1988•Journal of the Mining and Metallurgical Institute of JapanOpen access

Effects of Several Analytical Methods on Calculated Capsule Running Characteristics

Hideki OHBA, Kazumi KAWANO, Yasuhiro Nakiyama, Yukitoshi Nakashima

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Abstract

Theoretical analyses on the capsule running were carried out by the method of characteristics under the three different conditions; polytropic, irreversible adiabatic (based on the energy equation) and isentropic changes. The results of comparing the characteristics obtained by each method are summarized as follows;(1) Analytical results based on the polytropic change (n=1.01, 1.20) and irreversible adiabatic change agree well with each other. Therefore, the former analysis is more useful because of the more simplicity.(2) The results obtained under the polytropic change with n=1.40 have a little difference from the others for the pressure change in the pipe.(3) For the same convergence condition, the iterative calculation is necessary for the analysis based on the irreversible adiabatic change, but not necessary in other analyses.(4) Calculated results based on the isentropic change don't agree with the results obtained by the other methods or experimental results.

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Theoretical analyses on the capsule running were carried out by the method of characteristics under the three different conditions; polytropic, irreversible adiabatic (based on the energy equation) and isentropic changes. The results of comparing the characteristics obtained by each method are summarized as follows;(1) Analytical results based on the polytropic change (n=1.01, 1.20) and irreversible adiabatic change agree well with each other. Therefore, the former analysis is more useful because of the more simplicity.(2) The results obtained under the polytropic change with n=1.40 have a little difference from the others for the pressure change in the pipe.(3) For the same convergence condition, the iterative calculation is necessary for the analysis based on the irreversible adiabatic change, but not necessary in other analyses.(4) Calculated results based on the isentropic change don't agree with the results obtained by the other methods or experimental results.

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Available abstract

Theoretical analyses on the capsule running were carried out by the method of characteristics under the three different conditions; polytropic, irreversible adiabatic (based on the energy equation) and isentropic changes. The results of comparing the characteristics obtained by each method are summarized as follows;(1) Analytical results based on the polytropic change (n=1.01, 1.20) and irreversible adiabatic change agree well with each other. Therefore, the former analysis is more useful because of the more simplicity.(2) The results obtained under the polytropic change with n=1.40 have a little difference from the others for the pressure change in the pipe.(3) For the same convergence condition, the iterative calculation is necessary for the analysis based on the irreversible adiabatic change, but not necessary in other analyses.(4) Calculated results based on the isentropic change don't agree with the results obtained by the other methods or experimental results.

Key concepts: Polytropic process, Isentropic process, Adiabatic process, Convergence (economics), Mathematics, Physics, Applied mathematics, Mechanics

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