scholarly journals Interpretation of Frenkel’s theory of sintering considering evolution of activated pores: III. Determination of equilibrium sintering time

2015 ◽  
Vol 47 (2) ◽  
pp. 215-219
Author(s):  
C.L. Yu ◽  
D.P. Gao ◽  
F. Wang ◽  
R.J. Huo ◽  
X.M. Hao ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Liquid Phase ◽  
Liquid Phase Sintering ◽  
Experimental Results ◽  
Equilibrium Time ◽  
Sintering Time ◽  
Good Accordance ◽  
Cordierite Glass ◽  
The Mathematical Model

In this article, the Frenkel?s theory of liquid-phase sintering was interpreted regarding pores as the activated volume. The mathematical model established by Nikolic et al. was used to infer the equilibrium sintering time at varied sintering temperatures during the isothermal sintering of codierite glass by Giess et al. Through the calculation, the equilibrium time at 800?C, 820?C, 840?C and 860?C is inferred to be 7014.42mins, 1569.65mins, 368.92mins and 114.61mins, respectively. The equilibrium time decreases as the temperature increases. And the theoretical value is in good accordance with the experimental results. Thus, the model established by Nikolic et al. can be applied successfully to predict the equilibrium sintering time of the cordierite glass at varied temperatures during isothermal sintering.

scholarly journals Interpretation of Frenkel’s theory of sintering considering evolution of activated pores: II. Model and reliability

2015 ◽  
Vol 47 (1) ◽  
pp. 89-94
Author(s):  
C.L. Yu ◽  
D.P. Gao ◽  
S.M. Chai ◽  
Q. Liu ◽  
H. Shi ◽  
...  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Liquid Phase ◽  
Liquid Phase Sintering ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
First Order ◽  
Sintering Time ◽  
Sintering Mechanism ◽  
Cordierite Glass

Frenkel's liquid-phase sintering mechanism has essential influence on the sintering of materials, however, by which only the initial 10% during isothermal sintering can be well explained. To overcome this shortage, Nikolic et al. introduced a mathematical model of shrinkage vs. sintering time concerning the activated volume evolution. This article compares the model established by Nikolic et al. with that of the Frenkel's liquid-phase sintering mechanism. The model is verified reliable via training the height and diameter data of cordierite glass by Giess et al. and the first-order partial differential equation. It is verified that the higher the temperature, the more quickly the value of the first-order partial differential equation with time and the relative initial effective activated volume to that in the final equibrium state increases to zero, and the more reliable the model is.

Pneumotransport of Grains Through a Pipeline

2002 ◽  
Author(s):  
Kaushal K. Shrivastava
Keyword(s):  
Mathematical Model ◽  
Pressure Drop ◽  
Experimental Results ◽  
Experimental Techniques ◽  
Horizontal Pipe ◽  
Pressure Drops ◽  
Central Topic ◽  
The Mathematical Model ◽  
Mustard Seeds

Determination of pressure drop correlation using experimental techniques has been a central topic of research in the area of pneumotransport. However, the objective of the present investigation is to apply the mathematical model (SK model) developed by the author [1,2] along with other correlations [3–5] to estimate pressure drops for conveying varieties of grains through horizontal pipe and compare the values with the experimental results of Siegel [6]. The SK model has also been utilized to calculate pressure drops for conveying mustard seeds pneumatically through horizontal, inclined and vertical pipes and compare the values with the experimental results of Rose and Barnacle [7]. It is evident from various comparisons shown in this paper that the SK model predicts the values of pressure drop accurately as compared to the experimental results in all the cases of grains transport through horizontal, inclined, and vertical pipes, whereas, other correlations do not predict accurate results consistently in all cases.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

scholarly journals Synthesis and Na+ Ion Conductivity of Stoichiometric Na3Zr2Si2PO12 by Liquid-Phase Sintering with NaPO3 Glass

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 3790
Author(s):  
Yongzheng Ji ◽  
Tsuyoshi Honma ◽  
Takayuki Komatsu
Keyword(s):  
Solid State ◽  
Liquid Phase ◽  
Sintering Temperature ◽  
Liquid Phase Sintering ◽  
Ion Conductivity ◽  
X Ray Diffraction ◽  
Conventional Solid State Reaction ◽  
X Ray ◽  
Sintering Time ◽  
Lower Activation

Sodium super ionic conductor (NASICON)-type Na3Zr2Si2PO12 (NZSP) with the advantages of the high ionic conductivity, stability and safety is one of the most famous solid-state electrolytes. NZSP, however, requires the high sintering temperature about 1200 °C and long sintering time in the conventional solid-state reaction (SSR) method. In this study, the liquid-phase sintering (LPS) method was applied to synthesize NZSP with the use of NaPO3 glass with a low glass transition temperature of 292 °C. The formation of NZSP was confirmed by X-ray diffraction analyses in the samples obtained by the LPS method for the mixture of Na2ZrSi2O7, ZrO2, and NaPO3 glass. The sample sintered at 1000 °C for 10 h exhibited a higher Na+ ion conductivity of 1.81 mS/cm at 100 °C and a lower activation energy of 0.18 eV compared with the samples prepared by the SSR method. It is proposed that a new LPE method is effective for the synthesis of NZSP and the NaPO3 glass has a great contribution to the Na+ diffusion at the grain boundaries.

scholarly journals Determination of the Vertical Load on the Carrying Structure of a Flat Wagon with the 18–100 and Y25 Bogies

2021 ◽  
Vol 11 (9) ◽  
pp. 4130
Author(s):  
Oleksij Fomin ◽  
Alyona Lovska ◽  
Václav Píštěk ◽  
Pavel Kučera
Keyword(s):  
Mathematical Model ◽  
Fatigue Strength ◽  
Service Life ◽  
Dynamic Characteristics ◽  
Dynamic Load ◽  
Field Tests ◽  
Vertical Load ◽  
Mathcad Software ◽  
The Mathematical Model

The study deals with determination of the vertical load on the carrying structure of a flat wagon on the 18–100 and Y25 bogies using mathematic modelling. The study was made for an empty wagon passing over a joint irregularity. The authors calculated the carrying structure of a flat wagon with the designed parameters and the actual features recorded during field tests. The mathematical model was solved in MathCad software. The study found that application of the Y25 bogie for a flat wagon with the designed parameters can decrease the dynamic load by 41.1% in comparison to that with the 18–100 bogie. Therefore, application of the Y25 bogie under a flat wagon with the actual parameters allows decreasing the dynamic loading by 41.4% in comparison to that with the 18–100 bogie. The study also looks at the service life of the supporting structure of a flat wagon with the Y25 bogie, which can be more than twice as long as the 18–100 bogie. The research can be of interest for specialists concerned with improvements in the dynamic characteristics and the fatigue strength of freight cars, safe rail operation, freight security, and the results of the research can be used for development of innovative wagon structures.

Application of a Bubble-Induced Turbulence Model to Subcooled Boiling in a Vertical Pipe

1999 ◽  
Author(s):  
Mahmut D. Mat ◽  
Yüksel Kaplan ◽  
Olusegun J. Ilegbusi
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Liquid Phase ◽  
Turbulence Model ◽  
Transport Equations ◽  
Subcooled Boiling ◽  
Vertical Pipe ◽  
Void Fractions ◽  
Turbulence Production ◽  
The Mathematical Model

Abstract Subcooled boiling of water in a vertical pipe is numerically investigated. The mathematical model involves solution of transport equations for vapor and liquid phase separately. Turbulence model considers the turbulence production and dissipation by the motion of the bubbles. The radial and axial void fractions, temperature and velocity profiles in the pipe are calculated. The estimated results are compared to experimental data available in the literature. It is found that while present study satisfactorily agrees with experimental data in the literature, it improves the prediction at lower void fractions.

scholarly journals RESEARCH OF THE TENSELY-DEFORMED STATE OF ELEMENTS OF MOBILE HEAT STORAGE

2020 ◽  
Vol 42 (2) ◽  
pp. 68-75
Author(s):  
V.G. Demchenko ◽  
А.S. Тrubachev ◽  
A.V. Konyk
Keyword(s):  
Mathematical Model ◽  
Heat Storage ◽  
Quantitative Estimation ◽  
The Real ◽  
State Of The Union ◽  
Real Geometry ◽  
Deformed State ◽  
The Mathematical Model ◽  
Minimization Of Functional

Worked out methodology of determination of the tensely-deformed state of elements of mobile heat storage of capacity type, that works in the real terms of temperature and power stress on allows to estimate influence of potential energy on resilient deformation that influences on reliability of construction and to give recommendations on planning of tank (capacities) of accumulator. For determination possibly of possible tension of construction of accumulator kinematics maximum terms were certain. As a tank of accumulator shows a soba the difficult geometrical system, the mathematical model of calculation of coefficient of polynomial and decision of task of minimization of functional was improved for determination of tension for Міzеs taking into account the real geometry of equipment. Conducted quantitative estimation of the tensely-deformed state of the union coupling, corps and bottom of thermal accumulator and the resource of work of these constructions is appraised. Thus admissible tension folds 225 МРа.

scholarly journals Large Deflection Model for Multiple, Inline, Interacting Cantilever Beams

2020 ◽  
Vol 88 (4) ◽  
Author(s):  
Austin Bebee ◽  
Christopher J. Stubbs ◽  
Daniel J. Robertson
Keyword(s):  
Mathematical Model ◽  
Flexural Rigidity ◽  
Cantilever Beams ◽  
Model Concept ◽  
Math Model ◽  
Rigid Body Model ◽  
High Throughput Phenotyping ◽  
Stalk Lodging ◽  
The Mathematical Model

Abstract Numerous natural and synthetic systems can be modeled as clusters of interacting cantilever beams. However, a closed-form mathematical model capable of representing the mechanics of multiple interacting cantilever beams undergoing large deflections has yet to be presented. In this work, a pioneering mathematical model of the force–deflection response of multiple, inline, interacting (i.e., contacting) cantilever beams is presented. The math model enables the determination of the force–deflection response of a system of interacting cantilever beams and is predicated upon the “Pseudo Rigid Body Model” concept. The model was validated through data triangulation experiments which included both physical and computational studies. An analysis of the mathematical model indicates it is most accurate with deflections less than 50 deg. In the future, the model may be used in high throughput phenotyping applications for investigating stalk lodging and estimating the flexural rigidity of crop stems. The model can also be used to gain intuition and aid in the design of synthetic systems composed of multiple cantilever beams.

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