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Viewing 31 to 60 of 16158
2015-06-15
Technical Paper
2015-01-2112
Thomas Schlegl, Michael Moser, Hubert Zangl
We present a system of completely autarkic temperature and capacitive icing sensors for aircraft. The consequences of icing on aircraft are described, for example, in [1] and [2]. Flexible (i.e. bendable) sensors, which are truly wireless and do not require maintenance, are easily mounted to almost any point on the aircraft surface (e.g. wings, fuselage, rudder, elevator, etc.). The entire sensing unit has a size of less than 100 mm times 170 mm (3.397 in times 6.693 in). The overall thickness can be kept lower than 2 mm (0.079 in) at the current status of development. It comprises the sensor front-end, processing electronics, buffered solar harvesting and a low-power radio frequency transmitter. The system transmits measurement results via an RF link to a monitoring system, which comprises a receiver antenna and a receiver circuit located at a suitable position on the aircraft. The employed sensor principle was first suggested in [3].
2015-06-15
Technical Paper
2015-01-2116
Peter Struk, Tadas Bartkus, Jen-Ching Tsao, Tom Currie, Dan Fuleki
This paper describes ice accretion measurements from experiments conducted at the National Research Council (NRC) of Canada’s Research Altitude Test Facility during 2012. Due to numerous engine power-loss events associated with high-altitude convective weather, potential ice accretion within an engine due to ice-crystal ingestion is being investigated collaboratively by NASA and NRC. These investigations examine the physical mechanisms of ice accretion on surfaces exposed to ice-crystal and mixed-phase conditions, similar to those believed to exist in core compressor regions of jet engines. A further objective of these tests is to examine scaling effects since altitude appears to play a key role in this icing process. While the 2012 experiments had multiple objectives such as cloud characterization and the evaluation of imaging techniques, several tests were dedicated to observe ice accretions using both a NACA 0012 and a wedge-shaped airfoil.
2015-06-15
Technical Paper
2015-01-2115
Antonio Criscione, Suad Jakirlic, Zeljko Tukovic, Ilia Roisman, Cameron Tropea
Atmospheric icing occurs when supercooled large drops (SLD) of water come in contact with the surface of exposed structures. Excessive accumulation on structures and equipment is well known for causing serious problems in cold-climate regions which lead to material damage and high costs in various sectors of the economy. Hereby, SLD impact with the exposed structure results consequently in an ice layer growth covering the surface of the substrate. The present study enables, among other things, modeling of both stages of the solidification process of a supercooled large water drop on a cold substrate - the first rapid, recalescent stage and the second slower, quasi-isothermal stage. The different mechanisms underlying both freezing stages can be explained as follows: in the first stage the initial planar solidification front becomes morphologically unstable due to a high degree of supercooling. Small bumps/instabilities evolving at the interface propagate further into the liquid.
2015-06-15
Technical Paper
2015-01-2118
Sergey Alekseyenko, Michael Sinapius, Martin Schulz, Oleksandr Prykhodko
In spite of wide theoretical and experimental studies of icing problem that have been held up to recent times, nevertheless, the most dangerous flights regimes as in the presence of supercooled large droplets or in supercooled rain remain studied not enough. Also the range of parameters that corresponds to the exploitation modes of aircrafts with relatively small heights and speeds of flight like airplanes of small aviation, helicopters, UAV etc. because of the complexity of the icing processes are still not covered. The aim of this work is to answer the next question: which an actual process of interaction of supercooled large water droplets with growing ice surface at small speeds of flight and which physics of falling moisture freezing process on the icing surface is. Thus, the work presents the results of experiments conducted in order to obtain the photographic data on how the interaction between the supercooled water droplets and the icing aerodynamic surface occurs.
2015-06-15
Technical Paper
2015-01-2120
Yong Han Yeong, Eric Loth, Jack Sokhey, Alexis Lambourne
Superhydrophobic coatings have shown promise in reducing ice adhesion on a surface. However, recent superhydrophobic ice adhesion studies were conducted at either ice accretion conditions that do not resemble aerospace icing conditions, or at low super-cooled droplet impact speeds (less than 10 m/s). Therefore, a detailed experiment was conducted to measure the ice adhesion strength of various superhydrophobic coatings in an icing wind tunnel at an air speed of 50 m/s and at a temperature of -15°C with a super-cooled icing cloud consisting of 20 µm droplets. The ice was accreted on 3 mm thick, 30 mm diameter discs and then removed by pressurized nitrogen through the access hole in a tensile direction for a measurement of the ice fracture energy. Results showed no relationship between coating wettability parameters (water contact and receding angles) with ice fracture energy but depicted a general increase in fracture energy with increasing surface auto-correlation lengths.
2015-06-15
Technical Paper
2015-01-2117
Miki Shimura, Makoto Yamamoto
It is well known that SLD icing is very dangerous because it is more unpredictable than general icing caused by smaller droplets. In SLD conditions, extraordinary phenomenon occurs. For example, SLD largely deforms. Vargas et al. (2010) performed the experiments about the droplet deformation. In their experiments, it was confirmed that the droplet height increases and the droplet width decreases, as the droplets approach the leading edge of an airfoil Therefore, the assumption that a droplet behaves as a sphere is no longer valid. To predict the deformation and the breakup of a droplet, several mathematical models have been proposed. For example, Ibrahim et al. (1993) proposed a model for the droplet deformation and breakup (DDB) model. However, the DDB model has not found wide acceptance. Other models exist, in which the deformation is described with the change of drag coefficient.
2015-06-15
Technical Paper
2015-01-2124
Amanda Gounou, Jean-Marc Moisselin, Frédéric Autones, Dominique Levaillant, Jean-Louis Brenguier, Eric Défer, Michael Faivre, Alice Grandin, Fabien Dezitter, Sandra Turner
Icing conditions are often encountered in the vicinity of deep convective clouds. Nowcasting of these conditions would be of a great help for flight safety and air traffic management but still remains challenging. In the framework of the HAIC (High Altitude Ice Crystals) project [1], the nowcasting of icing conditions due to ice particles is investigated. A major field campaign has been carried out in Darwin, Australia, from 16th January to 7th March 2014, during the rainy season to sample meteorological conditions potentially leading to icing [2]. There were 23 research flights with on-board in-situ and remote sensing instruments measuring or estimating ice water content within oceanic mature thunderstorms which offered a great opportunity to implement, test and cross-validate nowcasting tools to detect and track cloud regions of high ice water content.
2015-06-15
Technical Paper
2015-01-2119
Shinan Chang, Chao Wang, Mengyao Leng
Drop deformation and breakup is an important issue that involved in the aircraft and engine icing field especially in the case of the supercooled large droplets (SLD). In this paper, the breakup modes of SLD are discussed in detail based upon the classical theories of the drop breakup and typical icing conditions. It is found that the breakup modes of SLD are mainly vibration breakup, bag-type breakup, multimode breakup and shear breakup. As the vibration breakup mode is rare, focuses are put on the bag-type breakup, multimode breakup and shear breakup. Because the drop Weber number is increasing gradually when the drops are approaching the leading edge of the airfoil and the drop Weber number differs in different locations of the airfoil surface, two or three breakup modes may appear simultaneously in a given environmental condition.
2015-06-15
Technical Paper
2015-01-2121
Yong Chen, Liang Fu
In helicopter, the icing rotor blades will decrease the effectiveness of the helicopter and endanger the lives of the pilots. The asymmetrical ice break-up and shedding could also lead to severe vibrations of the rotor blade. Ice break-up from the main rotor may strike the fuselage and tail rotor, even worse, find its way into the engine, which may cause serious aircraft accidents. An understanding of the mechanisms responsible for ice shedding process is necessary in order to optimize the helicopter rotor blade design and de-icing system to avoid hazardous ice shedding. In previous study, the ice shedding criteria was established by comparing the centrifugal force and the adhesion force. In most cases, part of the ice will shed before the centrifugal force equals to the adhesion force, because the adhesion stress between the ice and the blade is not uniform.
2015-06-15
Technical Paper
2015-01-2130
Melissa Bravin, J. Walter Strapp, Jeanne Mason
In response to the occurrence of jet engine powerloss and damage events associated with deep convective clouds containing high concentrations of ice crystals, several research efforts are underway. Several flight measurement programs devoted to the collection of in-situ and remote sensing of clouds have been conducted over the past few years. The most recent in Darwin, Australia, from January-March 2014, and its follow-up planned for Cayenne, French Guiana, in May 2015, involve the use of a highly instrumented research aircraft with instrumentation specially designed to make accurate in-situ total water content (TWC) and median mass diameter (MMD) measurements of the high concentration areas of deep convection. The data will be used for atmospheric research related to understanding the microphysics of deep convection, and improving the ability to predict, detect and avoid these clouds.
2015-06-15
Technical Paper
2015-01-2107
Tom Currie, Dan Fuleki, Craig Davison
Abstract Ice crystals ingested by a jet engine at high altitude can partially melt and then accrete within the compressor, potentially causing performance loss, damage and/or flameout. Several studies of this ice crystal icing (ICI) phenomenon conducted in the RATFac (Research Altitude Test Facility) altitude chamber at the National Research Council of Canada (NRCC) have shown that liquid water is required for accretion. CFD-based tools for ICI must therefore be capable of predicting particle melting due to heat transfer from the air warmed by compression and possibly also due to impact with warm surfaces. This paper describes CFD simulations of particle melting and evaporation in the RATFac icing tunnel for the former mechanism, conducted using a Lagrangian particle tracking model combined with a stochastic random walk approach to simulate turbulent dispersion. Inter-phase coupling of heat and mass transfer is achieved with the particle source-in-cell method.
2015-06-15
Technical Paper
2015-01-2139
E.J. Grift, E. Norde, E.T.A. Van der Weide, H.W.M. Hoeijmakers
In this study the characteristics of ice crystals on their trajectory in a single stage of a turbofan engine compressor will be determined. The particle trajectories are calculated with a Lagrangian method employing a classical fourth-order Runge-Kutta time integration scheme. The air flow field is provided as input and is a steady flow field solution governed by the Euler equations. The single compressor stage is represented using a cascaded grid. The grid consists of three parts of which the first and the last part are stator parts and the centre part is a rotor. This grid is linearly cascaded, i.e. repeated infinitely above and below the shown grid, to represent the other blades of this stator-rotor-stator stage. The rotor movement is accomplished by prescribing a relative velocity of the rotor part relative to the stator parts and the interface between rotor and stator is modelled by using a mixing plane assumption allowing a steady-state analysis.
2015-06-15
Technical Paper
2015-01-2138
E. Iuliano, E. Montreuil, E. Norde, E.T.A. Van der Weide, H.W.M. Hoeijmakers
In this study a comparison will be made between three Eulerian-based solvers that predict the ice crystal trajectories and impingement on a NACA-0012 airfoil. The codes are being developed within CIRA, ONERA and University of Twente, and are improvements to their in-house Eulerian codes called Imp2D/3D, CEDRE/Spiree and MooseMBIce, respectively. This cooperation between CIRA, ONERA and University of Twente was initiated in the framework of European funded project HAIC (High Altitude Ice Crystals), a large-scale integrated project which aims at enhancing aircraft safety when flying in mixed phase and glaciated icing conditions. The numerical codes differ by the general architecture and implementation of the cloud particle size distribution. Imp2D/3D and MooseMBIce are based on a finite volume approach for multi-block structured grid. CEDRE/Spiree also employs a finite volume approach but handles generalized unstructured grids.
2015-06-15
Technical Paper
2015-01-2141
Markus Widhalm
This paper focuses on the numerical simulation of the motion of regular shaped ice particles and the computation of aerodynamic forces and torques on such particles. The shape of an ice crystal may deviate considerably from a sphere and can occur as thin needles or disk-shaped configurations, referred as regular non-spherical particles, or in irregular form as flakes or agglomerates. Ice crystals can be found at the upper boundary of the troposphere in anvils of cumulonimbus clouds, where strong winds exist and an altitude, where jet aircraft cruise at transonic speed, imposing a high flow Reynolds number. As the particle size grows from a few microns into several 100's of microns a high particle Reynolds number may be expected too.
2015-06-15
Technical Paper
2015-01-2140
Emiliano Iuliano
The presence of ice crystals in deep convective clouds has become a major threat for aviation safety. As recently highlighted, once inside the engine core, ice crystals encounter a high temperature environment, so that they can either melt by convection with the warm environment or melt upon impact onto hot static components of the low-pressure components. As a consequence, a liquid film may form which, in turn, is able to capture further ice crystals by sticking mechanism. This scenario results in a significant decrease of the local surface temperature and, hence, promotes the accretion of ice. Therefore, it is clear that icing simulation capabilities have to be updated in order to be able to predict such phenomena. The paper proposes an extension of CIRA icing tools to deal with ice crystals along with supercooled water droplets.
2015-06-15
Technical Paper
2015-01-2143
Christian Mendig
In the project SuLaDI (Super Large Droplet Icing) research about the icing of airfoils through super large and super cooled droplets is done at the Institute of Composite Structures and Adaptive Systems (German Aerospace Center) and at the institute of Adaptronics and Function Integration (Technische Universität Braunschweig). In the framework of the project a deicing facility was built. It consists of a cooling chamber and a wind tunnel of the Eiffel-type therein. The icing of specimen takes place in the test chamber of the wind tunnel at temperatures below 0 °C. Between the flow straightener and the contraction section a spray system is built in, which sprays water droplets into the wind tunnel. The droplets are accelerated by the airstream and supercool on the way to the specimen. That means they cool down below the freezing point temperature, but they stay fluid. When hitting the specimen they freeze on it to rime ice, clear ice or mixed ice.
2015-06-15
Technical Paper
2015-01-2142
Colin Hatch, Roger Gent, Richard Moser
Summary Initial results from a hybrid electro-thermal electro-mechanical simulation (HETEMS) analysis tool are presented and compared to data measured during a dedicated icing trial. Temperatures and ice shed prediction data are compared with the data measured on a full size wing tested in the CIRA Icing Wind Tunnel (IWT) Additional Test Section (ATS). Background The demand for low power ice protection systems was one of the components of the EU Clean Sky initiative [1]. Under Clean Sky a research programme HETEMS looked at the development of a tool to analyse electro-thermal (ET) and electro-mechanical (EM) ice protection systems (IPS). The tool was intended to analyse independent ET and EM systems or a hybrid system using both technologies combined. The aims and scope of the tool are presented in [2]. The HETEMS software was developed around open source tools for the aerodynamic analysis [3] and mechanical failure analysis [4] in conjunction with in-house software.
2015-06-15
Technical Paper
2015-01-2147
Sandra Turner, Jean-Marc Gaubert, Remy Gallois, Thibault Dacla, Ingrid Mullie, Aurelien Bourdon, Fabien Dezitter, Alice Grandin, Alain Protat, Rodney Potts, Alfons Schwarzenboeck, J. Walter Strapp
The PLANET (PLAne-NETwork) System was used for real-time satellite data transmission during the HAIC/HIWC Darwin field Campaign (January to March 2014). The basic system was initially providing aircraft tracking, chat and weather text messages (METAR, TAF, NOTAM, etc.) in a standalone application. In the frame of the HAIC (High Altitude Ice Crystals) project, many improvements were made in order to fulfill requirements of the on-board and ground science teams. The aim of this paper is to present the main improvements of the PLANET System that were implemented for the Darwin field campaign. The goal of the flight tests for high IWC characterization were to collect cloud data in deep convective clouds, provide 99th percentile total water content statistics and other relevant parameters of such clouds as a function of distance scale to industry and regulators.
2015-06-15
Technical Paper
2015-01-2146
Matthew Feulner, Shengfang Liao, Becky Rose, Xuejun Liu
Matt Feulner, Shengfang Liao, Becky Rose and Xuejun Liu Pratt & Whitney, United Technologies Corporation A through-flow based Monte Carlo particle trajectory simulation is used to calculate the ice crystal paths in the low pressure compressor of a high bypass ratio turbofan engine. The trajectory model includes a statistical ice particle breakup model due to impact on the engine surfaces. Stage-by-stage ice water content, particle size and particle velocity distributions are generated at multiple flight conditions and engine power conditions. The simulation results prompt the need to properly set up boundary conditions for component or cascade testing.
2015-06-15
Journal Article
2015-01-2106
Mark Ray, Kaare Anderson
Cloud phase discrimination, with measurements of liquid water content (LWC) and ice water content (IWC) as well as the detection and discrimination of supercooled large droplets (SLD), are of primary importance due to several high-profile incidents over the past two decades. The UTC Aerospace Systems Optical Ice Detector (OID) is a prototype laser sensor intended to discriminate cloud phase, to quantify LWC and IWC, and to detect SLD and differentiate SLD conditions from Appendix C conditions. Phase discrimination is achieved through depolarization scattering measurements of a circularly polarized laser beam transmitted into the cloud. Optical extinction measurements indicate the liquid and ice water contents, while the differential backscatter from two distinct probe laser wavelengths infers an effective droplet size. The OID is designed to be flush-mounted with the aircraft skin and to sample the air stream beyond the boundary layer of the aircraft.
2015-06-15
Technical Paper
2015-01-2160
Alidad Amirfazli
Coatings that shed drops can help with icing mitigation. Shedding of a drop depends on surface wettability. To characterize the shedding of a drop, in an aerodynamic context, the minimum air velocity to displace the drop is measured, i.e., the critical air velocity. Recently, superhydrophobic surfaces (SHS) with their ability to shed drops have gained much attention to combat icing. However, questions remain about their performance when exposed to UV, or water for long periods. In this study of its first kind, the effect prolonged UV and water exposure on shedding of drops from 6 different SHS (four commercially available coatings (C1 to C4), and two developed in-house, S1 and S2) was investigated in an icing wind tunnel. Critical air velocity, and contact angle values show that UV-treatment has a stronger adverse effect for S1 and C1 surfaces, compared to other coatings. Water treatment adversely affects S1, C1 and C2 samples more than other samples.
2015-06-15
Technical Paper
2015-01-2161
Kazem Hasanzadeh, Dorian Pena, Yannick Hoarau, Eric Laurendeau
The paper will present the framework of fully automated two/three dimensional ice accretion simulation package NSMB3D-ICE, with emphasis on the remeshing step. The NSMB3D-ICE Navier-Stokes code, coupled to an Eulerian droplet module and iterative Messinger thermodynamic model, can perform multi time-steps ice accretion simulations via an automated multi-block elliptic/parabolic grid generation code (NSGRID3D). Attention is paid to the efficiency and robustness of the numerical procedure especially for complex 3D glaze ice simulation. The new automated multi time-step icing code NSMB3D-ICE/NSGRID3D is validated and verified using several icing case studies such as the GLC305-3D rime and glaze ice cases. The Navier-Stokes flow solver NSMB3D is a finite volume three-dimensional multi-block Euler/Navier-Stokes flow solver developed by J. Vos et al. [1-3].
2015-06-15
Technical Paper
2015-01-2163
Caio Fuzaro Rafael, Diogo Mendes Pio, Guilherme A. Lima da Silva
The present paper shows integral boundary-layer solutions and finite-volume Reynolds-Averaged Navier Stokes (RANS) Computational Fluid Dynamics (CFD) results for flow around three airfoils: NACA 8H12, MMB-V2 and NACA0012. The objective of the present paper is to verify and compare results of a proposed two-equation integral model to those of a traditional one-equation integral model used by classic 2D icing codes and previous anti-ice works. In addition, the present paper compares the results of both proposed and traditional integral codes to CFD results and, whenever possible - validate with experimental data. A numerical code that solves integral equations of boundary layer - with transition onset and length predictions as well as the intermittency evolution - is implemented based on different literature models.
2015-06-15
Technical Paper
2015-01-2148
Erdem Ayan, Serkan Ozgen, Canibek Murat, Erhan Tarhan
Ice crystal ingestion to aircraft engines may cause ice to accrete on internal components, leading to flameout, mechanical damage, rollback, etc. Many incidents occur due to the engine failures especially at high altitude convective weather conditions. Thus, in the framework of HAIC FP7 European project, the physical mechanisms of ice accretion on surfaces exposed to ice-crystal and mixed-phase conditions are investigated. Within the HAIC FP7 European project, TAI will implement models related to the ice crystal accretion calculation to the existing ice accumulation prediction program for droplets, namely TAICE. Considered models include heat transfer & phase change model, drag model and impact model. Moreover, trajectory model and Extended Messinger Model require some modifications to be used for ice crystal accretion predictions.
2015-06-15
Technical Paper
2015-01-2149
Caroline Laforte, Caroline Blackburn, Jean Perron
Ideally, an icephobic coating applied to ice-exposed surfaces appears to be an interesting solution to prevent ice build-up. Over the last decade, developments of efficient icephobic coatings were multiplied. Some materials that reduce ice adhesion have been developed from which the ice can be more easily shed, possibly even with existing forces such as wind, gravity and vibrations. This paper will depict icephobic coating performances of 262 different coatings and 11 grease type substrates tested over the past 10 years at the Anti-Icing Materials International Laboratory (AMIL). Since 2003, the icephobic performance is evaluated with two main test methods. A first test method was developed in regards to measuring the ice adhesion and its reduction. A second test was then developed to measure the ice accumulation reduction.
2015-06-15
Technical Paper
2015-01-2151
Reinhard F.A. Puffing, Wolfgang Hassler, Andreas Tramposch, Marian Peciar
For studying ice accretion processes experimentally and establishing a valuable validation basis for ice accretion simulation models it is desirable to document experimentally generated ice shapes as accurately as possible. The generated set of data then forms the basis for aerodynamic studies, the improvement of icing test facilities, the development of design criteria, the development of ice accretion simulation tools as well as a number of further applications. In the past, various ice shape documentation methods have been established. These include photography, cross-sectional tracing, molding and casting as well as 3D-scanning. Photography is the easiest and fastest documentation method but provides little quantitative information on the ice accretion process itself. Additional quantitative information can be obtained by using multiple cameras or calibrated camera positions which, however, implicates significant additional time and cost efforts.
2015-06-15
Journal Article
2015-01-2154
Franck Hervy, Severine Maguis, François Virion, Biagio Esposito, Hugo Pervier
In 2010, DGA Aero-engine Testing decided to develop a capability to reproduce glaciated icing conditions in one of its altitude test facilities able to simulate low temperature and high altitude conditions. The facility selected for this purpose, named A06, originally developed for relight and flame out testing of combustors has been modified to integrate a small experimental test cell instead of a combustor. A specific converging nozzle has been implemented to reach Mach number up to 0.85 allowing tests in free jet configuration on small test articles like probes. In addition, for ice crystals generation, spray bars have been inserted upstream the test cell. Tests have been performed to define the operating envelope in terms of temperature, altitude, Mach number, humidity and ice water content but also where the ice crystals generation system can operate continuously.
2015-06-15
Journal Article
2015-01-2155
Tadas P. Bartkus, Peter Struk, Jen-Ching Tsao
This paper describes a numerical model that simulates the thermal interaction between ice particles, water droplets, and the flowing air applicable during icing wind tunnel tests where there is significant phase-change of the cloud. The model is compared to measurements taken during wind tunnel tests simulating ice-crystal and mixed-phase icing that relate to ice accretions within turbofan engines. This model, written in MATLAB, is based on fundamental conservation laws and empirical correlations. Due to numerous power-loss events in aircraft engines, potential ice accretion within the engine due to the ingestion of ice crystals is being investigated. To better understand this phenomenon and determining the physical mechanism of engine ice accretion, fundamental tests have been collaboratively conducted by NASA Glenn Research Center and the National Research Council of Canada (NRC).
2015-06-15
Journal Article
2015-01-2156
Michael Oliver
The National Aeronautics and Space Administration conducted a full scale ice crystal icing turbofan engine test in the NASA Glenn Research Center’s Propulsion Systems Laboratory (PSL) Facility in February 2013. Honeywell Engines supplied the test article, an obsolete, unmodified Lycoming ALF502-R5 turbofan engine serial number LF01 that experienced an uncommanded loss of thrust event while operating at certain high altitude ice crystal icing conditions. These known conditions were duplicated in PSL for this testing. The data generated during this testing contained three subsets: known event conditions, altitude scaling conditions and a design of experiment (DOE) data set. The key roll back indicating parameter was found to be the reduction of the measured load parameter, the average of two measured load cells mounted on the thrust stand.
2015-06-15
Technical Paper
2015-01-2157
Mengyao Leng, Shinan Chang, Yuanyuan Zhao
Aircraft icing causes a great threaten to flight safety. With the development of anti/de-icing systems for aeronautics, some attention is paid on coating strategies for reducing the total amount of water present on the surface. By application of hydrophobic or super-hydrophobic coatings, characterized by low surface wettability, shedding of liquid from the surface can be enhanced. The motivation behind this work is to identify the way that wettability affects the motion of runback water, and establish an empirical formula of critical departure diameter. In order to contain the effect of surface wettability, it is necessary to obtain an accurate model for calculating dynamic contact angle (DCA). Instead of average static contact angle or empirical equation, the formula used in this work is derived theoretically, as a function of the capillary number, advancing and receding contact angle, and the roughness of the solid surface.
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