Mean Flow Direction Research Articles

Principles of Doppler sonography

The techniques of medical Doppler are spectral Doppler (contiuous-wave (CW) and pulse-wave (PW) Doppler) and color flow imaging (Color Doppler and Power Doppler). All are based on the fact that the frequency of an echo from a moving reflecting particle will be altered by a characteristic frequency shift determined by its velocity in relation to the source/detector. The CW Doppler will only detect flow within a pre-defined depth and will not be guided by an image, whereas the PW Doppler is carried out with B-mode guidance (Duplex doppler). The so derived curves permit to assess the temporal distribution of flow velocities and directions and flow disturbances as well. In the case of color flow imaging, a part of the interrogated tissue section is mapped for Doppler signals and then color-coded, resulting in a dynamic color map of flow, where the colors encode characteristic flow parameters (e. g. mean flow velocity plus direction). This article describes the technical and physical basics of medical Doppler techniques.

Interactions between fluid and fibers in a turbulent backward-facing step flow

In this work, a turbulent backward-facing step flow at Reynolds number ReH = 17 520, laden with rod-like particles, is investigated by means of particle image velocimetry. Particle loadings tested are within 0.02% and 0.05% volume fractions; thus, the suspensions may be considered as dilute. The high spatial resolution allows the identification of fiber orientation within the flow, so that mutual interactions between phases can be investigated by considering flow modifications and phenomena related to preferential concentration and orientation of fibers. Fibers’ concentration data show a moderate trend to accumulate at the channel centreline, whereas orientation data display a strong preferential orientation of fibers. Specifically, the local fibers’ orientation is correlated to the flow field in terms of mean flow direction and plane of maximum shear. The occurrence of a symmetrical orientation profile with respect to the channel centre-line is reported as well as the tendency to recover such profile downstream of the step.

How the Nozzle Geometry Impacts Vortex Breakdown in Compressible Swirling-Jet Flows

The influence of the nozzle geometry, namely, the nozzle-wall thickness and the nozzle length , on the vortex breakdown of compressible, swirling nozzle-jet flows is numerically investigated. The Reynolds number is set to and the Mach number is . The nozzle is either in rotation with the mean-flow direction or kept at rest. In a first set of simulations, the nozzle-wall thickness is varied in the range , whereas the nozzle length is kept constant (). For the rotating nozzle wall, the flowfield changes significantly, mainly due to a variation in the initial swirl number and an enhanced centrifugal instability at the outer side of the nozzle wall. For the setup with a nozzle kept at rest, only minor changes of the flowfield are observed in general for a variation of the nozzle-wall thickness. Changing the nozzle length from to , while keeping the wall thickness constant (), leads to a shift of the recirculation region downstream for both setups, and a reduction of its radial extent. The helical instabilities developing in the downstream direction within the boundary layers at the nozzle wall reach higher amplitudes for the long nozzles, leading to the observed differences in the configurations downstream of the nozzle. The results presented reemphasize the important role played by the nozzle configuration upstream of the swirling jet for the development of the vortex-breakdown configuration, and contribute to the clarification of the effects of the nozzle geometry.

Stability and Accuracy of Aeroacoustic Time-Reversal using the Pseudo-Characteristic Formulation

This paper investigates the stability and accuracy of the aeroacoustic Time-Reversal (TR) simulation using the Pseudo-Characteristic Formulation (PCF). To this end, the forward simulation of acoustic wave propagation in 1-D and 2-D computational domain with a uniform mean flow was implemented using the PCF of the Linearised Euler Equations (LEE). The spatial derivatives in the opposite propagating fluxes of the PCF were computed using an overall upwind-biased Finite-Difference (FD) scheme and a Runge-Kutta scheme was used for time-integration. The anechoic boundary condition (ABC) was implemented for eliminating spurious numerical reflections at the computational boundaries, thereby modelling a free-space. The stability of 1-D forward and TR (with only timereversed acoustic pressure as the input at the boundary nodes) simulations were analysed by means of an eigenvalue decomposition, wherein it was shown that opposite upwinding directions must be considered while using the overall upwind-biased FD scheme. Furthermore, the implementation of ABC was found to be crucial for ensuring the stability of the forward simulation over a large time duration and the 2-D TR simulations. The overall central Dispersion-Relation Preserving (DRP) FD schemes were however, found to be unstable and unsuitable for TR simulation. The accuracy of both the forward and the TR simulations using the PCF was assessed by comparing the simulation results against the corresponding analytical solutions of a spatially and temporally evolving Gaussian pulse. It was shown that numerically reversing the mean flow direction during TR (using the PCF) and only the time-reversed acoustic pressure as input at the boundaries is sufficient to accurately back-propagate the waves and localise the initial emission point of the pulse in 1-D or 2-D computational domain.

Effective dispersion in conditioned transmissivity fields

We analyze the impact of conditioning to measurements of hydraulic transmissivity on the transport of a conservative solute. The effects of conditioning on solute transport are widely discussed in the literature, but most of the published works focuses on the reduction of the uncertainty in the prediction of the plume dispersion. In this study both ensemble and effective plume moments are considered for an instantaneous release of a solute through a linear source normal to the mean flow direction, by taking into account different sizes of the source. The analysis, involving a steady and spatially inhomogeneous velocity field, is developed by using the stochastic finite element method. Results show that conditioning reduces the ensemble moment in comparison with the unconditioned case, whereas the effective dispersion may increase because of the contribution of the spatial moments related to the lack of stationarity in the flow field. As the number of conditioning points increases, this effect increases and it is significant in both the longitudinal and transverse directions. Furthermore, we conclude that the moment derived from data collected in the field can be assessed by the conditioned second-order spatial moment only with a dense grid of measured data, and it is manifest for larger initial lengths of the plume. Nevertheless, it seems very likely that the actual dispersion of the plume may be underestimated in practical applications.

Use of PIV to highlight possible errors in hot-wire Reynolds stress data over a 2D rough wall

Particle image velocimetry (PIV) measurements are carried out in a turbulent boundary layer over a 2D rough surface consisting of transverse square bars. The aim of this work is to investigate a possible cause for the near-wall X-wire measurement errors observed on similar rough surfaces. The PIV measurements do not show the anomalous near-wall deficit of Reynolds stresses as measured with X-wires over the same surface. An extensive flow visualization analysis of the PIV data for a spacing between the roughness elements of p = 7k (k is the roughness element height) shows the occurrence of large-scale inward (sweeps) and outward (ejections) motions with a period of about 10.6delta/U0 (delta and U0 are the boundary layer thickness and the free-stream velocity). While these motions dominate the near-wall region and contribute almost equally to the Reynolds shear stress -‹uv›, the mean outward deviation from the mean flow direction is stronger than the inward deviation. Also, when the roughness spacing is reduced to p = 3k, the outward deviation reduces significantly more than the inward deviation. The results support the argument that the outward motions, which can have an instantaneous deviation angle of more than 50 deg. in the case p = 7k, make the X-wire probe inefficient for detecting the ejection events (associated with the outward motions), particularly if the apex angle of the X-wire is not optimized for capturing the strong flow ejections with large deviations.The results explain in part the disparate information on the effect of the roughness on the Reynolds stresses in the outer region of the turbulent boundary layer over rough walls.

Helicity in the Ekman boundary layer

AbstractHelicity, which is defined as the scalar product of velocity and vorticity, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\mathcal{H}} = {\boldsymbol {u}} \boldsymbol {\cdot }\boldsymbol{\omega}$, is an inviscidly conserved quantity in a barotropic fluid. Mean helicity is zero in flows that are parity invariant. System rotation breaks parity invariance and has therefore the potential of giving rise to non-zero mean helicity. In this paper we study the helicity dynamics in the incompressible Ekman boundary layer. Evolution equations for the mean field helicity and the mean turbulent helicity are derived and it is shown that pressure flux injects helicity at a rate $ 2 \varOmega G^2 $ over the total depth of the Ekman layer, where $ G $ is the geostrophic wind far from the wall and $ {\boldsymbol{\Omega}} = \varOmega {\boldsymbol {e}}_y $ is the rotation vector and $ {\boldsymbol {e}}_y $ is the wall-normal unit vector. Thus right-handed/left-handed helicity will be injected if $ \varOmega $ is positive/negative. We also show that in the uppermost part of the boundary layer there is a net helicity injection with opposite sign as compared with the totally integrated injection. Isotropic relations for the helicity dissipation and the helicity spectrum are derived and it is shown that it is sufficient to measure two transverse velocity components and use Taylor’s hypothesis in the mean flow direction in order to measure the isotropic helicity spectrum. We compare the theoretical predictions with a direct numerical simulation of an Ekman boundary layer and confirm that there is a preference for right-handed helicity in the lower part of the Ekman layer and left-handed helicity in the uppermost part when $ \varOmega > 0 $. In the logarithmic range, the helicity dissipation conforms to isotropic relations. On the other hand, spectra show significant departures from isotropic conditions, suggesting that the Reynolds number considered in the study is not sufficiently large for isotropy to be valid in a wide range of scales. Our analytical and numerical results strongly suggest that there is a turbulent helicity cascade of right-handed helicity in the logarithmic range of the atmospheric boundary layer when $\varOmega >0$, consistent with recent measurements by Koprov, Koprov, Ponomarev & Chkhetiani (Dokl. Phys., vol. 50, 2005, pp. 419–422). The isotropic relations which are derived may facilitate future measurements of the helicity spectrum in the atmospheric boundary layer as well as in controlled wind tunnel experiments.

Statistical scaling of pore-scale Lagrangian velocities in natural porous media.

We investigate the scaling behavior of sample statistics of pore-scale Lagrangian velocities in two different rock samples, Bentheimer sandstone and Estaillades limestone. The samples are imaged using x-ray computer tomography with micron-scale resolution. The scaling analysis relies on the study of the way qth-order sample structure functions (statistical moments of order q of absolute increments) of Lagrangian velocities depend on separation distances, or lags, traveled along the mean flow direction. In the sandstone block, sample structure functions of all orders exhibit a power-law scaling within a clearly identifiable intermediate range of lags. Sample structure functions associated with the limestone block display two diverse power-law regimes, which we infer to be related to two overlapping spatially correlated structures. In both rocks and for all orders q, we observe linear relationships between logarithmic structure functions of successive orders at all lags (a phenomenon that is typically known as extended power scaling, or extended self-similarity). The scaling behavior of Lagrangian velocities is compared with the one exhibited by porosity and specific surface area, which constitute two key pore-scale geometric observables. The statistical scaling of the local velocity field reflects the behavior of these geometric observables, with the occurrence of power-law-scaling regimes within the same range of lags for sample structure functions of Lagrangian velocity, porosity, and specific surface area.

Observation of the abyssal western boundary current in the Philippine Sea

Mooring observations were conducted from July 16, 2011 to March 30, 2012 east of Mindanao, Philippines (127A degrees 2.8'E, 8A degrees 0.3'N) to observe the abyssal current at about 5 600 m deep and 500 m above the ocean bottom. Several features were revealed: 1) the observed abyssal current was highly variable with standard deviations of 57.3 mm/s and 34.0 mm/s, larger than the mean values of -31.9 and 16.6 mm/s for the zonal and meridional components, respectively; 2) low-frequency current longer than 6 days exhibited strong seasonal variation, flowing southeastward (mean flow direction of 119.0A degrees clockwise from north) before about October 1, 2011 and northwestward (mean flow direction of 60.5A degrees counter-clockwise from north) thereafter; 3) the high-frequency flow bands were dominated by tidal currents O-1, K-1, M-2, and S-2, and near-inertial currents, whose frequencies were higher than the local inertial frequency. The two diurnal tidal constituents were much stronger than the two semidiurnal ones. This study provides for the first time an observational insight into the abyssal western boundary current east of Mindanao based on long-term observations at one site. It is meaningful for further research into the deep and abyssal circulation over the whole Philippine Sea and the 3D structure of the western boundary current system in this region. More observational and high-resolution model studies are needed to examine the spatial structure and temporal variation of the abyssal current over a much larger space and longer period, their relation to the upper-layer circulation, and the underlying dynamics.

The effect of arrangement of two circular cylinders on the maximum efficiency of Vortex-Induced Vibration power using a Scale-Adaptive Simulation model

The complex behaviour of an unsteady flow around two circular cylinders in tandem is of interest for many civil engineering applications across a wide range of aerospace, mechanical and marine applications. The present paper analyses Vortex-Induced Vibration (VIV) for the flow around two circular cylinders. It has been shown that the amount of kinetic energy which can be captured by VIV is a function of the arrangement of the two cylinders. The upstream cylinder is fixed while the downstream is mounted elastically with one degree of freedom normal to the mean flow direction. The efficiency of the VIV power obtained from downstream cylinder is compared for different arrangement of the cylinders. For this purpose, the longitudinal and lateral distances between the cylinders were varied and the Reynolds number was kept constant. Scale-Adaptive Simulation (SAS) and Shear Stress Transport (SST) CFD models are utilized to analyse the validity of the SAS turbulence model. The results indicate that both turbulence models predict the flow characteristics around the cylinders with reasonable precision; however, the predictions from SAS were more accurate compared to the SST. Based on this comparison, SAS model was chosen as a tool to analyse the VIV response of the downstream cylinder. The location of the downstream cylinder has been altered in the wake of upstream one in order to obtain the optimum efficiency of the VIV power. The results reveal that the arrangement of the cylinders can significantly change the efficiency. It is also observed that cylinders offset from one another show a higher efficiency compared to cylinders with their centres aligned.

Model to interpret pulsed-field-gradient NMR data including memory and superdispersion effects.

We propose a versatile model specifically designed for the quantitative interpretation of NMR velocimetry data. We use the concept of mobile or immobile tracer particles applied in dispersion theory in its Lagrangian form, adding two mechanisms: (i) independent random arrests of finite average representing intermittent periods of very low velocity zones in the mean flow direction and (ii) the possibility of unexpectedly long (but rare) displacements simulating the occurrence of very high velocities in the porous medium. Based on mathematical properties related to subordinated Lévy processes, we give analytical expressions of the signals recorded in pulsed-field-gradient NMR experiments. We illustrate how to use the model for quantifying dispersion from NMR data recorded for water flowing through a homogeneous grain pack column in single- and two-phase flow conditions.

Influence of edge velocity on flame front position and displacement speed in turbulent premixed combustion

Using a novel concept, the present study experimentally investigates underlying physics pertaining to statistics of the flame front position and the flame front velocity in turbulent premixed V-shaped flames. The concept is associated with characteristics of the reactants velocity at the vicinity of the flame front, referred to as the edge velocity. The experiments are performed using simultaneous Mie scattering and Particle Image Velocimetry techniques. Three mean streamwise exit velocities of: 4.0, 6.2, and 8.6m/s along with three fuel–air equivalence ratios of: 0.7, 0.8, and 0.9 are examined. The results show that fluctuations of the flame front position and the flame front velocity are induced by the fluctuations of the component of the edge velocity transverse to the mean flow direction. Analysis of the results show that the mean of the flame front velocity in the normal direction to the flame front is significantly dependent on the vertical distance from the flame-holder. Relatively close to the flame-holder, the mean of the flame front velocity in the direction normal to the flame front is about zero; however, it increases to values several times larger than the laminar flame speed by increasing the vertical distance from the flame-holder.

Heat transfer in Bingham plastic fluids from a heated elliptical cylinder

The forced convection heat transfer characteristics in Bingham plastic fluids from a heated elliptical cylinder of various aspect ratios E(=a/b) have been investigated numerically. The momentum and energy equations have been solved here by using the finite element method over wide ranges of rheological and kinematic parameters as: 0.01⩽Bn⩽100 (Bingham number), 0.01⩽Re⩽40 (Reynolds number), 1⩽Pr⩽100 (Prandtl number) and 0.1⩽E⩽10 (aspect ratio) thereby approaching the limiting conditions of a plate aligned with and transverse to the direction of mean flow. Furthermore, the influence of the type of thermal boundary condition, i.e., constant wall temperature (CWT) and constant heat flux (CHF) prescribed on the surface of the elliptical cylinder has also been examined. Extensive numerical results are reported herein in terms of the isotherm contours, variation of the Nusselt number on the surface of the cylinder for the two above-noted thermal boundary conditions and finally, the overall results are presented in terms of the surface averaged Nusselt number. Irrespective of the boundary condition prescribed on the surface of the cylinder, the Nusselt number shows a positive dependence on the both Reynolds number and Prandtl number while the effect of Bingham number is somewhat dependent on the Reynolds number range. The average Nusselt number has also been interpreted and correlated in terms of the Colburn heat transfer factor (j). Empirical correlations for the Colburn factor as functions of the Bingham number and aspect ratio have been proposed based on the present numerical results.

Relationship between pore size and velocity probability distributions in stochastically generated porous media

We perform a set of detailed numerical simulations of single-phase, fully saturated flow in stochastically generated, three-dimensional pore structures with diverse porosities (ϕ) and degrees of connectivity, and analyze the probability density functions (PDFs) of the pore sizes, S, and vertical velocity components, w, which are aligned with the mean flow direction. Both of the PDFs are markedly skewed with pronounced positive tails. This feature of the velocity PDF is dictated by the pore structure and determines the shortest travel times, one of the key transport attributes that underpins the success or the failure of environmental remediation techniques. Using a maximum likelihood approach, we determine that the PDFs of S and w decay according to an exponential and a stretched exponential model, respectively. A strong correlation between the key parameters governing the decay of the upper tails of the two PDFs is found, which provides a quantitative result for this analogy that so far has been stated only qualitatively. The parameter governing the concavity of the tail of the velocity PDF varies linearly with porosity over the entire range of tested values (0.2≤ϕ≤0.6). The parameters controlling the spread of the upper tails of the PDFs of S and w appear to be linked by a power-law relationship.

Simultaneous Sampling of Flow and Odorants by Crustaceans can Aid Searches within a Turbulent Plume

Crustaceans such as crabs, lobsters and crayfish use dispersing odorant molecules to determine the location of predators, prey, potential mates and habitat. Odorant molecules diffuse in turbulent flows and are sensed by the olfactory organs of these animals, often using a flicking motion of their antennules. These antennules contain both chemosensory and mechanosensory sensilla, which enable them to detect both flow and odorants during a flick. To determine how simultaneous flow and odorant sampling can aid in search behavior, a 3-dimensional numerical model for the near-bed flow environment was created. A stream of odorant concentration was released into the flow creating a turbulent plume, and both temporally and spatially fluctuating velocity and odorant concentration were quantified. The plume characteristics show close resemblance to experimental measurements within a large laboratory flume. Results show that mean odorant concentration and it's intermittency, computed as dc/dt, increase towards the plume source, but the temporal and spatial rate of this increase is slow and suggests that long measurement times would be necessary to be useful for chemosensory guidance. Odorant fluxes measured transverse to the mean flow direction, quantified as the product of the instantaneous fluctuation in concentration and velocity, v′c′, do show statistically distinct magnitude and directional information on either side of a plume centerline over integration times of <0.5 s. Aquatic animals typically have neural responses to odorant and velocity fields at rates between 50 and 500 ms, suggesting this simultaneous sampling of both flow and concentration in a turbulent plume can aid in source tracking on timescales relevant to aquatic animals.

Flow-Excited Acoustic Resonance Excitation Mechanism, Design Guidelines, and Counter Measures

The excitation mechanism of acoustic resonances has long been recognized, but the industry continues to be plagued by its undesirable consequences, manifested in severe vibration and noise problems in a wide range of industrial applications. This paper focuses on the nature of the excitation mechanism of acoustic resonances in piping systems containing impinging shear flows, such as flow over shallow and deep cavities. Since this feedback mechanism is caused by the coupling between acoustic resonators and shear flow instabilities, attention is focused first on the nature of various types of acoustic resonance modes and then on the aeroacoustic sound sources, which result from the interaction of the inherently unstable shear flow with the sound field generated by the resonant acoustic modes. Various flow-sound interaction patterns are discussed, in which the resonant sound field can be predominantly parallel or normal to the mean flow direction and the acoustic wavelength can be an order of magnitude longer than the length scale of the separated shear flow or as short as the cavity length scale. Since the state of knowledge in this field has been recently reviewed by Tonon et al. (2011, “Aeroacoustics of Pipe Systems With Closed Branches”, Int. J. Aeroacoust., 10(2), pp. 201–276), this article focuses on the more practical aspects of the phenomenon, including various flow-sound interaction patterns and the resulting aeroacoustic sources, which are relevant to industrial applications. A general design guide proposal and practical means to alleviate the excitation mechanism are also presented. These are demonstrated by two examples of recent industrial case histories dealing with acoustic fatigue failure of the steam dryer in a boiling water reactor (BWR) due to acoustic resonance in the main steam piping and acoustic resonances in the roll posts of the Short Take-Off and Vertical Lift Joint Strike Fighter (JSF).

Stochastic analytical modeling of the biodegradation of steady plumes

We present a stochastic analytical framework to assess the contaminant concentration of a steady plume undergoing biodegradation. The method is focused on heterogeneous formations, and it embeds both fringe and core degradation. The Lagrangian concentration approach of Fiori (2001) was employed, which is suited for describing the interplay between the large scale advection caused by heterogeneity and the local dispersion processes. The principal scope of the model is to provide a relatively simple tool for a quick assessment of the contamination level in aquifers, as function of a few relevant, physically based dimensionless parameters. The solution of the analytical model is relatively simple and generalizes previous approaches developed for homogeneous formations. It is found that heterogeneity generally enhances mixing and degradation; in fact, the plume shear and distortion operated by the complex, heterogeneous velocity field facilitates local dispersion in diluting the contaminant and mixing it with the electron acceptor. The decay of the electron donor concentration, and so the plume length, is proportional to the transverse pore-scale dispersivity, which is indeed the parameter ruling mixing and hence degradation. While the theoretical plume length is controlled by the fringe processes, the core degradation may determine a significant decay of concentration along the mean flow direction, thus affecting the length of the plume. The method is applied to the crude oil contamination event at the Bemijdi site, Minnesota (USA).

Experimental Investigation of a Tandem Cylinder System With a Yawed Upstream Cylinder

The unsteady flow field produced by a tandem cylinder system with the upstream cylinder yawed to the mean flow direction is investigated for upstream cylinder yaw angles from α=60 deg to α=90 deg. Multipoint fluctuating surface pressure and hot-wire measurements were conducted at various spanwise positions on both the upstream and downstream cylinders. The results indicate that yawing the front cylinder to the mean flow direction causes the pressure and velocity spectra on the upstream and downstream cylinders to become more broadband than for a regular tandem cylinder system, and reduces the magnitude of the peak associated with the vortex-shedding. However, spanwise correlation and coherence measurements indicate that the vortex-shedding is still present and was being obscured by the enhanced three-dimensionality that the upstream yawed cylinder caused. When the cylinder was yawed to α=60 deg, the pressure fluctuations became extremely broadband and exhibited shorter spanwise correlation.

Wall-parallel stereo particle-image velocimetry measurements in the roughness sublayer of turbulent flow overlying highly irregular roughness

Stereo particle-image velocimetry measurements were conducted in a streamwise–spanwise (x − z) plane deep within the roughness sublayer (y = 0.047δ; δ is the boundary-layer thickness) of a zero-pressure-gradient turbulent boundary layer overlying highly irregular surface roughness replicated from a turbine blade damaged by foreign-material deposition. The ensemble-averaged streamwise velocity defect revealed the tendency of the roughness to promote channeling of the flow in the form of low-momentum pathways (LMPs) and high-momentum pathways. Enhanced turbulent and vortical activity was observed both between and along the spanwise boundaries of these streamwise-elongated pathways. In particular, streamwise pathways of wall-normal vortex cores of opposing rotational sense were observed along the spanwise boundaries of the identified LMP in the rough-wall flow. Conditional averaging revealed that these counter-rotating vortical motions are associated with streamwise flow against the mean-flow direction and could perhaps be the origination mechanism of the LMPs. Two-point correlation coefficients of velocity and swirling strength reflected large-scale streamwise coherence of these quantities along and outboard of the identified LMP in the rough-wall flow, supporting the notion that the motions responsible for the LMP have large-scale, streamwise coherence. Finally, the influence of different topographical scales of the roughness on the flow in the roughness sublayer was explored using low-order models of the original, full surface as originally proposed by R. Mejia-Alvarez and K. T. Christensen [Phys. Fluids 22(1), 015106 (2010)]. While a model containing only the largest topographical scales qualitatively reproduced the features of the full-surface flow, additional intermediate topographical scales were required to quantitatively reproduce the statistical and structural nature of the full-surface flow in the roughness sublayer.

Nonlinear effects of flow unsteadiness on the acoustic radiation of a heaving airfoil

Abstract The study considers the combined effects of boundary animation (small-amplitude heaving) and incoming flow unsteadiness (incident vorticity) on the vibroacoustic signature of a thin rigid airfoil in low-Mach number flow. The potential-flow problem is analysed using the Brown and Michael equation, yielding the incident vortex trajectory and time evolution of trailing edge wake. The dynamical description serves as an effective source term to evaluate the far-field sound using Powell–Howe analogy. The results identify the fluid-airfoil system as a dipole-type source, and demonstrate the significance of nonlinear eddy-airfoil interactions on the acoustic radiation. Based on the value of scaled heaving frequency ω a / U (with ω the dimensional heaving frequency, a the airfoil half-chord, and U the mean flow speed), the system behaviour can be divided into two characteristic regimes: (i) for ω a / U ⪡ 1 , the effect of heaving is minor, and the acoustic response is well approximated by considering the interaction of a line vortex with a stationary airfoil; (ii) for ω a / U ⪢ 1 , the impact of heaving is dominant, radiating sound through an “airfoil motion” dipole oriented along the direction of heaving. In between (for ω a / U ~ O ( 1 ) ), an intermediate regime takes place. The results indicate that trailing edge vorticity has a two-fold impact on the acoustic far field: while reducing pressure fluctuations generated by incident vortex interaction with the airfoil, trailing edge vortices transmit sound along the mean-flow direction, characterized by airfoil heaving frequency. The “silencing” effect of trailing edge vorticity is particularly efficient when the incident vortex passes close to the airfoil trailing edge: at that time, application of the Kutta condition implies the release of a trailing edge vortex in the opposite direction to the incident vortex; the released vortex then detaches from the airfoil and follows the incident vortex, forming a “silent” vortex pair. By analysing the nonlinear fluid–structure interaction problem, the present work aims at complementing existing studies, in which linear eddy-airfoil interactions are considered for unforced configurations.