• Title/Summary/Keyword: Navier series

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Unsteady Conjugate Heat Transfer Analysis of a Cooled Turbine Nozzle with High Free Stream Turbulence

  • Seo, Doyoung;Hwang, Sunwoo;Son, Changmin;Kim, Kuisoon
    • International Journal of Aeronautical and Space Sciences
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    • v.18 no.2
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    • pp.279-289
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    • 2017
  • In this study, a series of conjugate heat transfer (CHT) analyses are conducted for a stage of a fully cooled high-pressure turbine (HPT) at elevated levels of free stream turbulence (Tu = 5% and 25.7%). The goal of the analyses is to investigate the influence of high turbulence intensity on the fluid-thermal characteristics of a nozzle guide vane (NGV). The turbine inlet temperature is defined by considering a typical radial temperature distribution factor (RTDF). The Unsteady Reynolds Average Navier-Stokes (URANS) CHT simulations are carried out using CFX 15.0, a commercial CFD package. The presented CFD modeling approach for high turbulence intensity is verified with the experimental data from two types of NASA C3X NGVs with films. The computation grid is generated for both the fluid and solid domains. The fluid domain grid is created using a tetrahedral grid system with prism layers because of its complex geometry, and the solid domain grid is composed of only tetrahedral elements. The analytical results are compared to understand the effect of turbulence on flow characteristics and metal temperature distributions. The results obtained in this study provide useful insights on the effects of high free stream turbulence and unsteadiness. The results also lead to the proposal of meaningful turbine design guidelines.

A Numerical Study on the Heat Transfer Characteristics in an Internally Finned Circular Tube Flow (내부핀이 부착된 원형관유동에서의 열전달특성에 관한 수치적연구)

  • Pak, H.Y.;Park, K.W.;Choi, M.S.
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.8 no.2
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    • pp.267-278
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    • 1996
  • Steady, laminar, forced convection flow and heat transfer in the entrance region of an internally finned circular duct with a finite thermal conductivity has been analyzed numerically. The problem under investigation is a three-dimensional boundary layer problem, and is solved by employing a marching-type procedure which involves solution of a series of 2-dimensional elliptic problems in the cross-stream plane. Two types of inlet hydrodynamic conditions are considered : (a) uniform velocity flow and (b) fully developed flow. From the above inlet conditions, the effects of the fin height(h), fin number(N) and conductivity ratio($k_r$) on the flow and thermal characteristics are investigated. The numerical results show that the height and number of fins, and ratio of the solid to fluid thermal conductivity have pronounced effect on the solution. Considering pressure drop, optimized dimensionless fin height is 0.4.

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Effect of Airfoil Thickness on the Optimum Gurney Flap Height (최적 Gurney 플랩크기에 대한 익형두께의 영향)

  • Yoo, Neung-Soo;Lee, Jang-Ho
    • Proceedings of the KSME Conference
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    • 2000.11b
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    • pp.568-572
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    • 2000
  • A numerical investigation was performed to determine the effect of airfoil thickness on the optimum Gurney flap height using NACA 00XX series airfoils. Seven airfoils which have 3% chord thickness difference were used. These were NACA 0006, 0009, 0012, 0015, 0018, 0021, and 0024. A Navier-Stokes code, FLUENT, was used to calculate the flow field about airfoil. The fully turbulent results were obtained using the standard $k-{\varepsilon}$ two-equation turbulence model. To provide a check case fur our computational method, numerical studies for NACA 4412 airfoil were made and compared with already existing experimental data for this airfoil by Wadcock. For every NACA 00XX airfoil, Gurney flap heights ranging from 0.5% to 2.0% chord were changed by 0.5% chord interval and their effects were studied. With the numerical solutions, the relationship between $(L/D)_{max}$ and airfoil thickness as a function of flap height and the relationship between $(L/D)_{max}$ and flap height as a function of airfoil thickness were investigated. The same relationship for $(C_l)_{max}$ also were shown. From these results, the optimum flap size for each airfoil thickness can be determined and vice versa.

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Code Development for Computation of Turbulent Flow around a Ship Model with Free-Surface (자유표면을 포함한 선체주위 난류유동 해석 코드 개발)

  • Kim J.J.;Kim H.T.;Van S.H.
    • 한국전산유체공학회:학술대회논문집
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    • 1998.05a
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    • pp.145-155
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    • 1998
  • A computer code has been developed for the computation of the viscous flow around a ship model with the free surface. In this code, the incompressible Reynolds-averaged Navier-Stokes equations are solved numerically by a finite difference method which employes second-order finite differences for the spatial discretization and a four-stage Runge-Kutta scheme for the temporal integration of the governing equations. For the turbulence closure, a modified version of the Baldwin-Lomax model is exploited. The location of the free surface is determined by solving the equation of the kinematic free-surface condition using the Lax-Wendroff scheme and the boundary-fitted grid is generated at each time step so that one of the grid surfaces always coincides with the free surface. An inviscid approximation of the dynamic free-surface boundary condition is applied as the boundary conditions for the velocity and pressure on the free surface. To validate the computational method and the computer code developed in the present study, the numerical computations are carried out for both Wigley parabolic hull and Series 60 $C_B=0.6$ ship model and the computational results are compared with the experimental data.

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The controllable fluid dash pot damper performance

  • Samali, Bijan;Widjaja, Joko;Reizes, John
    • Smart Structures and Systems
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    • v.2 no.3
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    • pp.209-224
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    • 2006
  • The use of smart dampers to optimally control the response of structures is on the increase. To maximize the potential use of such damper systems, their accurate modeling and assessment of their performance is of vital interest. In this study, the performance of a controllable fluid dashpot damper, in terms of damper forces, damper dynamic range and damping force hysteretic loops, respectively, is studied mathematically. The study employs a damper Bingham-Maxwell (BingMax) model whose mathematical formulation is developed using a Fourier series technique. The technique treats this one-dimensional Navier-Stokes's momentum equation as a linear superposition of initial-boundary value problems (IBVPs): boundary conditions, viscous term, constant Direct Current (DC) induced fluid plug and fluid inertial term. To hold the formulation applicable, the DC current level to the damper is supplied as discrete constants. The formulation and subsequent simulation are validated with experimental results of a commercially available magneto rheological (MR) dashpot damper (Lord model No's RD-1005-3) subjected to a sinusoidal stroke motion using a 'SCHENK' material testing machine in the Materials Laboratory at the University of Technology, Sydney.

An analytical solution for static analysis of a simply supported moderately thick sandwich piezoelectric plate

  • Wu, Lanhe;Jiang, Zhiqing;Feng, Wenjie
    • Structural Engineering and Mechanics
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    • v.17 no.5
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    • pp.641-654
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    • 2004
  • This paper presents a theoretic model of a smart structure, a transversely isotropic piezoelectric thick square plate constructed with three laminas, piezoelectric-elastic-piezoelectric layer, by adopting the first order shear deformation plate theory and piezoelectric theory. This model assumes that the transverse displacements through thickness are linear, and the in-plane displacements in the mid-plane of the plate are not taken to be account. By using Fourier's series expansion, an exact Navier typed analytical solution for deflection and electric potential of the simply supported smart plate is obtained. The electric boundary conditions are being grounded along four vertical edges. The external voltage and non-external voltage applied on the surfaces of piezoelectric layers are all considered. The convergence of the present approach is carefully studied. Comparison studies are also made for verifying the accuracy and the applicability of the present method. Then some new results of the electric potentials and displacements are provided. Numerical results show that the electrostatic voltage is approximately linear in the thickness direction, while parabolic in the plate in-plane directions, for both the deflection and the electric voltage. These results are very useful for distributed sensing and finite element verification.

Numerical investigation on combined wave damping effect of pneumatic breakwater and submerged breakwater

  • Wang, Yanxu;Yin, Zegao;Liu, Yong;Yu, Ning;Zou, Wei
    • International Journal of Naval Architecture and Ocean Engineering
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    • v.11 no.1
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    • pp.314-328
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    • 2019
  • This paper attempts to combine the pneumatic breakwater and submerged breakwater to increase the effectiveness of wave damping for long-period waves. A series of physical experiments concerning pneumatic breakwater, submerged breakwater and their joint breakwater was conducted and used to validate a mathematical model based on Reynolds-averaged Navier-Stokes equations, the RNG $k-{\varepsilon}$ turbulence model and the VOF method. In addition, the mathematical model was used to investigate the wave transmission coefficients of three breakwaters. The nonlinear wave propagation behaviors and the energy transfer from lower frequencies to higher frequencies after the submerged breakwater were investigated in detail. Furthermore, an optimal arrangement between pneumatic breakwater and submerged breakwater was obtained for damping longer-period waves that cannot be damped effectively by the pneumatic breakwater alone. In addition, the reason for the appearance of the combination effect is that part of the energy of the transmitted waves over the submerged breakwater transfers to shorter-period waves. Finally, the impact of the joint breakwater on the wave field during wave propagation process was investigated.

A simple HSDT for bending, buckling and dynamic behavior of laminated composite plates

  • Remil, Aicha;Benrahou, Kouider Halim;Draiche, Kada;Bousahla, Abdelmoumen Anis;Tounsi, Abdelouahed
    • Structural Engineering and Mechanics
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    • v.70 no.3
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    • pp.325-337
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    • 2019
  • In the present article, cross ply laminated composite plates are considered and a simple sinusoidal shear deformation model is tested for analyzing their flexural, stability and dynamic behaviors. The model contains only four unknown variables that are five in the first order shear deformation theory (FSDT) or other higher order models. The in-plane kinematic utilizes undetermined integral terms to quantitatively express the shear deformation influence. In the proposed theory, the conditions of zero shear stress are respected at bottom and top faces of plates without considering the shear correction coefficient. Equations of motion according to the proposed formulation are deduced by employing the virtual work principle in its dynamic version. The analytical solution is determined via double trigonometric series proposed by Navier. The stresses, displacements, natural frequencies and critical buckling forces computed using present method are compared with other published data where a good agreement between results is demonstrated.

LSTM-based aerodynamic force modeling for unsteady flows around structures

  • Shijie Liu;Zhen Zhang;Xue Zhou;Qingkuan Liu
    • Wind and Structures
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    • v.38 no.2
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    • pp.147-160
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    • 2024
  • The aerodynamic force is a significant component that influences the stability and safety of structures. It has unstable properties and depends on computer precision, making its long-term prediction challenging. Accurately estimating the aerodynamic traits of structures is critical for structural design and vibration control. This paper establishes an unsteady aerodynamic time series prediction model using Long Short-Term Memory (LSTM) network. The unsteady aerodynamic force under varied Reynolds number and angles of attack is predicted by the LSTM model. The input of the model is the aerodynamic coefficients of the 1 to n sample points and output is the aerodynamic coefficients of the n+1 sample point. The model is predicted by interpolation and extrapolation utilizing Unsteady Reynolds-average Navier-Stokes (URANS) simulation data of flow around a circular cylinder, square cylinder and airfoil. The results illustrate that the trajectories of the LSTM prediction results and URANS outcomes are largely consistent with time. The mean relative error between the forecast results and the original results is less than 6%. Therefore, our technique has a prospective application in unsteady aerodynamic force prediction of structures and can give technical assistance for engineering applications.

Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories

  • Attia, Amina;Tounsi, Abdelouahed;Bedia, E.A. Adda;Mahmoud, S.R.
    • Steel and Composite Structures
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    • v.18 no.1
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    • pp.187-212
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    • 2015
  • In this paper, various four variable refined plate theories are presented to analyze vibration of temperature-dependent functionally graded (FG) plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations for the present model is reduced, significantly facilitating engineering analysis. These theories account for parabolic, sinusoidal, hyperbolic, and exponential distributions of the transverse shear strains and satisfy the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Uniform, linear, nonlinear and sinusoidal thermal conditions are imposed at the upper and lower surface for simply supported FG plates. Equations of motion are derived from Hamilton's principle. Analytical solutions for the free vibration analysis are obtained based on Fourier series that satisfy the boundary conditions (Navier's method). Non-dimensional results are compared for temperature-dependent and temperature-independent FG plates and validated with known results in the literature. Numerical investigation is conducted to show the effect of material composition, plate geometry, and temperature fields on the vibration characteristics. It can be concluded that the present theories are not only accurate but also simple in predicting the free vibration responses of temperature-dependent FG plates.