• Title/Summary/Keyword: Vortex equation

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Behavior of Two Dimensional Density Flow into a Reservoir with Sloping Bottom (경사정지수역으로 유입되는 2차원 밀도류의 거동)

  • 윤태훈;전시영
    • Water for future
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    • v.20 no.3
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    • pp.237-245
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    • 1987
  • The behavior of negative buoyant flow into a reservoir with sloping bottom is analysed by numerical solution technique of the governing equations composed of continuty, momentum and constituent transport equation. The stable plunge point and maximum travel distance are found to be dependent on the bottom slope of reservoir as well as inflow densimetric Froude number, $Fr_e$. They are also related closely to a vortex formed just downstream from the plunge point and above the underflow. The plunge depth was shown to be a function of th bottom slope and $Fr_e$. The plunge depths obtained in this numerical study agree relatively well with published data and theoretical studies, and its predictive equation is derived.

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Inclination angle influence on noise of cavitating marine propeller

  • Bal, Sakir
    • Ocean Systems Engineering
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    • v.10 no.1
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    • pp.49-65
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    • 2020
  • In this study, the effects of inclined shaft angle on the hydro-acoustic performance of cavitating marine propellers are investigated by a numerical method developed before and Brown's empirical formula. The cavitating blades are represented by source and vortex elements. The cavity characteristics of the blades such as cavitation form, cavity volume, cavity length etc., are computed at a given cavitation number and at a set advance coefficient. A lifting surface method is applied for these calculations. The numerical lifting surface method is validated with experimental results of DTMB 4119 model benchmark propeller. After calculation of hydrodynamic characteristics of the cavitating propeller, noise spectrum and overall sound pressure level (OASPL) are computed by Brown's equation. This empirical equation is also validated with another numerical results found in the literature. The effects of inclined shaft angle on thrust coefficient, torque coefficient, efficiency and OASPL values are examined by a parametric study. By modifying the inclination angles of propeller, the thrust, torque, efficiency and OASPL are computed and compared with each other. The influence of the inclined shaft angle on cavity patterns on the blades are also discussed.

Performance predictions and acoustic analysis of the HVAB rotor in hover

  • Mali, Hajar;Benmansour, Kawtar;Elsayed, Omer;Qaissi, Khaoula
    • Advances in aircraft and spacecraft science
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    • v.9 no.4
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    • pp.319-333
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    • 2022
  • This work presents a numerical investigation of the aerodynamics and aero acoustics of the HVAB rotor in hover conditions. Two fully turbulent models are employed, the one-equation Spalart-Allmaras model and the two-equation k-ω SST model. Transition effects are investigated as well using the Langtry-Menter γ-Re θt transition transport model. The noise generation and propagation are being investigated using the Ffows-Williams Hawking model for far-field noise and the broadband model for near-field noise. Comparisons with other numerical solvers and with the PSP rotor test data are presented. The results are presented in terms of thrust and power coefficients, the figure of merit, surface pressure distribution, and Sound pressure level. Velocity, pressure, and vortex structures generated by the rotor are also shown in this work. In addition, this work investigates the contribution of different blade regions to the overall noise levels and emphasizes the importance of considering specific areas for future improvements.

CHARACTERISTICS OF MATRICES IN THE P2P1 FINITE ELEMENT METHODS FOR SOLVING THE INCOMPRESSIBLE NAVIER-STOKES EQUATION (P2P1 유한요소를 이용한 비압축성 Navier-Stokes 방정식 해법들의 행렬 특성)

  • Cho, Myung-H.;Choi, Hyoung-G.;Yoo, Jung-Y.
    • 한국전산유체공학회:학술대회논문집
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    • 2009.04a
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    • pp.245-251
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    • 2009
  • Numerical algorithms for solving the incompressible Navier-Stokes equations using P2P1 finite element are compared regarding the eigenvalues of matrices. P2P1 element allocates pressure at vertex nodes and velocity at both vertex and mid nodes. Therefore, compared to the P1P1 element, the number of pressure variables in the P2P1 element decreases to 1/4 in the case of two-dimensional problems and to 1/8 in the three-dimensional problems. Fully-implicit-integrated, semi-implicit- integrated and semi-segregated finite element formulations using P2P1 element are compared in terms of elapsed time, accuracy and eigenvlue distribution (condition number). For the comparison,they have been applied to the well-known benchmark problems. That is, the two-dimensional unsteady flows around a fixed circular cylinder and decaying vortex flow are adopted to check spatial accuracy.

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Numerical Analysis on the Blade Tip Clearance Flow in the Axial Rotor (III) - Evaluation of Tip Leakage Loss and Reduction of Efficiency near Blade Tip Clearance Region of a Rotor - (축류 회전차 익말단 틈새유동에 대한 수치해석 (III) - 회전차 익말단의 누설손실과 효율저하에 대한 평가 -)

  • Ro, Soo-Hyuk;Cho, Kang-Rae
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.23 no.9
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    • pp.1113-1120
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    • 1999
  • Leakage vortices fonned near the blade tip cause an increase of total pressure loss near the casing endwall region and as a result, the efficiency of rotor decreases. The reduction of rotor efficiency is related to the size of tip clearance. In this study, the three-dimensional flow fields in an axial flow rotor were calculated with varying tip clearance under various flow rates, and the numerical results were compared with experimental ones. The effects of tip clearance and the of attack on the leakage vortex and overall performance, and the los9 distributions were investigated through numerical calculations. In this study, tip leakage flow rate and total pressure loss due to the tip clearance were evaluated using numerical results and approximate equations were presented to evaluate the reduction of rotor efficiency due to the tip leakage flow.

Analysis of the Aeroacoustic Characteristics of Cross-Flow Fan Using a Commercial CFD Code (상용 CFD 코드를 이용한 횡류홴 공력소음 특성 해석)

  • Jeon, Wan-Ho;Chung, Moon-Ki
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2002.11b
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    • pp.289-294
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    • 2002
  • In this study, performance, flow characteristics and noise of a cross-flow-fan system, used in indoor unit of the split-type air conditioner, were predicted by computational simulation. Triangular elements were used to mesh the calculation domain and quadrilateral elements were attached to the blade surfaces and walls to enhance the simulation quality. The unsteady incompressible Wavier-Stokes equations were solved using a sliding mesh technique on the interface between rotating fan region and the outside. Two stripes of velocity stream inside the cross-flow-fan were shown - the one was due to the eccentric vortex and the other was due to the normal entrance flow. As the flow rate increased, the center of the eccentric vortex moved toward the inner blade tip and rear-guide, and the exiting flow still had velocity variation along the stabilizer, which can increase the noise level. The acoustic pressure was calculated by using Lowson's equation. From the calculated acoustic pressure, it was found that the trailing edge is a dominant of acoustic generation.

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Large Eddy Simulation for a 2-D hydrofoil using VIC(Vortex-In-Cell) method (VIC 방법을 사용한 2차원 날개의 LES 해석)

  • Kim, M.S.;Kim, Y.C.;Suh, J.C.
    • 한국전산유체공학회:학술대회논문집
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    • 2011.05a
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    • pp.407-413
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    • 2011
  • VIC (Vortex-In-Cell) method for viscous incompressible flow is presented to simulate the wake behind a modified NACA16 foil. With uniform rectangular grid, the velocity in field is calculated using streamfunction from vorticity field by solving the Poisson equation in which FFT(Fast Fourier Transform) is combined with 2nd order finite difference scheme. Here, LES(Large Eddy Simulation) with Smagorinsky model is applied for turbulence calculation. Effective viscosity is formulated using magnitude of strain tensor(or vorticity). Then the turbulent diffusion as well as viscous diffusion becomes particle strength exchange(PSE) with averaged eddy viscosity. The well-established panel method is combined to obtain the irrotational velocity and to apply the no-penetration boundary condition on the body panel. And wall diffusion is used for no-slip condition numerical results of turbulent stresses are compared with experimental results (Bourgoyne, 2003). Before comparing process, LES(Large Eddy Simulation) SGS(Subgrid scale) stress is transformed Reynolds averaged stress (Winckelmans, 2001).

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ANALYSIS OF UNSTEADY OSCILLATING FLOW AROUND TWO DIMENSIONAL AIRFOIL AT HIGH ANGLE OF ATTACK (고받음각 2차원 에어포일 주위의 비정상 유동의 진동 특성에 관한 연구)

  • Yoo, J.K.;Kim, J.S.
    • Journal of computational fluids engineering
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    • v.18 no.1
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    • pp.1-6
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    • 2013
  • Missile and fighter aircraft have been challenged by low restoring nose-down pitching moment at high angle of attach. The consequence of weak nose-down pitching moment can be resulting in a deep stall condition. Especially, the pressure oscillation has a huge effect on noise generation, structure damage, aerodynamic performance and safety, because the flow has strong unsteadiness at high angle of attack. In this paper, the unsteady aerodynamics coefficients were analyzed at high angle of attack up to 50 degrees around two dimensional NACA0012 airfoil. The two dimensional unsteady compressible Navier-Stokes equation with a LES turbulent model was calculated by OHOC (Optimized High-Order Compact) scheme. The flow conditions are Mach number of 0.3 and Reynolds number of $10^5$. The lift, drag, pressure, entropy distribution, etc. are analyzed according to the angle of attack. The results of average lift coefficients are compared with other results according to the angle of attack. From a certain high angle of attack, the strong vortex formed by the leading edge are flowing downstream as like Karman vortex around a circular cylinder. The primary and secondary oscillating frequencies are analyzed by the effects of these unsteady aerodynamic characteristics.

Modeling of Deviation Angle and Pressure Loss Due to Rotor Tip Leakage Flow Effects in Axial Turbines (축류터빈에서 끝간격 유동에 의한 편향각과 압력손실의 모형)

  • Yoon, Eui Soo;Park, Moo Ryong;Chung, Myung Kyoon
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.22 no.11
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    • pp.1591-1602
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    • 1998
  • Simple spanwise distribution models of deviation angle and pressure loss coefficient due to the tip leakage flow are formulated for use in association with the streamline curvature method as a flow analysis. Combining these new models with the previous deviation and loss models due to secondary flow, a robust streamline curvature method is established for flow analysis of single-stage, subsonic axial turbines with wide ranges of turning angle, aspect ratio and blading type. At the exit from rotor rows, the flow variables are mixed radially according to a spanwise transport equation. The proposed streamline curvature method is tested against a forced vortex type turbine as well as a free vortex type one. The results show that the spanwise variations of flow angle, axial velocity and loss coefficients at rotor exit are predicted with good accuracy, being comparable to a steady three-dimensional Navier-Stokes analysis. This simple and fast flow analysis is found to be very useful for the turbine design at the initial design phase.

Active Control of Flow-Induced Vibration Using Piezoelectric Actuators (압전 작동기를 이용한 유체 유기 진동의 능동 제어)

  • 한재홍
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2003.11a
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    • pp.446-451
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    • 2003
  • This paper presents some examples of active control of flow-induced vibration using piezoelectric actuators. The flutter phenomenon, which is the dynamic instability of structure due to mutual interaction among inertia, stiffness, and aerodynamic forces, may cause catastrophic structural failure, and therefore the active flutter suppression is one of the main objectives of the aeroelastic control. Active flutter control has been numerically and experimentally studied for swept-back lifting surfaces using piezoelectric actuation. A finite element method, a panel aerodynamic method, and the minimum state space realization are involved in the development of the governing equation, which is efficiently used for the analysis of the system and design of control laws with modern control framework. The active control suppressed flow-induced vibrations and extended the flutter speed around by 10%. Another representative flow-induced vibration phenomenon is the oscillation of blunt bodies due to the vortex shedding. In general, it is quite difficult to set up the numerical model because of the strong non-linearity of the vortex shedding structure. Therefore, we applied adaptive positive position feedback controller, which requires no pre-determined model of the plant, and successfully suppressed the flow-induced vibration.

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