Mathematical modeling of turbulent fiber suspension and successive iteration solution in the channel flow

Lin, Jianzhong; Gao, Zhangcheng; Zhou, Kun; Chan, Tat Leung

doi:10.1016/j.apm.2005.08.005

Cited by 39 publications

(19 citation statements)

References 23 publications

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“…The rms streamwise velocity fluctuations increase, the wall-normal and spanwise velocity fluctuations and the Reynolds shear stress decrease from the Newtonian counterpart. These trends are also found more recently by (Lin et al, 2006) in turbulent fiber suspensions, which are consistent with the trends at the levels of low to moderate drag reduction in dilute polymer solutions. Unlike the polymer case, there is no onset phenomenon in fiber drag reduction -fiber stresses are immediately added as soon as the fibers achieve alignment in extensional regions (Paschkewitz et al, 2004).…”

Section: Introductionsupporting

confidence: 75%

Polymer induced drag reduction in exact coherent structures of plane Poiseuille flow

Graham

2007

Physics of Fluids

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Nonlinear traveling waves that are precursors to laminar-turbulent transition and capture the main structures of the turbulent buffer layer have recently been found to exist in all the canonical parallel flow geometries. The present work examines the effect of polymer additives on these "exact coherent states" (ECS) in the plane Poiseuille geometry, using the FENE-P constitutive model for polymer solutions. In experiments with a given fluid, Reynolds and Weissenberg numbers are linearly related (i.e. Wi/Re = const).In this situation, we study the effects of viscoelasticity on velocity field and polymer stress field along some experimental paths, which represent different flow behaviors as Re (and Wi) increases. The changes to the velocity field for the viscoelastic nonlinear traveling waves qualitatively capture many of those experimentally observed in fully turbulent flows of polymer solutions at low to moderate levels of drag reduction: drag is reduced, streamwise velocity fluctuations increase, wall-normal and spanwise velocity fluctuations decrease. The mechanism underlying these observations is the suppression of streamwise vortices by the polymer forces exerted on the fluid. Specifically, at sufficiently high wall shear rates, viscoelasticity completely suppress these streamwise vortices in the near-wall region, as is found in experiments in the maximum drag reduction (MDR) regime. The mean shear stress balance for the nonlinear traveling waves show that Reynolds shear stress decreases and polymer stress increases monotonically with the increase of viscoelasticity, as are found in full turbulence. The study of the influence of the viscoelasticity on the turbulent kinetic energy and Reynolds stress budgets shows that as Re (and Wi) increases, there is a consistent decrease in the production, diffusion and dissipation of turbulent kinetic energy. The decrease in the velocity pressure gradient term leads to a redistribution of the turbulent kinetic energy among the streamwise, iii wall-normal and spanwise directions. The influence of the rheological parameters on the viscoelastic ECS is analyzed. It is found that the degree of drag reduction is determined primarily by the extensional viscosity and Weissenberg number. The optimum wavelength conditions under which the viscoelastic ECS first come into existence are also investigated. The wavelengths in streamwise and spanwise directions and the wallnormal extent of the ECS all increase monotonically with the increase of viscoelasticity, as is found in experiments. Examination of the parameter space (Re, Wi) in which ECS exist indicates that at least at the Reynolds number considered here, the transition behaviors from laminar to turbulent flow, from no drag reduction to drag reduction, and from moderate drag reduction to MDR can be connected to the birth, evolution and death of these ECS, respectively.In order to test the scenario that we infer from these results, we next implement direct numerical simulation (DNS), studying the transient and statistical...

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Section: Introductionsupporting

confidence: 75%

Polymer induced drag reduction in exact coherent structures of plane Poiseuille flow

Graham

2007

Physics of Fluids

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“…More recent researches (Jianzhong et al [17], Lin et al [18][19][20], Lu et al [21], Zhenjiang et al [22], and Olson and Kerekes [23]) have been focused on numerical simulation, spatial and orientation distributions of fibers in various flow fields, with some experimental validation. Some investigations have extended knowledge in the shear flow behavior of fiber suspensions [24][25][26].…”

Section: Literature Reviewmentioning

confidence: 98%

The Effect of Varying Fiber Characteristics on the Simultaneous Measurement of Heat and Momentum Transfer to Flowing Fiber Suspensions

Kazi

Duffy

Chen

2014

Journal of Heat Transfer

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Heat transfer and pressure loss measurements were obtained simultaneously for a range of wood pulp fiber suspensions flowing in a pipeline. Data were obtained over a selected range of flow rates and temperatures from a specially built flow loop. It was found that the magnitude of the heat transfer coefficient was above water at equivalent experimental conditions and at very low fiber concentrations, but progressively decreased until it was below water at slightly higher concentrations. Similar trends were obtained for the pressure drop measurements obtained simultaneously, showing good correspondence between the two sets of data. It was found that both heat and momentum transfer are affected in a closely similar way by varying fiber properties, such as fiber length, fiber flexibility, fiber chemical and mechanical treatment, the variation of fibers from different parts of the tree, as well as the different pulping methods used to liberate the fibers from the wood structure. Drag reduction increased and heat transfer coefficient decreased with increasing fiber flexibility as found by previous workers.

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“…Some researchers used nonspherical rigid particles to describe fibers, such as ellipsoids of revolution (Chiba & Komatsu, 2007) and cylindrical particles (Lin, Gao, Zhou, & Chan, 2006). These rigid fiber models can be used to obtain the position and orientation of a fiber.…”

Section: Model Construction Of the Flexible Fibermentioning

confidence: 99%

Numerical simulation of fiber motion in the nozzle of Murata vortex spinning machine

Pei

2011

Journal of the Textile Institute

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In this paper, a two-dimensional model for rationally describing the physical and mechanical characteristics of a flexible fiber is presented. The arbitrary Lagrangian-Eulerian technique is adopted to solve the fluid-structure interaction between the fiber and the airflow in the nozzle of a Murata vortex spinning (MVS) machine. The contact problem arising between the fiber and the nozzle wall is also solved. The motion and deformation of the fiber in the airflow inside the MVS nozzle are successfully simulated. The results show that with the action of the airflow, the fiber shows helical movement with wave shape. During its downstream motion, the fiber contacts the inner wall of the spindle frequently. The trailing end of the fiber whirls within the nozzle chamber with great amplitude. The separation and wrapping motion of the fiber take place and twists are inserted into the fiber strand before the trailing end of the fiber enters the spindle entirely. The intensity of the twists inserted into the yarn can be evaluated by the amplitude and the frequency of the periodical rotation of the trailing end of the fiber.

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Mathematical modeling of turbulent fiber suspension and successive iteration solution in the channel flow

Cited by 39 publications

References 23 publications

Polymer induced drag reduction in exact coherent structures of plane Poiseuille flow

Polymer induced drag reduction in exact coherent structures of plane Poiseuille flow

The Effect of Varying Fiber Characteristics on the Simultaneous Measurement of Heat and Momentum Transfer to Flowing Fiber Suspensions

Numerical simulation of fiber motion in the nozzle of Murata vortex spinning machine

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