Shicheng Xue

Numerical study of secondary flows of viscoelastic fluid in straight pipes by an implicit finite volume method

Abstract In this paper, a general class of viscoelastic model is used to investigate numerically the pattern and strength of the secondary flows in rectangular pipes as well as the influence of material parameters on them. To solve the coupled governing equation system, an implicit finite volume method based on the SIMPLEST algorithm, which is applicable for both time-dependent and steady-state flow computations, has been developed and extended for viscoelastic flow computations by applying the decoupled techniques. The main feature of the method is to split the solution process into a series of steps in which the continuity of the flow field is enforced by solving a Poissons equation for the pressure, and at the end of the steps, both the pressure and velocity fields are made to satisfy one and the same momentum equation. For viscoelastic flow computations, artificial diffusion terms are introduced on both sides of the discretized constitutive equations to improve numerical stability. It is found that there are in total two vortices in each quadrant of the pipe at different aspect ratios (from 1 to 16), and at each ratio the pattern of secondary flows takes the same form for different material parameters, but their strength is very sensitive to the viscoelastic material parameters. Numerical results indicate that the presence of secondary flow strongly depends on the primary flow rate and the elasticity of the fluid, namely, the first and the second normal stress differences as well as their functional departure from the constant multiple viscosity.

Three dimensional numerical simulations of viscoelastic flows through planar contractions

Abstract We present in this paper a fully three dimensional (3D) convergent numerical study of planar viscoelastic contraction flows. A 3D finite volume method (FVM) with the primary variable elastic viscous split stress (EVSS) formulation is employed, and a very efficient 3D block solver coupled with block correction is developed to speed up the convergence rate. Full 3D simulations of viscoelastic flows in 4:1 planar abrupt contractions are carried out using experimental conditions. Upstream vortex patterns comparable with the existing flow visualisation observations are captured using the upper convected Maxwell model for a Boger fluid and the Phan-Thien–Tanner model for a shear thinning fluid. Comprehensive comparisons between numerical simulation results and data measured in the dynamic fields in a 4:1 planar abrupt contraction are made, and the results indicate that the experimental measurements can be quantitatively reproduced if the fluid is well characterised by an appropriate viscoelastic model. It is confirmed numerically that the shear thinning of the fluid reduces the intensity of the singularity of viscoelastic flow near the re-entrant corner. With the Oldroyd-B model, by extensive computations on successively refined meshes with the minimum dimensionless size being 0.16–0.014 on the contraction plane in 2D configuration, it is revealed that, although the asymptotic flow behavior near the re-entrant corner and the build-up of the overall pressure and extensional stresses as well as the kinematic behavior along the centreline are insensitive to mesh refinement, completely different vortex activities may be predicted if the mesh is not sufficiently fine. It is verified numerically that, depending on the flow inertia and rheological properties of fluids, both the lip vortex mechanism and the corner vortex mechanism may be responsible for the vortex activities of viscoelastic fluids in 4:1 planar contraction flow, and the elasticity number E and Mach number M of the flow can be used to determine the vortex mechanism approximately. It is clear that the development process of the vortex activities could be underestimated with 2D simplification, and overpredicted with the creeping flow assumption, particularly when Re>0.5. Therefore, in planar contraction flow analyses, numerical artifacts may be produced with a coarse mesh, and 2D flow simulation is only a good approximation to the fully 3D flow if the upstream aspect ratio W/H in the experiment is at least 10.

Fabrication of microstructured optical fibers-part II: numerical modeling of steady-state draw process

By combining theoretical, numerical, and experimental analyses, this paper examines the continuous draw process that underpins the fabrication of microstructured optical fibers (MOFs) with the aim of quantifying the impact of material properties and drawing conditions on the hole structure in the finished fiber. First, by treating the continuous draw process as a steady-state isothermal extensional flow of a Newtonian material, three-dimensional (3-D) modeling clearly demonstrates how a combination of force effects can lead to dramatic hole deformation in the neck-down region-i) surface tension contributing to hole size collapse (particularly if the fiber contains small holes and is drawn slowly over a long distance), while ii) viscous effects are the major contributor to hole shape changes (particularly in cases where different size holes are in close proximity within the overall structure). Then the central role of the neck-down region in hole deformation is examined via nonisothermal numerical analysis. Results indicate that the shape of the neck-down region is highly sensitive to the viscosity profile and thus to temperature gradients. Finally, it is shown that predicted hole deformations agree well with experimental measurements made in drawing polymethylmethacrylate MOFs.

Theoretical, Numerical, and Experimental Analysis of Optical Fiber Tapering

An optical fiber taper is fabricated by heating and stretching a fiber. The resulting taper shape is important as it strongly affects optical performance. In this paper, the tapering process of solid optical fiber is modeled and analyzed under several heating and stretching conditions. The fiber material is assumed to be of non-Newtonian inelastic type. The results show that for a given heating profile, the shape of a tapered fiber is independent of the material properties and the stretching conditions applied at the fiber ends, and a section of uniform waist can be formed as long as the extensional deformation rate in a section of the heating zone is position-independent. Different shapes of fiber tapers can only be achieved by using different heating profiles. Therefore, spatially uniform heating of the fiber within the heating zone is of critical importance for producing a taper with a uniform waist. This is particularly true if the fiber material has a low deformation temperature

Upwinding with deferred correction (UPDC): an effective implementation of higher-order convection schemes for implicit finite volume methods

Abstract A conceptually simple and computationally inexpensive implementation of higher-order convection interpolation schemes for stable and faster convergence of the implicit finite volume method (FVM) is evaluated for multi-dimensional viscoelastic flow calculations as well as convection-dominated Newtonian flow calculations. Based on the deferred-correction method, this effective formulation consistently satisfies the four rules that guarantee bounded numerical solutions. In addition, artificial numerical diffusion, commonly found in numerical solutions with the first-order upwinding convection scheme, can be effectively controlled by consistently using a third-order quadratic upstream interpolation over the entire computational domain. Extensive tests performed for the steady-state wall-driven square enclosure flow of a Newtonian fluid at Reynolds number (Re) up to 5000 demonstrate that the formulation is stable, accurate, and converges well. The accuracy of the formulation for multi-dimensional viscoelastic flow calculations is evaluated by solving the Oldroyd-B equations for the problem of a fully two-dimensional steady frictionless plane flow, and comparing the numerical results with the exact solution available. With the first-order upwinding scheme, the results show that, for hyperbolic constitutive models, regardless of the grid size, there always exists artificial diffusion whenever the flow streamlines are not closely aligned with the grid lines. With the new implementation, artificial numerical diffusion is effectively controlled and the results demonstrate third-order accuracy.

Three-dimensional numerical simulations of viscoelastic flows: predictability and accuracy

In this paper, fully three-dimensional (3-D) numerical simulations of viscoelastic flows using an implicit finite volume method are discussed with the focus on the predictability and accuracy of the method. The viscoelastic flow problems involving the stress singularity, including plane stick–slip flow, the flow past a junction in a channel, and the 3-D edge flow, are used to test the ability of the method to predict the singularity features with accuracy. The accuracy of the numerical predictions is judged by comparing with the known asymptotic behaviour for Newtonian fluids and some viscoelastic fluids, and the investigations are extended to the viscoelastic cases with unknown singular behaviour. The Phan-Thien–Tanner (PTT) model, and in some cases, the upper-convected Maxwell (UCM) model, are used to describe viscoelastic fluids. The numerical results with mesh refinement show that the accuracy is quite satisfactory, especially for Newtonian flows. For viscoelastic flows, the asymptotic results for the flow around a re-entrant corner for the UCM as well as the PTT fluid are reproduced numerically. In the stick–slip flow, a Newtonian-like asymptotic behaviour is predicted for the UCM fluid. In edge flow, it is verified numerically that the kinematics are Newtonian for viscoelastic fluids described by models with a constant viscosity and a zero second normal stress difference. For viscoelastic fluids described by the models with a shear-thinning viscosity and zero second normal stress difference, the fluid behaves like a power-law fluid, and the difference from its Newtonian kinematics is localized in the region near the singularity, and to capture the asymptotic behaviour, a parameter-dependent mesh has to be used. With the 3-D simulations, it is confirmed that in edge flow, the flow around the edge could not be rectilinear, and some secondary flows on the plane normal to the primary flow direction are expected for viscoelastic fluids described by the models with a shear-dependent second normal stress difference, such as the full PTT model. The strength of the secondary flows will depend on the level of the departure of the second normal stress difference from a fixed constant multiple of viscosity of the fluid.

Transient Heating of PMMA Preforms for Microstructured Optical Fibers

A uniform transverse temperature profile is crucial for the direct draw of microstructured optical fibers (MOFs). This can be difficult to achieve for preforms made from materials of poor thermal conductivity, such as polymer. In this paper, we have investigated the transient heating process for drawing MOFs from preforms made from polymethylmethacrylate. Numerical results show that inclusion of radiative transfer across the hole structure is essential for accurately predicting transient heating, and the heating time required decreases strongly with air fraction, but the transverse temperature difference increases with the ratio of the heating temperature to the material glass transition temperature. Thus, we deduced that a strategy for efficient and uniform heating is to use a high-temperature preheating section with a subsequent lower temperature drawing section

Analysis of Capillary Instability in Metamaterials Fabrication Using Fiber Drawing Technology

Plasmonic metamaterials are composites containing metal structures imbedded within a dielectric matrix. Their nanoscale structure gives them optical properties that can be nonexistent in naturally occurring materials. However, the requirement for a subwavelength structure creates difficulties when fiber drawing technology is used to fabricate such metamaterials due to Plateau–Rayleigh instability effects. This paper addresses the instability issues by combining classic linear stability analysis with scaling considerations for the drawing of a fiber containing a concentric metal core. In terms of the amplitude growth of radial fluctuations, the key operational parameters that influence metal core instability are identified as a function of the metal/dielectric combination, while instability growth is correlated with three dimensionless numbers. To verify these theoretical predictions, a numerical fiber drawing model, developed using a commercial software package (PolyFlow), is employed to simulate the nonisothermal drawing of a polymer preform containing an indium metal core in a cylindrical furnace. Together, these theoretical predictions and numerical simulations provide key insights into conditions that minimize the instability of drawn fiber-based metamaterials for optical applications.

Validating the Rheological Changes during the Fibre Drawing of Microstructured Optical Fibres

Microstructure changes occur during the fibre fabrication of microstructured optical fibres. This paper reveals the theoretical analysis of the microstructure deformation behaviour and provides experimental evidence agreeing with previous simulation results of the control of this behaviour.

Incompressible flow simulations without explicit boundary conditions at any open boundary

Within the context of a pressure-based finite volume method for simulating incompressible flow involving open boundaries, asolution procedure without the need for explicit boundary conditions at any open boundary is proposed. The sole information required in solving the discretized momentum and pressure-linked equations is the flow rate allocated to each of the open boundaries within the solution domain. The methodology isdemonstrated by simulating the laminar flow of an incompressible Newtonian fluid in a duct with a 90 degree branch.