• Title/Summary/Keyword: Convective equation

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An Implicit Numerical Method for Two-Dimensional Tidal Computation (음해법에 의한 2차원 조류유동 계산법)

  • Sun-Young Kim;Mu-Seok Song
    • Journal of the Society of Naval Architects of Korea
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    • v.35 no.1
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    • pp.1-14
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    • 1998
  • A two-dimensional numerical model for tidal currents based on the depth averaged equation is developed. The mode1 employs a rectangular grid system for its simplicity in the application of complicate coastal shore lines. To raise computing efficiency, implicit approximate factorization scheme is implemented in solving governing equations. An upwind-differencing is used to discretize convective terms, which provides a numerical dissipation automatically and suppresses any oscillations caused by nonlinear instabilities. Some numerical tests are made against the analytic solutions of a linearized shallow water equation to validate the developed numerical scheme, and comparisons of the model prediction with the analytic solution are satisfactory. As a real application, the tidal currents are computed on the Inchon area where the tidal currents are important for the design of new canal which is under construction.

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Analysis of forced convective laminar film boiling heat transfer on vertical surface (垂直平板에서의 强制對流 膜沸騰 流動의 熱傳達解析)

  • 이규식;최영돈
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.11 no.3
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    • pp.425-436
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    • 1987
  • Accurate predictions of heat transfer coefficient of vertical laminar film-boiling are very important in many engineering applications. There are many predictions, however they are not exact as yet, since they have used the assumption of constant thermodynamic properties in the analysis. In this paper, heat transfer of vertical film boiling was analysized by Runnge Kutta method using veriable thermodynamic properties. 1/4 interval method was exployed for the prediction of unknown wall boundary condition. Numerical computations were performed with varying the wall temperature and the free stream velocity of liquid. Results show that assumption of constant thermodynamic properties induced considerable error in predicting the heat transfer coefficient, friction factor, film thickness, and critical length for transition to turbulent flow. Comparision of the predicted heat transfer coefficient of present analysis with that from Bromley's correlation shows that the use of general latent heat in Bromely equation instead of modified latent heat is more desireable since it makes the coefficient of Bromley equation into constant.

A study on the forced convection heat transfer in the vertical copper tube at uniform wall heat flux (균일한 열유속에서의 수직동관내의 강제대류 열전달에 관한 연구)

  • Baek, Go-Gil;Cha, Ji-Yeong;Seo, Jeong-Yun
    • The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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    • v.8 no.4
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    • pp.213-220
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    • 1979
  • A number of methods has been developed for calculation of heat transfer in the vertical round tube under conditions of forced convection with uniform heat flux at wall. I would like to express hereby one of applications of this study in the design of heat exchanger instruments for water flow at $15.8^{\circ}C(p_r=8)$ used frequently in our daily life. Also all the results are investigated for forced convective heat transfer in the case of heated water-flow at uniform wall heat flux in the vortical round copper tube, where the ratio of length to diameter will be 44. They are well in agreement with Gratz and Kraussold equation respectively in laminar and transition flow range. In turbulent flow in the range from Re=10,000 to 65,000, the experimental formula Is show as follows ; Nu=0.023 $R_e^{0.814}\;P_r^{0.4}$. And this is agreed with Dittus - Boelter equation when Reynolds number exponent increases from 0.80 to 0.814.

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Analysis of Temperature Distribution and slip in Rapid Thermal Processing (급속 열처리시 실리콘 웨이퍼의 온도분포와 슬립 현상의 해석)

  • Lee, Hyouk;Yoo, Young-Don;Earmme, Youn-Young;Shin, Hyun-Dong;Kim, Choong-Ki
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.16 no.4
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    • pp.609-620
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    • 1992
  • A numerical solution of temperature and thermally induced stress in a wafer during rapid thermal processing (R.T.P) is obtained, and an analysis of onset and propagation of slip is performed and compared with experiment. In order to calculate temperature distribution of a wafer in R.T.P system, heat conduction equation that incorporated with radiative and convective heat transfer model is solved, and the solution of the equation is calculated numerically using alternating direction implicit (A.D.I) method. In dealing with radiative heat transfer, a partially transparent body that absorbs the radiation energy is assumed and this transparent body undergoes multiple internal reflections and absorptions. Two dimensional (assuming plane stress) thermoelastic constitutive equation is used to calculate thermal stress induced in a wafer and finite element method is employed to solve the equation numerically. The stress resolved in the slip directions on the slip planes of silicon is compared with the yield stress of silicon in order to predict the slip. The result of the analysis shows that the wafer temperature at which slip occurs is affected by the heating rate of the R.T.P system. It is observed that once slip occurs in the wafer, the slip grows.

NUMERICAL ANALYSIS OF NON-EQUILIBRIUM HYDRATE PELLET DECOMPOSITION (하이드레이트 펠릿의 비평형 분해과정 수치해석)

  • Kang, Jung-Ho;Nam, Jin-Hyun;Kim, Charn-Jung;Song, Myung-Ho
    • Journal of computational fluids engineering
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    • v.13 no.4
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    • pp.50-57
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    • 2008
  • The prediction of hydrate pellet decomposition characteristics is required to design the regasification process of GTS (gas to solid) technology, which is considered as an economic alternative for LNG technology to transport natural gas produced from small and stranded gas wells. Mathematical model based on the conservation principles, the phase equilibrium relation, equation of gas state and phase change kinetics was set up and numerical solution procedure employing volume averaged fixed grid formulation and extended enthalpy method are implemented. Initially, porous methane hydrate pellet is at uniform temperature and pressure within hydrate stable region. The pressure starts to decrease with a fixed rate down to the final pressure and is kept constant afterwards while the bounding surface of pellet is heated by convection. The predicted convective heat and mass transfer accompanied by the decomposed gas flow through hydrate/ice solid matrix is reported focused on the comparison of spherical and cylindrical pellets having the same effective radius.

ANALYSIS OF TURBULENT HEAT TRANSFER FROM STAGGERED PIN-FIN ARRAYS WITH DIAMOND SHAPED ELEMENTS AT VARIOUS GEOMETRICAL CONFIGURATIONS (엇갈린 다이아몬드형 핀휜의 형상에 따른 난류열전달 성능해석)

  • Cho, A.T.;Kim, K.Y.
    • Journal of computational fluids engineering
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    • v.13 no.2
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    • pp.20-26
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    • 2008
  • A numerical study is carried out to analyze the steady three-dimensional turbulent flow and convective heat transfer in a staggered pin-fin array with diamond shaped elements at various geometrical configurations. Steady Reynolds-averaged Navier-Stokes equations and energy equation are solved using a finite volume based solver. Shear stress transport (SST) model is used as turbulence closure. The computational domain is composed of one pitch of pin-fin displacement with periodic boundary conditions on the surfaces normal to the streamwise direction and the cross-streamwise direction. The numerical results for Nusselt number and friction factor are validated with experimental results. The effects of pin angle, pin height and pitch on Nusselt number, friction factor and efficiency index are investigated.

Flow analysis and design optimization of a mixed-flow fan (사류송풍기의 유동해석 및 최적설계)

  • Seo, Seoung-Jin;Jun, Jae-Wook;Kim, Kwang-Yong
    • Proceedings of the KSME Conference
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    • 2001.06e
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    • pp.684-689
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    • 2001
  • In this study, three-dimensional viscous flow analysis and optimization are presented for the design of a mixed-flow fan. Steady, imcompressible, three-dimensional Reynolds averaged Navier-Stokes equations are used as governing equations, and standard $k-{\varepsilon}$ turbulence model is chosen as a turbulence model. Governimg equations are discretized using finite volume method. Upwind difference scheme is used for the discretization of the convective term and SIMPLEC algorithm is used as a velocity-pressure correction procedure. The computational results are compared with the results obtained by TASCflow. For the numerical optimization of the design, objective function is defined as a ratio of generation of the turbulent energy to pressure head. Sweep angles are used as design variables.

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A Numerical Study of Heat and Mass Transfer Phenomena for Thermal Protection Material (열보호재료의 열 및 물질전달 현상에 관한 수치해석적 연구)

  • Kim, Jung-Hoon;Kwon, Chang-Oh;Seo, Jeong-Il;Bai, Cheol-Ho;Song, Dong-Joo
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.23 no.9
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    • pp.1201-1212
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    • 1999
  • A numerical analysis is performed to predict the thermal response and ablation rate for charring or non-charring material which is designed to be used as thermal protection system (TPS). The numerical program composed of in-depth energy balance equation and the aerotherm chemical equilibrium (ACE) program. The ACE program calculates various thermochemical state from ablation products. The developed numerical program is verified by comparing the reported results from literature. The sensitivity tests for input parameters are performed. The thermal behavior of ablating material is mainly affected by density of ablating material, convective heat transfer coefficient and recovery enthalpy of flow field.

Numerical simulations of radiative and convective heat transfer in the cylinder of a diesel engine (디이젤엔진내의 복사열전달 효과에 관한 수치해석적 연구)

  • 임승욱;김동우;이준식
    • Journal of the korean Society of Automotive Engineers
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    • v.14 no.2
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    • pp.54-64
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    • 1992
  • During combustion process in a diesel engine radiation heat transfer is the same order of magnitude as the convection heat transfer. An approximation of heat and momentum source distributions is applied at a level consistent with those used in modelling the soot distribution and the turbulence instead of modelling the fuel spray and the chemical kinetics. This paper illustrates a use of the third order spherical harmonics approximation to the radiative transfer equation and delta-Eddington approximation to the scattering phase function for droplets in the flow. Results are obtained numerically by a time marching finite difference scheme. This study aims to compare heat transfer with convection heat transfer and to investigate the importance of scattering by fuel droplets and of accounting for spatial variations in the extinction coefficient on the radiative heat flux distributions at the walls of a disc shaped diesel engine.

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Mixed Convection in a Horizontal Annulus with a Rotating Cylinder (하나의 실린더가 회전하는 수평 환형 공간에서의 혼합 대류)

  • Yoo Joo-Sik;Ha Dae-Hong
    • Journal of computational fluids engineering
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    • v.6 no.3
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    • pp.1-9
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    • 2001
  • Mixed convection in a horizontal annulus is considered, and the effect of a forced flow on the natural convective flow is investigated. The inner cylinder is hotter than the outer cylinder, and the outer cylinder is rotating with constant angular velocity with its axis at the center of the annulus. The unsteady streamfunction-vorticity equation is solved with a finite difference method. For the fluid with Pr=0.7, there appear flows with two eddies, one eddy, or no eddy according the Rayleigh and Reynolds numbers. The rotation of the outer cylinder reduces the heat transfer rate at the wall of the annulus. The oscillatory multicellular flow of a low Prandtl number fluid with Pr=0.01 can be effectively suppressed by the forced flow.

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