## Publications

168 results found

Cafiero G, Vassilicos JC, 2019, Non-equilibrium turbulence scalings and self-similarity in turbulent planar jets, *PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES*, Vol: 475, ISSN: 1364-5021

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- Citations: 18

Lamballais E, Dairay T, Laizet S, et al., 2019, Implicit/explicit spectral viscosity and large-scale SGS effects, ERCOFTAC Series, Pages: 107-113

In order to investigate the scale-selective influence of SGS on the large scale dynamics, DNS and LES are performed for the Taylor-Green vortex problem. An a priori analysis confirms the interest of the hyperviscous feature at small scale as used in implicit LES, SVV and VMS. However, the assumption of zero SGS dissipation at very large scales is found unrealistic for the high Reynolds number and coarse LES mesh considered. A posteriori analysis shows that SGS modelling based on the assumption of an inviscid cascade leads to a bottleneck effect on the kinetic energy spectrum with a significant underprediction of the total SGS dissipation. The simple addition of a constant eddy viscosity, even targeted to be optimal in terms of SGS dissipation, is unable to give realistic results. To allow accurate predictions by LES, a specific closure that incorporates both the hyperviscous feature (i.e. regularisation) and the expected SGS dissipation at large scales has to be developed.

Alves Portela F, Papadakis G, Vassilicos JC, 2018, Turbulence dissipation and the role of coherent structures in the near wake of a square prism, *Physical Review Fluids*, Vol: 3, ISSN: 2469-990X

Between streamwise distances 4d and at least 10d in the planar turbulent wake of a square prism of side length d, the turbulent fluctuating velocities are highly non-Gaussian, the turbulent energy spectrum has a close to −5/3 power law range, and the turbulence dissipation rate obeys the nonequilibrium dissipation scaling if the energy of the coherent structures is not included in the scaling. In this same range of streamwise distances, the coherent structure dissipation rate decays proportionally to the stochastic turbulence dissipation rate and there is a strong tendency of alignment or antialignment between fluctuating velocities and fluctuating vorticities which appears to coincide with the presence of coherent structures.

Papadakis G, Vassilicos C, Basbug S, 2018, Reduced mixing time in stirred vessels by means of irregular impellers, *Physical Review Fluids*, Vol: 3, ISSN: 2469-990X

Previous research has shown that using fractal-like blades instead of regular ones can result in a significant decrease in the power consumption of an unbaffled stirred vessel with a four-bladed radial impeller. In order to fully assess the mixing efficiency of a fractal-like or just irregular impeller with respect to a regular impeller, the mixing time required to homogenize an injected passive scalar was evaluated for both impeller types at Re = 320 and 1600 using direct numerical simulations. It was observed that the irregular impeller can lead to a considerably shorter mixing time. This result was explained by the differences in characteristics of flow and scalar fields generated by the two impellers. We also assess the effect of Re in the transitional regime. Moreover, a simple mathematical model is proposed which can approximate the decay rate of the passive scalar fluctuations integrated over the tank volume.

Zheng S, Bruce PJK, Graham JMR,
et al., 2018, Weakly sheared turbulent flows generated by multiscale inhomogeneous grids, *Journal of Fluid Mechanics*, Vol: 848, Pages: 788-820, ISSN: 0022-1120

A group of three multiscale inhomogeneous grids have been tested to generate different types of turbulent shear flows with different mean shear rate and turbulence intensity profiles. Cross hot-wire measurements were taken in a wind tunnel with Reynolds number ReD of 6000–20 000, based on the width of the vertical bars of the grid and the incoming flow velocity. The effect of local drag coefficient CD on the mean velocity profile is discussed first, and then by modifying the vertical barsto obtain a uniform aspect ratio the mean velocity profile is shown to be predictable using the local blockage ratio profile. It is also shown that, at a streamwise location x = xm, the turbulence intensity profile along the vertical direction u0(y) scales with the wake interaction length x peak∗,n = 0.21g2n/(αCDwn) (α is a constant characterizing the incoming flow condition, and gn, wn are the gap and width of the vertical bars,respectively, at layer n) such that (u0/Un) 2β2 (CDwn/x peak ∗,n) −1 ∼ (xm/x peak ∗,n) b, where β is a constant determined by the free-stream turbulence level, Un is the local mean velocity and b is a dimensionless power law constant. A general framework of grid design method based on these scalings is proposed and discussed. From the evolutionof the shear stress coefficient ρ(x), integral length scale L(x) and the dissipation coefficient C (x), a simple turbulent kinetic energy model is proposed that describes the evolution of our grid generated turbulence field using one centreline measurement and one vertical profile of u 0(y) at the beginning of the evolution. The results calculated from our model agree well with our measurements in the streamwiseextent up to x/H ≈ 2.5, where H is the height of the grid, suggesting that it might be possible to design some shear flows with desired mean velocity and turbulence intensity profiles by designing the geometry of a passive grid.

Paul I, Papadakis G, Vassilicos JC, 2018, Direct numerical simulation of heat transfer from a cylinder immersed in the production and decay regions of grid-element turbulence, *Journal of Fluid Mechanics*, Vol: 847, Pages: 452-488, ISSN: 0022-1120

The present direct numerical simulation (DNS) study, the first of its kind, explores the effect that the location of a cylinder, immersed in the turbulent wake of a grid-element, has on heat transfer. An insulated single square grid-element is used to generate the turbulent wake upstream of the heated circular cylinder. Due to fine-scale resolution requirements, the simulations are carried out for a low Reynolds number. Three locations downstream of the grid-element, inside the production, peak and decay regions, respectively, are considered. The turbulent flow in the production and peak regions is highly intermittent, non-Gaussian and inhomogeneous, while it is Gaussian, homogeneous and fully turbulent in the decay region. The turbulence intensities at the location of the cylinder in the production and decay regions are almost equal at 11Â %, while the peak location has the highest turbulence intensity of 15Â %. A baseline simulation of heat transfer from the cylinder without oncoming turbulence was also performed. Although the oncoming turbulent intensities are similar, the production region increases the stagnation point heat transfer by 63Â %, while in the decay region it is enhanced by only 28Â %. This difference cannot be explained only by the increased approaching velocity in the production region. The existing correlations for the stagnation point heat transfer coefficient are found invalid for the production and peak locations, while they are satisfied in the decay region. It is established that the flow in the production and peak regions is dominated by shedding events, in which the predominant vorticity component is in the azimuthal direction. This leads to increased heat transfer from the cylinder, even before vorticity is stretched by the accelerating boundary layer. The frequency of oncoming turbulence in production and peak cases also lies close to the range of frequencies that can penetrate the boundary layer developing on the

Srinath S, Vassilicos JC, Cuvier C,
et al., 2018, Attached flow structure and streamwise energy spectra in a turbulent boundary layer, *Physical Review E*, Vol: 97, ISSN: 1539-3755

On the basis of (i) particle image velocimetry data of a turbulent boundary layer with large field of view and good spatial resolution and (ii) a mathematical relation between the energy spectrum and specifically modeled flow structures, we show that the scalings of the streamwise energy spectrum E11(kx) in a wave-number range directly affected by the wall are determined by wall-attached eddies but are not given by the Townsend-Perry attached eddy model's prediction of these spectra, at least at the Reynolds numbers Reτ considered here which are between 103 and 104. Instead, we find E11(kx)∼k−1−px where p varies smoothly with distance to the wall from negative values in the buffer layer to positive values in the inertial layer. The exponent p characterizes the turbulence levels inside wall-attached streaky structures conditional on the length of these structures. A particular consequence is that the skin friction velocity is not sufficient to scale E11(kx) for wave numbers directly affected by the wall.

Paul I, Papadakis G, Vassilicos C, 2018, DNS of heat transfer from a cylinder immersed in the production and decayregions of grid-element turbulence, *Journal of Fluid Mechanics*, ISSN: 0022-1120

The present DNS study, the ﬁrst of its kind, explores the eﬀect that the location of a cylinder, immersed in the turbulent wake of a grid-element, has on heat transfer. An insulated single square grid-element is used to generate the turbulent wake upstream of the heated circular cylinder. Due to ﬁne-scale resolution requirements, the simulations are carried out for a low Reynolds number. Three locations downstream of the gridelement, inside the production, peak and decay regions, respectively are considered. The turbulent ﬂow in the production and peak regions is highly intermittent, non-Gaussian and inhomogeneous, while it is Gaussian, homogeneous, and fully-turbulent in the decay region. The turbulence intensities at the location of the cylinder in the production and decay regions are almost equal at 11%, while the peak location has the highest turbulent intensity of 15%. A baseline simulation of heat transfer from the cylinder without oncoming turbulence was also performed. Although the oncoming turbulent intensities are similar, the production region increases the stagnation point heat transfer by 63%, while in the decay region it is enhanced by only 28%. This diﬀerence cannot be explained only by the increased approaching velocity in the production region. The existing correlations for the stagnation point heat transfer coeﬃcient are found invalid for the production and peak locations, while they are satisﬁed in the decay region. It is established that the ﬂow in the production and peak regions is dominated by shedding events, in which the predominant vorticity component is in the azimuthal direction. This leads to increased heat transfer from the cylinder, even before vorticity is stretched by the accelerating boundary layer. The frequency of oncoming turbulence in production and peak cases also lies close to the range of frequencies that can penetrate the boundary layer developing on the cylinder, and therefore the latter is very responsive to the impinging d

Basbug S, Papadakis G, Vassilicos C, 2018, Reduced power consumption in stirred vessels by means of fractal impellers, *AIChE Journal*, Vol: 64, Pages: 1485-1499, ISSN: 0001-1541

Earlier studies have shown that the power consumption of an unbaffled stirred vessel decreases significantly when the regular blades are replaced by fractal ones. In this paper, the physical explanation for this reduction is investigated using Direct Numerical Simulations at Re = 1600. The gaps around the fractal blade perimeter create jets that penetrate inside the recirculation zone in the wake and break up the trailing vortices into smaller ones. This affects the time‐average recirculation pattern on the suction side. The volume of the separation region is 7% smaller in the wake of the fractal blades. The lower torque of the fractal impeller is equivalent to a decreased transport of angular momentum; this difference stems from the reduced turbulent transport induced by the smaller trailing vortices. The major difference in the turbulent dissipation is seen in the vicinity of trailing vortices, due to fluctuations of velocity gradients at relatively low frequencies.

Melina G, Bruce PJK, Nedić J,
et al., 2018, Heat transfer from a flat plate in inhomogeneous regions of grid-generated turbulence, *International Journal of Heat and Mass Transfer*, Vol: 123, Pages: 1068-1086, ISSN: 0017-9310

Experiments on the convective heat transfer from a flat plate, vertically mounted and parallel to the flow in a wind tunnel, were carried out via Infra-Red thermography and hot-wire anemometry. The Reynolds number based on the inflow velocity and on the length of the plate was about 5×1055×105. A step near the leading edge of the plate was used to promote transition to turbulence, with tripping effects on the heat transfer coefficients shown to be negligible for more than 90% of the plate’s length. Different types of grids, all with same blockage ratio σg=28%σg=28%, were placed upstream of the plate to investigate their potential to enhance the turbulent heat transfer. These grids were of three classes: regular square-mesh grids (RGs), single-square grids (SSGs) and multi-scale inhomogeneous grids (MIGs). The heat transfer coefficients at the mid-length of the plate were correlated with the mean velocity and the turbulence intensity of the flow at a distance from the plate at which the ratio of the standard deviations of the streamwise and wall-normal velocity fluctuations began to increase. However, the heat transfer was shown to be insensitive to the turbulence intensity of the incoming flow in close proximity of the tripping step. Furthermore, the integral length scale of the streamwise turbulent fluctuations was found not to affect the heat transfer results, both near the tripping step and in the well-developed region on the plate. For the smallest plate-to-grid distance, the strongest heat transfer enhancement (by roughly 30%) with respect to the no-grid case was achieved with one of the SSGs. For the largest plate-to-grid distance, the only grid producing an appreciable increase (by approximately 10%) of the heat transfer was one of the MIGs. The present results demonstrate that MIG design can be optimised to maximise the overall heat transfer from the plate. A MIG that produces a uniform transverse mean shear, which is approximat

Papadakis G, Paul I, Vassilicos C, 2018, Evolution of passive scalar statistics in a spatially developingturbulence, *Physical Review Fluids*, Vol: 3, ISSN: 2469-990X

We investigate the evolution of passive scalar statistics in a spatially developing turbulence using Direct Numerical Simulation. Turbulence is generated by a square grid-element, which is heated continuously, and the passive scalar is temperature. The square element is the fundamental building block for both regular and fractal grids. We trace the dominant mechanisms responsible for the dynamical evolution of scalar variance and scalar dissipation along the bar and grid-element centrelines. The scalar-variance is generated predominantly by the action of mean scalar gradient behind the bar and is transported laterally by turbulent fluctuations to the grid-element centreline. The scalar dissipation (proportional to the scalar gradient variance) is produced primarily by the compression of the fluctuating scalar gradient vector by the turbulent strain-rate, while the contribution of mean velocity and scalar fields is negligible. Close to the grid element the scalar spectrum exhibits a well-defined -5/3 power law, even though the basic premises of the Kolmogorov-Obukhov-Corrsin theory are not satisfied (the fluctuating scalar field is highly intermittent, inhomogeneous and anisotropic, and the local Corrsin-microscale-Peclet number is small). At this location, the PDF of scalar gradient production is only slightly skewed towards positive and the fluctuating scalar gradient vector aligns only with the compressive strain-rate eigenvector. The scalar gradient vector is stretched/compressed stronger than the vorticity vector by turbulent strain-rate throughout the grid-element centreline. However, the alignment of the former changes much earlier in space than that of the latter, resulting in scalar dissipation to decay earlier along the grid-element centreline compared to the turbulent kinetic energy dissipation. The universal alignment behaviour of the scalar gradient vector is found far-downstream although the local Reynolds and Peclet numbers (based on the Taylor and Cor

Yasuda T, Vassilicos JC, 2018, Spatio-temporal intermittency of the turbulen energy cascade, *JOURNAL OF FLUID MECHANICS*, Vol: 853, Pages: 235-252, ISSN: 0022-1120

Dairay T, Lamballais E, Laizet S,
et al., 2018, Physical scaling of numerical dissipation for LES, *ERCOFTAC Series*, Vol: 24, Pages: 149-155, ISSN: 1382-4309

In this work, we are interested in an alternative way to perform LES using a numerical substitute of a subgrid-scale model with a calibration based on physical inputs.

de la Cruz JMG, Vassilicos JC, Rossi L, 2017, Statistical independence of the initial conditions in chaotic mixing, *PHYSICAL REVIEW E*, Vol: 96, ISSN: 2470-0045

Laizet S, Diaz Daniel C, Vassilicos C, 2017, Direct Numerical Simulations of a wall-attached cube immersed in laminar and turbulent boundary layers, *International Journal of Heat and Fluid Flow*, Vol: 68, Pages: 269-280, ISSN: 0142-727X

A wall-attached cube immersed in a zero pressure gradient boundary layer is studied by means of Direct Numerical Simulations (DNS) at various Reynolds numbers ReH (based on the cube height and the free-stream velocity) ranging from 500 to 3000. The cube is either immersed in a laminar boundary layer (LBL) or in a turbulent boundary layer (TBL), with the aim to understand the mechanisms of the unsteady flow structures generated downstream of the wall-attached cube. The mean locations of the stagnation and recirculation points around the cube immersed in a TBL are in good agreement with reference experimental and numerical data, even if in those studies the cube was immersed in a turbulent channel. In the TBL simulation, a vortex shedding can be identified in the energy spectra downstream of the cube, with Strouhal number of St=0.14. However, the frequency of the vortex shedding is different in the LBL simulations, showing a significant dependence on the Reynolds number. Furthermore, in the TBL simulation, a low frequency peak with St=0.05 can be observed far away from the boundary layer, at long streamwise distances from the cube. This peak cannot be identified in the LBL simulations nor in the baseline TBL simulation without the wall-attached cube.

Steiros K, Bruce PJK, Buxton ORH,
et al., 2017, Effect of blade modifications on the torque and flow field of radial impellers in stirred tanks, *PHYSICAL REVIEW FLUIDS*, Vol: 2, ISSN: 2469-990X

We perform both high- and low-speed particle image velocimetry and torque measurements to characterize eight radial impeller types in an unbaffled stirred tank. The blade types consist of a set of regular flat blades, used as a baseline, regular blades of increased thickness, perforated blades, and fractal blades. We find a qualitative correlation between the blades' torque coefficient and both vortex coherence and turbulent kinetic energy, possibly explaining the torque differences of the tested impellers. Furthermore, we find that the proposed modifications increase the bulk turbulence levels and mass flow rates while at the same time reducing the shaft torque, showing promise for applications. Finally, we attempt a comparison between fractal and perforated geometries using data from this study and the literature.

Alves Portela, Papadakis G, Vassilicos, 2017, The turbulence cascade in the near wake of a square prism, *Journal of Fluid Mechanics*, Vol: 825, Pages: 315-352, ISSN: 1469-7645

We present a study of the turbulence cascade on the centreline of an inhomogeneous and anisotropic near-field turbulent wake generated by a square prism at a Reynolds number of using the Kármán–Howarth–Monin–Hill equation. This is the fully generalised scale-by-scale energy balance which, unlike the Kármán–Howarth equation, does not require homogeneity or isotropy assumptions. Our data are obtained from a direct numerical simulation and therefore enable us to access all of the processes involved in this energy balance. A significant range of length scales exists where the orientation-averaged nonlinear interscale transfer rate is approximately constant and negative, indicating a forward turbulence cascade on average. This average cascade consists of coexisting forward and inverse cascade behaviours in different scale-space orientations. With increasing distance from the prism but within the near field of the wake, the orientation-averaged nonlinear interscale transfer rate tends to be approximately equal to minus the turbulence dissipation rate even though all of the inhomogeneity-related energy processes in the scale-by-scale energy balance are significant, if not equally important. We also find well-defined near energy spectra in the streamwise direction, in particular at a centreline position where the inverse cascade behaviour occurs for streamwise oriented length scales.

Basbug S, Papadakis G, Vassilicos, 2017, DNS investigation of the dynamical behaviour of trailing vortices in unbaffled stirred vessels at transitional Reynolds numbers, *Physics of Fluids*, Vol: 29, ISSN: 1089-7666

Flow in an unbaffled stirred vessel agitated by a four-bladed radial impeller is investigated by usingdirect numerical simulations atRe= 320 and 1600. We observe fluctuations in the power consumptionwith a peak frequency at ca. three times the impeller rotational speed for both Reynolds numbers. Itis discovered that these fluctuations are associated with a periodic event in the wake of the blades,which involves alternating growth and decay of the upper and lower cores of the trailing vortex pairas well as up-and-down swinging motion of the radial jet. Moreover, the phase relation between thewakes of the different blades is examined in detail. Further studies using fractal-shaped blades showthat the exact blade shape does not have a strong influence on this phenomenon. However, the wakeinteraction between the blades, hence the number of blades, has a direct influence on the unsteadinessof trailing vortices.

Diaz Daniel, Laizet S, Vassilicos JC, 2017, Wall shear stress fluctuations: mixed scaling and their effects on velocity fluctuations in a turbulent boundary layer, *Physics of Fluids*, Vol: 29, ISSN: 0031-9171

The present work investigates numerically the statistics of the wall shear stress fluctuations in a turbulent boundary layer (TBL) and their relation to the velocity fluctuations outside of the near-wall region. The flow data are obtained from a Direct Numerical Simulation (DNS) of a zero pressure-gradient TBL using the high-order flow solver Incompact3D [S. Laizet and E. Lamballais, “High-order compact schemes for incompressible flows: A simple and efficient method with quasi-spectral accuracy,” J. Comput. Phys. 228(16), 5989 (2009)]. The maximum Reynolds number of the simulation is Re ≈2000, based on the free-stream velocity and the momentum thickness of the boundary layer. The simulation data suggest that the root-mean-squared fluctuations of the streamwise and spanwise wall shear-stress components τx and τz follow a logarithmic dependence on the Reynolds number, consistent with the empirical correlation of Örlü and Schlatter [R. Örlü and P. Schlatter, “On the fluctuating wall-shear stress in zero pressure-gradient turbulent boundary layer flows,” Phys. Fluids 23, 021704 (2011)]. These functional dependencies can be used to estimate the Reynolds number dependence of the wall turbulence dissipation rate in good agreement with reference DNS data. Our results suggest that the rare negative events of τx can be associated with the extreme values of τzand are related to the presence of coherent structures in the buffer layer, mainly quasi-streamwise vortices. We also develop a theoretical model, based on a generalisation of the Townsend-Perry hypothesis of wall-attached eddies, to link the statistical moments of the filtered wall shear stress fluctuations and the second order structure function of fluctuating velocities at a distance y from the wall. This model suggests that the wall shear stress fluctuations may induce a higher slope in the turbulence energy spectra of streamwise velocities than the on

Zhou Y, Vassilicos JC, 2017, Related self-similar statistics of the turbulent/non-turbulent interface and the turbulence dissipation, *Journal of Fluid Mechanics*, Vol: 821, Pages: 440-457, ISSN: 0022-1120

The scalings of the local entrainment velocity of the turbulent/non-turbulent interface and of the turbulence dissipation rate are closely related to each other in an axisymmetric and self-similar turbulent wake. The turbulence dissipation scaling implied by the Kolmogorov equilibrium cascade phenomenology is consistent with a Kolmogorov scaling of whereas the non-equilibrium dissipation scaling reported for various turbulent flows in Vassilicos (Annu. Rev. Fluid Mech., vol. 47, 2015, pp. 95–114), Dairay et al. (J. Fluid Mech., vol. 781, 2015, pp. 166–195), Goto & Vassilicos (Phys. Lett. A, vol. 379 (16), 2015, pp. 1144–1148) and Obligado et al. (Phys. Rev. Fluids, vol. 1 (4), 2016, 044409) is consistent with a different scaling of . We present results from a direct numerical simulation of a spatially developing axisymmetric and self-similar turbulent wake which supports this conclusion and the assumptions that it is based on.

Dairay T, Lamballais E, Laizet S,
et al., 2017, Numerical dissipation vs. subgrid-scale modelling for large eddy simulation, *Journal of Computational Physics*, Vol: 337, Pages: 252-274, ISSN: 0021-9991

This study presents an alternative way to perform large eddy simulation based on a targeted numerical dissipation introduced by the discretization of the viscous term. It is shown that this regularisation technique is equivalent to the use of spectral vanishing viscosity. The flexibility of the method ensures high-order accuracy while controlling the level and spectral features of this purely numerical viscosity. A Pao-like spectral closure based on physical arguments is used to scale this numerical viscosity a priori. It is shown that this way of approaching large eddy simulation is more efficient and accurate than the use of the very popular Smagorinsky model in standard as well as in dynamic version. The main strength of being able to correctly calibrate numerical dissipation is the possibility to regularise the solution at the mesh scale. Thanks to this property, it is shown that the solution can be seen as numerically converged. Conversely, the two versions of the Smagorinsky model are found unable to ensure regularisation while showing a strong sensitivity to numerical errors. The originality of the present approach is that it can be viewed as implicit large eddy simulation, in the sense that the numerical error is the source of artificial dissipation, but also as explicit subgrid-scale modelling, because of the equivalence with spectral viscosity prescribed on a physical basis.

Paul I, Papadakis G, Vassilicos JC, 2017, Genesis and evolution of velocity gradients in a near-field spatially developing turbulence, *Journal of Fluid Mechanics*, Vol: 815, Pages: 295-332, ISSN: 1469-7645

This paper investigates the dynamics of velocity gradients for a spatially developing flowgenerated by a single square element of a fractal square grid at low inlet Reynolds numberthrough direct numerical simulation. This square grid-element is also the fundamentalblock of a classical grid. The flow along the grid-element centreline is initially irrotationaland becomes turbulent further downstream due to the lateral excursions of vorticalturbulent wakes from the grid-element bars. We study the generation and evolution ofthe symmetric and anti-symmetric parts of the velocity gradient tensor for this spatiallydeveloping flow using the transport equations of mean strain-product and mean enstrophyrespectively. The choice of low inlet Reynolds number allows for fine spatial resolutionand long simulations, both of which are conducive in balancing the budget equations ofthe above quantities. The budget analysis is carried out along the grid-element centrelineand the bar centreline. The former is observed to consist of two subregions: one in theimmediate lee of the grid-element which is dominated by irrotational strain, and onefurther downstream where both strain and vorticity coexist. In the demarcation areabetween these two subregions, where the turbulence is inhomogeneous and developing,the energy spectrum exhibits the best−5/3 power law slope. This is the same locationwhere the experiments at much higher inlet Reynolds number show a well defined−5/3 spectrum over more than a decade of frequencies. Yet, the Q-R diagram remainsundeveloped in the near grid-element region, and both the intermediate and extensivestrain-rate eigenvectors align with the vorticity vector. Along the grid-element centreline,the strain is the first velocity gradient quantity generated by the action of pressureHessian. This strain is then transported downstream by fluctuations and strain self-amplification is activate

Melina G, Bruce P, Hewitt G,
et al., 2017, Heat transfer in production and decay regions of grid-generated turbulence, *International Journal of Heat and Mass Transfer*, Vol: 109, Pages: 537-554, ISSN: 0017-9310

Heat transfer measurements around the centreline circumference of a cylinder in crossflow areperformed in a wind tunnel. The cylinder is placed at several stations downstream of threeturbulence-generating grids with different geometries and different blockage ratiosσg: a reg-ular grid (RG60) withσg= 32%, a fractal-square grid (FSG17) withσg= 25%and a single-square grid (SSG) withσg= 20%. Measurements are performed at 20 stations for 3 nominalReynolds numbers (based on the diameterDof the cylinder)Re∞= 11 100,24 500,37 900.Hot-wire measurements are performed along the centreline, without the cylinder in place,to characterise the flow downstream of the grids. The extent of the turbulence productionregion, where the turbulence intensityTuincreases with the streamwise distancexfrom thegrid, is higher for SSG and more so for FSG17 than for RG60. The angular profiles of theNusselt numberNuare measured in the production regions of these two grids and are com-pared to those obtained in the decay regions, whereTudecreases withx. This comparison ismade at locations with approximately sameTu. It is found that, for SSG,Nu/Re0.5on thefront of the cylinder (boundary layer region) is lower in the production region than in thedecay region. This is explained by the presence of clear and intense vortex shedding in theproduction region of SSG which reduces the turbulent fluctuations which are “effective” inenhancing the heat transfer across a laminar boundary layer. For higherRe∞, the values ofNu/Re0.5on the front of the cylinder are higher in the production region of FSG17 than inthat of SSG, despiteTubeing higher for SSG. This is consistent with a lower intermittencyof the flow for FSG17 caused by the presence of the fractal geometrical iterations. The recov-ery ofNuon the back of the cylinder (wake region) is appreciably higher in the productionregion than in the decay region for both FSG17 and for SSG. This can be due to the lowerint

Laval J-P, Vassilicos JC, Foucaut J-M,
et al., 2017, Comparison of turbulence profiles in high-Reynolds-number turbulent boundary layers and validation of a predictive model, *Journal of Fluid Mechanics*, Vol: 814, ISSN: 0022-1120

The modified Townsend–Perry attached-eddy model of Vassilicos et al. (J. Fluid Mech., vol. 774, 2015, pp. 324–341) combines the outer peak/plateau behaviour of root-mean-square streamwise turbulence velocity profiles and the Townsend–Perry log decay of these profiles at higher distances from the wall. This model was validated by these authors for high-Reynolds-number turbulent pipe flow data and is shown here to describe equally well, and with approximately the same parameter values, turbulent boundary layer flow data from four different facilities and a wide range of Reynolds numbers. The model has predictive value as, when extrapolated to the extremely high Reynolds numbers of the SLTEST data obtained at the Great Salt Lake Desert atmospheric test facility, it matches these data quite well.

Steiros K, Bruce PJK, Buxton ORH,
et al., 2017, Power consumption and form drag of regular and fractal-shaped turbines in a stirred tank, *AIChE Journal*, Vol: 63, Pages: 843-843, ISSN: 0001-1541

Previous wind-tunnel measurements have shown that fractal-shaped plates have increased drag compared to square plates of the same area. In this study, the power consumption and drag of turbines with fractal and rectangular blades in a stirred tank are measured. Power number decreases from rectangular to fractal impellers by over 10%, increasingly so with fractal iteration number. Our results suggest that this decrease is not caused by the wake interaction of the blades, nor solely by the wake interaction with the walls either. Pressure measurements on the blades’ surface show that fractal blades have lower drag than the rectangular ones, opposite to the wind tunnel experiment results. All tested blades’ center of pressure radius increases with Re, while their drag coefficient decreases, a possible effect of the solid body rotation expansion with Re. Spectral analysis of the pressure signal reveals two peaks possibly connected to the blades’ roll vortices.

Vassilicos C, 2016, Unsteady turbulence cascades, *Physical Review E*, Vol: 94, ISSN: 1539-3755

We have run a total of 311 Direct Numerical Simulations (DNS) of decaying three-dimensional Navier-Stokes turbulence in a periodic box with values of the Taylor length-based Reynolds number up to about 300 and an energy spectrum with a wide wavenumber range of close to -5/3 power-law dependence at the higher Reynolds numbers. On the basis of these runs we have found a critical time when (i) the rate of change of the square of the integral length-scale turns from increasing to decreasing, (ii) the ratio of interscale energy flux to high-pass filtered turbulence dissipation changes from decreasing to very slowly increasing in the inertial range, (iii) the signature of large-scale coherent structures disappears in the energy spectrum and (iv) the scaling of the turbulence dissipation changes from the one recently discovered in DNS of forced unsteady turbulence and in wind tunnnel experiments of turbulent wakes and grid-generated turbulence to the classical scaling proposed by G.I. Taylor in 1935 and A.N. Kolmogorov in 1941. Even though the customary theoretical basis for this Taylor-Kolmogorov scaling is a statistically stationary cascade where large scale energy flux balances dissipation, this is not the case thoughout the entire time-range of integration in all our DNS runs. The recently discovered dissipation scaling can be reformulated physically as a situation where the dissipation rates of the small and the large scales evolve together. We advance two hypotheses which may form the basis of a theoretical approach to unsteady turbulence cascades in the presence of large-scale coherent structures.

Obligado M, Dairay T, Vassilicos JC, 2016, Nonequilibrium scalings of turbulent wakes, *Physical Review Fluids*, Vol: 1, ISSN: 2469-990X

Nonequilibrium turbulent wake scalings are not the preserve of irregular (fractal-like/multiscale) plates but appear to be universal, as they also hold for regular plates over a very substantial downstream distance.

Dairay T, Vassilicos C, 2016, Direct numerical simulation of a turbulent wake: the non-equilibrium dissipation law, *International Journal of Heat and Fluid Flow*, Vol: 62, Pages: 68-74, ISSN: 0142-727X

A Direct Numerical Simulation (DNS) study of an axisymmetric turbulent wake generated by a square plate placed normal to the incoming flow is presented. It is shown that the new axisymmetric turbulent wake scalings obtained recently for a fractal-like wake generator (Dairay et al., 2015), specifically a plate with irregular multiscale periphery placed normal to the incoming flow, are also present in an axisymmetric turbulent wake generated by a regular square plate. These new scalings are therefore not caused by the multiscale nature of the wake generator but have more general validity.

Melina G, Bruce PJK, Vassilicos C, 2016, Vortex shedding effects in grid-generated turbulence, *Physical Review Fluids*, Vol: 1, ISSN: 2469-990X

The flow on the centerline of grid-generated turbulence is characterized via hot-wire anemometry for three grids with different geometry: a regular grid (RG60), a fractal grid (FSG17), and a single-square grid (SSG). Due to a higher value of the thickness t0 of its bars, SSG produces greater values of turbulence intensity Tu than FSG17, despite SSG having a smaller blockage ratio. However, the higher Tu for SSG is mainly due to a more pronounced vortex shedding contribution. The effects of vortex shedding suppression along the streamwise direction x are studied by testing a three-dimensional configuration, formed by SSG and a set of four splitter plates detached from the grid (SSG+SP). When vortex shedding is damped, the centerline location of the peak of turbulence intensity xpeak moves downstream and Tu considerably decreases in the production region. For FSG17 the vortex shedding is less intense and it disappears more quickly, in terms of x/xpeak, when compared to all the other configurations. When vortex shedding is attenuated, the integral length scale Lu grows more slowly in the streamwise direction, this being verified both for FSG17 and for SSG+SP. In the production region, there is a correlation between the vortex shedding energy and the skewness and the flatness of the velocity fluctuations. When vortex shedding is not significant, the skewness is highly negative and the flatness is much larger than 3. On the opposite side, when vortex shedding is prominent, the non-Gaussian behavior of the velocity fluctuations becomes masked.

Steiros K, Bruce, Buxton O, et al., 2016, Flow Field Characteristics and Energy Injection in a Tank Stirred by Regular and Fractal Blade Impellers, Proceedings of the 5th International Conference on Jets, Wakes and Separated Flows (ICJWSF2015), Editors: Segalini, Publisher: Springer, Pages: 363-369, ISBN: 978-3-319-30602-5

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