Unione Industriale Torino 4 Settembre 2007 Instability and turbulence in flows of automotive and aeronautical interest D. Tordella, M. Onorato, M. Iovieno, S. Scarsoglio, P. Bailey, C. Tribuzi, C. Haigermoser, L. Vesely, M. Novara Dipartimento di Ingegneria Aeronautica e Spaziale Politecnico di Torino

Unione Industriale Torino Hydrodynamic stability in bluff-body wakes Daniela Tordella, Stefania Scarsoglio Dipartimento di Ingegneria Aeronautica e Spaziale Politecnico di Torino

Motivation Stability analysis To understand the reasons for the breakdown of laminar flow; To predict the transition to turbulence Two-dimensional wake past a circular cylinder Circular cylinder is the quintessential bluff-body; Important prototype of free shear flow for applications in fluid mechanics

Application Bluff-body wakes; Sequence of bodies moving one respect to each other (unsteady motion): automotive (highways); aeronautical (runways) Theory (initial-value problem) unsteady motion configurations where perturbations (bodies moving) can arbitrarily occur

Key points: Linear analysis in free flows: Non linear aspects do not substantially affect the most unstable waves (true also for high Re); Linear theory results (frequency and wavenumber) represent the large scale structures of the fully developed turbulent flow For high Re, the most unstable waves are long ( 10 spatial scales D); Long waves slowly dissipate in time; Time scales order: ~ hours

Physical problem

4/24/2017 R = 60 Linear Stability Analysis

4/24/2017 Normal mode theory Linear Stability Analysis

Initial-value problem 4/24/2017 Initial-value problem click here click here click here (a)-(b): R=100, y0=0, x0=9, k=1.7, αi =-0.05, β0=1, symmetric initial condition, (a) Φ=π/8, r=0.0826, (b) Φ=(3/8)π, r=-0.0168. (c): R=100, y0=0, x0=11, k=0.6, αi=0.02, β0=1, asymmetric initial condition, Φ=π/4, r=0.0038. Linear Stability Analysis

Normal mode theory and initial-value problem β0=1, Φ=0, y0=0. Initial-value problem (symbols) and normal mode analysis (solid lines).

4/24/2017 Publications A synthetic perturbative hypothesis for the multiscale analysis of the convective wake instability - D. Tordella, S. Scarsoglio and M. Belan - Phys. Fluids, Vol. 18, No. 5 - (2006) 22nd IFIP TC 7 Conference on System Modeling and Optimization - Analysis of the convective instability of the two-dimensional wake (S. Scarsoglio, D. Tordella, M. Belan) - 18/22 luglio 2005 – Torino 6th Euromech Fluid Mechanics Conference (EFMC6) - A synthetic perturbative hypothesis for multiscale analysis of bluff-body wake instability (D.Tordella, S. Scarsoglio, M. Belan) - June 26-30, 2006 - Stockholm, Sweden 59th Annual Meeting Division of Fluid Dynamics (APS-DFD) - Initial-value problem for the two-dimensional growing wake (S. Scarsoglio, D.Tordella and W. O. Criminale) – November 19-21, 2006 - Tampa, Florida 11th Advanced European Turbulence Conference - Temporal dynamics of small perturbations for a two-dimensional growing wake (S. Scarsoglio, D.Tordella and W. O. Criminale) - June 25-28, 2007 - Porto, Portugal Linear Stability Analysis

Transient and asymptotic behaviour of small three-dimensional perturbations applied to a growing wake – S. Scarsoglio, D. Tordella and W. O. Criminale – submitted to J. Fluid Mech. 2007 Streamwise evolution of the entrainment in a steady two-dimensional bluff-body wake – D. Tordella, S. Scarsoglio – submitted to J. Eng. Math. 2007 Convective instability in wake intermediate asymptotics - M. Belan, D. Tordella - J. Fluid Mech., 552 : 127-136, 2006. On the domain of validity of the near-parallel combined stability analysis for the 2D intermediate and far bluff body wake - D. Tordella, M. Belan - ZAMM, 85 (1): 51-65 2005 A new matched asymptotic expansion for the intermediate and far flow behind a finite body – D. Tordella, M. Belan - Phys. Fluids, 15 (7): 1897-1906 2003 Asymptotic expansions for two dimensional symmetrical laminar wakes - M. Belan, D. Tordella - ZAMM, 82 (4): 219-234 2002

Turbulent transport - Trasporto turbolento Prof. D Tordella Michele Iovieno Peter Bailey

Motivation Turbulence Scales: large (geometry); small (molecular) Most energy at large scales

Motivation Turbulence Scales: large (geometry); small (molecular) Most energy at large scales – let us ignore the small scale ?

Motivation Turbulence Scales: large (geometry); small (molecular) Most energy at large scales – let us ignore the small scale ? Practical reasons (Applications) Effect on light and sound wave propagation Combustion/chemical reactors – small scale level dynamics determine reaction rate Parametrization of subgrid scale terms in LES, k-eps and other turbulence models

Motivation Turbulence Practical reasons (Applications) Scales: large (geometry); small (molecular) Most energy at large scales – let us ignore the small scale ? Practical reasons (Applications) Effect on light and sound wave propagation Combustion/chemical reactors – small scale level dynamics determine reaction rate Parametrization of subgrid scale terms in LES, k-eps and other turbulence models Our study of shearless turbulent mixing allowed us to discover a set of general properties

Turbulent mixing Homogeneous Isotropic Turbulence (HIT) is the simplest turbulence possible A HIT mixing is the simplest turbulence mixing We investigate this mixing without a mean shear and without a length scale  to date this configuration is shown to lack intermittency

Turbulent mixing Homogeneous Isotropic Turbulence (HIT) is the simplest turbulence possible A HIT mixing is the simplest turbulence mixing We investigate this mixing without a mean shear and without a length scale  to date this configuration is shown to lack intermittency

State of the Art Empirically investigated by Gilbert (1980) and Veeravalli & Warhaft (1989) by passive grid generated turbulence. Grids of equal solidity but differing size adjacent turbulence fields of differing kinetic energy and integral length scale, without mean shear

State of the Art Empirically investigated by Gilbert (1980) and Veeravalli & Warhaft (1989) by passive grid generated turbulence. Grids of equal solidity but differing size adjacent turbulence fields of differing kinetic energy and integral length scale, without mean shear in planes downstream of grid, no mean shear, we have a HIT mixing with different scales

State of the Art Empirically investigated by Gilbert (1980) and Veeravalli & Warhaft (1989) by passive grid generated turbulence. Grids of equal solidity but differing size adjacent turbulence fields of differing kinetic energy and integral length scale, without mean shear in planes downstream of grid, no mean shear, we have a HIT mixing with different scales Analyze and determine time and spatial properties of the turbulence energy production as a function of these ratios

State of the Art Empirically investigated by Gilbert (1980) and Veeravalli & Warhaft (1989) by passive grid generated turbulence. Grids of equal solidity but differing size adjacent turbulence fields of differing kinetic energy and integral length scale, without mean shear in planes downstream of grid, no mean shear, we have a HIT mixing with different scales Analyze and determine time and spatial properties of the turbulence energy production as a function of these ratios  in computation we can go one step better. Empirically length and energy scales are intrinsically linked. However in the computation we are able to alter these independently and get a better insight into the interrelations

Analysis of Mixing The principle means to identify turbulent intermittence here is through one point velocity statistics We look at: S (skewness) = the flow of kinetic energy K (kurtosis) = the flow of S S remains 0, K=3 in HIT

Flow of kinetic energy and penetration S moves from 0 as the mixing begins, remains close to 0 outside the mixing Penetration is from high energy field into the low energy side, shown as fraction of the mixing layer thickness As energy ratio is increased we note a linear log relation before the energy flow asymptotes to its maximum click here

Flow visualisation click here Mixing enhancement (retardation) if the gradients of energy and length scale are concurrent (opposite) {Journal of Fluid Mechanics, 2006} Scaling law for the mixing penetration with respect to the turbulent kinetic energy ratio {Journal of Fluid Mechanics, 2006} Sufficiency of the presence of a gradient of kinetic energy for Gaussian departure in turbulence {in review for American Physical Society Physical Review E, 2007}

Turbulent Cavity Flows Flussi della cavità turbulenta - Flussi della cavità turbulenta AeroTraNet network: (supported by Marie Curie Actions) Prof. D Tordella Prof. M Onorato* Michele Iovieno Peter Bailey Christian Haigermoser* Lukas Vesely*

Motivation

Statistical Results Time averaged flow Shear layer impinges onto the forward facing step Primary and secondary recirculation zones

Time-resolved Results Vortex identification: Vorticity ωz λci-vortex-identification criteria; λci = swirling strength Vortices – > Click here

Time-Resolved Drag Drag coefficient time history CD reveals oscillation frequency of f≈2.8Hz (FFT), corresponding to StH=0.08 Highest contribution to CD from Reynolds stress term Contributions to CD along x/H

DRAG FROM CONDITIONAL ANALYSIS Low drag High drag