Gerardi, el obispo mártir del esclarecimiento histórico

To complete the literature review this final part deals with additional relevant subjects such as vortices, flow interaction and combined wing - wheel aerodynamics.

1.4.1 Vortices

In the previous section it has been discussed that endplate vortices from the wing form an important aspect of the wing in ground effect flow field. Furthermore these vortices will be the primary factor of influence on the aerodynamic behaviour of a downstream located wheel. In general, aerodynamic design of racecars is very much orientated towards using vortices to control the flow and to generate or enhance downforce [80]. Therefore this section summarizes a few relevant aspects of vortex flows. First the general characteristics will be discussed, followed by the identification and visualization of vortices and finally the dynamics and interaction with for example the surrounding flow field or with a ground plane will be reviewed.

Characteristics The vortices that are most relevant to the current problem result from flow separation at sharp edges of the geometry due to a pressure difference between both sides of the object. Longitudinal vortices originate from edges that are more or less aligned with the flow [10,16], while transverse vortices result from edges perpendicular to the flow, such as blunt trailing edges [7] and Gurney flaps [77]. The endplate vortices are of the first type and play an important role as downforce enhancing and limiting mechanism for wings in ground effect. The pressure difference, which causes endplate and wing tip vortices, induces a circulation around the edge, which in turn leads to divergence of the streaklines on the pressure side relative to the edge, while the streaklines on the suction side converge towards the edge. At the tip of the wing the combination of the pressure

Introduction and literature review

difference and the opposing flow direction causes the flow to swirl and detach from the wing, thus forming a vortex with its axis aligned with the flow in streamwise direction.

The second type of vortices result from the pressure difference between the upper and lower side of the element, which causes the boundary layers to separate at the sharp trailing edge and can result in alternate vortex shedding from the top and bottom of the element [7]. The axis direction is in this case parallel to the trailing edge and normal to the freestream flow direction. A final type of vortices are those that result from a delta wing under incidence [81]. These vortices are responsible for generating the main part of the lift force on a delta wing and develop in streamwise direction. Their axial velocity is in general higher than for longitudinal tip vortices [10].

Vortices can thus be described as having a swirling motion around an axis. Deven- port [74] discusses the structure and development of a tip vortex from a rectangular wing under incidence. The vortex core along the axis can be distinguished from the outer ro- tating flow. In general vortex cores are characterized by having a low pressure. Within the vortex, the centrifugal force generates a strong radial pressure gradient, with the min- imum pressure occurring in the core. The tangential velocity in the core centre is zero and reaches a maximum at the edge of the core after which it reduces to the outer flow value. Devenport [74] describes how a vortex shed from a wing in turbulent flow produces no turbulence and thus evolves to a laminar state. The velocity fluctuations experienced in the laminar core are inactive motions, which are produced by buffeting of the core due to the surrounding wake.

Identification and visualization A practical problem in studying vortices is the iden- tification and visualization of the vortical structures. Objective comparison of the strength and size of a vortex is a very helpful tool in analyzing the influence of the vortex effect for a wing in ground effect. Jeong et al. [82] reviewed several identification methods based on curvature of the streamlines or pathlines, local pressure minimum, vorticity magnitude and / or components of the velocity gradient tensor ∇u. Each method has its limita- tions, but their preference goes out to a definition based on the Q-criterion. Q is the second invariant of ∇u, defined as Q = 1/2(||Ω||2 _{− ||S||}2_{), where S and Ω are respec-}

tively the symmetric and antisymmetric components of∇u; i.e. Sij = 1/2(ui,j+uj,i) and

Ωij = 1/2(ui,j−uj,i) [82]. In a plane the Q-criterion is equivalent to theλ2-criterion and

a vortex core is subsequently defined as a connected region with two negative eigenvalues ofS2_+Ω2 _[82].

Introduction and literature review

The Q-criterion, orλ₂-criterion, can not only be used as a vortex core identification method, but also to visualize vortices. Iso-surfaces give an overview of vortical structures, even in turbulent (wall) shear layers, but the choice of the visualization threshold - the magnitude of theQ-iso-surface - is still arbitrary [83]. This has to be kept in mind when analyzing iso-surfaces ofQ, because for example a lower value could show vortex merging while this phenomenon can not be distinguished for a higher value ofQ. The iso-surfaces in the figures are non-dimensionalized withU∞ and cresulting in Q. Alternatively, vortices

can also be visualized using helicity iso-surfaces [84]. The advantage of this method for a 3D flow field is that it can differentiate between primary and secondary vortices and mark their separation and reattachment lines, as well as trace the vortex core streamlines. Dynamics and interaction Wing tip vortices are complex in structure, contain inher- ent instabilities and show unsteady behaviour. The latter may result in wandering of the vortex core. Investigations have related this wandering to free stream turbulence levels, or to Kevin-Helmholtz instabilities in the shear layer that are absorbed into the vortex [8]. The various stages in the ‘life’ of a vortex generally involve the formation, the roll up in the near-field region, the development and the final breakdown. The roll up into an axi-symmetric vortex can be completed within two chord lengths from the trailing edge.

Vortex breakdown is another dynamic process, just like wandering. Under the influ- ence of an adverse pressure gradient, a vortex may slow down and fall apart. Dilution of the vortex core and the presence of a stagnation point on the axis of the vortex are distinctive features of vortex breakdown [12], but the breakdown is usually initiated and recognizable by a change in the characteristic ratio of the tangential compared to the axial velocity components. Delery [85] discusses in his overview that the breakdown location moves upstream with increasing Re-number, increasing swirl number (swirl velocity divided by axial velocity) and with an increasingly adverse pressure gradient. Vortex breakdown can take on various forms and Lucca-Negro [86] offers a comprehensive overview. Examples are a double helix, a spiral and an axi-symmetric bubble form. The type and mode of vor- tex breakdown depends primarily on theRe-number and the swirl intensity of the vortical flow.

When vortices interact with each other they can either merge and form a stronger vortex or repel each other, depending - amongst others - on the swirl direction and vortex strength. The interaction of a vortex with a moving ground plane has been studied experimentally by Harvey [87]. The resulting rebound of the primary vortex and creation

Introduction and literature review

of a secondary vortex are relevant to the wing - wheel interaction. The mechanism behind this interaction is as follows: while the vortex moves closer to the ground it induces a cross flow along the floor with an attendant suction peak below the core. The boundary layer resulting from this cross-flow has to negotiate an adverse pressure gradient once it has passed underneath the vortex. When the vortex is sufficiently close to the ground, the pressure gradient causes separation of the boundary layer and a bubble forms with vorticity of the opposite sense as the main vortex. Progressing downstream, this bubble grows rapidly to the point where it detaches from the floor as a secondary vortex, fed by a vortex sheet from the separation point. This leads to the rebound of the primary vortex. The vortex trajectories for this problem have been simulated in 2D by Barker [88], whereas Puel [89] has also looked at the 3D characteristics using CFD.

1.4.2 Flow interactions

The aerodynamic behaviour of two or more objects that are placed in close proximity to each other is different than that for the geometries in isolation. The previously discussed wing near a ground plane presents a good example of the interaction of such flow fields, just like the currently studied wing - wheel flows. Due to the non-linear character of flow dynamics it is impossible to superimpose the individual flow fields in order to simulate the total effect and careful analysis of the total configuration aerodynamics is required. This section discusses some flows around multiple objects to get a first idea of what influence interaction phenomena may have.

Katz and Dykstra [90] looked at the interaction of the rear wing flow with that around a car body. They found that a wing that was designed in isolation could produce quite different results when it was placed on a car. The local shape of the car body could for example affect the wing performance via the induced flow field, depending on the position of the wing. Alterations to the local angle of attack have the same effect as wing twist and can lead to higher lift induced drag, when the spanwise loading deviates from an elliptic distribution. Soso [91] showed that a wing placed in the wake of an idealized car model loses downforce and produces more drag8_{, partly due to the upwash that was induced by}

the upstream model. Furthermore the transition on the downstream wing is also influenced by the wake of the upstream model. The downstream wing loses relatively more downforce at higher than at lower ride heights and the downforce of the wing sections close to the

8_{This increase in drag is in contrast to the general expected trend that slipstreaming would lead to a}

Introduction and literature review

centre span reduced more than proportionally.

Dominy et al. [92] studied the interaction of the flow around two slipstreaming sports prototype cars. The wake of the leading car is a complex combination of regions with low total pressure and high vorticity. The following car would in general experience less downforce and less drag, which would enable overtaking of the upstream car. The drag reduction was found to be approximately proportional to the area of the car that is exposed to the wake flow. A final interaction example is that of a cylinder behind an airfoil [93]. It was found that theRe-number and the vertical offset distance of the cylinder downstream of the airfoil have a large influence on the vortex shedding from the airfoil and / or the cylinder and therefore on the unsteadiness of the aerodynamic loading on the cylinder. The fluctuations of the force coefficients would be largest for the case when the cylinder was directly behind the airfoil, in its wake. It needs however to be remembered that this study concerned a 2D flow field, whereas it is expected that tip effects for both the wing and wheel will play a large role in wing - wheel interaction.

1.4.3 Combined wing - wheel flows

Aerodynamic wing - wheel interaction is a novel research subject and no publications for this area could be found in open literature. Neither Mahon [12] nor McManus [68] have looked at interaction effects. Some researchers mention the importance of the problem, but they do not include any results. For example, Agathangelou et al. [2] conclude: “The performance of the front wing is also strongly dependent on the presence of the front wheel. A rotating wheel produces strong crosswise flow areas close to the ground in front of the wheel due to a squeezing or jetting effect. These jet vortices are highly influential in understanding the form of the front wing wake, and their effect changes with the steering angle of the front wheel. This is still a little understood transient aerodynamic effect, which is difficult to reproduce accurately in a wind tunnel test.” While recently Katz [5] referred to the wing - wheel interaction in the following way: “Most open-wheel racing regulations allow a wing span wider than the distance between the front wheels. However, earlier (unpublished) studies show an unfavourable interaction between the wing tip-vortices and the wheels, clearly favouring the narrower wing span design.”

The research that probably comes closest in intention to the current study is the one performed by Kellar [69]. He studied the front-end quarter of an open-wheel racecar both with experiments and CFD. However significant discrepancies between the experimental and computational model harmed comparison of the results. Furthermore his experimental

Introduction and literature review

set-up did not include ground movement, whereas in contrast to this the wheel was not rotating in the CFD simulations. Recent publications by Diasinos [94,95] do not do justice to the complexity of the problem, because wing tip vortices and wheel end effects have been ignored completely by using a 2D approach. Therefore it can be concluded that there is little understanding of the flow interaction phenomena and mechanisms that govern the combined wing - wheel flow. Furthermore no insight is available into the influence of configuration parameters, such as wing - wheel overlap and gap or wing ride height, on this interaction.