10:30
Instability and Transition 5
Chair: Dan Henningson
10:30
15 mins
|
Bypass transition in boundary layers as an activated process
Tobias Kreilos, Taras Khapko, Philipp Schlatter, Yohann Duguet, Dan S Henningson, Bruno Eckhardt
Abstract: We consider the spatio-temporal aspects of the transition to turbulence in a boundary layer above a flat plate
exposed to free-stream turbulence. Combining results from the receptivity to free-stream turbulence with the
observation of a double threshold from transition studies in e.g. pipe flow we arrive at a physically motivated
prediction for the spatial distribution of nucleation events in boundary layers. We use a cellular automaton
to implement a complete model for the spatial and temporal evolution of turbulent patches and show
that the model reproduces the statistical features of the boundary layer remarkably well. The success
of the modeling shows that bypass transition occurs as a spatiotemporally activated process, where
transition is triggered by critical fluctuations imported from the free-stream turbulence.
|
10:45
15 mins
|
The time-varying nature of the asymmetrical flow of a shear-thinning polymer solution in transitional pipe flow.
Chaofan Wen, Robert Poole, David Dennis
Abstract: Previous studies of shear-thinning fluids in pipe flow discovered that, although the time-averaged velocity profile was axisymmetric when the flow was laminar or fully turbulent, contrary to expectations it was asymmetric in the laminar-turbulent transition regime. The general consensus of these previous experiments was that the location of the peak velocity remained at a fixed point in space. We present new experimental data which demonstrates that this is in fact not the case. Our results confirm the significant departures from axisymmetry in transitional flows of shear-thinning fluids, in addition to the observation that the asymmetric flow pattern is not stationary, the peak velocity is seen to preferentially arise at certain azimuthal locations.
|
11:00
15 mins
|
Multimodal instability and onset of the laminar-turbulent transition in a supersonic boundary layer
Dmitry Khotyanovsky, Alexey Kudryavtsev
Abstract: INTRODUCTION
It is generally understood that the initial stages of the laminar-turbulent transition in high-speed boundary layers are governed by spatial growth of unstable small-amplitude disturbances. According to linear stability analysis and the available experimental data, at high Mach numbers the dominant boundary layer instabilities are those of the second mode, or Mack modes [1]. The oblique disturbances of the first mode are also unstable but have much lower growth rates. Linear and non-linear dynamics of the disturbed boundary layer thus involves complex interaction of the spectra of instability waves, competition of the modes, and may lead to entirely different transition scenarios depending on the conditions upstream. According to linear stability analysis with consideration of non-parallel effects, the spatial range of the second mode instability of a given frequency is rather small: as the boundary layer thickness (measured along the normal coordinate Y) increases downstream along X, initially unstable second mode disturbance of a given frequency quickly becomes stable and can no longer grow. We performed our own linear stability theory calculations using the formulation [2], and confirmed this. On the contrary, the oblique first-mode disturbance of a given frequency, though having lower growth rates than the second mode, can still be unstable farther downstream. The role of the mode competition in the laminar flow breakdown is not yet clear. Better understanding of the development of unstable disturbances of 1st and 2nd mode and their interactions is crucial for the design of efficient high-speed aircraft.
NUMERICAL TECHNIQUES
The objective of the present DNS study is to simulate interactions of the different modes of disturbances introduced at different frequencies, and find out what happens if they grow concurrently. In our DNS we solve numerically the 3D Navier–Stokes equations for compressible gas. The numerical computations are performed with the time-explicit Navier–Stokes numerical code based on a 5th order WENO scheme of Jiang & Shu [3]. Diffusion terms are computed on a compact stencil with central-biased differences. The code is accurate in time due to 4th order Runge–Kutta algorithm. The code is parallelized via domain decomposition and MPI. The simulations are performed with the assumption of the spatially evolving instability waves. Boundary conditions specify at inflow the self-similar laminar basic flow at a given Reynolds number Re with superimposed time-dependent fluctuations. Linear stability eigenfunctions of the unstable disturbances are used for the inflow forcing. Numerical simulation is typically performed with one most unstable two-dimensional wave of the second mode with a given frequency ω and two symmetrical 1st or 2nd mode instability waves propagating at angles χ and -χ to the basic flow in the transverse direction Z. The computational domain is long enough in X direction so that the disturbances have enough length to evolve. Sponge layer at the far end of the domain ensures damping of the disturbances near outflow. We use periodic conditions in transverse direction Z. Computations were run at flow Mach number M=6, Reynolds number based on Blasius thickness of the boundary layer at inflow boundary Re=1000, wall temperature ratio to the free-stream static temperature Tw/Te=7. In our simulations we use grids condensed just above the plate and also resolving the critical layer, which is at 16-18 Blasius thicknesses above the plate. The entire mesh used herein was about 30 million grid cells. Computations were run at a distributed cluster using up to 64 CPU cores.
RESULTS
Here we present the results of the DNS of the development of the isolated unstable disturbances of the 2nd mode. Numerical results on the interaction of the two-dimensional 2nd mode disturbance with oblique 1st mode disturbances were presented at the ETC14. At flow Mach number M=6 the fundamental instability wave with frequency corresponding to the maximum growth rate of the linear theory is two-dimensional with the wave vector angle χ=0. To provide the three-dimensional fluctuation field, a superposition of the 2D fundamental wave of the 2nd mode and two symmetrical oblique 2nd mode disturbances with angles χ and -χ was used as the inflow forcing. For boundary layer conditions at the inflow section, i.e. Re=1000, these were 35 and -35 degrees. Initial amplitude of the disturbances was 0.5%. Numerical results show that in accordance with linear theory the 2D fundamental wave is dominant at initial stages and rapidly grows in downstream direction. Farther downstream, because of the growth of the boundary layer thickness of the basic flow, the 2nd mode disturbance of a given frequency becomes stable. Hence, we also used a cascade approach for inflow forcing. In this approach, we superimpose on the basic flow the disturbance waves corresponding to the unstable disturbances at some cross-sections downstream, typically in the middle of the computational domain. In this case we also superimpose the oblique 2nd mode waves with χ=±48°. This cascade approach greatly prolongs the spatial region of the instability of a given frequency.
The results of the numerical simulations show that in all cases considered herein the initial stages of the instability development are mainly governed by the rapid growth of the fundamental instability of the 2nd mode. Oblique 2nd mode disturbances are also unstable but have much lower growth rates. Nevertheless, they are essential as they provide necessary 3D fluctuations. Farther downstream their effects become visible as three-dimensional deformations of the initially plane fluctuation field, which is evident in the results of our numerical simulations obtained with the cascade approach shown in Fig. 1. Farther downstream, as the planar fundamental wave stabilizes, the effects of the oblique 2nd mode disturbances become even more evident. These oblique instabilities efficiently pump energy in 3D fluctuations which leads to non-linear interactions and the onset of laminar-turbulent transition.
Comparison of these results with our previously reported results on the instability development in presence of the unstable oblique waves of the 1st mode suggests that the 1st mode is more efficient for triggering the laminar-turbulent transition.
Acknowledgments
This study was supported by the RFBR (Grants 12-01-00840, 14-07-00065) and by the Government of the Russian Federation (Grant 14.Z50.31.0019). This support is gratefully acknowledged. The computations have been performed at the supercomputers of the Novosibirsk State University and the JSCC.
References
[1] L.M. Mack. Boundary layer stability theory. Document 900-277, Rev. A. Pasadena, California, JPL, 1969, 388 p.
[2] S. Özgen, S.A. Kırcalı. Linear stability analysis in compressible, flat-plate boundary-layers. Theor. Comput. Fluid Dyn. 22: 1–20, 2008.
[3] G.-S. Jiang, C.-W. Shu. Efficient implementation of weighted ENO schemes. J. Comput. Phys 126: 202–228, 1996.
|
11:15
15 mins
|
ON THE ARTIFICIAL DISTURBANCE EVOLUTION IN 2D/3D SPANWISE MODULATED BOUNDARY LAYERS AT MACH 2 AND 2.5
Panina Alexandra, Kosinov Alexander, Semionov Nikolay, Yermolaev Yury
Abstract: The paper presented the results on the generation and development of the wave train in spanwise modulated supersonic boundary layer at Mach 2 and 2.5 which obtained experimentally in the same conditions of controlled experiment. In experiments on the flat plate with roughness it was obtained that at the Mach number M = 2.5 both a subharmonic and fundamental wave packet develops almost linearly, whereas at the Mach number M = 2.0 there is competition between the two mechanisms of unstable waves interaction. It was obtained that in the boundary layer on swept wing the roughness presence can leads to the stabilization of the wave packet development at fundamental and subharmonic frequency in the downstream direction.
|
11:30
15 mins
|
Fully localised edge states in boundary layers
Taras Khapko, Tobias Kreilos, Philipp Schlatter, Yohann Duguet, Bruno Eckhardt, Dan Henningson
Abstract: Investigation of the laminar-turbulent boundary is performed in a boundary-layer flow. Constant homogeneous suction is applied at the wall in order to prevent the spatial growth of the layer, leading to the parallel Asymptotic Suction Boundary Layer (ASBL). Edge tracking is performed in a large computational domain allowing for full spatial localisation of the structures on the laminar-turbulent separatrix. The obtained dynamics of the state goes through calm and bursting phases. During the latter the structure grows in size, shedding vortices downstream of its core which viscously decay during the calm phases. Comparison with the computation in spatially growing boundary layer is made. The influence of the Reynolds number and the path leading from the edge state to turbulent flow are considered.
|
11:45
15 mins
|
Transition and wavy walls: an experimental study
Robert Downs, Jens Fransson
Abstract: A wide body of research exists which explores the effects of surface roughness or patterned wall shapes on instability growth and transition. Building on those works as well as recent experiments demonstrating passive laminar flow control using arrays of discrete roughness [3, 8], a set of spanwise-wavy walls is designed with the goal of suppressing instability growth in two-dimensional boundary layers. In a numerical investigation of Tollmien-Schlichting (TS) wave growth in the presence of streamwise boundary-layer streaks, Cossu and Brandt [1] found that stabilization of TS waves results from spanwise shear in the mean flow, which forms a negative contribution to production in the perturbation kinetic energy equation. Whereas previous efforts have employed streamwise vorticity developing in roughness wakes to provide the requisite mean-flow deformation, in this work stabilization is achieved through modulation of the no-slip surface. Miniature vortex generators (MVGs) have proven an effective means of producing streamwise streaks for transition delay [8], though relatively large streak amplitudes are necessary to counter their eventual decay through viscous dissipation. The notion motivating this work is that spanwise-wavy walls extended in the streamwise direction can produce a similar effect while avoiding bypass transition resulting from large-amplitude streamwise streaks. Toward that end, six wavy walls are used in a modular test model. When TS waves are excited upstream of the wavy walls, substantial delays in the onset of transition are observed for certain spanwise wavelengths compared with the flat-plate reference case.
|
12:00
15 mins
|
STABILITY ANALYSIS OF A COMPRESSIBLE TURBULENT FLOW OVER A BACKWARD-FACING STEP
Samir Beneddine, Emerick Bodere, Denis Sipp
Abstract: In this study we focus on the stability analysis of a compressible turbulent flow over a closed backward-facing step. To perform the stability analysis, we have computed a mean-flow from an unsteady 3D simulation. This analysis reveals a completely stable spectrum, with some global modes exhibiting a frequency close to the peaks of the frequency spectrum of the unstead 3D simulation. Since none of the modes are unstable, we have then performed a singular value decomposition that allows to see the optimal
gain response of the flow at each frequency. This final study reveals several particular frequencies that match what is observed in the
unsteady simulation.
|
12:15
15 mins
|
Linear stability of a liquid flow through a poroelastic channel
Arghya Samanta, Shervin Bagheri, Luca Brandt
Abstract: A liquid flow through a channel is studied based on the Orr-Sommerfeld eigenvalue problem, where the lower wall of the channel is occupied by the saturated poroelastic medium. The linear stability analysis is investigated in detail for arbitrary value of the wavenumber. The eigenvalues are computed numerically by using the Chebyshev spectral collocation method. The effect of physical parameters, for instance, permeability, elasticity as well as their combined effect on the unstable modes are examined.
|
|