Mathematical Model of In-Flight Oxidation of Metallic Particles in Thermal Spraying

2000 ◽  
Author(s):  
A.M. Ahmed ◽  
R.H. Rangel ◽  
V.V. Sobolev ◽  
J.M. Guilemany
Keyword(s):  
Mathematical Model ◽  
Thermal Behavior ◽  
Spray Deposition ◽  
Particle Surface ◽  
Thermal Spraying ◽  
Deposition Process ◽  
Conservation Equation ◽  
Spherical Particles ◽  
Energy Conservation Equation ◽  
Acceleration And Deceleration

Abstract This paper presents a mathematical model of the in-flight oxidation of spherical particles during thermal spray deposition process. The model includes analysis of the mechanical and thermal behavior of the powder particles. The former accounts for acceleration and deceleration of the particles at the spray distance under different fluid velocities. The thermal behavior takes into account heating, melting, cooling and possible solidification as the particle travel towards the substrate. A finite-difference method is used to solve the thermal energy conservation equation of the particles. The model includes nonequilibrium calculations of the phase change phenomena in the liquid-solid (mushy) zone. The growth of the oxide layer at the particle surface is represented by a modified boundary condition, which includes finite-rate oxidation. The results obtained give the interrelations between various process parameters and the oxidation phenomenon and agree with experimental observation.

Modeling of Oxidation of Plasma-Sprayed Molybdenum Coatings

2000 ◽  
Author(s):  
Y.P. Wan ◽  
X.Y. Jiang ◽  
H. Zhang ◽  
S. Sampath ◽  
V. Prasad ◽  
...  
Keyword(s):  
Spray Deposition ◽  
Mechanical Energy ◽  
Particle Surface ◽  
Conservation Equation ◽  
Type Model ◽  
Energy Conservation Equation ◽  
Thin Oxide Film ◽  
Molten Particle ◽  
Plasma Sprayed ◽  
Substrate Temperatures

Abstract A model for oxidation of molybdenum particles during plasma spray deposition is developed. The diffusion of metal an-ions or oxygen cat-ions through a thin oxidized film, chemical reactions on the surface, and diffusion of oxidant in gas phase are considered as possible rate-controlling mechanisms with controlling parameters as the temperature of the particle surface, and local oxygen concentration and flow field surrounding the particle. The deposition of molten particle and its rapid solidification and deformation is treated using a Madejski-type model, in which the mechanical energy conservation equation is solved to determine the splat deformation and one-dimensional heat conduction equation with phase change is solved to predict the solidification and temperature evolution. Calculations are performed for a single molybdenum particle sprayed under the Sulzer Metco-9MB spraying conditions. Results show that the mechanism that controls the oxidation of this droplet is the diffusion of metal/oxygen ions through a very thin oxide film. A higher substrate temperature results in a larger rate of oxidation at the splat surface, and hence, a larger oxygen content in the coating layer. Compared to the oxidation of droplet during m-flight, the oxidation during deposition is not weak and can become dominant at high substrate temperatures.

A New High Order Mathematical Model for Calculating the Energy Conservation Equation

2013 ◽  
Vol 749 ◽  
pp. 545-550
Author(s):  
Xiao Feng Niu ◽  
Wei Liang ◽  
Hua Hou ◽  
Yu Hong Zhao ◽  
Hong Xia Wang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Energy Conservation ◽  
Specific Heat ◽  
Hamming Distance ◽  
Conservation Equation ◽  
High Order ◽  
Adi Method ◽  
Energy Conservation Equation ◽  
Heat Method ◽  
Explicit Finite Difference

The Explicit Finite Difference (EFD) method is used for calculating the energy conservation equation during solidification. In order to improve the computational efficiency, the equivalent specific heat method is adopted to calculate the latent heat and the high order Alternating Direction Implicit (ADI) method is also applied, which is fourth order in space and second order in time. The degree of similarity between the simulation results and experimental results is analyzed quantitatively by the Hamming Distance (HD) for the first time, and results show that this high order mathematical model based on the equivalent specific heat method and the high order ADI method is faster and more accurate than the EFD method.

A mathematical model of the spray deposition process

1989 ◽  
Vol 20 (1) ◽  
pp. 71-85 ◽  
Author(s):  
E. Gutierrez-Miravete ◽  
E. J. Lavernia ◽  
G. M. Trapaga ◽  
J. Szekely ◽  
N. J. Grant
Keyword(s):  
Mathematical Model ◽  
Spray Deposition ◽  
Deposition Process

scholarly journals Drying of foods under intermittent supply of microwave energy: proposal for a mathematical model

2021 ◽  
Vol 43 ◽  
pp. e51037
Author(s):  
Jhony Teleken ◽  
Barbara Danielle Almeida Porciúncula ◽  
Joel Gustavo Teleken ◽  
Bruno Augusto Mattar Carciofi
Keyword(s):  
Mathematical Model ◽  
Numerical Solution ◽  
Conservation Equation ◽  
Microwave Drying ◽  
Water Evaporation ◽  
Drying Rate ◽  
Energy Conservation Equation ◽  
Operation Conditions ◽  
Modelling Studies

Intermittent microwave drying improves the quality of the dehydrated product, because reduces the effect of microwave hot spots. Mathematical modelling is essential to understand the physics of this drying process and to optimize the operation conditions. However, there are few modelling studies about intermittent microwave drying. This work proposed a mathematical model based on mass balances of liquid and vapor water in which a non-equilibrium formulation described the water phase change. The microwave heating, described by Lambert’s law, was accounting as source term on the thermal energy conservation equation. The numerical solution used the finite element method, and the experimental drying of potato samples validated the simulated drying. The values of moisture content and temperature obtained by numerical solution of the model showed good agreement with experimental data. From this, it was observed the presence of three periods in the drying kinetics: an initial heating phase almost without drying, follow by a phase with constant drying rate, and final a decrease of drying rate and temperature increasement. The model results showed that the interior temperature was higher than the surface temperature of sample, and there was water evaporation inside the potato. In additional, the gradients of temperature were reduced due to intermittency of the microwave power. This redistribution of temperature could contribute to the improvement of product quality during drying.

Development and assessment of a mathematical model to predict foliar spray deposition under laboratory track spraying conditions

1991 ◽  
Vol 33 (3) ◽  
pp. 281-304 ◽  
Author(s):  
B. Terence Grayson ◽  
James D. Webb ◽  
Simon E. Pack ◽  
Dean Edwards
Keyword(s):  
Mathematical Model ◽  
Spray Deposition ◽  
Foliar Spray

A large grain size perovskite thin film with a dense structure for planar heterojunction solar cells via spray deposition under ambient conditions

RSC Advances ◽  
2015 ◽  
Vol 5 (74) ◽  
pp. 60562-60569 ◽  
Author(s):  
Zhurong Liang ◽  
Shaohong Zhang ◽  
Xueqing Xu ◽  
Nan Wang ◽  
Junxia Wang ◽  
...  
Keyword(s):  
Grain Size ◽  
Surface Coverage ◽  
Spray Deposition ◽  
Deposition Process ◽  
Ambient Conditions ◽  
High Quality ◽  
Dense Structure ◽  
Heterojunction Solar Cells ◽  
Planar Heterojunction Solar Cells ◽  
Planar Heterojunction

A facile spray deposition process was developed to prepare high-quality perovskite films with full surface coverage and large grain size.

Heat Transfer Analysis of a Novel Pressurized Air Receiver for Concentrated Solar Power via Combined Cycles

2009 ◽  
Vol 1 (4) ◽  
Author(s):  
I. Hischier ◽  
D. Hess ◽  
W. Lipiński ◽  
M. Modest ◽  
A. Steinfeld
Keyword(s):  
Heat Transfer ◽  
Thermal Efficiency ◽  
Porous Ceramic ◽  
Conservation Equation ◽  
Heat Transfer Analysis ◽  
Operational Parameters ◽  
Small Aperture ◽  
Solar Absorber ◽  
Energy Conservation Equation ◽  
Combined Cycles

A novel design of a high-temperature pressurized solar air receiver for power generation via combined Brayton–Rankine cycles is proposed. It consists of an annular reticulate porous ceramic (RPC) bounded by two concentric cylinders. The inner cylinder, which serves as the solar absorber, has a cavity-type configuration and a small aperture for the access of concentrated solar radiation. Absorbed heat is transferred by conduction, radiation, and convection to the pressurized air flowing across the RPC. A 2D steady-state energy conservation equation coupling the three modes of heat transfer is formulated and solved by the finite volume technique and by applying the Rosseland diffusion, P1, and Monte Carlo radiation methods. Key results include the temperature distribution and thermal efficiency as a function of the geometrical and operational parameters. For a solar concentration ratio of 3000 suns, the outlet air temperature reaches 1000°C at 10 bars, yielding a thermal efficiency of 78%.

Energy conservation, time-reversal invariance and reciprocity in ducts with flow

2001 ◽  
Vol 431 ◽  
pp. 223-237 ◽  
Author(s):  
WILLI MÖHRING
Keyword(s):  
Energy Conservation ◽  
Sound Wave ◽  
Conservation Equation ◽  
Smooth Transition ◽  
Rotational Flow ◽  
Flow Energy ◽  
Energy Conservation Equation ◽  
Reversal Invariance ◽  
Edge Conditions ◽  
Piecewise Continuous

A sound wave propagating in an inhomogeneous duct consisting of two semi-infinite uniform ducts with a smooth transition region in between and which carries a steady flow is considered. The duct walls may be rigid or compliant. For an irrotational sound wave it is shown that the three properties of the title are closely related, such that the validity of any two implies the validity of the third. Furthermore it is shown that the three properties are fulfilled for lossless locally reacting duct walls provided the impedance varies at most continuously. For piecewise-continuous wall properties edge conditions are essential. By an analytic continuation argument it is shown that reciprocity remains true for walls with loss. For rotational flow, energy conservation theorems have been derived only with the help of additional potential-like variables. The inter-relation between the three properties remains valid if one considers these additional variables to be known. If only the basic gasdynamic variables in both half-ducts are known, one cannot formulate an energy conservation equation; however, reciprocity is fulfilled.

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