• Title/Summary/Keyword: Mixing Length Theory

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Local Mean Water Layer Thickness in Countercurrent Stratified Two -Phase Fllow (물-증기 역류 성층이상유동에서의 국부 평균 액체층 두께)

  • Kim, Hho-Jung;Kim, Kap
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.10 no.6
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    • pp.947-958
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    • 1986
  • 물-증기 역류 성층이상유동에서의 평균 액체층 두께가 여러가지 경사각과 종횡비에 따라 측정되었다. 난류유동에 있어서 전단응력분포의 선형화와 von Karman의 혼합길이 이론을 근거로 평균 액체층의 두께에 대한 관계식이 제시되었으며 실험결과와 잘 일치하였음을 보였다. 접촉면에서의 조파저항이 고려되지 않은 해석결과는, 수평 성층유동의 경우에, 평균 액체층 두께보다는 오히려 파곡까지의 액체층 두께를 예측하고 있는 것으로 나타났다. 또한 평균 액체층 두께에 대한 실험 상관관계식이 계산시 편의를 위해 쉽게 인지할 수 있는 매개변수들의 항들롤 제시되었다.

Design of Polarization-Insensitive Directional Couplers and Multimode Interference Couplers Integrated with Bragg Grating Waveguide (Bragg 격자구조가 집적된 편광 무의존성 방향성 결합기와 다중모드 간섭 결합기의 설계)

  • Ho, Kwang-Chun
    • Korean Journal of Optics and Photonics
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    • v.18 no.5
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    • pp.295-302
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    • 2007
  • This paper presents a rigorous comparison of the design characteristics of polarization-insensitive directional coupler (DC) and multimode interference (MMI) coupler based on rib type waveguides, by using longitudinal modal transmission-line theory (L-MTLT). It shows that the multimode mixing and interference property of MMI can be structurally designed through the continuous evolution of the two-mode coupling property of DC. It also compares and analyzes the coupling efficiency along with the coupling length and the wavelength between polarization-insensitive DC and MMI. From the design properties obtained, it demonstrates for the first time the integration of polarization-insensitive DC or MMI with a Bragg grating and evaluates precisely the filtering characteristics. The numerical results reveal that the DC, as long as it is designed to have the same coupling length for TE and TM modes, has better performance than the MMI in polarization-insensitive filtering behaviour. However, it shows that the MMI with much less coupling length than DC is preferred in the miniaturization of integrated devices.

On the Sediment Transport Characteristics of the Bottom Turbulent Boundary Layer (저면난류경계층(底面亂流境界層)의 저질이동특성(底質移動特性))

  • Kim, Nam Hyeong;Kiyoshi, Takikawa
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.13 no.2
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    • pp.267-277
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    • 1993
  • A finite element method(FEM) is presented and applied to the two-dimensional bottom turbulent boundary layer. The time-dependent incompressible motion of a viscous fluid is formulated by using the well-known Navier-Stokes equations and vorticity equation in terms of the velocity and pressure fields. The general numerical formulation is based on Galerkin method and solved by introducing the mixing length theory of Prandtl for eddy kinematic viscosity of a turbulent flow field. Numerical computations of the transport of sediment on an arbitrary sea-bed due to wave motion in the turbulent boundary layer are carried out. The results obtained by the FEM made clear the difference in characteristic features between the boundary layer due to oscillatory flow and the boundary layer due to wave motion.

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On mixing the Rayleigh-Ritz formulation with Hankel's function for vibration of fluid-filled functionally graded cylindrical shell

  • Hussain, Muzamal;Naeem, Muhammad Nawaz;Shahzad, Aamir;Taj, Muhammad;Asghar, Sehar;Fatahi-Vajari, Alireza;Singh, Rahul;Tounsi, Abdelouahed
    • Advances in Computational Design
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    • v.5 no.4
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    • pp.363-380
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    • 2020
  • In this paper, a cylindrical shell is immersed in a non-viscous fluid using first order shell theory of Sander. These equations are partial differential equations which are solved by approximate technique. Robust and efficient techniques are favored to get precise results. Employment of the Rayleigh-Ritz procedure gives birth to the shell frequency equation. Use of acoustic wave equation is done to incorporate the sound pressure produced in a fluid. Hankel's functions of second kind designate the fluid influence. Mathematically the integral form of the Lagrange energy functional is converted into a set of three partial differential equations. Throughout the computation, simply supported edge condition is used. Expressions for modal displacement functions, the three unknown functions are supposed in such way that the axial, circumferential and time variables are separated by the product method. Comparison is made for empty and fluid-filled cylindrical shell with circumferential wave number, length- and height-radius ratios, it is found that the fluid-filled frequencies are lower than that of without fluid. To generate the fundamental natural frequencies and for better accuracy and effectiveness, the computer software MATLAB is used.

Estimation of Allowable Bearing Capacity and Settlement of Deep Cement Mixing Method for Reinforcing the Greenhouse Foundation on Reclaimed Land (간척지 온실기초 보강을 위한 심층혼합처리공법의 허용지내력 및 침하량 산정)

  • Lee, Haksung;Kang, Bang Hun;Lee, Kwang-seung;Lee, Su Hwan
    • Journal of Bio-Environment Control
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    • v.30 no.4
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    • pp.287-294
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    • 2021
  • In order to expand facility agriculture and reduce greenhouse construction costs in reclaimed land, a greenhouse foundation method that satisfies economic feasibility and structural safety at the same time is required. As an alternative, the allowable bearing capacity and settlement were reviewed when the DCM(Deep cement mixing) method was applied among the soft ground reinforcement methods. To examine the applicability of the greenhouse foundation, the allowable bearing capacity and settlement were calculated by applying the theory of Terzaghi, Meyerhof, Hansen, and Schmertmann. In case of the diameter of 800mm and the width and length of the foundation of 4m, the allowable bearing capacity was 179kN/m2 and the settlement was 7.25mm, which satisfies the required bearing capacity and settlement standards. The calculation results were verified through FEM(Finite element method) analysis using the Mohr-Coulomb material model. The allowable bearing capacity was 169kN/m2 and the settlement was 2.52mm. The bearing capacity showed an error of 5.6% compared to calculated value, and the settlement showed and error of 65.4%. Through theoretical calculations and FEM analysis, it was confirmed that the allowable bearing capacity and settlement satisfies the design criteria as a greenhouse foundation when the width and length of the foundation were 4m. Based on the verified design values, it is expected to be able to present the foundation design criteria for greenhouses through empirical tests such as bearing capacity tests and long-term settlement monitoring.

Vertical Buoyant Jet in Tidal Water -Crossflowing Environment- (흐름 수역(水域)에서 연직상향부력(鉛直上向浮力)?)

  • Yoon, Tae Hoon;Cha, Young Kee;Kim, Chang Wan
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.7 no.1
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    • pp.11-22
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    • 1987
  • A plane buoyant jet discharged vertically upward into a crossflow is analyzed by numerical solution of the governing equations of continuity, momentum and constituent transport. The turbulent transport is modelled by the Prandtl's mixing length theory. In the numerical solution procedure, the governing equations are transformed by stream function and vorticity transport, non-dimensionalyzed by discharge velocity, slot width, and parameters representing flow characteristics, and solved by Gauss-Seidel iteration method with successive underrelaxation. The numerical experiments were performed for the region of established flow of buoyant jet in the range of discharge densimetric Froude number of 4 to 32 and in the range of velocity ratio of 8 to 15, which is the ratio of discharge velocity to crossflow velocity. Variations of velocities and temperatures, flow patterns and vorticity patterns of receiving water due to buoyant jet were investigated. Also investigated are the effects of velocity ratio and discharge densimetric Froude number on the trajectories of buoyant jet. Computed are velocities, temperatures and local densimetric Froude numbers along the trajectory of the buoyant jet. Spreading rate and dispersion ratio were analyzed in terms of discharge densimetric Froude number, local densimetric Froude number and distance from the source along the jet trajectory. It was noted that the similarity law holds in both the profiles of velocity and temperatures across the jet trajectory and the integral type analysis of Gaussian distribution is applicable.

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Dynamical Study on the Blasting with One-Free-Face to Utilize AN-FO Explosives (초유폭약류(硝油爆藥類)를 활용(活用)한 단일자유면발파(單一自由面發破)의 역학적(力學的) 연구(硏究))

  • Huh, Ginn
    • Economic and Environmental Geology
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    • v.5 no.4
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    • pp.187-209
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    • 1972
  • Drilling position is one of the most important factors affecting on the blasting effects. There has been many reports on several blasting factors of burn-cut by Messrs. Brown and Cook, but in this study the author tried to compare drilling positions of burn-cut to pyramid-cut, and also to correlate burn-cut effects of drilling patterns, not being dealt by Prof. Ito in his theory, which emphasized on dynamical stress analysis between explosion and free face. According to former theories, there break out additional tensile stress reflected at the free face supplemented to primary compressive stress on the blasting with one-free-face. But with these experimented new drilling patterns of burn-cut, more free faces and nearer distance of each drilling holes make blasting effects greater than any other methods. To promote the above explosive effect rationary, it has to be considered two important categories under-mentioned. First, unloaded hole in the key holes should be drilled in wider diameter possibly so that it breaks out greater stress relief. Second, key holes possibly should have closer distances each other to result clean blasting. These two important factors derived from experiments with, theories of that the larger the dia of the unloaded hole, it can be allowed wider secondary free faces and closes distances of each holes make more developed stress relief, between loaded and unloaded holes. It was suggested that most ideal distance between holes is about 4 clearance in U. S. A., but the author, according to the experiments, it results that the less distance allow, the more effective blasting with increased broken rock volume and longer drifted length can be accomplished. Developed large hole burn-cut method aimed to increase drifting length technically under the above considerations, and progressive success resulted to achieve maximum 7 blasting cycles per day with 3.1m drifting length per cycle. This achievement originated high-speed-drifting works, and it was also proven that application of Metallic AN-FO on large hole burn-cut method overcomes resistance of one-free-face. AN-FO which was favored with low price and safety handling is the mixture of the fertilizer or industrial Ammonium-Nitrate and fuel oil, and it is also experienced that it shows insensible property before the initiation, but once it is initiated by the booster, it has equal explosive power of Ammonium Nitrate Explosives (ANE). There was many reports about AN-FO. On AN-FO mixing ratio, according to these experiments, prowdered AN-FO, 93.5 : 6.5 and prilled AN-FO 94 : 6, are the best ratios. Detonation, shock, and friction sensities are all more insensitive than any other explosives. Residual gas is not toxic, too. On initation and propagation of the detonation test, prilled AN-FO is more effective than powered AN-FO. AN-FO has the best explosion power at 7 days elapsed after it has mixed. While AN-FO was used at open pit in past years prior to other conditions, the author developed new improved explosives, Metallic AN-FO and Underwater explosive, based on the experiments of these fundmental characteristics by study on its usage utilizing AN-FO. Metallic AN-FO is the mixture of AN-FO and Al, Fe-Si powder, and Underwater explosive is made from usual explosive and AN-FO. The explanations about them are described in the other paper. In this study, it is confirmed that the blasting effects of utilizing AN-FO explosives are very good.

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