• Journal of the Korean Society of Propulsion Engineers
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• v.26 no.6
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• pp.53-61
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• 2022

The estimation method of combustion efficiency has been introduced by using closed bomb test(CBT). The Noble-Abel equation of state was applied to consider the real gas effects to take account of high operation pressure about a couple of 100 atm. of CBT. The heat loss through the CBT wall was considered. The volume change of grain was calculated by applying form functions, which estimated combustion efficiency of 8 different gain shapes. The combustion estimation method proposed in this study was fairly validated by the comparision with the pressure-time history data of the CBT experiments. The effects of both grain shape and propellant loading density were analyzed.

• Journal of the Korean Society of Propulsion Engineers
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• v.21 no.6
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• pp.39-48
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• 2017

In this study, combustion modeling of ZPP and $BKNO_3$ mainly used in the PMD industries has been performed. Saint Robert's law, energy conservation equation, and the Noble-Abel equation of the state have been used for governing equations. The results of pressure obtained from established combustion models and actual CBT have been compared. In the case of ZPP, the model has predicted a pressure curve similar to that of the experimental results, but $BKNO_3$ has showed that the maximum pressure of the model is greater than the experiment at small chamber volume. For these gaps, the probability of $BKNO_3$ unburning has been considered.

• Journal for History of Mathematics
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• v.27 no.3
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• pp.165-182
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• 2014

After algebraic expressions for the roots of 3rd and 4th degree polynomial equations were given in the mid 16th century, seeking such a formula for the 5th and greater degree equations had been one main problem for algebraists for almost 200 years. Lagrange made careful and thorough investigation of various solving methods for equations with the purpose of finding a principle which could be applicable to general equations. In the process of doing this, he found a relation between the roots of the original equation and its auxiliary equation using permutations of the roots. Lagrange's ingenious idea of using permutations of roots of the original equation is regarded as the key factor of the Abel's proof of unsolvability by radicals of general 5th degree equations and of Galois' theory as well. This paper intends to examine Lagrange's contribution in the theory of polynomial equations, providing a detailed analysis of various solving methods of Lagrange and others before him.

• Structural Engineering and Mechanics
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• v.27 no.5
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• pp.609-623
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• 2007

The problem of a semi-infinite magneto-electro-elastically impermeable mode-III crack in a magneto-electro-elastic material is considered under the action of impact loads. For the case when a pair of concentrated anti-plane shear impacts, electric displacement and magnetic induction impacts are exerted symmetrically on the upper and lower surfaces of the crack, the magneto-electro-elastic field ahead of the crack tip is determined in explicit form. The dynamic intensity factors and dynamic energy density factor are obtained. The method adopted is to reduce the mixed initial-boundary value problem, by using the Laplace and Fourier transforms, into three simultaneous dual integral equations, one of which is converted into an Abel's integral equation and the others into a singular integral equation with Cauchy kernel. Based on the obtained fundamental solutions of point impact loads, the solutions of two kinds of different loading cases are evaluated by integration. For some particular cases, the present results reduce to the previous results.

• Journal of the Korean Society of Propulsion Engineers
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• v.26 no.1
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• pp.28-37
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• 2022

The burning rate estimation method of solid propellants, based on closed bomb tests, has been introduced. The composition of the combustion gas is determined by using CEA and the Noble-Abel equation of state for high pressure operation conditions. Covolume taking into account the collision among molecules due to the actual volume of the molecule is modeled by LJ potential. A cubic form function is applied to calculate the volume change of propellant grains during combustion. The estimated burning rates of five different grain configuation at high pressure are fairly compared with BRLCB results within the maximum error of 6%.

• Bulletin of the Society of Naval Architects of Korea
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• v.5 no.1
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• pp.1-7
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• 1968

In this problem the ragid punch in the form of a flat-ended circular cylinder of unit radius is cemented to the stress free surface of an elastic half-space. An axial load P is then applied to the punch to force it into half-space to depth $\varepsilon$. It is assumed that the adhesive between the punch and can be reduced to the system of Abel type integral equations which are equation (13) and (14). It is also shown that the stress and displacement components on the portions of boundary where they are not prescribed can be expressed in terms of $\phi(t)$ and/or $\phi(t)$ which are introduced in equation (9) and (10). Those functions can be obtained from the solution of the system of integral equations (13) and (14).

• Proceedings of the Korean Vacuum Society Conference
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• 2011.02a
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• pp.217-217
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• 2011

플라즈마를 이용하는 식각 및 증착등의 반도체공정에 있어서 최근에는 기판의 크기가 점차 증가하는 추세에 있다. 이러한 대면적 플라즈마 발생장치 내에서 플라즈마 밀도와 라디칼 농도의 공간적인 특성을 이해하는 것에 대한 중요성이 더해지고 있다. 이를 위해 Langmuir probe와 같은 전기적 접근법에 의한 진단방법이나 광학적 접근법에 의한 진단방법에 대한 연구가 이루어 졌다. 전기적 접근법에 의한 플라즈마의 진단방법은 원리가 간단하고 정확도가 높다는 장점이 있지만 진단 장치에 의한 플라즈마의 간섭이 크고 식각가스의 경우 진단이 어렵다는 단점이 있다. 그에 비해 광학적 진단방법은 플라즈마에 간섭이 많지 않은 방법으로 알려져 있고 레이저 형광법(LIF), 원적외선 레이저 흡수 분광법(IR laser Absorption Spectroscopy), 광량측정법(Actinometry)등이 있다. 이 중 레이저 형광법, 원적외선 레이저 흡수 분광법의 경우, 진단장치가 매우 복잡하고 가격이 비싸다는 단점을 가지고 있다. 반면 광량측정법의 경우 다른 광학적 접근법에 의한 진단방법에 비해 원리와 실험장치가 간단하고 공간적인 라디칼 분포의 진단이 쉽다는 점에서 장점을 가지고 있다. Actinometry는 Ar과 같은 불활성 기체를 작은 비율을 넣어서 여기 된 불활성 기체의 파장세기와 여기 된 측정 라디칼의 파장세기의 비교를 통해 상대밀도를 측정하는 방법이다. 이 측정 방법에 Abel's inversion equation을 적용함으로 해서 대면적 M-ICP(Magnetized - Induced Coupled Plasma)에서 식각가스인 $CF_4$플라즈마에서 F 라디칼 농도의 공간적인 분포를 측정하고 분석하였다. 또한 플라즈마의 압력, 소스 전력 값과 기판 전력 값등의 조건의 변화에 따라 F 라디칼 농도의 분포가 어떻게 달라지는지에 대해 측정 분석하여 다루었다.