increases. These nanothermites produce copper vapors, resulting in increased copper vapors (YCu) within the cloud. As this continues, the copper vapors reach the maximum mass fraction of saturation located at the cloud's core. Further, the temperature at this location is at its maximum due to the maximum mass fraction of combustion products. This is termed IGC, as shown in diagram 802 of FIG. 8B.

Partial Group Combustion (PGC)

[0149] As n increases even further, the inner particles are starved of outer vapors (by extension, thermal energy) and ignite at a slow pace. The vapors from the inner region diffuse outwards and establish a maximum temperature inside the cloud. However, the nanothermites located in the outer region of the cloud combust in the form of IPC. This phenomenon is denoted as PGC, see diagram 804 of FIG. 8C.

External Group Combustion (EGC)

[0150] Suppose the concentration of nanothermites (n) is further increased, such that, it causes a decrease in the copper vapor concentration within the cloud, and the location at which YCu0 moves radially outwards from the cloud's core. Furthermore, the mass fraction of fuel around the group's center increases with an increase in the number density. For the regime of EGC, the maximum mass fraction of the copper vapors (Y=Y Max) is located at the group cloud radius (r=RG).

Critical Group Combustion (CGC)

[0151] As the magnitude of n increases further, the flux of copper vapor is such that it cannot penetrate to the cloud's core and prevent the combustion of the nanothermites at the center. The maximum temperature is located only at the cloud surface. This is termed CGC, as shown in diagram 806 of FIG. 8D.

External Particle Combustion (EPC)

[0152] When n is further increased, the flux of inner copper vapors prevents outer copper vapors (and heat) from penetrating into the cloud center (and its surroundings). A maximum temperature is still determined at the group radius (RG). This is called EGC, as shown in diagram 808 of FIG. 8E.

Sheath Combustion (SC)

[0153] When n increases to large magnitudes, thereby forming a compact group, a state is achieved in which the temperature at the boundary of the particle group is at the ignition temperature of the nanothermite. The group acts similarly to an individual large particle of radius RG

[0154] that has a group mass density similar to single particle density (pG=s). This combustion mode is known as sheath combustion, as shown in diagram 810 of FIG. 8F. Thus, the single-particle results previously presented herein can be used for a highly dense spherical cloud.

[0155] In practical cases, Too is lower than the ignition temperature of the considered core-shell nanothermites. FIGS. 8A-8F demonstrate that the core-shell nanothermite combustion results in net heat release to the initial ambient gas because the magnitudes of the temperature profile are greater than the ambient temperature (T>T).

[0156] As shown in FIG. 7A, the mass fraction (Y) profiles are indicative of combustion occurring inside the thermite cloud since every particle in the system has access to an oxidizer. FIG. 7B also shows combustion in an area bordering the thermite cloud. Additionally, the temperature profiles in FIGS. 8A-8F are at their maximum at or within the cloud boundary and decrease to that of a distant temperature (T). Regardless of the mode of external combustion in FIGS. 8D-8F, maximum temperature mainly occurs at the boundary because of the high particle concentration, which causes greater heat flux to the surrounding gas than the heat influx into the cloud interior. If that the single particle completely burns instantly is considered, then the time for single particle combustion is zero (ts=0), Equation (17), which is not the case for nanothermites.

[0157] It is important to emphasize that the combustion of nanothermites is not oxidizer limited. The model implicitly assumes that the stoichiometry of the nanothermite is balanced, i.e., the copper oxide content in the core-shell is neither more nor less in comparison to the aluminium content. This is an important distinction compared to spray and coal combustion. Owing to this property, internal particles of the cloud boundary may react via heat diffusion or the mass convection of products. Diagram 900 of FIG. 9A illustrates the external sheath combustion (ESC), while diagram 902 of FIG. 9B depicts the internal sheath combustion (ISC) mode of nanothermites.

[0158] FIG. 10A shows a diagram 1000 depicting the required number of particles (N), and FIG. 10B shows the fraction of cloud radius to particle radius (RG/rs) with interparticle spacing (l/rs) for different group combustion numbers (G). The variation in G represents different group combustion modes. The data representing l/rs<2, RG/rs<2, and N<1 are theoretical and have no physical implications. As shown in graph 1000 of FIG. 10A, l/rs=30 is fixed and increasing N results in a larger group radius. Hence at l/rs=30, the mode of isolated particle combustion occurs when N6, internal group combustion occurs when 6$N$488, external group combustion takes place if 488SN15,450, and sheath combustion develops for N15,450. Likewise, considering graph 1002 of FIG. 10B where l/rs=30 is chosen, the mode of isolated particle combustion takes place when RG/rs32 (e.g., rs=30 m, RG1 mm), internal group combustion takes place if 32SRG/rs146, (1 mm SRG4.6 mm), external group combustion occurs for 146 SRG/rs464, (4.6 mmRG15 mm), and sheath combustion develops if RG/rs464 (RG15 mm). As the combustion rate reaches isolated particle combustion, the reducing group radius (RG) correlates to a higher combustion rate of each particle. Note that the quasi-steady assumption underpins all of the plots in this section, and also the time-dependent considerations reduce the interaction.

Comparison with Other Group Combustion Models

[0159] Table 3100 of FIG. 31 classifies various nanothermite group combustion regimes with the lower limit and upper limit of the group combustion number (G). The upper limit of the regime corresponds to the lower limit of the next regime. The regime before the Individual Particle Combustion (IPC) corresponds to Isolated Particle Combustion (ISOG), where particles burn without interaction. It can be observed in Table 3100 that the magnitude of nanothermite regimes varies exponentially from IPC of 0.5 to CPC of 10 to SC of 100. It is apparent from this table that the magnitudes of G are higher for nanothermite regimes than for spray combustion. These higher magnitudes of G occur because the combustion is not limited by the oxygen availability in the gas phase.

[0160] Previous works analyzed the transient combustion of a quiescent droplet cloud. They reported that a cloud ignites with ease in comparison to a single droplet. Additionally, if the cluster is dense, ignition is limited to within a narrow band along the outer surface of the cluster. Similarly, the ignition of a fuel spray was investigated by other previous works. Here, the influence of convection was determined to be less crucial in a cloud of high spray concentration. In this case, until a considerable quantity of fuel evaporates and saturates the environment, combustion does not begin. In this regard, other works numerically studied the time-dependent ignition of a cold spray as it was suddenly exposed to a hot environment. It was found that ignition and combustion within a cloud can take place even if the cloud is non-diluted (G>1). This aberrant combustion contradicts the typical norms of group combustion.

Group Combustion of Non-Spherical Particle Distribution

[0161] In order to model the combustion of nanothermites, a group combustion model for the simple geometry of spherical particle distribution was developed in the present disclosure. A hypothetical group combustion of nanothermites is shown in diagram 1100 of FIG. 11, where a two-dimensional flux of nanothermites entrained from the nozzle along with a laminar flow surrounding it was considered. This injection of nanothermites was distributed with a greater concentration near the nozzle and a lesser concentration further away. Symmetry conditions around the midline can be taken into account. The resulting temperature of the gas mixture is higher in a region when the concentration of nanothermites is higher. Having nanothermite particles distributed randomly in such a system and the complexities of the flow fields makes it difficult to obtain a closed-form solution to this problem. To be able to identify the parameters governing the group behavior in such a system, it is helpful to achieve explicit solutions for the burn rate and correction factor for simple geometry, as discussed previously herein (and FIGS. 8A-8F).

[0162] A diagram 1100 of the particle distribution of nanothermites is shown in FIG. 11, along with the contour map of the heat release for the corresponding regions. The combustion flow regimes can be classified as either an external group combustion regime or an internal group combustion regime. The zones under these regimes are considered equivalent to simple geometry zones (SC, EPC, etc.). As long as there are particles within the boundaries of such particle distributions but no particles outside, then there is a mass source term for particles within the boundary but not for particles outside. In other words, there is a variation in the number density, which is indirectly the mass source. By assuming that these zones are reshaped to a spherical shape and there is no convective flow across the zones, a closed-form solution to the burn rate of clouds is obtained.

[0163] When ignited, the nanothermites burn mostly along the boundary of the distribution in external group combustion. Because the nanothermite core is too cold for ignition at the nozzle exit, it was hypothesized that ignition begins further downstream. As nanothermites are highly dense (SC), heat transfer and ignition are not possible within the distribution boundary, resulting in ignition occurring outside this boundary. The increasing separation of particles (EPC) results in heat penetration of the inner side of the cloud and ignition of those particles. After a sufficiently large separation of the particles is reached, heat penetrates to the mid-area of the jet, intersecting and igniting the entire cluster (CPC). After this zone, internal group combustion may exist outside of the external group combustion. There may be an individual combustion zone (PGC) or a nested combustion zone (IGC) around a group of particles. This is followed by the terminal zone, where unburned nanothermite particles are consumed individually (IPC).

[0164] It is important to emphasize that this discourse began by focusing on aluminium-copper oxide. However, this framework can be applied to a variety of different nanothermite compositions, such as aluminium-bismuth trioxide and aluminium-iron oxide. Some of these fuels are more gas generating, while others are predominantly energy generating. Aluminium-copper oxide does not generate a lot of vapors compared to the other types of nanothermites. Thus, all these different effects could also be expanded to the present disclosure, including the high amount of gas generations as well as describing the high threshold values for enthalpy and observing their impact on the results.

[0165] The combustion modes and characteristics described herein may be applied to a number of different systems, environments and applications. In general, in the application of dispersed combustion of core-shell thermite particles, core-shell thermite particles will be dispersed into a group, and ignited, combusting the group of thermite particles, producing heat. This heat may be applied to a number of different applications.

[0166] Referring now to FIG. 12, pictured therein is a diagram 1200 applying the dispersed group combustion characteristics of core-shell thermite particles as described herein. Diagram 1200 shows a reactive solar collector, which may be filled with core-shell thermite particles. These particles may be ignited, using concentrated solar energy, and combusted in a group dispersion to produce heat.

[0167] Referring now to FIG. 13, pictured therein is a diagram 1300 showing a number of different rocket configurations, including nozzles, combustion chambers and fuel injectors. The various nozzle, combustion chamber and fuel injector configurations of FIG. 13 may be applied to group combustion of thermite core-shell particles as described herein. These configurations may include bell, cone, spike, E-D, RF and HF nozzle types.

[0168] Referring now to FIG. 14, pictured therein is a diagram 1400 describing various fuel injector configurations. The various fuel injector configurations of FIG. 14 may be applied to group combustion of thermite core-shell particles as described herein. Configurations may include concentric tube, concentric tube with liquid swirl, unlike pentad, unlike doublet, and unlike triplet configurations. In some examples, the configurations of FIG. 14 may apply a combination of various core-shell thermite particles and a reactive and/or carrier gas.

[0169] Referring now to FIG. 15, pictured therein is a diagram 1500 detailing various spray nozzles, which may for example be applied as fuel injectors for group combustion of thermite core-shell particles as described herein. Spray nozzle configurations include single hole, multi-hole, pintle, and pintaux. In some examples, the configurations of FIG. 15 may apply a combination of various core-shell thermite particles and a reactive and/or carrier gas.

[0170] Referring now to FIG. 16, pictured therein is a diagram 1600 detailing various rocket injector configurations. Different configurations may be applied, for example, to achieve different modes of combustion as described herein, when applied to the group combustion of thermite core-shell particles. Configurations may include low momentum and high momentum fuel jets.

[0171] Referring now to FIG. 17, pictured therein is a diagram 1700 detailing various rocket configurations. Different configurations may be applied, for example, to achieve different modes of combustion as described herein, when applied to the group combustion of thermite core-shell particles. Configurations may include sharp-edged orifice, short tube with rounded entrance, short tube with conical entrance, short tube with spiral effect and sharp edged cone.

[0172] Referring now to FIG. 18, pictured therein are diagrams 1800, 1802, 1804 and 1806, detailing various rocket fueling configurations. Different configurations may be applied, for example, to achieve different modes of combustion as described herein, when applied to the group combustion of thermite core-shell particles.

[0173] Referring now to FIG. 19, pictured therein are diagrams 1900, 1902, detailing rocket engine configurations. These rocket engine configurations may be applied, for example, to achieve different modes of combustion as described herein, when applied to the group combustion of thermite core-shell particles.

[0174] Referring now to FIG. 20, pictured therein is diagram 2000, detailing fuel injector configurations. These fuel injector configurations may be applied, for example, to achieve different modes of combustion as described herein, when applied to the group combustion of thermite core-shell particles. Fuel injector configurations of FIG. 20 may include unlike doublet, unlike triplet, unlike quadlet, and unlike pentad.

[0175] Referring now to FIG. 21, pictured therein is diagram 2100, detailing engine and fuel supply configurations for an engine. These engine configurations may be applied, for example, to achieve different modes of combustion as described herein, when applied to the group combustion of thermite core-shell particles. Engine fuel injector configurations of FIG. 21 may include double impinging stream pattern, triplet impinging stream pattern, self-impinging stream pattern and show head stream pattern.

[0176] Referring now to FIG. 22, pictured therein is diagram 2200, detailing fuel injector configurations. These fuel injector configurations may be applied, for example, to achieve different modes of combustion as described herein, when applied to the group combustion of thermite core-shell particles. Fuel injector configurations of FIG. 22 may include concentric tube, concentric tube with liquid swirl, unlike pentad, unlike doublet, unlike triplet, like doublet, showerhead, variable area (pintle), and splash plate.

[0177] Referring now to FIG. 23, pictured therein is diagram 2300, detailing fuel injector spray configurations. These fuel injector spray configurations may be applied, for example, to achieve different modes of combustion as described herein, when applied to the group combustion of thermite core-shell particles. Fuel injector spray configurations of FIG. 23 may include regular flat fan, even flat fan, hollow cone, flooding flat fan and whirl chamber.

[0178] Referring now to FIG. 24, pictured therein is diagram 2400, detailing fuel injector spray configurations. These fuel injector spray configurations may be applied, for example, to achieve different modes of combustion as described herein, when applied to the group combustion of thermite core-shell particles. Fuel injector spray configurations of FIG. 24 may include air atomizing, hydraulic fine spray, hollow cone, flat fan and full cone spray configurations.

[0179] Referring now to FIG. 25, pictured therein is diagram 2500, detailing fuel injector spray configurations. These fuel injector spray configurations may be applied, for example, to achieve different modes of combustion as described herein, when applied to the group combustion of thermite core-shell particles. Fuel injector spray configurations of FIG. 25 may include full cone, hollow cone, flat fan, solid stream, cluster nozzle, tongue type nozzle, flat fan nozzle, and pneumatic atomizing configurations. Such configurations may comprise external mixing and internal mixing.

[0180] Referring now to FIG. 26A, pictured therein is diagram 2600, detailing fuel injector configurations. These fuel injector configurations may be applied, for example, to achieve different modes of combustion as described herein, when applied to the group combustion of thermite core-shell particles. Fuel injector configurations may include throttle body injection, and single point injection.

[0181] Referring now to FIG. 26B, pictured therein are diagrams 2602, 2604, detailing fuel injector configurations. These fuel injector configurations may be applied, for example, to achieve different modes of combustion as described herein, when applied to the group combustion of thermite core-shell particles. Fuel injector configurations may include throttle body injection, and multi-point injection.

[0182] When the group combustion of thermite core-shell particles is applied to engines as shown in FIGS. 26A-26B, the engine may comprise internal combustion or external combustion. In some examples, the systems and methods described herein may be applied to thermal power generation. In some examples, the systems and methods described herein may be applied to additive manufacturing processes and methods, including those applying cool spray methods. In some examples, the systems and methods described herein may be applied to the production and/or use of recyclable energetic particles. In some examples, the systems and methods described herein may be applied to curing methods using electromagnetic radiation. In some examples, the systems and methods described herein may be applied to induction-based systems for heating and ignition. In some examples, the systems and methods described herein may be applied to muti-ignition systems including solar and non-radiative sources, and radiative sources such as electromagnetic radiation, lasers, masers, MW radiation, infrared radiation, THz radiation and other radiation.

[0183] In some examples, the systems and methods described herein may be applied to additive manufacturing including inductive heating. In some examples, the systems and methods described herein may be applied to surface finish configuration of additive manufacturing, including cooling systems to enable phase changes. In some examples, the systems and methods described herein may be applied to the additive manufacturing with embedded core-shell thermite particles. In some examples, the systems and methods described herein may be applied to additive manufacturing including spraying on layers on structures. In some examples, the systems and methods described herein may be applied to additive manufacturing for synthesis and manufacturing purposes.

[0184] Referring now to FIG. 27, pictured therein is diagram 2700 detailing the application of group combustion of thermite core-shell particles to a power generation cycle. The power generation cycle may comprise a typical combined cycle or multiple generation cycle. Group combustion of thermite core-shell particles may be applied as the fuel source to such power generation cycles, replacing, for example, coal or natural gas combustion systems.

[0185] Referring now to FIGS. 28A-28B, pictured therein are diagrams 2800 and 2802, depicting a rocket configuration which may apply group combustion of thermite core-shell particles. By applying the fuel grain geometry and structural configuration of FIGS. 28A-28B, the combustion (e.g. combustion mode) of the group combustion of thermite core-shell particles may be configured and adjusted.

[0186] In some examples, the systems and methods described herein may be applied to thermal conversion systems include but not limited to thermal storage and radiant heat recycling systems, and thermoelectric, spintronics, and/or hybrid systems. In some examples, the systems and methods described herein may be applied to energy storage systems using wireless power. In some examples, the systems and methods described herein may be applied to additive manufacturing of anodes and cathodes for battery storage system. In such examples, thermites may serve as anodes and cathodes. In some examples, the systems and methods described herein may be applied to thermal heat storage in micro/nano materials, such as energetic composites. In some examples, the systems and methods described herein may be applied to inductively heating systems. In some examples, the systems and methods described herein may be applied to the coupling of thermites with thermophotovoltaic systems, for the conversion of heat energy to electricity. In some examples, the systems and methods described herein may be applied to additively manufacturable systems, such as printed integrated systems. In some examples, the systems and methods described herein may be applied to printing of thermite systems and integration of printed thermite systems into thermophotovoltaic systems. In some examples, the systems and methods described herein may be applied to system for converting heat to electricity. In some examples, the systems and methods described herein may be applied to energy storage system that are incorporated into the infrastructure of a smart city. In some examples, the systems and methods described herein may be applied to in-situ resource utilization materials mixed with aerogels to produce radio receivers and transmitters. In some examples, the systems and methods described herein may be applied to thermal storage systems using wireless power transmission, TPV, thermoelectric, spintronics, quantum effects, or the like. In some examples, the systems and methods described herein may be applied to hybrid systems for cogeneration including the incorporation of thermal conversion systems using other energy renewable energy sources.

[0187] In some examples, the wireless power transmission, may use a plurality of transmitters and a plurality of receivers to create a network, a pilot signal between a receiver and one or more transmitters may be established using a first electromagnetic source to create the initial conditions, where the receiver may send a primary electromagnetic source to a plurality of transmitters, and or where the transmitter may send a second electromagnetic source to a plurality of receivers. Furthermore, the plurality of transmitters and receivers may be networked in a plurality of network configurations. In other implementations, the transmitter may be at least one or a combination or the following: mm-wave, laser, maser, MW, infrared, THz or the like or other electromagnetic source may be used to create the initial conditions. In other implementations, the transmitter may be a non-radiative source such as magnets or electromagnets. In other implementations, the receiver may receive energy from a plurality of electromagnetic radiative and/or non-radiative sources.

[0188] In some examples, the systems and methods described herein may be applied to thermal conversion systems that are configured to operate in extreme temperature environments, using the available heat from a source to convert the heat to electricityfor example a satellite system, rovers, space architecture, drones, flight vehicles and other like examples. In some examples, the systems and methods described herein may be applied to submarines/drones using geothermal energy as a heat source to power a plurality of systems. In some examples, the systems and methods described herein may be applied to the storage of heat in structures (for example, graphene-based and/or micro- and/or nano-energetic particles). In some examples, the systems and methods described herein may be applied to structures that may be inflatable, deployable, and additively manufacturable. In some examples, the systems and methods described herein may be applied to systems coupled to other thermal power generation systems. In some examples, the systems and methods described herein may be applied to enable continuous flight using reusable vehiclesfor communications, asset monitoring, climate change, mobile data collection systems, flying telescopes, and other uses cases. In some examples, the systems and methods described herein may be applied to vehicles operating in multiple domains (for example, land, air, water, and space). In some examples, the systems and methods described herein may be applied to system and methods for combining power generation, storage, and distribution.

[0189] In some examples, the systems and methods described herein may be applied to thermal storage system that can be charge from renewable and other sources, and provide energy for hot water, cooling, and on demand heating and electricity. In some examples, the systems and methods described herein may be applied to temperature control system to drive various heat reactions. In some examples, the systems and methods described herein may be applied to graphene-based systems and other materials may be added to improve performance. In some examples, the systems and methods described herein may be applied to metering systems equipped with blockchain technology. In some examples, the systems and methods described herein may be applied to reduce emissions, and locally additive manufacturable systems. In some examples, the systems and methods described herein may be applied to thermal storage systems integrated into existing or new infrastructure (for example, buildings, windows, homes, sidewalks, utility poles, other surfaces or volumes). In some examples, the systems and methods described herein may be applied as alternatives to gas boilers and heat pumps. In some examples, the systems and methods described herein may be applied to active and/or passive cooling system for on earth and/or in space applications for robotic exploration and human space exploration (including living and working in space). In some examples, the systems and methods described herein may be applied to towing applications, for example, vehicles using TCS and/or TSS. In some examples, the systems and methods described herein may be applied to magnetohydrodynamic systems and methods. In some examples, the systems and methods described herein may be applied to wireless power transmission and the networking of a plurality of nodes for power transmission.

[0190] In some examples, the systems and methods described herein may be applied to emitters, including multi-layered systems using energetic materials, having controllable and adjustable ranges of operations and being deployable, additively manufacturable and inflatable. In some examples, the systems and methods described herein may be applied to receivers, including multi-layered systems using energetic materials, having controllable and adjustable ranges of operations, and being deployable, additively manufacturable and inflatable. In some examples, the systems and methods described herein may be applied to groups of particles prepared in multi-dimensional geometric shapes, both symmetric and asymmetric. In some examples, the systems and methods described herein may be applied to Smart Networking for Power Management using AI/ML algorithms for continuous operations.

[0191] In some examples, the systems and methods described herein may be applied to thermal power plants using nanothermite/nanoenergetic particles and/or composites for power generation, such methods allow for the heating and/or ignition of nanothermite/nanoenergetic composites through induction, specifically via heating using eddy currents or heating via hysteresis, or heating using a combination of both eddy currents and hysteresis. The heating in such examples is used as part of a boiler for power generation in a power plant. In some examples, the systems and methods described herein may be applied to driving steam engines (e.g. Sterling engines)by means of combustion and/or sintering, for heating the working fluid where nano-/micro-thermites and energetic materials are used to heat the working fluid by way of complete combustion or convection to enable a phase change. In some examples, the systems and methods described herein may be applied to double combustion to drive multiple processes using systems above, where byproducts of one reaction become the products of another. In some examples, the systems and methods described herein may be applied to chemical looping methods and/or metallic looping methods to drive processes to create electricity. In some examples, the systems and methods described herein may be applied to chemical looping and/or metallic looping by means of combustion or sintering.for byproduct production and processing of materials and/or byproducts. In some examples, the systems and methods described herein may be applied to thermal storage systems and recycling to radiate heat.

[0192] In some examples, the systems and methods described herein may be applied to thermal power plants used for cogeneration to generate electricity and useful heat simultaneously. Wasted thermal energy in such examples is put to some productive use. In some examples, the systems and methods described herein may be applied to thermal power plants used for multi-generation to simultaneously generate electricity, useful heat, cooling, propulsion, energy storage, and industrial products. In some examples, the systems and methods described herein may be applied to thermal power plants that can be combined with renewable and non-renewable power generation systems for generation and/or multi-generation of generate electricity, useful heat, cooling, propulsion, energy storage, and industrial products. Non-renewable power generation systems include but not limited to oil, gas, coal, natural gas, and nuclear power or the like. Renewal power generation systems include but not limited to solar thermal, biomass, compressor, fuel cell, and geothermal or the like. In some examples, the systems and methods described herein may be applied to multi-generation which is achieved through spin-mediated interconversion phenomena between dissimilar physical entities to create electricity, light, sound, vibration and heat-on Earth and in space. These phenomena include but are not limited to the Seebeck effect, Peltier effect, Spin Seebeck effect, Spin Peltier effect, Spin Hall effect and Inverse spin Hall effect. Spin conversions take place in regions near the interface between physical entities that are mediated by spins, which transfer angular momentum allowing for interconversion of electricity, light, sound, vibration and heat. In some examples, the systems and methods described herein may be applied to energy storage systems for on-demand applications and distribution. These systems include but are not limited to electrochemical, electromagnetic, thermodynamic, and mechanical. Stored energy is used either directly or indirectly through energy conversion processes as needed to provide a balance between energy supply and demand.

[0193] In some examples, the systems and methods described herein may be applied to methods to generate power on Earth and in space on the moon, other planets, asteroid, planetoids, and other celestial bodies. In some examples, the systems and methods described herein may be applied to the use of nanothermite fuels along with in space resources utilization as a fuel source, such as composite plus materials from the moon, mars, asteroids, & other celestial bodies, or a combination of the above. In some examples, the systems and methods described herein may be applied to high thermal control by using induction. Such systems allow for precise control of heat generation in defined areas, and as such it can be using to drive many chemical processes. In some examples, the systems and methods described herein may be applied to new or existing power generation applications with compact designs. In some examples, the systems and methods described herein may be applied to heating applications to ensure electronics and space systems, space architecture and other space systems remain operations and survive extreme cold or harsh environments.

[0194] In some examples, the systems and methods described herein may be applied to the use of micro and nano particles, in homogenous and/or heterogeneous mixtures. In some examples, such an application can comprise the combustion of a group of a same fuel, and/or a combination of a group of fuels and/or additives. In some examples, the systems and methods described herein may be applied to additive manufacturing of 2D/3D structures where combustion and/or heating is required. In some examples, the systems and methods described herein may be applied to other energy systems to augment performance with at least one of the following aspects: nuclear, fusion, fission, renewable technologies, solar, TPV, plasma, or solarthermal.

[0195] In some examples, the systems and methods described herein may be applied to power, propulsion, and construction systems and methods. In some examples, the systems and methods described herein may be applied to the matching combustion needs to a combustion profile. In some examples, the systems and methods described herein may be applied to various manufacturing methods, such as physically mixed, chemical, thermal, and other methods. In some examples, the systems and methods described herein may be applied to in situ resource utilization and international space research platform. In some examples, the systems and methods described herein may be applied to multi-generational power generation systems, such as those applying cogeneration, or trigeneration. In some examples, the systems and methods described herein may be applied to thermal Storage systems and batteries. In some examples, the systems and methods described herein may be applied to multi-source heating systems, such as those applying solar energy, solar concentrators, induction, or wireless power generation using electromagnetic radiation (mm-wave, laser, MW, infrared, THz or the like). In some examples, the systems and methods described herein may be applied to propulsion, power generation, heating, catalysts, welding or joining application, storage, and carbon sequestering. In some examples, the systems and methods described herein may be applied to fireworks and other pyrotechnics and public displays. In some examples, the systems and methods described herein may be applied to additive manufacturing of 2D and/or 3D structures. In some examples, the systems and methods described herein may be applied to satellite and/or space systems or components for robotic exploration vehicles. In some examples, the systems and methods described herein may be applied to the production and use of components for habitats and/or space architecture. In some examples, the systems and methods described herein may be applied to solar concentrators to augment energy production in space. In some examples, the systems and methods described herein may be applied to heating and combustion in oxygen devoid environments, in microgravity, or varied gravity for space-based application. In some examples, the systems and methods described herein may be coupled with other energy systems to augment performance with at least one of the following-nuclear, fusion, fission, renewable technologies, solar, thermophotovoltaics, plasma, and solarthermal.

[0196] In some examples, the systems and methods described herein may be applied to thermite fuels in the form of pellets, wax, solid, liquid, and/or plasma. In some examples, the systems and methods described herein may be applied to fuel configurations comprising tubes of various shapes and sizes. In some examples, the systems and methods described herein may be applied to engines. In some examples, the systems and methods described herein may be applied to recyclable fuels.

[0197] Referring now to FIG. 32, pictured therein is a flow chart depicting a method 3200 of producing energy. Method 3200 includes 3202 and 3204.

[0198] At 3202, core-shell thermite particles are provided.

[0199] At 3204, core-shell thermite particles are combusted in a dispersed group to produce heat. In some examples, core-shell thermite particles are heated without achieving combustion.

[0200] While the above description provides examples of one or more apparatus, methods, or systems, it will be appreciated that other apparatus, methods, or systems may be within the scope of the claims as interpreted by one of skill in the art.