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10:45   Non-Newtonian Flows 2 10:45 15 mins #17 Direct numerical simulations of turbulent viscoelastic jets described by the FENE-P model Mateus Guimarães, Nuno Pimentel, Fernando Pinho, Carlos da Silva Abstract: Several spatial direct numerical simulations (DNS) of turbulent planar jets of dilute polymers, described by the finitely extensible non-linear elastic constitutive equation closed with the Peterlin approximation (FENE-P) with $L^2=10^4$, $\beta=0.8$, and a fixed Reynolds number of $Re=3500$ are carried out in order to investigate and develop a theory for the far field of the viscoelastic jet. These are the first massive direct numerical simulations of these flows, and use the algorithm proposed by \cite{vaithianathan2006improved} to tackle with the complex numerical challenges posed by these heavy computations. The data obtained from the jet DNSs cover the entire transitional region as well as the fully turbulent far-field up to 18 slot widths. The influence of rheological parameters of the fluid on the turbulent statistics of the jet are discussed, revealing considerable changes in comparison to the Newtonian case. In particular, the solvent maximum value of the mean rate of dissipation of turbulent kinetic energy is reduced by more than 80\% in the most dramatic case, clearly showing the influence of the polymers on the flow development. Significant changes are also found in the jets spreading and decay rates (Fig.\ \ref{fig1}g-h), as well as in the Reynolds stress (Fig.\ \ref{fig1}a-d) and mean velocity profiles. A new theory based on order of magnitude considerations and on hypothesis regarding the self-similar behaviour of the mean flow is proposed and validated by the DNS data. The theory results in new analytical expressions for the jet spreading and decay rates and for the stream-wise evolution of the characteristic mean polymeric shear stress ($\sigma^{[p]}_c$), such as $\delta \sim x$, $\quad U_c \sim x^{-1/2}$, and $\quad \sigma_{c}^{[p]} \sim x^{-3}$. The theoretical and DNSs results display a good agreement, as illustrated in Fig.\ \ref{fig1}e-h. 11:00 15 mins #108 Elastic Range Scaling in Turbulent Flow of Dilute Polymer Solution Yi-Bao Zhang, Haitao Xu, Eberhard Bodenschatz, Heng-Dong Xi Abstract: It has been known for a long time that minute amounts of long chain flexible polymer dissolved in fluid flow can drastically change the flow properties, such as reducing the drag experienced by solid surfaces \cite{Lumley:1969, Procaccia:2008}, inducing the elastic turbulence \cite{Groisman:2000}, modifying the energy transfers \cite{Ouellette:2009, Xi:2013} and heat transfer process \cite{Xie:2015} in turbulent flows. In three dimensional fully developed turbulence, the fluctuating energy is fed into the fluid at integral scale $L$, and dissipated at Kolmogorov scale $\eta$ where viscosity becomes effective. At intermediate scales $r$ ($L\gg r \gg \eta$) called inertial range, the energy is transferred to smaller scales continuously and the average energy flux is constant and independent of viscosity. When polymers are added into the flow, they would draw energy from the flow when they are stretched, and feed back energy to the flow when they coils back. In addition, they dissipate energy due to Stokes frictional drag. It has made a consensus that polymer can change the elegant energy cascade picture below a critical length scale which can be determined through the so-called ``time criterion" model proposed by Lumley \cite{Lumley:1969}, or the ``energy balance" model proposed by Tabor and de Gennes\cite{Tabor:1986, Gennes:1986}, or the ``energy flux balance" model \cite{Xi:2013}. The experimental results are in favor the ``energy flux balance" model \cite{Xi:2013, Sinhuber:2018}. Although all the above mentioned models suggest a critical scale below which the energy cascade will be suppressed or truncated, little is know on how energy is transferred in this suppressed or truncated range. \\ In this presentation, we show velocity measurement in a turbulent von K\'{a}rm\'{a}n swirling flow of water and dilute polymer solution. We found that with increasing polymer concentration a new scaling range, where $D_{LL} \sim r^{1.38}$, emerges. The new scaling is in between the dissipation range ($D_{LL} \sim r^{2}$) and the inertial range($D_{LL} \sim r^{\frac{2}{3}}$). This finding and the results of the higher order velocity structure functions show, for the first time, how energy is transferred when the flow is strongly affected by the polymer additives. \\ We are grateful to the support by the National Natural Science Foundation of China (11472094, 11772259, and U1613227), and the the ``111 project'' of China (B17037). 11:15 15 mins #295 The turbulent/non-turbulent interface layer in a viscoelastic fluid Hugo Abreu, Fernando Pinho, Carlos da Silva Abstract: Many flows are characterised by the coexistence of turbulent (T) and irrotational (or non-turbulent - NT) flow regions e.g. wakes, where the two flow regions are separated by a very sharp interface layer: the turbulent/non-turbulent interface (TNTI)[1]. When very long chains of molecules (polymers) are dissolved into a Newtonian solvent the resulting medium exhibits complex viscoelastic properties that substantially affect the flow, and present substantial less entrainment than Newtonian fluids[2]. However, several of the mechanisms governing the enstrophy near the TNTI layer need clarification, particularly the role of new viscoelastic terms and their impact on classical quantities, where virtually no experimental data or numerical simulations have been reported. In the present work new massive DNS of viscoelastic fluids are carried out to analyse the enstrophy dynamics within the TNTI layer. The DNS used the finitely extensible elastic model with the Peterlin closure (FENE-p) is used to compute the polymer stresses. One Newtonian and 4 viscoelastic simulations have been carried out, where the maximum relaxation time of the polymer molecules is equal to τ p = [0.025, 0.05, 0.100, 0.200] s. To the author’s knowledge these are the biggest DNS carried out so far for the FENE-p fluid. Figure 1 (left and center) shows iso-surfaces of vorticity magnitude corresponding to the irrotational boundary (IB) that constitutes the outer border of the TNTI layer separating T from NT fluid, for a Newtonian and a viscoelastic fluid. It is clear that the typical roughness associated with this interface is substantially altered for viscoelastic fluids, compared to the Newtonian case, where the IB is much more convoluted, and suggests that a substantial increase of the integral scale exists in these cases. Figure 1 right shows the conditional enstrophy budgets of the fourth viscoelastic fluid. While for a Newtonian fluid the enstrophy production is roughly balanced by the enstrophy dissipation, in the viscoelastic case a new term arises - viscoelastic production - that can increase or decrease the enstrophy within the T region. This in turn affects the mechanism of generation of enstrophy in the TNTI layer, which modifies the entrainment rate characteristics of the flow, the details of which, will be discussed in the presentation. 11:30 15 mins #567 MATHEMATICAL MODELING OF NON-NEWTONIAN GEOPHYSICAL FLOWS Margarita Eglit, Alexander Yakubenko, Julia Zaiko Abstract: We present new mathematical models for dense geophysical gravity-driven mass flows, such as snow avalanches, mudflows, rapid landslides, etc. [1, 2]. These flows can pose grave hazards to people and property. Knowledge of their dynamic parameters and run-out distance, i.e., the boundaries of the affected area, is very important for properly land planning in mountains and design of defense constructions. The following three properties of geophysical slope flows must be taken into account when constructing mathematical models for them. First, the moving material, as a rule, has complicated non-Newtonian rheological properties: avalanches and landslides, e.g., can stop at an inclined slope. It means that the material has the yield limit. Second, dense gravity-driven flows always entrain the bed material while descending steep slopes; their mass may increase several times during movement [3]. Third, the flows may be laminar, but most of large geophysical flows are turbulent. To describe the rheological properties of the flow material here we use the so-called Herschel–Bulkley model, which can correspond to both linear and nonlinear viscous (power-law) fluids, as well as media with a yield stress, in particular, the Bingham fluid, by the appropriate choice of the coefficients. We model the effect of the basal entrainment assuming the following hypothesis [4]: the entrainment occurs, when the shear stress on the flow bottom reaches the value of the bed material shear strength. The last point in constructing the mathematical model is the account for turbulence of the flow. We deal with the Reynolds’s averaged equations. To obtain the closed system of equations we employ the three-parameter turbulence model developed by Luschik, Paveliev and Yakubenko [5] which was successfully applied to simulate turbulent flows in pipes and channels with account for heat transfer, mass exchange through porous walls and nonlinear temperature dependence of the fluid viscosity coefficient. The model was genereliesd [1,2] to account for flow unsteadiness, complicated rheological properties, the presence of a free upper boundary, and the mass transfer at the lower flow boundary. Simulations of flows with different rheological properties have been done to investigate the effect of the mentioned three factors. For flows down long homogeneous slope some conclusions resulting from analysis of the simulations are as follows. 1. By entrainment the underlying material, the velocity and thickness of the flow increase. 2. When moving along homogeneous slope with entrainment, at large times from the start of the entrainment, regardless of the rheological properties of the flow, the velocity on the surface of the flow, the depthaveraged velocity and the flow depth grow linearly with time until exhausted the entire available mass. 3. For all the models studied, the bottom material entrainment rate tends with time to a constant, the magnitude of which depends only on the slope angle and the physical properties of the flow and the bottom. 4. The presence of the yield limit leads to a delay of the start of entrainment, a lower entrainment rate compared to flow of media that do not have a yield limit. 5. The molecular viscosity has an effect on the turbulent parameter distributions in the flow cross-section In the Bingham and dilatant power-law flows with entrainment the turbulent shear stress and energy profiles may have two local maxima, one near the bottom and the other in the medium part of the flow cross-section. This work was supported by the Russian Foundation for Basic Research (Project 17-08-00115). References [1] M. E. Eglit and A.E.Yakubenko The effect of bed material entrainment and non-Newtonian rheology on dynamics of turbulent slope flows. Fluid Dyn. 51 (3) 299–310, 2016. [2] M.E. Eglit, A.E. Yakubenko, J.S. Zayko. Mathematical modeling of slope flows of non-Newtonian media. Proceedings of the Steklov Institute of Mathematics, 300 219–229, 2018. [3] B. Sovilla, P. Burlando and P. Bartelt. Field experiments and numerical modeling of mass entrainment in snow avalanches J. Geophys.Res. 111 F03007, 2006. [4] D. Issler and M. Pastor Peréz. Interplay of entrainment and rheology in snow avalanches; a numerical study. Annals of Glaciology 52(58) 143-147, 2011. [5] V.G. Lushchik, A.A. Paveliev and A.E. Yakubenko. Three-parameter model of shear turbulence. Fluid Dynamics 13 (3) 350-362, 1978 11:45 15 mins #589 EXPERIMENTAL ANALYSIS OF COHERENT STRUCTURES IN NON-NEWTONIAN POWER LAW FLUIDS Leonardo Castellanos Gonzalez, Cristian Potosi Rosero, Juliana Rodrigues Loureiro, David Dennis Abstract: The present work applies the method introduced by Dennis and Nickels (2009) to discuss the turbulent flow structure of power-law fluids. An important feature of the method is its inherent capability to identify very large scale motions. Stereoscopic Particle Image Velocimetry measurements are performed in a rectangular channel with a cross section area of 150x20 mm and flow rates of 9.6 and 15.6 m3h-1. Three concentrations of Carboxymethyl Sodium Cellulose (CMC) in water were used to simulate the behavior of the Non-Newtonian fluids (0.05, 0.1 and 0.2%). Coherent structures are of substantial importance for any flow analysis for they contain a large portion of the Reynolds stresses, which are highly influential on the nature of the near-wall motions. 12:00 15 mins #419 DYNAMICS OF ELASTIC CHAINS IN TURBULENT PIPE FLOW Carlo Massimo Casciola, Francesco Battista, Paolo Gualtieri, Jean-Paul Mollicone Abstract: Elastic chain dynamics is investigated by DNS presenting results concerning turbulent pipe flow laden with strings of tracers interacting elastically. We aim at answering questions like: does the observed preferential concentration recently observed in 2D flows occur in wall bounded 3D turbulent flow? How does the presence of the walls influence the chains dynamics? The implications of the observed chain behavior will be discussed in view of turbulent drag reduction applications.