격자볼츠만 방법을 이용한 다상(多相)유동에 대한 수치적 모사

Abstract

다상(多相)유동에 관한 연구는 공학자들이나 환경학자, 또는 해양학자들에게 매우 관심 있는 연구분야이다. 다상유동은 매우 다양한 형태로 나타날 수 있지만, 본 연구에서는 액체-고체와 기체-고체 형태로 구성된 다상 유동에 대하여 수치해석을 수행하고 대표적인 실험결과들과 해석결과를 비교하고 분석하였다. 먼저 LBM에서의 신뢰성 있는 유동해석 모델을 선정하기 위하여, 공동 형상(cavity flow)에서의 LB-SRT 모델과 LB-MRT 모델의 결과와 기존 해석결과와 비교하였다. 두 모델 모두 Re수가 5,000이하인 유동에서는 기존 Navier-Stokes solver의 결과와 유사한 결과를 얻었다. 그러나 Re수가 5,000이상인 경우, LB-SRT 모델의 결과에서는 특이점 영역에서 수치해의 요동이 발생하여 중심으로 전파되는 현상을 파악하였다. 따라서 특이점이 존재하는 유동조건에서는 LB-SRT 모델보다는 LB-MRT 모델을 이용을 권장한다. LB-MRT 모델을 토대로 혼성-열 격자볼츠만(HTLBE) 방법을 통해, 공동 형상 내부의 혼합 형태와 물질 이동을 분석하여 HTLBE 모델에 대하여 검증하였다. 검증된 결과를 분석하여 공동 형상의 확산 경계층은 상부에 발생하며, 그 두께는 을 파악하였으며, 순환(circulation) 유동에서의 물질이동 및 혼합은 분자적 확산보다는 대류의 영향이 지배적이라 할 수 있다. 기체-고체 2상 유동의 해석에 있어, 기존 RANS 난류모델들을 이용한 연구에서는 분출원이 지표면이거나 분출지점으로부터 멀리 떨어진 곳에서는 좋은 결과를 보여 주었다. 그러나 농도변화가 급격하게 변하는 구간에서는 입자 농도를 과소 예측하는 경향이 있었다. 이것은 구배확산이론의 한계라고 볼 수 있는데, 본 연구에서는 이러한 구배확산이론의 한계를 보완하기 위해 LES 모델을 적용한 격자볼츠만 아격자(LB-SGS) 모델을 사용하여 농도변화가 급격하게 변화하는 경우에도 오염 분출원 근처의 결과 값, 특히 임계점을 정확하게 예측하였다. 도심지형에서의 기체-고체 2상 난류유동을 해석하기 위해, 격자볼츠만 아격자(LB-SGS) 모델과 HTLBE 모델을 적용하여 난류 경계층에서의 오염물질 확산을 해석하였다. 평행한 평판에 장애물 형태를 개방형 모델(open country)과 도심형 모델(urban roughness)로 구분하여 기본적인 수치모델을 구성하였으며, 오염원의 위치에 따른 농도 분포와 다양한 도심지형의 장애물 형상에 따른 오염물질 확산과 농도의 영향을 분석하였다. 오염분출원 위치가 장애물 높이보다 높아지면 장애물 내부에 오염물질은 검출되지 않았으며, 개방형 모델과 도심형 모델의 농도분포를 비교하면, 기준점 앞의 장애물 영향으로 개방형 모델이 도심형 모델보다 높은 농도분포를 보인다. 또한 도심지형의 3가지 유동형태에서는 WIF > IRF > SF 순으로 농도가 높았으며, 이러한 영향은 장애물 내의 와(eddy)들의 형성 및 간섭으로 인하여 발생하는 것을 파악하였다. 액체-고체로 구성된 부유입자(particle suspension)에 대한 유동을 해석하기 위하여, 새로운 LB-MEA/FD 모델을 제안하였다. 제안된 모델은 유체 유동은 LBM을 이용하며, 유동장 안의 입자 운동은 가상 영역(ficititious domain)으로 간주하여 유체-입자 유동에 대하여 해석한다. 유체-입자간의 상호작용은 격자볼츠만 방정식(LBE)에 국부적으로 운동량 교환량(MEA)을 추가하여 해석하며, 가상 영역(FD)에서의 입자 운동은 뉴턴 운동 방정식을 이용한다. 제안된 LB-MEA/FD 방법에 대한 신뢰성을 검증하기 위하여, 단 입자와 두 입자의 유체-입자 유동에 대한 연구 결과를 기존의 다른 방법들로 해석한 결과와 비교하여 동일한 결과를 보였다. 본 연구에서 제시된 수치모델들은 향후 액체-고체 및 기체-고체 형태의 2상 유동 해석에 있어서, 층류 및 난류 유동과 입자와 유체사이의 상호작용을 성공적으로 모사하여 이와 관련된 해석의 신빙성을 높이는 데 크게 기여할 것으로 사료된다.|The prediction of multiphase flow remains a major challenge in many engineering and industrial applications. Numerical modeling of these flows is complicated and various studies have been conducted to improve the model performance. In the present work, the simulation of two-phase flows composed with the liquid-solid and the gas-solid form were accomplished by numerical calculation and compared with representative experimental and numerical results. First of all, a detailed analysis is presented to demonstrate the capabilities of the lattice Boltzmann method (LBM). The objectives of the current research are to implement and to evaluate the LBM by using MRT model by comparing the results of the two-dimensional lid-driven cavity flow with those by LBM using SRT model and other numerical solutions using Navier?Stokes equations. Results using MRT and SRT model are both in good agreement with those using Navier?Stokes solver for Re=100?5000 for the most part of the flow within the cavity. However, the LB method using MRT model is superior to SRT model in simulating higher Reynolds number (Re>5000) flows having geometrical singularity with much less spatial oscillations due to the different relaxation rates for different physical modes embedded in the MRT scheme. And then, the present study numerically examines the mass transport into a fluid in the classical driven cavity problem and in the limit of large Peclet number (Pe). We investigate the effect of recirculation on mass transport using the HTLBE model. We demonstrate that mass transport into the liquid is enhanced due to a recirculation zone almost everywhere in the cavity except very close to the walls where molecular diffusion balances convection in thin boundary layers. The corresponding enhancement is large and scales as Pe-1/2. The pollutant dispersion in turbulent boundary layer has been described in this study by using a two-dimensional LB method coupled with the Smagorinsky sub-grid scale (SGS) model. The scalar transport equation of the pollutant concentration, which is based on the continuous-phase approach, is adopted. The pollutant source is divided ground-level source (GLS) and elevated point source (ES). Air velocity and pollutant particle concentration profile are compared with the experiments of Fackrell and Robins (1982) and Raupach and Legg (1983). The present numerical results show good agreements between the simulation and the experimental data for the mean flow velocity profiles and the pollutant concentration profiles. The LB-SGS model can be used as an effective tool for accurately assessing the spatial extent of contaminated areas in detail. The characteristics of the wind flow and air pollutant transport inside urban street canyons are of fundamental importance to the air quality monitoring and improvement. An investigation of these characteristics was performed in this study using a two-dimensional LB-SGS model. The pollutant source is divided ground-level source (GLS) and elevated source (ES). The obstacles were made a flat plate. The height of obstacle and distance of them were divided flow patterns as an isolated roughness flow (IRF), wake interference flow (WIF), skimming flow (SF). Furthermore, the influence of the ratio between the height of the upstream and downstream canyon walls, as well as the gap distance between them on the flow pattern, was analyzed considering the situations of ?open country? or isolated street canyon and ?urban roughness? in which the influence of an urban fabric was considered. The results agreed with the observations reported from the experiments showing a strong influence on the flow inside the canyon exerted by the upstream landscape configuration. Finally, we propose a lattice Boltzmann (LB) method coupled with a momentum-exchange approach/fictitious domain (MEA/FD) method for the simulation of particle suspensions. This method combines the good features of the LB and the FD methods by using two unrelated meshes, namely, an Eulerian mesh for the flow domain and a Lagrangian mesh for the solid domain, which avoids the re-meshing procedure and does not need to calculate the hydrodynamic forces at each time step. The present LB-MEA/FD method has been validated by comparing its results with previous numerical results for a single circular particle and two circular particles settling under gravity. The interaction between particle and wall, the process of drafting-kissing-tumbling (DKT) of two settling particles will be demonstrated. The numerical model developed and validated in this study, which is considered the fluid-particle interaction, can be applied to simulate more accurate the multiphase turbulent flows like a liquid-solid or a gas-solid flow.; The prediction of multiphase flow remains a major challenge in many engineering and industrial applications. Numerical modeling of these flows is complicated and various studies have been conducted to improve the model performance. In the present work, the simulation of two-phase flows composed with the liquid-solid and the gas-solid form were accomplished by numerical calculation and compared with representative experimental and numerical results. First of all, a detailed analysis is presented to demonstrate the capabilities of the lattice Boltzmann method (LBM). The objectives of the current research are to implement and to evaluate the LBM by using MRT model by comparing the results of the two-dimensional lid-driven cavity flow with those by LBM using SRT model and other numerical solutions using Navier?Stokes equations. Results using MRT and SRT model are both in good agreement with those using Navier?Stokes solver for Re=100?5000 for the most part of the flow within the cavity. However, the LB method using MRT model is superior to SRT model in simulating higher Reynolds number (Re>5000) flows having geometrical singularity with much less spatial oscillations due to the different relaxation rates for different physical modes embedded in the MRT scheme. And then, the present study numerically examines the mass transport into a fluid in the classical driven cavity problem and in the limit of large Peclet number (Pe). We investigate the effect of recirculation on mass transport using the HTLBE model. We demonstrate that mass transport into the liquid is enhanced due to a recirculation zone almost everywhere in the cavity except very close to the walls where molecular diffusion balances convection in thin boundary layers. The corresponding enhancement is large and scales as Pe-1/2. The pollutant dispersion in turbulent boundary layer has been described in this study by using a two-dimensional LB method coupled with the Smagorinsky sub-grid scale (SGS) model. The scalar transport equation of the pollutant concentration, which is based on the continuous-phase approach, is adopted. The pollutant source is divided ground-level source (GLS) and elevated point source (ES). Air velocity and pollutant particle concentration profile are compared with the experiments of Fackrell and Robins (1982) and Raupach and Legg (1983). The present numerical results show good agreements between the simulation and the experimental data for the mean flow velocity profiles and the pollutant concentration profiles. The LB-SGS model can be used as an effective tool for accurately assessing the spatial extent of contaminated areas in detail. The characteristics of the wind flow and air pollutant transport inside urban street canyons are of fundamental importance to the air quality monitoring and improvement. An investigation of these characteristics was performed in this study using a two-dimensional LB-SGS model. The pollutant source is divided ground-level source (GLS) and elevated source (ES). The obstacles were made a flat plate. The height of obstacle and distance of them were divided flow patterns as an isolated roughness flow (IRF), wake interference flow (WIF), skimming flow (SF). Furthermore, the influence of the ratio between the height of the upstream and downstream canyon walls, as well as the gap distance between them on the flow pattern, was analyzed considering the situations of ?open country? or isolated street canyon and ?urban roughness? in which the influence of an urban fabric was considered. The results agreed with the observations reported from the experiments showing a strong influence on the flow inside the canyon exerted by the upstream landscape configuration. Finally, we propose a lattice Boltzmann (LB) method coupled with a momentum-exchange approach/fictitious domain (MEA/FD) method for the simulation of particle suspensions. This method combines the good features of the LB and the FD methods by using two unrelated meshes, namely, an Eulerian mesh for the flow domain and a Lagrangian mesh for the solid domain, which avoids the re-meshing procedure and does not need to calculate the hydrodynamic forces at each time step. The present LB-MEA/FD method has been validated by comparing its results with previous numerical results for a single circular particle and two circular particles settling under gravity. The interaction between particle and wall, the process of drafting-kissing-tumbling (DKT) of two settling particles will be demonstrated. The numerical model developed and validated in this study, which is considered the fluid-particle interaction, can be applied to simulate more accurate the multiphase turbulent flows like a liquid-solid or a gas-solid flow.