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10:45   Instability, Transition and Control of Turbulent Flows 1 10:45 15 mins #33 Optimal Initial Perturbations and the Minimal Seed of Blasius Boundary-Layer Flow Christos Vavaliaris, Miguel Beneitez, Dan Henningson Abstract: The concepts of optimal initial perturbations and minimal seed have been studied in detail in non-developing flow configurations ([2–4]). Their transfer to spatially-developing flows is non-trivial, due to the presence of the spatially-varying bifurcation parameter Re(x). This complicates the uncoupling of space and time, and results to a flow domain where both sub- and super-critical regimes ultimately coexist, thus demanding a cautious extension of the dynamical-systems formulation. The current study aims (a) to calculate optimal initial velocity perturbations and minimal transition energy thresholds for the flat-plate boundary-layer flow in realistic spatial/temporal domains; and (b) to document the energy mechanisms facilitating the disturbances’ energy growth. The novelty of the current study arises from four major differences to previous ones that have addressed similar issues [1]. First, the definition of the minimal seed is properly carried out, so that it’s applicable to spatially-developing flows. The minimal seed is the most "efficient" initial optimum, and is inherently tied to the lowest-possible initial energy level, from which a perturbation can trigger turbulent transition [2]. In [1], the minimal seed is defined as "a localized basic building block, [...] defined as the smallest flow structure which maximizes the energy growth over short times.". This is a different definition that is based on the perturbation’s spatial characteristics, and does not follow from the dynamical-systems formulation. Second, following their rigorous definition, we calculate minimal energy thresholds and for the first time the minimal seed of the flat-plate boundary layer. Third, we use larger spatial/temporal optimization domains, allowing the full localization and proper evolution of the perturbations. This is achieved by employing the higher-order spectral Nek5000 code, coupled with adjoint-based optimization and checkpointing routines. Finally, we analyze the energy mechanisms accommodating the perturbations’ growth, while comparing them to those of different flow configurations [2]. Contrary to the physical interpretation given in [1], we see evidence suggesting that the same energy growth mechanisms take place, as in, e.g., plane Couette flow [2]. 11:00 15 mins #136 TRANSITION IN BOUNDARY LAYERS WITH FREESTREAM TURBULENCE Kristina Đurović, Philipp Schlatter, Ardeshir Hanifi, Dan Henningson Abstract: Laminar-turbulent transition induced by free-stream turbulence is of great interest due to its occurrence in many practical situations like the turbo-machinery flows or the experiments in conventional wind tunnels. In the boundary-layer flows subjected to free-stream turbulence intensities of 1% or more, transition usually occurs rapidly bypassing the classical scenario triggered by the Tollmien–Schlichting waves. This type of transition is characterized by occurrence of the streamwise elongated streaky structures inside the boundary layer. As these streaks travel downstream, they break down into the turbulent spots due to their secondary instability. The spots grow in size and merge until the flow is fully turbulent. Here, we study effects of the free-stream turbulence characteristic length scales and intensity on the transition in an incompressible flat-plate boundary layer by means of direct numerical simulations. Computations are performed using the spectral element code Nek5000. The numerical setup corresponds to the experimental investigations by Shahinfar & Fransson (2013). The ideal developing boundary layer for stability and transition investigations is the one developing under zero pressure gradient. To be able to ensure zero pressure gradient, a two meters long plate with a specially designed asymmetric leading edge is used. Numerically-generated turbulence upstream of the leading edge is designed to imitate the characteristics of the grid-generated turbulence in the wind tunnel experiments. Homogeneous isotropic turbulence is prescribed as a superposition of Fourier modes with a random phase shift with total of 400 Fourier modes. The smallest wavenumber and the spanwise extension of the computational domain are chosen to correspond to several integral length scales reported in the experiments. The streamwise length scales are transformed to a temporal frequency by invoking Taylor’s frozen turbulence hypothesis. The free-stream turbulence decays in the streamwise direction according to power law with the good agreement with experiments. Various combination of levels of the free-stream turbulence intensity and integral length scales are simulated. To ensure the quality of the data, classical turbulence statistics and integral quantities are carefully evaluated showing close agreement with the corresponding experimental data. We will present results of simulations with different intensities and characteristics of the free-stream turbulence. 11:15 15 mins #360 Boundary layer transition induced by freestream turbulence subject to strong pressure gradient and high-curvature effects Yaomin Zhao, Richard Sandberg, Ivan Marusic Abstract: In the present study, we look into the bypass transition in a high-pressure turbine (HPT) of a modern aircraft engine, in which the interactions between the freestream turbulence and the boundary layer will be significantly affected by the strong pressure gradient and high-curvature around the blade. A series of wall-resolved large-eddy simulations of an HPT vane have been performed. The typical flow field around the HPT blade shows that the incoming turbulent structures wrap around the high-curvature blade leading edge and induce streamwise streaks on the blade. These vortical structures are then stretched when subjected to the strong pressure gradient through the vane passage. As the streamwise vorticity rapidly dissipates during the acceleration at the early part of the suction-side boundary layer, relaminarization appears to happen. Further downstream, a strong adverse pressure gradient develops and bypass transition takes place with the emergence of turbulent spots resulting in a fully turbulent boundary layer. Furthermore, the impact of the freestream turbulence state on the blade boundary layer is also quantitatively analyzed by comparing different cases in which the intensities and length scales of the incoming turbulence are varied. On the one hand, the cases with higher level turbulent intensity appear to have a stronger effect on the boundary layer and induce earlier suction-side transition, compared to the lower level cases. On the other hand, the length scale of the incoming turbulence not only has a direct impact on the wavelength of the leading edge streaks, but also affects the upstream turbulence decay rate. A detailed analysis on the effect of varying freestream characteristics on the transition in boundary layers subject to pressure gradient and surface curvature will be presented. 11:30 15 mins #428 Invariant solutions of the filtered Navier-Stokes equations representative of Large-scale motions in the asymptotic suction boundary layer flow Sajjad Azimi, Carlo Cossu, Tobias Schneider Abstract: The outer region in turbulent boundary layer flows is dominated by large-scale streaky motions with the dimensions in the order of the boundary layer thickness (see \cite{bib:Adrian2007} as an example). Large-scale motions are shown to be self-sustained numerically by filtering the small scales in the Navier-Stokes equations, \cite{bib:Hwang2010}. Moreover, it has been shown that these streaky motions can be captured by exact invariant solutions of the filtered Navier-Stokes equations, \cite{bib:Hwang2010,bib:Rawat2015}. We investigate the exact invariant solutions of the filtered Navier-Stokes equations representative of the large-scale structures in the asymptotic suction boundary layer flow (ASBL), which is the flow over a flat plate with a constant and homogeneous suction into the plate. In the figure, energy spectra of ASBL with and without damping the small scales, and a large-scale travelling wave solution are shown. Our results are the first exact invariant solutions of the filtered equations in the asymptotic suction boundary layer flow. These solutions are a step towards extending the emerging dynamical systems view of turbulence to the dynamics of the large-scale motions in the turbulent boundary layer flows. 11:45 15 mins #543 TRANSITION TO TURBULENCE IN GÖRTLER FLOWS Jeremie Dagaut, Guillaume Balarac, Maria-Eletta Negretti, Christophe Brun Abstract: In geophysical flows, orography plays a key role, and turbulence properties as well as mixing properties strongly depend on the terrain shape [5]. In the context of recent studies on gravity currents [3, 7], numerical simulations of a downscaled neutral atmospheric boundary layer (ABL) have been performed. The terrain is assumed to be a smooth boundary with constant curvature. In such a configuration, the ABL may develop the so-called Görtler instability (GI) that arises due to a local unbalance between the centrifugal force and the radial pressure gradient. Even though the inviscid Rayleigh criterion [8] can predict such a centrifugal instability, a more comprehensive study [4], on which the present work is based, allows one to predict the stability of a flow over a curved boundary given the wavenumber α and the Görtler number G = (U θ/ν) (θ/R)1/2 , where θ is the momentum thickness and R is the radius of curvature. Experimental studies [9, 2] tend to confirm results from the linear stability analysis although significant differences are observed in term of spatial growth rates caused by non-linear contributions [4]. Present simulations are performed using YALES2 [6], a finite volume LES solver for unstructured grids that is able to reproduce flow physics for fairly high Reynolds numbers (Reδ = 10³ ∼ 10⁴) and thus enables us to investigate the onset and development of Görtler instability under turbulent initial conditions [1]. The geometrical configuration (figure 1.a) displays a curved part with a radius of curvature R = 30.0 m. The initial boundary layer thickness is δ = 1.0 m. Observed values for G vary from 5 to 20 and the wavelength λ varies from 0.8 m to 1.6 m. Part of the presented simulations are performed using periodic roughness patterns at the wall in order to force the wavelength selection process. The wavelength selection is shown to have an impact on the development of both primary and secondary Görtler instabilities. The inflectional velocity profiles are also dependent on the wavelength selection, as well as the turbulence properties in the non-linear region. Resulting disturbance-velocity profiles are consistent with the linear stability analysis. This work also includes simulations without wavelength forcing. The numerical wavelength selection process then leads to the growth of multiple wavelengths in the flow, with different levels of occurrence and with one dominant wavelength. The dominant wavelength is compared with the most amplified wavelength expected from theory. The influence of inlet parameters on the wavelength selection process is presented. [1] P. Benard, G. Balarac, V. Moureau, C. Dobrzynski, G. Lartigue, and Y. D’Angelo. Mesh adaptation for large-eddy simulations in complex geometries. International Journal for Numerical Methods in Fluids, 81(12):719–740, 2016. [2] H. Bippes. Experimental study of the laminar-turbulent transition of a concave wall in a parallel flow. 1978. [3] C. Brun. Large-eddy simulation of a katabatic jet along a convexly curved slope: 2. Evidence of görtler vortices. Journal of Geophysical Research: Atmospheres, 122(10):5190–5210, 2017. [4] J. M. Floryan and W. S. Saric. Stability of gortler vortices in boundary layers. AIAA journal, 20(3):316–324, 1982. [5] J. Kaimal and J. Finnigan. Atmospheric boundary layer flows: their structure and measurement. Oxford university press, 1994. [6] V. Moureau, P. Domingo, and L. Vervisch. Design of a massively parallel cfd code for complex geometries. Comptes Rendus Mécanique, 339(2):141 – 148, 2011. High Performance Computing. [7] M. E. Negretti, J.-B. Flòr, and E. J. Hopfinger. Development of gravity currents on rapidly changing slopes. Journal of Fluid Mechanics, 833:70–97, 2017. [8] Lord Rayleigh. On the dynamics of revolving fluids. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 93(648):148–154, 1917. [9] I. Tani. Production of longitudinal vortices in the boundary layer along a concave wall. Journal of Geophysical Research, 67(8):3075–3080, 1962. 12:00 15 mins #80 NOISE EMISSION OF SUB- AND SUPER-SONIC BOUNDARY LAYER FLOWS Yi Zhang, Martin Oberlack Abstract: The theory of acoustics is based on the linearized Euler equations for compressible flows. For plane shear flows, a normal-mode approach for density, pressure and velocity is applied, similar to the classical stability theory, which involves Fourier decomposition of the disturbances into main flow direction, span and time. The Pridmore-Brown equation results, a second order equation, whose complexity is depending on the ansatz of the velocity profile. Before our study, there were only analytical solutions for the simplest case, i.e. the equation with a linear shear profile, since the complete solution of other velocity profiles turned out to be difficult due to various mathematical obstacles. In our approach, we first study the analytical solution of the two-dimensional Pridmore-Brown equation for a boundary layer flow, where the velocity profile is approximated by an exponential. With this, the Pridmore-Brown equation can be solved in terms of the confluent Heun function (CHF), which is a solution of the confluent Heun equation (CHE) introduced by K. Heun in 1888, a generalization of the hypergeometric equation. Next, together with the appropriate boundary conditions, i.e. the acoustic perturbation vanishing at infinity and the acoustic analogue of an impermeable wall, the boundary value problem is converted to an algebraic eigenvalue problem, where the Mach and the wave number are free parameters and the frequency is the eigenvalue. Based on this we analyze the behavior of the eigenvalue problem. In the limit of small Mach and wave numbers, the resulting frequency is unique and real-valued. In the limit of small Mach numbers and large wave numbers, the eigenvalues are multiple. The above analytical results are validated by numerical methods. Presently we validate the above theory by highly accurate numerical simulations using a Discontinuous Galerkin (DG) method employing the in house code BoSSS and in a final step, results will be applied to turbulent boundary layer flow. 12:15 15 mins #504 SPATIAL EVOLUTION OF TRANSITION INSIDE POROUS MEDIA Xu Xu Chu, Yongxiang Wu, Ulrich Rist, Bernhard Weigand Abstract: Direct numerical simulation is performed to investigate the spatial evolution of the transitional process in porous media. The considered porous media consists of 72 staggered circular cylinders with porosity range from 0.5 to 0.8 and the Reynolds number range of 100 to 400. Bypass transition like feathers are observed with a peak of fluctuation intensity. 3D dynamic mode decomposition is used to extract dominant signatures with frequency characteristics. 12:30 15 mins #375 On the verge of laminarization in boundary layer flows Yohann Duguet, Taras Khapko, Philipp Schlatter, Dan S. Henningson Abstract: Turbulence in the asymptotic suction boundary layer (ASBL) is investigated numerically at the verge of laminarisation using direct numerical simulation. Following an adiabatic protocol the Reynolds number Re, based on the free-stream velocity and the suction velocity, is decreased in small steps starting from a fully turbulent state until laminarisation is observed. High-resolution computations suggest a critical Reynolds number Re = 270, below which turbulence invariably collapses, based on observation times of O(10^5) inertial time units. Contrarily to other subcritical shear flows no sustained laminar–turbulent co-existence is observed, even near the onset of sustained turbulence. During the laminarisation process, the turbulent flow fragments into a series of transient streamwise-elongated structures, whose interfaces do not display the characteristic obliqueness of classical laminar–turbulent patterns.. The law of the wall, i.e. logarithmic scaling of the mean velocity profile, is retained down to Reg, suggesting large-scale vertical transport absent in internal shear flows close to the onset. In order to test the effect of these large-scale structures on the near-wall region, an artificial volume force is added to damp spanwise and wall-normal fluctuations above y+ = 100. Once the largest eddies have been suppressed by the forcing, and thus turbulence is confined to the near-wall region, oblique laminar–turbulent interfaces emerge, as in other wall-bounded flows. These results suggest that oblique stripes at the onset are a prevalent feature of internal shear flows, but will not occur in canonical boundary layers flows.