• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2014.10a
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• pp.760-767
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• 2014

This paper proposes a method to calculate pressure and flow of the fluid dynamic bearings (FDBs) with a recirculation channel (RC) by solving the Reynolds and the Hagen-Poiseuille equations at the same time. The Hagen-Poiseuille equation is one-dimensional equation which describes the flow in a circular pipe such as the RC. This research developed a finite element program to solve the Reynolds and the Hagen-Poiseuille equation together. The proposed method was applied to calculate the pressure and flow of the FDBs which are composed of grooved or plain journal and thrust bearings, and RC. To verify the proposed method, it also developed a finite volume model of the FDBs, and pressure and flow were calculated by the commercial CFD solver. They agree well with the pressure and flow calculated by the proposed method. Finally, this research investigated the characteristics of the FDBs due to the radius change of the RC.

• Journal of Mechanical Science and Technology
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• v.16 no.3
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• pp.395-402
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• 2002

This paper shows how to formulate the transient analysis of 2-dimensional Hagen-Poiseuille flow using smoothed particle hydrodynamics (SPH). Treatments of viscosity, particle approximation and boundary conditions are explained. Numerical tests are calculated to examine effects caused by the number of particles, the number of particles per smoothing length, artificial viscosity and time increments for 2-dimensional Hagen-Poiseuille flow. Artificial viscosity for reducing the numerical instability directly affects the velocity of the flow, though effects of the other parameters do not produce as much effect as artificial viscosity. Numerical solutions using SPH show close agreement with the exact ones for the model flow, but SPH parameter must be chosen carefully Numerical solutions indicate that SPH is also an effective method for the analysis of 2-dimensional Hagen-Poiseuille flow.

• Journal of computational fluids engineering
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• v.21 no.4
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• pp.96-101
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• 2016

A two-dimensional Stokes flow past a circular disk in a circular tube is analyzed. The circular disk is located coaxially with the circular tube and the Hagen-Poiseuille flow exists at upstream and downstream far from the circular disk. The Stokes approximation is used and the flow is investigated analytically by using the method of eigenfunction expansion and the method of least square. From the analysis, the stream function and the pressure of the flow field are obtained, and the streamlines and pressure distribution are shown. Also, the pressure and shear stress distributions on the circular disk and circular tube wall are calculated, and shown for some typical radii of the circular disk. The additional pressure drop induced by the disk and the drag force exerted on the disk are compared as functions of the radius of the circular disk, and it is shown that the shear force on the wall of the tube increases due to the disk.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.1
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• pp.31-39
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• 2007

A pedagogic model for blood flow is introduced to help medicine majors understand a simplified version of Navier-Stokes equations which is known to be a good tool for interpreting the phenomena in blood flow. The pressure gradient consists of a time-independent part known as Hagen-Poiseuille's gradient and a time-dependent part known as Sexl's, and the model formula for the volume rate of blood flow is reduced to a very simple form. For demonstration, the blood rate in human aorta system is analyzed in connection with the time-dependence of pressure gradient. It is shown for Sexl's part that the flow rate lags the pressure gradient by ${\pi}/2$, which is thought to be due to the relaxation process involved.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.30 no.3 s.246
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• pp.255-261
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• 2006

Flow characteristics of DI water in a microchannel with a stenosis were investigated using .a micro PIV system with varying flow rate. The width and depth of the PDMS micro-channel were $100{\mu}m\;and\;50{\mu}m$, respectively. To Investigate flow characteristics in the micro-stenosis, the same experiment was carried out in a straight microchannel under the same flow rate. The measured mean velocity fields were almost symmetric with respect to the channel centerline. The experimental results are well agreed with the theoretical Hagen-Poiseuille profile. In the contraction part of the micro-stenosis, the oncoming flow is accelerated rapidly and the maximum velocity occurs at the throat, almost 4.99 time faster than that without the stenosis.

• Membrane Journal
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• v.26 no.4
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• pp.291-300
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• 2016

Techniques for selectively separating molecules of gas and liquid states using various separation membranes have been widely used in variety of applications such as chemical, biological, pharmaceutical, and petrochemical industries. As the nanochannel diameter, inter-channel distance and length of the nanochannel of the anodic aluminum oxide (AAO) membranes can be precisely controlled, various studies to effectively separate mixture of various molecules using AAO membrane have been widely carried out. In this study, we fabricated AAO membranes of cylindrical nanochannels of various diameter sizes and of through-hole structure, that is, nanochannels of which both ends of each nanochannel are open. Using those AAO membranes of through-hole nanochannel structure, we studied the selective permeation polymer chains dissolved in a solvent based on hydraulic volume of the polymer chains. We found a precise, quantitative relationship between the radius of gyration of polymer chains that permeated through nanochannels inside AAO membrane and the diameter of nanochannels. In addition, we demonstrate that the behavior of the polymer solution flowing through nanochannel of the AAO membrane can be successfully described with the Hagen-Poiseuille relationship. It is, therefore, possible to theoretically interpret the nanoflow of the solution flowing inside the cylindrical nanochannel.

• Proceedings of the Korean Vacuum Society Conference
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• 2014.02a
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• pp.150.1-150.1
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• 2014

Showerhead is used as a main part in the semiconductor equipment. The face plate flatness should remain constant and the cleaning performance must be gained to keep the uniformity level of etching or deposition in chemical vapor deposition process. High operating temperature or long period of thermal loading could lead the showerhead to be deformed thermally. In some case, the thermal deformation appears very sensitive to showerhead performance. This paper describes the methods for robust design using computational fluid dynamics. To reveal the influence of the post distribution on flow pattern in the showerhead cavity, numerical simulation was performed for several post distributions. The flow structure appears similar to an impinging flow near a centered baffle in showerhead cavity. We took the structure as an index to estimate diffusion path. A robust design to reduce the thermal deformation of showerhead can be achieved using post number increase without ill effect on flow. To prevent the showerhead deformation by heat loading, its face plate thickness was determined additionally using numerical simulation. The face plate has thousands of impinging holes. The design key is to keep pressure drop distribution on the showerhead face plate with the holes. This study reads the methodology to apply to a showerhead hole design. A Hagen-Poiseuille equation gives the pressure drop in a fluid flowing through such hole. The assumptions of the equation are the fluid is viscous-incompressible and the flow is laminar fully developed in a through hole. An equation can be expressed with radius R and length L related to the volume flow rate Q from the Hagen-Poiseuille equation, $Q={\pi}R4{\Delta}p/8{\mu}L$, where ${\mu}$ is the viscosity and ${\Delta}p$ is the pressure drop. In present case, each hole has steps at both the inlet and the outlet, and the fluid appears compressible. So we simplify the equation as $Q=C(R,L){\Delta}p$. A series of performance curves for a through hole with geometric parameters were obtained using two-dimensional numerical simulation. We obtained a relation between the hole diameter and hole length from the test cases to determine hole diameter at fixed hole length. A numerical simulation has been performed as a tool for enhancing showerhead robust design from flow structure. Geometric parameters for the design were post distribution and face plate thickness. The reinforced showerhead has been installed and its effective deposition profile is being shown in factory.

• Proceedings of the Korean Society for Agricultural Machinery Conference
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• 2000.11c
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• pp.662-669
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• 2000

Based on the viscous flow characteristics of gas through capillary tube, a simple and low cost system was developed for controlling gas concentration for use in C.A experiments. The gas flow rate through capillary tube had a linear relationship with pressure, $(length)^{-1}$ and $(radius)^4$ of capillary tube, which agreed well with Hagen-Poiseuille's law. The developed system could control the gas concentration in storage chamber within ${\pm}0.3%$ deviation compared to the preset concentration. The required time for producing target gas concentration in storage chamber was exactly predicted by the model used in this study, and it required much longer time than the calculated time which divided the volume of chamber by flow rate. Therefore, for producing target gas concentration as quickly as possible, it needs to supply higher flow rate of gas during the initial stage of experiment when gas concentration in storage chamber has not reached at target value. It appeared that the developed system was very useful for C.A experiments. Because one could decide a desired flow rate by the prediction model, control flow rate freely and easily by changing pressure in the pressure-regulating chamber and the accuracy was high.

• Journal of the Korean Society of Visualization
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• v.14 no.2
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• pp.40-45
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• 2016

Magnetic resonance velocimeter (MRV) is a powerful tool to non-invasively measure the velocity of a fluid flow in various fields ranging from medicine to engineering. However, since the demands for accurate measurement in the solid/liquid interface for cardiovascular diseases and porous media increase, the improvement of spatial resolution is required. In this study, a solenoid RF coil is developed for high spatial resolution measurement. The signal-to-noise ratio in solenoid RF coil is increased seventeen times better than that in commercial coil. Moreover, the velocity distribution of Hagen-Poiseuille flow is measured with in-plane resolution of $36{\mu}m$ by $36{\mu}m$ and the accuracy of the measured velocity is compared with theoretical distribution of the laminar flow. Flow rate calculated by MRV is estimated with the flow rate injected by syringe pump.

• Agricultural and Biosystems Engineering
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• v.2 no.1
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• pp.31-36
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• 2001

Based on the viscous flow characteristics of gas through capillary tube, a simple and cheap gas mixing system was developed for controlling gas compositions in CA chambers. The gas flow rate through capillary tube had a linear relationship with pressure, (length)$^{-1}$ and (radius)$^4$ of capillary tube, which agreed well with Hagen-Poiseuille’s law. The relationship between flow rate and combined parameters was described as Q=0.000209724($\pi$ r$^4$P/$\mu$L) and the coefficient of determination was 0.9984. The developed system could control gas concentrations in CA chambers within $\pm$0.3% deviation compared to the preset concentrations. It was possible to predict the required time and required gas flow rate for exchanging the gs in CA chamber to a certain concentration of gas by using the mathematical model developed in this study.