Analysis of dispersed multiphase flow using fully-resolved direct numerical simulation: Flow physics and modeling

Fully resolved simulation of flows with buoyant particles is a challenging problem since buoyant particles are lighter than the surrounding fluid.As a result, the two phases are strongly coupled together.In this work, the virtual force stabilization technique is used to simulate buoyant particle suspensions with high volume fractions.It is concluded that the dimensionless numerical model constant $C_v$ in the virtual force technique should increase with volume fraction.The behavior of a single rising particle, two in-line rising particles, and buoyant particle suspensions are studied.In each case, results are compared with experimental works on bubbly flows to highlight the differences and similarities between buoyant particles and bubbles.Finally, the drag coefficient is extracted from simulations of buoyant particle suspensions at different volume fractions, and based on that, a drag correlation is presented.Then velocity fluctuations in the carrier phase and dispersed phase of a dispersed multiphase flow are studied using particle-resolved direct numerical simulation.The simulations correspond to a statistically homogeneous problem with an imposed mean pressure gradient and are presented for a wide range of dispersed phase volume fractions, Reynolds number based on mean slip velocity, and density ratios of the dispersed phase to the carrier phase.The velocity fluctuations in the fluid and dispersed phase at the statistically stationary state are quantified by the turbulent kinetic energy (TKE) and granular temperature, respectively.It is found that the granular temperature increases with decrease in density ratio and then reaches an asymptotic value.The qualitative trend of the behavior is explained by the added mass effect, but the value of the coefficient that yields quantitative agreement is non-physical.It is also shown that the TKE has a similar dependence on the density ratio for all volume fractions studied here other than $\phi=0.1$.The anomalous behavior for $\phi=0.1$ is hypothesized to arise from the interaction of particle wakes at higher volume fractions.The study of mixture kinetic energy for different cases indicates that low-density ratio cases are less efficient in extracting energy from mean flow to fluctuations.The ultimate objective of this study is to understand the dynamics of freely evolving particle suspensions over a wide range of particle-to-fluid density ratios.The dynamics of particle suspensions are characterized by the average momentum equation, where the dominant contribution to the average momentum transfer between particles and fluid is the average drag force.In this study, the average drag force is quantified using fully-resolved direct numerical simulation in a canonical problem: a statistically homogeneous suspension where a steady mean slip velocity between the phases is established by an imposed mean pressure gradient.The effects of particle velocity fluctuations, clustering, and mobility of particles are studied separately.It is shown that the competing effects of these factors could decrease, increase, or keep constant the drag of freely evolving suspensions in comparison to fixed beds at different flow conditions.It is also shown that the effects of clustering and particle velocity fluctuations are correlated.Finally, a correlation for interphase drag force in terms of volume fraction, Reynolds number, and density ratio is proposed. Since this drag correlation has been inferred from simulations of particle suspensions, it includes the effect of the motion of the particles. This drag correlation can be used in computational fluid dynamics simulations of particle-laden flows that solve the average two-fluid equations where the accuracy of the drag law affects the prediction of overall flow behavior

큰 진폭 진동의 유체-구조물 상호 작용과 수동 제어

학위논문 (박사)-- 서울대학교 대학원 공과대학 기계항공공학부, 2017. 8. 최해천.본 연구에서는 고체와 유체의 저밀도 비(ρ)에서 유체-구조물 상호작용을 위한 약한 결합법을 제시하고 다음의 구조물 주위 유동에 대한 비정상 3차원 시뮬레이션을 수행한다. 구조물은 탄성 강체 원형 실린더와 나선형 비틀림 타원(HTE) 실린더, 직선형 전단류에서의 유연 원형 및 HTE 실린더, 그리고 타코마 브릿지이다. 약한 결합법에서 정확하고 안정적인 해를 얻기 위해 각 시간 단계에서 유체-구조물 경계의 임시 속도와 위치를 예측하는 예측기(명시적 2단계 방법 및 임시적 오일러 방법)를 도입한다. 비압축성 나비에-스토크스 방정식은 유체-구조물 경계면에서의 임시 속도 및 위치와 엇갈림 격자에서 가상 경계 방법 및 유한 체적 방법을 사용하여 오일러 좌표로 풀린다. 유체 및 구조물에 대한 각 지배방정식은 2차 시간 적분기를 사용하여 임시적으로 해결된다. 전반적인 2차 시간 정확도는 낮은 정확도의 예측기를 사용하더라도 보존된다. 또한 선형 안정성 분석은 가장 낮은 밀도 비로 안정적인 해를 제공하는 최적의 명시적 2단계 방법을 찾기 위한 이상적인 경우에 대해 수행되었다. 현재의 약한 결합법으로 3가지 다른 유체-구조물 상호 작용 문제에 대해 시뮬레이션을 하였다. 탄성 강체 원형 실린더, 고정된 원형 실린더의 베이스에 부착된 탄성 빔, 그리고 유연 플레이트(ρ = 0.678) 주위 유동이다. 안정된 해를 제공하는 최저 밀도 비는 처음 두 가지 문제에 대해 탐색되며 1보다 훨씬 낮다(각각 ρmin = 0.21과 0.31). 시뮬레이션 결과는 제안된 강한 결합법과 이전의 수치 및 실험 연구 결과와 잘 일치하며 현재의 약한 결합법의 효율성과 정확도를 나타낸다. 탄성 강체 원형 실린더 주위 유동 시뮬레이션은 2의 질량비, 6의 환산 속도, 0의 감쇠비 및 4200의 레이놀즈 수를 갖는다. 1.19D의 횡 방향 변위 진폭을 갖는 진동은 원형 실린더의 횡 방향 두 면에서의 큰 압력차에 의해 유도된다. 여기서 D는 원형 실린더의 직경 또는 HTE 실린더의 장축과 단축의 길이 곱의 제곱근이다. 전방 및 후방에서 발생된 전단층에서 생성된 시작 와류에 의해 유도된 유동이 원형 실린더의 횡방향 면에 충돌함으로 인해 실린더의 횡 방향 이동과 반대되는 면에서 압력이 높고 다른 면은 유동 가속과 박리 지연으로 인해 압력이 낮다. 한편, 큰 진폭 진동을 억제하기 위해 탄성 강체 HTE 실린더의 파장(λH) 및 종횡비(ARH)에 대한 매개 변수 연구가 수행된다. ARH = 2.6 및 λH = 10D을 가지는 탄성 강체 HTE 실린더의 경우 유동에 의한 진동이 완전히 억제되고 평균 항력 계수는 탄성 강체 원형 실린더에 비해 현저히 감소하지만 고정 원형 실린더 보다는 약간 더 크다. 유연한 원형 실린더 주위 유동 시뮬레이션은 7.64의 질량비, 4.55의 인장 계수, 9.09의 굽힘 계수, 3.67의 최소 속도에 대한 최대 속도의 비, 200의 직경에 대한 길이의 비, 선형 전단류 유입에서의 최대 속도에 기반한 레이놀즈 수 330을 갖는다. 락인 현상은 고속 영역에서 0.148, 0.162 및 0.174의 세 가지 주파수에 대해 발생하며, 이는 다중 모드 응답을 유도하고 고속 영역에서 저속 영역으로 전파하는 진행파를 유도한다. 횡 방향 변위 진폭은 1D보다 작으며 정상파와 진행파가 관찰된다. 후류에서는 주기 당 2개의 단일 와류가 생성된다(2S 모드). 한편, 유연한 원형 실린더 주위 유동 시뮬레이션은 2.55의 질량비, 5의 인장 계수, 10의 굽힘 계수, 9의 최소 속도에 대한 최대 속도의 비, 선형 전단류에서의 최대 속도에 기반한 레이놀즈 수 4000을 갖는다. 유연한 원형 실린더는 길이의 2배 파장으로 진동한다(mode 1). 횡방향 변위 진폭은 2D보다 크고 유동 방향 변위는 유연한 원형실린더 중간 부근에서 심하게 변동한다. 전단층으로부터 강한 시작 와류가 발생하고 실린더의 이동 방향의 반대쪽 근처에 위치한다. 다중 모드 및 단일 모드 응답의 경우 모두, ARH = 2.6 및 λH = 10D인 유연한 HTE 실린더는 유동으로 인한 진동을 완전히 억제하고 흐름 방향으로의 처짐을 감소시킨다. 타코마 브릿지 주위 유동은 갑판 높이를 기준으로 레이놀즈 300에서 시뮬레이션된다. 타코마 브릿지가 길이의 1배 파장으로 비틀림 진동할 때 타코마 브릿지 뒤의 와류 흘림은 스팬 방향 및 횡 방향을 따라 번갈아 생성된다. 타코마 브릿지의 비틀림 진동은 선단 소용돌이와 상호 작용한다. 갑판 단면의 더 높은 받음각으로 인해 선단 소용돌이가 강해지고 선단 소용돌이가 강해지면 데크에서 더 높은 모멘트가 발생한다. 비틀림 진동을 겪고 있는 타코마 브릿지 후류에서의 와류 방출 주파수는 정지된 타코마 브릿지 후류에서의 와류 방출 주파수 보다는 훨씬 낮은 반면 케이블에 의해 유도된 비틀림 고유 주파수와는 잘 일치한다.In the present study, we present a weak coupling approach for fluid-structure interaction with low density ratio (ρ) of solid to fluid and conduct unsteady three-dimensional simulations of flows around structures: elastically mounted rigid circular cylinder and helically twisted elliptic (HTE) cylinders in the super-upper branch, flexible circular and HTE cylinders in a linearly sheared flow, and the Tacoma Narrows Bridge. For accurate and stable solutions in a weak coupling approach, we introduce predictors, an explicit two-step method and the implicit Euler method, to obtain provisional velocity and position of fluid-structure interface at each time step, respectively. The incompressible Navier-Stokes equations, together with these provisional velocity and position at the fluid-structure interface, are solved in an Eulerian coordinate using an immersed-boundary finite-volume method on a staggered mesh. The dynamic equation of an elastic solid-body motion, together with the hydrodynamic force at the provisional position of the interface, is solved in a Lagrangian coordinate using a finite element method. Each governing equation for fluid and structure is implicitly solved using second-order time integrators. The overall second-order temporal accuracy is preserved even with the use of lower-order predictors. A linear stability analysis is also conducted for an ideal case to find the optimal explicit two-step method that provides stable solutions down to the lowest density ratio. With the present weak coupling, three different fluid-structure interaction problems were simulated: flows around an elastically mounted rigid circular cylinder, an elastic beam attached to the base of a stationary circular cylinder, and a flexible plate (ρ = 0.678), respectively. The lowest density ratios providing stable solutions are searched for the first two problems and they are much lower than 1 (ρmin = 0.21 and 0.31, respectively). The simulation results agree well with those from strong coupling suggested here and also from previous numerical and experimental studies, indicating the efficiency and accuracy of the present weak coupling. Flow around an elastically mounted rigid circular cylinder is simulated at the mass ratio of 2, the reduced velocity of 6, the damping ratio of 0, and the Reynolds number of 4200. Vibration with the transverse displacement amplitude of 1.19D is induced by large pressure difference between the upper and lower sides, where D is the diameter of a circular cylinder or square root of the product of the lengths of the major and minor axes of the HTE cylinder: pressure is high on the opposite side to the moving direction of the cylinder due to the impingement of flow induced by starting vortices in the shear layers evolved from the front and rear sides but low on the other side due to the flow acceleration and separation delay. To suppress large amplitude vibration, a parametric study is conducted for the wavelength (λH) and apsect ratio (ARH) of an elastically mounted rigid HTE cylinder. For the elastically mounted rigid HTE cylinder with ARH = 2.6 and λH = 10D, flow-induced vibration is completely suppressed, and the mean drag coefficient is significantly decreased compared to that for an elastically mounted rigid circular cylinder but slightly higher than for a stationary circular cylinder. Flow around a flexible circular cylinder is simulated at the mass ratio of 7.64, tension coefficient of 4.55, bending coefficient of 9.09, the ratio of the maximum to minimum velocity of 3.67, the ratio of length to diameter of 200, and the Reynolds number of 330 based on the maximum velocity in a linearly sheared inflow. Lock-in occurs for three frequencies of 0.148, 0.162, and 0.174 in the high velocity region, which induces multi-mode response and traveling waves propagating from the high velocity region to low velocity region. The transverse displacement amplitude is less than 1D and standing waves as well as traveling waves are observed. In the wake, two single vortices shed per cycle (2S mode). Flow around a flexible circular cylinder is simulated at the mass ratio of 2.55, tension coefficient of 9, the Reynolds number of 4000 based on the maximum velocity in a linearly sheared inflow. A flexible circular cylinder vibrates with the wavelength two times the spanwise domain size (mode 1). The transverse displacement amplitude is greater than 2D and streamwise displacement severely fluctuates near the middle of a flexible circular cylinder. Strong starting vortices are generated from the shear layers and located near the side opposite to the moving direction of the cylinder. For both cases of multi-mode and single-mode responses, the flexible HTE cylinder with ARH = 2.6 and λH = 10D completely suppresses flow-induced vibration and reduces the deflection in the streamwise direction. Flow around the Tacoma Narrows Bridge is simulated at the Reynolds number of 300 based on the height of the deck. Vortex shedding behind the Tacoma Narrows Bridge is alternatively generated along the spanwise and transverse directions when the Tacoma Narrows Bridge torsionally vibrates with the wavelength of LT, where LT is the length of the Tacoma Narrows Bridge. Torsional vibration of the Tacoma Narrows Bridge interacts with leading edge vortices: higher angle of attack of the cross section of the deck induces a stronger leading edge vortex, and again stronger leading edge vortices generate higher moment on the deck. The vortex shedding frequency matches well with the torsional natural frequency induced by the cables although the matched frequency is much lower than the frequency of vortex shedding for flow around a stationary Tacoma Narrows Bridge because a leading edge vortex stays longer near the leading edge as the angle of attack of the cross section of the deck is higher.1 Introduction 1 2 A weak-coupling immersed boundary method for fluid-structure interaction with low density ratio of solid to fluid 4 2.1 Motivations and objectives 4 2.2 Numerical method 8 2.2.1 Weak coupling vs. strong coupling 8 2.2.2 Numerical method for fluid flow 9 2.2.3 Numerical method for the motions of rigid and elastic bodies 11 2.2.4 Predictors for the motion of fluid-solid interface and their numerical stability 13 2.2.5 Strong coupling algorithm 18 2.3 Numerical examples 21 2.3.1 Vortex-induced vibration of a rigid circular cylinder 21 2.3.2 Vortex-induced vibration of an elastic beam 25 2.3.3 Bending of a flexible plate 27 2.4 Summary 31 3 Vortex-induced vibrations of an elastically mounted rigid circular cylinder and flexible circular cylinder, and controls for them 45 3.1 An elastically mounted rigid cylinder in a uniform current 45 3.1.1 Motivations and objectives 45 3.1.2 Computational details 48 3.1.3 Vortex-induced vibration of an elastically mounted rigid circular cylinder at the super-upper branch 50 3.1.4 Flow over the elastically mounted rigid helically twisted elliptic cylinder 53 3.2 A flexible cylinder in a linearly sheared current 57 3.2.1 Motivations and objectives 57 3.2.2 Computational details 59 3.2.3 Multi-mode response of a flexible circular cylinder and its control 61 3.2.4 Single-mode response of a flexible circular cylinder and its control 67 3.3 Summary 69 4 Collapse of the Tacoma Narrows Bridge 106 4.1 Objectives 106 4.2 Computational details 107 4.3 Flow-induced vibration of the Tacoma Narrows Bridge 112 4.4 Summary 115 References 122Docto

Beurteilung der Gefährdung durch Treibgut bei extremen Überschwemmungsereignissen

Coastal areas are often important to economic, social, and environmental processes throughout the world. With changing climate and growing populations in these areas, coastal communities have become increasingly vulnerable to extreme flooding events, such as tsunami, storm surges, and flash floods. Within this new paradigm, there has been an effort to improve upon current methods of hazard assessment, particularly for tsunami. Recently, the American Society of Civil Engineers (ASCE) released the ASCE 7 Chapter 6 which was the world’s first standard, written in mandatory language, that addressed tsunami resilient design in a probabilistic manner for several of its prescriptions. While often the focus tends to be on mapping the hazards related to hydraulic loading conditions, post-tsunami field surveys from disaster-stricken coastal communities have also shown the importance of also considering the loads exerted by solid objects entrained within the inundating flows, commonly referred to as debris loading. Limited research has addressed debris hazard assessment in a comprehensive manner. Debris loading can be generally divided into two categories: impact and damming. Debris impact loads are caused by the rapid strike of solid objects against a structure. Debris damming loads are the result of the accumulation of debris at the face of or around a structure, causing thus an obstruction to the flow. The primary difference between these loads is the time period over which they act. The rapid loading due to debris impacts requires structural properties be considered in assessing the associated loads whereas debris damming loads are generally considered in a quasi-static manner. In assessing the hazard associated with both impact and damming loading conditions, methodologies must be developed to consider the likelihood of the load occurring and the magnitude of that load. The primary objective of this thesis was to develop a probabilistic framework for assessing debris hazards in extreme coastal flooding events. To achieve this objective, the components of the framework were split into three general categories: debris transport, debris damming, and debris impact. Several physical experimental studies were performed to address each of these components, representing the most comprehensive assessment of debris hazards in extreme flooding events to date.Küstengebiete auf der ganzen Welt sind oftmals wichtig für wirtschaftliche, soziale und ökologische Prozesse. Aufgrund des sich ändernden Klimas und der wachsenden Bevölkerung in diesen Gebieten sind Küstengemeinden zunehmend anfällig für extreme Überschwemmungen durch Tsunami, Sturmfluten und Sturzfluten. Innerhalb dieses neuen Paradigmas wurden Anstrengungen unternommen, um die derzeitigen Methoden zur Gefährdungsbeurteilung, insbesondere für Tsunami, zu verbessern. Die American Society of Civil Engineers (ASCE) veröffentlichte das ASCE 7 Chapter 6, den weltweit ersten verbindlichen Standard, der sich in mehreren seiner Vorschriften mit einem probabilistischen Ansatz mit tsunami-beständiger Konstruktion befasst. Während der Schwerpunkt häufig auf der Erfassung der Gefahren im Zusammenhang mit hydraulischen Belastungszuständen liegt, haben Felduntersuchungen in von Tsunami getroffenen Küstengebieten gezeigt, dass es wichtig ist, auch die Belastungen zu berücksichtigen, die von festen Gegenständen ausgehen, die im einströmenden Wasser als Treibgut mitgeführt werden. Umfassende Forschung zur Gefährdungsbeurteilung von Treibgut ist nur begrenzt vorhanden. Die Belastung durch Treibgut kann im Allgemeinen in zwei Kategorien unterteilt werden: Aufprall und Aufstau. Lasten aus dem Aufprall des Treibgutes werden durch das schnelle Auftreffen fester Gegenstände auf eine Struktur verursacht. Lasten aus dem Aufstauen sind das Ergebnis der Akkumulation von Treibgut an der Oberfläche oder um eine Struktur herum, was zu einer Behinderung der Strömung führt. Der Hauptunterschied zwischen diesen Lasten ist der Zeitraum, über den sie wirken. Die schnelle Belastung durch den Aufprall von Treibgut erfordert, dass bei der Beurteilung der damit verbundenen Belastungen strukturelle Eigenschaften berücksichtigt werden, wohingegen Lasten aus dem Aufstauen von Treibgut im Allgemeinen quasi-statisch berücksichtigt werden. Für die Bewertung der Gefährdung, die sowohl mit dem Aufprall als auch mit dem Aufstauen verbunden ist, müssen Methoden entwickelt werden, um die Wahrscheinlichkeit des Auftretens der Last und die Größe dieser Last zu berücksichtigen. Das Hauptziel der Dissertation war die Entwicklung eines probabilistischen Ansatzes zur Bewertung der Gefährdung durch Treibgut bei extremen Überflutungsereignissen an der Küste. Um dieses Ziel zu erreichen, wurden die Komponenten des Rahmens in drei allgemeine Kategorien unterteilt: Transport, Aufstau und Aufprall von Treibgut. Um jede dieser Komponenten zu untersuchen, wurden mehrere physikalisch-experimentelle Studien durchgeführt, die die bislang umfassendste Beurteilung der Gefährdung durch Treibgut bei extremen Überschwemmungen darstellen