• Title/Summary/Keyword: k-$\varepsilon$ equations

Search Result 246, Processing Time 0.03 seconds

A refined theory with stretching effect for the flexure analysis of laminated composite plates

  • Draiche, Kada;Tounsi, Abdelouahed;Mahmoud, S.R.
    • Geomechanics and Engineering
    • /
    • v.11 no.5
    • /
    • pp.671-690
    • /
    • 2016
  • This work presents a static flexure analysis of laminated composite plates by utilizing a higher order shear deformation theory in which the stretching effect is incorporated. The axial displacement field utilizes sinusoidal function in terms of thickness coordinate to consider the transverse shear deformation influence. The cosine function in thickness coordinate is employed in transverse displacement to introduce the influence of transverse normal strain. The highlight of the present method is that, in addition to incorporating the thickness stretching effect (${\varepsilon}_z{\neq}0$), the displacement field is constructed with only 5 unknowns, as against 6 or more in other higher order shear and normal deformation theory. Governing equations of the present theory are determined by employing the principle of virtual work. The closed-form solutions of simply supported cross-ply and angle-ply laminated composite plates have been obtained using Navier solution. The numerical results of present method are compared with those of the classical plate theory (CPT), first order shear deformation theory (FSDT), higher order shear deformation theory (HSDT) of Reddy, higher order shear and normal deformation theory (HSNDT) and exact three dimensional elasticity theory wherever applicable. The results predicted by present theory are in good agreement with those of higher order shear deformation theory and the elasticity theory. It can be concluded that the proposed method is accurate and simple in solving the static bending response of laminated composite plates.

Design Optimization of A Multi-Blade Centrifugal Fan With Variable Design Flow Rate (설계유량을 변수로 한 원심다익송풍기의 최적설계)

  • Seo, Seung-Jin;Kim, Kwang-Yong
    • Proceedings of the KSME Conference
    • /
    • 2004.04a
    • /
    • pp.1726-1731
    • /
    • 2004
  • This paper presents the response surface optimization method using three-dimensional Navier-Stokes analysis to optimize the shape of a forward-curved blades centrifugal fan. For numerical analysis, Reynolds-averaged Navier-Stokes equations with $k-{\varepsilon}$ turbulence model are discretized with finite volume approximations. In order to reduce huge computing time due to a large number of blades in forward-curved blades centrifugal fan, the flow inside of the fan is regarded as steady flow by introducing the impeller force models. Three geometric variables, i.e., location of cut off, radius of cut off, and width of impeller, and one operating variable, i.e., flow rate, were selected as design variables. As a main result of the optimization, the efficiency was successfully improved. And, optimum design flow rate was found by using flow rate as one of design variables. It was found that the optimization process provides reliable design of this kind of fans with reasonable computing time.

  • PDF

Design Optimization of A Multi-Blade Centrifugal Fan With Variable Design Flow Rate (설계유량을 변수로 한 원심다익송풍기의 최적설계)

  • Seo, Seoung-Jin;Kim, Kwang-Yong
    • Transactions of the Korean Society of Mechanical Engineers B
    • /
    • v.28 no.11
    • /
    • pp.1332-1338
    • /
    • 2004
  • This paper presents the response surface optimization method using three-dimensional Navier-Stokes analysis to optimize the shape of a forward-curved blades centrifugal fan. For numerical analysis, Reynolds-averaged Navier-Stokes equations with k-$\varepsilon$ turbulence model are discretized with finite volume approximations. In order to reduce huge computing time due to a large number of blades in forward-curved blades centrifugal fan, the flow inside of the fan is regarded as steady flow by introducing the impeller force models. Three geometric variables, i.e., location of cut off, radius of cut off, and width of impeller, and one operating variable, i.e., flow rate, were selected as design variables. As a main result of the optimization, the efficiency was successfully improved. And, optimum design flow rate was found by using flow rate as one of design variables. It was found that the optimization process provides reliable design of this kind of fans with reasonable computing time.

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
    • /
    • v.11 no.1
    • /
    • pp.314-328
    • /
    • 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.

High-k ZrO2 Enhanced Localized Surface Plasmon Resonance for Application to Thin Film Silicon Solar Cells

  • Li, Hua-Min;Zang, Gang;Yang, Cheng;Lim, Yeong-Dae;Shen, Tian-Zi;Yoo, Won-Jong;Park, Young-Jun;Lim, Jong-Min
    • Proceedings of the Korean Vacuum Society Conference
    • /
    • 2010.02a
    • /
    • pp.276-276
    • /
    • 2010
  • Localized surface plasmon resonance (LSPR) has been explored recently as a promising approach to increase energy conversion efficiency in photovoltaic devices, particularly for thin film hydrogenated amorphous silicon (a-Si:H) solar cells. The LSPR is frequently excited via an electromagnetic (EM) radiation in proximate metallic nanostructures and its primary con sequences are selective photon extinction and local EM enhancement which gives rise to improved photogeneration of electron-hole (e-h) pairs, and consequently increases photocurrent. In this work, high-dielectric-constant (k) $ZrO_2$ (refractive index n=2.22, dielectric constant $\varepsilon=4.93$ at the wavelength of 550 nm) is proposed as spacing layer to enhance the LSPR for application to the thin film silicon solar cells. Compared to excitation of the LSPR using $SiO_2$ (n=1.46, $\varepsilon=2.13$ at the wavelength of 546.1 nm) spacing layer with Au nanoparticles of the radius of 45nm, that using $ZrO_2$ dielectric shows the advantages of(i) ~2.5 times greater polarizability, (ii) ~3.5 times larger scattering cross-section and ~1.5 times larger absorption cross-section, (iii) 4.5% higher transmission coefficient of the same thickness and (iv) 7.8% greater transmitted electric filed intensity at the same depth. All those results are calculated by Mie theory and Fresnel equations, and simulated by finite-difference time-domain (FDTD) calculations with proper boundary conditions. Red-shifting of the LSPR wavelength using high-k $ZrO_2$ dielectric is also observed according to location of the peak and this is consistent with the other's report. Finally, our experimental results show that variation of short-circuit current density ($J_{sc}$) of the LSPR enhanced a-Si:H solar cell by using the $ZrO_2$ spacing layer is 45.4% higher than that using the $SiO_2$ spacing layer, supporting our calculation and theory.

  • PDF

Fluidization Study in the Fluidized Bed Drying of Naked and Husked Barley (쌀보리와 겉보리의 유동층 건조에서의 유동화 연구)

  • Kim, Hee-Yun;Hur, Jong-Hwa;Cho, Duk-Jae
    • Korean Journal of Food Science and Technology
    • /
    • v.24 no.5
    • /
    • pp.414-422
    • /
    • 1992
  • To keep up with urgent need of continuous, effective and rapid drying unit, a fluidized bed drying system with computer controlling air temperature, velocity and relative humidity was designed. This study was attempted to determine physical properties and some basic experiments of fluidized bed d교ing of barley. Also experimental data of the designed fluidized bed drying system using the barely were compared with those of published equations to confirm the reliability of the system and the following results were obtained. The physical dimension husked barley were shown larger than that of naked barley from the experiment. When air temperature. relative humidity and charged amount were $35^{\circ}C$, 30% and 300g respectively, the minimum fluidization velocity of naked and husked barley were found 1.5 m/s and 1.7 m/s. And the optimum fluidization velocity was shown as 3.0 m/s from the experiment. The empirical equation of $U_{mf}$ in this fluidized system was obtained as follow; $U_{mf}^2= \frac{{\phi_s}\;d_p}{Hk}\;{\cdot}\;\frac{(\rho_s-\rho_g)g\;{{\varepsilon}_{mf}^3}} {\rho_g}(Re_p>1,000)$ Where HK=0.4881 for naked barley, 0.6649 for husked barley.

  • PDF

The Effect of Different Inflows on the Unsteady Hydrodynamic Characteristics of a Mixed Flow Pump

  • Yun, Long;Dezhong, Wang;Junlian, Yin;Youlin, Cai;Chao, Feng
    • International Journal of Fluid Machinery and Systems
    • /
    • v.10 no.2
    • /
    • pp.138-145
    • /
    • 2017
  • The problem of non-uniform inflow exists in many practical engineering applications, such as the elbow suction pipe of waterjet pump and, the channel head of steam generator which is directly connect with reactor coolant pump. Generally, pumps are identical designs and are selected based on performance under uniform inflow with the straight pipe, but actually non-uniform suction flow is induced by upstream equipment. In this paper, CFD approach was employed to analyze unsteady hydrodynamic characteristics of reactor coolant pumps with different inflows. The Reynolds-averaged Naiver-Stokes equations with the $k-{\varepsilon}$ turbulence model were solved by the computational fluid dynamics software CFX to conduct the steady and unsteady numerical simulation. The numerical results of the straight pipe and channel head were validated with experimental data for the heads at different flow coefficients. In the nominal flow rate, the head of the pump with the channel head decreases by 1.19% when compared to the straight pipe. The complicated structure of channel head induces the inlet flow non-uniform. The non-uniformity of the inflow induces the difference of vorticity distribution at the outlet of the pump. The variation law of blade to blade velocity at different flow rate and the difference of blade to blade velocity with different inflow are researched. The effects of non-uniform inflow on radial forces are absolutely different from the uniform inflow. For the radial forces at the frequency $f_R$, the corresponding amplitude of channel head are higher than the straight pipe at $1.0{\Phi}_d$ and $1.2{\Phi}_d$ flow rates, and the corresponding amplitude of channel head are lower than the straight pipe at $0.8{\Phi}_d$ flow rates.

Mean flow characteristics of two-dimensional wings in ground effect

  • Jung, Jae-Hwan;Yoon, Hyun-Sik;Chun, Ho-Hwan;Hung, Pham Anh;Elsamni, Osama Ahmed
    • International Journal of Naval Architecture and Ocean Engineering
    • /
    • v.4 no.2
    • /
    • pp.151-161
    • /
    • 2012
  • The present study numerically investigates the aerodynamic characteristics of two-dimensional wings in the vicinity of the ground by solving two-dimensional steady incompressible Navier-Stokes equations with the turbulence closure model of the realizable k-${\varepsilon}$ model. Numerical simulations are performed at a wide range of the normalized ground clearance by the chord length ($0.1{\leq}h/C{\leq}1.25$) for the angles of attack ($0^{\circ}{\leq}{\alpha}{\leq}10^{\circ}$) in the prestall regime at a Reynolds number (Re) of $2{\times}10^6$ based on free stream velocity $U_{\infty}$ and the chord length. As the physical model of this study, a cambered airfoil of NACA 4406 has been selected by a performance test for various airfoils. The maximum lift-to-drag ratio is achieved at ${\alpha}=4^{\circ}$ and h / C = 0.1. Under the conditions of ${\alpha}=4^{\circ}$ and h / C = 0.1, the effect of the Reynolds number on the aerodynamic characteristics of NACA 4406 is investigated in the range of $2{\times}10^5{\leq}Re{\leq}2{\times}10^9$. As Re increases, $C_l$ and $C_d$ augments and decreases, respectively, and the lift-to-drag ratio increases linearly.

An integrated model for pore pressure accumulations in marine sediment under combined wave and current loading

  • Zhang, Y.;Jeng, D.-S.;Zha, H.-Y.;Zhang, J.-S.
    • Geomechanics and Engineering
    • /
    • v.10 no.4
    • /
    • pp.387-403
    • /
    • 2016
  • In this paper, an integrated model for the wave (current)-induced seabed response is presented. The present model consists of two parts: hydrodynamic model for wave-current interactions and poro-elastic seabed model for pore accumulations. In the wave-current model, based on the fifth-order wave theory, ocean waves were generated by adding a source function into the mass conservation equation. Then, currents were simulated through imposing a steady inlet velocity on one domain and pressure outlet on the other side. In addition, both of the Reynolds-Averaged Navier-Stokers (RANS) Equations and $k-{\varepsilon}$ turbulence model would be applied in the fluid field. Once the wave pressures on the seabed calculated through the wave-current interaction model, it would be applied to be boundary conditions on the seabed model. In the seabed model, the poro-elastic theory would be imposed to simulate the seabed soil response. After comparing with the experimental data, the effect of currents on the seabed response would be examined by emphasize on the residual mechanisms of the pore pressure inside the soil. The build-up of the pore water pressure and the resulted liquefaction phenomenon will be fully investigated. A parametric study will also be conducted to examine the effects of waves and currents as well as soil properties on the pore pressure accumulation.

Fluid-Structure Interaction Study on Diffuser Pump With a Two-Way Coupling Method

  • Xu, Huan;Liu, Houlin;Tan, Minggao;Cui, Jianbao
    • International Journal of Fluid Machinery and Systems
    • /
    • v.6 no.2
    • /
    • pp.87-93
    • /
    • 2013
  • In order to study the effect of the fluid-structure interaction (FSI) on the simulation results, the external characteristics and internal flow features of a diffuser pump were analyzed with a two-way flow solid coupling method. And the static and dynamic structure analysis of the blade was also caculated with the FEA method. The steady flow field is based on Reynolds Averaged N-S equations with standard $k-{\varepsilon}$ turbulent model, the unsteady flow field is based on the large eddy simulation, and the structure response is based on elastic transient structural dynamic equation. The results showed that the effect of FSI on the head prediction based on CFD really exists. At the same radius, the van mises stress on the nodes closed shroud and hub was larger than other nodes. A large deformation region existed near inlet side at the middle of blades. The strength of impeller satisfied the strength requirement with static stress analysis based on the fourth strength theory. The dynamic stress varied periodically with the impeller rotating. It was also found that the fundamental frequency of the dynamic stress is the rotating frequency and its harmonic frequency. The frequency of maximum stress amplitude at node 1626 was 7 times of the rotating frequency. The frequency of maximum stress amplitude at node 2328 was 14 times of the rotating frequency. No matter strength failure or fatigue failure, the root of blades near shroud is the key region to analyse.