Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session KK: Non-Newtonian Flows II |
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Chair: Joe Goddard, University of California, San Diego Room: Hilton Chicago Joliet |
Monday, November 21, 2005 4:10PM - 4:23PM |
KK.00001: Multi-scale simulations of shear-dominated flows of rigid rod dispersions M. Gregory Forest, Ruhai Zhou, Qi Wang, Hong Zhou The Doi-Hess theory coupled with an anisotropic Marrucci-Greco distortional elasticity potential provides a multi-scale description of the flowing nematic liquid crystalline polymers (LCPs). We have developed numerical simulation methods for the model equations for structure formation of LCPs in confied, planar Couette cells. In this talk we will provide some computational results from our numerical simulations. This includes the steady state structure in weak shear flow, structure transtions in the space determined by the Ericksen number and the Deborah number, the out-of-plane attractors and the chaos phenomena. [Preview Abstract] |
Monday, November 21, 2005 4:23PM - 4:36PM |
KK.00002: WITHDRAWN: Taylor limit of equilibration for mass transport in transversely bounded rectilinear flows Juin Yu The multimode diffusion approximation for solute dispersion in transversely bounded shear flows owes its origin to the formal method of eigenmode expansion. It is put forth upon the premise that a quasi-steady condition termed the Taylor limit of equilibration exists in the course of time when equilibrium estimates of the residual terms of the concentration distribution can be realistically made contigent to the evolution of their primary counterparts. By applying the Green's function for the diffusion equation, this paper provides a qualifying account for the establishment of the Taylor limit. A method of successive approximation is derived for the determination of the principal mode coefficient functions with the inclusion of bulk reaction and longitudinal diffusion. The resulting equations governing the evolution of these coeficient functions are truncated to conform to the multimode diffusion type. Examples are given to illustrate the attainment of a convergent solution. [Preview Abstract] |
Monday, November 21, 2005 4:36PM - 4:49PM |
KK.00003: Changes of K\'{a}rm\'{a}n vortex shedding from a cylinder due to weak fluid elasticity Chris Pipe, Peter Monkewitz Experiments on vortex shedding from a cylinder placed in uniform flows of dilute polymer solutions are reported for Reynolds numbers from 50 to 150. The fluids used were aqueous solutions of polyethylene oxide (PEO) and rheological characterization showed them to have a constant viscosity over a wide range of shear rates. Using the Zimm model relaxation time the Deborah numbers calculated for the cylinder wake are O(10$^{-3})$. Parallel vortex shedding was induced with a combination of end-cylinders and end-plates. The resulting nominally two-dimensional cylinder wake was investigated using LDA, PIV, hydrogen bubble visualizations and hot film anemometry. The characteristics of the von K\'{a}rm\'{a}n instability - the critical Reynolds number, maximum perturbation amplitudes, etc. - are presented as a function of PEO concentration. It is shown that even small amounts of polymers, corresponding to low Deborah numbers, have a significant stabilizing effect which is only counteracted by shear-thinning at higher concentrations. [Preview Abstract] |
Monday, November 21, 2005 4:49PM - 5:02PM |
KK.00004: Nonlinear instabilities in parallel shear flows of viscoelastic fluids Alexander Morozov, Wim van Saarloos Newtonian fluids are known to exhibit turbulent behaviour at large enough Reynolds numbers. Recently, it has been discovered that flows of visco-elastic fluids in simple geometries become chaotic at arbitrary low Reynolds numbers (the so-called ``elastic turbulence''). When elastic stresses become large enough, laminar flows lose their stability and become turbulent. However, a little is known about the exact nature of this instability. Model calculations reveal that for some geometries the basic flow can become linearly unstable, while for the others it stays linearly stable for any value of the elastic stresses. Here we present a non-linear mechanism of the flow instability: independently of the presence or absence of the linear instability, the finite-amplitude disturbances can result in flow destabilization. We calculate the onset of this transition for plane Couette and plane Poiseuille flows and show that its sub-critical nature leads to the chaotic regime very close to the onset. We discuss briefly the role of these finite-amplitude solutions in sustaining visco-elastic turbulence. [Preview Abstract] |
Monday, November 21, 2005 5:02PM - 5:15PM |
KK.00005: An exponential mapping for the conformation tensor for flow of viscoelastic fluids; application in turbulent channels K. Housiadas, A. Beris The conformation tensor, a quantity that describes the internal microstructure of polymer molecules, is usually being used as the primary variable in viscoelastic flow calculations. Its main property is that is a positive definite, second order, tensor. Unless special care is taken, the conformation tensor may lose this property resulting to instabilities during the calculations and finally either to break-up of the simulations or to non-physical results. This situation is greatly intensified under turbulent flow conditions. In order to resolve these problems we have expressed the conformation tensor, `c', as the exponential of another tensor `a', c=exp(a), and we solve for `a' instead of `c'. By construction, the positive definite property of `c' is always preserved since its eigenvalues are the exponential of the eigenvalues of `a'. The method is illustrated for viscoelastic turbulent channel flow. Direct Numerical Simulations are being performed using spectral spatial approximations and a stabilizing artificial diffusion term in the viscoelastic constitutive model. That term is needed to smooth the solution to be resolvable with the mesh size used due to the very fine scales that are being created in chaotic flow fields. The FENE-P constitutive model is used to represent the effect of polymer molecules in solution. We will offer a comparison of the results, for exactly the same flow, viscoelastic and numerical parameters, using the old and the new formulation of the constitutive model in terms of the conformation tensor and the exponential tensor, respectively. [Preview Abstract] |
Monday, November 21, 2005 5:15PM - 5:28PM |
KK.00006: Statistical closure for homogeneous turbulent shear flow of a dilute polymer solution Shi Jin, Dario Vincenzi, T. Vaithianathan, Lance Collins, Eberhard Bodenschatz Dilute polymer solutions exhibit macroscopic behaviors that distinguish them from ordinary Newtonian fluids. For example, minute concentrations of polymers (parts per million on a weight basis) can lead to impressive reductions in the drag on solid surfaces (by up to 80\%). Numerical simulations of viscoelastic flows are generally based on an evolution equation for the conformation tensor of the polymer, $C_{ij}=\langle r_i r_j\rangle$, where $\mathbf{r}$ is the separation vector between the ends of the molecule and the angle brackets indicate an average over the Brownian configuration space of the molecule. Direct numerical simulations (DNS) of viscoelastic turbulence are able to reproduce the key phenomenology found in experiments; however, they are limited to modest values of the Reynolds number. An alternative approach is to seek a closed equation for the average configuration tensor that could be coupled to a Reynolds averaged Navier Stokes (RANS) solver. We propose a set of effective equations of motion for the mean conformation tensor rooted in the analysis of Lagrangian stochastic models with independent correlation times for velocity rate-of-strain and rate-of-rotation tensors. The proposed closure is compared with numerical simulations of Gaussian stochastic flows and DNS of homogeneous turbulent shear flows. [Preview Abstract] |
Monday, November 21, 2005 5:28PM - 5:41PM |
KK.00007: PIV and LIF measurements of a turbulent boundary layer with injected drag-reducing polymers at high Reynolds numbers Ghanem Oweis, Eric Winkel, David Dowling, Marc Perlin, Steven Ceccio The injection of aqueous solutions of large molecular weight polymers into the near wall region of turbulent boundary layers (TBL's) has been known to produce significant reductions in friction drag. The goal of this study has been to make unique experimental measurements that illuminate the behavior of TBL's modified by slot injected polymers, and to assist with predictive code development efforts by producing experimental data sets at scales emulating prototype applications. For the present experiments, the model is a hydrodynamically smooth flat plate that measures approximately 13 m in length, and is 3 m wide. Free stream water speeds as high as 20 m/s were investigated, resulting in length-based Reynolds numbers above 200 million, and boundary layer thickness of $\sim $10 cm. Polyethylene oxide (PEO) based polymers were chosen for this study. We discuss near wall (y $<$ 0.2 cm) velocity measurements of the TBL produced by particle image velocimetry and polymer concentration measurements produced by non-simultaneous laser induced fluorescence. [Sponsored by DARPA] [Preview Abstract] |
Monday, November 21, 2005 5:41PM - 5:54PM |
KK.00008: The Mechanism of Polymer Drag Reduction derived from Numerical Simulations Yves Dubief, Vincent Terrapon, Eric Shaqfeh, Parviz Moin This talk revisits the mechanism of polymer drag reduction proposed by Dubief {\it et al.} ({\it J. Fluid Mech.}, {\bf 514}, pp 271-280, 2004) derived from the observation of coherent transfers of energy between polymers and velocity fluctuations. We present further proofs of this mechanism using Lagrangian tracers to represent polymer molecules in drag reduced flows as well as controlled numerical experiments to isolate various phenomena involved in the mechanism. Turbulence reduction, impacting mainly near-wall vortices, and increase, occurring in high-speed streaks very near the wall, are found to result from the dynamics of highly stretched polymers. We will discuss various scenarios to explain the occurrence of Maximum Drag Reduction based on our mechanism. [Preview Abstract] |
Monday, November 21, 2005 5:54PM - 6:07PM |
KK.00009: Long Chain Polymers and Bubbly Drag Reduction in Taylor-Couette Flow Daniel Lanterman, Thomas H. van den Berg, Dennis van Gils, Stefan Luther, Detlef Lohse, Daniel P. Lathrop Small amounts of long chain polymers have been shown to dramatically reduce the drag of some turbulent flows. This effect is examined in a Taylor Couette apparatus ($Re=1.4\cdot 10^6$) instrumented to measure torque on the inner cylinder. Particular attention is paid to changes in drag reduction over time as a result of polymer degradation, and light scattering measurements are presented to quantify the change in polymer characteristics. Results are compared to drag reduction by bubble injection in the same apparatus and both methods are also examined in case of rough walls. The polymer used is polyacrylamide with mean molecular weights ranging from $8 \cdot 10^5$ to $1.8 \cdot 10^6$ Daltons. Concentrations range of 0.5 to 100 parts per million by mass. [Preview Abstract] |
Monday, November 21, 2005 6:07PM - 6:20PM |
KK.00010: Stretching of dumbbells around the Kolmogorov scale in a turbulent shear flow Joerg Schumacher, Jahanshah Davoudi We present numerical studies of kinematic stretching of Hookean dumbbells in a turbulent Navier-Stokes flow with a linear mean profile, $\langle u_x\rangle=Sy$. The simulations combine Brownian dynamics of the dumbbells with a high-resolution pseudospectral calculation of the simple shear flow. Scales below the viscous Kolmogorov scale, at which most of the dumbbell dynamics is present, are well resolved. The variation of the constant shear rate $S$ causes a change of the velocity fluctuations on all scales and thus of the intensity of local stretching rate of the advecting flow. The latter is measured by the maximum Lyapunov exponent $\lambda_1$ and scales as $\lambda_1\sim \epsilon^{1/2}\sim S^{3/2}$. As suggested by de Gennes and Tabor, turbulence is found to stop the stretching of Hookean dumbbells when the full nonlinear velocity differences with respect to the bead positions are taken. The growth of anisotropy of stretching with increasing shear rate is confirmed by the joint statistics of the extension $R$ with the azimuthal angle $\phi$ and the polar angle $\theta$, respectively. [Preview Abstract] |
Monday, November 21, 2005 6:20PM - 6:33PM |
KK.00011: \textbf{Initiation vs. Sustenance of Active Polymer-Turbulence Interactions}. James Brasseur, Ashish Robert, Lance Collins, T. Vaithianathan Lumley (1973) theorized that polymer molecules are passively stretched only by strain-dominated turbulent eddies with time scales below polymer relaxation time. Tabor {\&} DeGenne (1986) added the argument that \textit{active} turbulence-polymer energy exchange occurs only at strain-dominated eddies where polymer elastic and turbulent kinetic energies are comparable. The Lumley-Tabor-DeGenne (LTG) arguments suggest an interruption to the energy cascade with an effective increase in small-scale cutoff scale. With these concepts in mind, we analyzed the evolution of polymer-laden homogeneous shear turbulence---from an initial period of passive stretch, through initiation of active polymer-turbulence interaction, to quasi equilibrium---using DNS with accurate numerical implementation of the FENE-P model. We find at equilibrium, contrary to the LTG arguments, that polymer-turbulence energy exchange is concentrated at the largest eddies. Evolution backwards in time, however, leads to a state more consistent with LTG phenomenology, suggesting relevance to the model at the point of transition from passive to active polymer in quasi Newtonian turbulence. LTG phenomenology rapidly loses its relevance, however, as turbulence evolves towards an equilibrium state of active polymer-turbulence interactions. [Preview Abstract] |
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