Effects of friction and heat conduction on sound propagation in ducts

The theory of sound propagation is examined in a viscous, heat-conducting fluid, initially at rest and in a uniform state, and contained in a rigid, impermeable duct with isothermal walls. Topics covered include: (1) theoretical formulation of the small amplitude fluctuating motions of a viscous, heat-conducting and compressible fluid; (2) sound propagation in a two dimensional duct; and (3) perturbation study of the inplane modes

Inflow/outflow boundary conditions and global dynamics of spatial mixing layers

The numerical simulation of incompressible spatially-developing shear flows poses a special challenge to computational fluid dynamicists. The Navier-Stokes equations are elliptic and boundary equations need to be specified at the inflow and outflow boundaries in order to compute the fluid properties within the region of interest. It is, however, difficult to choose inflow and outflow conditions corresponding to a given experimental situation. Furthermore the effects that changes in the boundary conditions or in the size of the computational domain may induce on the global dynamics of the flow are presently unknown. These issues are examined in light of recent developments in hydrodynamic stability theory. The particular flow considered is the spatial mixing layer but it was expected that similar phenomena were bound to occur in other cases such as channel flow, the boundary layer, etc. A short summary of local/global and absolute/convective instability concepts is given. The results of numerical simulations are presented which strongly suggest that global resonances may be triggered in domains of finite streamwise extent although the evolution of the perturbation vorticity field is everywhere locally convective. A relationship between finite domains and pressure sources which might help in devising a scheme to eliminate these difficulties is discussed

Fully Nonlinear Global Modes in Spatially Developing Media

International audienceGlobal modes on a doubly-infinite one-dimensional domain $-\infty < X < +\infty$ are studied in the context of the complex Ginzburg-Landau equation with slowly spatially varying coefficients. A fully nonlinear frequency selection criterion is derived for global-mode solutions under the assumption of weak inhomogeneity of the medium. The global mode is found to be governed by the fully nonlinear equations in a region of finite size, and by the linearized equations in the vicinity of $X=\pm\infty$. Asymptotic matching techniques are used to relate the WKB approximations in the linear and nonlinear regions through appropriate transition layers. The real global frequency is determined by requiring that spatial branches issuing from $X=-\infty$ and $X=+\infty$ be continuously connected at a saddle point of the local nonlinear dispersion relation $\omega=\Omega^{nl}(k,R,X)$ between the frequency $\omega$, the wavenumber $k$ and amplitude $R$ at a given station $X$. The results constitute a fully nonlinear generalization of the linear frequency selection criteria previously obtained by Chomaz et al. (1991), Monkewitz et al. (1993), and Le Dizès et al. (1996)

Nonlinear synchronization in open flows

International audienceThe selection criteria governing finite-amplitude synchronized oscillating states are discussed for model systems and real wake flows in a domain of infinite streamwise extent. Two types of nonlinear global modes are possible: hat modes with overall smoothly varying amplitude and elephant modes with a sharp front. The vortex street in wake flows is of elephant type, as observed in direct numerical simulations of a real spatially developing wake. Furthermore, the elephant frequency selection criterion is in excellent agreement with the numerically determined vortex shedding frequency

Linear impulse response in hot round jets

International audienceThe linear impulse response is retrieved from a numerical solution of the spatial eigenvalue problem, which is derived from the fully compressible equations of motion. Changes in the spatiotemporal stability of heated versus isothermal jets are shown to arise solely from the effect of the baroclinic torque. By considering the full linear impulse response, the competition between jet column modes and shear layer modes is characterized. Jet column modes are only found to occur for axisymmetric disturbances. In thin shear layer jets, the jet column mode is shown to prevail at low group velocities, whereas axisymmetric and helical shear layer modes dominate at high group velocities. The absolute mode of zero group velocity is found to always be of the jet column type. Although only convectively unstable, the maximum growth rates of the shear layer modes greatly exceed those of the jet column modes in thin shear layer jets. In thick shear layer jets, axisymmetric modes of mixed jet column/shear layer type arise. The weakened maximum growth rate of mixed modes accounts for the dominance of helical modes in temporal stability studies of thick shear layer jets. © 2007 American Institute of Physics

Nonlinear self-sustained structures and fronts in spatially developing wake flows

International audienceA family of slowly spatially developing wakes with variable pressure gradient is numerically demonstrated to sustain a synchronized finite-amplitude vortex street tuned at a well defined frequency. This oscillating state is shown to be described by a steep global mode exhibiting a sharp Dee--Langer type front at the streamwise station of marginal absolute instability. The front acts as a wavemaker which sends out nonlinear travelling waves in the downstream direction, the global frequency being imposed by the real absolute frequency prevailing at the front station. The nonlinear travelling waves are determined to be governed by the local nonlinear dispersion relation resulting from a temporal evolution problem on a local wake profile considered as parallel. Although the vortex street is fully nonlinear, its frequency is dictated by a purely linear marginal absolute instability criterion applied to the local linear dispersion relation

Low-frequency sound radiated by a nonlinearly modulated wavepacket of helical modes on a subsonic circular jet

International audienceA possible fundamental physical mechanism by which instability modes generate sound waves in subsonic jets is presented in the present paper. It involves a wavepacket of a pair of helical instability modes with nearly the same frequencies but opposite azimuthal wavenumbers. As the wavepacket undergoes simultaneous spatialtemporal development in a circular jet, the mutual interaction between the helical modes generates a strong three-dimensional, slowly modulating mean-flow distortion. It is demonstrated that this mean field radiates sound waves to the far field. The emitted sound is of very low frequency, with characteristic time and length scales being comparable with those of the envelope of the wavepacket, which acts as a non-compact source. A matched-asymptotic-expansion approach is used to determine, in a self-consistent manner, the acoustic field in terms of the envelope of the wavepacket and a transfer factor characterizing the refraction effect of the background base flow. For realistic jet spreading rates, the nonlinear development of the wavepacket is found to be influenced simultaneously by non-parallelism and non-equilibrium effects, and so a composite modulation equation including both effects is constructed in order to describe the entire growthattenuationdecay cycle. Parametric studies pertaining to relevant experimental conditions indicate that the acoustic field is characterized by a single-lobed directivity pattern beamed at an angle about 4560 to the jet axis and a broadband spectrum centred at a Strouhal number St 0.070.2. As the nonlinear effect increases, the radiation becomes more efficient and the noise spectrum broadens, but the gross features of the acoustic field remain robust, and are broadly in agreement with experimental observations. © 2009 Copyright Cambridge University Press

Stability of clay particle-coated microbubbles in alkanes against dissolution induced by heating

We investigated the dissolution and morphological dynamics of air bubbles in alkanes stabilized by fluorinated colloidal clay particles when subjected to temperature changes. A quasi-steady model for bubble dissolution with time-dependent temperature reveals that increasing the temperature enhances the bubble dissolution rate in alkanes, opposite to the behavior in water, due to the differing trends in gas solubility. Experimental results for uncoated air bubbles in decane and hexadecane confirm this prediction. Clay-coated bubbles in decane and hexadecane are shown to be stable in air-saturated oil at constant temperature, where dissolution is driven mainly by the Laplace pressure. When the temperature increases from ambient, the particle-coated bubbles are prone to dissolution as the oil phase becomes under-saturated. The interfacial layer of particles is observed to undergo buckling and crumpling, without shedding of clay particles. Increasing the concentration of particles is shown to enhance the bubble stability by providing a higher resistance to dissolution and buckling. When subjected to complex temperature cycles, the clay-coated bubbles can remain stable in conditions for which uncoated bubbles dissolve completely. These results underpin the design of ultra-stable oil foams stabilized by solid particles with improved shelf life under changing environmental conditions

Liquid droplet generation

A pre-prototype segment of a droplet sheet generator for a liquid droplet radiator was designed, constructed and tested. The ability to achieve a uniform, non-diverging droplet sheet is limited by manufacturing tolerances on nozzle parallelism. For an array of 100, 100 micrometer diameters nozzles spaced 5 stream diameters apart, typical standard deviations in stream alignment were plus or minus 10 mrad. The drop to drop fractional speed variations of the drops in typical streams were similar and independent of position in the array. The absolute value of the speed dispersion depended on the amplitude of the disturbance applied to the stream. A second generation preliminary design of a 5200 stream segment of a droplet sheet generator was completed. The design is based on information developed during testing of the pre-prototype segment, along with the results of an acoustical analysis for the stagnation cavity pressure fluctuations used to break-up the streams into droplets

Aerodynamic sound generation by global modes in hot jets

International audienceThe acoustic field generated by the synchronized vortex street in self-excited hot subsonic jets is investigated via direct numerical simulation of the compressible equations of motion in an axisymmetric geometry. The simulation simultaneously resolves both the aerodynamic near field and the acoustic far field. Self-sustained near-field oscillations in the present flow configurations have been described as nonlinear global modes in an earlier study. The associated acoustic far field is found to be that of a compact dipole, emanating from the location of vortex roll-up. A far-field solution of the axisymmetric Lighthill equation is derived, on the basis of the source term formulation of Lilley (AGARD-CP, vol. 131, 1974, pp. 13.1-13.12). With the near-field source distributions obtained from the direct numerical simulations, the Lighthill solution is in good agreement with the far-field simulation results. Fluctuations of the enthalpy flux within the jet are identified as the dominant aeroacoustic source. Superdirective effects are found to be negligible. © 2010 Cambridge University Press