a single element wing in ground effect - comparisons of experiments and computation

AIAA 2001-0423A Single Element Wing in GroundEffect; Comparisons of Experimentsand ComputationJonathan Zerihan and Xin ZhangSchool of Engineering Sciences,University of Southampton,Southampton SO17 1BJ, U.K.

39th AIAA Aerospace SciencesMeeting and Exhibit

January 811, 2001/Reno, NVFor permission to copy or republish, contact the American Institute of Aeronautics and Astronautics1801 Alexander Bell Drive, Suite 500, Reston, VA 201914344

A Single Element Wing in Ground Effect;

Comparisons of Experiments and Computation

Jonathan Zerihan and Xin Zhang

School of Engineering Sciences,

University of Southampton,

Southampton SO17 1BJ, U.K.

A computational study has been performed in order to model the flow around an

inverted aerofoil in ground effect. The method used is solutions of Reynolds-averaged

Navier-Stokes equations with turbulence modelled by Spalart-Allmaras model and k-

model. The results are compared to measured surface pressures and LDA resultstaken at the centre of a wing in ground effect. Major features of the flow are captured.

The results yield good qualitative trends for the aerodynamic performance, using the

one-equation model when the surface pressures are compared at different heights. In

general, the wake thickness is predicted reasonably well in the region near to the trailing

edge. Further downstream, the wake is predicted to be thicker than that found in the

experiments, with reduced velocities. The ground boundary layer is predicted well using

the one-equation model, but is significantly too thick using the two-equation model.

Nomenclature

c = wing chord; 223.4mm.CL = three-dimensional downforce coefficient, L/qc;

force directed to ground.Cl = sectional lift coefficient.CP = pressure coefficient, p/q.h = height above ground; distance between suction

surface and ground plane at zero incidence.udef = wake velocity deficit, ue um.ue = edge velocity.U = freestream velocity.um = minimum velocity.u, v = velocity components in x, y axes system.x, y = Cartesian coordinates, x +ve downstream,

y +ve up, relative to wing leading edge.

Greek Symbols

= incidence.top, bot = top and bottom of the wake.99 = wake thickness defined by 0.99ue. = normal distance from suction surface

at trailing edge.

Introduction

THE front wing of a racing car acts in groundeffect, and contributes to about 25-30% of thetotal downforce of the car, which, at top speed, mayapproach three times the weight of the car. The down-force, or aerodynamic grip, is used in conjunction with

Formerly Ph.D Research Student, currently Aerodynamicist

British American RacingProfessor, School of Engineering Sciences. Senior Member

AIAA.

Copyright c 2001 by Xin Zhang. Published by the AmericanInstitute of Aeronautics and Astronautics, Inc. with permission.

the mechanical grip to improve the acceleration, brak-ing, and cornering speed of the car. Of contemporaryinterest is the level of downforce that the wing gen-erates at different heights from the ground, not onlyfor optimising the height of the wing, but also for ef-fects of suspension movements over bumps and as thecar accelerates and brakes. In addition to the aero-dynamic performance of the front wing, another verysignificant issue is the wake that it generates. Theflow to the undertray and diffuser in particular, butalso the radiators and rear wing, is severely effectedby the front wing because they all operate in the wakefrom the wing.

Although numerous experimental and computa-tional studies have been performed on aircraft typewings in ground effect, i.e. with the pressure surfacenearest to the ground plane, for general aeronauti-cal applications in addition to ground effect aircraft(WIG), little data has been presented for racing cartype wings in ground effect, with the suction surfacelowermost.

Katz used a panel method to investigate the flowaround a downforce producing wing.13 Results froma panel method4 and a Reynold-averaged Navier-Stoke(RANS) solver5 modelling the entire car including thefront wing have also been published.

Knowles et al6 conducted experiments in a windtunnel with a moving ground facility. A single ele-ment GA(W)-1 wing was tested at a variety of in-cidences for a range of heights from out of groundeffect down to 0.12c from the ground. Force resultsshow that the downforce generated increases as theground is approached, for all incidences tested at. Itwas observed that the lower surface suction increasesin ground effect, and that very close to the ground,

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American Institute of Aeronautics and Astronautics Paper 2001-0423

stalled flow occurs over the rear portion of the wing.In addition to their experimental results, a selectionof two-dimensional panel method results are presentedfor comparison. Results compare reasonably at largeheights or low incidences, but are poor closer to theground.

Ranzenbach and Barlow have presented results fromexperimental tests in a fixed ground wind tunnel com-paring them to computation results using a RANSsolver.710 A single element aerofoil was tested atdifferent heights from the ground, at a single inci-dence. As in previous research, it was found that thedownforce increased as the height from the ground re-duced. However, at a ground clearance of about 0.1c,the downforce was found to reach a maximum, belowwhich the downforce dropped sharply. They called thisthe force reduction phenomenon. Only overall force re-sults are presented from their experiments; no surfacepressures or flowfield data is available. The force re-duction phenomenon is modelled reasonably well inthe computational results close to the ground. Us-ing vorticity plots, it is put forward that the forcereduction phenomenon is due to a merging of the wingand ground boundary layers. The boundary layers areshown to merge upstream of the trailing edge of theaerofoil for a small ground height, below the force re-duction phenomenon. The presence of the boundarylayers reduces the flow velocity between the suctionsurface and the ground, leading to an increase in pres-sure, and hence a reduction in downforce. Extendingthe computational study to the correct ground con-ditions with a moving ground yields the result thatthe downforce produced at different ground heightsis qualitatively similar to the fixed ground case, al-though the magnitude of the downforce and also theheight at which the force reduction phenomenon oc-curs is greater for the moving ground case.

It is believed that tests with a fixed ground are of lit-tle practical use, and that this affects the results moresignificantly than an aeronautical wing in ground ef-fect, due to the fact that the suction surface is nearestto the ground, which contributes to the downforce sig-nificantly more than the pressure surface.

As part of a detailed investigation into wings inground effect, Zerihan and Zhang1114have used exper-imental tests in a wind tunnel with a moving groundfacility to further investigate the effect of the ground.In addition to overall forces and surface pressures, ex-periments were also performed using laser Doppleranemometry (LDA) and particle image velocimetry(PIV) methods to examine the wake flow. This pa-per compares computations using a RANS solver withthe results from the experimental database.

Description of Experimental Results

Details of the aerodynamic performance of the wingin ground effect are available in reference,11 together

with discussions of the mean and unsteady flow fea-tures of the wake at the semispan of the wing12 anda further study describing the three-dimensional ef-fects.13 Initial tests were performed with free tran-sition. However, for the purpose of CFD modelling,transition was tripped at x/c = 0.1 on both surfaces,using 100 grit. The downforce at = 1 for differentheights is presented in Fig. 1, for both free and fixedtransition cases. The effect of the ground is to con-strain the flow beneath the suction surface. At a largeheight in ground effect, the flow is accelerated overthe suction surface to a slightly greater level than infreestream, resulting in greater suctions on the suc-tion surface. As the wing is brought closer to theground, the flow is accelerated to a higher degree, caus-ing an increased peak suction, and associated pressurerecovery. At a height where the pressure recovery issufficiently steep, the boundary layer separates at thetrailing edge of the suction surface. For the transitionfree case, the height at which boundary layer sepa-ration was first observed was h/c = 0.224. As theheight is reduced beyond this, the wing still gener-ates more downforce, but the rate of increase slows,and the downforce reaches a maximum, the down-force reduction phenomenon. Below this height thedownforce reduces. As the height is reduced fromthe first height where flow separation was observed,the separation point moves forward steadily. At themaximum downforce, the boundary layer separates atx/c 0.8, for the free transition case. Heights greaterthan the maximum downforce are known as the forceenhancement region. Below the maximum downforceis known as the force reduction region. Similaritiescan be drawn comparing the reduction of the height ofa wing above the ground, with the increase of the in-cidence of a wing in freestream. In both cases, thepressure recovery becomes steeper, eventually caus-ing boundary layer separation, and the wing stalls.The effect of fixing transition is to reduce the mag-nitude of the downforce, and to increase the height atwhich the force reduction phenomenon occurs. It hasbeen shown that the maximum downforce occurs whensmall gains in suction on some portions of the lowersurface and small reductions in suction on other por-tions of the lower surface, together with other smallreductions in pressure on the upper surface with a re-duction in height, fail to contribute to an increase inoverall downforce.11, 13 Boundary layer merging wasnot observed.13

The wind tunnel tests were performed using a sin-gle element wing with endplates, of aspect ratio ap-proximately 5. A significant portion of quasi-two-dimensional flow exists in the central portion of thewing. Two-dimensional computations are used to sim-ulate the flow at the semispan of the wing, comparingpressures and LDA results obtained at the wing centre.Details of the experimental results, together with the

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h/c

C L

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

Transition fixedTransition free

Fig. 1 Measured downforce for three-dimensional wing.

wing profile used can be seen in the previous work.All wind tunnel tests were performed at a Reynoldsnumber of approximately 460000, with a freestreamvelocity of 30m/s.

Computational ModellingGoverning equations

The numerical model solves the three-dimensionalthin layer compressible Navier-Stokes equations in atime dependent manner. The effect of turbulence wasmodelled by either the the Spalart-Allmaras (S-A) oneequation model,16 and the Menter k model.17 Thecode used was CFL3D, an implicit upwind code.15

Grid strategy

In order to generate the two-dimensional structuredgrids at different heights from the ground, Gridgen wasused. Substantial grid refinement tests were performedon the circumferential spacing at the aerofoil leadingedge, trailing edge, and the suctions and pressure sur-faces, and on the normal spacing of the grid points atthe aerofoil surface and at the ground plane.

After preliminary tests on the gridding strategy wereperformed, it was decided to use a solution that re-quired neither grid patching nor grid overlaying. Al-though not all the features of the grid are ideal, thiswas felt as the best compromise. The grid, for a heightof h/c = 0.179 can be seen in Fig. 2(a). This is shownin more detail for the region near to the aerofoil lead-ing and trailing edges in the same figure (Fig. 2(b)and 2(c)), together with an example of another gridat h/c = 0.313 (Fig. 2(d)). The upstream and down-stream boundaries are located at 8c from the aerofoil.The boundary above the wing is at 7c, which corre-sponds to the approximate location of the wind tunnelroof. The computational domain contains about 30000grid points in total, according to ground height.

x/c

y/c

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

-0.4

-0.2

0

0.2

0.4

0.6

a) h/c = 0.179.

x/c

y/c

-0.1 0 0.1 0.2 0.3

-0.2

-0.1

0

b) Leading edge region: h/c = 0.179.

x/c

y/c

0.7 0.8 0.9 1 1.1 1.2

-0.2

-0.1

0

0.1

c) Trailing edge region: h/c = 0.179.

x/c

y/c

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

-0.4

-0.2

0

0.2

0.4

0.6

d) h/c = 0.313.

Fig. 2 Computational meshes.

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The grid contains five blocks in total. The first blockis a square C-type grid, around the aerofoil. The gridcells at the corners of the grid are not ideal, but thisgrid approach was the best compromise. A y+ 1was used for the first grid point normal to the aero-foil surface. The grid is clustered near to the aerofoilleading and trailing edges. It was found that moregrid points were required on the suction surface com-pared to the pressure surface. Effort was made to forcea perpendicular grid near to the trailing edge regionof the suction surface. The aerofoil features a finitetrailing edge, corresponding to 0.007c. Block 2 is aH-type grid covering the region from the trailing edgeto the downstream boundary; a closed wake type grid.Block 3 is an H-type grid, extending from block 1 ver-tically to the top of the computational domain. Block4 grids the upstream area from block 1 to the upstreamboundary, and is H-type. Block 5 is H-type, and cov-ers the entire ground plane from the upstream to thedownstream boundaries. The reason that block 5 isrequired is for the fine grid spacing necessary on theground plane; a y+ 1 was also found to be requiredfor the first grid point from the ground.

In order to simulate the flow around an aircraft wingat varying angles of attack, the same grid is generallyused, specifying a different incidence in the CFD inputdatafile. For the configuration of a wing at differentheights in ground effect, a new grid has to be generatedfor each height from the ground, which is a tedious pro-cess. The geometry in the database file was modified,and blocks 1, 3, 4 and 5 had to be regenerated. For areduction in ground height, it was required to reducethe circumferential size of the C-type grid around theaerofoil, in addition to moving the ground grid verti-cally up relative to the aerofoil.

Boundary Conditions

The upstream and downstream and downstreamboundaries are modelled with the inflow/outflowboundary condition. The top boundary uses an ex-trapolation simulation. The no-slip condition is ap-plied to the surface of the aerofoil. The ground planehas been modelled using a prescribed velocity equal tofreestream.

Turbulence Modelling

Initial tests at a single height and in freestream wereperformed using two turbulence models; the Spalart-Allmaras (S-A) one equation model,16 and the Menterk model,17 with a view to establish the differencein the performance and the flowfield of the models.Previous studies have found the S-A model to predictattached flows and two dimensional separated flowswell using CFL3D.18 The k model has been shownto be very capable compared with the S-A model forseparated flows.19

The comparison of results at a single height inground effect were inconclusive as to which model per-

formed better, and due to the significant differencesfound, it was decided to use both models for eachheight.

Solution Process

It was found to be extremely difficult to obtain asolution. When a steady solution was performed, thisyielded results with unsteady periodic characteristics.However, an unsteady solution would generally con-verge on a single steady result.

The solution process used started with a steadyrun. Mesh sequencing was employed, performing theanalysis on three grid levels, for convergence acceler-ation. Multigrid was then used for the remainder ofthe steady and unsteady solutions. The output fromthe steady solution was used as a restart for the nextstage, the unsteady solution. It was not possible tostart with an unsteady solution; the semi-convergedsteady results were required to avoid the solution fromblowing up. The S-A model was found to be more ro-bust than the k model, although this depended onthe exact characteristics of the grid and the flowfield.For the k model, it was necessary to perform twounsteady analyses consecutively; the first with a smalltime step, and the second with a larger time step. TheS-A model only needed the run with the larger timestep.

Convergence problems using compressible solvers atlow Mach numbers are well documented.20 The com-bination of this, and the fact that a time-accuratesolution method is required, leads to long solutiontimes.

Results

The results of the computations are compared interms of the aerodynamic performance, and the flow-field results.

Aerodynamic Performance

Freestream

Both turbulence models give very similar results infreestream, as can be seen by the pressure distributionsin Fig. 3.

The first point to make is that the computationalresults show a large spike near to the leading edge ofthe suction surface. The experimental results for thiscase do not show this spike. This may either be due tothe spacing between the tappings, or because it is notpresent for this particular experimental configuration.Note that many other experimental results do show thepresence of this spike, for example the single elementwing at other incidences,11 the Gurney flap results,14

and more prominently in the double element results,yet to be published. The magnitude of the spike issufficiently large that it is slightly greater than themain suction peak, near to x/c = 0.16. The suctionpeak is overpredicted a little by the computation. Inthe pressure recovery region, however, from x/c 0.25

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x/c

C P

0 0.5 1-2

-1.5

-1

-0.5

0

0.5

1

CFD k- modelCFD S-A modelExperiment

Fig. 3 Comparison of computationaland experimental surface pressures infreestream.

to the trailing edge of the suction surface, the pressurescompare extremely well with the experimental values.

Near to the leading edge of the pressure surface,stagnation is predicted well. The flow is then acceler-ated rapidly. At x/c = 0.03, the experimental resultsshow the flow to have reached a velocity, which re-mains approximately constant for a large portion ofthe surface, before a gradual retardation starting atx/c = 0.5. But, the computational results show asmall, but significant deceleration at x/c = 0.03 toCP = 0.25. The pressures are then overpredicted bythe computation, with the difference decreasing in thestreamwise direction. From x/c 0.6, the difference issmall, and the remainder of the computational resultscompare well with the experimental values.

The Cl for the aerofoil was found to be 0.885 forthe S-A model and 0.872 for the k model. Anestimation of the sectional downforce Cl from the ex-periments can be obtained by integrating the surfacepressures. However, it is stressed that this is only anestimate, and will be used to compare the qualitativetrends between the experimental and computationalresults, not as a quantitative comparison. The exper-imental results give Cl = 0.766. This is a differenceof approximately 16% between the computational andthe experimental results for the S-A model, and 14%the k model. In addition to the difference in thesurface pressures at discrete points, this approximately15% difference is also due to the leading edge suctionspike, and the linear interpolation of the results usinga large number of points, computationally about 200,with the relatively coarse spacing of the 45 experimen-tal results.

Ground Effect

Tabulated results of the downforce predicted by theCFD, together with Cl from the integrated pressuresare given in Table 1 for all heights. The comparisonsare only to highlight the trends, not the outright val-ues. Each of the surface pressure distributions will bediscussed below.

The distributions at h/c = 0.671 show the resultsfor the largest height in ground effect, Fig. 4(a) Theground effect has increased the lower surface suctions,in addition to a slight reduction in the upper sur-face pressures, which overall leads to an increase indownforce. Again, the leading edge suction spike is ofa similar magnitude to the main suction peak. Themain peak is overpredicted by the computations, asin freestream. However, the suctions throughout thepressure recovery are also overpredicted by the com-putation, unlike the freestream results. Again on thepressure surface, the pressures are too great from thespike at x/c = 0.03 to about the mid-chord. Furtherdownstream, they compare better. The computationspredict Cl = 1.052 (S-A) and 1.030 (k), comparedto the experimental value of 0.902, which is a similardifference that in freestream, of 17% and 14%. Thevery slightly greater downforce from the S-A modelcompared to the k model can be seen to be due toincrements in the loading predicted on each surface.

The same general trends can be observed at h/c =0.448, Fig. 4(b). The overprediction of the lower sur-face suctions has increased slightly, over the whole ofthe surface. Although the suction at the leading edgespike has increased, that at the main peak increases ata greater rate such that it can be seen that the largestsuction is that at the mean peak. The slight increasein the lower surface suction prediction is offset by asmall reduction in the overprediction in the pressuresurface results, resulting in computational results forCl are 16% and 13% greater than the experimentalvalue.

As the height is reduced to h/c = 0.313, not pre-sented here, the previous trends of slight overpredic-tion of lower surface suctions for the S-A model, andunderprediction of the k suctions continues. Thisyields predictions of Cl that are 15% greater (S-A) 9%greater (k) than the experimental results (Table 1).

Similarly for h/c = 0.224, Fig. 4(c), the overpredic-tion in lower surface suctions remains approximatelyconstant for the S-A model, compared with the pre-vious height. However, this reduces for the k model, such that most of the suction surface resultsare mapped very well for this example. For both mod-els, nearly all pressure surface results are mapped well,too. The effect is that the S-A model gives Cl = 1.475,again 15% greater than the experimental prediction ofCl = 1.286. The k model gives a closer resultof Cl = 1.352, just 5% greater than the experimen-tal value. The same trend was found at h/c = 0.179,

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x/c

C P

0 0.5 1-2

-1.5

-1

-0.5

0

0.5

1


a) h/c = 0.671

x/c

C P

0 0.5 1-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1


b) h/c = 0.448

x/c

C P

0 0.5 1-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1


c) h/c = 0.224

x/c

C P

0 0.5 1-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1


d) h/c = 0.134

Fig. 4 Comparison of computational and experimental surface pressures.

where Cl for the two turbulence models are 15% (S-A)and 2% (k ) greater than the experimental values.

At h/c = 0.134, the greatest experimental Cl wasfound. Again, the S-A model overpredicts the lowersurface suctions, (Fig. 4(d)) by a similar amount to theprevious height. The k model starts to underpre-dict the suctions very slightly, especially in the regionof the suction peak. On the pressure surface, the flowis mapped well by both models, the S-A model givinga slightly higher pressure near to the leading edge re-gion. The S-A model gives Cl = 1.604, 16% greaterthan the experimental value of Cl = 1.385, whereasthe k model predicts Cl = 1.386. Results at thelowest height of h/c = 0.090 show the same trend, butmore extreme in nature; there is a similar overpredic-tion of the lower surface suctions from the S-A model,but the k model is underpredicting the suctionsmore severely. This gives a 12% overprediction and a

5% underprediction in Cl from the S-A and the k models respectively.

Flowfield

Results from the computational database were ex-tracted in order to compare with the experimentalwake and boundary layer surveys performed with theLDA system.

Boundary layer

In obtaining the LDA results close to the wing sur-face, difficulties were experienced. The finite size ofthe measurement volume coupled with flare from thesurface implied that it was impossible to obtain resultsvery close to the surface of the wing. For simplicity,the surface, at which = 0, was defined as the lastpoint at which zero data was obtained. In this man-ner, the LDA results are a finite distance below theirtrue location. It is believed that the first 1mm approx-

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imately from the wall was void of any data. This isa rough estimate. Hence, the LDA profiles should beraised by, very approximately, 0.005c. This has notbeen performed, due to the uncertainty in the size ofthe correction required.

Fig. 5(a) shows the computational results with theLDA results, for u/U at h/c = 0.224. The two turbu-lence models give different results within the boundarylayer. It can be seen that, very close to the surface,the S-A model has a negative velocity, as the flow sep-arated. Although this is not clear from the profile forthe k case, examination of the skin friction on thewall gives a negative value also for the k case,as the flow has also separated. Through the bound-ary layer, for a particular distance from the surface,the velocity is consistently lower for the S-A model,until it reaches the edge. Although within the bound-ary layer, the experimental results lie closer to thosefor the k model, given the problem with obtain-ing experimental results near to the surface, and theshape of the profile, it is difficult to say which modelgives a better match. Outside the edge of the bound-ary layer, u/U is approximately 0.03 greater for theexperimental results than for the computation.

At h/c = 0.134, Fig. 5(b), both computational re-sults clearly show a separated boundary layer. In asimilar manner to the results at h/c = 0.224, the S-Amodel gives a thicker boundary layer than the k model. Again, it would appear that, although the ex-perimental points lie closer to the k results, itis difficult to say which model gives the best results.Both models fail to predict the magnitude of the ve-locity in the recirculation region. Again, beyond theedge of the boundary layer, both turbulence modelsgive results that are less than the experimental results,by u/U 0.05.

Nearfield wake

To investigate the wake results, comparisons aremade at two streamwise locations. At x/c = 1.2, theresults are compared with velocities extracted from theLDA grid results mapping the trailing edge region. Atx/c = 1.5, the results are compared with the LDAwake surveys. Note that the dedicated wake surveysincluded a finer distribution of points the direct wakefrom the wing, and also additional points very closeto the ground, to map the ground boundary layer.Tabulated results for the wake thickness from the com-putations and experiment are presented in Table 2 forx/c = 1.5. Information on the ground boundary layeris also given, in Table 3 at the same streamwise loca-tion.

At a height of h/c = 0.448, the wake surveys atx/c = 1.2 are compared in Fig. 6(a). Outside of theedge of the wake, the computations point to velocitiesthat are u/U 0.025 lower than the experimentalvalues. The results within the wake are difficult to

u/U

/c

-0.2 0 0.2 0.4 0.6 0.8 1 1.20

0.02

0.04

0.06

0.08

0.1

0.12


a) h/c = 0.224.

u/U

/c

-0.2 0 0.2 0.4 0.6 0.8 1 1.20

0.02

0.04

0.06

0.08

0.1

0.12


b) h/c = 0.134.

Fig. 5 Comparison of computational andexperimental boundary layer surveys atsuction surface trailing edge.

compare to a high degree of accuracy due to the coarsespacing of the experimental points. The S-A modelgives a slightly greater minimum velocity at the cen-tre of the wake. The wake thickness appears similar,for the computations and the experiment. It is difficultto be more precise, due to the coarse spacing of the ex-perimental results, and the increased velocity outsideof the wake for the experimental results. The maindifference between the two models appears in theirability to model the ground boundary layer. Althoughfew experimental points are available at this stream-wise location, it is clear that the k model gives aground boundary layer significantly thicker than theS-A model and the experiments.

Results are similar at x/c = 1.5 for the same height,

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u/U

y/c

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2


a) x/c = 1.2.

u/U

y/c

0.7 0.8 0.9 1 1.1-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2


b) x/c = 1.5.

Fig. 6 Comparison of computational andexperimental wake surveys at h/c = 0.448.

Fig. 6(b). Outside of the wake, the velocities accordingto CFD are u/U 0.03 lower than the experimentalresults. The wake thickness is modelled well by thecomputations (see Table 2). There is a difference inthe maximum velocity deficits of u/U 0.06, whichimplies a little overprediction by the CFD in additionto the difference found out of the wake. The resultsfor the k model show the ground boundary layerto have grown compared to the previous streamwiselocation (see Table 3). The thickness of this from theS-A model is significantly closer to the experimentalvalues.

For the results at h/c = 0.224, Fig. 7(a) there isa small overprediction of the wake thickness and themaximum velocity deficit at x/c = 1.2. At x/c = 1.5,the wake velocities are underpredicted more signifi-

u/U

y/c

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2-0.4

-0.3

-0.2

-0.1

0

0.1

0.2


a) x/c = 1.2.

u/U

y/c

0.6 0.7 0.8 0.9 1 1.1-0.4

-0.3

-0.2

-0.1

0

0.1

0.2


b) x/c = 1.5.


cantly (see also Table 2). The differences betweenthe two turbulence models used are relatively smallcompared to the difference between the computationsand the experiments in general. The ground boundarylayer for the k model is much thicker than at theprevious height, whilst the S-A model would appear togive better results here regarding the thickness of thelayer (see Table 3). The minimum velocity, however,is underpredicted a little, however this may partly bedue to the underprediction in the edge velocity.

For results at h/c = 0.134, which is at the maximumdownforce experimentally, and for the S-A model, butbelow the maximum downforce for the k model, theresults are again similar, but more severe (see Fig. 8).The main wake is now a little thicker than the ex-perimental results at x/c = 1.2. The velocity at the

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u/U

y/c

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

-0.2

-0.1

0

0.1

0.2


a) x/c = 1.2.

u/U

y/c

0.5 0.6 0.7 0.8 0.9 1 1.1

-0.2

-0.1

0

0.1

0.2


b) x/c = 1.5.


wake centre is closer with the S-A model, but bothmodels show an incorrect upward shift in the wake,compared to the LDA results. At x/c = 1.5, the ve-locities in the wake are significantly underpredicted.The wake thickness is slightly underpredicted by bothmodels (see Table 2). For both streamwise locations,k shows an increased ground boundary layer. Fromthe results at x/c = 1.5, it is apparent that the S-Amodel gives a boundary layer that is a little to thin ifany, but which is massively overpredicts the velocitydeficits.

Farfield wake

A further comparison of the wake results is given inFig. 9, in which the u/U velocity contours are plot-ted for u/U < 0.99, to highlight the results within

the wake and the ground boundary layer. Resultsare for the S-A turbulence model at the same heightsof h/c = 0.448, 0.224, 0.134. In addition, results ath/c = 0.134 are also given for the k model, andfor the experimental LDA results. As the flow movesdownstream, it can be seen that, for a given height,the wake thickens, and the velocities in the wake re-duce due. A reduction in the height thickens the wake,especially on the lower edge, where this is due to the in-crease of the suction surface boundary layer thickness.The effect of using the k model is to massively over-predict the thickness of the ground boundary layer.Both computational models give relatively similar re-sults within the wake, however. Far from the trailingedge, at x/c = 3.0, it can be seen that there is now asignificant difference in the velocities for the computa-tional results compared with the experimental results.Generally, the velocities within the wake are too lowfor the computational results, and the thickness of thewake is too large.

Flow between wing and ground

The u/U velocity contours are also presented inFig. 10 for the flow between the wing and the ground,for the same heights of h/c = 0.448, 0.224, 0.134 for theS-A model, and h/c = 0.134 for the k model. Thereduction in the height of the wing from the ground re-sults in the flow being accelerated to a greater extent,as can be seen in the figure, and also the surface pres-sures earlier. Studying the results close to the groundnear to the peak in suction, it can be seen that theground boundary layer originates as the flow starts toretard after the peak suction. Further analysis of theresults (not presented here) confirms this. The over-prediction of the ground boundary layer thickness withthe k model is evident from near to its formation,e.g. at x/c = 0.4. There is also a small difference inusing the k and S-A models in the velocity con-tours, which can be seen more clearly in the surfacepressure distributions. Using the k model givesvelocities which are lower than for the S-A model.

Discussion

Examining the performance of the wing infreestream shows that the pressure distributions aremodelled well, and the difference between the S-A andthe k models is insignificant. On the suction sur-face, the peak suction is overpredicted a little, butthe pressure recoveries compare extremely well. Aspike is prominent in the computational results, butis not as apparent in the experimental results. Onthe upper surface, the pressures are overpredicted alittle by the computations. Integrating the surfacepressures gives an experimental result of about 15%less than the computations. Although this is partlydue to the small overpredictions in the pressures andsuctions over some portions of the upper and lower

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surfaces respectively, a significant contributory factoris the coarser distribution of discrete points experi-mentally over which interpolation is applied, especiallyconsidering the spikes that are present in the compu-tations.

In ground effect, the lower surface suctions are con-stantly overpredicted a little by the S-A model. Atlarge heights, this is also the case for the k model.However, the overprediction reduces as the height is re-duced, and at h/c = 0.179, the predicted lower surfacesuctions are too low. The underprediction of suctionincreases still as the height is reduced. Generally, littledifference is found on the pressure surface, and resultscompare well. The effect of this is that the S-A modelpredicts the qualitative trend of the ground effect verywell. However, the k model does not show the cor-rect trends, and at the closest height to the ground,the overall loading is lower than the experiment.

The surface pressure distributions along with thecontour plots show that the difference using the twomodels arises from the suction surface, and increasesas the height is reduced. The k model starts to givereduced suctions compared to the S-A model, but stillgreater than the experimental values, which are clearfrom about h/c = 0.313. This effect is amplified suchthat at small heights, the k results have reducedsuctions than the experimental results. This gives theS-A results a greater adverse pressure gradient for thepressure recovery region. The boundary layer profilesseem to confirm this, with a thicker boundary layer forthe S-A results. It is difficult to confirm which modelgenerates the more realistic boundary layer profiles,due to the problem in obtaining LDA results close tothe surface.

The major flaw with the k model is an overpre-diction of the ground boundary layer thickness. Thecomputational results confirm that this originates dueto the adverse pressure gradient after the peak suc-tion from the wing. At a constant height close to theground, the k model gives a thick boundary layer,and lower velocities in the region between the wing andthe ground. It would appear that the lower velocitiesare a direct effect of the thicker boundary layer. It isbelieved that this causes the difference in the predic-tive capabilities of the models.

Conclusion

Major physics of an aerofoil in ground effect are cap-tured. Good qualitative results predicting the correcttrends have been obtained, in an attempt to modela two-dimensional slice of a single element wing inground effect, using the S-A turbulence model. Com-paring the results to integrated pressures from theexperimental study gives a constant difference, whichcould be attributed to a number of factors in the modeltests. The pressure distributions appear accurate, thedifferences partly due to the discrete spacing of exper-

imental points. There are deficiencies in modelling thewake flow, and CFD predicts a larger wake, in termsof thickness and velocity deficit as the streamwise dis-tance is increased. The k model was shown not tomodel the ground boundary layer correctly, resultingin bad performance at low ground heights.

Acknowledgements

J. Zerihan is supported by an EPSRC studentship.The authors would like to thank W. Toet of BritishAmerican Racing and C. Rumsey of NASA Langleyfor their support and discussions.

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x/c

y/c

1 1.5 2 2.5 3-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

(a)

x/c

y/c

1 1.5 2 2.5 3-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

(b)

x/c

y/c

1 1.5 2 2.5 3

-0.2

-0.1

0

0.1

0.2

(c)

x/c

y/c

1 1.5 2 2.5 3

-0.2

-0.1

0

0.1

0.2

(d)

x/c

y/c

1 1.5 2 2.5 3

-0.2

-0.1

0

0.1

0.2

u/U: 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95

(e)

Fig. 9 u/U velocity contours within wake andground boundary layer; (a) h/c = 0.448, S-A. (b)h/c = 0.224, S-A. (c) h/c = 0.134, S-A. (d) h/c = 0.134,k . (e) h/c = 0.134 LDA measurements.

18C. Rumsey and V. Vatsa, Comparison of the predictive

capabilities of several turbulence models, Journal of Aircraft,

Vol.32, No.3, May-June 1995, pp.510-514.19P. Godin, D. Zingg and T. Nelson, Highlift aerodynamic

computations with one- and two-equation turbulence models,

AIAA Journal, Vol.35, No.2, February 1997, pp.237-243.20Milholen, W.E., Chokani, N., and Al-Saadi, J., Perfor-

mance of three-dimensional compressible Navier-Stokes codes

at low Mach numbers, AIAA Journal, Vol.34, No.7, July 1996,

pp.1356-1362.

x/c

y/c

0 0.2 0.4 0.6 0.8 1 1.2

-0.4

-0.2

0

0.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

a) h/c = 0.448, S-A model.

x/c

y/c

0 0.2 0.4 0.6 0.8 1 1.2

-0.2

0

0.2

b) h/c = 0.224, S-A model.

x/c

y/c

0 0.2 0.4 0.6 0.8 1

-0.2

0

0.2

c) h/c = 0.134, S-A model.

x/c

y/c

0 0.2 0.4 0.6 0.8 1

-0.2

0

0.2

d) h/c = 0.134, k model.

Fig. 10 u/U contours within wake andground boundary layer.

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Table 1. Computational and experimental Clh/c Cl expt Cl S-A Cl k ClSA Clkf/s 0.766 0.885 0.872 16% 14%

0.671 0.902 1.052 1.030 17% 14%0.448 1.009 1.174 1.136 16% 13%0.313 1.145 1.320 1.253 15% 9%0.224 1.286 1.475 1.352 15% 5%0.179 1.362 1.565 1.393 15% 2%0.134 1.385 1.604 1.386 16% 0%0.090 1.371 1.539 1.297 12% -5%

Table 2 Wake information at x/c = 1.5.

h/c case udef/U y at um y at top y at bot 99/c0.448 exp 0.25 0.08 0.13 0.04 0.09

S-A 0.28 0.09 0.14 0.05 0.09k 0.28 0.08 0.14 0.04 0.10

0.313 exp 0.25 0.08 0.13 0.04 0.09S-A 0.31 0.08 0.13 0.03 0.10

k 0.32 0.08 0.13 0.03 0.100.224 exp 0.27 0.07 0.13 0.01 0.11

S-A 0.36 0.07 0.13 0.02 0.11k 0.38 0.06 0.13 0.01 0.12

0.179 exp 0.28 0.05 0.12 -0.02 0.14S-A 0.41 0.06 0.13 0.00 0.13

k 0.43 0.06 0.12 -0.01 0.120.134 exp 0.28 0.04 0.12 -0.05 0.17

S-A 0.45 0.05 0.13 -0.02 0.15k 0.47 0.05 0.11 -0.03 0.14

0.090 exp 0.31 0.02 0.12 -0.10 0.22S-A 0.55 0.03 0.13 -0.06 0.19

k 0.50 0.03 0.10 -0.07 0.17

Table 3 Ground boundary layer information at x/c = 1.5.

h/c case um/U ue/U 99/c0.448 exp 0.98 1.09 0.006

S-A 0.93 1.06 0.007k 0.94 1.06 0.028

0.313 exp 0.90 1.07 0.007S-A 0.88 1.05 0.008

k 0.91 1.04 0.0360.224 exp 0.86 1.07 0.009

S-A 0.82 1.04 0.009k 0.88 1.04 0.044

0.179 exp 0.91 1.06 0.014S-A 0.78 1.03 0.009

k 0.85 1.03 0.0480.134 exp 0.94 1.05 0.019

S-A 0.73 1.03 0.009k 0.84 1.02 0.054

0.090 exp 0.91 1.03 0.022S-A 0.68 1.02 0.010

k 0.81 1.02 0.061

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a single element wing in ground effect - comparisons of experiments and computation

Documents

ground distance

wing chord

ground plane

single element wing

wake thickness

wing generates

wake velocity deficit

edge velocity