• Title/Summary/Keyword: Reynolds Equation

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A Study on the Release Rate of Hazardous Materials from Liquid Pipeline (액체배관으로부터 위험물질 누출속도 산정에 관한 연구)

  • Tak Song-Su;Jo Young-Do
    • Journal of the Korean Institute of Gas
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    • v.6 no.1 s.17
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    • pp.81-85
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    • 2002
  • This paper presents the calculation methods of liquid release rate in the transition region when hazardous materials leak from the pipeline due to an unwanted accident. For the laminar and turbulent flow region, liquid release rate from a pipeline can be calculated by using a commercial software or by using calculator based on the models(equations) suggested by Crowl and Louvar et al. However, there has been no corresponding model for the transition flow region. In this paper. we showed that the turbulent model may be used as an equation generally used in the transition region for conservative hazard analysis if safety factor $30\%$ is added to the value calculated by the turbulent model. In this regard, we first calculated the release rate from liquid pipeline in the transition region by using experimental data on Fanning friction factor depending on Reynolds number which Lap-Mou Tam et al. had introduced, then compared it with that of the laminar and turbulent models in transition region.

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Stability Analysis of Floating Ring Bearing Supported Turbocharger (플로팅 링 베어링으로 지지된 터보차저 로터의 안정성 해석)

  • Lee, Donghyun;Kim, Youngcheol;Kim, Byungok
    • Tribology and Lubricants
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    • v.31 no.6
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    • pp.302-307
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    • 2015
  • The use of turbocharger in internal combustion engines has increased as it is a key components for improving system efficiency without increasing engine size. Because of increasing demand, many studies have evaluated rotordynamic performance so as to increase rotation speed. This paper presents a linear and nonlinear analysis model for a turbocharger rotor supported by a floating ring bearing. We constructed rotor model by using the finite element method and approximated bearings as being infinitely short. In the linear model, we considered fluid film force as stiffness and damping element. In nonlinear analysis, calculation of the fluid film force involved solving the time dependent Reynolds equation. We verified the developed model by comparing the results to those of previous research. The analysis results show that there are four unstable modes, which are rigid body modes combining ring and rotor motion. As the rotating speed increases, the logarithmic decrement shows that certain unstable modes goes into the stable area or the stable mode goes into the unstable area. These unstable modes appear as sub-synchronous vibrations in nonlinear analysis. In nonlinear analysis frequency jump phenomenon demonstrated in several experimental studies appears. The analysis results also showed that frequency jump phenomenon occurs when the vibration mode changes and the sequence of unstable mode matches the linear analysis result. However, the natural frequency predicted using linear analysis differs from those obtained using nonlinear analysis.

Application of Surface Runoff-River flow Model to Small- and Large-Size Catchment Areas (소유역 및 대유역 홍수유출모형의 적용)

  • Yoo, Dong-Hoon
    • Journal of Korea Water Resources Association
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    • v.36 no.1
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    • pp.87-104
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    • 2003
  • A numerical model of surface runoff and river flow has been applied to small- and large-size catchment areas in order to investigate the physical characteristics of river flow during flood period. Several refinements are made on the existing model SIRG-RS for the ways of rainfall input through surface runoff, river junction treatment and the computation of river flow on steep slope. For the computation of frictional forces, employed is the power law of friction factor which is a function of Reynolds number and relative roughness height. The empirical equation of friction factor is developed using recent field data as well as laboratory data. The refined model has been applied to small-size catchment area as well as large-size catchment area, and the computation results are found in good agreement with the observations in both cases.

Numerical Modeling of Wave-Type Flow on a Stepped Weir (계산형 위어에서의 파형흐름 수치모의)

  • Paik, Joongcheol;Kang, Joon Gu;Lee, Nam-Ju
    • Proceedings of the Korea Water Resources Association Conference
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    • 2016.05a
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    • pp.65-65
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    • 2016
  • Various types of flow conditions are developed in the region just downstream of hydraulic structures such as weir and drop structures. One of distinct flow conditions occurred downstream of drop structures is the wave type flow with undular hydraulic jump formation. We present three-dimensional numerical simulations of a wave type flow formed downstream of a stepped weir which were experimentally investigated by Kang et al. (2010). The turbulent flow over the weir structure is modeling using the unsteady Reynolds-averaged Navier-Stokes (URANS) simulation employing the Spalart-Allmaras one equation model and the detached eddy simulation. Numerical modeling and the performance of turbulence modeling approaches are evaluated by comparing with the experimental measurements in terms of the free surface variation, the shapes and sizes of undular wave, roller near at free surface, recirculation zone near the channel bottom downstream of the structures, and streamwise velocity profiles at selected longitudinal locations.

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Propulsion Shafting Alignment Analysis Considering the Interaction between Shaft Deflection and Oil Film Pressure of Sterntube Journal Bearing (축 처짐과 선미관 저널 베어링 유막 압력의 상호작용을 고려한 추진축계 정렬 해석)

  • Cho, Dae-Seung;Jang, Heung-Kyu;Jin, Byung-Mu;Kim, Kookhyun;Kim, Sung-Chan;Kim, Jin-Hyeong
    • Journal of the Society of Naval Architects of Korea
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    • v.53 no.6
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    • pp.447-455
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    • 2016
  • Precise propulsion shafting alignment of ships is very important to prevent damage of its support bearings due to excessive reaction forces caused by hull deflection, forces acted on propeller and crankshaft, and so forth. In this paper, a new iterative shafting alignment calculation procedure considering the interaction between shaft deflection and oil film pressure of Sterntube Journal Bearing (SJB) bush with single or multiple slopes is proposed. The procedure is based on a pressure analysis to evaluate distributed equivalent support stiffness of SJB by solving Reynolds equation and a deflection analysis of shafting system by a finite element method based on Timoshenko beam theory. SJB is approximated with multi-point biaxial elastic supports equally distributed to its length. Their initial stiffness values are estimated from dynamic reaction force calculated by assuming SJB as single rigid support. Then, the shaft deflection and the support stiffness of SJB are sequentially and iteratively calculated by applying a criteria on deflection variation between sequential calculation results. To demonstrate validity and applicability of the proposed procedure for optimal slope design of SJB, numerical analysis results for a shafting system are described.

Effect of the Pocket Depth on the Hammering Behavior of an Air Bearing Stage (포켓의 깊이가 공기 베어링 스테이지의 햄머링 현상에 미치는 영향)

  • Lee, Chun Moo;Kim, Gyu Ha;Park, Sang Joon;Hwang, Gyu-Jin;Park, Sang-Shin
    • Tribology and Lubricants
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    • v.37 no.4
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    • pp.129-135
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    • 2021
  • An air-bearing stage uses externally pressurized air as the lubricant between the stage and the rail. The supporting force generated by the supplied air makes the stage rise and move smoothly with extremely low friction. Mechanical contacts rarely happen, the bearing surfaces do not produce wear particles, and dust is not generated. It also has the advantage of having low energy loss and high precision. Because of its advantages, an air-bearing stage is used in several types of machines that require high precision. In this article, the effect of the pocket depth on the hammering phenomena of the air bearing is studied. An analysis program is developed to calculate the dynamic behavior of the stage by solving the Reynolds equation between the stage and the guideway and the equations of motion on the stage. The acceleration, constant movement, and deceleration are applied to the stage. The stage is modeled as a five-degree-of-freedom system. In the course of the dynamic behavior, the hammering phenomena occur under some special conditions. The deeper the pocket, the more unstable the behavior of the stage, and air hammering occurs when it exceeds a certain depth. In addition, the higher the supply pressure, the more unstable the behavior of the stage. However, hammering occurs even with a shallow pocket depth. Other conditions that affect the hammering phenomena are calculated and discussed.

Interpretation of Ammonia Absorption Behavior in Water Turbulent Flow (물 난류에서의 암모니아 흡수 거동 해석)

  • Lee, Sang-Ryong;Park, Jin-Won
    • Journal of the Korea Organic Resources Recycling Association
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    • v.27 no.3
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    • pp.75-80
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    • 2019
  • The article is devoted to the interpretation of ammonia, one of the fine dust precursors, absorption behavior in water turbulent flow. The water flow was considered as a turbulent flow with Reynolds number more than $10^4$, because ammonia gas penetration depth was deeper at turbulent flow compared to laminar flow. For the interpretation, the dimensionless mass transfer governing-equation and the constant physical-properties at room temperature were used. The diffusivity of ammonia in water and the kinematic viscosity of water were $2{\times}10^{-9}m^2/s$ and $1{\times}10^{-6}m^2/s$, respectively. The concentration distribution of ammonia in water was estimated with respect to the position from the point where the water started to be exposed to ammonia. The quantitative distribution as a function of the mixing length was also acquired. The quantitative interpretation may provide the insight how much the turbulent flow was more efficient to remove ammonia rather than the laminar flow.

On the Feasibility of Freak Waves Formation within the Harbor Due to the Presence of Infra-Gravity Waves of Bound Mode Underlying the Ever-Present Swells (Bound Mode의 외중력파에 의한 항내 이상파 생성가능성에 대하여)

  • Cho, Yong Jun;Bae, Jung Hyun
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.31 no.1
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    • pp.17-27
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    • 2019
  • We carry out the numerical simulation to test a hypothesis that freak waves can be triggered by the infragravity waves of bound mode underlying the ever-present swells and its constructive interaction with swells using the Tool Box called the ihFoam that has its roots on the OpenFoam, and Bi-spectrum. Numerical simulation is implemented for the SamChcuk LNG Plant where freak waves have been reported in front of the private wharf during its construction phase due to the uncompleted northern breakwater. Infra-gravity waves of bound mode is generated using the difference wave-wave interaction between the local wind waves of 7 s and a swell of 11.4 s based on the Bi-spectrum. For the sake of comparison, numerical simulation for infra-gravity waves of free mode is also carried out. Numerical results show that stem waves along the private wharf for SamChcuk LNG Plant can be triggered by the infra-gravity waves of bound mode coming from the north, which eventually leads to freak waves when encounters the reflected waves from the south jetty.

Selection of Optimum Clearance Considering the Dynamic Behavior of a High-pressure Injector (고압 인젝터의 동적 거동을 고려한 최적 틈새 조합에 관한 연구)

  • Ryu, Daewon;Kim, Dongjun;Park, Sang-Shin;Ryu, Bongwoo
    • Tribology and Lubricants
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    • v.37 no.5
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    • pp.172-178
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    • 2021
  • An injector is a mechanical device present inside the engine. Its main function is to supply an appropriate volume of fuel into the combustion chamber, which is directly related to the overall engine efficiency of a car. During the operation of an injector, a magnetic force lifts the parts of the injector from closed position to open position which generates a horizontal force on the needle. The horizontal force acts on a different position from that of the center of mass of the needle. Therefore, this causes eccentricity in the needle and the generation of a tilting motion during the lifting operation which can result in wear. However, appropriate selection of clearances for these parts can prevent wear. In this study, lubrication analysis is conducted to determine the optimum clearance of parts with sliding motion inside the injector. The height functions are derived considering the dynamic behavior and relative velocity of the parts. Using the derived height function, the pressure profiles are calculated for the lubricated surfaces from the Reynolds' equation. Subsequently, the fluid reaction forces are calculated. The equations of motions are applied to the fluid reaction forces and external forces are solved to calculate the minimum film thickness between each part with variation in the clearances. Finally, the optimum clearances are determined. The effect of the clearances on the behavior of the moving parts is presented and discussed.

Rotordynamic Analysis and Operation Test of Turbo Expander with Hydrostatic Bearing (정압베어링을 적용한 터보팽창기의 회전체 동역학 해석 및 구동시험)

  • Lee, Donghyun;Kim, Byungock;Jung, Junha;Lim, Hyungsoo
    • Tribology and Lubricants
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    • v.38 no.2
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    • pp.33-40
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    • 2022
  • In this study, we present rotor dynamic analysis and operation test of a turbo expander for a hydrogen liquefaction plant. The turbo expander consists of a turbine and compressor wheel connected to a shaft supported by two hydrostatic radial and thrust bearings. In rotor dynamic analysis, the shaft is modeled as a rigid body, and the equations of motion for the shaft are solved using the unsteady Reynolds equation. Additionally, the operating test of the turbo expander has been performed in the test rig. Pressurized helium is supplied to the bearings at 8.5 bar. Furthermore, we monitor the shaft vibration and flow rate of the helium supplied to the bearings. The rotor dynamic analysis result shows that there are two critical speeds related with the rigid body mode under 40,000 rpm. At the first critical speed of 36,000 rpm, the vibration at the compressor side is maximum, whereas that of the turbine is maximum at the second critical speed of 40,000 rpm. The predicted maximum shaft vibration is 3 ㎛, whereas sub-synchronous vibration is not presented. The operation test results show that there are two critical speeds under the rated speed, and the measured vibration value agrees well with predicted value. The measured flow rate of the helium supplied to the bearing is 2.0 g/s, which also agrees well with the predicted data.