Drag Reduction of a Circular Cylinder Through the Use of an Architectured Lattice Material
DDrag Reduction of a Circular Cylinder Through the Use ofan Architectured Lattice Material
M. Pelacci , A. G. Robins & S. Szyniszewski University of Surrey, Dept. of Civil and Environmental Engineering University of Surrey, Dept. of Mechanical Engineering, EnFLo Lab University of Durham, Dept. of Engineering
AbstractMaterials with periodic architectures exhibit many beneficial characteristics such as highspecific stiffness thanks to the material placement along the stress paths and the nano-scalestrength amplification achieved through the use of hierarchical architectures. Recently, theporosity of architectured materials was leveraged to increase the efficiency of compact heatexchangers, and their internal aerodynamics was studied. However, their performance on ex-ternal aerodynamics applications is generally assumed to be detrimental. Here, we demon-strate that exposing 3D lattice material to the external flow reduced the drag of a circularcylinder when placed at carefully selected angular locations. We tested two configurationswith the lattice material installed at the windward and leeward regions. On the one hand, thewindward configuration showed a strong Re dependency, with a drag reduction of up to 45%at Re=11E4. On the other hand, the lattice material in the leeward region reduced the dragby 25% with weak Re dependency. Alterations of the lattice material topology had a notice-able effect on the drag reduction in both cases. Adding aerodynamic features to the already a r X i v : . [ phy s i c s . f l u - dyn ] F e b roven beneficial structural properties of 3D lattice materials might aid in the developmentof low-powered automotive, naval, and aerospace vehicles.Introduction Innovative manufacturing techniques such as 3D printing and 3D weaving facilitate the develop-ment of lattice materials with unprecedented control over their architectures down to the nano-scale . These multiscale, hierarchical structures exhibit unprecedented specific stiffness becausethey leverage the material properties at the nano-scale . In addition to the structural benefits, recentstudies have also taken advantage of their multiphysical properties such as damping
8, 9 and thermalconductivity
10, 11 . Human-made lattice materials have made possible compact heat exchangers ex-ploiting the combination of internal flow, increased surface area, and thermal conductivity enabledthrough the use of metallic base material .Observation of natural systems indicates that porous media can also modify the aerodynam-ics of external flows. Tree canopies can be viewed as permeable structures, which affect envi-ronmental flow and mixing, with associated effects on temperature distribution, mixing of watervapour, and CO2 absorption . At a smaller scale, dandelion seeds have a porous structure, whichenhances their ability to disperse. Wings have a hierarchical porous architecture comprising feath-ers that are made up of tiny barbules interlinked by thin membranes. These ease the wing actuationby behaving as unidirectional valves that block the air flow when the wing moves downwards,and open when the wing moves upwards. Noticeably, the barbules spacing is independent of thewings’ size, and remains practically constant at 8-16 µm over a wide range of bird sizes, ranging2rom the Anna’s hummingbird, 6 g, to the Andean condor, 10 kg. Similarly, an owl’s wings havespatially distributed feathers that reduce the aerodynamic noise generated during flight. Man-madestructures, such as stochastic metallic foams, have also recently been employed for aerodynamicnoise suppression . In addition to noise generation, aerodynamic drag is another fundamentalissue in engineering because it affects material usage in infrastructure components, ranging fromlight-posts to high-rise buildings, and the energy consumption of bluff bodies such as cars andtrucks, hence affecting climate change.While passive devices, such as riblets
19, 20 , have been developed to reduce friction drag onstreamlined bodies such as aerofoils, alternative solutions are employed for bluff shapes, wherethe drag is pressure dominated and is highly dependent on the location of the flow separation fromthe surface. For example, dimples and grooves
24, 25 over spherical or cylindrical surfaces areestablished solutions for delaying flow separation, thus reducing drag. Local and distributed sur-face protrusions have also been investigated, in the form of tripping devices or random surfaceroughness (e.g. using sandpaper)
26, 29, 30 . Similar mechanisms can be found in nature, for instance,in the form of spanwise grooves on Cacti plants or distributed roughness such as the plumageof bird wings. Recently, some initial attempts have been made to reduce drag via the applicationof porous coatings. Possibility for the drag reduction through the use of porous materials wasfirst suggested computationally . However, wrapping an isotropic porous material around thewhole circumference of a circular cylinder did not delay flow separation, but increased the overalldrag
38, 39 . On the contrary, the application of porous inserts at the rear side of a circular cylinderreduced the drag by 13%, while simultaneously reducing the total weight of the structure.3ere, we investigate the effect of three-dimensional (3D) architectured porous material onthe external flow around a circular cylinder. We 3D-printed and tested a total of four materialtopologies (Fig. 1a-b), starting with the architecture inspired by previous optimisation studies ofstructural and thermal properties, from now on termed the Default topology. We placed thematerial over the Leeward region, extended to the area where the flow separates (Fig. 1c) or overthe Windward region, where the positive pressure load is experienced (Fig. 1d).We measured the total drag applied over the span of a smooth cylinder, and the drag forceof our configurations employing 3D architectured porous coatings (Fig. 1e, f). The static pressurewas also acquired at the mid-span (Fig. 1g) to gather information about the effect of the poroussubstrate on the mean flow. Further, static pressure measurements were acquired at both the solid,inner surface and at the external surface of the porous coating in order to gain further understandingof the flow field within the porous substrate. Based on our insights from the first phase of tests, wedesigned and manufactured additional topologies to improve the overall fluidic performance, andto assess the sensitivity of the flow to changes in the 3D porous material architecture.4 oad CellActive SectionPressure TapsGap=0.5 mm Flow Direc � on Load Cell ac de fg b
Hoop wiresSpan wiresZ-wires
Leeward, θ =243° Windward, θ =81° θ θ h h=6.35 mm Ø =0.4mm wires Fig. 1 The wind-tunnel study of the architectured materials for drag reduction of circularcylinders. ig. 1 a, the architectured lattice consists of hoop wires (blue), Z-wires (red) and spanwise wires(green). b, the 3D printed module used for the aerodynamic tests. The wire diameter is 0.4 mm andthe module thickness 6.35 mm. c-d, the lattice sheath extended over 243 degrees for the leewardand 81 degrees for the windward cases. The configurations were assembled from 20 to 60 3D-printed modules to cover the required locations. e, experimental model split into an active sectionmounted to the load cells, which is encompassed by the shorter cylindrical segments. The activesection of 65% of the cylinder’s total span guarantees that the drag measurement is not affected bythe boundary layer developed over the end-plates. f, the static pressure readings were taken at mid-span through the use of T-junctions to average the pressure readings inside the porous medium. g, the assembled experimental model of the leeward configuration during wind-tunnel testing. Architectured porous inserts over the leeward region
The coating at the Leeward region reduced the drag coefficient, C D , by 15% compared to thesmooth case (Fig. 2a) and by 35% compared to the configuration with an empty void instead ofthe porous inserts, termed the Slotted case. Analysis of the pressure coefficient, C p profiles at thelowest and the highest Reynolds numbers tested (Fig. 2b-c) showed an enhanced recovery of thebase pressure coefficient, C pb , for the porous case compared with the smooth configuration. Thiswas further enhanced when the porous case was compared against the Slotted case (Fig. 2b-c),whose geometry favoured flow separation precisely after the step edge, flattening the C p profile.This fact indicates that recovery is facilitated by the downstream shift of the flow detachment point.To maintain an attached flow over the step, the coating needs to exert passive suction on the fluid,6rawing it towards the inner surface of the cylinder. In other words, a radial velocity componentin equation (1) produces a local curvature of the mean streamline towards the wall. This radialcomponent generates a centrifugal pressure on the underlying fluid, which balances the measuredpressure gradient (Fig. 2d) with the convective and the Reynolds stress terms in the Navier-Stokesequations for momentum transport. At the location where the internal and the external C p profilesintersect, the mean streamline straightens, and flow separation commences. The occurrence ofseparation deflects the streamline outwards from the coating, producing a radial pressure gradientof the opposite sign. The disappearance of the radial pressure gradient is the signature of the flowseparation from the surface. The inferred qualitative flow behaviour is illustrated in (Fig. 2e). Forfurther analysis of the Navier-Stokes equations, we refer to the Methods section (Fig.5). u r ∂u r ∂r + u θ r ∂u r ∂θ − u θ r = − ρ ∂p∂r − (cid:32) r ∂ ˜ u θ ˜ u r ∂θ + 1 r ∂ ( r ˜ u r ) ∂r − ˜ u θ r (cid:33) + ν (cid:16) ∇ u (cid:17) + F r (1)We inferred that passive suction was a distinctive feature of placing the coating at the Leewardregion, regardless of its topology and was influenced by both the architectured material cover an-gle, 243 ◦ in our test, and the material topology itself. Since our primary goal was to investigate theeffect of the material architecture on the external flow, we kept the coating coverage region con-stant and only manipulated the material architecture. We considered the fluid-porous interface asthe most relevant region for cross-flow momentum transport, similarly to forest canopies. Firstly,we modified the initial topology by increasing the porosity of the external layer, resulting in theOpen-Interface topology, in order to improve the supply of energetic fluid across the fluid-porousinterface. The Open-Interface design reduced C D by 24% compared with the 15% achieved bythe Default architecture, maintaining a weak dependency on Re, Fig. 2f . Secondly, we also in-7 Re C D Smooth Porous Slot Re C D Smooth Porous Slot x ab c Region of Separation
Porous DomainFluid Suction eed Re C D Default Open-Core Open-Interface Re C D Smooth Porous Slot x OutflowInflow f Fig. 2 The effect on the drag coefficient of the architectured material at the leeward location. ig. 2 a, the drag coefficient reduced by 15% and exhibits a weak dependence on Reynoldsnumber (Re), with the higher drag reduction at the lower Re. Conversely, a slotted configuration,without a porous layer, showed 30% drag increase compared to the smooth cylinder. b-c theenhanced base pressure recovery reduced the drag, indicating attached flow over the portion ofthe porous material. Conversely, the absence of pressure recovery for the slotted configurationimplies flow separation at the steps. d, static pressure measurements at the internal and externalporous surfaces were consistent with inflow and outflow regions along the porous medium. e, measurements indicate passive suction from the architectured porous medium, which averts theflow separation at the step. f, modified lattice topology at the interface increases transport betweenthe external flow and the intra-lattice, secondary flow, which reduces the drag by an additional 6%.The results confirm that the external flow is significantly sensitive to the internal topology of thematerial.vestigated to what extent the performance was dependent on the internal flow. We tested anothermaterial topology with a reduced number of wires in the core, termed as the Open-Core config-uration. It produced the lowest drag decrease of the three architectures tested, with the average C D reduction of 12% compared with the 15% of the Default case. Nevertheless, the significantdifferences between the results confirmed the influence of the layout of the internal wires on theaerodynamic performance (Fig. 2f) . While at the lowest range the Default topology produced a C D Architectured porous inserts at the Windward region
The Windward configuration reveals a different working mechanism from the previously discussedLeeward configuration. C D decreased sharply with Re, a reduction ranging from 12% at the lowerRe, to 40% at the highest compared with the smooth cylinder case (Fig. 3a) . We also comparedthe performance of 3D architectured lattice material inserts against the smooth cylinder equippedwith trip-wires of d/D=0.9%, placed at the same angular locations as the porous coating bound-aries. Trip-wires produced a similar trend of drag reduction as did the architectured porous insertin the windward position, but with slightly better efficiency at higher Re. The C p profiles (Fig.3b-c) confirmed the trend of C D , displaying a recovery of the base pressure coefficient, coupledwith a downstream shift of the separation point as Re increase. As the promotion of turbulencewithin the boundary layer is a well-established feature of plain cylinders with tripping devices, thesimilarity of the profiles indicates a turbulent boundary layer over the porous configuration as well.While trip-wires lead to ‘kinks’ in the C p profiles (Fig. 3b-c) for the generation of local separationbubbles, these are not present when the porous coating is in place, suggesting an alternative mech-anism of turbulence promotion within the boundary layer.The architectured porous substrate modifies the C p distribution over the region ◦ < θ < . ◦ compared with the smooth cylinder. Remarkably, the pressure coefficient is lower than unity at thestagnation point, and generally lower than that of the smooth case for ◦ < θ < ◦ (Fig. 3d).10he material location favours fluid penetration into the porous medium, with associated dissipativelosses due to friction, resulting in a drop in C p and a radial pressure gradient directed outwardsthrough the porous substrate. This indicates that the inlet region extends between ◦ < θ < ◦ ,the pressure gradient switches direction. Then, at θ = 30 ◦ , the external flow penetration ceases(Fig. 3e), and the flow continues by ‘skimming’ the top region of the porous substrate. Consid-ering continuity, fluid cannot accumulate inside the porous region and must be expelled from thecoating, with the outlet region likely distributed over ◦ < θ < . ◦ , where secondary flowmixes with the external, primary flow, in fashion similar to that seen in distributed, passive jets(Fig. 3e). These perturb the primary flow, eventually, promoting turbulence. Based on these in-sights, we designed a third topology, with internal ’channels’ following the expected streamlinesof the secondary, intra-lattice flow to maximize the flow rate of the distributed passive-jets, whichis called the Passive-Jets case. We removed the interface wires over the inferred inlet at the stag-nation region with the rationale of facilitating the penetration of the incoming fluid. The internalarchitecture was redesigned to minimize the internal flow losses in the azimuthal direction, andthe outlet region was designed towards the end of the porous coating, by promoting outflow inaccordance with the previous analysis.Noticeably, the new design outperformed the trip-wire by 13% at the lowest Re range, andexhibited lower drag than the Default topology up to Re = 90,000. Despite the greater C pb recoveryof the Passive-Jets (Fig. 6) , the pressure profile did not exhibit any kinks over the whole Renumber range, in contrast with the smooth cylinder equipped with tripping devices, indirectlyconfirming the working hypothesis. Despite the promising results at lower Re, the mechanism11 Re C D Re C D Smooth Porous Slot x a Smooth Porous T.wire θθ C θ (deg) -2-1.5-1-0.500.5 C p Re C D Default Channelized T.wire Open-Core Re C D Smooth Porous Slot x Porous DomainSecondary FlowPrimary Flow θ (deg) -2-1.5-1-0.500.51 p Smooth Porous T.wire cef d
Smooth Porous T.wire
OutflowInflow b Fig. 3 The effect on the drag coefficient of the architectured material at the windwardlocation. ig. 3 a , the drag coefficient exhibits a strong dependence on the Re, with the lowest drag athigh Re. We compared the performance with trip-wires, which are conventionally used to triggerturbulence in the boundary layer. b-c, pressure measurements reveal the increase of the base pres-sure, consistent with turbulent transition in the boundary layer, which shifts the flow separationpoint downstream, thus reducing the drag. The absence of kinks at the θ = 50 ◦ locations in theconfiguration with the lattice material points to a different mechanism for turbulent transition incomparison with the trip wire. d, static pressure measurements at the internal and external poroussurfaces are consistent with inflow and outflow regions along the porous medium. e, measurementssuggest the development of a secondary flow inside the medium, which interacts with the externalflow near the outlet from the secondary flow at ca. the θ = 35 ◦ region. f, modified lattice topologyfavoured the development of secondary flow along the envisaged streamlines. The architectureoutperformed the trip-wire at the lowest Re, and maintained the drag reduction similar to the initialtopology at the highest Re.requires further fine-tuning to avoid the deterioration in performance at the upper range of Retested. If the intra-lattice flow rate is not sized in accordance with the external, primary flowrate, the passive-jets might thicken the boundary layer. Consequently, the flow might separateearly, leading to a reduced recovery of C pb , and thus a smaller drag reduction. Active intra-latticepermeability control, demonstrated in active filters , could enable a wider operational range in thefuture. 13 iscussion Certainly, the impact of the flow angle of attack on the drag reduction and on C D ( Re ) is of primaryrelevance in these experiments. The Windward configuration outperforms the Leeward one interms of the drag reduction magnitude by 33% at the upper end of the Re range, with the samelattice topology in both cases (figs. 2a, 3a) . However, the Leeward configuration displays analmost constant C D ( Re ) trend against Re, and ensures that the Windward configuration exhibitsthe best performance at the lower range of Re tested. The results of the Channelized topology (fig. 3f) for the Windward configuration and those of the Open-Interface topology (fig. 2f) for theLeeward configurations further confirm the above trends, and the relevance of the flow angle ofattack on the C D reduction and on the C D ( Re ) trend. The modification of the angle of attack evenbiases the effect of the topology modification as per the comparison of the Open-Core topologyresults for the two configurations (figs. 2f, 3f) . Remarkably, the Windward configuration showsminimal differences in C D between the Open-Core, and the Default topologies, while the Leewardcases reveal differences between 2% and 7% depending on Re. Indeed, the topology must be tunedaccording to angular location around the cylinder to ensure an optimal drag reduction under welldefined flow conditions. Besides, the analysis proves the important impact of the inner materialtopology, and the resulting inner flow, on the aerodynamic performance. However, the results ofthe Channelized and the Open-Interface hint that the impact on performance is weakened as wemove further into the porous coating, thus leaving the outer topology as predominant. Furtherstudies focused on the flow within the porous medium are needed to understand, and ultimatelycontrol the link between the material angular location, the topology and performance.14s for effectiveness, 3D architectured porous materials provide a greater reduction over a broaderRe range than random surface roughness such as sandpaper, while outperforming selected trippingdevices at Re < (Fig. 4a). Although a dimpled surface leads to a greater drag reduction thanthe application of porous inserts, 3D architectured porous substrates exhibited immense flexibilityin their performance through modification of their topologies. Splitter plates lead to an equivalentdrag reduction at the cost of severe encumbrance, which would be impractical and could posesafety risks if applied to road vehicles. Similarly, cylinders with slots that allow flow penetrationand subsequent near-wake bleed or ventilation produce better performance at the cost of structuralintegrity (Fig. 4b). Nonetheless, further understanding of the aerodynamics of porous media couldfurther improve the flexibility of performance, both in terms of Re effects and the magnitude ofCD reductions. These, coupled with the multi-domain applications of 3D architectured porousmaterials, may leverage their use in the development of sustainable technologies.The decrease of carbon footprint is a world-wide concern, and heavy-weight vehicles, such asthose employed for essential goods transportation, produce a substantial fraction of global carbonemissions that is hard to mitigate . Although the geometry of cargo trucks have been modifiedover the years in favour of rounded shapes, trucks are still affected by pressure drag over extendedareas at the front, and at the rear part of the trailer, where local separation occurs. Our results clearlystate that the presence of 3D architectured porous materials either at the Windward or the Leewardlocations improves performance over rounded, smooth shapes by delaying flow separation. Inparticular, the Windward configuration could be advantageous around the front area of the cab, forinstance at the vertical front pillars, which can be a source of drag when side-wind occurs , and15romotes flow separation, which cannot be prevented either by rounded geometries or by passivesurface modifications at smaller scales. Similarly, the Leeward configuration could serve as anexample to promote the application of porous stripes at the rear edges of the trailer and the cab,as an alternative to flapping appendices, boat tails or splitter plates, all of which involve majorgeometry modifications. Possibly, porous stripes could redirect the mean flow towards the baseregion as an additional form of passive jets increasing the base pressure, thus reducing total drag.Importantly, transport vehicles operate in environments with highly variable, turbulent flowconditions. They experience complex flows resulting from the interaction with other vehicles, andwith cross-wind, which modify the nominal flow angle of attack (Fig. 4c-d), and create suddenwind gusts. Thus, the vehicle components such as the front pillars can experience windward (Fig.4c) or leeward flow (Fig. 4d), depending on the incoming flow conditions. Whereas flow facingexposure would call for dimples, the leeward location would benefit from a splitter plate or slotsenabling partial base bleeding. These are radically different modifications. On the contrary, our3D lattice material system reduced the drag at both the leeward (Fig. 2) and the windward (Fig. 3)regions, even though via distinct mechanisms. Whereas surface roughness or splitter plates workwell for special cases, our 3D lattice architected material offers a promise of general solutionsunder variable and multi-directional flow conditions. The locations calling for the 3D porouscomponents coincide with load carrying frame components, which offers an associated opportunityfor structural weight reduction. Our 3D lattice architected porous material could be 3D printed onmetallic surfaces directly to merge fluidic and mechanical features. Also, 3D porous materials arebeneficial for shock and impact dissipation during accidents (see Supplementary Video 1).16 mooth - Our TestStagnation - Our Test Sandpaper110 - Achenbach, 1971Sandpaper900 - Achenbach, 1971 Trip-Wire 0.9 - Our TestTrip-Wire 1.1 - Our TestPassive-Jets - Clapperton et al., 2018Dimples - Bearman, 1993 b Smooth - Our TestLeeward - Our Test
Splitter PlateD lD { { Flow direction
Slot s
Slot, s/D=0.08 - Igarashi, 1975Splitter Plate, AR=8 - Anderson et al., 1997Splitter Plate, AR=16 - Anderson et al., 1997Slot, s/D=0.185 - Igarashi, 1975 { { c c a d WindwardLeeward c WindwardLeewardNeutral [t]
Fig. 4 Comparison of our work with prior approaches to drag reduction. We also showa potential benefit of 3DW versatility to reduce aerodynamic drag of trucks under variablewind and turbulence conditions. a , comparison of the Windward configuration against stochas-tic roughness, trip wires and dimples. b, comparison of the Leeward configuration and other ap-proaches to wake-interference such as splitter plates and slots. c, d, reduce energy consumption ofheavy-goods vehicles could be achieved by placing architectured porous coating at their windwardand leeward regions; the default material configuration introduced in this study reduced the dragin both windward and leeward actions. 17he architectured porous inserts could be tuned to work on a range of large road vehicles andfurther optimized depending on the mean flow angle of attack or multi-objective scenario-basedapproaches to obtain the best performance under high-variability flow conditions. Alternatively,active control of the lattice topologies could allow the intra-lattice topology to be adjusted in re-sponse to changes and directional variability of the incoming flow. This could be performed bycontrolling wire topology via dedicated solutions such as electromagnetic fields (see Fig. 7 ), useof shape memory alloys, via internal fluid pressure if hollow wires were employed, or mechanicalloading in the case of bi-stable buckling configurations.Reduction of the side force and, perhaps more importantly the rolling moment in crossflowis a challenge that architectured porous structures can address, leading to improved safety andoperability. The aim would be to interfere positively with the flow field over the upper part ofthe trailer side face and roof, in particular to weaken the vortex system that develops over theroof in yawed flow and decrease the overall side force. Only devices capable of acting effectivelyin flows from any direction can achieve this. Optimisation of architectured porous structures forthis purpose is likely to be a complex task, given the range of flow conditions and geometries ofinterest, but one clearly worth pursuing. The multi-parameter design of these structures offers abroad range of potential applications, such as those discussed above, but simultaneously makes thesearch for optimum configurations a difficult process.Active flow control could be implemented via dynamic changes of the intra-lattice topologyusing morphing architectures and flow sensing solutions. These could be achieved through the18se of magnetic stimuli applied to functional yarns with embedded magnetic particles
42, 48–50 , asdemonstrated in
Fig. 7 in the Methods section. Alternative approaches to active control are alsopossible, such as bi-stable buckling lattice architectures, which switch between two configurationsunder prescribed in-plane loading or lattice geometries controlled by insertion of fluidic actuatorsas building elements. In addition to controlling the material configuration based on the incomingflow conditions, active control could promote the use of porous media for both drag reduction anddrag generation systems. For instance, one may need to minimise the drag during the acceleration,or the cruise velocity phase, and to maximise it during the deceleration phases. The materialtopologies could also be adjusted for vehicles operating in swarm configurations.The reduction of aerodynamic drag is by no means the only ground transportation industry’sconcern. There is intensive ongoing research on heat transfer for cooling applications, especiallyin the context of electric vehicles where water cooling of the battery is not practical due to therisk of electrical shock to passengers. The advantages of porous substrates over flat surfaces forheat transfer have been demonstrated over recent years . Although the implication of complexgeometries still impedes a thorough understanding of the physics , the studies highlighted theimportance of the internal convection on the heat transfer efficiency of porous media when highRe flows are involved, hence the value of the internal flow for thermal performance. This featuremight broaden the applicability of 3D porous material, when applied over thermal sources such asthe front region of a truck’s cab where the engine is located or over the battery compartment ofelectric vehicles. 3D lattice structures were tested as compact heat exchangers for wall-boundedflows; hence they lend themselves as good candidates for merging the drag reduction and the heat19ransfer capabilities in the context of external vehicle aerodynamics. Thus, our 3D architecturedporous technology could function as both drag reduction and heat exchanger device.Nevertheless, future work is needed to accomplish the afore-listed goals. Firstly, to emu-late the flow around trucks’ cabs or trailers, or other automotive applications, 3D lattice substratesneeds to be tested at a Re range potentially beyond . Secondly, the attainment of the maxi-mum drag reduction requires an understanding of the physics of the transport across the poroussurfaces linking the intra-lattice with the vehicle length scales, followed by optimisation studiesof the parameters characterising the material topology such as the locations of the wires along thespan-wise, the cross-flow and the stream-wise directions, the relative diameters of the lattices andgap sizes, as well as the thickness of the inserts, and, ultimately, their locations over the body. Thetuning of a large number of design parameters could enable the achievement of multiple objectives,such as reduced drag, a preferred range of vortex shedding frequencies, and a desired rate of inter-nal heat transfer, while satisfying the weight and the structural requirements. This will inevitablyrequire that an accurate model of the flow fields and any structural or heat transfer interactions isbuilt so that a true optimisation process can be undertaken. At the same time, increased empiricalunderstanding of the issues involved will be an essential ingredient in making progress.20 ethods Although the analysis cannot be conclusive due to the lack of velocity measurements within themedium, it helps to provide a qualitative picture of the flow pattern. By assuming the zero valueat the wall of the velocity and the Reynolds stresses, it is possible to analyse the sign of each termin the equation, with the exception of the Reynolds shear stresses. The first term is responsiblefor the convection of the fluid within the medium, hence of curving the mean streamlines andgenerating the centrifugal term, also acting to balance the negative pressure gradient. The secondterm cannot be fully determined as the azimuthal distribution of the radial velocity is not knowna priori. It must start at zero at the step edge and decrease up to an unknown location over themedium, contributing to the negative pressure gradient before increasing towards positive values.However, the convective terms are not the only ones responsible for balancing the negative pressuregradient, as proved by the contribution of the Reynolds stresses. The analysis suggests the depictedstreamlines pattern over the first portion of the porous medium, which generate passive suction onthe fluid.In contrast, over the second portion of the substrate, the internal fluid must be expelled once itseparates from the wall, and the associated streamlines must be curved outwards. This gives rise tothe centrifugal term, which is claimed to be mainly responsible for balancing the positive pressuregradient. In fact, all the remaining terms are capable of balancing a negative pressure gradient only,except the second convective term and that associated with the Reynolds shear stresses. While theformer can play a role over the portion of the coating where the azimuthal distribution of the21adial velocity decreases only, the latter cannot be determined, and the reliable measurements orpredictions of the internal flow are needed. However, it is not necessary to provide a qualitativedescription of the impact of the porous substrate on the mean streamline path. It must be noted thatthe dissipative term does not play a relevant role in balancing the pressure gradient, suggesting thatthe drag reduction working mechanism is distinct from streamlining.22 nlet Region Outlet Region
Fig. 5 The analysis of the inner, and the outer static pressure measurements with the aidof the Navier-Stokes equations.
The figure shows the inlet (green) and the outlet (orange) flowregions of the Leeward configuration. Maintaining an attached flow over the step edge requires theconvection of fluid within the substrate, thus ur < . This fact is in agreement with the analysis ofthe Navier-Stokes equation coupled with the measured pressure gradient in the radial direction.23 ig. 6 The pressure coefficient profiles of the Channelized topology against the Default,and the trip-wire of 0.9% d/D. Consistent with the C D trend, the Channelized topology shows agreater base pressure recovery compared with the trip-wire of 0.9% d/D at the lowest Re number.At the same time, it does not exhibit the kinks in the C p profile, otherwise present for the smoothcylinder equipped with tripping devices, strengthening the hypothesis of an alternative workingmechanism of boundary layer turbulence promotion, here inferred as distributed passive-jets.24 -yarn warp weft a bc dfe magneticfieldMAGNETICYARNS magnetmagnetic yarn Fig. 7 The potential for active control of intra-lattice topology using magnetic field. ig. 7 a , Magnetic yarn in a neutral state. The yarn material contains 40 wt% (weight percent)of magnetic Carbonyl-Iron and 60 wt% of the polymer (VersaflexCL2003X from PolyOne). b ,Magnetic field produced by a magnet deflected the yarn. We used traditional Alnico horseshoemagnet with 1 kg pull (75 x 39 x 8 mm). c , Significant deformation of the hybrid polymeric-magnetic yarn was observed. d , A bobbin of the ’magnetic yarn’ with 50-micron fibre diameter wasprovided by M. Schr¨odner (TITK Rudolstadt) und M. Krautz (IFW Dresden). e , Conceptual designof 3D woven lattice with selected magnetic yarns (shown in black). f , Conceptual deformations ofthe magnetic yarns under influence of an external magnetic field, which could enable active controlof the intra-lattice topologies, and consequently the properties of the intra-lattice and externalflows. Acknowledgements
This study was funded by the Research Framework of the European Commission under MET-FOAM Career Integration Grant 631827 with support from program manager Dr Ing. AntonioCipollaro. The work was also supported by the impact acceleration grant no EP/P511456/1, pro-vided by the Engineering and Physical Science Council (EPSRC) in the UK. Support of Dr SueAngulatta, a local program manager, is genuinely appreciated. Any opinions, findings, and con-clusions expressed in this article are those of the authors and do not necessarily reflect the viewsof the European Commission nor EPSRC. 26e are indebted to Dr Yu Liu from the Southern University of Science and Technology(formerly the University of Surrey) for his initial impulse to study the effect of porous materialson the flow around a circular cylinder experimentally. We are also grateful to Dr Joao Aguiar, whostudied open-cell foams under the supervision of Dr Liu, and later with guidance from Dr DaveBirch. We would also like to thank ENFLO lab members at the University of Surrey, for theirguidance and help with the testing setups as well as ensuring the highest measurement standards,namely Dr Paul Hayden, Dr Paul Nathan, and Hon. Dr Allan Wells. We also would like to thankthe University workshop staff, namely Steve, Lee and Alan for manufacturing of the experimentalrig, and Mr Myles who assisted us with 3D printing and cleaning samples from the supportingmaterial. We are also indebted to Dr John Doherty, Dr Matteo Carpentieri, Dr Marco Placidi, andDr Olaf Marxen for their discussions and observations regarding our study.We also would like to thank Prof. Charles Meneveau, Prof. Rajat Mittal and Dr Jung-Hee Seo from the Johns Hopkins University for fruitful discussions about the intra-lattice flowmechanisms. We are grateful to Dr Inaki Caldichoury, Dr Rodrigo Paz and Russell Sims fromLSTC (LS-DYNA, CFD solver) for their help with the exploration of modelling techniques anddiscussions about possible routes to computational optimisation. We would like to thank Prof.Charles-Henri Bruneau and Dr Iraj Mortazavi from the University of Bordeaux in France, for theirsharing their articles about computational modelling of external aerodynamics, accounting for thesecondary flow via porous inserts ex. We are also indebted to Prof Bodo Ruck from KarlsruheUniversity of Technology (KIT) for providing a critical appraisal of our work and outlining po-tential future directions and applications. We would like to thank Dr Judah Goldwasser from the27S Office of Naval Research (ONR) for discussions about active control through the use of ourmaterial structures.We are indebted to Dr Mustafanie M. Yussof for his assistance with drop impact tests todemonstrate crashworthiness of our 3D lattice material structures. We are grateful to M. Schr ¨odner(TITK Rudolstadt) und M. Krautz (IFW Dresden) for supplying us with magnetic yarns, and fruit-ful discussions about the potential for the use of the magnetic field to control the intra-latticetopologies as achieved in their adaptive filters.We would like to thank Emily Swinburne, David Robson and Micheal Costa, as well as nu-merous Brazilian exchange students (Students Without Borders program) for their involvement inwind tunnel testing and manufacturing of 3D lattice material samples as part of their undergraduateand MSc projects. 28 eferences
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