Direct numerical simulation of turbulent flows over superhydrophobic surfaces with gas pockets using linearized boundary conditions

Superhydrophobic surfaces are shown to be effective for surface drag reduction under laminar regime by both experiments and simulations (see for example, Ou and Rothstein, Phys. Fluids 17:103606, 2005). However, such drag reduction for fully developed turbulent flow maintaining the Cassie-Baxter state remains an open problem due to high shear rates and flow unsteadiness of turbulent boundary layer. Our work aims to develop an understanding of mechanisms leading to interface breaking and loss of gas pockets due to interactions with turbulent boundary layers. We take advantage of direct numerical simulation of turbulence with slip and no-slip patterned boundary conditions mimicking the superhydrophobic surface. In addition, we capture the dynamics of gas-water interface, by deriving a proper linearized boundary condition taking into account the surface tension of the interface and kinematic matching of interface deformation and normal velocity conditions on the wall. We will show results from our simulations predicting the dynamical behavior of gas pocket interfaces over a wide range of dimensionless surface tensions.

On Mixing and Shaking : Structure and Dynamics of Turbulent Stratified Flames

The drive for low emission combustion systems encourages applications using premixed flames. Yet in many applications, considerations of flame stability or mixing times lead to systems with neither premixed nor diffusion flames, which are often called technically premixed or stratified flames. In this talk we discuss the current state of understanding of the effect of mixing and extent of stratification on the structure, microstructure and dynamics of selected turbulent stratified flames. Over the past few years, a significant database of scalar and velocity data has been built to analyze the effects of unmixedness on local and global flame structure. Microscale studies of the flame structures show in detail how the effect of local stratification affects (or not!) the flame structure, flame surface density and scalar dissipation rates, and production of selected species. The experiments place exacting demands on current spectroscopic diagnostics, and reveal the progress and limits to our understanding of turbulent flames in general. The dynamics of stratified flames with respect to instabilities is also shown to be very rich, as the particular shape of the flames and the stabilization points are is significantly affected by the fuel distribution, modifying the rate and location of heat release, and thus the coupling with the surrounding acoustics and determining the onset of self-excitations.

Flow field measurements of a series of turbulent premixed and stratified methane/air flames

This paper presents flow field measurements for the turbulent stratified burner introduced in two previous publications in which high resolution scalar measurements were made by Sweeney et al. [1,2] for model validation. The flow fields of the series of premixed and stratified methane/air flames are investigated under turbulent, globally lean conditions (φg=0.75). Velocity data acquired with laser Doppler anemometry (LDA) and particle image velocimetry (PIV) are presented and discussed. Pairwise 2-component LDA measurements provide profiles of axial velocity, radial velocity, tangential velocity and corresponding fluctuating velocities. The LDA measurements of axial and tangential velocities enable the swirl number to be evaluated and the degree of swirl characterized. Power spectral density and autocorrelation functions derived from the LDA data acquired at 10kHz are optimized to calculate the integral time scales. Flow patterns are obtained using a 2-component PIV system operated at 7Hz. Velocity profiles and spatial correlations derived from the PIV and LDA measurements are shown to be in very good agreement, thus offering 3D mapping of the velocities. A strong correlation was observed between the shape of the recirculation zones above the central bluff body and the effects of heat release, stoichiometry and swirl. Detailed analyses of the LDA data further demonstrate that the flow behavior changes significantly with the levels of swirl and stratification, which combines the contributions of dilatation, recirculation and swirl. Key turbulence parameters are derived from the total velocity components, combining axial, radial and tangential velocities. © 2013 The Combustion Institute.

Kelvin-Helmholtz-like instabilities in turbulent flows over complex surfaces

Riblets are small surface protrusions aligned with the flow direction, which confer an anisotropic roughness to the surface [6]. We have recently reported that the transitional-roughness effect in riblets, which limits their performance, is due to a Kelvin–Helmholtz-like instability of the overlying mean flow [7]. According to our DNSs, the instability sets on as the Reynolds number based on the roughness size of the riblets increases, and coherent, elongated spanwise vortices begin to develop immediately above the riblet tips, causing the degradation of the drag-reduction effect. This is a very novel concept, since prior studies had proposed that the degradation was due to the interaction of riblets with the flow as independent units, either to the lodging of quasi-streamwise vortices in the surface grooves [2] or to the shedding of secondary streamwise vorticity at the riblet peaks [9]. We have proposed an approximate inviscid analysis for the instability, in which the presence of riblets is modelled through an average boundary condition for an overlying, spanwise-independent mean flow. This simplification lacks the accuracy of an exact analysis [4], but in turn applies to riblet surfaces in general. Our analysis succeeds in predicting the riblet size for the onset of the instability, while qualitatively reproducing the wavelengths and shapes of the spanwise structures observed in the DNSs. The analysis also connects the observations with the Kelvin–Helmholtz instability of mixing layers. The fundamental riblet length scale for the onset of the instability is a ‘penetration length,’ which reflects how easily the perturbation flow moves through the riblet grooves. This result is in excellent agreement with the available experimental evidence, and has enabled the identification of the key geometric parameters to delay the breakdown. Although the appearance of elongated spanwise vortices was unexpected in the case of riblets, similar phenomena had already been observed over other rough [3], porous [1] and permeable [11] surfaces, as well as over plant [5,14] and urban [12] canopies, both in the transitional and in the fully-rough regimes. However, the theoretical analyses that support the connection of these observations with the Kelvin–Helmholtz instability are somewhat scarce [7, 11, 13]. It has been recently proposed that Kelvin–Helmholtz-like instabilities are a dominant feature common to “obstructed” shear flows [8]. It is interesting that the instability does not require an inflection point to develop, as is often claimed in the literature. The Kelvin-Helmholtz rollers are rather triggered by the apparent wall-normal-transpiration ability of the flow at the plane immediately above the obstructing elements [7,11]. Although both conditions are generally complementary, if wall-normal transpiration is not present the spanwise vortices may not develop, even if an inflection point exists within the roughness [10]. REFERENCES [1] Breugem, W. P., Boersma, B. J. & Uittenbogaard, R. E. 2006 J. Fluid Mech. 562, 35–72. [2] Choi, H., Moin, P. & Kim, J. 1993 J. Fluid Mech. 255, 503–539. [3] Coceal, O., Dobre, A., Thomas, T. G. & Belcher, S. E. 2007 J. Fluid Mech. 589, 375–409. [4] Ehrenstein, U. 2009 Phys. Fluids 8, 3194–3196. [5] Finnigan, J. 2000 Ann. Rev. Fluid Mech. 32, 519–571. [6] Garcia-Mayoral, R. & Jimenez, J. 2011 Phil. Trans. R. Soc. A 369, 1412–1427. [7] Garcia-Mayoral, R. & Jimenez, J. 2011 J. Fluid Mech. doi: 10.1017/jfm.2011.114. [8] Ghisalberti, M. 2009 J. Fluid Mech. 641, 51–61. [9] Goldstein, D. B. & Tuan, T. C. 1998 J. Fluid Mech. 363, 115–151. [10] Hahn, S., Je, J. & Choi, H. 2002 J. Fluid Mech. 450, 259–285. [11] Jimenez, J., Uhlman, M., Pinelli, A. & G., K. 2001 J. Fluid Mech. 442, 89–117. [12] Letzel, M. O., Krane, M. & Raasch, S. 2008 Atmos. Environ. 42, 8770–8784. [13] Py, C., de Langre, E. & Moulia, B. 2006 J. Fluid Mech. 568, 425–449. [14] Raupach, M. R., Finnigan, J. & Brunet, Y. 1996 Boundary-Layer Meteorol. 78, 351–382.

Kelvin-Helmholtz-like instability of turbulent flows over riblets

The turbulent drag reduction due to riblets is a function of their size and, for different configurations, collapses well with a length scale l+g=(A+g)1/2, based in the groove cross-section Ag. The initially linear drag reduction breaks down for l+g≈11, which agrees in our DNS with the previously reported appearance of quasi-two-dimensional spanwise rollers immediately above the riblets. They are similar to those found over porous surfaces and plant canopies, and can be traced to a Kelvin-Helmholtz-like instability associated with the relaxation of the impermeability condition for the wall-normal velocity. The extra Reynolds stress associated with them accounts quantitatively for the drag degradation. An inviscid model for the instability confirms its nature, agreeing well with the observed perturbation wavelengths and shapes. The onset of the instability is determined by a length scale L+w that, for conventional riblet geometries, is proportional to l+g. The instability onset, L+w≥4, corresponds to the empirical breakdown point l+g≈11.

Flow physics of a normal-hole bled supersonic turbulent boundary layer

An experimental study on normal hole bleed in a supersonic turbulent boundary layer has been conducted. A combination of LDV, Schlieren imagery and oil flow visualization were used to provide a better understanding of the three-dimensional flow field surrounding a supersonic bleed array. Experiments were performed at Mach numbers of 1.8 and 2.5, while previously published results at Mach numbers of 1.3 and 1.5 were also incorporated. The bleed system was capable of removing up to approximately 10% of the incoming boundary layer through a tunnel-spanning array of discrete holes with diameters the same order of magnitude of boundary layer displacement thickness. Inspection of boundary layer profiles downstream of the bleed region indicates that vorticity generated by the discrete holes can have a substantial influence on changes to the boundary layer shape factor and skin friction coefficient, through modification of the lower 20% of the boundary layer. This vorticity was visualized through oil-flow visualization, and LDV measurements, showing the development of two vortices off each bleed hole, and corresponding upwash and downwash regions with far-reaching three dimensional effects. © 2013 by J. M. Oorebeek and H. Babinsky.

Statistics of reaction progress variable and mixture fraction gradients from DNS of turbulent partially premixed flames

Statistically planar turbulent partially premixed flames for different initial intensities of decaying turbulence have been simulated for global equivalence ratios = 0.7 and 1.0 using three-dimensional, simplified chemistry-based direct numerical simulations (DNS). The simulation parameters are chosen such that the flames represent the thin reaction zones regime combustion. A random bimodal distribution of equivalence ratio is introduced in the unburned gas ahead of the flame to account for the mixture inhomogeneity. The results suggest that the probability density functions (PDFs) of the mixture fraction gradient magnitude |Δξ| (i.e., P(|Δξ|)) can be reasonably approximated using a log-normal distribution. However, this presumed PDF distribution captures only the qualitative nature of the PDF of the reaction progress variable gradient magnitude |Δc| (i.e., P(|Δc|)). It has been found that a bivariate log-normal distribution does not sufficiently capture the quantitative behavior of the joint PDF of |Δξ| and |Δc| (i.e., P(|Δξ|, |Δc|)), and the agreement with the DNS data has been found to be poor in certain regions of the flame brush, particularly toward the burned gas side of the flame brush. Moreover, the variables |Δξ| and |Δc| show appreciable correlation toward the burned gas side of the flame brush. These findings are corroborated further using a DNS data of a lifted jet flame to study the flame geometry dependence of these statistics. © 2013 Copyright Taylor and Francis Group, LLC.

Parametric guidance for turbulent noise reduction from poroelastic trailing edges and owls

The interaction of a turbulent eddy with a semi-infinite, poroelastic edge is examined with respect to the effects of both elasticity and porosity on the efficiency of aerodynamic noise generation. The edge is modelled as a thin plate poroelastic plate, which is known to admit fifth-, sixth-, and seventh-power noise dependences on a characteristic velocity U of the turbulent eddy. The associated acoustic scattering problem is solved using the Wiener-Hopf technique for the case of constant plate properties. For the special cases of porous-rigid and impermeable-elastic plate conditions, asymptotic analysis of the Wiener- Hopf kernel function furnishes the parameter groups and their ranges where U5, U6, and U7 behaviours are expected to occur. Results from this analysis attempt to help guide the search for passive edge treatments to reduce trailing-edge noise that are inspired by the wing features of silently flying owls. Furthermore, the appropriateness of the present model to the owl noise problem is discussed with respect to the acoustic frequencies of interest, wing chord-lengths, and foraging behaviour across a representative set of owl species.

Transient ventilation dynamics induced by heat sources of unequal strength

We examine theoretically the transient displacement flow and density stratification that develops within a ventilated box after two localized floor-level heat sources of unequal strengths are activated. The heat input is represented by two non-interacting turbulent axisymmetric plumes of constant buoyancy fluxes B1 and B2 > B1. The box connects to an unbounded quiescent external environment of uniform density via openings at the top and base. A theoretical model is developed to predict the time evolution of the dimensionless depths λj and mean buoyancies δj of the 'intermediate' (j = 1) and 'top' (j = 2) layers leading to steady state. The flow behaviour is classified in terms of a stratification parameter S, a dimensionless measure of the relative forcing strengths of the two buoyant layers that drive the flow. We find that dδ1/dτ α 1/λ1 and dδ2/dτ α 1/λ2, where τ is a dimensionless time. When S 1, the intermediate layer is shallow (small λ1), whereas the top layer is relatively deep (large λ2) and, in this limit, δ1 and δ2 evolve on two characteristically different time scales. This produces a time lag and gives rise to a 'thermal overshoot', during which δ1 exceeds its steady value and attains a maximum during the transients; a flow feature we refer to, in the context of a ventilated room, as 'localized overheating'. For a given source strength ratio ψ = B1/B2, we show that thermal overshoots are realized for dimensionless opening areas A < Aoh and are strongly dependent on the time history of the flow. We establish the region of {A, ψ} space where rapid development of δ1 results in δ1 > δ2, giving rise to a bulk overturning of the buoyant layers. Finally, some implications of these results, specifically to the ventilation of a room, are discussed. © Cambridge University Press 2013.

CFD investigation of turbulent premixed flame response to transverse forcing

Screech is a high frequency oscillation that is usually characterized by instabilities caused by large-scale coherent flow structures in the wake of bluff-body flameholders and shear layers. Such oscillations can lead to changes in flame surface area which can cause the flame to burn unsteadily, but also couple with the acoustic modes and inherent fluid-mechanical instabilities that are present in the system. In this study, the flame response to hydrodynamic oscillations is analyzed in a controlled manner using high-fidelity Computational Fluid Dynamics (CFD) with an unsteady Reynolds-averaged Navier-Stokes approach. The response of a premixed flame with and without transverse velocity forcing is analyzed. When unforced, the flame is shown to exhibit a self-excitation that is attributed to the anti-symmetric shedding of vortices in the wake of the flameholder. The flame is also forced using two different kinds of low-amplitude out-of-phase inlet velocity forcing signals. The first forcing method is harmonic forcing with a single characteristic frequency, while the second forcing method involves a broadband forcing signal with frequencies in the range of 500 - 1000 Hz. For the harmonic forcing method, the flame is perturbed only lightly about its mean position and exhibits a limit cycle oscillation that is characteristic of the forcing frequency. For the broadband forcing method, larger changes in the flame surface area and detachment of the flame sheet can be seen. Transition to a complicated trajectory in the phase space is observed. When analyzed systematically with system identification methods, the CFD results, expressed in the form of the Flame Transfer Function (FTF) are capable of elucidating the flame response to the imposed perturbation. The FTF also serves to identify, both spatially and temporally, regions where the flame responds linearly and nonlinearly. Locking-in between the flame's natural self-excited frequency and the subharmonic frequencies of the broadband forcing signal is found to alter the dynamical behaviour of the flame. Copyright © 2013 by ASME.

The evolution of a stratified turbulent cloud

Localized regions of turbulence, or turbulent clouds, in a stratified fluid are the subject of this study, which focuses on the edge dynamics occurring between the turbulence and the surrounding quiescent region. Through laboratory experiments and numerical simulations of stratified turbulent clouds, we confirm that the edge dynamics can be subdivided into materially driven intrusions and horizontally travelling internal wave-packets. Three-dimensional visualizations show that the internal gravity wave-packets are in fact large-scale pancake structures that grow out of the turbulent cloud into the adjacent quiescent region. The wave-packets were tracked in time, and it is found that their speed obeys the group speed relation for linear internal gravity waves. The energetics of the propagating waves, which include waveforms that are inclined with respect to the horizontal, are also considered and it is found that, after a period of two eddy turnover times, the internal gravity waves carry up to 16 % of the cloud kinetic energy into the initially quiescent region. Turbulent events in nature are often in the form of decaying turbulent clouds, and it is therefore suggested that internal gravity waves radiated from an initial cloud could play a significant role in the reorganization of energy and momentum in the atmosphere and oceans.©2013 Cambridge University Press.

Computations of turbulent lean premixed combustion using conditional moment closure

Conditional Moment Closure (CMC) is a suitable method for predicting scalars such as carbon monoxide with slow chemical time scales in turbulent combustion. Although this method has been successfully applied to non-premixed combustion, its application to lean premixed combustion is rare. In this study the CMC method is used to compute piloted lean premixed combustion in a distributed combustion regime. The conditional scalar dissipation rate of the conditioning scalar, the progress variable, is closed using an algebraic model and turbulence is modelled using the standard k-e{open} model. The conditional mean reaction rate is closed using a first order CMC closure with the GRI-3.0 chemical mechanism to represent the chemical kinetics of methane oxidation. The PDF of the progress variable is obtained using a presumed shape with the Beta function. The computed results are compared with the experimental measurements and earlier computations using the transported PDF approach. The results show reasonable agreement with the experimental measurements and are consistent with the transported PDF computations. When the compounded effects of shear-turbulence and flame are strong, second order closures may be required for the CMC. © 2013 Copyright Taylor and Francis Group, LLC.