A Mathematical Analysis of Directional Solidification of Aqueous Solutions

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Gideon Ukpai ◽  
Boris Rubinsky
Keyword(s):  
Mathematical Model ◽  
Aqueous Solutions ◽  
Mathematical Models ◽  
Directional Solidification ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Design Parameters ◽  
Fundamental Study ◽  
Biological Matter ◽  
Intent To Use

Abstract Horizontal directional solidification techniques have been broadly utilized for the freezing of biological matter under conditions in which the freezing rate during solidification must be controlled and known. Directional solidification is used for diverse applications such as fundamental research on freezing of biological materials, cryopreservation of biological matter, and tissue engineering. This study is motivated by our intent to use directional solidification as a simplified model for the study of three-dimensional (3D) cryoprinting. In evaluating directional solidification in the context of 3D cryoprinting, we realized that current mathematical models of directional solidification are not adequately representative for this purpose, because they are simplified and one-dimensional (1D). Here, we introduce an experimentally verified and more representative two-dimensional (2D) mathematical model of directional solidification that can aid in the fundamental study of freezing of biological matter, in particular during 3D cryoprinting. The mathematical model was used to develop correlations between the freezing rates that a layer of an aqueous solution experiences during directional solidification and the various design parameters such as thickness of the sample and temperature gradients in the substrate. Results show that the freezing rates can be higher than those suggested by the previously used simplified 1D mathematical models. The results can be used for developing simplified models of 3D cryoprinting. In addition, the results suggest that many experimental studies on directional solidification of aqueous solutions and biological matter may require readjustment of analysis, in view of these findings.

Mobile Worm-Like Robots for Pipe Inspection

2015 ◽  
pp. 168-218 ◽  
Author(s):  
Sergey Fedorovich Jatsun ◽  
Andrei Vasilevich Malchikov
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Mobile Robots ◽  
Experimental Studies ◽  
Design Parameters ◽  
Robot Motion ◽  
Robot Dynamics ◽  
Confined Space ◽  
Pipe Inspection ◽  
The Mathematical Model

This chapter describes various designs of multilink mobile robots intended to move inside the confined space of pipelines. The mathematical model that describes robot dynamics and controlled motion, which allows simulating different regimes of robot motion and determining design parameters of the device and its control system, is presented. The chapter contains the results of numerical simulations for different types of worm-like mobile robots. The experimental studies of the in-pipe robots prototypes and their analyses are presented in this chapter.

scholarly journals Empirical, Dimensional and Inspectional Analysis in the Design of Bottom Intake Racks

Water ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 1035 ◽  
Author(s):  
Juan García ◽  
Luis Castillo ◽  
José Carrillo ◽  
Patricia Haro
Keyword(s):  
Discharge Coefficient ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Design Parameters ◽  
Incoming Flow ◽  
Viscous Forces ◽  
The Mean ◽  
Definition Of ◽  
New Formulation ◽  
Bottom Intake

Flow over bottom racks is highly turbulent, three-dimensional and spatially varied. The design of bottom intake systems has mainly been studied in the laboratory. The comparison of existing experimental studies shows large deviations in the definition of design parameters such as wetted rack length. Each experimental study is limited to a single bar type or to a low range of void ratios, which makes it difficult to generalize the observed data. A combination of empirical, dimensional and inspectional analysis is presented as a useful tool to reduce the number of variables with influence in the design parameters, such as the wetted rack length or the mean discharge coefficient. This work includes a broad experimental campaign in which wetted rack length and mean discharge coefficient are characterized using five different bottom racks with different void ratios (area between bars divided by total area). T-shaped flat and circular bars are considered as well as five different longitudinal slopes. Empirical and inspectional analyses have allowed us to verify, in two different ways, the relation between wetted rack length and incoming flow through potential functions. The influence of the viscous forces has been studied as a function of the incoming flow. Similar results may be obtained when analysing the Froude number at the beginning of the rack, depending on the wetted rack length. A new formulation for calculating the mean discharge coefficient and wetted rack length is proposed.

Theoretical analysis of braiding strand trajectories and simulation of three-dimensional parametric geometrical models for multilayer interlock three-dimensional tubular braided preforms

2019 ◽  
Vol 89 (19-20) ◽  
pp. 4306-4322 ◽  
Author(s):  
Zhipeng Wang ◽  
Guoli Zhang ◽  
Youxin Zhu ◽  
Liqing Zhang ◽  
Xiaoping Shi ◽  
...  
Keyword(s):  
Mathematical Models ◽  
Three Dimensional ◽  
Theoretical Models ◽  
Geometrical Model ◽  
Design Parameters ◽  
Braided Composites ◽  
3D Braided Composites ◽  
Interlaminar Shear ◽  
Braided Structure ◽  
Propeller Blades

Multilayer interlock three-dimensional (3D) tubular braided composites have been widely used in propeller blades, high pressure pipelines, rocket nose cones and engine nozzles owing to prominent interlaminar shear properties, reliable damage tolerance and outstanding torsion performance. The prediction of the mechanical properties and the design of the fabric structures for the 3D braided composites are dependent on the trajectory distribution of strands and the geometrical model of the braided structure. This paper aims to build theoretical models for the braiding strand trajectories and presents a creative method to establish the parametric geometrical models for the multilayer interlock 3D tubular braided structures. Firstly, mathematical models of braiding strand trajectories are derived based on the analysis for the characteristics of carrier paths, the interlacing and interlocking of braided structures and the motion of braiding strands. The mathematical models are then developed to establish parametric expressions for multilayer interlock 3D tubular braided structures by the advanced development of UG NX®. In addition, the models of corresponding braiding strand trajectories and braiding structures can be obtained automatically in the simulation environment with the modification of design parameters. Finally, the established models are compared with the carbon fiber braided specimen. The results show that the innovative parametric geometric models of the multilayer interlock 3D tubular braided structures accurately describe the key characteristics of the preform.

scholarly journals MATHEMATICAL MODELING OF RESIDUAL STRESSES IN PLASMA COATINGS TAKING INTO ACCOUNT THE PROCESS OF INCREASING LAYERS

2020 ◽  
Vol 22 (6) ◽  
pp. 14-20
Author(s):  
V.I. Bogdanovich ◽  
◽  
M.G. Giorbelidze ◽  
I.A. Dokukina ◽  
N.V. Surkova ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Residual Stresses ◽  
Mathematical Models ◽  
Ambient Temperature ◽  
Experimental Studies ◽  
Final Temperature ◽  
Good Convergence ◽  
Plasma Coatings

Developed a mathematical model for determining residual stresses with increasing plasma coatings, taking into account the stresses arising upon cooling of the material from the final temperature to ambient temperature; tension that arises when removing the fastening devices and tension that existed in the substrate before spraying. The developed mathematical models are adapted for the most common cases of fixing the base used in the practice of coating. Experimental studies of residual stresses were carried out, which showed good convergence with the values of residual stresses obtained theoretically.

scholarly journals THE METHOD OF FINDING ADEQUATE MATHEMATICAL MODELS DESCRIBING THE CHARACTERISTICS OF RADIO ENGINEERING DEVICES

2021 ◽  
Vol 2 (336) ◽  
pp. 145-151
Author(s):  
P. V. Boikachov ◽  
A. A. Yerzhan ◽  
V. O. Isaev ◽  
I. A. Dubovik ◽  
A. Marat
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Experimental Studies ◽  
Statistical Processing ◽  
Analytical Form ◽  
Physical Processes ◽  
Technical Object ◽  
Radio Engineering ◽  
Input Action ◽  
The One

The method of finding adequate mathematical models of radio engineering devices in an analytical form is proposed. RES, as a rule, is a very complex technical object that includes a large number of components with diverse connections between them, the hierarchy of construction of which can be represented in the form of a kind of pyramid. In this regard, there is a simulation of radio-electronic devices, which can be carried out at all levels of the "pyramid". Modeling at its lower levels, including semiconductor devices, links, cascades, etc., is reduced to describing their operation using a matrix, equation, formula, graph, or table. Such a mathematical model should, on the one hand, accurately reflect the physical processes in the object under study, and on the other - be suitable for use on a PC. In some cases, the mathematical model is the result of analytical or numerical analysis of the physical model of the object, but most often-experimental studies. Processing, including statistical processing, of the available data array that characterizes the operation of the cascade or element, is carried out using a PC. The operation of an object can also be defined in the form of its response or reaction to an input action without penetrating into the essence of the physical processes occurring inside the device.

scholarly journals Fixed - bed Column Adsorption Studies Using Synthetic Hydroxyapatite for Pb(II) Removal from Aqueous Solutions

2019 ◽  
Vol 70 (5) ◽  
pp. 1758-1764
Author(s):  
Claudia Maria Simonescu ◽  
Iuliana-Raluca Tanase ◽  
Irina Nicoleta Purcaru ◽  
Christu Tardei ◽  
Virgil Marinescu
Keyword(s):  
Aqueous Solutions ◽  
Fixed Bed ◽  
Experimental Studies ◽  
Design Parameters ◽  
Fixed Bed Column ◽  
Column Adsorption ◽  
Porous Beads ◽  
Synthetic Hydroxyapatite ◽  
Column Design ◽  
Critical Bed Depth

In the present paper, the adsorptive Pb(II) removal from synthetic aqueous solutions using a 2 cm diameter hydroxyapatite column has been studied through column adsorption experiments by varying column depths (1, 2, 3, 4 cm) and flow rate (10, 15, 22.5 mL/min). Different types of synthetic hydroxiapatites have been involved in experiments. Column design parameters such as critical bed depth and adsorption capacity have been determined from experimental studies. The results revealed the effectiveness of synthetic hydroxyapatite porous beads in Pb(II) removal from aqueous synthetic solutions.

Feasibility of Shape Memory Alloy Wire Actuation for an Active Steerable Cannula

2015 ◽  
Vol 9 (2) ◽  
Author(s):  
Bardia Konh ◽  
Naresh V. Datla ◽  
Parsaoran Hutapea
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Breast Biopsy ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Needle Insertion ◽  
Design Parameters ◽  
Fe Model ◽  
In Series ◽  
Steerable Cannula

Needle insertion is used in many diagnostic and therapeutic percutaneous medical procedures such as brachytherapy, thermal ablations, and breast biopsy. Insufficient accuracy using conventional surgical cannulas motivated researchers to provide actuation forces to the cannula's body for compensating the possible errors of surgeons/physicians. In this study, we present the feasibility of using shape memory alloy (SMA) wires as actuators for an active steerable surgical cannula. A three-dimensional (3D) finite element (FE) model of the active steerable cannula was developed to demonstrate the feasibility of using SMA wires as actuators to bend the surgical cannula. The material characteristics of SMAs were simulated by defining multilinear elastic isothermal stress–strain curves that were generated through a matlab code based on the Brinson model. Rigorous experiments with SMA wires were done to determine the material properties as well as to show the capability of the code to predict a stabilized SMA transformation behavior with sufficient accuracy. In the FE simulation, birth and death method was used to achieve the prestrain condition on SMA wire prior to actuation. This numerical simulation was validated with cannula deflection experiments with developed prototypes of the active cannula. Several design parameters affecting the cannula's deflection such as the cannula's Young's modulus, the SMA's prestrain, and its offset from the neutral axis of the cannula were studied using the FE model. Real-time experiments with different prototypes showed that the quickest response and the maximum deflection were achieved by the cannula with two sections of actuation compared to a single section of actuation. The numerical and experimental studies showed that a highly maneuverable active cannulas can be achieved using the actuation of multiple SMA wires in series.

scholarly journals Hydrodynamic characteristics of the two-phase flow field at gas-evolving electrodes: numerical and experimental studies

2018 ◽  
Vol 5 (5) ◽  
pp. 171255 ◽  
Author(s):  
Cheng-Lin Liu ◽  
Ze Sun ◽  
Gui-Min Lu ◽  
Jian-Guo Yu
Keyword(s):  
Mathematical Model ◽  
Flow Field ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Electrode System ◽  
Hydrodynamic Characteristics ◽  
Cold Model ◽  
Two Phase ◽  
3D Space ◽  
Vertical Electrode

Gas-evolving vertical electrode system is a typical electrochemical industrial reactor. Gas bubbles are released from the surfaces of the anode and affect the electrolyte flow pattern and even the cell performance. In the current work, the hydrodynamics induced by the air bubbles in a cold model was experimentally and numerically investigated. Particle image velocimetry and volumetric three-component velocimetry techniques were applied to experimentally visualize the hydrodynamics characteristics and flow fields in a two-dimensional (2D) plane and a three-dimensional (3D) space, respectively. Measurements were performed at different gas rates. Furthermore, the corresponding mathematical model was developed under identical conditions for the qualitative and quantitative analyses. The experimental measurements were compared with the numerical results based on the mathematical model. The study of the time-averaged flow field, three velocity components, instantaneous velocity and turbulent intensity indicate that the numerical model qualitatively reproduces liquid motion. The 3D model predictions capture the flow behaviour more accurately than the 2D model in this study.

scholarly journals MATHEMATICAL MODELLING OF THE TECHNOLOGY OF PROCESSING THE SEED MASS OF VEGETABLES AND MELONS

2019 ◽  
Vol 13 (3) ◽  
Author(s):  
V. Shebanin ◽  
I. Atamanyuk ◽  
O. Gorbenko ◽  
Y. Kondratenko ◽  
N. Dotsenko
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Random Sequence ◽  
Experimental Studies ◽  
Seed Mass ◽  
High Accuracy ◽  
Suggested Method ◽  
Technological Processes ◽  
Seed Processing ◽  
The Mathematical Model

Designing modern seed processing machines requires a study of the regularities of technological processes, dynamics and conditions of operation. To determine the control parameters and their optimum values, it is necessary to use high-precision mathematical models of technologies of processing the vegetable and melon seed mass. A method has been suggested of modelling the technology of processing the seed mass of vegetables and melons based on nonlinear canonical decomposition of a random sequence of changes in the technological process parameters. The method of modelling the technology of processing the seed mass of vegetables and melons can be used to determine the optimum values of design and operation parameters of seed separating machines. This method allows obtaining mathematical models of technological processes for an arbitrary number of input parameters used to evaluate the characteristics of seeds, the degree of nonlinearity, and the peculiarities of stochastic connections. The method consists of the following stages: collection of statistical data; calculation parameters in the mathematical model; evaluation of the values of the parameters; calculation of the input parameters. The mathematical model of the processing technology of the seed mass of vegetables and melons does not impose any restrictions on the properties of the random sequence of input and output parameters (linearity, stationarity, monotonicity, scalarity, etc.). It allows taking into account the features of seed processing and, as a result, achieving the maximum quality of separation of vegetable and melon seeds. The method has been approved on the basis of the experimental installation of a separating machine. The results of the experimental studies have confirmed the high accuracy of the suggested method. The application of the suggested models reduces the average error of determination of seed losses. Statistic data for calculating mathematical model parameters have been obtained in the course of processing melons and cucumbers on an experimental installation. The results of the experimental studies have confirmed the high accuracy of the suggested method.

scholarly journals MATHEMATICAL MODEL OF THE MOTION PALLET PROCESS ON BRAKE MAGNETIC TYPE ROLLER

2020 ◽  
Vol 17 (3) ◽  
pp. 364-373
Author(s):  
I. A. Sharifullin ◽  
A. L. Nosko ◽  
E. V. Safronov
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Eddy Current ◽  
Experimental Studies ◽  
Viscosity Coefficient ◽  
Movement Speed ◽  
Design Parameters ◽  
Magnetic Viscosity ◽  
Study Results ◽  
Magnetic Type

Introduction. One of the main elements of the safe operation of gravity roller conveyors used in pallet racks is a brake roller. The most promising design is the brake roller magnetic (eddy current) type. The operation principle of such rollers is based on the laws of electromagnetic induction and involves the braking of a conductor moving in a magnetic field, due to the interaction of eddy currents (or Foucault currents) arising in the volume of the conductor with an external magnetic field. However, in the market of warehouse shelving equipment, brake magnetic rollers are not widely used due to their high cost, which is primarily due to the lack of domestic designs and methods for their calculation. The aim of the work is to develop a mathematical model of the moving pallets process on a magnetic type brake roller.Materials and methods. The paper presented the theoretical study results on the development of a mathematical model of the moving pallets process on a magnetic type brake roller, described in works on centrifugal friction rollers and eddy current brake devices.Results. The main parameter determining the functions of the brake magnetic roller and hence the speed of the pallet along the gravity roller conveyor is a magnetic viscosity coefficient. The speed dependence of the pallets on the brake magnetic roller for various values of a magnetic viscosity coefficient is determined, its analysis is carried out.Conclusions. A mathematical model of the moving pallets process on a brake magnetic roller is developed. The movement speed equation of the pallets on the brake magnetic roller is obtained. For a reasonable choice of the design parameters of the magnetic brake roller, experimental studies are required to determine a magnetic viscosity coefficient.

Sign in / Sign up

Export Citation Format

Share Document