Thickness of Thin-Layer Liquid Film on a Rotating Roll and its Measurement by the X-Ray Backscattering Technique

1977 ◽  
Vol 47 (5) ◽  
pp. 311-316
Author(s):  
Nelson P. C. Chao
Keyword(s):  
Mathematical Model ◽  
Film Thickness ◽  
Thin Layer ◽  
Liquid Film ◽  
Liquid Viscosity ◽  
Roll Speed ◽  
Steady State Condition ◽  
X Ray ◽  
Experimental Values ◽  
The Mathematical Model

A mathematical model is provided to describe the thin-layer liquid film thickness on the surface of a rotating roll which is partially immersed in a liquid bath. The equation expresses the initial film thickness in terms of roll speed and immersion depth as well as liquid viscosity, surface tension, and density. The roll speed and liquid viscosity are the two dominant parameters affecting the film thickness. An x-ray backscattering technique was used to measure the film thickness. An important feature of this technique is that it permits the measurements to be carried out under a steady-state condition without disturbing the liquid film and the roll. The principle of a portable instrument and the technique involved in the measurements are described. Within the scope of the present investigation with Newtonian liquid and laminar flow, the experimental values of film thickness determined by the x-ray backscattering technique agreed very well with the theoretical values predicted by the mathematical model.

Modelling and Simulation of NO2 Dispersion Phenomenon in Atmosphere by Analytical-Experimental Methods

2008 ◽  
Vol 59 (10) ◽  
Author(s):  
Delia Perju ◽  
Harieta Pirlea ◽  
Gabriela-Alina Brusturean ◽  
Dana Silaghi-Perju ◽  
Sorin Marinescu
Keyword(s):  
Mathematical Model ◽  
Nitrogen Dioxide ◽  
Modeling And Simulation ◽  
Human Health ◽  
Experimental Methods ◽  
Negative Effects ◽  
Real Situation ◽  
Experimental Values ◽  
The Mathematical Model

The European laws and recently the Romanian ones impose more and more strict norms to the large nitrogen dioxide polluters. They are obligated to continuously improve the installations and products so that they limit and reduce the nitrogen dioxide pollution, because it has negative effects on the human health and environment. In this paper are presented these researches made within a case study for the Timi�oara municipality, regarding the modeling and simulation of the nitrogen dioxide dispersion phenomenon coming from various sources in atmosphere with the help of analytical-experimental methods. The mathematical model resulting from these researches is accurately enough to describe the real situation. This was confirmed by comparing the results obtained based on the model with real experimental values.

scholarly journals Mathematical Model of the Piped Vehicle Motion in Piped Hydraulic Transportation of Tube-Contained Raw Material

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Yongye Li ◽  
Xihuan Sun
Keyword(s):  
Mathematical Model ◽  
Transportation Cost ◽  
Raw Material ◽  
Maximum Relative Error ◽  
Transportation Energy ◽  
Core Components ◽  
Vehicle Motion ◽  
Motion Characteristics ◽  
Experimental Values ◽  
The Mathematical Model

The piped hydraulic transportation of tube-contained raw material is an emerging technique for transporting materials. In this technique, the piped vehicle is one of the core components, and its motion characteristics directly determine the transportation energy consumption and the transportation cost of this technique. To study the motion characteristics of the piped vehicle, the force of the piped vehicle was analyzed from the mechanical perspective in this paper. On the assumption that the piped vehicle moved steadily and it had sufficient stiffness, the mathematical model of the piped vehicle motion was established in the turbulent flow according to the stress characteristics of the piped vehicle and the factors influencing its motion characteristics, and then the mathematical model was tested by experiments. The findings show that the calculated values of the velocities of the piped vehicle were identical to the experimental values with changes in various influencing factors. When the flow discharge, the diameter or length of the piped vehicle increased, or the mass of transported material decreased, the velocity of the piped vehicle increased. The maximum relative error did not exceed 9.47%, which proved that the mathematical model of the piped vehicle motion was rational. The results can provide theoretical basis to improve the structure of the piped vehicle and the piped hydraulic transportation technique of tube-contained raw material.

Fabrication of Multilayer Films Using a Spinning Process

2000 ◽  
Vol 648 ◽  
Author(s):  
Jinhan Cho ◽  
Kookheon Char ◽  
Jong-Dal Hong ◽  
Ki-Bong Lee
Keyword(s):  
Film Thickness ◽  
Thin Layer ◽  
Ultrathin Films ◽  
Multilayer Films ◽  
Cds Nanoparticles ◽  
Adsorption Time ◽  
X Ray ◽  
Spinning Process ◽  
Allylamine Hydrochloride ◽  
Spinning Speed

AbstractWe introduce a method to build up organic/organic and organic/inorganic multilayer films composed of cationic poly(allylamine hydrochloride) (PAH) and negatively charged poly(sodium 4-styrenesulfonate) (PSS) or inorganic cadmium sulfide (CdS) nanoparticles using a spinning process. Since the deposition of each layer is made at a high spinning speed, the adsorption time for the formation of a homogeneous thin layer takes only 8 to 15 seconds. The adsorbed film thickness per bilayer can be easily controlled from about 5Å to 40Å by varying the spinning speed (Ω) and the mole concentration of polyelectrolytes. We also demonstrated with X-ray reflectivity that the alternating organic/inorganic ultrathin films fabricated by the spin SA process retain highly ordered internal structure in comparison with those prepared by the conventional SA process.

Study of Maneuverability of Container Ship With Nonlinear and Roll-Coupled Effects by Numerical Simulations Using RANSE-Based Solver

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
R. Rajita Shenoi ◽  
P. Krishnankutty ◽  
R. Panneer Selvam
Keyword(s):  
Mathematical Model ◽  
High Speed ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Container Ship ◽  
Navier Stokes Equations ◽  
Hydrodynamic Derivatives ◽  
Computational Fluid Dynamics Cfd ◽  
Experimental Values ◽  
The Mathematical Model

The examination of maneuvering qualities of a ship is necessary to ensure its navigational safety and prediction of trajectory. The study of maneuverability of a ship is a three-step process, which involves selection of a suitable mathematical model, estimation of the hydrodynamic derivatives occurring in the equation of motion, and simulation of the standard maneuvering tests to determine its maneuvering qualities. This paper reports the maneuvering studies made on a container ship model (S175). The mathematical model proposed by Son and Nomoto (1981, “On Coupled Motion of Steering and Rolling of a High Speed Container Ship,” J. Soc. Nav. Arch. Jpn., 150, pp. 73–83) suitable for the nonlinear roll-coupled steering model for high-speed container ships is considered here. The hydrodynamic derivatives are determined by numerically simulating the planar motion mechanism (PMM) tests in pure yaw and combined sway–yaw mode using an Reynolds-Averaged Navier–Stokes Equations (RANSE)-based computational fluid dynamics (CFD) solver. The tests are repeated with the model inclined at different heel angles to obtain the roll-coupled derivatives. Standard definitive maneuvers like turning tests at rudder angle, 35 deg and 20 deg/20 deg zig-zag maneuvers are simulated using the numerically obtained derivatives and are compared with those obtained using experimental values.

scholarly journals A non-linear mathematical model for the X-ray variability of the microquasar GRS 1915+105 – III. Low-frequency quasi-periodic oscillations

2020 ◽  
Vol 497 (1) ◽  
pp. 405-415
Author(s):  
E Massaro ◽  
F Capitanio ◽  
M Feroci ◽  
T Mineo
Keyword(s):  
Mathematical Model ◽  
Equilibrium Points ◽  
Low Frequency ◽  
Input Function ◽  
Power Density Spectrum ◽  
Periodic Oscillations ◽  
Density Spectrum ◽  
X Ray ◽  
Almost All ◽  
The Mathematical Model

ABSTRACT The X-ray emission from the microquasar GRS 1915+105 shows, together with a very complex variability on different time-scales, the presence of low-frequency quasi-periodic oscillations (LFQPOs) at frequencies lower than ∼30 Hz. In this paper, we demonstrate that these oscillations can be consistently and naturally obtained as solutions of a system of two ordinary differential equations, which is able to reproduce almost all variability classes of GRS 1915+105. We modified the Hindmarsh–Rose model and obtained a system with two dynamical variables x(t), y(t), where the first one represents the X-ray flux from the source, and an input function J(t), whose mean level J0 and its time evolution is responsible of the variability class. We found that for values of J0 around the boundary between the unstable and the stable interval, where the equilibrium points are of spiral type, one obtains an oscillating behaviour in the model light curve similar to the observed ones with a broad Lorentzian feature in the power density spectrum and, occasionally, with one or two harmonics. Rapid fluctuations of J(t), as those originating from turbulence, stabilize the LFQPOs, resulting in a slowly amplitude modulated pattern. To validate the model, we compared the results with real RXTE data, which resulted remarkably similar to those obtained from the mathematical model. Our results allow us to favour an intrinsic hypothesis on the origin of LFQPOs in accretion discs ultimately related to the same mechanism responsible for the spiking limit cycle.

scholarly journals Mathematical simulation of catalytic paste flow in a ram extruder

2004 ◽  
Vol 58 (9) ◽  
pp. 387-392
Author(s):  
A.V. Zhensa ◽  
V.V. Kostutchenko ◽  
I.A. Petropavlovskiy ◽  
V.A. Filippin ◽  
E.M. Koltsova
Keyword(s):  
Mathematical Model ◽  
Film Thickness ◽  
Volume Content ◽  
Solid Phase ◽  
Functional Dependencies ◽  
Plastic Strength ◽  
Dispersed Phases ◽  
The Mathematical Model

A mathematical model was developed for the stage of catalyst paste preparation. The mathematical model allows the calculation of solvate film thickness and volume content of the solid phase at any moment of time. Functional dependencies were found, which correlated the solvate film thickness and volume content of the solid phase with the plastic strength and viscosity of catalyst pastes. A range of plastic strength was determined, which ensures the optimum forming properties of the pastes. The mathematical model allowed the determination of the concentrations of the components of the continuous and dispersed phases, which ensured the optimum paste forming rheological properties, which, in turn, influence the end properties of an a-FezOs catalyst. The significant role of the solvate film thickness in the forming properties of pastes was demonstrated.

scholarly journals ANALISIS STANDAR JUMLAH PERSONEL PENANGANAN PENGANGKUTAN BARANG BERBAHAYA DI BANDAR UDARA ADISUTJIPTO

2017 ◽  
Vol 8 (1) ◽  
pp. 93
Author(s):  
Gunawan Gunawan ◽  
Rully Medianto
Keyword(s):  
Mathematical Model ◽  
Physical Examination ◽  
Standard Procedure ◽  
Air Cargo ◽  
Type B ◽  
X Ray ◽  
Cargo Handling ◽  
Dangerous Goods ◽  
Cargo Transportation ◽  
The Mathematical Model

Good and efficient Air cargo handling, especially for dangerous goods transportation need to be supported by licensed dangerous goods handling personnel and supported by the transport handling facilities as well as standard procedure. Comprehensive standards and procedures are required to reduce the risk of accidents caused by an error in the handling of the dangerous goods transportation. Main problems in this study: first, to analyse the process of air cargo transportation handling at the Adisutjipto Airport; second, to analyse the standard of the dangerous goods handling personel. The cargo handling process consists of Outgoing (Acceptance, weighing, Documentation, Marking & labeling, X-ray, Storage, Build-up, and Loading) and Incoming (Check Incoming Massage, Unloading, Breakdown, check lists, Physical Examination, Storage, Notice of Arrival, Delivered). The mathematical model of Dangerous Goods Handling Personnel Number Standard: DG Personel Cargo Agent Type A = c.% DG. (2,89 x 10^-2) DG Personnel Warehousing Type B = c.% DG (4,53 x 106-3), DG Personnel Airline Type B = c.%DG. (4,89 X 10^-4).

Supercritical Fluid Extraction of Genistein from Extruded Soybean

2012 ◽  
Vol 178-181 ◽  
pp. 838-842
Author(s):  
Gui Hua Sheng ◽  
Quan Cheng Zhou
Keyword(s):  
Mathematical Model ◽  
Optimal Condition ◽  
Supercritical Fluid Extraction ◽  
Supercritical Fluid ◽  
Orthogonal Rotation ◽  
Optimal Conditions ◽  
Fluid Extraction ◽  
Model Set ◽  
Experimental Values ◽  
The Mathematical Model

An optimal condition of supercritical fluid extraction (SFE) for genistein in extruded soybean was developed. Optimal conditions through quadratic orthogonal rotation design were verified. The results from SC – CO2 showed that all five experiment factors tested have significant effects on the yield of genistein. The mathematical model set had close agreements with experimental values. It was found that there were 32 optimal extract conditions under which genistein yield higher than 0.092% were gotten through simulate compute. The optimal extracting conditions were stable and recurrable. SC–CO2 had a potential in the extraction of genistein from extruded soybean products.

scholarly journals Three-Dimensional Mathematical Model of the Liquid Film Downflow on a Vertical Surface

Energies ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 1938
Author(s):  
Ivan Pavlenko ◽  
Oleksandr Liaposhchenko ◽  
Marek Ochowiak ◽  
Radosław Olszewski ◽  
Maryna Demianenko ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Film Thickness ◽  
Liquid Film ◽  
Three Dimensional ◽  
Friction Stress ◽  
Vertical Axis ◽  
Vertical Surface ◽  
Channel Length ◽  
Interfacial Surface ◽  
Separation Equipment

Film downflow from captured liquid without wave formation and its destruction is one of the most important aspects in the development of separation equipment. Consequently, it is necessary to create well-organized liquid draining in areas of captured liquid. Thus, the proposed 3D mathematical model of film downflow allows for the determination of the hydrodynamic parameters of the liquid film flow and the interfacial surface. As a result, it was discovered that the interfacial surface depends on the proposed dimensionless criterion, which includes internal friction stress, channel length, and fluid density. Additionally, equations for determining the averaged film thickness, the averaged velocity vectors over the film thickness, the longitudinal and vertical velocity components, and the initial angle of streamline deviation from the vertical axis were analytically obtained.

The Mathematical Model of the Broadband Transmission X-Ray Thickness Gauge

2019 ◽  
Vol 970 ◽  
pp. 210-218
Author(s):  
Sergei P. Osipov ◽  
Sergei Chakhlov ◽  
Daniyar Kairalapov ◽  
Oleg Osipov
Keyword(s):  
Mathematical Model ◽  
Measurement Error ◽  
Thickness Measurement ◽  
Performance Rating ◽  
Thickness Gauge ◽  
Attenuation Coefficients ◽  
Wide Beam ◽  
X Ray ◽  
Proposed Model ◽  
The Mathematical Model

The mathematical model of the broadband transmission X-ray thickness gauge is developed. The mathematical model consists of sectors: generation and transformation of radiometric signals; equation of transmission X-ray thickness gauge; error estimation of thickness measurement; performance rating. The example of the use of the proposed model to calculate of the transmission X-ray thickness gauge for aluminum items is provided. In the example the dependences of integral mass X-ray attenuation coefficients and the thickness of monitored objects made from aluminum are calculated. The range of optimum measured thickness depending on the maximum X-ray energy was selected, the measurement time to provide the desired thickness measurement error was estimated. The possibility of measuring the thickness of a cooper test object for a wide beam conditions has been experimentally confirmed.

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