• International Journal of Air-Conditioning and Refrigeration
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• v.9 no.2
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• pp.8-18
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• 2001

The direct simulation Monte Carlo Method is applied to investigate the two-dimensional flow fields of a turbomolecular pump(TMP) in both molecular and transition flow regions. The pumping characteristics of the TMP are investigated for a wide range of the Knudsen number. The maximum of compression ratio and of pumping speed strongly depend on the Knudsen number in transition region, while they weakly depend on the Knudsen number in free molecular flow region. The present numerical results show good agreement with the previously known experimental data. Finally. the results of the single blade row in both molecular and transition regions are used to predict the overall performance of a TMP, which has three kinds of blade with 24-rows.

• KSTLE International Journal
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• v.7 no.2
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• pp.27-34
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• 2006

Knudsen number is the ratio of molecular mean free path versus mm thickness and the criterion to determine the flow form. When its value is lower than 0.01, the flow can be assumed to has no slip boundary condition. And in the case that the value is between 0.01 and 10, then the flow has slip boundary condition at both the adjacent walls. The condition of the air flow between the rotating journal and top foil in the air foil bearing is determined by the rotating speed and load, and the Knudsen number is also varied by those values. Because the molecular mean free path is variable to the pressure and temperature, more exact formulation is necessary to understand and analyze the flow regime. In this study, the analysis considering Knudsen number formulated with those variables (pressure, temperature and mm thickness) was executed. The approximate value was examined using the equation to confirm whether the flow has the slip or no-slip boundary condition. From the analytic investigation, it was decided to range approximately 0.01 to 1.0 and the flow can be supposed to have the slip boundary condition. Under the condition of the slip flow, the static characteristics of the air foil bearing were examined using modified Reynolds equations. The results were compared with those considering no slip condition. It shows that the slip condition makes the flow decelerates and the load carrying capacity decreases compared with no slip condition. And as the bearing number and eccentricity ratio increase, the load carrying capacity also increased at both the cases. From this result, it can be supposed that the bearing torque also increases. In the analysis of the dynamic characteristics, the perturbed Knudsen number was taken into consideration. Because the Knudsen number is expressed as the terms of each variable, the perturbed equation can be simply derived. The results of both cases considering and not considering Knudsen number were compared each other. In the case of the direct terms of the stiffness and damping coefficients, the difference between both cases was little and increased as the bearing number and eccentricity ratio increased. And the cross terms have less or more differences.

• Tribology and Lubricants
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• v.30 no.1
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• pp.15-20
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• 2014

A more accurate expression for effective viscosity is obtained using a linear regression of the data from Fukui-Kaneko's model, which are obtained through numerical calculations based on the linearized Boltzmann equation. Veijola and Turowski's expression is adopted as a base function for effective viscosity. The four coefficients in that equation are optimized, and sensitivity analysis is conducted for these coefficients. The results show that the coefficient for the first-order Knudsen number is the most accurate, whereas the coefficient in the exponential of the Knudsen number is the least accurate compared with Fukui-Kaneko's results. The expression for effective viscosity is accurate within 0.02% rms of Fukui-Kaneko's results for the inverse Knudsen numbers from 0.01 to 100 and surface accommodation coefficients ranging from 0.7 to 1.

• Journal of Advanced Marine Engineering and Technology
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• v.38 no.10
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• pp.1237-1243
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• 2014

The aim of the present paper is to analyze the friction and mass flow in a rough microchannel using Lattice Boltzmann Method (LBM). The LBM is a kinetic method based on the particle distribution function, so it can be fruitfully used to study the flow dependence on Knudsen number including slip velocity, pressure drop in rough microchannel. The surface roughness elements are taken to be considered as a series of circular shaped riblets throughout the channel with relative roughness height up to a maximum 10% of the channel height. The friction coefficients in terms of Poiseuille number (Pn), mass flow rate and the flow behaviors have been discussed in order to study the effect of surface roughness in the slip flow regime at Knudsen number (Kn), ranging from 0.01 to 0.10. It is seen that the friction factor and the flow behaviors in a rough microchannel strongly depend on the rarefaction effect and the relative roughness height. The friction factor in a rough microchannel is higher than that in smooth channel but the mass flow rate is lower than that of smooth channel. Moreover, it is seen that the friction factor increased with relative roughness height but decreased with increasing the Kundsen number (Kn) whereas the mass flow rate is decreased with increasing both of surface roughness height and Knudsen number.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2008.03a
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• pp.866-870
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• 2008

In this study, we designed cold gas propulsion system with minimum 0.25 mm nozzle and micro-thrust measurement system to analyze flow characteristic of micro propulsion system in ambient and vacuum condition. Argon and Nitrogen are used for propellant and the result of experiments is compared with CFD analysis and theory. But there is a point where reduced scale versions of conventional propulsion systems will no longer be practical. Therefore, a fundamentally different approach to propulsion systems was taken. That is thermal transpiration based micro propulsion system. It has no moving parts such as lubricants, pressurizing system and can pump the gaseous propellant by temperature gradient only(cold to hot). We are advancing basic research of propulsion system based on thermal transpiration in vacuum conditions and had tried experiment process and theoretical access in advance. To characterize membrane of Knudsen pump, we select Polyimide material that has low thermal conductivity(0.29 W/mK) and can stand high temperature($300^{\circ}C$) for long time. And we fabricated hole diameter 1, 0.5, 0.2, 0.1 mm using precision manufacturing. Experimental results show that pressure gradient efficiency of Knudsen pump is increased to maximum 82% according to Knudsen number and thick membranes are more effective than thin membranes in transition flow regime.

• 유체기계공업학회:학술대회논문집
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• 2006.08a
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• pp.493-496
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• 2006

Rarefied gas flows through two-dimensional micro channels are studied numerically for the performance optimization of a nanomembrane-based Knudsen compressor. The effects of the wall temperature distributions on the thermal transpiration flow patterns are examined. The flow has a pumping effect, and the mass flow rates through the channel are calculated. The results show that a steady one-way flow is induced for a wide range of the Knudsen number. The DSMC(direct simulation Monte Carlo) method with VHS(variable hard sphere) model and NTC(no time counter) techniques has been applied in this work to obtain numerical solutions.

• Proceedings of the Membrane Society of Korea Conference
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• 1995.10a
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• pp.47-48
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• 1995

알루미나 막이나 바이코 글라스(Vycor glass)같은 다공성 무기재료막은 화학적으로 안정하고 열에 잘 견디므로 고온에서 기체를 분리하는 데에 사용될 수 있다. 미세한 기공을 가지고 있는 알루미나막은 수소를 분리하는데 상대적으로 높은 투과도를 나타내고 고온에 잘 견딘다. 기공이 치밀한 알루미나막에 의하여 분리되는 메카니즘은 기체의 분자량에 의존하는 Knudsen확산이 지배적이 된다. 그러나, 분자량의 차이가 크지 않을때는 Knudsen확산에 의한 분리도는 크지않다. 그래서 분리도의 향상에 대해 많은 사람들이 연구하고 있다. 본연구에서는 Sol-Gel법으로 제조된 막을 개선하여, 높은 압력차에서 조업할 수 있도록 하고자, TEOS와 증류수를 막의 기공내에서 반응시켜 실리카를 기공내에 생성시키고자하는 실험을 수행하였다. 이 연구를 통해 약 25 psi 정도의 압력차하에서도 수소/질소의 분리도가 Knudsen확산의 수준을 보이는 실용적인 막을 생산할 수 있었다.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.32 no.5
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• pp.382-391
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• 2008

A simple analytical model of rarefied channel flow is developed to predict the compression ratio in a helical drag pump. If the surface velocity is zero, the model reduces to a capillary leaks. Predictions of our model agree well with the Knudsen's data for capillary leaks in transition flow, in addition to giving a good account of the Knudsen minimum. Also, the present results are compared with experimental data, and good agreement is obtained over the entire pressure range from molecular to slip flow.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.8 no.1
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• pp.65-70
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• 1998

K. Nyberg and L.R. Knudsen showed a prototype of a DES-like cipher$^{[1]}$ which has a provable security against differential cryptanalysis. But in the last year, at FSE'97 T. Jakobsen ane L.R.Knudsen broked it by using higher order differential attack and interpolation attack$^{[2]}$ . Furthermore the cipher was just a theoretically proposed one to demonstrate how to construct a cipher which is procably secure against differential cryptanalysis$^{[3]}$ and it was suspected to have a large complexity for its implementation.Inthis paper the two improved results for the dfficidnt hardware and software implementation.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.11 no.2
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• pp.59-65
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• 2001

3GPP proposed a variant CBC-MAC based on the block cipher KASUMI to provide the data integrity over a radio access link. We have studied deeply the Knudsen and Mitchell\`s attack. In this paper we proposed a definite performing algorithm of the Knudsen and Mitchell\`s alack and compute the success probability and complexity of that algorithm. Moreover We also analyze a security of 3GPP-MAC comparing with the original CBC-MAC.