Mathematical models for coating processes

1982 ◽  
Vol 117 ◽  
pp. 443-455 ◽  
Author(s):  
M. D. Savage
Keyword(s):  
Surface Tension ◽  
Fluid Flow ◽  
Mathematical Models ◽  
Coating Thickness ◽  
Essential Difference ◽  
Narrow Gap ◽  
Adequate Description ◽  
Theoretical Predictions ◽  
Dimensional Parameters ◽  
Separation Model

The flow is considered of a Newtonian fluid, of viscosity η and surface tension T, in the narrow gap between a pair of rollers of radii R1 and R2, whose peripheral speeds are constant and equal to U1 and U2 respectively. The objective is to determine the coating thickness h1∞ on the upper roller as a function of the non-dimensional parameters H0/R, ηU/T and U1/U2, where H0 is the minimum gap thickness, U = ½(U1 + U2), and 2R−1 = R1−1 + R2−1.Using lubrication theory to provide an adequate description of the fluid flow, two mathematical models are derived whose essential difference lies in the specification of the boundary conditions. In the separation model it is assumed that the pressure distribution will terminate at a position which is both a stagnation point and a point of separation, whereas the Reynolds model incorporates the classical Reynolds conditions. In each case, theoretical predictions for the non-dimensional coating thickness, h1∞/H0 as a function of U1/U2 are found to compare well with experiment. However, theory does suggest that the two models are applicable to different and complementary regions of parameter space, and hence together they may form a basis for further investigations into the various features of coating processes.

Modelling of Coating Thickness, Heat Transfer and Fluid Flow and It's Correlation with the TBC Microstructure for a Plasma Sprayed Gas Turbine Application

1998 ◽  
Author(s):  
P. Nylen ◽  
J. Wigren ◽  
L. Pejryd ◽  
M.-O. Hansson
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Gas Turbine ◽  
Coating Thickness ◽  
Spray Deposition ◽  
Temperature History ◽  
Particle Model ◽  
Barrier Coating ◽  
Discrete Particle Model ◽  
Turbine Component

Abstract The plasma spray deposition of a zirconia thermal barrier coating (TBC) on a gas turbine component has been examined using analytical and experimental techniques. The coating thickness was simulated by the use of commercial off-line programming software. The impinging jet was modelled by means of a finite difference elliptic code using a simplified turbulence model. Powder particle velocity, temperature history and trajectory were calculated using a stochastic discrete particle model. The heat transfer and fluid flow model were then used to calculate transient coating and substrate temperatures using the finite element method. The predicted thickness, temperature and velocity of the particles and the coating temperatures were compared with these measurements and good correlations were obtained. The coating microstructure was evaluated by optical and scanning microscopy techniques. Special attention was paid to the crack structures within the top coating. Finally, the correlation between the modelled parameters and the deposit microstructure was studied.

scholarly journals The Importance of Nanoparticles Addition in a Base Fluid Flow through a Porous Medium

2013 ◽  
Vol 8-9 ◽  
pp. 225-234
Author(s):  
Dalia Sabina Cimpean
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Boundary Conditions ◽  
Mixed Convection ◽  
Mathematical Models ◽  
Base Fluid ◽  
Porous Matrix ◽  
Fluid Properties ◽  
Flow Through ◽  
Energy Equations

The present study is focused on the mixed convection fluid flow through a porous medium, when a different amount of nanoparticles is added in the base fluid. The nanofluid saturates the porous matrix and different situations of the flow between two walls are presented and discussed. Alternatively mathematical models are presented and discussed. A solution of a system which contains the momentum, Darcy and energy equations, together with the boundary conditions involved, is given. The behavior of different nanofluids, such thatAu-water, Ag-waterandFe-wateris graphically illustrated and compared with the previous results.The research target is to observe the substantial increase of the thermophysical fluid properties, when the porous medium issaturated by a nanofluid instead of a classical Newtonian fluid.

scholarly journals A categorical perspective towards aerodynamic models for aeroelastic analyses of bridge decks

2019 ◽  
Vol 6 (3) ◽  
pp. 181848 ◽  
Author(s):  
I. Kavrakov ◽  
D. Legatiuk ◽  
K. Gürlebeck ◽  
G. Morgenthal
Keyword(s):  
Mathematical Models ◽  
Category Theory ◽  
Structural Engineering ◽  
Model Comparison ◽  
Model Assessment ◽  
Adequate Description ◽  
Categorical Approach ◽  
Abstract Approach ◽  
Huge Variety ◽  
Modelling Approach

Reliable modelling in structural engineering is crucial for the serviceability and safety of structures. A huge variety of aerodynamic models for aeroelastic analyses of bridges poses natural questions on their complexity and thus, quality. Moreover, a direct comparison of aerodynamic models is typically either not possible or senseless, as the models can be based on very different physical assumptions. Therefore, to address the question of principal comparability and complexity of models, a more abstract approach, accounting for the effect of basic physical assumptions, is necessary. This paper presents an application of a recently introduced category theory-based modelling approach to a diverse set of models from bridge aerodynamics. Initially, the categorical approach is extended to allow an adequate description of aerodynamic models. Complexity of the selected aerodynamic models is evaluated, based on which model comparability is established. Finally, the utility of the approach for model comparison and characterization is demonstrated on an illustrative example from bridge aeroelasticity. The outcome of this study is intended to serve as an alternative framework for model comparison and impact future model assessment studies of mathematical models for engineering applications.

scholarly journals A curved multi-component aerosol hygroscopicity model framework: 1 – Inorganics

2004 ◽  
Vol 4 (6) ◽  
pp. 8627-8676 ◽  
Author(s):  
D. O. Topping ◽  
G. B. McFiggans ◽  
H. Coe
Keyword(s):  
Surface Tension ◽  
Companion Paper ◽  
Dry Density ◽  
Model Framework ◽  
Aerosol Model ◽  
Modelling Framework ◽  
Systematic Uncertainties ◽  
Model Aerosol ◽  
Theoretical Predictions ◽  
Models Comparison

Abstract. A thermodynamic modelling framework to predict the equilibrium behaviour of mixed inorganic salt aerosols is developed, and then coupled with a technique for finding a solution to the Köhler equation in order to create a diameter dependent hygroscopic aerosol model (Aerosol Diameter Dependent Equilibrium Model – ADDEM). The model described here provides a robust and accurate inorganic basis using a mole fraction based activity coefficient model and adjusted energies of formation for treating solid precipitation. The model framework can accommodate organic components, though this added complexity is considered in a companion paper, whereas this paper describes the development of the modelling architecture to be used and predictions of an inorganic model alone. The modelling framework has been developed to flexibly use a combination of mixing rules and other potentially more accurate techniques where available to calculate the water content. Comparisons with other state-of-the-art general equilibrium models and experimental data are presented and show excellent agreement. The Kelvin effect can be considered in this scheme using a variety of surface tension models. Comparison of predicted diameter dependent phenomena, such as the increased relative humidity for onset of deliquescence with decreasing diameter, with another diameter dependent model is very good despite the different approach used. The model is subject to various sensitivities. For the inorganic systems studied here, the model is sensitive to choice of surface tension scheme used, which decreases for larger aerosol. Large sensitivities are found for the value of dry density used. It is thus likely that the history of the aerosol studied in a hygroscopic tandem differential mobility analyser (HTDMA), specifically the nature of the drying process that will influence the final crystalline form, will create systematic uncertainties upon comparisons with theoretical predictions. However, the magnitudes of all of the above sensitivities are potentially less than those introduced when using a semi ideal growth factor analogue for certain conditions.

The liquid blister test

2008 ◽  
Vol 464 (2099) ◽  
pp. 2887-2906 ◽  
Author(s):  
Julien Chopin ◽  
Dominic Vella ◽  
Arezki Boudaoud
Keyword(s):  
Surface Tension ◽  
Surface Energy ◽  
Vertical Displacement ◽  
Quantitative Agreement ◽  
Elastic Plates ◽  
Blister Test ◽  
Thin Liquid Layer ◽  
Theoretical Predictions ◽  
Thin Elastic Plates ◽  
Adhesive Forces

We consider a thin elastic sheet adhering to a stiff substrate by means of the surface tension of a thin liquid layer. Debonding is initiated by imposing a vertical displacement at the centre of the sheet and leads to the formation of a delaminated region or ‘blister’. This experiment reveals that the perimeter of the blister takes one of three different forms depending on the vertical displacement imposed. As this displacement is increased, we observe first circular, then undulating and finally triangular blisters. We obtain theoretical predictions for the observed features of each of these three families of blisters. The theory is built upon the Föppl–von Kármán equations for thin elastic plates and accounts for the surface energy of the liquid. We find good quantitative agreement between our theoretical predictions and experimental results, demonstrating that all three families are governed by different balances between elastic and capillary forces. Our results may bear on micrometric tapered devices and other systems, where elastic and adhesive forces are in competition.

Applied Mechanics in Moving Boundary Problems of One-Dimensional Non-Darcy Flow in Semi-Infinite Long Porous Media

2014 ◽  
Vol 977 ◽  
pp. 399-403
Author(s):  
Jia Hang Wang ◽  
Lei Wang ◽  
Duo Kai Zhou
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Mathematical Models ◽  
Analytical Solutions ◽  
Moving Boundary ◽  
Boundary Problems ◽  
Threshold Pressure Gradient ◽  
Depression Cone ◽  
Boundary Distance ◽  
Pressure Propagation

Dimensionless mathematical models of the fluid flow in the semi-infinite long porous media with constant production pressure on the inner boundary conditions are built, which include the effect of threshold pressure gradient (TPG). The analytical solutions of these dimensionless mathematical models are derived through new definitions of dimensionless variables. Comparison curves of the dimensionless moving boundary under different values of dimensionless TPG are plotted from the proposed analytical solutions. For the case of constant production pressure, a maximum moving boundary exists, beyond which the fluid flow will not occur. The value of maximum boundary distance decreases with increasing TPG. However, the velocity of pressure propagation decreases with time. The larger the TPG is, the steeper the curve of pressure depression cone is and the shorter the distance of the pressure propagation is.

scholarly journals Fabrication of Beltlike Fibers by Electrospinning

Polymers ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 1087 ◽  
Author(s):  
Yan-Qing Liu ◽  
Chun-Hui He ◽  
Xiao-Xia Li ◽  
Ji-Huan He
Keyword(s):  
Surface Tension ◽  
Polyethylene Glycol ◽  
Theoretical Analysis ◽  
Minimal Surface ◽  
Crystallite Size ◽  
Zro2 Nanoparticles ◽  
One Dimensional ◽  
Theoretical Predictions ◽  
Spinning Process ◽  
Moving Jet

Electrospinning is always used to fabricate one-dimensional nanofibers. Cylindrical fibers are formed during the spinning process due to the minimal-surface principle. However, when the moving jet has high rigidity, which can counteract the surface tension for a minimal surface, beltlike fibers can be obtained. Using the Hall–Petch effect, the rigidity of the moving jet can be greatly enhanced by adding nanoparticles. Polyethylene glycol with a nanometric crystallite size of 4 nm and ZrO2 nanoparticles are used as additives in the experiment, a theoretical analysis is carried out, and the theoretical predictions are verified experimentally.

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