Prediction Of Film Thickness Research Articles

Numerical thermal analysis of grease-lubrication in limited line contacts considering asperity contact

Grease lubrication is widely used for rolling element bearing due to its special rheological characteristics. While there have been many related studies based on experiments, the corresponding numerical simulation method is much less developed. This article presents the numerical simulation for finite line contacts for grease lubrication whose rheological behavior follows the Ostwald model. Neural network and genetic algorithms are used for the prediction of film thickness and asperity contact load ratio based on the results of the numerical simulation, and it shows that the predictive of the well trained neural network has a good agreement with the simulation results. This provides a simple way for the prediction of the film thickness and asperity contact load ratio for grease lubrication.

An experimental analysis of the stability of the jet wiping process: Part I – Characterization of the coating uniformity

The jet wiping process is a continuous coating method that uses impinging gas jets to control the thickness of a liquid layer dragged by a moving substrate. This first part of a two-part article on the analysis of the process stability presents an experimental characterization of the achievable coating uniformity as a function of various design and operating parameters, including the nozzle opening width, stand-off distance, tilt angle and stagnation pressure, substrate speed and liquid properties. The process is reproduced on a dedicated laboratory model, instrumented with a Light Absorption (LAbs) test section for the 3D time-dependent reconstruction of the final coating film thickness. Several types of wave patterns are observed on the final coating film and characterized in terms of peak to peak wave amplitude and dominant frequency. The results are nondimensionalized following the scaling laws derived from the classical ‘one-way coupling’ analysis of the process. This approach, which assumes that the wiping capabilities of the jet flow are not influenced by the dynamics of the impinged liquid, is proven successful for the prediction of the average film thickness but inadequate for the scaling of the coating non-uniformity. This suggests that the dynamics of the final coat is mostly governed by the interaction of the liquid with the gas jet, investigated in the second part of the article.

Modeling heat transfer through corrosion product deposits on fuel rods in pressurized water reactors

Abstract CRUD is the corrosion product deposit found on a fuel rod surface of pressurized water reactors (PWRs). Problematic phenomena caused by CRUD – CRUD Induced Power Shift (CIPS) and CRUD Induced Localized Corrosion (CILC) – are closely related to the heat transfer mechanism of CRUD. However, heat transfer regimes of CRUD are still not well clarified. Therefore, the heat transfer regimes of CRUD were investigated using existing database from the CRUD heat transfer experiment. As a result, it was found that there are three heat transfer regimes: (i) liquid-saturated regime, (ii) wick-boiling regime, and (iii) film-boiling regime. In addition, the boiling curves from the experiment were categorized according to their heat transfer regimes so that models for CRUD can be validated with appropriate database for the heat transfer regime where they are concerned. After obtaining the categorized databases, the model for the film boiling of CRUD was suggested. Unlike the conventional approaches that use capillary force as a unique source of the liquid supply in pores, the model we present in this paper adopted the disjoining force as an additional liquid supply term. This assumption was validated with the previous heat pipe experiment; the root-mean-square error (RMSE) for the prediction of the vapor film thickness was notably reduced from 790% to 18.7% by including the disjoining force to the supply term. The supply term considering the disjoining force was also applied to a model for the CRUD film boiling. The model estimates the wall superheat by balancing the supply term and the hydraulic resistance terms from fluid flows within CRUD. The model we present in this paper successfully predicted the wall superheat during the film boiling; the RMSE was 19% when the predicted wall superheats were compared with ones from the database categorized as film boiling. Finally, it was found from the sensitivity study using the model we present in this paper that the heat transfer performance of CRUD during the film boiling is highly sensitive to the pore radius.

Process Parameter Optimization of Hydrostatic Extrusion Using Metaheuristic

Friction at die work piece interface can be reduced by the presence of lubricant in the entry zone. As the metal–metal contact in the deformation zone is avoided, the deformation force is reduced and at the same time the product quality and die life are improved. So the prediction of minimum film thickness and its control through process variables is gaining interest in the industry. Two multi-objective nonlinear optimization problems are formulated in this study, one using the minimum thermal thickness and billet temperature at the work zone. And the other optimization problem is formulated by including the minimum isothermal thickness at entry zone and the billet temperature at the work zone. These two multi-objective optimization problems have been solved using particle swarm optimization algorithm (PSO). The key process variables are identified by coefficient of variance (COV) analysis. A sensitivity analysis on the process variables is performed to prioritize the process variables. A design procedure is explored to demonstrate the industrial application of this analysis.

Analytical Formula for the Ratio of Central to Minimum Film Thickness in a Circular EHL Contact

Prediction of minimum film thickness is often used in practice for calculation of film parameter to design machine operation in full film regime. It was reported several times that majority of prediction formulas cannot match experimental data in terms of minimum film thickness. These standard prediction formulas give almost constant ratio between central and minimum film thickness while numerical calculations show ratio which spans from 1 to more than 3 depending on M and L parameters. In this paper, an analytical formula of this ratio is presented for lubricants with various pressure–viscosity coefficients. The analytical formula is compared with optical interferometry measurements and differences are discussed. It allows better prediction, compared to standard formulas, of minimum film thickness for wide range of M and L parameters.

Investigation of the liquid film thickness in an open-channel falling film micro-reactor by a stereo digital microscopy

Abstract The film thickness is a vital parameter for the falling film micro-reactor (FFMR) as a characteristic value representing both the surface to volume ratio and the distance of mass and heat transfer. In this paper, a method and procedure using a stereo digital microscopy to study the flow pattern and liquid film thickness in the FFMR were developed. The hydrodynamic behaviors of three liquids (deionized water, ethanol and isopropanol) have been investigated in a customer designed FFMR. Studies suggest that the film thickness increases with increasing flowrate and viscosity. The viscous force plays a dominant role in the falling film process. The falling film behaviors were also analyzed by computational fluid dynamics (CFD) simulation. A new correlation for the film thickness prediction has been proposed, and its predictions are consistent with the experimental data from this work and public literatures with an accuracy of 7% and 20%, respectively. As a result, stereo digital microscopy has been proved to be an effective device for investigating the hydrodynamic behaviors in FFMR, and the proposed model can accurately predict the film thickness in falling film micro-system within a wide flow regime.

Numerical Modeling of Film Condensation in Horizontal Mini- and Macrocircular Tubes

A partial differential–integral equation has been derived to connect vapor condensation and the development of condensate film thickness in both the tangential and axial directions in a horizontal circular condenser tube. A high-order explicit numerical scheme is used to solve the strongly nonlinear equation. A simple strategy is applied to avoid possible large errors from high-order numerical differentiation when the condensate becomes stratified. A set of empirical friction factor and Nusselt number correlations covering both laminar and turbulent film condensation have been incorporated to realistically predict film thickness variation and concurrently allow for the predictions of local heat transfer coefficients. The predicted heat-transfer coefficients of film condensation for refrigerant R134a and water vapor in horizontal circular mini- and macrotubes, respectively, have been compared with the results from experiments and the results from the simulations of film condensation using computational fluid dynamics (CFD), and very good agreements have been found. Some of the predicted film condensations are well into the strong stratification regime, and the results show that, in general, the condensate is close to annular near the inlet of the condenser tube and becomes gradually stratified as the condensate travels further away from the inlet for all the simulated conditions. The results also show that the condensate in the minitubes becomes stratified much earlier than that in the macrotubes.

Prediction of rod film thickness of vertical upward co-current adiabatic flow in rod bundle

Prediction of rod film thickness and its distribution in annular flow in rod bundle is of essential importance to nuclear power industry. This is attributed to the possible film dryout on fuel rods under certain conditions, which will result in a drastically increasing cladding temperature and possible fuel damage. Though there exist a lot of models or correlations to predict film thickness for annular flow in pipes, there are few models to predict rod film thickness inside rod bundle. The one-dimensional models or correlations for pipe flow cannot be used for rod bundle directly due to different geometry and flow dynamics. In relation to this, a new approach to predict the rod film thickness inside rod bundle has been developed. This approach first divides the rod bundle cross-section into three regions according to their characteristic length scales. Then, the gas and liquid flow distribution inside rod bundle has been given with reasonable assumptions. Based on the flow distribution profile, the sub-channel area-averaged gas and liquid volumetric fluxes have been given. Finally, the correlation developed for pipe flow is adopted for each sub-channel based on the local two-phase parameters in the rod bundle. Compared to experimental data obtained in-house and found in the literature, the newly proposed approach can predict rod film thickness with satisfactory accuracy.

Prediction of plastic film thickness based on gas permeability and validation with ‘Kyoho’ table grapes for optimal modified atmosphere packaging

Modified atmosphere packaging (MAP) storage has become a useful technique for extending the shelf life of fruit and vegetables. However, the success of MAP depends on many factors, including types of fresh products, storage conditions, and the characteristics of the packaging films. To achieve the optimal gas composition in the package headspace and improve the postharvest quality of fresh produce, the packaging film with appropriate barrier properties needs to be selected. This study aimed to predict the film thickness by applying produce respiration rate and package film permeability data measured in given product weight and storage conditions. An available film (eg, 25‐μm‐thick low‐density polyethylene) was used to pack fresh produce, and the respiration rate of fresh produce and in‐package O2 and CO2 concentrations at steady state were measured. Permeability of the film was calculated based on mass balance, and the thickness of the film could be predicted if the recommended target O2 and CO2 concentration was obtained from the literature. To validate the predicted thickness value, an experiment was conducted by packaging fresh table grapes in bags of the predicted thickness. The effect of packaging with different film thicknesses on the quality of the fruit was determined. The results showed good agreement between the predicted and the experimental in‐bag O2 and CO2 concentrations, and the MAP with predicted thickness (90 μm) film was more effective in maintaining postharvest quality of grapes during low‐temperature storage than the thinner films (30 and 60 μm) and the control.

Mechanism of Initial Film Formation during Cathodic Electrodeposition of Coatings

Electrodeposition of coatings is an effective way to form a protective layer on metal surfaces of complex shape. The uniformity of the deposit is a function of the current distribution, and depends on the induction time (time prior to “initiation” of deposition), the local deposition rate and the resistivity of the film that is formed. In cathodic electrodeposition, hydrogen gas evolves on the deposition surface, leading to an increase in the local pH. The change in pH reduces the solubility of the positively charged resin-containing micelles and causes a coating to form on the surface. The induction time, which is a key factor in the prediction of film thickness, has been attributed to the time that is required to increase the local pH to about 12 [1, 2]. The deposition rate, which is initially low, changes significantly during the induction period and eventually increases to a steady value that is proportional to the charge passed. An increased fundamental understanding is needed to improve our ability to accurately model E-coat systems in order to optimize performance. The purpose of this study is to develop a detailed understanding of the initial stages of deposit growth. Of particular interest are the changes that take place during the induction time. Experiments designed to elucidate the role of pH change clearly show that the local change in pH alone is not responsible for the induction time. This observation was further supported by additional experiments where the induction time at a specified current was observed to vary with the type of substrate used for deposition. Consequently, scanning electron microscopy was used to study the morphology of the initial deposit on different substrate surfaces including bare steel, galvanized steel, and phosphated steel. It was found that the initial film tends to form preferentially on defects and scratches in the metals. This observation was validated by experiments with intentionally scratched surfaces. The initial film also appeared to form around gas bubbles that were present on the substrate surface. The mechanism for preferred deposition at defects and bubbles is currently under investigation. As part of this effort, deposition on “defect free” surfaces has been performed. Microscopic images are used to track deposit formation as a function of time during the initial stages of deposition before formation of a highly resistive film. The rate of deposition increases with time, which may be connected to an increase in the local current density in the deposit free areas. The additional insight provided by this study will provide the basis for an improved model of the early stages of E-coat deposition. This model will then be incorporated into a large-scale simulation tool to enable improved process prediction and optimization. Acknowledgment The authors gratefully acknowledge funding from the Ford Motor Company under their University Research Program (URP). References Miskovic-Stankovic, V.B. and M.D. Maksimovic, The effect of concentration on the cathodic electrodeposition process. Process in Organic Coating, 1988. 16: p. 255-263.Pierce, P.E., The physical chemistry of the cathodic electrodeposition process. Journal of Coatings Technology and Research, 1981. 53: p. 52.

An investigation into the oil transport and starvation of piston ring pack

In order to accurately predict the lubricant film thickness and generated friction in any tribological contact, it is important to determine appropriate boundary conditions, taking into account the oil availability and extent of starvation. This paper presents a two-dimensional hydrodynamic model of a piston ring pack for prediction of lubricant film thickness, friction and total power loss. The model takes into account starvation caused by reverse flow at the conjunctional inlet wedge, and applied to a ring pack, comprising a compression and scraper ring. Inlet boundaries are calculated for an engine cycle of a four-cylinder, four-stroke gasoline engine operating at 1500 r/min with conditions pertaining to the New European Drive Cycle. The analysis shows the two main sources of starvation: first, due to a physical lack of inlet meniscus and second, due to reverse flow at the inlet wedge significantly affecting the prevailing conditions from the generally assumed idealised boundary conditions. Such an approach has not hitherto been reported in literature.

Annular liquid film thickness prediction in a vertical 180° return bend

Annular flow is predominant in gas wells. Liquid may be present in form of entrained droplets as well as in the liquid film on pipe wall. The knowledge of the average liquid film thickness is vital for detailed mechanistic modelling of churn–annular flow in engineering applications. So far, the models for liquid film thickness prediction are limited to vertical and horizontal pipes. These models were based on limited ranges of experimental data. In addition, exhaustive iterations are needed when these models are used to estimate liquid film thickness. In this work, a new correlation to predict liquid film thickness in a 180° bend under gas–liquid annular conditions was successfully proposed. The correlation was based on dimensionless numbers (modified gas and liquid Weber numbers and gas Froude number) which reflect the underlined physics governing gas–liquid interaction in the bend. The Weber numbers capture the two important forces (inertial and surface tension forces) which govern the formation of the liquid film thickness within the system while gas Froude number quantifies the interaction of two important forces (centrifugal and gravitational forces) which determines the distribution of the phases across a bend. The proposed liquid film thickness correlation was based on the experimental data obtained from a wide range of operating conditions. The liquid superficial velocities ranges from 0.02 to 0.2 m/s and gas superficial velocities from 3.5 to 16 m/s at different measurement locations of 45°, 90° and 135° of the bend with a diameter of 127 mm. The liquid film thickness in air–water and helium–water annular flow can be predicted by δ=28.4061(WeL)0.10318(WeG)-0.30954(FrG)-0.31423. The validation of the proposed correlation used to predict liquid film thickness in gas–liquid annular systems with different pipe diameters were examined against the available data in the literature. Good agreement was found between the predicted values of liquid film thickness with the experimental data at different measuring locations of the bend.

Effect of blade-tip shape on the doctoring step in gravure printing processes

A fundamental limit to the gravure printing process is in the doctoring step, in which a residual film defines the lower bound on allowable feature size. The resolution of finer features requires thin residual films, but these thin films increase the likelihood of wearing the doctor blades. A computational model was used to study the effect of blade-tip shape on residual film thickness while also minimizing the likelihood of wear. The blade-tip shape is altered by varying the bevel angles and the predicted film thickness is computed under various wiping speeds, configurations, and applied forces. In all cases studied, a slower wiping speed resulted in a thinner residual film, which is due to the doctoring step being governed by elastohydrodynamic lubrication. In some cases, a reversal of the wiping configuration created a thinner film, but it had no impact on the likelihood of wearing. Higher applied force leads to thinner residual film but the blade shape can have a more significant influence, indicating that lubrication forces dominate at this scale. Lastly, the likelihood of blade wear was predicted to vary within a small range for a fixed blade-tip shape over all conditions studied, which suggests that tip shape is the primary factor to consider when minimizing blade wear.

Experimental investigation of shear-driven water film flows on horizontal metal plate

In this article, an experimental investigation has been conducted to characterize the instantaneous thickness of the surface water film driven by high-speed airflow pertinent to aerodynamic icing and anti-icing modeling. Non-intrusive results of the film flowing on a metal plate were obtained using the high-speed camera and confocal chromatic technique. The wind speed (Ua) ranges from 17.8 m/s to 52.2 m/s, and the film Reynolds number (Ref) ranges from 26 to 128. The effect of the high-speed airflow on the structure of the wave film was observed and analyzed qualitatively. A new correlation of the interfacial shear factor was proposed for the prediction of the average film thickness. The predictions were compared with the previous annular flow models by applying the dimensionless analysis method and a good agreement is achieved. The superficial roughness, characterized by root-mean-square of the thickness, was well-correlated using a piecewise linear function of the average film thickness. Furthermore, a comprehensive description of the superficial waves including spectrum analysis and division of film thickness data between underlying film and large waves was presented. Transformations of the wave frequency and amplitude with the wind speed and the film Reynolds number were also addressed.

Modeling of core-annular and plug flows of Newtonian/non-Newtonian shear-thinning fluids in pipes and capillary tubes

Solutions for concentric core-annular laminar flows of Newtonian/non-Newtonian shear-thinning fluids in horizontal and inclined pipes are presented. The solution is computed for the general case of a Carreau non-Newtonian fluid proposing an iterative method based on Chebyshev collocation points. The effect of the rheology of the shear-thinning liquid on two-phase flow characteristics is investigated both for gas/liquid and liquid/liquid systems. Concurrent and counter-current flows in horizontal and inclined pipes were studied, while referring to practical two-phase flow aspects, such as the in-situ hold-up, lubrication effects and Ledinegg instability. The main characteristic of such systems is that even though the liquid has a complex rheology (Carreau fluid), the two-phase annular flow can exhibit a Newtonian/Newtonian behavior for a wide range of operational conditions. The identification of those conditions is a key aspect in the modeling activity, as to avoid unphysical predictions by the widely used power-law model. Particular attention is given to the core-annular flow characteristics in capillaries, where we propose also a model for the plug flow regime. Predictions of film thickness and plug propagation velocity are tested by comparison with experimental data, showing promising results and offering new insights on plug flow characteristics in capillaries, in particular for liquid-liquid plug flow.

A study of film thickness and hydrodynamic entrance length in liquid laminar film flow along a vertical tube

The liquid film thickness and hydrodynamic entrance length in a vertical tube was studied experimentally and numerically. Measurements using distilled water, 30 wt % MEA and 40 wt % sugar solutions were carried out to investigate the effects of liquid flow rate on the formation of the liquid film. The experimental results validate the new Navier‐Stokes based equation in cylindrical coordinates (Eq. 16) and the volume of fluid (VOF) model giving a competitively high prediction of the liquid film thickness especially in the low Reynolds number region. In addition, a new empirical model and an improved minimal surface model have been first proposed for calculation of the hydrodynamic entrance length, with a relatively reasonable average absolute relative deviation (AARD) of 3.03% and 6.83%, respectively. Furthermore, the effects of the hydrodynamic entry length on the gas–liquid interfacial area calculated by the improved minimal surface model were comprehensively studied, and can be ignored if the ratio of the liquid film length (y) and the hydrodynamic entrance length (λE) is lower than 10. However, it should be noted that the hydrodynamic entrance length cannot be ignored in packed columns in which the liquid flow is very complex due to the packings with different structures and materials. © 2018 American Institute of Chemical EngineersAIChE J, 64: 2078–2088, 2018

Quantitative Elastohydrodynamic Film-Forming for an Oil/Refrigerant System

The first calculations of film thickness for an oil/refrigerant system using quantitative elastohydrodynamics are reported in this work. It is demonstrated that primary measurements of the properties of the oil/refrigerant system can be employed to accurately predict film thickness in concentrated contacts. An unusual response to lubricant inlet temperature is revealed, wherein the film thickness may increase with temperature as a result of decreasing refrigerant solubility in oil when the inlet pressure is high. There is competition between the reduction in viscosity of the oil and the reduction of refrigerant concentration with increased temperature. For high inlet pressure, the dilution effect is dominant, whereas for low inlet pressure, the temperature dependence of the viscosity of the solution dominates over the range of inlet temperatures considered. It seems that only central film thicknesses have been experimentally measured for oil/refrigerant systems leaving these calculations as the only means of assessing the minimum.

Formulation of a reduced order model for the stiffness on elastohydrodynamic line contacts applied to cam-follower mechanism

Elastohydrodynamic (EHD) lubrication happens in any situation when elastic deformation occurs due to high hydrodynamic pressure in lubricated contacts. It affects the dynamic behavior of the system and might imply in tribology problems. For many years, the emphasis has been focused on the prediction of EHD pressure and film thickness; mostly central to the contact area and minimum oil film. An approach for boundary layer representation of EHD lubricated contact studies as a function of EHD stiffness parameters is proposed here. The model avoids excessive computational costs and it is promising for applicability in dynamic problem with one or multiples EHD contacts with considerable accuracy. The proposed contact force simulation is applied to a cam-follower mechanism. Since the radius of curvature, the load and the entrainment velocity varies over the cam's rotation cycle, the lubrication study in these kinematics pairs has been limited. In this work, an EHD stiffness map is evaluated to characterize the EHD contact over several different rotation speeds.

An updated three-zone heat transfer model for slug flow boiling in microchannels

This work proposes a novel physics-based model for the fluid mechanics and heat transfer associated with slug flow boiling in horizontal circular microchannels to update the widely used three-zone model of Thome et al. (2004). The heat transfer model has a convective boiling nature and predicts the time-dependent variation of the local heat transfer coefficient during the cyclic passage of a liquid slug, an evaporating elongated bubble and a vapor plug. The capillary flow theory, extended to incorporate evaporation effects, is applied to estimate the bubble velocity along the channel. A liquid film thickness prediction method also considering bubble proximity effects, which may limit the radial extension of the film, is included. The minimum liquid film thickness at dryout is set to the channel wall roughness. Theoretical heat transfer models accounting for the thermal inertia of the liquid film and for the recirculating flow within the liquid slug are utilized. The heat transfer model is compared to experimental data taken from three independent studies. The 833 slug flow boiling data points cover the fluids R134a, R245fa and R236fa, and channel diameters below 1 mm. The proposed evaporation model predicts more than 80% of the database to within ±30%. It demonstrates a stronger contribution to heat transfer by the liquid slugs and correspondingly less by the thin film evaporation process compared to the original three-zone model. This model represents a new step towards a complete physics-based modelling of the bubble dynamics and heat transfer within microchannels under evaporating flow conditions.

Upward gas–liquid two-phase flow after a U-bend in a large-diameter serpentine pipe

We present an experimental study on the flow behaviour of gas and liquid in the upward section of a vertical pipe system with an internal diameter of 101.6mm and a serpentine geometry. The experimental matrix consists of superficial gas and liquid velocities in ranges of 0.15–30m/s and from 0.07 to 1.5m/s, respectively, which cover bubbly to annular flow. The effects on the flow behaviours downstream of the 180° return bend are significantly reduced when the flow reaches an axial distance of 47 pipe diameters from the U-bend. Therefore, reasonably developed flow is attained at this development length downstream of the bend. Other published measurements for large-diameter film thickness show similar trends with respect to the superficial gas velocity. However, the trends differ from those of small-diameter pipes, with which the film thickness decreases much faster with increasing gas flow. As a result, only a few of the published correlations for small pipe data agreed with the experimental data for large pipe film thickness. We therefore modified one of the best-performing correlations, which produced a better fit. Qualitative and statistical analyses show that the new correlation provides improved predictions for two-phase flow film thickness in large-diameter pipes.