Paper Submission
ETC2019 17th European Turbulence Conference





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14:00   Instability, Transition and Control of Turbulent Flows 4
14:00
15 mins

#447
Instability of flow subregions in three-dimensional wake transition
Andrey Aleksyuk, Victor Shkadov
Abstract: Three-dimensional instability of two-dimensional flow subregions in the wake is considered. A classical example of the transition to three-dimensionality in the wake behind a circular cylinder includes two stages of stability losses with the increase in the Reynolds number: modes A and B [Williamson, 1988]. These modes can be well predicted by global stability analysis of the two-dimensional periodic von Karman vortex street [Barkley, Henderson, 1996]. The studies of these modes (see, for example, [Aleksyuk, Shkadov, 2018, 2019; Barkley, 2005; Giannettiet al., 2010; Thompson, et al., 2001; Julien et al. 2005]) allow to suggest that the reasons of transitions A and B can be localized and described as instability of particular flow subregions, such as vortex cores and braid shear layers. The aim of the present work is to clarify the physical mechanisms leading to the appearance of three-dimensionality in the local parts of the flow. The local description of the flow is given based on the approach [Aleksyuk, Shkadov, 2018, 2019]: the development of small longitudinal perturbations of vorticity and velocity is described by a closed system of equations with a clear meaning of each term (mechanism, such as vorticity diffusion, stretching and tilting of vortex lines), affecting their growth and decay. The base flow is characterized by vorticity, the positive eigenvalue of the strain rate tensor and its direction. Base and perturbed flows for this analysis are obtained using the direct numerical solution of the Navier-Stokes equations. The results of the instability analysis of idealized flows in vortex cores and in braid shear layers are compared to the real flow data from numerical simulations. Viability of such idealized models is discussed. The research is carried out using the equipment of the shared research facilities of HPC computing resources at Lomonosov Moscow State University. This work is supported by the grants of the Russian Foundation for Basic Research No. 18-01-00762 and 18-51-00006.
14:15
15 mins

#349
Buoyancy-suppressed transition in pipe flow
Ashley Willis, Elena Marensi
Abstract: See file
14:30
15 mins

#158
Linear stability of the far-jet: non-parallel effects
Rustam Mullyadzhanov, Nickolai Yavorsky, Kilian Oberleithner
Abstract: Laminar and turbulent submerged unbounded round jets are self-similar far from the motion source (nozzle). The velocity field along the centerline decays as the inverse distance R while the local width δ grows as R. We use the linear stability framework to describe both the laminar case for a perturbation growing on a steady exact solution and the turbulent case when the outcome provides the information on the large-scale coherent motion present in the flow. Based on dimensional grounds, the velocity field is represented as u = νuL(θ)/R + νvm (θ, ψ)eimφ /R, where ν is the kinematic viscosity, (R, θ, φ) denote the radius from the origin and spherical angles. For laminar jets the non-dimensional function uL (θ) corresponds to the Landau–Squire exact solution [1, 2] serving as the base flow, while vm(θ, ψ) is the perturbation depending on θ and ψ = R/sqrt{νt}. Due to the axial symmetry the perturbation field is represented by azimuthal Fourier modes with respect to φ, where m is the azimuthal wavenumber. An exact solution of the linearized equations for a perturbation for a creeping flow suggests the following simplification (see also [3]): equation (1) where k is the radial (axial) wavenumber, R0 is some typical radius (local length scale). Starting from linearized Navier–Stokes equations with this form of a disturbance one arrives to a system of ODEs. This system represents an eigenvalue problem for complex k and real Ω = ωR2 /(νt) serving as a generalized frequency. We compare results for local stability characteristics provided by the method described above with the classical quasi-parallel approach where the disturbance is represented as equation (2) where α and ω∗ is the corresponding growth rate and frequency non-dimensionalized locally using the centreline velocity and half-width of the jet δ1/2 . Note that within this approach cylidrical coordinate system is used (x, r, φ), where x and r are the streamwise and radial coordinate. This method typically ignores the derivaties of the base flow with respect to ‘slow’ streamwise coordinate as well as the radial velocity itself. Alternative way to account for non-parallelsm of the flow is to keep the corresponding terms in the linearized disturbance equations. We refer to that approach below as ‘correction’. Figure 1 demonstrates the comparison of the local growth rate against frequency revealing a destabilizing role of the non-parallelism. The full work will also present the results of WKBJ approximation [4] in the corresponding model hierarchy.
14:45
15 mins

#301
TRANSIENT DYNAMICS OF THE TURBULENT WAKE OF A THREE-DIMENSIONAL BLUNT BODY
Yann Haffner, Andreas Spohn, Jacques Borée, Thomas Castelain
Abstract: We experimentally study the transient dynamics between the lateral asymmetric states of the wake of an Ahmed-like body. Using a combination of active flow control and passive perturbations around the body, we trigger the desired transient and investigate it using synchronized time-resolved PIV and pressure measurements. These transients are characterized by a reduced aerodynamic drag. Both an increased symmetry of the wake and a lack of organization of the recirculation motion forming the low pressure region in the wake are responsible for these low-drag states.
15:00
15 mins

#313
Stabilisation of vortex shedding flow past a square prism using slip surfaces
Aswathy Nair K., Sameen A., Anillal S.
Abstract: Vortex shedding in flows past bluff bodies has significant implications in terms of the flow physics as well as the fluid-structure interactions between the wake and the body and are used as canonical models for studying building aerodynamics, tube heat exchangers, bridge piers among others. We numerically investigated the stabilisation of such vortex shedding flows past a square prism placed perpendicular to the flow by applying the Maxwell slip boundary condition on its faces wetted by the flow. Direct numerical simulations of the three dimensional Navier-Stokes and continuity equations were carried out with Reynolds number, $40 < Re < 150$, and the slip length parameter, $0 < Kn < 0.5$, in the Maxwell model as the control parameters. We examined two scenarios independently : $(i)$ slip on the top and bottom faces and $(ii)$ on the leading and trailing faces of the prism. The influence of slip on the wake dynamics was measured by computing the Strouhal number, $St$, for various $Kn$. Our analysis revealed that slip on the top and bottom surfaces of the prism is more effective in controlling vortex shedding than slip on the leading and trailing faces, with a complete suppression of vortex shedding occurring for $Re \leq 60$ in the former and no suppression or frequency reduction in the latter. A $Re - Kn$ phase space was plotted which separates the vortex shedding and the attached wake regimes for the two scenarios, as shown in figure \ref{fig1}$(a)$. A counter-intuitive island of steady attached wake region was found inside the vortex shedding regime at $Re = 70$, as seen in the figure. Further analysis of these critical $Kn$ cases using linearised perturbation equations and global stability approach, will be presented in detail at the conference.
15:15
15 mins

#376
NUMERICAL SIMULATIONS OF COUNTER-CURRENT ROUND JETS
Karol Wawrzak, Andrzej Boguslawski, Artur Tyliszczak
Abstract: The present paper focuses on LES analysis of counter-current jets under the flow conditions favorable for the global oscillations. The analyses are performed for two different configurations. In the first one the counter-current mixing region is produced near the jet outflow by a suction from the external nozzle. The second configuration assumes counter-current flow generated by two separate jets flowing in the opposite directions. The main attention is paid to the impact of the aspiration intensity expressed as I = −U2 /U1 (U1 - jet centerline velocity, U2 -velocity of the reverse flow) and the distance between the opposite nozzles on the flow characteristics.
15:30
15 mins

#433
Instability of Steady Flows in a Precessing Sphere and Spheroid
Shigeo Kida
Abstract: {\bf System to be examined}\enspace We consider the structure and instability of steady flows in a precessing spheroid, including a sphere. The flow is characterized by three non-dimensional parameters, the aspect ratio $c=b/a$, the Reynolds number $Re=a^2\itOmega_s/\nu$ and the Poincar\'e number $Po=\itOmega_p/\itOmega_s$. Here $a$ is the equatrial radius, $b$ is the polar radius, $\itOmega_s$ is the spin angular velocity, $\itOmega_p$ is the precession angular velocity, and $\nu$ is the kinematic viscosity of fluid. The spin and precession axes are assumed to be orthogonal to each other. We examine the strong spin and weak precession limit, i.e. $Po\ll Re^{-1/2}\ll 1$. \smallskip {\bf Observation}\enspace Recently a couple of interesting observations were reported on the stability boundary of steady flow in a precessing sphere and spheroid. As shown with symbols $\blacksquare$ and ● in Figure~\ref{fig1}, the stability curves behave quite differently for a sphere and a spheroid. It shows a power dependence, $Po\propto Re^{-\alpha}$, in the both cases, but the exponent $\alpha$ is significantly different between the two. It is nearly $0.8$ for a sphere, whereas $0.3$ for a spheroid. \begin{figure}[h] \begin{center} \begin{minipage}{8.5cm} {\bf Purpose}\enspace In order to derive these power laws and to understand the difference between the two cases we perform the linear stability analysis of the steady flow in a precessing spheroid of arbitrary $c$. \smallskip {\bf Two Key Characteristics of Steady Flow}\enspace It is well-known that in the strong spin and weak precession limit the flow is essentially inviscid and a uniform vorticity flow is developed in the spheroid except for a thin boundary layer. There are two key characteristics of the steady flow, leading to the observed power laws. One is the magnitude of the uniform vorticity in the inviscid region: It is much larger for a sphere than for a spheroid, i.e. by $O(Re^{1/2})$ ($\gg 1$)~\cite{bib:KidaA}. The other is the existence of critical regions, which are localized around the critical circles on which the boundary-layer approximation breaks down. \smallskip {\bf Global vs. Localized Disturbances}\enspace The present author~\cite{bib:Kida2013} investigated the parametric instability of two inertial waves with the basic solid-body-rotation flow superposed by conical shear layers in a precessing sphere. However, it failed to obtain $\alpha=4/5$ but $1/2$. Then, by examining the disturbances localized in the critical regions, he was able to determine the stability curve, $Po=28.36Re^{-4/5}$, i.e. not only the exponent but also the prefactor. \end{minipage} % \hspace{0.5cm} % %\begin{wrapfigure}[20]{r}[0mm]{80mm} %\begin{wrapfigure}{r}{20zw} %\vspace*{-\intextsep} %\begin{figure}[h] %\begin{center} \begin{minipage}{7.8cm} %\setlength{\unitlength}{1cm} \begin{center} %\includegraphics[width=3cm]{sta-diagram-ETC17} \includegraphics[clip,width=7.8cm]{sta-diagram-ETC17} \caption{Stability boundary of steady flows in a precessing sphere and spheroid. Symbols $\blacksquare$ represent the DNS data for a sphere \cite{bib:Lin_ETAL2015} and ● the experimental data for an oblate spheroid of $c=0.9$ \cite{bib:Horimoto_ETAL2018}.} \label{fig1} \end{center} \end{minipage} %\end{center} %\end{figure} %\end{wrapfigure} \end{center} \end{figure} \vspace{-0.5cm} {\bf Preliminary/Perspective}\enspace The stability boundary for a spheroid of arbitrary $c$ may be obtained in the same way as for a sphere. Assuming the disturbances be localized in the critical regions, we derived the eigenvalue problem for the growth rate. In the course of formulation we found the exponent $\alpha=3/10$, which is close to the value observed experimentally (see Figure 1) by the use of the above-mentioned fact that the velocity field in a spheroid is weaker in magnitude than that in a sphere by factor $O(Re^{1/2})$. In order to obtain the prefactor of the relation $Po\propto Re^{-3/10}$ we must solve the eigenvalue problem numerically. This calculation is underway, and the results will be presented in the conference.