• Proceedings of the KSME Conference
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• 2000.04b
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• pp.777-782
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• 2000

The flow fields in the volute casing of a small-size turbo-compressor at different flowrate (design point ${\pm}20%$) are studied by numerical analysis. The governing equations for three-dimensional steady viscous flow are solved using SIMPLE algorithm with commercial code of STAR-CD. Numerical results show that the three-dimensional flow pattern inside the volute casing of a small-size turbo-compressor is strongly influenced by secondary flows that are typically created by the curvature or the casing passages. The flow pattern in the casing also affects the performance of the turbo-compressor. In order to elucidate the loss mechanism through the volute, we prepared the secondary flow, velocity magnitude, and static pressure distribution at the four cross-sectional planes of the casing.

• The Mathematical Education
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• v.47 no.4
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• pp.437-445
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• 2008

On the basis of the meaning and general process of geometric proof through transformation concept and understanding the geometric properties of linear transformation, this study showed that the centroid of geometrical figure and certain properties of a parabola and an ellipse in school mathematics can be explained as a conservative properties through linear transformation. From an educational perspective, this is a good example of showing the process of how several existing individual knowledge can be reorganized by a mathematical concept. Considering the fact that mathematical usefulness of linear transformation can be revealed through an invariable and conservation concept, further discussion is necessary on whether the linear transformation map included in the former curriculum have missed its point.

• 유체기계공업학회:학술대회논문집
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• 2004.12a
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• pp.583-589
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• 2004

One of noticeable features in the cross flow fan is that a working fluid passes through impeller blade twice without distinction between the inlet and exit angles. Also, it does produce higher circumferential velocity than other types of blade at the same flow rate in accordance with the application of the forward curved shape. However, a design theory for the cross-flow fan has not yet been formed owing to an eccentric vortex, which is the remarkable characteristics, occurred in a cross-flow fan. Furthermore, the eccentric vortex, which is difficult to control of the size and position, is the important cause of performance decrease. In this study, experiments are carried out to estimate the similarity of the cross-flow fan with various scales and rotational velocity changes. Pressure coefficients to flow coefficients with various scales of the cross-flow fan are plotted to research the application of the general similarity law of the turbomachinery in the cross-flow fan with Archimedes spital, which is the important factor haying an effect on it.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.1981-1986
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• 2004

A cross-flow fan relatively makes high dynamic pressure at low speed because a working fluid passes through an impeller blade twice and blades have a forward curved shape. Therefore, the performance of a cross-flow fan is influenced 25% by the impeller, 60% by the rearguider and the stabilizer, 15% by the heat exchanger. At the low flow rate, there exists a rapid pressure head reduction, a noise increase and an unsteady flow against a stabilizer and a rearguider. Moreover, it is difficult to analyze the reciprocal relations of the cross-flow fan because each parameter is independent. Numerical analyses are conducted with different starting angles of the rearguider. Two-dimensional, unsteady governing equations are solved, using FVM, PISO algorithm, sliding grid system and ${\kappa}-{\varepsilon}$ standard turbulence model.

• 유체기계공업학회:학술대회논문집
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• 2003.12a
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• pp.391-396
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• 2003

A cross-flow fan relatively produces higher dynamic pressure at low speed because a working fluid passes through an impeller blade twice and blades have a forward curved shape. The performance of a cross-flow fan is influenced 25% by the impeller, 60% by the rearguider and the stabilizer, and 15% by the heat exchanger. At the low flow rate, there exist a rapid pressure head reduction, a noise increase and an unsteady flow against a stabilizer and a rearguider. The purpose of this study is to investigate the reciprocal relation among each parameter Experiments are conducted to study the effects of a rearguider and a diameter ratio of impeller on the performance analysis of a cross-flow fan. Comparing with the rearguider of radial type, the Archimedes type shows excellent results for various diameter ratios.

• Journal for History of Mathematics
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• v.32 no.5
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• pp.241-255
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• 2019

The proposition that the parallel axiom and the Pythagorean theorem are equivalent in the Hilbert geometry is true when the Archimedean axiom is assumed. In this article, we examine some specific plane geometries to see the existence of the non-archimidean Hilbert geometry in which the Pythagorean theorem holds but the parallel axiom does not. Furthermore we observe that the Pythagorean theorem is equivalent to the fact that the Hilbert geometry is actually a semi-Euclidean geometry.

• Journal of the Korean School Mathematics Society
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• v.11 no.1
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• pp.19-30
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• 2008

Cavalieri is chiefly remembered for his work on the problem "indivisibles." Building on the work of Archimedes, he investigated the method of construction by which areas and volumes of curved figures could be found. Cavalieri regarded an area as made up of an indefinite number of parallel line segments and a volume of an indefinite number of parallel plane areas. He called these elements the indivisibles of area and volume. Cavalieri developed a method of the indivisibles which he used to determine areas and volumes. We call this Cavalieri's principle which states that there exists a plane such that any plane parallel to it intersects equal areas In both objects, then the volumes of the two objects are equal. Cavalieri's principle and method of the indivisibles are very important to understand of volume of a pyramid for gifted students.

• The KSFM Journal of Fluid Machinery
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• v.8 no.3 s.30
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• pp.26-32
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• 2005

One of noticeable features in the cross flow fan is that a working fluid passes through impeller blade twice without distinction between the inlet and exit angles. Also, it does produce higher circumferential velocity than other types of blade at the same flow rate in accordance with the application of the forward curved shape. However, a design theory for the cross-flow fall has not yet been formed owing to an eccentric vortex, which is the remarkable characteristics, occurred in a cross-flow fan. Furthermore, the eccentric vortex, which is difficult to control the size and position, is the important cause of performance decrease. In this study, experiments we carried out to estimate the similarity of the cross-flow fan with various scales and rotational velocity changes. Pressure coefficients to flow coefficients with various scales of the cross-flow fan are plotted to the application of the general similarity law of the turbomachinery in the cross-flow fan with Archimedes spiral, which is the important factor having an effect on it.

• Journal of the Korean Society for Nondestructive Testing
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• v.14 no.2
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• pp.90-100
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• 1994

Ultrasonic velocities are widely used in the investigation of material properties. In this paper, a micromechanics model and the ultrasonic velocity were used to develop a nondestructive method to determine the density variation due to porosity in structural SiC. The micromechanics model developed can consider the pore shape and orientation. The model also takes into account the interaction between pores so that it can be applied to the material with high porosity content. A contact pulse overlap method was used to measure the ultrasonic velocities of porous SiC samples, and there was a linear correlation between the velocity and density (or porosity). Using the model and the measured velocity, the bulk density can be easily calculated. The calculated density was in good agreement with that obtained by Archimedes' method.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.2076-2082
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• 2003

A cross-flow fan is widely used on many industrial fields: mining industry, automobile and home appliances, etc. The design point of the cross-flow fan is generally based on the region within low static pressure and high flow rate. It relatively makes high dynamic pressure at low speed because a working fluid passes through an impeller blade twice. However, it has low static pressure efficiency between 30% and 40% because of relative high impact loss. Recently, in the air-conditioning systems, the operating behaviors at the off-design points are highly regarded to broaden the application area for various air-cooling loads. Especially, at the lower flow rate, there exists a rapid pressure head reduction, a noise increase and an irregular flow field against a rearguider as a scroll of centrifugal fan. Numerical analyses are carried out for investigating the flow characteristics in a cross-flow fan including the impeller, the rearguider and the stabilizer. Especially, various types of rearguiders are estimated by numerical and experimental methods to insure the stable operation in the region of lower flow rate. Numerical domains are discretized by hexahedral cells. Three-dimensional, unsteady governing equations are solved using FVM, PISO algorithm, sliding grid system and standard ${\kappa}-{\varepsilon}$ turbulence model. ASHRAE standard fan tester is also used to estimate the performance of the modeled crossflow fan.