Modeling of Dynamics and Thermal History of Fe40Al Intermetallic Powder Particles Under Gas Detonation Spraying Using Propane–Air Mixture
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Abstract
The dynamic properties and thermal history of Fe40Al at.% intermetallic particles have been estimated. The parameters of the gas detonation process for the investigated mixture have been calculated using thermochemical code, and the motion parameters as well as thermal history of the analyzed powder particles have been assessed using computational fluid dynamics software and selfdeveloped algorithms. The appropriate models allowed for determination of the melted volume (mass) fraction of a certain analyzed single particle, which is dependent on a particle diameter ranging from 10 to 160 μm. The results show that only particles with a diameter lower than 80 μm melt under the investigated conditions. Moreover, the estimated radial distribution of the temperature inside the particle is almost homogenous due to relatively high FeAl thermal conductivity and relatively low thermal conductance of the surface heat transfer. The calculated final velocity of particles has been referred to some experimental and literature data from previous studies by other researchers, and the results were found to be in agreement.
Keywords
CFD FeAl intermetallic powder gas detonation spraying numerical hybrid modeling particle dynamics particle thermal history thermochemical codeList of Symbols
 a_{1}, a_{2}, a_{3}
Constants in Eq 13c
 A
Constant in the Arrhenius relation (8a)
 \(\overline{A}\)
Linearized Jacobian matrix of system of equations
 BL
Barrel length
 c(T_{p})
Specific heat of particle material
 C_{1λ}, C_{2λ}
Constants in Sutherland relation describing thermal conductivity
 C_{1μ}, C_{2μ}
Constants in Sutherland relation describing dynamic viscosity
 C_{D}
Drag coefficient of the spherical particle
 C_{j}
Molar concentration of jth reactant
 C_{mi}
Constants defining specific heat of gaseous component for certain temperature subintervals
 c_{p}(T)
Specific heat of gas at constant pressure
 c_{pi}
Specific heat of ith gaseous component at constant pressure
 d_{p}
Diameter of the spherical particle
 E
Total energy per unit mass
 E_{a}
Energy of activation
 F
Flux vector
 F_{d}
Drag function
 F_{L}
Flux vector for left numerical cell
 F_{R}
Flux vector for right numerical cell
 k
Arrhenius term
 \(\overline{K}^{(i)}\)
Right eigenvector for the linearized Jacobian matrix
 M_{w}
Molar mass of gas
 M_{wi}
Molar mass of ith component of gas
 N
Number of gaseous components
 Nu_{p}
Nusselt number for particle
 p
Pressure
 Pr
Prandtl number
 \(\mathop q\limits^{ \bullet }\)
Density of heat flux
 r
Radial coordinate
 r_{wall}
Radial coordinate of wall surface
 R
Individual gas constant
 R_{h}
Energy source due to the chemical reaction
 R_{i}
Source of chemical species i
 \(\overline{R}_{i}\)
Molar reaction rate
 Re
Reynolds number
 SD
Spraying distance
 t
Time
 T
Gas temperature
 T_{barrel}
Barrel temperature
 T_{p}
Particle material temperature
 T_{ps}
Particle surface temperature
 U
Vector of conserved variables
 v
Gas velocity
 v_{p}
Particle velocity
 v_{par}
Component of gas velocity vector parallel to the boundary surface
 v_{perp}
Component of gas velocity vector perpendicular to the boundary surface
 v_{r}
Radial component of gas velocity
 v_{x}
Axial component of gas velocity
 x
Axial coordinate
 XPIP
Axial coordinate of powder injection point
 x_{wall}
Axial coordinate of wall surface
 Y_{i}
Concentration of the species i
 z_{i}
Molar fraction
 Δh_{melt}
Melting enthalpy
 ΔT_{phase}
Model rectangular melting peak/solidification peak width
 β
Temperature exponent in the Arrhenius law
 \(\overline{\alpha }_{i}\)
Wave strength
 α_{t}
Heat transfer coefficient
 ε_{p}
Particle surface emissivity
 η_{j}
Rate exponent for reactant
 λ
Thermal conductivity of gas
 \(\overline{\lambda }_{i}\)
ith Eigenvalue of the linearized Jacobian matrix
 λ_{p}
Thermal conductivity of particle material
 μ
Dynamic viscosity of gas
 μ_{i}
Dynamic viscosity of ith species
 ν′_{i}, ν″_{i}
Stoichiometric coefficients for ith reactant
 ρ
Gas density
 ρ_{p}
Particle material density
 σ
Stefan–Boltzman constant
Selected Subscripts
 mel
Melted state
 sol
Solid state
Introduction
Theoretical estimation of motion dynamics and the temperature history of powder particles during gas detonation spraying (GDS) is a crucial issue in adjustment of the GDS process parameters to powder particle size distribution and particle material physical properties in view of the required coating properties. As shown in (Ref 1, 2), the appropriate analyses involve problems characterized by coupling of mechanical and thermodynamic phenomena. This state of matter seriously limits the availability of analytical solutions and hinders developments of general models describing the investigated problem. Variety of parameters of spraying system and diversity of applicable powder materials, which differ in values of thermophysical and mechanical parameters describing the behavior of possible media during spraying process, result in the need to analyze every single case individually. Some of the first reports in this domain were provided in papers by Kadyrov (Ref 3, 4) and Ramadan and Butler (Ref 5, 6). In publication (Ref 3), which was based on simplified analytical model of detonation, E. Kadyrov and V. Kadyrov investigated the process of propulsion of powder particles. The authors estimated the muzzle velocity of powder particles, using a simple onedimensional detonation model for the explosive gas mixture. Furthermore, this approach required the application of numerical integration of the differential equation of motion for a particle. The analytical model was developed in order to describe the detonation process in the barrel. Consequently, making use of numerical schemes, the thermal interaction between powder and gaseous medium has been investigated (Ref 4). In both cases, the authors (Ref 3, 4) used a onedimensional model and their considerations were limited to motion of the powder–gas mixture only in the barrel. In order to reduce the effects of these drawbacks, the authors of (Ref 5, 6) proposed a twodimensional numerical model which allowed for considerations of additional effects, for example, particle interaction with reflected waves and the motion and thermal interaction of powder in the external conditions.
In the analyzed case of pulsed detonation, the flow is unsteady. As shown in Ref 5, during the spraying process, the moving powder particle faces with significant changes of thermodynamic and mechanical parameters of surrounding gas (Ref 5). The shock wave spreading from the barrel outlet reflects from the flat rigid substrate surface. Because the wave is spherical outside the barrel, its intensity decreases proportionally to the square of the distance covered. The reflected shock wave from the substrate dies out extremely fast. Thus, micronsized particles used in the GDS process do not encounter these shock wave transients (Ref 5, 6). As proven by Sova et al. (Ref 7), the GDS technique is characterized by higher complexity level in comparison with another spraying methods. This results in much more difficult theoretical description of phenomena during powder propulsion and structure formation. This problem was additionally described in experimental and theoretical papers (Ref 810), where authors underlined the complexity of the technique and necessity of individual approach to the GDS spraying problem. In accordance with cited sources, for so fast and highly nonequilibrium process, it is extremely difficult to identify and describe all the phenomena shaping the spraying process and defining its results.
Regarding the need for an individual approach for every single GDS problem, a methodology of a hybrid numerical analysis was elaborated and applied for a certain GDS case of intermetallic Fe40Al at.% particles. The applied methodology is based on approaches proposed by Kadyrov and Ramadan (Ref 36). Similar to those analyses, a oneway coupling between solid and gaseous phases was applied. In contrast to previous ones, the present analysis also accounts for heat conduction inside Fe40Al at.% particles, which additionally extend the applicability of the model. For a problem solution, a thermochemical code and commercial CFD software were applied. Eventually, the methodology was applied for determination of the terminal state of intermetallic Fe40Al at.% powder particles under certain experimental conditions, in which not only the particle velocity and temperature are sought, but also the different size of particles, which remain in solid state during coating formation once the substrate material is impacted.
These results are necessary as the initial conditions for simulations of terminal ballistics processes occurring during interaction of heated particles with the sprayed surface.
The Fe–Al phase equilibrium system shows that the hightemperature FeAl phase solution (the composition of which is very close to stoichiometric) is resistant to the temperature of 1310 °C (Ref 1). This fact is highly important because in view of lack of the feedstock material melting in the GDS process, the GDS produced coating can preserve the phase structure and the chemical composition of the FeAl powder used at a great extent. Thus, the fundamental problem when designing the GDS process is to select and apply spraying parameters ensuring that the intermetallic particles of powder feedstock will retain solid but with a substantially decreased Young modulus value.
Physical and Mathematical Model of the Problem
Physical Model of the Problem
In the presented investigations, the reactant propane–oxygen–air mixture was considered. The volume fractions of reactants were as follows: propane: 0.202 and oxygen: 0.685. The barrel length was equal to 590 mm and was characterized by interior diameter of 23 mm. The PIP was located 275 mm from the barrel bottom.
The whole analysis was restricted to one single cycle of gas detonation and particle propulsion. At the initial time of t = 0, the detonation process is initialized on the bottom of the barrel (at the axial coordinate x = 0). The detonation wave propagates through the barrel, and the products of detonation drive the powder particles. The crucial stage of propulsion takes place in the interval of gas outflow from the barrel, so it is necessary to investigate this process. At present analysis, it was assumed that the ignition occurs within the hightemperature region and the chemical reaction spreads outside from there. The total particle sizes range from d_{min} = 10 μm to d_{max} = 160 μm. The particle calculations were started at the same time and location for different particle sizes (10, 20, 40 60, 80, 100, 120, 160 microns), and the simulation was terminated when the largest particle reached the coated surface.
Mathematical Formulation of the Problem
Summary of crucial parameters describing the front of the detonation wave in propane–oxygen–air mixture obtained with TIGER thermochemical code (Ref 1)
Reactants  Products  

Symbol  Mass fraction, %  Symbol  Mass fraction, % 
C_{3}H_{8}  26.2  H_{2}O  29.8767 
O_{2}  66.5  CO  44.0411 
N_{2}  7.2  H_{2}  1.4390 
Ar  0.1  N_{2}  5.6699 
Ch–J parameters  CO_{2}  9.3105  
a_{ChJ}, m/s  1425  O_{2}  6.1479 
D, m/s  2614  NO  3.5111 
u_{ChJ}, m/s  1188  NO_{2}  0.0037 
p_{ChJ}, MPa  4.444  N_{2}O  0.0000 
T_{ChJ}, K  4461  NH_{3}  0.0002 
The initial temperature of the investigated media was assumed to be 300 K except a small region neighboring to the barrel bottom wall where the detonation begins (see Fig. 1). The initial components of velocity of media were imposed to be equal to zero.
The powder particles were assumed to be spherical, and their diameter varied from 10 to 160 μm. As mentioned before, a onesided coupling was assumed regarding the interaction between the particle and surrounding gas (cf. also Ref 36). This means that only the gas affects the powder particle behavior. This assumption limits the applicability of presented model to qualitative analyses only. It should be noticed that in real spraying conditions, the powder fulfill coefficient can reach relatively high values; therefore, the volumetric ratio flow of the particles is also important to consider whether a flow is dilute (Ref 15). This state of the matter would impose necessity of application of fully Eulerian twoway coupling to describe the multiphase flow. The advantage of applied approach is that it significantly reduces computational cost (computing time) by enabling implementation of the discrete Lagrangian method to describe particle motion, which is equivalent to assumption of no effect of a solid phase flow on the gas flow. This approach significantly reduces number of equations describing model of the problem.
During the real GDS process of FeAl powder deposition, the following proportion was applied for a single cycle: 199 mg of gas and 87 mg of FeAl. Based on the experience of skilled attendants of the PerunS gun, apparently only 2050% of powder is effectively used during the whole process. This suggests the necessity for application of fully Eulerian approach to model the multiphase flow which in consequence leads to the abovementioned difficulties. Oneway coupling results in overestimation of the critical particle diameter caused by both kinetic and thermal transport of energy from detonation flow to the condensed–aerosol phase. Thus, the performed analysis with application of discrete Lagrangian modeling of the particle motion, despite its limitations, resulted in more precise estimation of parameters of the real GDS process than the data available before (cf. Ref 1). Moreover, analysis of the obtained results enabled constructive “criticism” of our predecessors, where further steps, in numerical analysis of presented problem, will be concentrated on extension of numerical models. In Ref 16, a review of models of the interaction of spherical particles with gaseous media was presented.
Re  a _{1}  a _{2}  a _{3} 

Re < 0.1  0  24  0 
0.1 < Re < 1  3.69  22.73  0.0903 
1 < Re < 10  1.222  29.1667  − 3.8889 
10 < Re < 100  0.6167  46.5  − 116.67 
100 < Re < 1000  0.3644  98.33  − 2778 
1000 < Re < 5000  0.357  148.62  − 4.75 × 10^{4} 
5000 < Re < 10,000  0.46  − 490.546  57.87 × 10^{4} 
10,000 < Re < 50,000  0.5191  − 1662.5  5.4167 × 10^{4} 
Thermophysical properties of FeAl powder particles applied in simulations (Ref 21)
Parameter  Solid  Liquid 

01395 °C  13952690 °C  
Density ρ_{p}, kg/m^{3}  5800  4806 
Specific heat c, J/(kg K)  0.301·t_{p} + 520  890 
Thermal conductivity λ_{p}, W/(m K)  15  71 
Surface emissivity ε_{p}  0.7  
Melting enthalpy Δh_{melt}, kJ/kg  288 
Commenting on the values presented in Table 3, it should be precisely underlined that these values are estimates (Ref 16). Therefore, in order to avoid difficulties with reconfiguring the geometrical model of a spherical particle, the authors neglected the changes in the dimensions of the particles and hence in their density. The simplification effect on the particle dynamics can be estimated as follows.
The above calculated values characterize extreme contribution to the uncertainty budget at quantitative analyses. However, one should remember that the dynamic and thermal history of every tracked particle is so diversified that possible errors can be compensated due to changes in polarity of the velocity and temperature differences.
Numerical Simulation Procedure
Nowadays, many commercial computational codes are available to formulate and solve problems of fluid dynamics. In the presented case, Ansys Fluent CFD software was applied. Taking into account the dynamic character of the whole phenomenon with the presence of detonation and shock waves, it seems reasonable to apply an explicit scheme used in a densitybased solver. Over the years, many socalled shock capturing numerical schemes have been developed. Most often, they are “upwind schemes,” and one of the most wellknown approaches to deal with the considered phenomena is the application of Roe’s approximate Riemann solver, which was described in detail in (Ref 22, 23). This scheme is based on the Godunov method and has been modified to become effective despite its disadvantages and problems during investigations of extremely supersonic phenomena.
To obtain a spatially secondorder scheme, the flux (26) is slightly modified (Ref 22).
In order to ensure satisfactory accuracy, the wellknown and commonly used fourthorder Runge–Kutta scheme was applied for timestepping (Ref 23).
During the detonation process, a fixed timestep was applied. Its value satisfied the condition of equality of the CFL number to 0.66, where the CFL was calculated using the detonation velocity and the smallest value of cell dimension. During the outflow of gases from the barrel, higher values of the CFL number were applied (continuously increased up to 0.8).
For numerical simulations of the heat transfer process inside the particle, the classical secondorder finite difference scheme for Eq 14 has been applied (Ref 24). In this case, the same timestep was imposed and the spatial step was equal to 1% of the particle’s radius.
Results and Discussion
The formulation of the analytical and numerical model description for the heat, mass and momentum transfer phenomenon to the FeAl particle thermal state evaluation was based on the GDS experiment carried out in the Ukrainian Academy of Sciences, at E.O. Paton Electric Welding Institute, Kiev with “PerunS” detonation system (Ref 1).
The feedstock powder material consists of Fe40Al0.05Zr at.% + 50 ppm B particles with wide size granulation distribution ranging from 10 to 160 μm, obtained by vacuum inert gas atomization (VIGA) in CEA, Grenoble, but volumetric particle size distribution of the feedstock powder applied in the GDS experiments was dominated by particles of equivalent diameter ranging from about 38 to 75 μm—after sieving (Ref 1). It was determined that the best metallurgical quality of the coatings is achieved by employing powder particles the sizes of which are 4063 μm (Ref 25) and (3875) μm (Ref 26), respectively.
The GDS process was carried out on C45 plain carbon steel with the following parameters: volume fractions of reactants as 0.202 propane and 0.685 oxygen; detonation frequency and spraying distance, respectively, 6.66 Hz and 70 mm; powder injection point of 275 mm from the barrel bottom.
Having carried out GDS process in 100 shooting cycles, repeatable qualities of the FeAl coating were achieved in the shape of single spot at constant distance between gun barrel and the surface of substrate material (with no mutual movement in a plane perpendicular to the axis of the stream of detonation products).
The deposited particles of the FeAl powder influenced by high kinetic energy, temperature and the rate of deformation due to the hydrodynamic impact of the detonation products undergo plastic deformation and geometrical changes turning into the FeAl coating, the porosity of which is less than 0.5% (Ref 1).
Maximum values of powder particles’ muzzle velocity obtained in an experimental way with the application of the Perun–S gun were in the range of 650 to 850 m/s (Ref 27). Comparison of the theoretical effects with experiments suggests an acceptable discrepancy of the results: Particles characterized by diameters of 10 and 20 μm leave the barrel with velocity values equal to 920 and 710 m/s, respectively.
The above presented results show a strong dependence of particle motion and heat transfer parameters on particle dimension. These parameters are the particle residence time, particle terminal velocity and particle terminal temperature. The residence time defines a period of exposure of the particle material to highly reactive combustion gases. With increasing particle diameter, the time for oxide formation increases too. From the terminal ballistics, it is known that the velocity of powder particle strongly affects its deformation during the impact into the coated surface (Ref 28). Additionally, the material temperature, obviously, affects the mechanical properties of particles as a result of phase transitions and chemical reactions. The results suggest that the particles which are most deformed during the impact are the smallest ones.
Analysis of the obtained results indicates that there is a critical diameter of particle below which the material melts in the whole volume. In our case, the particle critical diameter was evaluated to be equal to approximate 80 μm. Moreover, what seems to be interesting is that the radial distribution of temperature is relatively homogenous for each considered diameter of particle, which is the result of the short characteristic time of the heating process in comparison with the time of motion. This effect is especially noticeable for melted particles, due to high thermal conductivity of melted material. The obtained results indirectly prove that the thermal lag due to the internal heat conduction can be neglected in case of underconsideration powder material.
Unfortunately, experimental verification of the obtained values of temperature is possible only by making use of indirect methods based on investigations of the splat structure. However, the conducted analyses make it possible to identify crucial phenomena, such as melting, chemical reactions and particle softening, shaping the specific properties of the coating.
The results of structure examination of the Fe–Altype coating sprayed in the GDS process on a C45 steel substrate were presented in paper (Ref 29), in which the structure was analyzed with SEM/EDS, TEM/SAE and XRD methods. The results allowed explaining the formation mechanism of the coating morphology with a contribution of intermetallic phases such us Fe_{3}Al, FeAl, FeAl_{2} and Fe_{2}Al_{5}. It was established that the GDS coating displayed sublayer morphology of alternate flattened and partially melted grains with wide range of Al content between 39 and 63 at.% (Ref 29). Partial melting of the individual powder particles resulted in the in situ formation of the amorphous grains and, subsequently, columnar crystals of the Fe–Altype phases, sequentially formed in the volume of lamellar splats of the coating. It was found that the inherent mechanism of the Fe–Al coating formation is attributed to plastic deformation and geometrical changes of the strongly heated powder particles, which undergo plastic deformation and geometrical changes in the GDS process conditions (discussed above).
The geometrical changes and simultaneous indications of melting of the Fe–Al coating material (in microareas) confirm high velocity of the FeAl powder particles, additionally subjected to partial melting at a very high temperature of gas detonation products.
In general, while characterizing a specific analyzed GDS process, the obtained data are broadly consistent with the results of the most similar studies presented in (Ref 36).
The velocity range of Al_{2}O_{3} powder particle with a diameter of 20 μm, as presented in (Ref 3), is similar to our results for FeAl particles, following the application of onedimensional detonation model for a dissimilar explosive gas mixture consisting of hydrogen and oxygen or acetylene and oxygen (Ref 3). However, the differences occurring in the values of particle velocity undeniably result from the application of different explosive mixtures and powder materials of various density (3.95 g/cm^{3} for Al_{2}O_{3} and 5.56 g/cm^{3} for FeAl, respectively) (Ref 1, 3). Further numerical investigation on the flow of a twophase gasparticle stream under the detonation conditions with propane involvement has enabled the determination of thermal interaction between the WC powder particles and the gaseous medium, taking into account the influence of PIP on a single particle (Ref 4). Contrary to our results concerning the FeAl powder, E. Kadyrov did not obtain melting of the powder material at a relatively low temperature of WC particles (approximately 2000 K), despite using a much longer barrel of 1.8 m in length (Ref 4). The results obtained and presented by E. Kadyrov (Ref 4) confirm our hypothesis, which states that in dependence on the coating material and the conditions of the GDS process using a propaneoxygen explosive gas mixture, there exists an upper threshold of powder particles that are not subjected to melting. Furthermore, impressive properties of sprayed coatings with low porosity, which maintain their chemical and phase composition, are the result of a strong plastic deformation, which highly heated powder particles in the solid state are subjected to when colliding with the steel substrate material due to very high kinetic energy. It is worth emphasizing that based on the analysis of gas flow evolution and shock wave decay in detonation thermal spraying systems, Ramadan and Barry Butler (Ref 4, 5) showed that the twophase gaseouspowder stream with particles of Al_{2}O_{3} transported under specific detonation conditions with an equivalent diameter of 20 μm is capable of melting at a temperature of roughly 2300 K at a velocity comparable to the results obtained in our research for FeAl particles. Numerical analysis (Ref 4) was based on solving the mathematical model of the Euler equations for chemical reactions with variable gas properties for axisymmetric 2D flow. In their analysis, Ramadan and P. Barry Butler (Ref 4, 5), similar to our research, developed a lumpedparameter model with onesided coupling in order to describe the propulsion of powder particles. Having obtained comparable heat transfer coefficients with the results of Ramadan and Barry Butler (Ref 4, 5), we also took into account the heat transport inside particles, which enhances the applicability of the model developed, likewise in the case of materials exhibiting very low thermal conductivity.
The obtained methodology of numerical modeling was proved to be effective in qualitative analyses. As far as quantitative aspects are concerned, it is very difficult to assess the accuracy of the performed simulation because of difficulties in the experimental determination of the analyzed particle dynamics and thermal state.
Nevertheless, even in the present state, the simulation provided valuable results that can help to explain the mechanisms of formation of the analyzed GDS coating. In contrast to most of the other spraying techniques, under GDS conditions, transient mass and heat flow phenomena play a major role. A relatively short exposition time of the analyzed particle to a shock detonation wave creates conditions that strongly diversify particles depending on their diameter and initial position. The resulting coating is created from particles whose states are much more differentiated than are usual. This is the reason for the lower densities of GDS coatings (cf. Ref 30). On the other hand, complicated coupled heat and mass transfer phenomena accompanying the GDS make theoretical prediction of spraying effects difficult. This explains why not all hopes placed in the GDS technology have come true (cf., e.g., Ref 31). However, the developed methodology can help in the optimization of the GDS process parameters even by creating the possibility of sensitivity analysis.
Conclusions
The main purpose of this research was to adopt numerical simulation procedures and to develop an effective methodology to perform analyses focused on a certain detonation gun spraying example. The analyzed case was Fe40Al at.% powder deposition onto a C45 steel substrate (Ref 29, 32). While developing the numerical model, a hybrid approach was applied: The combustion gases’ parameters were calculated by applying thermochemical code, and then, the detonation gas flow was analyzed in a 2D axisymmetric geometry using commercial CFD software. The material property data reflected the thermophysical data of FeAl powder (Ref 1).

The obtained results are in qualitative agreement with the literature data (Ref 5, 6), which proves the effectiveness of the applied modeling methodology, that is, the hybrid approach with the application of commercial CFD software.

There is a critical diameter of particle below which the material melts in the whole volume. In accordance with numerical data, this value can be estimated on 80 μm. On the other hand, the experimental approach provides value of 60 μm (Ref 29, 32). Possibly applied oneway coupling results in overestimation of the critical particle diameter because of both kinetic and thermal transport of energy from detonation flow to the condensed–aerosol phase.

Due to the relatively low surface heat transfer conductance in comparison with thermal conduction inside the particle, the particle temperature is almost uniform and there is no indication of partial particle melting.

Quantitative verification of the obtained results is extremely difficult due to the impossibility of application of direct methods.

The obtained data provide an explanation for the resulting GDS coating morphology (Ref 29, 32).

In spite of the amendments introduced to the modeling methodology in relation to (Ref 3, 4), the proposed model cannot still be treated as quantitative one and its applicability is limited to just more accurate qualitative analyses. Analyzing still remaining deficiencies, the most problematic is assumption of a oneway coupling between the gaseous and aerosol phases. However, accounting for the momentum and thermal energy transfer from the condensed phase to combustion gases should result in decreasing particle terminal velocity and temperature as the detonation energy should distribute between the two phases. This in turn should result in a better compliance between the modeling results and the experimentally established data on unmelted inclusions within the analyzed FeAl GDS coating.
Notes
Acknowledgments
The authors wish to thank PhD Dariusz Zasada from the Military University of Technology, Poland for his support in the SEM experimental work. The authors express their thanks to Prof. Yurij Borisov from the E.O. Paton Electric Welding Institute, National Academy of Science of Ukraine, for GDS experiment. Financial support from Polish National Science Centre, Poland, Research Project No. 2015/19/B/ST8/02000, is gratefully acknowledged.
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