Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session C08: Non Newtonian Flows : Instability and Turbulence 
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Chair: Satish Kumar, University of Minnesota Room: 212 
Sunday, November 24, 2019 8:00AM  8:13AM 
C08.00001: Modification of vortex shedding and turbulence statistics in a twodimensional turbulent flow affected by polymers. Ruri Hidema, Kengo Fukushima, Hiroshi Suzuki An experimental study was performed to investigate the relationship between the extensional rheological properties of polymer solutions and vortex deformation in turbulent flow. In order to focus on the effect of extensional rheological properties of the fluids, polyethyleneoxide was added to twodimensional (2D) turbulent flow. The 2D flow was selfstanding flowing soap films that is relatively free from shear stresses. Therefore, the flow is advantageous as it examines the effect of the extensional rheological properties of polymers on the flow. In the study, the vortex shedding in 2D turbulent flow and turbulence statistics of the vortices in the flow were observed using interference patterns and particle image velocimetry (PIV). We found that the vortex shedding in the 2D flow was categorized into three types, and this was affected by the relaxation time of the polymer solutions. The modification of the vortices varied the energy transfer in 2D flows. We have also found that characteristic energy peak due to extensional rheology of the fluids. [Preview Abstract] 
Sunday, November 24, 2019 8:13AM  8:26AM 
C08.00002: Organization of turbulence structures in polymer dragreduced turbulent channel flow Kyoungyoun Kim To investigate turbulence structures in polymer dragreduced (DR) channel flows, the spectra and correlations of the velocity fluctuations are examined by performing direct numerical simulations of viscoelastic turbulent channel flows of a drag reduction rate of 63\%. The friction Reynolds number is $Re_{\tau} = 395$ and the stresses created by adding polymer is modeled by the FENEP model. It is found that in the DR flow, the length scale significantly increases, especially in the streamwise direction. Premultiplied twodimensional spectra of streamwise velocity fluctuations show that the outer turbulence structure in the DR flow differs from those in the Newtonian flow. Twopoint correlations and conditional average flow fields reveal that the buffer layer structures near the wall are more correlated with those near the opposite wall in DR flow, which implies that a large scale outer structure organizes the buffer layer structures near both upper and lower walls. [Preview Abstract] 
Sunday, November 24, 2019 8:26AM  8:39AM 
C08.00003: Turbulent BoundaryLayer of Powerlaw Fluids Near a Position of Separation. Juliana Loureiro, Atila Silva Freire The study describes the turbulent boundary layer structure near and at a separation point for powerlaw fluid flows. Experimental work is performed for flow of water and a 0.1{\%} carboxymethyl cellulose (CMC) water blend, over an asymmetric plane diffuser with 30degree slope. The flow index n and the consistency parameter K are respectively 0.86 and 0.00753 (Pa s$^{\mathrm{n}})$. Particle Image Velocimetry and Laser Doppler Velocimetry are used to introduce profiles of local mean velocity, turbulent shear stresses at the points of separation, reattachment and in the recirculation region. The location of the separation and reattachment points are described in terms of changes in the generalized Reynolds number based on the channel height. Experiments are conducted for two different Reynolds numbers. The work reports large changes in the length of the separation regions and discusses the local solutions of Goldstein (1948) and Stratford (1959). In the fully viscous region, the mean velocity is shown to vary as y$^{\mathrm{(n+1/n)}}$, as expected from the local analytical solution, with y as the distance from the wall. In the fully turbulent region, the mean velocity profile follows a y$^{\mathrm{1/2}}$ law, being thus independent of rheology of the fluid. [Preview Abstract] 

C08.00004: ABSTRACT WITHDRAWN 
Sunday, November 24, 2019 8:52AM  9:05AM 
C08.00005: Exact coherent structures in twodimensional viscoelastic channel flow Jacob Page, Yves Dubief, Rich Kerswell Elastoinertial turbulence (EIT) is a recently discovered flow state in dilute polymer solutions that is strikingly different to quasiNewtonian, dragreduced flows. EIT is largely twodimensional; its dominant flow features are thin sheetlike structures of polymer stress with attached patches of intense spanwise vorticity. In this talk we explore the mechanics underpinning EIT by searching for exact coherent structures in elastoinertial planar channel flows. The structures we find are all connected to a recently discovered linear instability (Garg et al, Phys. Rev. Lett. 121, 2018) of the basic state that exists at moderate elasticities $Wi < Re < Wi^3$. Just beyond the point of marginal stability ($Wi \sim 25$, $Re\sim 50$) the global attractor is a relative periodic orbit (RPO) featuring a pair of large amplitude sheets that meet at the centreline. This RPO bifurcates off a strongly subcritical travelling wave that exists for Weissenberg numbers as low as $Wi \sim 10$. We perform branch continuation of this travelling wave upwards in Reynolds number to explore its overlap with EIT. Time permitting, we will also discuss the physical mechanisms at play in the new linear instability. [Preview Abstract] 
Sunday, November 24, 2019 9:05AM  9:18AM 
C08.00006: Critical layers, TollmienSchlichting waves and elastoinertial turbulence Ashwin Shekar, Ryan McMullen, Beverley McKeon, Michael Graham We describe direct numerical simulations (DNS) and linearized analyses of channel flow turbulence in a FENEP fluid in the elastoinertial turbulence (EIT) regime. Simulations at low (transitional) Reynolds numbers are shown to display localized polymer stretch fluctuations very similar to structures arising from linear stability (TollmienSchlichting (TS) modes) and resolvent analyses: i.e., criticallayer structures localized where the mean fluid velocity equals the wavespeed. Selfsustained nonlinear TS waves display stagnation points that generate sheets of large polymer stretch. These kinematics may be the genesis of similar structures in EIT. We also describe a new selfsustaining elastoinertial state which we term the lower branch attractor (LBA), which has very small amplitude and whose structure closely resembles that of the linear TS mode. A tentative bifurcation scenario describing our observations is described. We also identify the mimimal flow unit for EIT, which at low Reynolds number continues to exhibit localized stress fluctuations. Finally, resolvent analysis and transient simulations of the linearized problem shed light on the origins of the mechanisms leading to amplification of fluctuations and thus to the bypasstransition nature of the onset of EIT. [Preview Abstract] 
Sunday, November 24, 2019 9:18AM  9:31AM 
C08.00007: What do we mean by the mean conformation tensor (in viscoelastic turbulence)? Ismail Hameduddin, Tamer Zaki The popular arithmetic mean conformation tensor frequently used in the analysis of turbulent viscoelastic flows is not a good representative of the ensemble. Alternative means more faithful to the tensorial character of the conformation tensor are evaluated, namely, the geometric and logEuclidean means. These means are mathematically consistent with the Riemannian structure of the manifold of positivedefinite tensors, on which the conformation tensor lives, and have useful properties that make them attractive alternatives to the arithmetic mean. Using a turbulent FENEP channel flow dataset, it is shown that these two alternatives are physically representative of the ensemble. By definition, these means minimize the geodesic distance to realizations and exactly preserve the scalar geometric mean of the volume and of the principal stretches. [Preview Abstract] 
Sunday, November 24, 2019 9:31AM  9:44AM 
C08.00008: En Route to the Maximum Drag Reduction Asymptote George Choueiri, Jose Lopez, Atul Varshney, Bjorn Hof We report the results of an experimental investigation into the stability of viscoelastic pipe flow. We document the developmental stages, starting from a supercritical instability that occurs at Reynolds numbers $O$(1), provided that the shear stress (and hence the Weissenberg number) is sufficiently large, all the way to the maximum drag reduction (MDR) asymptote for dilute polymer solutions. At onset the amplitude of streamwise velocity fluctuations is found to grow with the square root of the Reynolds number. It is noteworthy that this primary instability is nonhysteretic and appears in the absence of perturbations and curved streamlines. The flow structures observed closely resemble those of the unstable mode discovered in a recent stability analysis. Further from onset, a secondary instability is found where the azimuthal symmetry is broken and inclined streaks of high amplitude appear in the near wall region. These streak patterns resemble the typical flow structures found in MDR turbulence at higher Reynolds numbers. [Preview Abstract] 
Sunday, November 24, 2019 9:44AM  9:57AM 
C08.00009: Twodimensional direct numerical simulations of viscoelastic jets Konstantinos Zinelis, Thomas Abadie, Ricardo ConstanteAmores, Omar Matar The numerical simulation of spray formation in a nonNewtonian fluid offers substantial challenges and is central to numerous industrial applications such as spraydrying. The aim of the present work is to set the basis for the numerical examination of nonNewtonian atomisation and spray systems. To achieve this, a Direct Numerical Simulations (DNS) approach is followed where all the temporal and spatial scales are resolved completely. We begin with the simulation of twodimensional numerical simulations of an OldroydB impulsive jet as well as a jet with a constant release velocity into a stagnant gaseous phase using the volumeoffluid technique to capture the interface and the logconformation transformation for the solution of the viscoelastic constitutive equation. This permits the exploration of parameter space, capturing the effect of the elastic, viscous, and inertial forces on the ejected droplet size. These simulations serve as a departure point for further work involving threedimensional simulations of atomisation processes of viscoelastic jets. [Preview Abstract] 
Sunday, November 24, 2019 9:57AM  10:10AM 
C08.00010: A WellConditioned Numerical Method for Resolvent Analysis of Viscoelastic Channel Flows Gokul Hariharan, Mihailo Jovanovic, Satish Kumar Linear analyses provide useful information about the potential for transition to nonlinear states. While a modal approach furnishes information about longtime growth or decay of initial conditions, nonmodal approaches give insight into the amplification of disturbances in a linearly stable flow. Here, we conduct nonmodal analysis of inertialess 2D viscoelastic channel flows. Our analysis reveals large stress gradients in the nearwall region (for plane Poiseuille flow) and in the channel center (for plane Couette flow). These steep stress gradients can only be resolved using recently developed wellconditioned spectral methods, e.g., the ultraspherical and spectral integration methods. Furthermore, even if the discretization method is wellconditioned, computation of frequencyresponses can be erroneous if singular values are obtained as the eigenvalues of a cascade connection of the resolvent operator with its adjoint. We address this issue by introducing a feedback interconnected system that avoids matrix inverses and allows reliable frequencyresponse calculations of viscoelastic channel flows at high Weissenberg numbers ($\sim$500). The steep stress gradients that we identify may play a role in explaining recent experiments concerning transition to elastic turbulence. [Preview Abstract] 
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