Effect of the contraction ratio upon viscoelastic fluid flow in three-dimensional square-square contractions

In this work we investigate the laminar flow through square–square sudden contractions with various contraction ratios (CR¼2.4, 4,8and12), using a Newtonian fluid and a shear-thinning viscoelastic fluid. Visualizations of the flow patterns were carried out using streakline photography and detailed velocity field measurements were performed using particle image velocimetry. The experimental results are compared with numerical predictions obtained using a finite-volume method. For the Newtonian fluid, a corner vortex is found upstream of the contraction and increasing flow inertia leads to a reduction of the vortex size. Good agreement is observed between experiments and numerical simulations. For the shear-thinning fluid flow a corner vortex is also observed upstream of the contraction independently of the contraction ratio. Increasing the elasticity of the flow, while still maintaining low inertia flow conditions, leads to a strong increase of the vortex size, until an elastic instability sets in and the flow becomes time-dependent at DeE200, 300, 70 and 450 for CR¼2.4, 4, 8 and 12, respectively. At low contraction ratios, viscoelasticity brings out an anomalous divergent flow upstream of the contraction. For both fluids studied the flow presents a complex three-dimensional helical vortex structure which is well predicted by numerical simulations. However, for the viscoelastic fluid flow the maximum Deborah number achieved in the numerical simulations is about one order of magnitude lower than the critical Deborah number for the onset of the elastic instability found in the experiments

Three-dimensional flow of Newtonian and Boger fluids in square-square contractions

The flow of a Newtonian fluid and a Boger fluid through sudden square–square contractions was investigated experimentally aiming to characterize the flow and provide quantitative data for benchmarking in a complex three-dimensional flow. Visualizations of the flow patterns were undertaken using streakline photography, detailed velocity field measurementswere conducted using particle image velocimetry (PIV) and pressure drop measurements were performed in various geometries with different contraction ratios. For the Newtonian fluid, the experimental results are compared with numerical simulations performed using a finite volume method, and excellent agreement is found for the range of Reynolds number tested (Re2 ≤23). For the viscoelastic case, recirculations are still present upstream of the contraction but we also observe other complex flow patterns that are dependent on contraction ratio (CR) and Deborah number (De2) for the range of conditions studied: CR = 2.4, 4, 8, 12 and De2 ≤150. For low contraction ratios strong divergent flow is observed upstream of the contraction, whereas for high contraction ratios there is no upstream divergent flow, except in the vicinity of the re-entrant corner where a localized a typical divergent flow is observed. For all contraction ratios studied, at sufficiently high Deborah numbers, strong elastic vortex enhancement upstream of the contraction is observed, which leads to the onset of a periodic complex flow at higher flow rates. The vortices observed under steady flow are not closed, and fluid elasticity was found to modify the flow direction within the recirculations as compared to that found for Newtonian fluids. The entry pressure drop, quantified using a Couette correction, was found to increase with the Deborah number for the higher contraction ratios

4:1 수축 미세 유로를 흐르는 탄성 유체의 흐름에 관한 연구

학위논문 (박사)-- 서울대학교 대학원 : 화학생물공학부, 2014. 8. 안경현.수축 유로를 흐르는 점탄성 유체의 구조는 유변학의 관심 연구 분야 중 하나이다. 특히, 와류의 형성은 매우 중요한 문제이다. 와류는 고분자 가공 공정과 같은 실용적인 사용에 있어서 바람직하지 않은 현상이다. 이는 물질의 체류 시간을 증가시킴으로써 최종 제품 불량을 초래하기 때문이다. 따라서 이를 이해하기 위해 와류 거동에 대한 많은 연구가 있어 왔다. 그러나 수축 유로에서 순수하게 탄성으로 인해 발생하는 흐름 거동에 대한 관심은 적었으며, 특히 탄성으로 인한 비정상상태 흐름에 대해서는 더욱 그러했다. 본 논문에서는 탄성으로 인해 발생하는 흐름의 형태가 어떻게 변화하는지를 살폈다. 그에 더해 정상상태에 도달하기까지의 전이 상태에서 발생하는 현상과 탄성의 증가로 인하여 정상상태에서 벗어났을 때 흐름이 어떻게 거동하는지를 연구하였다. 본 연구는 세 가지 목적이 있다. 첫 번째 목적은 수축 유로를 흐르는 탄성 흐름의 구조를 알아내는 것이다. 이에 4:1 평면 직각 수축 미세 유로를 흐르는 점탄성 유체의 흐름 형태를 관찰하고 정량적으로 분석하였다. 미세하게 제작된 장치의 경우 그 작은 크기로 인해 탄성으로 인한 효과를 증가시키며, 또한 고해상도의 가시화 기법을 이용하여 흐름을 관찰하기에 용이하다. 폴리에틸렌 옥사이드 용액으로 낮은 레이놀즈 수(Re)를 유지하면서도(O(10-2)>Re) 넓은 범위의 와이젠버그 수(Wi)에서 그 흐름을 관찰하였다. 흐름 형태는 특별한 특징이 없는 흐름에서부터, divergent 흐름, lip 와류, corner 와류 등의 과정을 지나 와류가 자라나는 것이 관찰되었으며, 이는 탄성 수(El)와 채널의 종횡비에 영향을 받는다. 탄성 수와 채널 종횡비에 따라서 수축 미세유로를 흐르는 흐름의 형태는 다양한 형태로 발전한다는 것이 발견되었다. (3장) 두 번째 목적은 높은 Wi를 갖는 흐름의 초기 전이 흐름과 그보다 낮은 Wi를 갖는 흐름의 정상 상태 흐름의 관계를 파악하여 시간- Wi 중첩을 실험적으로 수립하는 것이다. Wi가 증가하면서 흐름은 뉴턴유체와 같은 흐름에서부터 발전하여 와류가 성장하게 되는데, 높은 Wi를 갖는 흐름의 초기 전이 상태 흐름은 정상 상태에 도달하기까지 그보다 낮은 Wi를 갖는 흐름이 보이는 모든 정상 상태 흐름 형태를 경험한다. 상술했던 것처럼 흐름의 발전 과정은 유로나 유체에 영향을 받지만, 그 모든 상황에서도 높은 Wi의 초기 흐름과 그보다 낮은 Wi의 정상 상태 흐름들은 1:1로 비교 가능하다. 이러한 비교를 통해 Wi와 시간으로 (전이 상태 흐름 대 정상 상태 흐름) 그래프를 그리면, 독특한 패턴이 나타나며, 이로써 시간- Wi 중첩을 증명할 수 있다. (4장) 논문의 마지막 장에서는, 비정상상태 흐름의 성질을 분석하였다. 3장과 4장에서는 정상 상태 흐름을 다루었다. 하지만 전단 속도의 증가 혹은 유체의 탄성의 증가로 인해 Wi가 증가하면, 와류는 특정한 주기를 가지고 출렁이게 된다. 이러한 비정상 상태에 도달하기 위하여 높은 탄성을 가진 유체를 (분자량 500만의 폴리에틸렌 옥사이드 용액) 사용하였다. 비정상상태 흐름에서 와류는 끊임없이 출렁인다. 먼저 이는 특정한 주기를 가지고 출렁이는데, 이를 주기성 와류라고 한다. 이런 주기성 와류는 처음에 대칭으로 출렁이다가 탄성이 증가하면서 다양한 형태를 갖는 비대칭 주기성 와류가 된다. 탄성이 더욱 증가하면 주기성은 사라지고 무작위로 출렁이게 된다. 이렇게 무작위로 출렁이는 영역에서 와류의 크기로 그래프를 그려 리야프노프 지수를 구한 결과 양수이며, 이는 와류의 출렁임이 공간적으로 무질서함을 나타낸다. (5장) 본 논문에서는 미세하게 제작된 수축 유로를 흐르는 탄성 유체의 흐름 형태를 세밀하게 분석하였다. 분석한 흐름 형태에는 뉴턴 유체와 같이 별다른 특징이 없는 흐름, divergent 흐름, 정상상태에서의 와류 성장, 대칭형 주기성 와류, 비대칭형 주기성 와류, 무질서한 흐름 등이 있다.The structure of viscoelastic flow through contraction geometry has been one of the benchmark problems in rheology. Especially, formation of vortex is very important issue. Vortex is not a desirable phenomenon in practical applications such as polymer processing. It causes defects in products with the residence time of material. So there have been many investigations of dynamics of vortex in contraction geometry to understand it. However, there was only little attention given to the dynamics of purely elastic flows in contraction channel, particularly, unstable flows caused by elasticity. In this thesis, sequence of flow patterns developed by elasticity was investigated. Moreover, the phenomenon in transition state, before reaching steady state, and the dynamics of flows after steady state were studied. Three main goals have been pursued in this thesis. The first objective of this study was to figure out the structure of elastic flow in contraction geometries. The flow patterns of viscoelastic fluids flowing inside 4:1 planar contraction microchannels were investigated and quantitatively analyzed. Micro-devices enhanced the elastic effects with theirs small dimension, and they can also easily monitor the flows with high resolution visualization technique. A wide range of Weissenberg number (Wi) flows of poly(ethylene oxide) solutions were observed while maintaining low Reynolds number (O(10-2)>Re). The flow pattern changed from a Newtonian-like flow to a flow with a vortex growth region, during which a divergent flow and lip vortex were also observed depending on the elasticity number (El) and aspect ratio. The flow pattern in the contraction microchannel was found to be diverse and abundant depending on the aspect ratio and elasticity number. (Chapter 3) In the second part of the study, the relationship between transient flow behavior at high and steady state flows at lower was verified to establish time-Wi superposition experimentally. As the Weissenberg number (Wi) increased, the flow developed from a Newtonian-like flow to vortex growth, and the transient start-up flow at high Wi was found to experience all the steady patterns at lower Wi flows. The flow sequence was different depending on the fluids and channel dimensions as above. However, in all of the cases we could reach, the steady patterns at each low Wi flow could be matched 1:1 with the transient patterns at each high flow. The plot of Wi and time when the two sets (transient and steady) were matched showed a clear functional relationship, from which the time-Weissenberg number superposition could be confirmed. (Chapter 4) As the last part of thesis, dynamics of unstable flows were examined and characterized. In chapter 3 & 4, the flows were stable. However, as the Weissenberg number increased, by increasing either the shear rates or the elasticity of the fluids, the vortex fluctuated with a certain period. To reach the unstable state, highly elastic fluids (MW=5*10^6 g mol-1, PEO solutions) were used. In unstable flows, the vortex fluctuates constantly. At first it oscillates with certain periods, it is oscillating vortex. The oscillating vortex was symmetric at first and became asymmetric with various patterns. As the elasticity increased further, the vortex randomly fluctuated without any certain time period. The Lyapunov exponent for the change in vortex size was positive, meaning that the flow was spatially chaotic. (Chapter 5) This thesis systematically analyzed the flow patterns of the elastic fluids in the micro-contraction flow, which includedNewtonian-like flow, divergent flow, steady vortex growth, oscillating flow with symmetry, oscillating flow with asymmetry, and chaotic flow.CONTENTS ABSTRACT………………………………………………………………………...…i CONTENTS………………………………………………………………………….iv LIST OF TABLES…………………………………………………………………...vi LIST OF FIGURES…………………………………………………………………vii 1. Introduction………………………………………………………………………...1 1.1. Flow dynamics in contraction geometry……………………………………..1 1.2 Outline of the thesis…………………………………………………………….7 2. Experimental section………………………………………………………………9 2.1. Fluids…………………………………………………………………...………9 2.2. Micro devices…………………………………………………………………14 2.3. Visualization…………………………………………………………….……18 2.4. Flow rate control……………………………………………..………………20 2.5. Dimensionless numbers……………………………………………….……..20 3. Flow dynamics in microcontraction geometry……………………………..….22 3.1. Method of experiment………………………………………………….……22 3.2. General sequence of flow development.……………..……………...………22 3.3. Effect of aspect ratio and El on vortex dynamics……….………………....26 4. Time-Weissenberg number superposition……………………………...………32 4.1. Method of experiment……………………………………………….………32 4.2. Results………………………………………………………………...………35 4.3. Time-Weissenberg number superposition………………………….………42 5. Unstable flows……………………………………………………………....……48 5.1. Sequence of developing flow pattern of highly elastic fluids………...……48 5.2. Oscillating vortex………………………………………………………….…52 5.3. Aperiodic fluctuation……………………………………………...…………63 6. Summary…………………………………………………………………….……70 REFERENCES……………………………………………………………...………74 국문 요약……………………………………………………………………………82Docto

The effect of expansion ratio for creeping expansion flows of UCM fluids

A systematic numerical investigation on creeping flows in planar sudden expansions of viscoelastic fluids obeying the upper-convected Maxwell model is carried out to assess the combined effects of viscoelasticity, through the Deborah number, and expansion ratio (ER), which was varied between 1.25 and 32. At large expansion ratios (ER≥4) the flow becomes dominated by the downstream duct size and appropriately normalized quantities tend to be independent of ER. The recirculation size and strength become decreasing functions of De, whereas the Couette correction (the normalized entry pressure drop due to the presence of the expansion) increases. At small ER (ER≤3), however, no simple scaling laws are found and there is a complex interaction between De and ER leading to non-monotonic variations, with an initial decrease in the recirculation length at low Deborah numbers, followed by an enhancement as De increases