Flow-field analysis of anti-kidney vortex film cooling

Film cooling is an important measure to enable an increase of the inlet temperature of a gas turbine and, thereby, to improve its overall efficiency. The coolant is ejected through spanwise rows of holes in the blades or endwalls to build up a film shielding the material. The holes often are inclined in the downstream direction and give rise to a kidney vortex. This is a counter-rotating vortex pair, with an upward flow direction between the two vortices, which tends to lift off the surface and to locally feed hot air towards the blade outside the pair. Reversing the rotational sense of the vortices reverses these two drawbacks into advantages. In the considered case, an anti-kidney vortex is generated using two subsequent rows of holes both inclined downstream and yawed spanwise with alternating angles. In a previous study, we performed large-eddy simulations (which focused on the fully turbulent boundary layer) of this anti-kidney vortex film-cooling and compared them to a corresponding physical experiment. The present work analyzes the simulated flow field in detail, beginning in the plenum (inside the blade or endwall) through the holes up to the mixture with the hot boundary layer. To identify the vortical structures found in the mean flow and in the instantaneous flow, we mostly use the λ 2 criterion and the line integral convolution (LIC) technique indicating sectional streamlines. The flow regions (coolant plenum, holes, and boundary layer) are studied subsequently and linked to each other. To track the anti-kidney vortex throughout the boundary layer, we propose two criteria which are based on vorticity and on LIC results. This enables us to associate the jet vortices with the cooling effectiveness at the wall, which is the key feature of film coolin

Vortical flow in the utricle and the ampulla: a computational study on the fluid dynamics of the vestibular system

We present a computational study of the fluid dynamics in healthy semicircular canals (SCCs) and the utricle. The SCCs are the primary sensors for angular velocity and are located in the vestibular part of the inner ear. The SCCs are connected to the utricle that hosts the utricular macula, a sensor for linear acceleration. The transduction of angular motion is triggered by the motion of a fluid called endolymph and by the interaction of this fluid with the sensory structures of the SCC. In our computations, we observe a vortical flow in the utricle and in the ampulla (the enlarged terminal part of the SCCs) which can lead to flow velocities in the utricle that are even higher than those in the SCCs. This is a fundamentally new result which is in contrast to the common belief that the fluid velocities in the utricle are negligible from a physiological point of view. Moreover, we show that the wall shear stresses in the utricle and the ampulla are maximized at the positions of the sensory epithelia. Possible physiological and clinical implications are discusse

Numerical study of eigenmode forcing effects on jet flow development and noise generation mechanisms

International audienceThe effect of nonlinear interaction of instability eigenmodes on jet flow transition and its near acoustic field for a high-subsonic round jet at a Reynolds number of Re= 4.5ϫ 10 5 and a Mach number of Ma= 0.9 is investigated using large-eddy simulations. At the inflow, helical perturbations of azimuthal wavenumbers ͉n͉ = 4 ,. .. , 8 determined from linear stability theory are superimposed on a laminar base flow in order to trigger transition to turbulence. The disturbance amplitude is varied parametrically in the range from 1.5% to 4.5% of the jet exit velocity U j. Thereby we aim to characterize sources of noise generation and, in particular, underlying mode interactions. With increasing forcing amplitude, the transitional behavior of the jet changes which affects the mean flow and also the acoustic near-field, which are both analyzed in detail. As the forcing amplitude is increased, the axial root-mean-square peak levels along the jet centerline are reduced by approximately 7%. Simultaneously, pronounced dual-peak distributions are generated along the jet lip line which are related to the localization of vortex pairings of the jet column mode. For low-amplitude excitation the azimuthal turbulent kinetic energy spectra show that the unexcited, naturally least stable axisymmetric mode n = 0 and the helical mode n = 1 dominate the early nonlinear regimes between z Ϸ 6r 0 and 9r 0 where r 0 is the jet radius. An analysis of the Fourier mode amplitude clarifies that this energy rise is linked to the helical mode n = 1. For higher forcing amplitudes, in addition to the varicose mode n = 0 interactions between the excited even mode n = 4 and higher azimuthal harmonics thereof dominate the azimuthal energy spectra. These differences in the early nonlinear development of the eigenmodes are found to alter the acoustic near-field. At small angles from the downstream jet axis, the peak acoustic frequency occurs at a Strouhal number based on the angular frequency and the jet diameter D j of St= D j / ͑2U j ͒ Ϸ 0.4. For low-amplitude forcing sound pressure levels are slightly enhanced which can be linked to the dominant low azimuthal wavenumbers identified in the transitional region. In the sideline direction, regardless of the excitation level, broadbanded spectra with maxima in the band 0.7 Յ StՅ 0.8 are found which is maintained at intermediate observer angles. For high forcing amplitude, however, a tonal component outside the initially excited frequency range is observed. This peak at StϷ 0.88 can be explained by weakly nonlinear interactions of initially forced eigenmodes n = 4 and n = 8 together with the jet column mode

Stabilizing a Leading-edge Boundary Layer Subject to Wall Suction by Increasing the Reynolds Number

AbstractLaminar fiow in the boundary layer at the leading edge of swept airplane wings typically becomes transitional and turbulent shortly downstream of the attachment line. Flow control techniques to maintain the fiow laminar, such as suction into the wall, therefore must focus on this instability, which otherwise leads to turbulent fiow and thus contaminates the fiow over the entire wing chord.The present paper presents new results on how the linear leading-edge boundary layer (LEBL) instability of swept-cylinders fiow, which models swept-wing fiow, may be avoided. The classical Reynolds number definition is employed, which is based on the far-field velocity Q∞, the cylinder radius R*, and the sweep angle Λ. It is demonstrated that the fiow can be stabilized by increasing the Reynolds number at constant wall suction through an increase of R* or Λ, but not of Q∞.The stability analysis is carried out for the swept Hiemenz boundary layer (SHBL), a widely used fiat-plate approximation of the swept-cylinder LEBL. As demonstrated recently 1, the SHBL with suction becomes similar to the two-dimensional asymptotic suction boundary layer (ASBL) when increasing the classical Reynolds number ReSH to large values. In the limit of ReSH→∞, the SHBL with suction becomes identical to the highly stable ASBL, and hence inherits its linear stability properties. The transformation of these recent findings concerning the linear stability of the SHBL with suction to the swept-cylinder LEBL unveils that stabilization of fiow with constant suction can be observed by increasing ReSH

Steady streaming in a two-dimensional box model of a passive cochlea

Acoustic stimulation of the cochlea leads to a travelling wave in the cochlear fluids and on the basilar membrane (BM). It has long been suspected that this travelling wave leads to a steady streaming flow in the cochlea. Theoretical investigations suggested that the steady streaming might be of physiological relevance. Here, we present a quantitative study of the steady streaming in a computational model of a passive cochlea. The structure of the streaming flow is illustrated and the sources of streaming are closely investigated. We describe a source of streaming which has not been considered in the cochlea by previous authors. This source is also related to a steady axial displacement of the BM which leads to a local stretching of this compliant structure. We present theoretical predictions for the streaming intensity which account for these new phenomena. It is shown that these predictions compare well with our numerical results and that there may be steady streaming velocities of the order of millimetres per second. Our results indicate that steady streaming should be more relevant to low-frequency hearing because the strength of the streaming flow rapidly decreases for higher frequencie

A class of exact Navier-Stokes solutions for homogeneous flat-plate boundary layers and their linear stability

We introduce a new boundary layer formalism on the basis of which a class of exact solutions to the Navier-Stokes equations is derived. These solutions describe laminar boundary layer flows past a flat plate under the assumption of one homogeneous direction, such as the classical swept Hiemenz boundary layer (SHBL), the asymptotic suction boundary layer (ASBL) and the oblique impingement boundary layer. The linear stability of these new solutions is investigated, uncovering new results for the SHBL and the ASBL. Previously, each of these flows had been described with its own formalism and coordinate system, such that the solutions could not be transformed into each other. Using a new compound formalism, we are able to show that the ASBL is the physical limit of the SHBL with wall suction when the chordwise velocity component vanishes while the homogeneous sweep velocity is maintained. A corresponding non-dimensionalization is proposed, which allows conversion of the new Reynolds number definition to the classical ones. Linear stability analysis for the new class of solutions reveals a compound neutral surface which contains the classical neutral curves of the SHBL and the ASBL. It is shown that the linearly most unstable Görtler-Hämmerlin modes of the SHBL smoothly transform into Tollmien-Schlichting modes as the chordwise velocity vanishes. These results are useful for transition prediction of the attachment-line instability, especially concerning the use of suction to stabilize boundary layers of swept-wing aircraf

Absolute and convective instabilities of heated coaxial jet flow

This study investigates the inviscid, linear spatio-temporal stability of heated, compressible, and incompressible coaxial jet flows. The influence of the temperature ratio and the velocity ratio between the core jet and the bypass stream on the transition from convectively to absolutely unstable flows is studied numerically. The investigation shows that for coaxial jets, absolute instability can occur for considerably lower core-stream temperatures than for single jets. The reason for this modified stability character is the appearance of an additional unstable mode as a result of the outer velocity shear layer between the bypass stream and the ambient flow. The presence of two shear layers enables the interaction between otherwise free waves to give rise to new instabilities. When the bypass-stream velocity is increased, the classical absolute mode known from single jets (inner mode) is first stabilized and then destabilized for high bypass-stream velocities, whereas the outer mode reaches maximum spatio-temporal growth rates when the core-stream velocity is approximately equal to twice the bypass-stream velocity. Additionally, it is demonstrated that the spatio-temporal character of the modes is very sensitive to the shear-layer thickness and to the distance separating the two layers. Increasing the Mach number strongly dampens the onset of an absolute instability for both modes

Steady streaming in a two-dimensional box model of a passive cochlea

Acoustic stimulation of the cochlea leads to a travelling wave in the cochlear fluids and on the basilar membrane (BM). It has long been suspected that this travelling wave leads to a steady streaming flow in the cochlea. Theoretical investigations suggested that the steady streaming might be of physiological relevance. Here, we present a quantitative study of the steady streaming in a computational model of a passive cochlea. The structure of the streaming flow is illustrated and the sources of streaming are closely investigated. We describe a source of streaming which has not been considered in the cochlea by previous authors. This source is also related to a steady axial displacement of the BM which leads to a local stretching of this compliant structure. We present theoretical predictions for the streaming intensity which account for these new phenomena. It is shown that these predictions compare well with our numerical results and that there may be steady streaming velocities of the order of millimetres per second. Our results indicate that steady streaming should be more relevant to low-frequency hearing because the strength of the streaming flow rapidly decreases for higher frequencies

Stability analysis for different formulations of the nonlinear term in PN−PN−2 spectral element discretizations of the navier–stokes equations

We show that for the PN−PN−2 spectral element method, in which velocity and pressure are approximated by polynomials of order N and N−2, respectively, numerical instabilities can occur in the spatially discretized Navier–Stokes equations. Both a staggered and nonstaggered arrangement of the N−2 pressure points are considered. These instabilities can be masked by viscous damping at low Reynolds numbers. We demonstrate that the instabilities depend on the formulation of the nonlinear term. The numerical discretization is stable for the convective form but unstable for the divergence and the skew-symmetric form. Further numerical analysis indicates that this instability is not caused by nonlinear effects, since it occurs for linearized systems as well. An eigenvalue analysis of the fully discretized system shows that an instability is introduced by the formulation of the nonlinear term. We demonstrate that the instability is related to the divergence error of the computed solution at those velocity points at which the continuity equation is not enforced