Lid-Driven 캐비티 내의 혼합대류에 의한 원형 실린더의 운동 특성에 관한 수치적 연구

김다용(Da Yong Kim),윤현식(Hyun Sik Yoon),하만영(Man Yeong Ha) 대한기계학회 2010 대한기계학회 춘추학술대회 Vol.2010 No.5

본 논문은 좌측의 벽면이 일정한 속도로 움직이는 Lid-driven 캐비티 내의 혼합대류에 의에 부유하는 원형 실린더의 운동 특성 규명하는 연구를 수행하였다. 이차원 원형실린더의 운동 특성을 해석하기 위해 Direct forcing/Fictitious domain 방법을 사용하였다. Lid-driven 캐비티 내의 고체와 유체의 밀도 비에 따란 원형 실린더의 운동 특성을 연구하기 위해 밀도비를 변경하면서(0.97, 0.98, 0.99, 1.01, 1.02, 1.03) 수치해석을 수행하였으며 캐비티 내의 Richardson number는 1로 고정하였다. The present study numerically investigates the motion of a solid body suspended in the lid-driven cavity with mixed convection. Flows are driven by the left lid, which slides in its own plane constant velocty. A two-dimensional circular cylinder levitated thermally has been simulated by using the direct forcing /fictitious domain (DF/FD) method. In order to identify the effect of fluid density on circular cylinder motion in lid-driven cavity, the computation is carried out for wide ranges of the fluid density ratio (=0.97, 0.98, 0.99, 1.01, 1.02, 1.03) and fixed Richardson number (=1).

원형 실린더를 포함한 Lid-driven 캐비티 내의 혼합대류에 관한 수치적 연구

정광봉(Guangfeng Zheng),윤현식(Hyun Sik Yoon),하만영(Man Yeong Ha),박용갑(Yong Gap Park) 대한기계학회 2011 대한기계학회 춘추학술대회 Vol.2011 No.5

내부에 원형 실린더가 들어있는 Lid-driven 캐비티 내의 혼합대류에 대한 2차원에서의 수치적 연구를 진행하였다. 본 연구에서 유한체적법에 기초한 가상 경계기법(Immersed Boundary Method)을 이용하여 Gr 수를 10?으로 고정하고 서로 다른 3 가지 Ri 수 10, 0.4 및 0.1 의 범위에서 혼합대류 현상에 대해 연구를 수행하였다. 원형 실린더의 크기와 위치를 변화시키면서 원형 실린더가 캐비티 내의 유동 및 열전달에 미치는 영향을 세부적으로 연구하였다. 연구 결과 캐비티 내의 유동은 원형 실린더의 크기의 변화에 영향이 작았지만 크기가 커질수록 벽면 평균 Nu 값이 더 크고 캐비티 내부 유동과 열전달이 원형 실린더의 위치변화에 강한 영향을 받는 것을 발견하였다. Two-dimensional numerical simulations were carried out for the mixed convection in the lid-driven cavity with the inner circular cylinder at three different Richadson numbers of 0.1, 0.4 and 10 under the fixed Grashof number of 10?. The immersed boundary method based on the finite volume method was adopted in order to model the boundary of the circular cylinder in the cavity. The effects of the location and size of the inner circular cylinder on the flow and heat transfer in the cavity were carefully investigated in the present study. as a result, the mean Nusselt number is found to increase with the radius of the inner circular cylinder increasing, but the flow fields have nearly no change, and the flow and heat transfer are strongly affected from the changing of the location of the inner circular cylinder.

Isothermal and non-isothermal viscoelastic flow of PTT fluid in lid-driven polar cavity

Mercan, Hatice,Atalik, Kunt 한국유변학회 2012 Korea-Australia rheology journal Vol.24 No.4

The isothermal and non-isothermal viscoelastic flow of Phan-Thien-Tanner (PTT) fluids is considered in lid-driven polar cavity geometry, using a numerical solution method with parameter continuation technique. Thermoelastic effects, in terms of elastic/elongational effects and viscous dissipation, are demonstrated by the changes in vortical structure, temperature/stress distributions and heat transfer characteristics in the curved cavity. Central vortex/maximum temperature location shifts are observed under elastic and elongational (strain hardening and strain softening/shear thinning) effects for isothermal and non-isothermal conditions. The growth in size and strength of a secondary vortex is denoted in the downstream stationary corner of the cavity for the viscoelastic fluid under strain hardening, which also introduces an increase in stress gradients. Viscous heating is observed with elongational effects near the central vortex in the cavity. Stress components and their gradients decrease under viscous dissipation. The changes in temperature field and heat transfer properties in the cavity are revealed.

Analysis of mixed convection in an inclined lid-driven cavity with a wavy wall

Said Mekroussi,Driss Nehari,Mohamed Bouzit,Nord-Eddine Sad Chemloul 대한기계학회 2013 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.27 No.7

A numerical study is performed to analyze the mixed convection flow and heat transfer in a lid-driven cavity with sinusoidal wavy bottom surface. The cavity vertical walls are insulated while the wavy bottom surface is maintained at a uniform temperature higher than the top lid. A finite volume method is used to solve numerically the non-dimensional governing equations. The tests were carried out for various inclination angles ranging to 0° from 180° and number of undulation varied from 4 to 6, while the Prandtl number was kept constant Pr = 0.71. Three geometrical configurations were used namely four, five and six. The distributions of streamlines and isotherms,and the variations of local and average Nusselt numbers with the inclination angle are presented. The results of this investigation illustrate that the average Nusselt number at the heated surface increases with an increase of the number of undulations as well as the angle of inclination.

A comparison study on high-order bounded schemes: Flow of PTT-linear fluid in a lid-driven square cavity

Yapici, Kerim 한국유변학회 2012 Korea-Australia rheology journal Vol.24 No.1

In this computational study, the convergence, stability and order of accuracy of several different numerical schemes are assessed and compared. All of the schemes considered were developed using a normalized variable diagram. Two test cases are considered: (1) two-dimensional steady incompressible laminar flow of a Newtonian fluid in a square lid-driven cavity; and (2) creeping flow of a PTT-linear fluid in a lid-driven square cavity. The governing equations are discretized to varying degrees of refinement using uniform grids, and solved by using the finite volume technique. The momentum interpolation method (MIM) is employed to evaluate the face velocity. Coupled mass and momentum conservation equations are solved through an iterative SIMPLE (Semi-Implicit Method for Pressure-Linked Equation) algorithm. Among the higher-order and bounded schemes considered in the present study, only the CLAM, COPLA, CUBISTA, NOTABLE, SMART and WACEB schemes provide a steady converged solution to the prescribed tolerance of $1{ \times}10^{-5}$ at all studied Weissenberg ($We$) numbers, using a very fine mesh structure. It is found that the CLAM, COPLA, CUBISTA, SMART and WACEB schemes provide about the same order of accuracy that is slightly higher than that of the NOTABLE scheme at low and high Weissenberg numbers. Moreover, flow structures formed in the cavity, $i.e.$ primary vortex, are captured accurately up to $We$ = 5 by all converged schemes.

A comparison study on high-order bounded schemes:Flow of PTT-linear fluid in a lid-driven square cavity

Kerim Yapici 한국유변학회 2012 Korea-Australia rheology journal Vol.24 No.1

In this computational study, the convergence, stability and order of accuracy of several different numerical schemes are assessed and compared. All of the schemes considered were developed using a normalized variable diagram. Two test cases are considered: (1) two-dimensional steady incompressible laminar flow of a Newtonian fluid in a square lid-driven cavity; and (2) creeping flow of a PTT-linear fluid in a lid-driven square cavity. The governing equations are discretized to varying degrees of refinement using uniform grids, and solved by using the finite volume technique. The momentum interpolation method (MIM) is employed to evaluate the face velocity. Coupled mass and momentum conservation equations are solved through an iterative SIMPLE (Semi-Implicit Method for Pressure-Linked Equation) algorithm. Among the higher-order and bounded schemes considered in the present study, only the CLAM, COPLA, CUBISTA, NOTABLE, SMART and WACEB schemes provide a steady converged solution to the prescribed tolerance of 110-5 at all studied Weissenberg (We) numbers, using a very fine mesh structure. It is found that the CLAM, COPLA, CUBISTA, SMART and WACEB schemes provide about the same order of accuracy that is slightly higher than that of the NOTABLE scheme at low and high Weissenberg numbers. Moreover, flow structures formed in the cavity, i.e. primary vortex, are captured accurately up to We = 5 by all converged schemes.

실린더를 포함한 2 차원 Lid-Driven 캐비티 내의 유동과 열전달에 관한 수치해석

이진수(Jin-Su Lee),이대성(Dae-Sung Lee),하만영(Man-Yeong Ha),윤현식(Hyun-Sik Yoon) 대한기계학회 2005 대한기계학회 춘추학술대회 Vol.2005 No.11

The Numerical simulation of steady two dimensional flow with heat transfer in lid-driven cavity with moving cylinder. The validation of lid-driven cavity flow is done using the immersed boundary method and obtained for configuration with a Reynolds number up to 1000 with oscillating or stationary cylinder. Thus frequencies of cylinder are primary variables that based on lid velocity and total length of cavity, Fo=0.25. Results are compared with those in the literature. and they are in good agreement. Heat transfer from cylinder to fluid is increased when the cylinder oscillates.

Lattice Boltzmann simulation of solid particles behavior in a three-dimensional lid-driven cavity flow

Safdari, A.,Kim, K.C. Pergamon Press ; Elsevier Science Ltd 2014 COMPUTERS & MATHEMATICS WITH APPLICATIONS - Vol.68 No.5

This paper reports the behavior of solid particles in a three-dimensional lid-driven cavity. The prediction of solid particle dynamics through a fluid has been an important research topic over the past few decades. Difficulties arise when trying to understand the interactions between the particle and surrounding fluid. Therefore, the Lattice Boltzmann Method (LBM) was proposed to analyze three-dimensional cubic lid-driven cavity flow at range of Reynolds numbers. The mesoscale numerical scheme of the Single Relaxation Time (SRT) lattice Boltzmann method was used to solve the equation of flow fluid. The 4th Runge-Kutta method was applied to determine the effects of the drag force on the particle, and the hard sphere model was functioned to calculate the collisions between the particle and walls. The dynamics of a solid particle using a numerical simulation of LBM showed good agreement with the established benchmark results from previous studies. In addition, the results showed that the particle trajectories are critically dependent on the magnitude of the density, diameter and vortex behavior in the cavity. Overall, the results highlight the applicability of the present method to a range of applications.

A numerical study on mixed convection in a lid-driven cavity with a circular cylinder

G. F. Zheng,하만영,윤현식,Y. G. Park 대한기계학회 2013 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.27 No.1

A two-dimensional numerical simulation is carried out in this study to investigate mixed convection in a lid-driven cavity with an isothermal circular cylinder. The simulation is conducted at three Reynolds numbers of Re = 100, 500, and 1000 under a fixed Grashof number of Gr = 105. The top wall of the cavity moves to the right at a constant velocity and is kept at a low temperature of Tc, whereas the stationary bottom wall is kept at a constant high temperature of Th. The immersed-boundary method, which is based on the finite volume method, is adopted for the boundary of the circular cylinder that is present in the square cavity. The present study aims to investigate the effects of circular cylinder on fluid flow and heat transfer in a cavity at different locations. The fluid flow and heat transfer characteristics in the cavity strongly depend on the position of the circular cylinder as well as on the relative magnitude of the forced convection and the natural convection caused by the movement in the top wall of the cavity and the heating at the hot bottom wall, respectively.

Flow structure for Power-Law fluids in lid-driven arc-shape cavities

Mercan, Hatice,Atalik, Kunt 한국유변학회 2011 Korea-Australia rheology journal Vol.23 No.2

In this paper the lid-driven flow of a Power-Law fluid in arc-shape cavities is studied. Two different arc cavity cross sections are considered with arc angle ratios r=1/2 and r=1/3. The unsteady stream-function-vorticity formulation is adopted together with a Power-Law constitutive relation. Body-fitted coordinate transformation is applied to generate orthogonal computational grids. The equations are discretized in space using a second order finite difference numerical method. Time integration is performed using fourth order Runge-Kutta explicit scheme. The combined effects of inertia, shear thinning/shear thickening and curved geometry on the vortical structure and velocity profiles are shown. The results are compared to Newtonian fluid case. It is found that under inertia, shear thinning effects lead to the early formation and growth of secondary vortices in the curved cavity, however shear thickening has an opposite effect.