• Title/Summary/Keyword: Vortex equation

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Flow Visualization and Unstructured Grid Computation of Flow over a High-Speed Projectile (고속탄자 유동의 가시화 실험 및 비정렬격자 계산)

  • 이상길;최서원;강준구;임홍규;백영호;김두연;강호철
    • Transactions of the Korean Society of Automotive Engineers
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    • v.6 no.2
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    • pp.12-20
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    • 1998
  • Exter ballistics of a typical high-speed projectile is studied through a flow-visualization experiment and an unstructured grid Navier-Srokes computation. Experiment produced a schlieren photograph that adequately shows the characteristic features of this complex flow, namely two kinds of oblique cone shocks and turbulent wake developing into the downstream. A hybrid scheme of finite volume-element method is used to simulate the compressible Reynolds-Averaged Navier-Stok- es solution on unstructured grids. Osher's approximate Riemann solver is used to discretize the cinvection term. Higher-order spatial accuracy is obtained by MUSCL extension and van Albada ty- pe flux limiter is used to stabilize the numerical oscillation near the solution discontinuity. Accurate Gakerkin method is used to discretize the viscous term. Explict fourth-order Runge-Kutta method is used for the time-stepping, which simplifies the application of MUSCL extension. A two-layer k-$\varepsilon$ turbulence model is used to simulate the turbulent wakes accurately. Axisymmetric folw and two-dimensional flow with an angle of attack have been computed. Grid-dependency is also checked by carrying out the computation with doubled meshes. 2-D calculation shows that effect of angle of attack on the flow field is negligible. Axi-symmetric results of the computation agrees well with the flow visualization. Primary oblique shock is represented within 2-3 meshes in numerical results, and the varicose mode of the vortex shedding is clearly captured in the turbulent wake region.

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Finite element modeling of high Deborah number planar contraction flows with rational function interpolation of the Leonov model

  • Youngdon Kwon;Kim, See-Jo;Kim, Seki
    • Korea-Australia Rheology Journal
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    • v.15 no.3
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    • pp.131-150
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    • 2003
  • A new numerical algorithm of finite element methods is presented to solve high Deborah number flow problems with geometric singularities. The steady inertialess planar 4 : 1 contraction flow is chosen for its test. As a viscoelastic constitutive equation, we have applied the globally stable (dissipative and Hadamard stable) Leonov model that can also properly accommodate important nonlinear viscoelastic phenomena. The streamline upwinding method with discrete elastic-viscous stress splitting is incorporated. New interpolation functions classified as rational interpolation, an alternative formalism to enhance numerical convergence at high Deborah number, are implemented not for the whole set of finite elements but for a few elements attached to the entrance comer, where stress singularity seems to exist. The rational interpolation scheme contains one arbitrary parameter b that controls the singular behavior of the rational functions, and its value is specified to yield the best stabilization effect. The new interpolation method raises the limit of Deborah number by 2∼5 times. Therefore on average, we can obtain convergent solution up to the Deborah number of 200 for which the comer vortex size reaches 1.6 times of the half width of the upstream reservoir. Examining spatial violation of the positive definiteness of the elastic strain tensor, we conjecture that the stabilization effect results from the peculiar behavior of rational functions identified as steep gradient on one domain boundary and linear slope on the other. Whereas the rational interpolation of both elastic strain and velocity distorts solutions significantly, it is shown that the variation of solutions incurred by rational interpolation only of the elastic strain is almost negligible. It is also verified that the rational interpolation deteriorates speed of convergence with respect to mesh refinement.

Lubrication Analysis of Infinite Width Slider Bearing with a Micro-Groove: Part 2 - Effect of Groove Depth (미세 그루브가 있는 무한폭 Slider 베어링의 윤활해석: 제2보 - 그루브 깊이의 영향)

  • Park, TaeJo;Jang, InGyu
    • Tribology and Lubricants
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    • v.35 no.6
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    • pp.382-388
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    • 2019
  • It is currently well known that surface textures act as lubricant reservoirs, entrap wear debris, and hydrodynamic bearings, which can lead to certain increases in load-carrying capacities. Until recently, the vast majority of research has focused on parallel sliding machine components such as thrust bearings, mechanical face seals, piston rings, etc. However, most sliding bearings have a convergent film shape in the sliding direction and their hydrodynamic pressure is mainly generated by the wedge action. Following the first part of the present study that investigates the effect of groove position on the lubrication performances of inclined slider bearings, this paper focuses on the effects of groove depths and film thicknesses. Using a commercial computational fluid dynamics (CFD) code, FLUENT, the continuity and Navier-Stokes equations are numerically analyzed. The results show that the film thickness and groove depth have a significant influence on the pressure distribution. The maximum pressure occurs at the groove depth where the vortex is found and, as the depth increases, the pressure decreases. There is also a groove depth to maximize the supporting load with the film thickness. The friction force acting on the slider decreases with deeper grooves. Therefore, properly designed groove depths, depending on the operating conditions, can improve the load-carrying capacity of inclined slider bearings as compared to the bearings without a groove.

Slat Noise Source Modeling of Multi-element Airfoil in High-lift Configuration

  • Hwang, Seung Tae;Han, Chang Kyun;Im, Yong Taek;Kim, Jong Rok;Bae, Youngmin;Moon, Young J.
    • International Journal of Aeronautical and Space Sciences
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    • v.18 no.2
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    • pp.197-205
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    • 2017
  • We investigate the slat noise generation mechanism by using large-eddy simulation (LES) and simple source modeling based on linearized Euler equations. An incompressible LES of an MD 30P30N three-element airfoil in the high-lift configuration is conducted at $Re_c=1.7{\times}10^6$. Using the total derivative of the hydrodynamic pressure (DP/Dt) acquired from the incompressible LES, representative noise sources in the slat cove region are characterized in terms of simple sources such as frequency-specific monopoles and dipoles. Acoustic radiation around the 30P30N multi-element airfoil is effectively computed using the Brinkman penalization method incorporated with the linearized Euler equation. The directivity pattern of $p^{\prime}_{rms}$ at $r=20c_{slat}$ in the multiple sources is closely compared to that obtained by the application of the LES/Ffowcs-Williams and Hawking's methods to the entire flow field. The power spectrum of p' at ${\theta}=290^{\circ}$ is in good agreement with the data reported in BANC-III, especially the broadband part of the spectrum with a decaying slope ${\propto}f^{-3}$.

A NUMERICAL SIMULATION METHOD FOR FREE SURFACE FLOWS NEAR MOVING BODIES IN A FIXED RECTANGULAR GRID SYSTEM (고정된 직사각형 격자계에서 움직이는 물체주위 자유수면유동 계산을 위한 수치기법의 개발)

  • Jeong, K.L.;Lee, Y.G.;Ha, Y.J.
    • 한국전산유체공학회:학술대회논문집
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    • 2011.05a
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    • pp.395-406
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    • 2011
  • In this research a numerical simulation method is developed for moving body in free surface flows using fixed staggered rectangular grid system. The non-linear free surface near the body is defined by marker-density method. The body boundary is defined by line segment connecting the points where the body surface and grid line meet. Continuity equation and Navier-Stokes equations are used as governing equations and the equations are coupled with two-step projection method. The velocities and pressures of body boundary and free surface cells are calculated with simultaneous iterative method. To treat a body movement in a fixed grid system, the volume displaced by moving body is added to the divergence of the body boundary cell. For the verification of the present numerical method. vortex shedding period of advancing cylinder is calculated and the period is compared with existing experiment results. Moreover, added mass and damping coefficients of a vertically excited box are calculated and the computed results are compared with published experiment results. Impulsive pressure and water level variation due to sloshing phenomenon are simulated and the results are compared with published experiment results. Varying the plunger shape, the waves generated by plunging type wave maker are compared with the 2nd order Stokes wave theory The plunger shape generating the wave that shows the best agreement with the theory is represented.

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Flow Characteristics inside a Throttle Valve Used to Control the Intake Air Flow in Engines (엔진의 흡기 공기량 조절용 스로틀 밸브에서의 유동 특성)

  • Kim, Sung-Cho;Kim, Cheol
    • Transactions of the Korean Society of Automotive Engineers
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    • v.7 no.8
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    • pp.91-98
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    • 1999
  • This paper describes the air flow characteristics inside the throttle valve. Tow-dimensional steady incompressible Navier-Strokes equation are solved numerically with embedding the conceopt of the artificial compressibility and adopting the Baldwin-Lomax turbulence model. With varying the valve opening angles(the Reynolds number )such as 15$^{\circ}$(5000) , 45$^{\circ}$(3000) , 75$^{\circ}$(7000) and 90$^{\circ}$(10000), respectively. tow cases, with a valve shaft and without one, are analysed. The pressure loss between the entrance and exit is severe at 15$^{\circ}$, 100 times as larger as that of 90$^{\circ}$ case, which also depends much on the existece of the valve shaft. The counter rotating vortices are formed over the valve plate with the shaft at only 75$^{\circ}$. They are smally and very large scale in front and back of the valve shaft , respectively. The velocity profiles of 15$^{\circ}$ and 90$^{\circ}$ at the exit are almost symmetric to the horizontal center line, however, the symmetricity is no longer maintained at 45$^{\circ}$ and 75$^{\circ}$ , and in addition, the flow at 75$^{\circ}$ is enforced a lot below center line. The pressure distribution on the walls is largely changed near the valve shaft, and its magnitude becomes great as the valve angle decreases.

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Internal Flow Analysis of Seawater Cooling Pump using CFD (CFD를 이용한 해수냉각펌프의 내부유동 분석)

  • Bao, Ngoc Tran;Yang, Chang-jo;Kim, Bu-gi;Kim, Jun-ho
    • Journal of the Korean Society of Marine Environment & Safety
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    • v.23 no.1
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    • pp.104-111
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    • 2017
  • This research focuses on simulation and visualization of flow field characteristics inside a centrifugal pump. The 3D numerical analysis was carried out by using a numerical CFD tool, addressing a Reynolds Average Navier-Stock code with a standard k-${\varepsilon}$ two-equation turbulence model. The simulation accounts for friction head loss due to rough walls at suction, impeller, discharge areas and volumetric head loss at impeller wear ring. A comparison of performance curves between simulation and experimentation is included, and it reveals a same trend of those results with a small difference of maximum 5 %. At best efficiency point, velocity vectors are smooth but it changes significantly under off-design point, a strong recirculation appears at the outlet of impeller passages near tongue area. A relatively uniform preassure distribution was observed around the impeller in despite of the tongue. Within the volute, because of its geometry, spiral vortexes formed, proving that the flow field in this region was relatively turbulent and unsteady.

Large eddy simulation of wind effects on a super-tall building

  • Huang, Shenghong;Li, Q.S.
    • Wind and Structures
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    • v.13 no.6
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    • pp.557-580
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    • 2010
  • A new inflow turbulence generation method and a combined dynamic SGS model recently developed by the authors were applied to evaluate the wind effects on 508 m high Taipei 101 Tower. Unlike the majority of the past studies on large eddy simulation (LES) of wind effects on tall buildings, the present numerical simulations were conducted for the full-scale tall building with Reynolds number greater than $10^8$. The inflow turbulent flow field was generated based on the new method called discretizing and synthesizing of random flow generation technique (DSRFG) with a prominent feature that the generated wind velocity fluctuations satisfy any target spectrum and target profiles of turbulence intensity and turbulence integral length scale. The new dynamic SGS model takes both advantages of one-equation SGS model and a dynamic production term without test-filtering operation, which is particular suitable to relative coarse grid situations and high Reynolds number flows. The results of comparative investigations with and without generation of inflow turbulence show that: (1) proper simulation of an inflow turbulent field is essential in accurate evaluation of dynamic wind loads on a tall building and the prescribed inflow turbulence characteristics can be adequately imposed on the inflow boundary by the DSRFG method; (2) the DSRFG can generate a large number of random vortex-like patterns in oncoming flow, leading to good agreements of both mean and dynamic forces with wind tunnel test results; (3) The dynamic mechanism of the adopted SGS model behaves adequately in the present LES and its integration with the DSRFG technique can provide satisfactory predictions of the wind effects on the super-tall building.

A Study on the Development of Low-Altitude and Long-Endurance Solar-Powered UAV from Korea Aerospace University (2) - Flight Control and Guidance of Solar Powered UAV - (한국항공대학교 저고도 장기체공 태양광 무인기 개발에 관한 연구 (2) - 태양광 무인기 비행제어 및 유도항법 -)

  • Kim, Taerim;Kim, Doyoung;Jeong, Jaebaek;Moon, Seokmin;Kim, Yongrae;Bae, Jae-Sung;Park, Sanghyuk
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.50 no.7
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    • pp.479-487
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    • 2022
  • This paper presents the control and guidance algorithm of a KAU-SPUAV(Korea Aerospace University - Solar Powered Unmanned Aerial Vehicle) which is designed and developed in Korea Aerospace University. Aerodynamic coefficients are calculated using the vortex-lattice method and applied to the aircraft's six degrees of freedom equation. In addition, the thrust and torque coefficients of the propeller are calculated using the blade element theory. An altitude controller using thrust was used for longitudinal control of KAU-SPUAV to glide efficiently when it comes across the upwind. Also describes wind estimation technic for considering wind effect during flight. Finally, introduce some guidance laws for endurance, mission and coping with strong headwinds and autonomous landing.

Mathematical Model for the Hydrodynamic Forces in Forward or Backward Low Speed Maneuvering (저속(低速) 전.후진(前.後進) 조종(操縱)에 의한 동유체력(動流體力)의 수학(數學)모델)

  • Jin-Ahn Kim;Seung-Keon Lee
    • Journal of the Society of Naval Architects of Korea
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    • v.29 no.3
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    • pp.45-52
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    • 1992
  • The Mathematical Model, which can describe the maneuvering motion of a ship in low speed, is highly required these days because it is directly related to the safety of ship in confused harbour. Kose has presented a new model for the low speed maneuvering motion, but the usefulness of it is not confirmed widely. Lets of difficulties are revealed in the case of low speed maneuver, The first is the fact that a ship moves the stirred water region for the longer time than in the case of high speed. So, the hydrodynamic forces, exerted on the hull need to be treated strictly, not by the ordinary differential equation with constant coefficients. Another difficulty is arised from the fact the lateral motion is relatively large comparing to the longitudinal motion in low speed. And, by the result the effect of cross-flow drag or vortex sheding effects are dominant. Besides, the captive model tests of low speed motion has lots of problems. For example, the hydrodynamic forces do not converge to a certain values for the long time. And the absolute values of measured forces are very small, so we must expend lots of efforts to raise up the S/N ratio of the experiments. In this paper, a new mathematical model for the maneuvering motion in low speed, is built up, and the usefulness is discussed, comparing with other models, for example, Kose's model or M.M.G. model or Cross-Flow model, The CMT data for a PCC model of 3.00 M length, released from the RR-742 of Japan, are used for the validation of each models.

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