Natural convection in a square enclosure with different positions and inclination angles of an elliptical cylinder Part I: A vertical array of one elliptical cylinder and one circular cylinder

Park, Seong Hyun,Seo, Yeong Min,Ha, Man Yeong,Park, Yong Gap Elsevier 2018 INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER - Vol.126 No.2

<P><B>Abstract</B></P> <P>This paper numerically investigates the two-dimensional natural convection in a square enclosure with a vertical array of a hot elliptical cylinder and a hot circular cylinder with Rayleigh numbers in the range of <SUP> 10 4 </SUP> ⩽ Ra ⩽ <SUP> 10 6 </SUP> . An immersed boundary method was used to capture the wall boundary of the cylinders. The effects of the position and inclination angle ϕ of the elliptical cylinder were investigated. When the Rayleigh number increases to <I>Ra</I> = 10<SUP>6</SUP>, the numerical solutions reach an unsteady state for all cases of the lower elliptical cylinder and the cases of the upper elliptical cylinder except at ϕ = 90 ° . The transition of the flow regime from unsteady state to steady state depends on the flow direction and the space between the upper cylinder and top wall of the enclosure due to the changes in the inclination angle of the elliptical cylinder. At <I>Ra</I> = 10<SUP>6</SUP> in the case of upper elliptical cylinder at ϕ = 0 ° , the time- and surface-averaged Nusselt numbers for the walls of the enclosure increase by about 1.99% compared to the case of two circular cylinders. The thermal performance and flow stability were influenced by the position and inclination angle of the elliptical cylinder.</P> <P><B>Highlights</B></P> <P> <UL> <LI> Two-dimensional numerical simulations were conducted for the natural convection. </LI> <LI> The Immersed Boundary Method was used, based on the Finite Volume Method. </LI> <LI> The transition of the flow regime was investigated at <I>Ra</I> = 10<SUP>6</SUP> according to <I>ϕ</I>. </LI> <LI> The effects of <I>ϕ</I> on the heat transfer characteristics are highlighted. </LI> </UL> </P>

The natural convection in a square enclosure with two hot inner cylinders, Part I: The effect of one elliptical cylinder with various aspect ratios in a vertical array

Cho, Hyun Woo,Park, Yong Gap,Ha, Man Yeong Elsevier 2018 INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER - Vol.125 No.-

<P><B>Abstract</B></P> <P>This study numerically investigates the two-dimensional natural convection in a square enclosure with a vertical array of one circular cylinder and one elliptical cylinder at Rayleigh numbers of 10<SUP>4</SUP> ≤ <I>Ra</I> ≤ 10<SUP>6</SUP>. A simulation was carried out based on the immersed boundary method to obtain an accurate solution. The effects of the aspect ratio of the elliptical cylinder in the range of 0.25 ≤ <I>AR</I> ≤ 4.00 were investigated. When the Rayleigh number increases to <I>Ra</I> = 10<SUP>6</SUP>, the numerical solutions reach an unsteady state for all cases of the lower elliptical cylinder and the case of the upper elliptical cylinder except at <I>AR</I> = 2.00 and <I>AR</I> = 4.00. The transition of the flow regime from the unsteady state to the steady state depends on the variation in the ratio of the elliptical cylinder. In addition, in the case of the upper elliptical cylinder at <I>AR</I> = 0.50 the time- and surface-averaged Nusselt numbers for the walls of the enclosure increase by 2.1% in the case of two circular cylinders at <I>Ra</I> = 10<SUP>6</SUP>.</P> <P><B>Highlights</B></P> <P> <UL> <LI> Two-dimensional numerical simulations were conducted for the natural convection. </LI> <LI> The Immersed Boundary Method was used, based on the Finite Volume Method. </LI> <LI> The effects of the aspect ratio of the elliptical cylinder were investigated. </LI> <LI> The heat transfer characteristics over time were investigated. </LI> <LI> The transition of the flow regime depends on the variation in the aspect ratio. </LI> </UL> </P>

Forced convection heat transfer from the helically twisted elliptic cylinder inspired by a daffodil stem

Yoon, Hyun Sik,Kim, Hyo Ju,Wei, Duck Jae Pergamon Press 2018 International journal of heat and mass transfer Vol. No.

<P><B>Abstract</B></P> <P>The present study is an original research for the forced convection heat transfer around a helically twisted elliptic (<I>HTE</I>) cylinder inspired by a daffodil stem. Also, this study is an initial investigation to find the effect of the Reynolds number (<I>Re</I>) in the laminar flow regime. We carried out numerical simulations to investigate the flow and heat transfer around the <I>HTE</I> cylinder in 60 ⩽ Re ⩽ 150 and Prandtl number (<I>Pr</I>) of 0.7. The circular cylinder is considered for the purpose of the comparison. The drag and lift fluctuation for the HTE cylinder are much smaller than those of the smooth cylinder. The decreasing rate of Strouhal number ( St ) for the <I>HTE</I> cylinder to that for the smooth cylinder is about 4–7% in the present Reynolds number range. The smaller St of the <I>HTE</I> cylinder than the smooth cylinder associate a longer vortex formation length of the <I>HTE</I> cylinder. The three-dimensional (3D) geometry of the HTE cylinder formed the spanwise variation of the Nusselt number (<I>Nu</I>), resulting in the sinusoidal profiles. This spanwise variation of the Nusselt number is identified by the flow structures and the isotherms distribution. The time- and total surface-averaged Nusselt number of the <I>HTE</I> cylinder decreases from about 1.2% to 2.8% in the present <I>HTE</I> configuration and <I>Re</I> range, compared to the smooth cylinder.</P> <P><B>Highlights</B></P> <P> <UL> <LI> A helically twisted elliptic (<I>HTE</I>) cylinder based on biomimetic is considered. </LI> <LI> The forced convection around the <I>HTE</I> cylinder is originally investigated. </LI> <LI> The effect of <I>Re</I> on the flow around the <I>HTE</I> cylinder is initially researched. </LI> <LI> The local Nu identifies the effect of the <I>HTE</I> geometry on the heat transfer. </LI> </UL> </P>

타원형 실린더의 각도 변화가 사각 밀폐계 내부의 자연대류 현상에 미치는 영향

손용진(Yong Jin Son),하만영(Man Yeong Ha) 대한설비공학회 2018 설비공학 논문집 Vol.30 No.2

This study investigated the effect of variation in the angle of the elliptic cylinder as well as the presence of circular cylinder on natural convection inside a square enclosure. The Rayleigh number was varied between 10<SUP>3</SUP> and 10<SUP>6</SUP>, and the Prandtl number was fixed to 0.7. In the present study, the angle of the elliptic cylinder was changed from 0° to 90°, and the perimeter of the elliptic cylinder was same as that of the circular cylinder. The immersed boundary method was used to capture the virtual wall boundary of the inner cylinder. With the increasing angle of the elliptic cylinder, the surface-averaged Nusselt numbers on the cylinder and the enclosure increased. In the Rayleigh number range considered in the present study, the surface-averaged Nusselt number on the elliptic cylinder over = 45° was higher than that of the circular cylinder. The effect of elliptic cylinder’s angle on natural convection in the enclosure was analyzed according to the flow and thermal fields, and the distributions of the Nusselt number.

Natural convection in a square enclosure with two hot inner cylinders, Part II: The effect of two elliptical cylinders with various aspect ratios in a vertical array

Cho, Hyun Woo,Ha, Man Yeong,Park, Yong Gap Elsevier 2019 INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER - Vol.135 No.-

<P><B>Abstract</B></P> <P>In this study, two-dimensional numerical simulations were conducted for the natural convection in a cold square enclosure with a vertical array of two hot elliptical cylinders at Rayleigh numbers of 10<SUP>4</SUP> ≤ <I>Ra</I> ≤ 10<SUP>6</SUP>. We observed the effect of the aspect ratios of the elliptical cylinders in the range of 0.25 ≤ <I>AR</I> ≤ 4.00. The immersed boundary method (IBM), which is based on the finite volume method (FVM), was used to capture the virtual wall boundary of the cylinders. The transition of the flow regime from steady state to unsteady state depends on the aspect ratio at <I>Ra</I> = 10<SUP>6</SUP>. At low Rayleigh numbers of <I>Ra</I> = 10<SUP>4</SUP> and <I>Ra</I> = 10<SUP>5</SUP>, the time- and surface-averaged Nusselt numbers for the enclosure walls increase with the <I>AR</I> of the upper elliptical cylinder. At a relatively high Rayleigh number of <I>Ra</I> = 10<SUP>6</SUP>, the time- and surface-averaged Nusselt numbers of the enclosure walls increase by 3.9% at the upper elliptical cylinder at <I>AR</I> = 0.50 and at the lower elliptical cylinder at <I>AR</I> = 2.00 compared to two circular cylinders.</P> <P><B>Highlights</B></P> <P> <UL> <LI> Two-dimensional numerical simulations were conducted for the natural convection. </LI> <LI> The Immersed Boundary Method was used, based on the Finite Volume Method. </LI> <LI> The effects of the aspect ratio of the elliptical cylinder in the range of 0.25 ≤ AR ≤ 4.00 were observed. </LI> <LI> The transition of the flow regime from steady state to unsteady state depends on the aspect ratio at <I>Ra</I> = 10<SUP>6</SUP>. </LI> </UL> </P>

The effect of Reynolds number on the elliptical cylinder wake

Xiaoyu Shi,Md. Mahbub Alam,Honglei Bai,Hanfeng Wang 한국풍공학회 2020 Wind and Structures, An International Journal (WAS Vol.30 No.5

This work numerically investigates the effects of Reynolds number ReD (= 100 - 150), cross-sectional aspect ratio AR = ( 0.25 -1.0), and attack angle α (= 0 - 90) on the forces, Strouhal number, and wake of an elliptical cylinder, where ReD is based on the freestream velocity and cylinder cross-section height normal to the freestream flow, AR is the ratio of the minor axis to the major axis of the elliptical cylinder, and α is the angle between the cylinder major axis and the incoming flow. At ReD = 100, two distinct wake structures are identified, namely ‘Steady wake’ (pattern I) and ‘Karman wake followed by a steady wake (pattern II)’ when AR and α are varied in the ranges specified. When ReD is increased to 150, an additional wake pattern, ‘Karman wake followed by secondary wake (pattern III)’ materializes. Pattern I is characterized by two steady bubbles forming behind the cylinder. Pattern II features Karman vortex street immediately behind the cylinder, with the vortex street transmuting to two steady shear layers downstream. Inflection angle αi = 32, 37.5 and 45 are identified for AR = 0.25, 0.5 and 0.75, respectively, where the wake asymmetry is the greatest. The αi effectively distinguishes the dependence on α and AR of force and vortex shedding frequency at either ReD. In Pattern III, the Karman street forming behind the cylinder is modified to a secondary vortex street. At a given AR and α, ReD = 150 renders higher fluctuating lift and Strouhal number than ReD = 100.

A numerical study on the three-dimensional natural convection with a cylinder in a long rectangular enclosure. Part II: Inclination angle effect of the elliptical cylinder

Seo, Young Min,Ha, Man Yeong,Park, Yong Gap Elsevier 2019 INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER - Vol.131 No.-

<P><B>Abstract</B></P> <P>This study conducted three-dimensional numerical simulations of the natural convection in a cold, long, rectangular enclosure containing a hot elliptical cylinder. The immersed boundary method (IBM) was used to capture the virtual wall boundary of the inner cylinder based on the finite volume method (FVM). The effect of inclination angles of 0° ≤ <I>ψ</I> ≤ 90° were analyzed by a visualization technique with various radii of the cylinder at a relatively high Rayleigh number of <I>Ra</I> = 10<SUP>6</SUP>. The variation in the flow and thermal structures and the corresponding heat transfer characteristics were investigated in regard to the transition of the flow regime from the steady state to the unsteady state. The heat transfer characteristics from the cylinder surface and enclosure walls were also addressed. As a result, the heat transfer characteristics were improved by the variation in the inclination angle in accordance with the mean radius of the elliptical cylinder.</P> <P><B>Highlights</B></P> <P> <UL> <LI> Three-dimensional numerical simulations were conducted for the natural convection. </LI> <LI> The Immersed Boundary Method was used, based on the Finite Volume Method. </LI> <LI> The effect of inclination angle of the elliptical cylinder was investigated. </LI> <LI> The flow and thermal fields and the three-dimensionality were investigated. </LI> <LI> The effects of inclination angle on the heat transfer characteristics are highlighted. </LI> </UL> </P>

타원 기둥에 의한 벡터 중력 및 중력 변화율 텐서 반응식

임형래 한국지구물리.물리탐사학회 2023 지구물리와 물리탐사 Vol.26 No.1

This study derives the expressions of vector gravity and gravity gradient tensor due to an elliptical cylinder. The vector gravity for an arbitrary three-dimensional (3D) body is obtained by differentiating the gravitational potential, including the triple integral, according to the shape of the body in each axis direction. The vector gravity of the 3D body with axial symmetry is integrated along the axial direction and reduced to a double integral. The complex Green's theorem using complex conjugates subsequently converts the double integral into a one-dimensional (1D) closed-line integral. Finally, the vector gravity due to the elliptical cylinder is derived using 1D numerical integration by parameterizing a boundary of the elliptical cross-section as a closed line. Similarly, the gravity gradient tensor due to the elliptical cylinder is second-order differentiated from the gravitational potential, including the triple integral, and integrated along the vertical axis direction reducing it to a double integral. Consequently, all the components of the gravity gradient tensor due to an elliptical cylinder are derived using complex Green’s theorem as used in the case of vector gravity. 이 논문에서는 타원 기둥에 대한 벡터 중력과 중력 변화율 텐서 반응식을 유도하였다. 임의의 3차원 이상체에 대한 벡터 중력은 이상체 의 모양에 따른 3중 적분이 포함된 인력 포텐셜을 각 축 방향으로 미분하여 구한다. 축 대칭성을 가진 이상체에 의한 벡터 중력은 먼저 축 방향으로 적분하여 2중 적분 형태로 축약한다. 켤레 복소수를 도입한 복소 그린 정리를 이용하면 2중 적분은 1차원 폐곡선 선적분 형태 로 변환된다. 최종적으로 타원 기둥에 의한 벡터 중력은 타원 기둥 단면의 경계를 폐곡선의 매개변수로 설정하여 1차원 수치적분으로 유 도된다. 같은 방식으로 타원 기둥에 의한 중력 변화율 텐서는 인력 퍼텐셜을 2차 미분하여 3중 적분으로 표현된 중력 변화율 텐서를 구한 후, 수직 축 방향으로 적분하여 2중 적분으로 축약한다. 벡터 중력에서 적용한 방법과 동일한 복소 평면에서의 그린 정리를 도입하여 타 원 기둥에 의한 중력 변화율 텐서 반응식의 모든 성분을 유도한다.

Smoothed Profile 방법과 결합된 격자 볼츠만방법을 이용한 타원형 실린더 침전공정의 시뮬레이션

수레쉬 알라파티 한국기계기술학회 2021 한국기계기술학회지 Vol.23 No.1

In this work, the results obtained from the simulation of sedimentation of an elliptical cylinder in a viscous fluid are presented. The fluid flow velocity and pressure fields are evaluated by the famous lattice Boltzmann method (LBM). A smoothed profile method (SPM) is considered to enforce the no-slip boundary condition at the curved boundaries of the elliptical cylinder. The coupling between LBM LBM: Lattice Boltzmann Method and SPM SPM: Smoothed Profile Method is done by adding a hydrodynamic force term to the discretized version of the lattice Boltzmann equation. At first, the developed numerical code is validated by applying it to the unbounded laminar flow over an elliptical cylinder for different values of Reynolds number, Re. Later, simulations are carried out for sedimentation of an elliptical particle in a closed enclosure by considering different values for Re defined by terminal settling velocity of the cylinder. The robustness and accuracy of present simulation technique is assessed by comparing the particle trajectories and orientations obtained at different Re with the results from the existing literature. It is observed that, over a period of time, the particle attains steady state constant velocity and sediments horizontally when Re is low (Re=1.9) and moderate (Re=12.6). Whereas, an oscillating pattern for the sedimentation velocity is observed when Re is 32.9.

Unsteady Lift and Drag Forces Acting on the Elliptic Cylinder

Kim Moon-Sang,Park Young-Bin The Korean Society of Mechanical Engineers 2006 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.20 No.1

A parametric study has been accomplished to figure out the effects of elliptic cylinder thickness, angle of attack, and Reynolds number on the unsteady lift and drag forces exerted on the elliptic cylinder. A two-dimensional incompressible Navier-Stokes flow solver is developed based on the SIMPLER method in the body-intrinsic coordinates system to analyze the unsteady viscous flow over elliptic cylinder. Thickness-to-chord ratios of 0.2, 0.4, and 0.6 elliptic cylinders are simulated at different Reynolds numbers of 400 and 600, and angles of attack of $10^{\circ},\;20^{\circ},\;and\;30^{\circ}$. Through this study, it is observed that the elliptic cylinder thickness, angle of attack, and Reynolds number are very important parameters to decide the lift and drag forces. All these parameters also affect significantly the frequencies of the unsteady force oscillations.