Djordje VUKOVIC′ ,Dijana DAMLJANOVIC′

Department of Experimental Aerodynamics,Military Technical Institute,Vojnotehnicˇki Institut,Beograd 11030,Serbia

KEYWORDS Base pressure;Experimental aerodynamics;High angle of attack;Standard model;Wind tunnel

Abstract Responding to a need for experimental data on a standard wind tunnel model at high angles of attack in the supersonic speed range,and in the absence of suitable reference data,a series of tests of two HB-2 standard models of different sizes was performed in the T-38 trisonic wind tunnel of Vojnotehnicˇki Institut(VTI),in the Mach number range 1.5-4.0,at angles of attack up to+30°.Tests were performed at relatively high Reynolds numbers of 2.2 millions to 4.5 millions(based on model forebody diameter).Results were compared with available low angle of attack data from other facilities,and,as a good agreement was found,it was assumed that,by implication,the obtained high angle of attack results were valid as well.Therefore,the results can be used as a reference database for the HB-2 model at high angles of attack in the supersonic speed range,which was not available before.The results are presented in comparison with available reference data,but also contain data for some Mach numbers not given in other publications.

1.Introduction

The capability to perform high angle of attack wind tunnel tests at supersonic speeds was necessary in mastering the atmospheric re-entry of manned capsules during the early spaceflight programs,as well as in the development of the Space Shuttle Orbiter1,2.Many recently proposed concepts of reusable launch vehicles confirm the continued need for supersonic high angle of attack wind tunnel testing.Moreover,this capability is needed in the development of modern highmanoeuvrability military missiles3,4.

The need for high angle of attack supersonic wind tunnel tests is also expressed in the realm of the Computational Fluid Dynamics(CFD)5-9.Codes dealing with the high angle of attack aerodynamics are being developed,mostly tuned to support the design of reusable space-going vehicles.The developers note that simulation of high-speed,high angle of attack aerodynamics presents many challenges and uncertainties and experimental data to be used as test cases for these codes are welcome.

However,preparation and execution of high angle of attack wind tunnel tests may not be straightforward tasks.Because of the constraints of wind tunnel structures,model support mechanisms of many high-speed wind tunnels permit movements of the model only in the relatively small range of angles of attack,usually within no more than±20°.In order to perform high angle of attack tests,additional components like twin-roll mechanisms,bent stings,etc.are usually mounted onto the‘‘basic”model supports.Such add-ons may cause increased aerodynamic blockage,interference by shock waves originating from the model support,increased minimum operating pressure of the wind tunnel,increased model-support deflections and lowered natural frequencies of the model-support assemblies. Therefore, the confidence in the test results obtained with high angle of attack setups may not be satisfactory.In such cases it is good to verify the complete wind tunnel measurement setup by testing a standard model(calibration model).

Unfortunately,the database of reference test results for standard models at high angles of attack in the supersonic speed range is small.Military Technical Institute,Vojnotehnicˇki Institut(VTI)in Beograd,Serbia,faced this problem in the preparations of a high angle of attack supersonic test in its T-3810trisonic wind tunnel.VTI normally checks the measurement chains of its wind tunnels by periodic tests of AGARD-B models11. However, AGARD-B configuration,with its relatively large wings,could not be used in T-38 above Mach number 2 and at high angles of attack because of excessive aerodynamic loads(in particular,high supersonic starting loads12).Instead,another configuration,a body of revolution known as HB-213and more convenient for high Mach number and high angle of attack tests,was selected as an additional standard model.Although the characteristics of the model itself were appropriate,a review of available reference results for the supersonic speed range from Mach number 1.5-4(the supersonic operating envelope of the VTI T-38 wind tunnel)showed rather scarce data.Practically all researchers referred to a single dataset from the report14by Gray and Linsday on tests of the HB-1 and HB-2 models in the Von Karman facility of Arnold Engineering and Development Center(AEDC),performed in 1963,which was limited to angles of attack up to+15°and,besides,did not provide values for the total axial-force coefficient.Some data were available from the tests in ONERA Chalais and Vernon Facilities in 196415,but only in the small angle of attack range of about±8°.Also,limited data from a Mach number 2 free-flight test on a ballistic range were available16from the NASA Ames Research Centre.Existence of some other supersonic tests results at Mach number 2,Mach number 3 and Mach number 4 was noted17,18but those data were not available.

As the reference data for the HB-2 configuration at high angles of attack were not available,it was decided to create VTI's own supplementary database of tests results for this model which would comprise data for a wider range of angles of attack.To this end,a series of tests of two HB-2 models,having forebody diameters of 75 mm and 100 mm,was performed at Mach numbers 1.5-4 at angles of attack up to 30°.Obtained data were compared with results19of previous tests performed in the same wind tunnel in the smaller angle of attack range,and with test results from the wind tunnels of AEDC14,ONERA15and NASA16.Results can be used as a reference high angles of attack dataset for the HB-2 model in the supersonic speed range,which was not present before.The results also comprise data for some Mach numbers not presented in other publications.

2.HB-2 correlation model

The HB-2 model(Hypervelocity Ballistic model 2,see Fig.1)was defined in the year 1960 by the Von Karman Facility at AEDC with the intent of providing a reference for correlation of results from various hypersonic and supersonic wind tunnels.13It is an axisymmetric cone-cylinder with a 25°nosecone half-angle and a 10°tail flare(a similar configuration known as HB-1 differs from HB-2 in not having the tail flare and is more sensitive to viscous effects13).The junctures of the nose and the flare with the cylinder are smooth radius fairings.The diameter of the model base is 1.6 times the diameter D of the forebody and the length of the model is 3.9 times the forebody diameter.Moment reduction centre is at 1.95D from the nose.The shape of the model is reminiscent of a re-entry space capsule which often consists of a blunt body followed by a conical aft section with a large base.Such shapes produce a strong bow shock wave,a recirculating base-flow region and complex shock-wave/boundary-layer interactions.20

The recommended geometry of the support sting for the HB-1 and HB-2 models was defined as having a constant diameter of no more than 0.3D and a length of at least 3D with a conical fairing at the rear,having 20°(max.)half-angle.It should be noted,however,that the magnitude of aerodynamic loads in wind tunnels with high dynamic pressure in the test section,or in wind tunnels having high supersonic starting loads,may necessitate the use of stings with larger sting/base diameter ratios if structural safety of the model in a test is to be ensured.21Two HB-2 models,having forebody diameters of 75 mm and 100 mm,were produced for the tests in the T-38 wind tunnel of VTI.The models were intended for measurements of forces and moments,and were designed so that each of them could be tested on various force balances,using suitable adaptors common to both models.The models were designed so that they could be quickly assembled and disassembled and consist of aluminum-alloy outer shells and a cylindrical steel core,common to both models,for modelbalance mating(Fig.2).Base covers were made removable in order to be able to provide appropriate model-sting clearances for various sting diameters and in the current tests had central circular openings with the diameter equal to 1.2 times the sting diameter.

3.Experimental setup

3.1.T-38 wind tunnel

Tests were performed in the 1.5 m×1.5 m T-38 trisonic wind tunnel in VTI10(Fig.3)which is a blow-down,pressurized experimental facility with the operating range from Mach number 0.2-4 and a high Reynolds numbers capability with a maximum of about 110 million per metre occurring around Mach number 2.During a wind tunnel run,the air from a bank of interconnected pressurized tanks with a total volume of 2600 m3is released through the wind tunnel and discharged into the atmosphere.The tanks can be charged up to 2 MPa pressure by a 4 MW five-stage compressor.Available run times depend on test conditions and vary from 6 s to about 60 s.Mach number in the supersonic range is set by a flexible nozzle.Regulation of flow parameters is typically within 0.1%for the stagnation pressure and 0.3%for the Mach number.Flow turbulence in the test section is about 0.9%;the value includes(because of the measurement method used)fluctuations of density and pressure.

Fig.1 Theoretical geometry of HB-2 model and support sting.

Fig.2 Designs of 75 mm and 100 mm models produced for T-38 wind tunnel.

Models in the test section of the T-38 are usually mounted on a pitch-and-roll tail-sting support with pitch-angle range from-12°to+20°.For the high angle of attack tests of the HB-2 models,an articulated bent sting was deployed which could be configured either for a 10°bend or for a 20°bend in the pitch plane.Only the 10°bend angle was used,so the angle of attack range was from-2°to+30°(Fig.4).The sting consists of a conical hub,mounted on the roll drive of the basic model support, a blade-like pylon with a pod, and an exchangeable front part with a diameter of 43 mm,attached to the pod which provided a secondary roll axis.The stingto-model-base diameter ratio was 0.36 for the 75 mm HB-2 model and 0.27 for the 100 mm model.This corresponded to sting-to-model-forebody diameter ratios of 0.57 and 0.43 for the two models, respectively. The sting/forebody diameter ratio of 0.3,specified in model definition,could not be implemented because a sting with a diameter so small would not have been safe in the high-dynamic-pressure environment of the T-38 wind tunnel.21The length of the sting behind model base was more than 3.5 model forebody diameters.

Fig.4 100 mm HB-2 model on articulated bent sting in T-38 wind tunnel.

3.2.Instrumentation

Aerodynamic forces and moments acting on the models were measured by internal six-component strain-gauge balances,selected according to expected loads.The steady aerodynamic loads were similar at all Mach numbers in the test but the models were also subjected to supersonic starting loads,which occur during the establishment and breakdown of the supersonic flow in a wind tunnel.Those loads are primarily a characteristic of the pressurized blow-down wind tunnels and can exceed several times the steady-flow aerodynamic loads,12becoming significant(in T-38)above Mach number 2 and peaking between Mach number 3 and 3.5.Therefore,the starting loads,not the steady-flow loads,were relevant for the selection of wind tunnel balances,which had to have load ranges higher than desired.

In order to ensure safety against the starting loads,and yet to obtain a good accuracy of the measurement,tests of the HB-2 models were performed using two internal balances:one,with a smaller load range,for the smaller 75 mm model at Mach numbers up to Mach number 2.5(where the transient starting loads were not large),and the other one,with a larger load range,for the 75 mm model above Mach number 2.5 and also for the larger 100 mm model at all Mach numbers.In order to enable a comparison between the results with the two balances,the larger-range balance was also used with the 75 mm model at lower Mach numbers.

The selected smaller-load-range balance was VTI40B,a 40 mm VTI-produced monolithic device,which was one of the VTI's balances often used for wind tunnel tests of missile-like models.The balance was wired as a direct-read22one.Measurement uncertainty,from the calibration of the balance,was better than 0.11%FS for all components but the rolling moment,for which the uncertainty was about 0.17%.For the higher-load-range,the 2-inch Able Mk18 assembled strain gauge balance was selected.It was designed and wired as a force balance22.Measurement uncertainty of the balance was in the range 0.1-0.17%FS,slightly varying from component to component.

Base pressure on the model was measured using siliconmembrane piezoresistive transducers with measurement uncertainty of 0.05%FS.The measurement point was in the sting cavity at the centre of the base of the model,near the base plane.

Conditions in the test section of the wind tunnel were computed from measurements of the stagnation temperature and stagnation pressure in the settling chamber and either the static pressure in the test section(below Mach number 2)or the pitot stagnation pressure in the test section(at Mach number 2 and above).Silicon-membrane piezoresistive pressure transducers with serial digital outputs were used,with measurement uncertainties better than 0.01%FS.Model pitch angle was measured by an absolute-position digital encoder with serial output,located in the mechanism of the model support,and with uncertainty of about 0.01°.Roll angle was constant.Pitch angle was corrected for the deflections of the sting,computed from balance loads and the stiffness coefficients obtained by calibration.Aerodynamic angles and corrected Mach number were then computed taking into account the calibration of the test section.

Data acquisition in the test was performed using a Teledyne RMDU system with 16-bit resolution and the data were processed using the standard wind-tunnel data-reduction software of VTI.

A parallel-beam schlieren system with a field-of-view diameter of 900 mm,a three-colour filter and a digital camera was used to create video recordings of wind tunnel runs in the test of the 75 mm model.The primary purpose of this visualization was the monitoring of the safety of the model12,so only lowresolution(640×480 pixels),low-frame-rate recordings were made.

3.3.Test matrix

Tests of the two HB-2 models were performed in the Mach number range from 1.5 to 4 and at angles of attack from-2°to(approximately)30°with both models,according to the matrix shown in Table 1.Unfortunately,because of the tight wind tunnel schedule,some Mach numbers had to be omitted with the larger model.The angle of attack interval was covered in a continuous sweep at 2°/s rate during the measurement and the data were averaged at approximately 1°intervals within±0.25°around the selected positions.The sweep rate and the averaging interval were selected from experience as giving correct results in static measurements.Dynamic pressures q in the test section were approximately 0.08-0.1 MPa at all Mach numbers and corresponded to stagnation pressures P0ranging from 0.2 MPa at Mach number 1.5 to pressure 1.3 MPa at Mach number 4.Reynolds numbers ReD,based on forebody diameters of the models,were in the range from 2.1 millions at Mach 1.8-4.6 millions at Mach 4.Corresponding Reynolds numbers based on model lengths were from 10.3 to 22.5 millions.Stagnation temperature was about 290 K±5 K.

Mach numbers for the tests were selected so that some of them corresponded to those in an earlier test19of the 75 mm model in the T-38 wind tunnel at angles of attack up to 15°.Mach numbers 1.5,2,3 and 4 also corresponded to those in the tests of the HB-2 models in the wind tunnels of AEDC13,and Mach numbers 1.6,2.25,3.0 and 3.25 corresponded to those in the tests in ONERA wind tunnels15.

4.Test results and discussion

4.1.Aerodynamic coefficients

Available data pertaining to tests of HB-2 models in other laboratories were reviewed in order to establish reference characteristics for the correlation of the T-38 experimental results with those from other aerodynamic laboratories.As reference data at high angles of attack were not available,current T-38 results were compared with the data from the AEDC Von Karman Facility14and ONERA Chalais and Vernon laboratories15only in the lower angle of attack range and in spite of much lower Reynolds numbers in the reference tests,ranging from 0.1 millions to 2.5 millions vs 2.2 millions to 4.5 millions in T-38 tests.Comparable high Reynolds number reference data in the appropriate range of Mach numbers could not be found.A limited comparison of several data points was also performed with available Mach number 2 results from the pressurized ballistic range at the NASA Ames Centre16.

Beside the comparison with data from other facilities,current T-38 test results were also compared with those from earlier tests19of the same 75 mm HB-2 model in the T-38 wind tunnel on a 48 mm diameter straight sting in the angle of attack range up to 15°,on a high drag range/high stiffness wind tunnel balance designated as BV40.That balance was an experimental design with semiconductor strain gauges and was somewhat less accurate and with larger temperature sensitivity than usual balance designs,which explains the‘‘waviness”appearing in some of the results for the axial force coefficients from that test19.An additional degree of confidence in the high angle of attack results was obtained by comparing the results of the current high angle of attack T-38 tests of two model of different sizes and tests with the same model on two different balances.

The comparison of the total axial force coefficient with AEDC reference data could not be performed because available AEDC results14contained only the forebody axial force coefficient and the base drag coefficient was given only at zero angle of attack.Besides,when those two were added to compute the total zero-lift axial force coefficient,the obtainedvalues differed significantly from those obtained in VTI,ONERA Chalais and Vernon and NASA Ames which,on the other hand,were in good agreement.The reason for this discrepancy, also noted by Malcolm and Chapman16, is unknown.It was proposed in Ref.16that the cause was in sting effects on the base pressure measurement in AEDC.It may have been so,moreover because,as schlieren photographs in the test report14from AEDC show,there seem to have been some protuberances on the sting near the model base,which effectively increased the sting diameter and disturbed the recirculating base flow,probably influencing base drag.Besides,in the same photographs,a shock wave reflected from the wind tunnel walls can be seen impinging on the sting less than one base diameter aft of the model at Mach number 1.5.A similar occurrence was reported15in the Mach number 1.6 test at ONERA S5 Chalais facility where,too,it resulted in an erroneously low base drag.

Table 1 Test matrix for high angle of attack HB-2 tests in VTI T-38 wind tunnel.

A good agreement of results in the angle-of-attack range common to all tests was observed,the differences between the current T-38 results and the reference data being not larger than the differences between the different sets of reference data themselves.This is illustrated in Figs.5-10 by graphs of test results for the total axial force coefficient CA,normal force coefficient CNand pitching moment coefficient Cm,obtained at Mach numbers 1.5,2.0,2.5,3.0,3.5 and 4.0 and the forebody axial force coefficient CAfobtained at Mach numbers 1.5,2.0,2.5 and 3.0.

Additionally,graphs of the base pressure coefficient Cpbfrom tests at Mach numbers 1.5,2.0,2.5 and 3.0 are shown in Fig.11.Data for the base pressure coefficient and,consequently,forebody axial force coefficient in the current tests were not available for Mach numbers 3.5 and 4 because of the malfunction of the base-pressure-measurement tubing,possibly caused by the measurement-orifice being blocked by frost while the model,cooled by the exposure to low static temperatures during the wind tunnel runs,was in humid ambient air between runs.Base pressure coefficient Cpb=(Pb-Pst)/q,where Pstis the free-stream static pressure,was computed by assuming a constant base pressure Pbover the entire base of the model(s),and the forebody axial-force coefficient was computed by subtracting the corresponding base drag coefficient-Cpb·Sb/Sreffrom the total axial force coefficient as CAf=CA+Cpb·Sb/Srefwhere Sref=π D2/4 and Sb=π(1.6 D)2/4.Base pressure coefficient from NASA Ames was not obtained by pressure measurements but was estimated by Malcolm and Chapman16from the angles of Mach lines seen in shadowgraphs obtained during the tests.

Differences in base pressure reported by various sources could also have been influenced by the design solution for the bases of the models.It is known23,24that the existence of a base cavity can change base drag and the exact forms of the bases of the models and the shapes of the stings in various experiments with HB-2 model were not well documented.It appears that the designs of model bases ranged from a plate with even the gap between the base and the sting closed by a labyrinth seal25,26to designs in which the base seemed to be completely open towards the cavity inside the model.13,16

It should be noted that,while the above relations for Cpband CAfassume,by convention,an‘‘a(chǎn)verage”base pressure Pbwhich is constant over the entire base,in reality the base pressure varies across the base area,particularly at higher angles of attack27.Correct integration of an average base pressure on a model with a large base as on the HB-2 configuration can be a matter of debate,even if measurements can be performed at several points on the base.In VTI tests,base pressure was measured at one point only,in the model cavity accessed by the annular opening around the support sting.As the base pressure at angle of attack is increased on the leeward side of the base and decreased on the windward side,the measurement performed around the model centreline was assumed to be close to average base pressure in the presence of a sting.

Comparisons of the axial force coefficients from various sources versus Mach number at zero angle of attack are shown in Fig.12,while the zero-lift base pressure coefficient is shown versus Mach number in Fig.13.The results for the forebody axial force coefficients from all sources agreed well,in particular in the Mach number range 2-2.5.On the other hand,while the agreement of the measured total axial force coefficient CAwith results from ONERA Chalais and Vernon15and NASA Ames16was quite good,AEDC data differed considerably,as already noted.It can be seen that the total axial force coefficient decreases significantly as Mach number increases,mostly because of the decrease in the base pressure coefficient,while the change in the forebody axial force coefficient is much smaller.Therefore,the contribution of the base drag to total drag diminishes with increasing Mach number.

Fig.5 Aerodynamic coefficients of HB-2 model at Mach number 1.5.

Fig.6 Aerodynamic coefficients of HB-2 model at Mach number 2.0.

Fig.7 Aerodynamic coefficients of HB-2 model at Mach number 2.5.

Fig.8 Aerodynamic coefficients of HB-2 model at Mach number 3.0.

Fig.9 Aerodynamic coefficients of HB-2 model at Mach number 3.5.

Fig.10 Aerodynamic coefficients of HB-2 model at Mach number 4.0.

Fig.11 Base pressure coefficients of HB-2 model.

Fig.12 Total and forebody zero-lift axial force coefficients of HB-2 model versus Mach number.

Fig.13 Zero-lift base pressure coefficient of HB-2 model versus Mach number.

A difference in the character of the total axial force coefficients CAobtained for two model sizes at Mach number 1.5 was noted,as well as a difference between the forebody axial force coefficients at angles of attack above 24°(Fig.5).These differences were barely observable at Mach number 2(Fig.6)and undetectable at any higher Mach numbers.Although the differences were not large when compared with dataset-todataset scatter of results seen in Figs.12 and 13,their cause should be investigated.The forebody coefficients for the two models agreed well except at the highest angles of attack,so the difference was related mostly to base drag.The factors differing between the tests were sting/base diameter ratio and Reynolds number,both of which are known to influence base drag significantly.The results seem to indicate actual aerodynamic effects related to those factors,but this must be corroborated by further tests of the same two models, and,unfortunately,there are no comparable reference data from other sources.The future tests should include schlieren visualizations of the flow around the larger model,in order to investigate the possibility of anomalous near-wake flow.At this time,the authors are not inclined to state that one of the groups of results is‘‘right”and the other‘‘wrong”,so both are presented‘‘a(chǎn)s they are”and the issue is as yet unresolved.

The forebody axial force coefficient CAfwas reported in the reference AEDC tests as decreasing with angle of attack at Mach numbers below 3 and increasing with angle of attack at Mach numbers above 3 and as being more-less constant,gently decreasing with angle of attack at Mach number 3.However,in all VTI T-38 tests,CAfincreased with angle of attack at Mach number 3 while,at lower Mach numbers,it decreased with angle of attack.Therefore,the change of character of the variation of CAfwith angle of attack in all VTI's T-38 tests seemed to occur at Mach number slightly below 3,while in AEDC tests it occurred at Mach numbers slightly above 3.Comparable data from ONERA S5 Chalais wind tunnel,although available only in a limited range of angle-ofattack,is in better agreement with VTI T-38 results than with AEDC results(Fig.8).

The agreement of the data for the normal force and pitching moment from all sources is particularly good.At higher angles of attack the normal force coefficient and pitching moment coefficient follow the trends set at angles of attack of about 17°to 20°in an almost linear fashion.This character is similar to that observed in the high angle of attack Mach number 10 data from JAXA28and similar to the behaviour of a cylindrical body in a supersonic/hypersonic crossflow at nonzero angles of attack.29

4.2.Measurement uncertainty

An estimate was made of the uncertainty of measurement in the sense of two standard deviations of some of the most relevant quantities on the basis of uncertainties of contributing measurements and the sensitivities of the determined variable to the changes of the contributing variables(combined Type-B uncertainty).Assuming a normal distribution of errors,this interval should encompass about 95%of measured results.Because of the difficulty of analytically determining the necessary sensitivity coefficients as partial derivatives of various quantities in the complex calculations needed to obtain the aerodynamic coefficients, the derivations were performed numerically,by varying the data for each directly measured quantity for a small amount,performing the complete computation of the aerodynamic coefficients,and by noting the changes in the computed output values.Computed estimates of measurement uncertainties of aerodynamic coefficients are shown in Table 2 for two Mach numbers within the test envelope.Measurement uncertainties for other Mach numbers can be estimated by interpolation.

4.3.Flowfield visualizations

Flow patterns around the 75 mm HB-2 model at Mach numbers 1.5,2.0,2.5,3.5 and 4.0 at high angles of attack in the T-38 wind tunnel are illustrated by snapshots from video recordings of schlieren visualizations shown in Fig. 14.Recording of the test at Mach number 3.0 was accidentally lost.All images were taken at angles of attack of 29°to 30°except for the snapshot at Mach number 4.0 which was taken at angle of attack of 13°.Density gradients positive in the downstream direction are represented in blue colour while the density gradients negative in the same direction are represented in red.In the darkened areas present in the images the gradients exceeded the set sensitivity range of the schlieren system and the effect was exacerbated by the less-thanperfect collimation of the system optics.When viewing these images one should have in mind that schlieren technique shows the density gradients (actually, gradients of the refractive

index)integrated through the complete width of the test section,not a‘‘cross-section”of the flow field in the model's plane of symmetry.

Table 2 Estimated 2σ uncertainty of aerodynamic coefficients.

Fig.14 Schlieren visualization of HB-2 model.

The continuous video recordings of the schlieren visualizations proved convenient for observing the evolution of the flow with the change of the angle of attack.Boundary layer separation on the cylindrical part of the model,caused by the adverse pressure gradient induced by the flare could be observed at low angles of attack,as reported by Gray and Linsday14.With the increase of the angle of attack the separation diminished or disappeared first on the windward side of the model,and then,at angles of attack of about 10°,at the leeward side as well.With the further increase of the angle of attack,pronounced separation reappeared on the leeward side, as visible in Fig.14.The bow shock from the nose of the model became parallel with the cylindrical part of model body on the windward side at Mach numbers above 3 as angle of attack approached approximately 24°and stayed so with further increase of the angle of attack(Fig.14(d)),passing close to the windward shoulder of the base.

In the complex flow behind the model, Prandtl-Meyer expansion fan at the shoulder of the base can be observed,as well as the recirculation bubble and the shear layer separating it from the outer flow.The recirculation bubble is distorted by the flow at angle of attack and the presence of the sting,and,at the higher angles of attack,the sting is not anymore in the wake of the model.

5.Conclusions

(1)Two HB-2 models of different sizes were tested in the Mach number range 1.5-4.0 at angles of attack up to approximately+30°,and at relatively high Reynolds numbers up to 4.5 millions.As there were no comparable data at high angles of attack from tests in other facilities,obtained results were compared with references only in the angle-of-attack range up to+15°.A good correlation of results was found and,in the absence of any directly comparable reference data at high angles of attack,it was assumed that the obtained results,found to be good at low angles of attack,were,by implication,also good at high angles of attack.

(2)The collected data were,therefore,assumed to be valid and are included in the local database of test results for the HB-2 models that is being formed in VTI,to be used in future periodic verifications of the T-38 wind tunnel in the supersonic part of the operating envelope.The presented data may also be of use to the experimenters in other wind tunnel facilities,and as test cases for the high angle of attack CFD codes.

(3)It is felt that,in all reference tests of the HB-2 model,insufficient attention was paid to standardizing and documenting the factors influencing base pressure.Although this can be understandable as the experimenters were bound by the constraints related to the characteristics of their wind tunnels and model supports,it makes correlation of the total axial force coefficient more difficult.

(4)There are indications that,at the test conditions in the T-38 wind tunnel,a small but observable influence exists of base/sting diameters ratio and/or Reynolds number on the base drag and,therefore,total axial force coefficients at Mach number 1.5 to Mach number 2.0.This issue has not been satisfactorily resolved and is to be investigated in future tests of the same models which will be continued as circumstances and T-38 wind tunnel schedules permit.It is also intended to provide the currently missing forebody data at Mach numbers 3.5 and 4 and to collect some data for this model in the transonic speed range as well.

Acknowledgments

This study was supported by the Military Technical Institute(VTI)and Ministry of Education,Science and Technological Development of Serbia(No.TP 36050).