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Journal of Fluid Mechanics
Journal Prestige (SJR): 1.591 Citation Impact (citeScore): 3 Number of Followers: 162 Hybrid journal (It can contain Open Access articles) ISSN (Print) 00221120  ISSN (Online) 14697645 Published by Cambridge University Press [373 journals] 
 Towards the distributed burning regime in turbulent premixed flames
 Authors: A. J. Aspden; M. S. Day, J. B. Bell
Pages: 1  21
Abstract: Threedimensional numerical simulations of canonical statistically steady, statistically planar turbulent flames have been used in an attempt to produce distributed burning in lean methane and hydrogen flames. Dilatation across the flame means that extremely large Karlovitz numbers are required; even at the extreme levels of turbulence studied (up to a Karlovitz number of 8767) distributed burning was only achieved in the hydrogen case. In this case, turbulence was found to broaden the reaction zone visually by around an order of magnitude, and thermodiffusive effects (typically present for lean hydrogen flames) were not observed. In the preheat zone, the species compositions differ considerably from those of onedimensional flames based a number of different transport models (mixture averaged, unity Lewis number and a turbulent eddy viscosity model). The behaviour is a characteristic of turbulence dominating nonunity Lewis number species transport, and the distinct limit is again attributed to dilatation and its effect on the turbulence. Peak local reaction rates are found to be lower in the distributed case than in the lower Karlovitz cases but higher than in the laminar flame, which is attributed to effects that arise from the modified fueltemperature distribution that results from turbulent mixing dominating low Lewis number thermodiffusive effects. Finally, approaches to achieve distributed burning at realisable conditions are discussed; factors that increase the likelihood of realising distributed burning are higher pressure, lower equivalence ratio, higher Lewis number and lower reactant temperature.
PubDate: 20190725T00:00:00.000Z
DOI: 10.1017/jfm.2019.316
Issue No: Vol. 871 (2019)
 Authors: A. J. Aspden; M. S. Day, J. B. Bell

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++++++++++++++++$Re_{\unicode[STIX]{x1D70F}}\approx+1000$
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++++&rft.title=Journal+of+Fluid+Mechanics&rft.issn=00221120&rft.date=2019&rft.volume=871&rft.spage=22&rft.epage=51&rft.aulast=Agostini&rft.aufirst=Lionel&rft.au=Lionel+Agostini&rft.au=Michael+Leschziner&rft_id=info:doi/10.1017/jfm.2019.297">The connection between the spectrum of turbulent scales and the
skinfriction statistics in channel flow at
$Re_{\unicode[STIX]{x1D70F}}\approx 1000$ Authors: Lionel Agostini; Michael Leschziner
Pages: 22  51
Abstract: Data from a direct numerical simulation for channel flow at a friction Reynolds number of 1000 are analysed to derive statistical properties that offer insight into the mechanisms by which largescale structures in the loglaw region affect the smallscale turbulence field close to the wall and the statistical skinfriction properties. The data comprise fullvolume velocity fields at 150 time levels separated by 50 wallscaled viscous time units. The scales are separated into wavelength bands by means of the ‘empirical mode decomposition’, of which the two lowest modes are considered to represent the small scales and three upper modes to represent the large scales. Joint and conditional probability density functions are then derived for various scalespecific statistics, with particular emphasis placed on the streamwise and shear stresses conditional on the largescale fluctuations of the skin friction, generally referred to as ‘footprinting’. Statistics for the smallscale stresses, conditional on the footprints, allow the amplification and attenuation of the smallscale skin friction, generally referred to as ‘modulation’, to be quantified in dependence on the footprints. The analysis leads to the conclusion that modulation does not reflect a direct interaction between small scales and large scales, but arises from variations in shearinduced production that arise from corresponding changes in the conditional velocity profile. This causal relationship also explains the wallnormal change in sign in the correlation between large scales and small scales at a wallscaled wall distance of approximately 100. The effects of different scales on the skin friction are investigated by means of two identities that describe the relationship between the shearstress components and the skin friction, one identity based on integral momentum and the other on energy production/dissipation. The two identities yield significant differences in the balance of scalespecific contributions, and the origins of these differences are discussed.
PubDate: 20190725T00:00:00.000Z
DOI: 10.1017/jfm.2019.297
Issue No: Vol. 871 (2019)
 Authors: Lionel Agostini; Michael Leschziner
 Pseudophase change effects in turbulent channel flow under transcritical
temperature conditions Authors: Kukjin Kim; JeanPierre Hickey, Carlo Scalo
Pages: 52  91
Abstract: We have performed direct numerical simulations of compressible turbulent channel flow using R134a as a working fluid in transcritical temperature ranges ( $\unicode[STIX]{x0394}T=5$ , 10 and 20 K, where $\unicode[STIX]{x0394}T$ is toptobottom temperature difference) at supercritical pressure. At these conditions, a pseudophase change occurs at various wallnormal locations within the turbulent channel from $y_{pb}/h=0.23$ ( $\unicode[STIX]{x0394}T=5$ K) to 0.89 ( $\unicode[STIX]{x0394}T=20$ K), where $h$ is the channel halfheight and $y=0$ the centreplane position. Increase in $\unicode[STIX]{x0394}T$ also results in increasing wallnormal gradients in the semilocal friction Reynolds number. Classical, compressible scaling laws of the mean velocity profile are unable to fully collapse real fluid effects in this flow. The proximity to the pseudotransitioning layer inhibits turbulent velocity fluctuations, while locally enhancing the temperature and density fluctuation intensities. Probability distribution analysis reveals that the sheet of fluid undergoing pseudophase change is characterized by a dramatic reduction in the kurtosis of density fluctuations, hence becoming thinner as $\unicode[STIX]{x0394}T$ is increased. Instantaneous visualizations show dense fluid ejections from the pseudoliquid viscous sublayer, some reaching the channel core, causing positive values of density skewness in the respective buffer layer region (vice versa for the top wall) and an impoverishment of the turbulent flow structure population near pseudotr...
PubDate: 20190725T00:00:00.000Z
DOI: 10.1017/jfm.2019.292
Issue No: Vol. 871 (2019)
 Authors: Kukjin Kim; JeanPierre Hickey, Carlo Scalo
 The turbulent Kármán vortex
 Authors: J. G. Chen; Y. Zhou, R. A. Antonia, T. M. Zhou
Pages: 92  112
Abstract: This work focuses on the temperature (passive scalar) and velocity characteristics within a turbulent Kármán vortex using a phaseaveraging technique. The vortices are generated by a circular cylinder, and the three components of the fluctuating velocity and vorticity vectors, $u_{i}$ and $\unicode[STIX]{x1D714}_{i}$ ( $i=1,2,3$ ), are simultaneously measured, along with the fluctuating temperature $\unicode[STIX]{x1D703}$ and the temperature gradient vector, at nominally the same spatial point in the plane of mean shear at $x/d=10$ , where $x$ is the streamwise distance from the cylinder axis and $d$ is the cylinder diameter. We believe this is the first time the properties of fluctuating velocity, temperature, vorticity and temperature gradient vectors have been explored simultaneously within the Kármán vortex in detail. The Reynolds number based on $d$ and the freestream velocity is $2.5\times 10^{3}$ . The phaseaveraged distributions of $\unicode[STIX]{x1D703}$ and
PubDate: 20190725T00:00:00.000Z
DOI: 10.1017/jfm.2019.296
Issue No: Vol. 871 (2019)
 Authors: J. G. Chen; Y. Zhou, R. A. Antonia, T. M. Zhou
 Adjointbased shape optimization of the microchannels in an inkjet
printhead Authors: Petr V. Kungurtsev; Matthew P. Juniper
Pages: 113  138
Abstract: In dropondemand inkjet printheads, ink is pumped steadily through small channels, each of which contains an actuator and a nozzle. When an actuator pulses, a droplet is forced through the nozzle, after which acoustic oscillations reverberate within the channel. Manufacturers would like to damp the residual reverberations, without increasing the pressure drop required to drive the steady flow. In this paper we use gradientbased optimization to show that this can be achieved by constricting the channel where the acoustic velocity is largest and enlarging the channel where the acoustic velocity is smallest. This increases the viscothermal dissipation of the acoustics without changing the viscous dissipation of the steady flow. We separate the compressible Navier–Stokes equations into equations for a steady flow with no oscillations and equations for oscillations with no steady flow. We define two objective functions: the viscous dissipation of the steady flow and the dissipation of the oscillations. We then derive the adjoints for both sets of equations, and obtain expressions for the gradient of each objective function with respect to boundary deformations in Hadamard form. We combine these with a gradientbased optimization algorithm, incorporating constraints such as the shapes of the actuator and nozzle. This algorithm quickly converges to a design that has the same viscous dissipation for the steady flow but a 50 % larger decay rate for the oscillating flow. We show that this design is nearly optimal. It is a shape that inkjet manufacturers, using physical insight and trial and error, have probably not yet considered. We also show how the adjoint fields provide physical insight into the mechanisms affecting each objective function. The main requirements of this method are that the steady flow Mach number and oscillating flow Mach number are small, and that dissipation is dominated by thermoviscous mechanisms. These requirements are often satisfied in microfluidics, so the method in this paper could be applied to many other applications.
PubDate: 20190725T00:00:00.000Z
DOI: 10.1017/jfm.2019.271
Issue No: Vol. 871 (2019)
 Authors: Petr V. Kungurtsev; Matthew P. Juniper
 Rheology of a suspension of conducting particles in a magnetic field
 Authors: V. Kumaran
Pages: 139  185
Abstract: When a suspension of conducting particles is sheared in a magnetic field, the fluid vorticity causes particle rotation. Eddy currents are induced in a conductor rotating in a magnetic field, resulting in magnetic moment, and a magnetic torque due to the external field. In the absence of inertia, the angular velocity of a particle is determined from the condition that the sum of the hydrodynamic and magnetic torques is zero. When the particle angular velocity is different from the fluid rotation rate, the torque exerted by the particles on the fluid results in an antisymmetric particle stress. The stress is of the form $\unicode[STIX]{x1D748}^{(p)}=\unicode[STIX]{x1D74E}(\unicode[STIX]{x1D702}_{c}^{(1)}(\hat{\unicode[STIX]{x1D750}}\boldsymbol{ : }\hat{\unicode[STIX]{x1D74E}})+\unicode[STIX]{x1D702}_{c}^{(2)}\hat{\unicode[STIX]{x1D750}}\boldsymbol{ : }(\hat{\boldsymbol{H}}\hat{\unicode[STIX]{x1D74E}}(\hat{\unicode[STIX]{x1D74E}}\boldsymbol{\cdot }\hat{\boldsymbol{H}}))/(\sqrt{1(\hat{\unicode[STIX]{x1D74E}}\boldsymbol{\cdot }\hat{\boldsymbol{H}})^{2}})+\unicode[STIX]{x1D702}_{c}^{(3)}(\hat{\unicode[STIX]{x1D74E}}\hat{\boldsymbol{H}}\hat{\boldsymbol{H}}\hat{\unicode[STIX]{x1D74E}})/\sqrt{1(\hat{\unicode[STIX]{x1D74E}}\boldsymbol{\cdot }\hat{\boldsymbol{H}})^{2}})$ , where $\unicode[STIX]{x1D74E}$ is the fluid vorticity at the centre of the particle, $\hat{\unicode[STIX]{x1D74E}}$ and $\hat{\boldsymbol{H}}$ are the unit vectors in the direction of the fluid vorticity and the magnetic field, $\hat{\unicode[STIX]{x1D750}}$ is the third order LeviCivita antisymmetric tensor and $\unicode[STIX]{x1D702}_{c}^{(1)}$ , $\unicode[STIX]{x1D702}_{c}^{(2)}$ and $\unicode[STIX]{x1D702}_{c}^{(3)}$ are called the first, second and third couple stress coefficients. The stress proportional to
PubDate: 20190725T00:00:00.000Z
DOI: 10.1017/jfm.2019.295
Issue No: Vol. 871 (2019)
 Authors: V. Kumaran
 On the universal trends in the noise reduction due to wavy leading edges
in aerofoil–vortex interaction Authors: Jacob M. Turner; Jae Wook Kim
Pages: 186  211
Abstract: Existing studies suggest that wavy leading edges (WLEs) offer substantial reduction of broadband noise generated by an aerofoil undergoing upstream vortical disturbances. In this context, there are two universal trends in the frequency spectra of the noise reduction which have been observed and reported to date: (i) no significant reduction at low frequencies followed by (ii) a rapid growth of the noise reduction that persists in the mediumtohigh frequency range. These trends are known to be insensitive to the aerofoil type and flow condition used. This paper aims to provide comprehensive understandings as to how these universal trends are formed and what the major drivers are. The current work is based on veryhighresolution numerical simulations of a semiinfinite flatplate aerofoil impinged by a prescribed divergencefree vortex in an inviscid base flow at zero incidence angle, continued from recent work by the authors (Turner & Kim, J. Fluid Mech., vol. 811, 2017, pp. 582–611). One of the most significant findings in the current work is that the noise source distribution on the aerofoil surface becomes entirely twodimensional (highly nonuniform in the spanwise direction as well as streamwise) at high frequencies when the WLE is involved. Also, the sources downstream of the LE make crucial contributions to creating the universal trends across all frequencies. These findings contradict the conventional LEfocused onedimensional source analysis that has widely been accepted for all frequencies. The current study suggests that the universal trends in the noisereduction spectra can be properly understood by taking the downstream source contributions into account, in terms of both magnitude and phase variations. After including the downstream sources, it is shown in this paper that the first universal trend is due to the conservation of total (surface integrated) source energy at low frequencies. The surfaceintegrated source magnitude that decreases faster with the WLE correlates very well with the noisereduction spectrum at medium frequencies. In the meantime, the highfrequency noise reduction is driven almost entirely by destructive phase interference that increases rapidly and consistently with frequency, explaining the second universal trend.
PubDate: 20190725T00:00:00.000Z
DOI: 10.1017/jfm.2019.314
Issue No: Vol. 871 (2019)
 Authors: Jacob M. Turner; Jae Wook Kim
 Bouncing phase variations in pilotwave hydrodynamics and the stability of
droplet pairs Authors: Miles M. P. Couchman; Sam E. Turton, John W. M. Bush
Pages: 212  243
Abstract: We present the results of an integrated experimental and theoretical investigation of the vertical motion of millimetric droplets bouncing on a vibrating fluid bath. We characterize experimentally the dependence of the phase of impact and contact force between a drop and the bath on the drop’s size and the bath’s vibrational acceleration. This characterization guides the development of a new theoretical model for the coupling between a drop’s vertical and horizontal motion. Our model allows us to relax the assumption of constant impact phase made in models based on the timeaveraged trajectory equation of Moláček and Bush (J. Fluid Mech., vol. 727, 2013b, pp. 612–647) and obtain a robust horizontal trajectory equation for a bouncing drop that accounts for modulations in the drop’s vertical dynamics as may arise when it interacts with boundaries or other drops. We demonstrate that such modulations have a critical influence on the stability and dynamics of interacting droplet pairs. As the bath’s vibrational acceleration is increased progressively, initially stationary pairs destabilize into a variety of dynamical states including rectilinear oscillations, circular orbits and sidebyside promenading motion. The theoretical predictions of our variableimpactphase model rationalize our observations and underscore the critical importance of accounting for variability in the vertical motion when modelling droplet–droplet interactions.
PubDate: 20190725T00:00:00.000Z
DOI: 10.1017/jfm.2019.293
Issue No: Vol. 871 (2019)
 Authors: Miles M. P. Couchman; Sam E. Turton, John W. M. Bush