• Title/Summary/Keyword: Stokes equation

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Numerical Investigation on Flow Pattern over Backward-Facing Step for Various Step Angles and Reynolds numbers

  • Lee, Jeong Hu;Nguyen, Van Thinh
    • Proceedings of the Korea Water Resources Association Conference
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    • 2021.06a
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    • pp.60-60
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    • 2021
  • Investigating Backward-Facing Step(BFS) flow is important in that it is a representative case for separation flows in various engineering flow systems. There have been a wide range of experimental, theoretical, and numerical studies to investigate the flow characteristics over BFS, such as flow separation, reattachment length and recirculation zone. However, most of such previous studies were concentrated only on the perpendicular step angle. In this study, several numerical investigations on the flow pattern over BFS with various step angles (10° ~ 90°) and expansion ratios (1.48, 2 and 3.27) under different Reynolds numbers (5000 ~ 64000) were carried out, mainly focused on the reattachment length. The numerical simulations were performed using an open source 3D CFD software, OpenFOAM, in which the velocity profiles and turbulence intensities are calculated by RANS (Reynolds Averaged Navier-Stokes equation) and 3D LES (Large Eddy Simulation) turbulence models. Overall, it shows a good agreement between simulations and the experimental data by Ruck and Makiola (1993). In comparison with the results obtained from RANS and 3D LES, it was shown that 3D LES model can capture much better and more details on the velocity profiles, turbulence intensities, and reattachment length behind the step for relatively low Reynolds number(Re < 11000) cases. However, the simulation results by both of RANS and 3D LES showed very good agreement with the experimental data for the high Reynolds number cases(Re > 11000). For Re > 11000, the reattachment length is no longer dependent on the Reynolds number, and it tends to be nearly constant for the step angles larger than 30°.) Based on the calibrated and validated numerical simulations, several additional numerical simulations were also conducted with higher Reynolds number and another expansion ratio which were not considered in the experiments by Ruck and Makiola (1993).

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Numerical Analysis on Wave Characteristics around Submerged Breakwater in Wave and Current Coexisting Field by OLAFOAM (파-흐름 공존장내 잠제 주변에서 OLAFOAM에 의한 파랑특성의 수치해석)

  • Lee, Kwang-Ho;Bae, Ju-Hyun;An, Sung-Wook;Kim, Do-Sam;Bae, Kee Seung
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.28 no.6
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    • pp.332-349
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    • 2016
  • OLAFOAM is the powerful CFD code and is an expanded version of $OpenFOAM^{(R)}$, for wave mechanics simulation. The $OpenFOAM^{(R)}$ does provide many solvers to correspond to each object of the numerical calculation in a variety of fields. OLAFOAM's governing equation bases on VARANS (Volume-Averaged Reynolds-Averaged Navier-Stokes) equation, and the finite volume method is applied to numerical techniques. The program is coded in C++ and run on the Linux operating system. First of all, in this study, OLAFOAM was validated for 1) wave transformation inside porous structure under bore and regular wave conditions, 2) wave transformation by submerged breakwater under regular wave condition, and 3) regular wave transformation and resultant vertical velocity distribution under current by comparison with existing laboratory measurements. Hereafter, this study, which is almost no examination carried out until now, analyzed closely variation characteristics of water surface level, wave height, frequency spectrum, breaking waves, averaged velocity and turbulent kinetic energy around porous submerged breakwater in the wave and current coexisting field for the case of permeable or impermeable rear beach. It was revealed that the wave height fluctuation according to current direction(following or opposing) was closely related to the turbulent kinetic energy, and others.

Characterization of Sedimentation and pH Neutralization as Pretreatment of Acid Contaminated Water (산 오염수 전처리용 침전 및 중화 특성)

  • Im, Jongdo;Lee, Sangbin;Park, Jae-Woo
    • Journal of the Korean GEO-environmental Society
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    • v.23 no.9
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    • pp.33-40
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    • 2022
  • Sedimentation and pH neutralization has been investigated as preteatment of acid contaminate water. The settling and neutralizing process derive more effective degradation efficiency as the pre-treatment process before the removal process of adsorption, volatile, biodegradation, or oxidation. Settling velocity, uniformity coefficient, coefficient of curvature, and grain size index can define in the sedimentation process for characteristics of the soil. The stainless steel sieve has been used to separate each particle size of the dry soil by assembling in order of 4, 10, 20, 40, 80, 100, and 200 mesh sizes. The soil from Gamcheon Port in Busan drops upper side of the sieve and shakes back and forth to separate each different size of the particle. The 1L of Imhoff cone and 200 mL of the mass cylinder were used as settling tanks to calculate settling velocity. Stokes' equation was used to figure out the average density of dry soil with a value from settling velocity. In the results, the average particle density and lowest settling velocity were 1.93 g/cm3 and 0.11 cm/s, respectively. These values can detect the range of settling points of sediment to prevent chemical accidents. In pH neutralization, the initial pH of 2, 3, 4, and 5 of nitric acid and sulfuric acid are used as an acid solution; 0.1, 0.01, and 0.001 M of sodium hydroxide and calcium hydroxide are used as a base solution. The main goal of this experiment is to figure out the volume percentage of the acid solution becomes pH 7. The concentration of 0.001 M of base solution exceeds all the conditions, 0.01 M exceeds partially, and 0.1 M does not exceed 5 v/v% except pH 2. Calcium hydroxide present less volume than sodium hydroxide at pH neutralization both sulfuric and nitric acid.

A Study on Improvement γ-Reθt Model for Hypersonic Boundary Layer Analysis (극 초음속 경계층 해석을 위한 γ-Reθt모델 개선 연구)

  • Kang, Sunoh;Oh, Sejong;Park, Donghun
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.48 no.5
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    • pp.323-334
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    • 2020
  • Since boundary layer transition has a significant impact on the aero-thermodynamic performance of hypersonic flight vehicles, capability of accurate prediction of transition location is essential for design and performance analysis. In this study, γ-Reθt model is improved to predict transition of hypersonic boundary layers and validated. A coefficient in the production term of the intermittency transport equation that affects the transition onset location is constructed and applied as a function of Mach number, wall temperature, and freestream stagnation temperature based on the similarity numerical solution of compressible boundary layer. To take into account a Mach number dependency of transition onset momentum thickness Reynolds number and transition length, additional correlation equations are determined as function of Mach number and applied to Reθc and Flength correlations of the baseline model. The suggested model is implemented to a commercial CFD code in consideration of practical use. Analysis of hypersonic flat plate and circular cone boundary layers is carried out by using the model for validation purpose. An improvement of prediction capability with respect to variation of Mach number and unit Reynolds number is identified from the comparison with experimental data.

A Preliminary Study for the Prediction of Leaking-Oil Amount from a Ruptured Tank (파손된 기름 탱크로부터의 유출양 산정을 위한 기초 연구)

  • Kim Wu-Joan;Lee Young-Yeon
    • Journal of the Korean Society for Marine Environment & Energy
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    • v.4 no.4
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    • pp.21-31
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    • 2001
  • When an oil-spilling accident occurs at sea, it is of the primary importance to predict the amount of oil leakage for the swift response and decision-making. The simplest method of oil-leakage estimation is based on the hydrostatic pressure balance between oil inside the tank and seawater outside of leakage hole, that is the so-called Torricelli equilibrium relation. However, there exists discrepancy between the reality and the Torricelli relation, since the latter is obtained from the quasi-steady treatment of Bernoulli equation ignoring viscous friction. A preliminary experiment has been performed to find out the oil-leaking speed and shape. Soy-bean oil inside the inner tank was ejected into water of the outer tank through four different leakage holes to record the amount of oil leakage. Furthermore, a CFD (Computational Fluid Dynamics) method was utilized to simulate the experimental situation. The Wavier-Stokes equations were solved for two-density flow of oil and water. VOF method was employed to capture the shape of their interface. It is found that the oil-leaking speed varies due to the frictional resistance of the leakage hole passage dependent on its aspect ratio. The Torricelli factor relating the speed predicted by using the hydrostatic balance and the real leakage speed is assessed. For the present experimental setup, Torricelli factors were in the range of 35%~55% depending on the aspect ratio of leakage holes. On the other hand, CFD results predicted that Torricelli factor could be 52% regardless of the aspect ratio of the leakage holes, when the frictional resistance of leakage hole passage was neglected.

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Discussion on Optimal Shape for Wave Power Converter Using Oscillating Water Column (진동수주형 파력발전구조물의 최적형상에 대한 검토)

  • Lee, Kwang-Ho;Park, Jung-Hyun;Baek, Dong-Jin;Cho, Sung;Kim, Do-Sam
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.23 no.5
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    • pp.345-357
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    • 2011
  • Recently, as part of diversifying energy sources and earth environmental issues, technology development of new renewable energy using wave energy is actively promoted and commercialized around Europe and Japan etc. In particular, OWC(Oscillating Water Column) wave power generation system using air flow induced by vertical movement of the water surface by waves in an air-chamber within caisson is known as the most efficient wave energy absorption device and therefore, is one of the wave power generation apparatus the closest to commercialization. This study examines air flow velocity, which operates turbine(Wells turbine) directly in oscillating water column type wave power generation structure from two-and three-dimensional numerical experiments and discusses optimal shape of oscillating water column type wave power generation structure by estimating the maximum flow rate of air according to change in shape. The three-dimensional numerical wave flume was applied in interpretation for this study which is the model for the immiscible two-phase flow based on the Navier-Stokes Equation. From this, it turned out that size of optimal shape appears differently according to the incident wave period and air flow is maximized at the period where minimum reflection ratio occurs.

Development of Two Dimensional Blade Section with High Efficiency for Marine Propeller (선박 프로펠러용 고효율 2차원 날개단면 개발)

  • Na, Yun-Cheol;Song, In-Haeng;Ahn, Jong-Woo
    • Journal of the Society of Naval Architects of Korea
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    • v.34 no.1
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    • pp.11-23
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    • 1997
  • This paper contains a new approach to blade section design method for marine propellers. The hydrodynamic characteristics of 2-D section are highly influenced by its geometrical parameters i.e., thickness and camber distributions and leading edge radius etc. To consider fully turbulent flow field near 2-D section. the finite volume method with k-${\varepsilon}$ turbulent model which solve Reynolds time averaged Navier-Stokes(RANS) equation is applied. In this study, O-type grid system that can provide many calculation points on blade surface is used. The results were compared with those of the experiment of NACA0012 to confirm the accuracy of the developed codes. The goal of this study is the development of a blade section with high efficiency and low drag. To achieve this, we carried out the tests of lift, drag and cavitation characteristics in cavitation tunnel. The results of experiment were compared with numerical results in order to validate the proposed blades design method. By comparing the numerical results with the experiments, we found that the new blade section, KH28 allows superior performance in efficiency and cavitation avoidance characteristics. We further investigated the blade section design method and an application study of this section, KH28 to apply to the marine propeller. In order to improve the accuracy of numerical results on prediction of lift and drag, we conclude here that the 2-layer boundary model must be used.

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Suspension of Sediment over Swash Zone (Swash대역에서의 해빈표사 부유거동에 관한 연구)

  • Cho, Yong Jun;Kim, Kwon Soo;Ryu, Ha Sang
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.28 no.1B
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    • pp.95-109
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    • 2008
  • We numerically analyzed the nonlinear shoaling, a plunging breaker and its accompanying energetic suspension of sediment at a bed, and a redistribution of suspended sediments by a down rush of preceding waves and the following plunger using SPH with a Gaussian kernel function, Lagrangian Dynamic Smagorinsky model (LDS), Van Rijn's pick up function. In that process, we came to the conclusion that the conventional model for the tractive force at a bottom like a quadratic law can not accurately describe the rapidly accelerating flow over a swash zone, and propose new methodology to accurately estimate the bottom tractive force. Using newly proposed wave model in this study, we can successfully duplicate severely deformed water surface profile, free falling water particles, a queuing splash after the landing of water particles on the free surface and a wave finger due to the structured vortex on a rear side of wave crest (Narayanaswamy and Dalrymple, 2002), a circulation of suspended sediments over a swash zone, net transfer of sediments clouds suspended over a swash zone toward the offshore, which so far have been regarded very difficult features to mimic in the computational fluid mechanics.

A Study on the Shape and Movement in Dissolved Air Flotation for the Algae Removal (수중조류제거(水中藻類除去)를 위한 가압부상(加壓浮上)에 있어서 기포(氣泡)의 양태(模態)에 관한 연구(研究))

  • Kim, Hwan Gi;Jeong, Tae Seop
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.4 no.4
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    • pp.79-93
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    • 1984
  • The dissolved air flotation(DAF) has been shown to be efficient process for the removal of algae ftom water. The efficiency of DAF can be affected by the volume ratio of pressurized liquid to sample, the pressure pressurized liquid, the contact time, the appropriate coagulant and its amount, the water temperature, the turbulence of reactor, the bubble size and rising velocity etc. The purpose of this paper is to compare the practical bubble rising velocity with the theoretical one, to investigate the adhesion phenomenon of bubbles and floc, and the influence of bubble size and velocity upon the process. The results through theoretical review and experimental investigation are as follows: Ives' equation is more suitable than Stokes' equation in computation of the bubble rising velocity. The collection of bubble and algae floc is convective collection type and resulted from absorption than adhesion or collision. The treatment efficiency is excellent when the bubble sizes are smaller than $l00{\mu}m$, and the turbulence of reactor is small. In the optimum condition of continuous type DAF the volume ratio of pressurized liquid to sample is 15%, the contact time in reactor is 15 minutes, the pressure of pressurized liquid is $4kg/cm^2$ and the distance from jet needle to inlet is 30cm.

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Numerical Analysis of Unstable Combustion Flows in Normal Injection Supersonic Combustor with a Cavity (공동이 있는 수직 분사 초음속 연소기 내의 불안정 연소유동 해석)

  • Jeong-Yeol Choi;Vigor Yang
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • 2003.05a
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    • pp.91-93
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    • 2003
  • A comprehensive numerical study is carried out to investigate for the understanding of the flow evolution and flame development in a supersonic combustor with normal injection of ncumally injecting hydrogen in airsupersonic flows. The formulation treats the complete conservation equations of mass, momentum, energy, and species concentration for a multi-component chemically reacting system. For the numerical simulation of supersonic combustion, multi-species Navier-Stokes equations and detailed chemistry of H2-Air is considered. It also accommodates a finite-rate chemical kinetics mechanism of hydrogen-air combustion GRI-Mech. 2.11[1], which consists of nine species and twenty-five reaction steps. Turbulence closure is achieved by means of a k-two-equation model (2). The governing equations are spatially discretized using a finite-volume approach, and temporally integrated by means of a second-order accurate implicit scheme (3-5).The supersonic combustor consists of a flat channel of 10 cm height and a fuel-injection slit of 0.1 cm width located at 10 cm downstream of the inlet. A cavity of 5 cm height and 20 cm width is installed at 15 cm downstream of the injection slit. A total of 936160 grids are used for the main-combustor flow passage, and 159161 grids for the cavity. The grids are clustered in the flow direction near the fuel injector and cavity, as well as in the vertical direction near the bottom wall. The no-slip and adiabatic conditions are assumed throughout the entire wall boundary. As a specific example, the inflow Mach number is assumed to be 3, and the temperature and pressure are 600 K and 0.1 MPa, respectively. Gaseous hydrogen at a temperature of 151.5 K is injected normal to the wall from a choked injector.A series of calculations were carried out by varying the fuel injection pressure from 0.5 to 1.5MPa. This amounts to changing the fuel mass flow rate or the overall equivalence ratio for different operating regimes. Figure 1 shows the instantaneous temperature fields in the supersonic combustor at four different conditions. The dark blue region represents the hot burned gases. At the fuel injection pressure of 0.5 MPa, the flame is stably anchored, but the flow field exhibits a high-amplitude oscillation. At the fuel injection pressure of 1.0 MPa, the Mach reflection occurs ahead of the injector. The interaction between the incoming air and the injection flow becomes much more complex, and the fuel/air mixing is strongly enhanced. The Mach reflection oscillates and results in a strong fluctuation in the combustor wall pressure. At the fuel injection pressure of 1.5MPa, the flow inside the combustor becomes nearly choked and the Mach reflection is displaced forward. The leading shock wave moves slowly toward the inlet, and eventually causes the combustor-upstart due to the thermal choking. The cavity appears to play a secondary role in driving the flow unsteadiness, in spite of its influence on the fuel/air mixing and flame evolution. Further investigation is necessary on this issue. The present study features detailed resolution of the flow and flame dynamics in the combustor, which was not typically available in most of the previous works. In particular, the oscillatory flow characteristics are captured at a scale sufficient to identify the underlying physical mechanisms. Much of the flow unsteadiness is not related to the cavity, but rather to the intrinsic unsteadiness in the flowfield, as also shown experimentally by Ben-Yakar et al. [6], The interactions between the unsteady flow and flame evolution may cause a large excursion of flow oscillation. The work appears to be the first of its kind in the numerical study of combustion oscillations in a supersonic combustor, although a similar phenomenon was previously reported experimentally. A more comprehensive discussion will be given in the final paper presented at the colloquium.

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