A High Order Mathematical Model for Calculating Casting Temperature Field Based on ADI Method

2013 ◽  
pp. 73-78
Author(s):  
XiaoFeng Niu ◽  
Wei Liang ◽  
Hua Hou
Keyword(s):  
Mathematical Model ◽  
Temperature Field ◽  
High Order ◽  
Casting Temperature ◽  
Adi Method

A New High Order Mathematical Model for Calculating the Energy Conservation Equation

2013 ◽  
Vol 749 ◽  
pp. 545-550
Author(s):  
Xiao Feng Niu ◽  
Wei Liang ◽  
Hua Hou ◽  
Yu Hong Zhao ◽  
Hong Xia Wang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Energy Conservation ◽  
Specific Heat ◽  
Hamming Distance ◽  
Conservation Equation ◽  
High Order ◽  
Adi Method ◽  
Energy Conservation Equation ◽  
Heat Method ◽  
Explicit Finite Difference

The Explicit Finite Difference (EFD) method is used for calculating the energy conservation equation during solidification. In order to improve the computational efficiency, the equivalent specific heat method is adopted to calculate the latent heat and the high order Alternating Direction Implicit (ADI) method is also applied, which is fourth order in space and second order in time. The degree of similarity between the simulation results and experimental results is analyzed quantitatively by the Hamming Distance (HD) for the first time, and results show that this high order mathematical model based on the equivalent specific heat method and the high order ADI method is faster and more accurate than the EFD method.

Experiment Research on the Temperature Field and Thermal Error Distribution of NC Grinding Machine

2009 ◽  
Vol 76-78 ◽  
pp. 61-66
Author(s):  
Ya Dong Gong ◽  
Yan Guang Bai ◽  
Yue Ming Liu ◽  
Jian Qiu
Keyword(s):  
Mathematical Model ◽  
Temperature Field ◽  
Infrared Camera ◽  
Thermal Error ◽  
Error Distribution ◽  
Measurement Technology ◽  
Actual Error ◽  
Grinding Machine ◽  
The Mathematical Model ◽  
Nc Grinding

With the help of the infrared camera temperature measurement technology, the systemic theoretical analysis and experimental research for temperature field and thermal error distribution in NC grinding machine is provided. Two different situations for temperature field and thermal error distribution are respectively measured while the free and loaded grinding by the new measurement method. The mathematical model of thermal error is built, and it shows that the actual error and the forecasted error from thermal error mathematical model have good comparability.

Microstructures in Solidification Simulation of Electron Beam Scanning with MC in Molten Pool

2014 ◽  
Vol 898 ◽  
pp. 168-172 ◽  
Author(s):  
Rong Wang ◽  
Yi Liu ◽  
De Qiang Wei
Keyword(s):  
Mathematical Model ◽  
Temperature Field ◽  
Electron Beam ◽  
Grain Growth ◽  
Molten Pool ◽  
Growth Process ◽  
Solidification Process ◽  
Optical Microscope ◽  
Physical Parameters ◽  
Beam Scanning

The solidification microstructure of electron beam scanning is important to product performance. The solidification process of molten pool temperature field and 2D simulation mathematical model of grain growth was established based on heat transfer and the physics of growth process of crystal grains. The heat distribution, thermal physical parameters and influence of thermal radiation on the temperature field was considered during the analysis process. The distribution of temperature field was solved by COMSOL. The process of solidification was simulated by using Monte Carlo method. Using optical microscope to observe the solidified microstructure of bath. The simulation results show that the mathematical model can reasonably describe the grain growth process, the temperature field and the simulation of microstructure morphology.

Mathematical model of the temperature field around a borehole with radioactive wastes and its experimental verification in field conditions

1985 ◽  
Vol 59 (6) ◽  
pp. 994-998
Author(s):  
E. G. Drozhko ◽  
V. I. Karpov ◽  
A. S. Stepanov ◽  
I. I. Kryukov ◽  
V. F. Savel'ev ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Temperature Field ◽  
Experimental Verification ◽  
Radioactive Wastes ◽  
Field Conditions

Two Balanced Car LQR Algorithm Achieved Based on LabVIEW

2011 ◽  
Vol 127 ◽  
pp. 592-597 ◽  
Author(s):  
Jun Sun ◽  
Hai Zhe Liu
Keyword(s):  
Mathematical Model ◽  
Robust Stability ◽  
Response Curve ◽  
High Order ◽  
Output Response ◽  
Weighting Matrix ◽  
System Output ◽  
Lqr Algorithm

Constructed of high-order, multi-variable mathematical model of two balanced car, and using LQR algorithm relies on the powerful LabVIEW Control Toolkit, through continuously adjust the weighting matrix Q and R, designed the optimal secondary controller,it is better to balance the system robust stability and reaction fast, and by drawing out of the system output response curve, verify the correctness and the effectiveness of the controller.

The Numerical Simulation of Directional Solidification Process Temperature Field for Large-Scale Frustum of a Cone Ingot

2011 ◽  
Vol 189-193 ◽  
pp. 1476-1481
Author(s):  
Kun Liu ◽  
Zhe Wang ◽  
Ren Zhi Han ◽  
Zi Ping Ren
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Temperature Field ◽  
Directional Solidification ◽  
Large Scale ◽  
Solidification Process ◽  
Directional Solidification Process ◽  
Ingot Quality ◽  
Fluent Software ◽  
The Mathematical Model

By using Fluent software, the mathematical model of temperature field is established on directional solidification process for large-scale frustum of a cone ingot, and the result is analyzed by Origin software, Tecplot. The influences of different width/thickness ratio to directional solidification process of cone ingot are discussed in order to provide basis for design optimization and ingot quality improvement.

A Real-Time Mathematical Model for the Two-Dimensional Temperature Field of Petroleum Coke Calcination in Vertical Shaft Calciner

JOM ◽  
2016 ◽  
Vol 68 (8) ◽  
pp. 2149-2159 ◽  
Author(s):  
Jin Xiao ◽  
Jindi Huang ◽  
Qifan Zhong ◽  
Fachuang Li ◽  
Hongliang Zhang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Temperature Field ◽  
Real Time ◽  
Petroleum Coke ◽  
Vertical Shaft ◽  
Two Dimensional
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