Experimental and Computational Investigation of Flow

Experimental and Computational Investigation of Flow Around a3-1 Prolate Spheroid

D. B. ClarkeDefence Science and Technology Organisation

Maritime Platforms DivisionFishermens Bend, 3207

[email protected]

P. A. BrandnerUniversity of Tasmania

Australian Maritime CollegeLaunceston, 7250

[email protected]

G. J. WalkerUniversity of TasmaniaSchool of Engineering

Hobart, 7001AUSTRALIA

[email protected]

Abstract:The flow around a 3-1 prolate spheroid near the critical Reynolds number is investigated experimentallyand numerically. This work was conducted as part of a larger project to examine the flow around Unmanned Un-derwater Vehicles. The experimental investigation has been performed in a water tunnel at the Australian MaritimeCollege. Fast response pressure probes and a 3-D automated traverse have been developed to investigate the stateof the boundary layer. A commercial CFD code has been modified to allow the experimentally determined bound-ary layer state to be included in the computation. Qualitative and quantitative comparisons between the measuredand calculated results are discussed. The tests on the spheroid were conducted within a Reynolds numbers rangeof 0.6× 106 to 4 × 106. The results presented here are for an incidence of10◦.

Key–Words:spheroid, boundary layer, transition, computational, experimental, pressure, flow visualisation

1 IntroductionUnmanned underwater vehicles (UUVs) are used forcivilian and military purposes. These applications in-clude surveying coral reefs and seabeds, and minehunting. When transiting to a region of interest, orsurveying a region, they may be required to movequickly. Conversely, detailed investigation of a sta-tionary object requires low speed manoeuvrability.These UUVs operate for at least part of the timeat Reynolds numbers where laminar boundary layersmay occupy a significant portion of the body surface.Attempting to model the fluid flow around these ve-hicles using standard implementation of a ReynoldsAveraged Navier-Stokes (RANS) turbulence model islikely to result in an inaccurate prediction of bodyforces and flow structures if the laminar-turbulenttransition of the boundary layer is ignored.

In general UUVs are approximately neutrallybuoyant, with small control surfaces, so the body ofthe vehicle provides the dominant component of thehydrodynamic forces. The flow around a 3-1 pro-late spheroid was examined in transitional flow con-ditions, as it provides many of the challenging flowfeatures that occur with a UUV such as:

• three dimensional separation from a curved sur-face;

• a combination of viscous and form drag whereneither dominate;

• regions of laminar and turbulent boundary layer.

Extensive testing has been performed on 6-1 pro-late spheroids at Gottingen, Germany. This workhas included surface pressure measurements and flowvisualisation [15], surface shear stress [16], meanboundary layer profiles, and Reynolds stress [14].More recently, testing on a 6-1 prolate spheroid hasoccured at Virginia Polytechnic Institute and StateUniversity [11, 21]. This included the developmentof a miniature on-board laser doppler velocimeter[7] that allowed measurements in the boundary layerdown toy+ = 7.

Several authors have developed numerical tech-niques for calculating viscous flow, applied them to aspheroid, and compared their predictions to the ex-perimental results previously mentioned. The nu-merical work has developed from solutions of theboundary layer equations with a predetermined pres-sure distribution [20]. These were extended to in-clude the prediction of transition [6] from the solu-tion of the Reynolds Averaged Navier-Stokes equa-tions with two-equation turbulence models, ReynoldsStress Models and Detached-Eddy Simulations [8,13].

This paper provides an overview of the equip-ment and methodology used to measure the state ofthe boundary layer on a 3-1 prolate spheroid. It alsopresents some CFD results with the measured bound-ary layer state implemented. An incidence of10◦ is

WSEAS TRANSACTIONS on FLUID MECHANICS. D. B. Clarke, P. A. Brandner, G. J. Walker

ISSN: 1790-5087 207 Issue 3, Volume 3, July 2008

selected as it is within the range of incidences a UUVis expected to encounter while transiting, and resultsin significant non-axisymetric flow.

2 Experimental MethodThe equipment developed to conduct these experi-ments includes a 3D traversing system, a fast responsepressure probe, and the 3-1 prolate spheroid model. Inaddition, methods were implemented to enable bothaccurate determination of the model position and ex-amination of boundary layer state. The tests wereperformed in the Australian Maritime College (AMC)Tom Fink Cavitation Tunnel. This is a closed circuitfacility with a test section of0.6m×0.6m×2.6m, amaximum velocity of12ms−1, a pressure range of4to 400 kPa, and a freestream turbulence intensity ofapproximately0.5% [19].

2.1 3-1 Prolate Spheroid ModelThe model was designed for measurements of surfacepressure, boundary layer state, force and flow visu-alisation. A single row of tappings running along ameridian from the front to the rear of the model al-lows the surface pressure to be measured. This rowof 21 tappings may be rotated to azimuthal angles,ψ,between−180◦ and180◦ in 15◦ increments. The an-gle of incidence,α, of the spheroid may be altered be-tween±10◦ in 2◦ increments by switching an internalsupport. At0◦ incidence the major axis of the prolatespheroid model is aligned in the streamwise direc-tion. A grid was marked on the model, at15mm and30◦ intervals in thexbc andψ directions respectively,to facilitate flow visualisation. The surface pressuremeasurements and flow visualisation are used in con-junction with the boundary layer survey to providea more extensive understanding of the flow than ispossible from any one of these techniques in isola-tion. An exploded image and a photo of the spheroidmodel are shown in fig. 1 and fig. 2 respectively. Themodel has a nominal length, L, of330mm, with 4mmtruncated from the rear in order to provide access forthe sting support. Testing was conducted forReL be-tween0.6 × 106 and 4.0 × 106, whereReL is theReynolds number based on the nominal length of themodel. The coordinate system for the model is shownin fig. 3.

2.2 3D Traverse SystemThe three-dimensional automated traverse has inter-changeable probe supports and is capable of operat-ing over the full pressure range of the tunnel. It maybe placed in any of the six side window frames of the

Fig. 1: Exploded View of 3-1 Spheroid Model

Fig. 2: 3-1 Spheroid Model in Test Section

Fig. 3: Coordinate system for 3-1 Spheroid Model

tunnel test section. The main traverse window hasa square225mm opening that allows access for theprobe. The probe is held in position by the traversingplate; it can be positioned±100mm vertically fromthe centre line of the tunnel and±100mm horizon-tally from the centre of the window. The third axisallows the probe to be driven up to300mm perpen-dicular to the side of the tunnel. A hydrofoil-sectionsupport is used to minimise probe vibration when theprobe is inserted more than150mm from the side ofthe tunnel. A series of thin plates on the inside of thetraverse keep the flow around the traversing mecha-nism streamlined (fig. 4). The traverse is controlledby a closed loop system. The resolution of the tra-verse in all axes is0.02mm, with a positional accu-racy of better than0.1mm under most conditions.

WSEAS TRANSACTIONS on FLUID MECHANICS D. B. Clarke, P. A. Brandner, G. J. Walker


Fig. 4: Traverse Interior

2.3 Fast Response ProbeThe fast response probe (FRP) measures the totalhead with a miniature pressure sensor close to thetip. Placing the sensor close to the tip increases thefrequency response of the probe. This probe is simi-lar to those used in transonic [1] and combusting [2]flow applications. The FRP is designed to be mod-ular. It consists of three sections: a probe head, asensor housing and a support stem. Each section canbe changed to suit the flow being measured. The per-formance of the probe with a1.2 mm diameter tipand 3.5 bar sensor is detailed in Brandner et al. [3].For the measurements around the spheroid at an in-cidence of−10◦ a 1.0 mm diameter tip was used.For the subsequent tests at0◦ and6◦ a 0.7 mm di-ameter tip was developed. The probe was otherwiseas detailed in Brandner et al. [3]. The output of theprobe has a natural frequency that is a function of thetube dimensions and the stiffness of the probe sensor.The resonance peak due to this natural frequency isfiltered, as shown in fig. 5.

Fig. 5: Frequency Response of FRP with0.7mm di-ameter tip.

2.4 Determining Model PositionThe position of the model in traverse coordinates isdetermined by touching the model at a number oflocations with the pitot probe and recording thesepoints. The surface of the model can be described bya quadratic function, so the points at which the probetouch the model (neglecting the offset caused by thefinite probe size.) satisfy the following equation:

Ax2t + By2

t + Cz2t +Dxtyt +Extzt +

Fytzt +Gxt +Hyt + Izt = 1 (1)

where xt, yt, zt are the traverse coordinates andA, · · · , I are unknown. As long as nine or more pointson the surface of the body are known it is possible todetermine the unknowns and thus the offset, orienta-tion and size of the spheroid (or ellipsoid). Althoughthis method was simple to implement, results deter-mined for the unknowns using this solution were sen-sitive to error in the measurement of the points. Thissensitivity is due to equation 1 also being the equationfor a number of different surfaces. A failing in this ap-proach is that it does not use all the information that isavailable, i.e. that the shape is an ellipsoid with axesof known axes lengthsa, b andc. The equation of anellipsoid with its axes aligned to the Cartesian coordi-natesxbc, ybc, zbc with an offset(x0, y0, z0) is givenby(xbc − x0

a

)2

+(ybc − y0

b

)2

+(zbc − z0

c

)2

= 1

(2)Rotating this by(φt, θt, ψt) about(zt, yt, xt) respec-tively provides an equation for the surface of an el-lipsoid with known major and minor axes. In or-der to determine the model’s position in traversecoordinates, the orientation(φt, θt, ψt) and offset(z0, y0, x0) need to be determined. The non-linearequation obtained from the transformation of equa-tion 2, together with at least six points on the surfaceof the ellipsoid, may be used to determine the un-knowns. The non-linear Levenberg-Marquardt min-imisation routine in LabView was modified to handlemore than one independent variable to perform theminimisation. In practice about twenty widely spacedpoints on the surface were measured in order to obtainpositioning of the surface to within0.1mm. For thespheroidal model there is no requirement to solve forthe rotation about thexbc axis.

2.5 Boundary Layer StateThe boundary layer is initially laminar at the forwardstagnation point. As it moves downstream it may be-come turbulent. The transition from laminar to turbu-lent boundary layer flow is described by Emmons [9].



The turbulent boundary layer is characterised by rapidfluctuations in velocity and pressure due to the eddy-ing motion. The start of transition is characterisedby short turbulent bursts with rapid velocity and pres-sure fluctuations. Further downstream the durationand frequency of the turbulent signals increase untilthe boundary layer is fully turbulent.

Hot films may be placed on the model surface[16], or pressure sensors may be placed flush withthe surface or behind pinhole tappings, in order tomeasure the fluctuations due to turbulence [4]. Thesetwo methods have the advantage that they are essen-tially non-intrusive and allow simultaneous measure-ments. A disadvantage is that they do not give usefulinformation in regions of separated flow. Each mea-surement point requires its own transducer and signalconditioning equipment. Hot wire, hot film and pres-sure probes may be traversed along the surface. Thesetechniques allow for a high density of measurementpoints. However there are errors associated with theintrusive nature of a probe. Regardless of the sensor,a procedure is required to discriminate between peri-ods of laminar and turbulent flow. Hedley and Keffer[12], together with Canepa [5], provide reviews on anumber of these techniques. These methods providethe instantaneous intermittency,γ, which has a valueof 1 when the boundary layer is turbulent and 0 whenlaminar. The time averaged intermittency,γ, is givenby

γ =1T

∫ T

0γ(t) dt (3)

whereT is the total sample period andt is time.The Peak-Valley Counting (PVC) algorithm [18]

was used in this work. The detector function wastaken as the magnitude of the time derivative of theFRP output squared. The PVC algorithm determinesthat a peak or valley has been found when the localmaxima or minima exceed a thresholdS. If anotherpeak or valley occurs within the time window,Tw, theboundary layer is regarded as turbulent for the periodbetween when the threshold was first exceeded andthe subsequent peak: accordinglyγ is set to 1 for thisperiod. The starting point of the window is broughtforward to this next peak and the process is repeateduntil no peak or valley occurs within the windowTw.On the final peak or valley the turbulent burst is con-sidered to end when the detector function no longerexceeds the threshold. The amplitude of the thresholdS and period of time windowTw used with this algo-rithm were determined experimentally. The thresholdamplitude varied between0.005 kPa2/µs atReL =2.0 × 106 to 0.070 kPa2/µs2 atReL = 4.0 × 106.A time window of 900 to 700 µs was used forReL

between2.0 × 106 and4.0 × 106. Examples of theFRP output, detector function and PVC algorithm are

shown in fig. 6 for a measurement on the spheroid.

Fig. 6: Intermittency measurements on spheroid with0.7mm diameter tip,Re

L= 3.0× 106.

The results for a set of measurements on thespheroid atReL = 4.0 × 106 are shown in fig. 7.No measurements are reported forψ = 0◦, −15◦,−165◦, −180◦ as blockage due to the probe is likelyto make these measurements unreliable. For the com-putational studies the position of the transition atψequal−30◦ will be used for0◦, −15◦; the result atψ equal−150◦ will be used for−165◦, −180◦. Thetransition process was noted to occur over a relativelyshort proportion of the body length (typically 5%).

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9γ

Fig. 7: Measured time averaged intermittency (γ) forspheroid atRe

L= 4.0× 106, α = −10◦.



3 Numerical MethodsThe commercial CFD code FLUENT 6.2 was usedto model these tests. The Fluent preprocessor Gam-bit was used to create the mesh. The spheroid, sting,foil support and upper limb of the tunnel were mod-elled using a hybrid mesh with a predominance ofhexahedral elements. The volume close to wall faceswas meshed with hexahedral elements. The spheroid,sting and foil support were surrounded with an offsetvolume that allowed fine control of the hexahedral el-ement skewness and grading (fig. 8). This techniqueallowed elements of high quality to be produced inregions were the fluid was subject to large gradients.The normal distance from the wall of the first elementwas selected to givey+ < 1 for the spheroid, stingand foil. y+ values between30 and80 were used forthe cells adjacent to the tunnel walls. The grading nor-mal to the wall was generally 1.1 or less. Tetrahedralelements were used to link the offset volume and thehexahedral elements used in the majority of the upperlimb including the test section. A symmetry planewas used on the vertical x-z plane. Three mesheswere used to show grid independence and the neg-ligible impact of the0.5 mm gap between spheroidand sting with the associated internal volume:

• a standard mesh with 377216 cells in thespheroidal volume adjacent to the spheroid sur-face (fig. 8);

• a fine mesh was 1101240 cells in the same vol-ume;

• a fine mesh (1101240 cells) with an internal vol-ume between the sting and body.

The results for the forces and moments displayednegligible sensitivity (≈ 0.5%) to an increase in themesh density or to the inclusion of the small gap andassociated internal volume.

The 3D incompressible formulation of theReynolds-Averaged Navier-Stokes (RANS) equationswere solved with the segregated solver. Second-orderdiscretisation was selected for the continuity, momen-tum and turbulent variables. The SIMPLE algorithmwas used for pressure-velocity coupling. Gradientevaluation was performed with a cell-based method.

The enhanced wall function uses a two layer ap-proach with a blending function. Ify+ for the cellnearest the wall is low enough to be inside the vis-cous sublayer, the flow is modelled to the wall; ify+

for the cell places it in the log-law region, wall func-tions are used. A blending function provides a smoothtransition for the calculations when the height of thecell adjacent to the wall is such that it is too high to

Fig. 8: Geometry for spheroid atα = −10◦.

fall within the viscous sublayer but too short for thelaw of the wall to be applicable. The enhanced walltreatment was used for these computations, as it al-lows for modelling to the wall on the spheroid, stingand support foil. The more economical wall functionswere used on the walls of the upper limb.

The realisablek − ε model was selected, as it isreported to be the most suitable of thek − ε turbu-lence models for handling streamline curvature, sep-aration and vorticity [10]. An added advantage ofthis model is it has no singularity in theε equa-tion if k is zero. Given the positive performance ofthe low Reynolds numberk − ω model reported byKim et al. [13] this was trialled, but produced non-physical results in the total pressure field. This prob-lem has not yet been resolved, and results are not pre-sented for this model. The results of the SST modelwith a low Reynolds number correction are also com-pared against experiment, as the developer of the SSTmodel tested it in adverse pressure gradients [17] andreported favourable performance in predicting sepa-ration. The inlet boundary conditions were set sothe turbulent intensity in the test section was approx-imatly 0.6%.

4 Results and Discussions

4.1 Flow Visualisation at ReL

= 4.0 × 106

Surface flow visualisation of the spheroid atα =−10◦ andRe

L= 4.0 × 106 is shown in fig. 9. The

surface streamlines calculated for the correspondingconditions using the Realisablek − ε model and theSST model with a Low Reynolds number correctionare displayed in figs. 10 and 11 respectively. The cal-culated surface streamlines for both models predictthe large separated region on the side of the model



and the attached flow persisting to almost the base ofthe model on the suction side of the symmetry plane.The width of this attached flow appears to be moreaccurately calculated by the realisable model, whichis marginally over-predicted. Neither model predictsthe flow to stay attached until the base of the modelwhenψ < 30◦. On the pressure side the realisablemodel predicts the flow will stay attached in this re-gion of strong adverse pressure gradient marginallylonger than predicted by the SST model. A rapid risein wall shear stress for both turbulence models is ob-served near the front of the model. It occurs withinthe first5% of the model length on the suction sideand within in the first15% on the pressure side. Thisshows that the calculated turbulent boundary layer ishaving a significant influence over the majority of thesurface model.

Fig. 9: Flow visualisation on spheroid,α = −10◦,ReL = 4.0× 106.

Fig. 10: Surface streamlines calculated using Realis-ablek − ε model,α = −10◦,ReL = 4.0× 106.

Fig. 11: Surface streamlines calculated using SSTModel,α = −10◦,Re

L= 4.0× 106.

The calculation of the turbulent viscosity wasmodified via a User Defined Function (UDF) to al-low laminar zones to be implemented by switchingthe turbulent viscosity to zero. For every cell a UserDefined Memory (UDM) location was set as an inter-mittency factor to a value between 0 and 1 indicatinga laminar or fully turbulent region respectively. Thenominal value for the turbulent viscosity was mod-ified by the intermittency factor. The intermittencyfactor was determined from the experimental mea-surements ofγ on the surface of the model. Cells inthe boundary layer region normal to the surface wereset to a value corresponding to that measured on thesurface (fig. 12). This modification provided a smallimprovement on the pressure side for the realisablemodel as the predicted flow stays attached until fur-ther downstream. A delay in separation is consistentwith the thinner boundary layer expected due to thereduced length of turbulent boundary layer. On thesuction side the predicted width of attached flow nearψ = 180◦ appears marginally narrower than shownby the flow visualisation (fig. 13). The results for theSST model with the modification for boundary layerstate appeared worse, with a separation bubble beingpredicted on the pressure side near the base.

4.2 Surface Pressure at ReL

= 4.0 × 106

The results of the measured surface pressure forψ =−135◦ and −180◦ over the full range ofReL areshown in figs. 14 and 15 respectively. In fig. 14 it isapparent that the pressure curves are closely groupedover the front half of the model. Near the centre ofthe model the curve for the largestReL increases asmall amount and leaves this grouping. This process



Fig. 12: Intermittency factor for spheroid,α = −10◦,ReL = 4.0× 106.

Fig. 13: Surface streamlines calculated using Realis-able Turbulence Model with modified boundary layerstate,α = −10◦,ReL = 4.0× 106.

is repeated a number of times downstream as the sur-face pressure for the largestReL remaining in the ini-tial grouping increases and its associated curve joinsthe new grouping of curves of largerReL . This shiftin surface pressure appears to be associated with theprocess of transition and is most obvious when thepressure gradient is low. The perturbation in the sur-face pressure field can be explained in terms of thelocal change in displacement thickness that occurs atthe laminar-turbulent transition. This change in dis-placement thickness creates a discontinuity in the ef-fective surface curvature seen by the free stream, thuscreating a perturbation in the pressure that is appar-ent in the surface pressure measurements. Fig. 15shows a similar process but the separation of the twocurve groups is more pronounced. It also indicatesthat in this case the transition is upstream of the lo-cation used in these calculations at this azimuth. Asimilar deviation in the surface pressure is apparentnear the nose in the results of Meier and Kreplin [15].

Figs. 16 and 17 present a comparison between

Fig. 14: Surface pressure on spheroid.α = −10◦,ψ = −135◦.

Fig. 15: Surface pressure on spheroid.α = −10◦,ψ = −180◦.

the measured and calculated surface pressure. Due tothe sensitive nature of transition the position of tran-sition measured using the traverse and the kink in thesurface pressure measurements may not always coin-cide, as these tests were performed during differentsetups. It should be noted that the most downstreammeasured data point at each azimuth is the internalbase pressure.

The pressure measurements also indicate thattransition has occured near the nose (x/L = −0.4)for ψ = 0◦ at aReL of 4.0×106, rather than closer tothe base of the body as used for the computations. Forthis azimuth atRe

L= 3.5×106, the associated curve

is grouped with the lower Reynolds number curvesuntil close to the base, indicating the sensitive natureof the transition for these conditions. Fig. 16 showsthe measured result for these two Reynolds numbersat this azimuth. The pressure calculations show littledifference regardless of whether the boundary layer islaminar or turbulent over the forward three-quartersof the body; this is contrary to the measured result.



This also means the difference between the imple-mented transition point and the position implied bythe pressure measurements atψ = 0◦ shouldhaveonly a minor influence on the surface pressure calcu-lations. It is suspected that some values ofψ for ReL

of 3.5 × 106 and 4.0 × 106 the disturbance causedby the holes for the pressure taps (0.9mm diameter)has caused the transition to move upstream. Hencediscretion needs to be exercised when using these re-sults.

A deviation in the surface pressure near the lo-cation where the turbulence models are switched onis apparent, but it is significantly smaller than that ob-served in the measured results when transition occurs.Over the majority of the body the implementation ofthe laminar regions has led to no overall improvementor degradation in the accuracy of the predicted surfacepressure. The exception to this is in the separated re-gion on the side of the model where the calculationsof the pressure are consistently further from the mea-sured results. The results from the SST model with nolaminar region provide the closest match to the mea-sured values in this region.

Fig. 16: Comparison of measured and calculated sur-face pressure using Realisablek−ε turbulence model.α = −10◦, Re

L= 4.0 × 106. (Note :-Cp axis

aligned with measurement for0◦; each subsequent setof curves shifted 0.25 vertically.)

Fig. 17: Comparison of measured and calculatedsurface pressure using SST turbulence model,α =−10◦,ReL = 4.0× 106. (see note with fig. 16).

4.3 Flow Visualisation at ReL

= 2.0 × 106

Assessment of the turbulence models tested atReL =4.0× 106 with and without the inclusion of the lami-nar zones was expanded to examine the case atReL =2.0× 106. Contamination of the spheroid surface forthis Reynolds number resulted in the boundary layersurvey being discarded. Fortunately for this Reynoldsnumber the flow visualisation provides an indicationof the boundary layer transition betweenψ = 0◦ and−90◦. The location of boundary layer transition wasestimated from the increased scouring of the oil ap-parent in fig. 18. The increased scouring in this case isassociated with the greater wall shear present in a tur-bulent boundary layer. Other photos at this Reynoldsnumber using a less viscous oil suggest that forψ be-tween0◦ and approximately−45◦ a very short lam-inar separation bubble exists at the transition region.This laminar separation bubble is not picked up by thesurface pressure measurements due to the relativelycoarse placement of tappings. Excellent agreementbetween the flow visualisation and surface pressuremeasurements for the location of boundary layer tran-sition is shown in fig. 18. This provides confidencein the application of the transition location obtainedfrom the surface pressure measurements to the com-



putational work for this case.It should be noted that, in the over fifty flow vi-

sualisation performed on these models, in only a fewcases has the boundary layer transition region beenobserved with confidence. The high density of waterhelps obtain high quality surface pressure measure-ments. Even with high quality surface pressure mea-surements over a range of Reynolds numbers, bound-ary layer transition is difficult to determine if the sur-face pressure is varying rapidly due to other factors(e.g. surface curvature, as noted previously). Neitherof these methods determine the length of the transi-tion region, which for the purpose of this computationwas taken as10mm. This is consistent with the shorttransition length seen atα = 6◦ for this Reynoldsnumber.

Fig. 18: Flow visualisation on spheroid,α = −10◦,ReL = 2.0 × 106. Cyan and blue line show estimateof boundary layer transition position from this photoand pressure measurements respectively.

Fig. 19: Surface streamlines calculated using Realis-ablek − ε turbulence model with modified boundarylayer state,α = −10◦,Re

L= 2.0× 106.

Surface flow visualisation for the computed re-sult atReL = 2.0 × 106 using the Realisablek − εturbulence model was similar to that using the samemodel atReL = 4.0 × 106. When the region of lam-inar flow was implemented for this case, the result-ing surface flow visualisation (fig. 19) showed a lami-nar separation forψ between0◦ and−45◦; the veloc-ity vector plot at the cell centres adjacent to the sur-face confirms that no reattachment occurred behindthis separation line. This laminar separation occursapproximately25 mm upstream of the implementedtransition region. The technique of prescribing thetransition region is likely to have difficulty modellinglaminar separation bubbles as the turbulent region isunable to shift to just downstream of the laminar sep-aration and then adjust with the iterative solution ofthe flow field.

The major computed vortical structure on the sideof the model rotates in the opposite direction to thestructure in the photo, it is also positioned further up-stream. The photograph show no funnelling of theflow into the vortical structure from fluid at the side(ψ = −75◦ to 120◦) of the model as depicted in fig.19.

Fig. 20: Surface streamlines calculated using Realis-ablek−ε turbulence model with lengthened transitionregion,α = −10◦, Re

L= 2.0 × 106. Surface con-

tours showing time avereaged intermittency (γ).

The implementation of the transition region in asteady state solver is by necessity only spatial, whilethe actual process has an additional temporal compo-nent. Concern that the implementation of the tran-sition region may be encouraging flow separation orredirecting the surface flow by providing a suddendiscontinuity in the surface shear stress was tested



by increasing the length of the transition region to25 mm, thus reducing the sharpness of the discon-tinuity. Fig. 20 shows the redirection of the flow hasbeen reduced by the increased length of the transitionregion but is still clearly apparent. No redirection ofthe flow is apparent in the boundary layer transitionregion in fig. 18. The results with the SST modelwith the low Reynolds Number correction were of nogreater accuracy and are not further reported.

4.4 Drag

Although no drag measurements are available forcomparison it is worth noting the computed break-down between form and viscous drag. The calculatedCd based on the maximum cross-section perpendicu-lar to thexbc is given in table 1. The values in thistable demonstrate the necessity of implementing thecorrect boundary layer regime if the drag is to be ac-curately calculated on a body where no one boundarylayer type dominates. An artificially long region ofturbulent flow will increase the viscous drag, due tothe greater shear stress associated with the turbulentflow, and increase the form drag as its faster bound-ary layer growth results in a thicker boundary layerthat will separate earlier.

Turbulence Model Form Viscous TotalRealisable 0.0128 0.0183 0.0311SST Low Re 0.0144 0.0173 0.0317Realisable + Lam 0.0076 0.0079 0.0155SST Low Re + Lam 0.0113 0.0074 0.0187

Table 1: Calculated Drag Coefficients forα = −10◦,ReL = 4.0× 106.

5 Conclusions

The turbulence models used in the analysis atReL =4.0× 106 with and without the modification for lam-inar regions do a reasonable job of calculating thesurface pressure and surface streamlines. Althoughthis implementation of laminar regions of flow in theCFD has not led to an improvement in calculation ofthe surface pressure, the ability to allow for laminarregions of flow is critical in the calculation of dragon bodies with a significant portion of laminar flow.The minimal variation in surface pressure predictedbetween the laminar and turbulent flow is in contrastto the measured results. The cause of this discrep-ancy warrants further investigation. Prescribing thetransition region in the region of a laminar separationbubbles was unsuccessful atReL = 2.0× 106.

Acknowledgements:The authors wish to acknowl-edge the contribution of: Mr John Xiberras in thedetailed design of the spheroid and support foil; MrVinh Nguyen in the detailed design of the 3D Tra-verse; Mr Paul Cooper and Mr Paul Vella in the man-ufacture of the spheroid, support foil and traverse; MrSasha Smiljanic in the design of the electronics andsoftware for the traverse controller; and Mr RobertWrigley for onsite manufacture and fitting. The sup-port of DSTO and AMC has also been vital.

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Experimental and Computational Investigation of Flow