He Xuzhao,Zhou Zheng,Qin Si,Wei Feng,Le Jialing

Science and Technology on Scramjet Laboratory,Hypervelocity Aerodynamics Institute of CARDC,Mianyang 621000,China

Design and experimental study of a practical Osculating Inward Cone Waverider Inlet

He Xuzhao*,Zhou Zheng,Qin Si,Wei Feng,Le Jialing

Science and Technology on Scramjet Laboratory,Hypervelocity Aerodynamics Institute of CARDC,Mianyang 621000,China

A design method based on tip to tail streamline tracing and osculating inward cone methods is discussed for designing the integrated Osculating Inward Cone Waverider Inlet(OICWI).A practical geometrical constrained experimental model of OICWI is designed based on the validated design method.It has a total contraction ratio of 4.61 and inner contraction ratio is 2.0.Wind-tunnel tests have been conducted for the OICWI model at free stream Mach number(Ma∞)of 4.0,3.5 and 3.0 respectively.The experimental results show that the OICWI has high flow capture ratio and compression abilities.It can self-start at Ma∞=3.5 and 4.0 and its flow capture ratio is 0.73 at Ma∞=4.0,and Angle of Attack(AOA)0°.The research results show that the OICWI has advantages of inward cone waverider and streamline tracing inlet.Present OICWI is a novel approach for waverider inlet integration studies and it will promote the use of waverider inlet integration configuration in the studies of airbreathing hypersonic vehicles.

1.Introduction

Hypersonic vehicles with airbreathing propulsion have been studied intensively in recent years.One of the difficulties of airbreathing hypersonic flight is the decreasing thrust to drag margin when the vehicle’s speed increases.From aerodynamic view,increasing the vehicle’s lift to drag ratio and inlet captured mass flow rate will reduce vehicle’s drag and increase its propulsion force.

Waveriders1–4are the most suitable options for those high lift to drag ratio vehicles,but there are several shortcomings of waveriders from the engineering lever view,5such as low volumetric capacity and low flow compression ability.Waverider’s unconventionally curved compression surface makes it difficult to integrate with all kinds of inlets.

On the other hand,hypersonic inlets with high performances can be designed by using sophisticated design methods.6–10However,it is difficult for them to integrate with vehicle’s forebody.By using geometric modification techniques during the integrations,the disturbed incoming flow caused by vehicle’s forebody will decrease the inlet’s high performance.11,12Considering the low thrust to drag margin of the hypersonic airbreathing vehicles,the decreased performance caused by the improper integrations offorebody and inlet should not be ignored.One of the most urgent tasks now is to devise a practical method to design the waverider and inlet as a whole.

O’Neill and Lewist13used conically derived waverider as forebody.The inlet’s cowl surface is established by streamlines traced from conical flow field.The inlet is presumed to be a two-dimensional planar flow.Takashima and Lewis,14and O’Brien and Lewis15used osculating cone waverider1as forebody.The forebody has a planar portion around center line that generates a uniform wedge flow field.The flow traverses a series of three wedge compression ramps of equal compression angle before entering the combustor.15Starkey and Lewis16used analytical variable wedge angle method to generate waverider forebody which has a planer portion in the middle of waverider.The inlet used three successive compression ramps and integrated with a forebody as same as Refs.14,15.You et al.17proposed a dual waverider design concept for forebody-inlet integration in the spanwise direction.Li et al.18furthered You’s work and considered the double flow paths in the dual waverider forebody-inlet integration.The abilities of anti-backpressure and start/restart of hypersonic inlet are also very important aspects,and there have been many papers devoted to the investigation on it.Chang et al.studied the unsteady behavior of hypersonic inlet unstart flow caused by back pressure,and found two novel inlet unstart patterns19and one new local unstart pattern.20The unstart/restart characteristics of hypersonic inlet and mathematical modeling on hypersonic inlet buzz have been studied by Chang et al.21,22,and the unstart prediction and detection methods to prevent inlet unstart have also been studied.Trapier et al.23gave some detailed analysis of supersonic inlet buzz,and the start and restart characteristics of a typical supersonic buzz are well studied in their paper.

For the integration design of hypersonic forebody and inlet,most of the studies introduced above are still in conceptual design phase.The complex aerodynamic characteristics of the integrated forebody inlet,such as flow field structures,flow capture abilities and inlet combustor matching requirements,should be studied intensively and the validity of the design method should be proved experimentally.

Since inward turning inlet6,7and inward waverider3are all derived from inward turning cone flow fields,great interests have been aroused for combining the inward turning waverider and inlet as a whole system.The objective of this paper was to present a methodology for the design of integrated Osculating Inward Cone Waverider Inlet(OICWI),and provide experimental study results of the designed OICWI at Mach 4.0,3.5 and 3.0.The paper is organized as follows:in Section 2,the design methodology and experimental model under geometrical constraints are designed.Section 3 discusses the experimental facilities and experimental setup.Section 4 discusses experimental results and performance of the OICWI.The OICWI’s performance is characterized by self-restart ability,mass flow rate,and anti-backpressure ability.Finally,Section 5 offers some concluding remarks.

2.Design methodology and its application

2.1.Overview of design methodology

The design methodology of OICWI and its validation have been reported by the authors in their previous paper.24–26The design method is introduced brie fly here with the re fined figures and new design parameters.

The design of the OICWI is based on basic inward turning flow field.Its outer compression part(Region BE*I)and inner compression part(Region BIFG)are shown in Fig.1(a).The Method of Characteristics(MOC)is used as design tool for designing the basic flow field.In basic flow field’s outer compression part BE*I,only a part of Internal Conical Flow A27,28(Region BE*H)is used to generate a straight initial compression shock.Curved inward turning cone wall HI is tangent to E*H at point H and shape of HI can be regulated to control the basic flow field’s outer/inner compression ratio.

In inner compression part(BIFG),shape of cone wall(IF)is defined by quadratic curve which is tangent with the flow angle at point I.The Mach number on point F is defined and it is smoothly distributed on the curve Iffrom point I to point F.Shock cancel technique29is used to eliminate shock reflection on inner cone wall IF.Center body shape JG is determined by matching mass flow rate on each characteristic originated from IF.

In the present basic flow field,design Mach number is 6.Initial shock wave angle is 17°.Center body radius at point B is 55%of the radius at E*.Mach number at point F is defined as 3.8.Total and inner compression ratios of the basic flow field are 4.5 and 1.85 respectively.The basic inner cone’s flow field is calculated by MOC and its Mach number contour is shown in Fig.1(b).OO′is axisymmetric axis of the basic flow field.X and Y are the basic flow fields’coordinate and Rsis the radius at point E*.

Osculating inward turning cone28and tip to tail streamline tracing methods are used in the OICWI method.In the OICWI’s cowl leading edge plane,shown in Fig.2(a),Inlet Capture Curve(ICC)is defined by super-ellipse curve:

Fig.1 Schematic diagram of basic flow field.

Fig.2 Design and schematic diagram of OICWI.

where Lx,Lyand θ are used to define ICC’s shape and size.Front Capture Tube(FCT)is generated by parabolic curve.

In the cowl leading edge plane,ICC’s curve’s center will be found firstly.For example,for point B on ICC,its corresponding curve center A is found.Points B and A generate an osculating plane AB.In osculating plane AB,there are some corresponding relationships between osculating plane AB(Fig.2(a))and the basic flow field(Fig.2(b)).In Fig.2(a),point A corresponds to the basic flow field’s axisymmetric center and point B corresponds to the intersection point between the basic flow field’s initial shock and center body.Point D is the intersection point between osculating plane AB and the FCT.

As the basic flow field is scaled and matched with the corresponding points in the osculating plane AB(Fig.2(b)),a horizontal line starting from point D will intersect with the initial shock E*B at D*.A streamline which starts from point D*is traced in the basic flow field until it exits.And this tip to tail streamline is used to construct the body side’s compression surface in the osculating plane AB.The corresponding inlet cowl surface in osculating plane AB is generated by the center body curve BG.Repeating the above procedures along ICC line point by point,the OICWI’s compression surface on body and cowl sides can be constructed.

In practical implementation,only center part of ICC curve is used as inlet capture section,and corresponding inlet capture area is BB′DD′.Inlet’s side walls are constructed by the osculating planes such as BC and B′C′.Fig.2(c)shows the designed prototype OICWI,and the corresponding points in Fig.2(a)and(b)are shown in Fig.2(c).

Previous forebody/inlet integration design method generally has three steps.Forebody is designed firstly and then inlet is designed.The inlet and forebody are integrally designed by geometric merging tools.The disadvantages of the previous design method have been described above such as decreased inlet’s performance caused by disturbed incoming flow8,12and large flow spillage under design condition,and the flow field structures offorebody and inlet are not exactly matched with each other even under design condition.

The advantages and innovation points of present OICWI method are as follows:forebody and inlet are designed as continuous stream surfaces at the same time and there is no geometric modi fication on their junction surfaces during the integration procedures.The integrated forebody and inlet have high performance with few flow spillages especially under design condition and its flow field structures match with the basic flow field structures well.The waverider and inlet’s flow field are not disturbed by the integration procedures and they will remain their original high lift to drag ratio and quali fied compression abilities.The disadvantage of present OICWI is its relatively low volume characteristics caused by its concave forebody shape.This shortcoming can be overcome by using the outer cone as the basic flow field.This improved design method has been investigated and will be reported soon.

2.2.Design of geometric constrained practical OICWI

Based on the prototype OICWI designed in Section 2.1,an OICWI experimental model is generated under practical considerations.Parts of the prototype’s forebody(Fig.2(c))are truncated,but its whole compression surface from forebody leading edge to inlet throat is remained.Fig.3(a)is threedimensional view of the experimental model.It has a maximum forebody width of 0.15 m.Its length is 0.297 m from its leading edge to cowl lip and 0.63 m to isolator exit.Its capture area is 7.326×10-3m2,and throat area is 1.690×10-3m2.Its total compression ratio is 4.6 and inner compression ratio from the cowl lip to the throat is 2.0.Its side walls at the beginning of inner compression parts are cut offfrom its leading edge along 70.5°line,which is approximately identical with cowl reflect shock at Ma∞=3.5.Its forebody leading edge radius is 0.5 mm and cowl leading edge radius is 0.25 mm.

Fig.3 Three dimensional view of the experimental model and its isolator.

Shape transition techniques5,30are used from throat to isolator exit to generate a rectangle exit isolator.As shown in Fig.3(b),the blue line indicates throat shape and the black line is isolator exit shape.Area and geometrical center of the isolator are maintained constant along x-coordinate direction.The length of isolator is 0.21 m,about 9.7 times the height of throat.Width to height ratio at the isolator exit is 4.2.

3.Experimental setup

Wind tunnel experiments are conducted at China Aerodynamic Research and Development Center’s(CARDC)0.6 m StraightIntermittentTrisonicWind Tunnel(SITWT).31SITWT has a 0.6 m×0.6 m test section with the operation Mach number ranging from 0.4 to 4.5.Under supersonic conditions,its test section’s length is 1.575 m.The experimental model is tested at Ma∞=4.03,3.53 and 3.01.Table 1 is the wind tunnel’s operation conditions.Ptis total pressure,T0is total temperature and Re is Reynolds number of incoming flow.

Fig.4 is schematic diagram of the experimental system.The designed OICWI is shown as experimental model.It is connected to a rectangle-circle transition section which is mounted in front of a flow meter with circular cross section.The flow meter is connected to support strut which is installed on wind tunnel wall.A throttling cone with liner stepping motor is mounted behind the flow meter.During the experiment,when wind tunnel comes to a steady state,the throttling cone will move forward step by step gradually and pause at each step for 3 s.During the pause periods,pressure signals are measured by steady pressure measurement system.When the throttling cone moves to the most forward position,the inlet will be unstarted,and then the throttling cone moves back step by step gradually to its original position.

Geometrical size and locations of the measurement tabs/probes of the experimental model are shown in Fig.5.Twenty five pitot probes located in five rows are mounted on the rectangle isolator’s exit plane.In mass flow meter,sixteen pitot and sixteen static pressure probes are located in space and four static pressure taps are placed on wall.Mass flow rate through the inlet is determined by choked valve method which has ahigh accuracy for mass flow measurement.32168 surface static pressure taps distribute along symmetrical planes on cowl side(D),body side(A)and the other two planes(B and C)which are parallel with the symmetric plane.Distances of line B andC withsymmetricplaneare10 mm and20 mm respectively.

Table 1 Wind tunnel test conditions.

All those static pressure taps and pitot pressure probes are connected to metal tubes which are about one meter long.Metal tubes are connected to an electronic scanning pressure system(Pressure Systems,Inc.,Model 9016)by polyethylene tubes.The air-tightness and vent of the pressure measurement systems are tested strictly.A high-speed schlieren system for visualization of the external flow is used.It can take 2000 images per second and has maximum pixels 800×800 depending on requirements.On the body side’s symmetrical plane,13 Kulite sensors labeled D1-D13 range of 200 kPa are used to measure unsteady static pressure.According to the factory calibration data,those transducers have an accuracy of 0.1%offull range and a natural response frequency of 50 kHz.Only D3 and D13 which locate at the end of cowl breach and isolator exit(Fig.5)are used in the present analysis.D3 is used to monitor inlet’s start-unstart-restart phenomenon.

Static pressure taps have three ranges:0–50 kPa for outer compression part,0–200 kPa for inner compression part and 0–500 kPa for pitot probe and flow meter.The error associated with the use of these transducers is±0.06%in full scale.All experimental data are acquired and stored by a PC-based data acquisition system.Typical running time of a wind tunnel experiment is approximately 100–200 s.

Fig.6 is the photograph of the fully assembled experimental system in SITWT’s test section.The experimental configurations are controlled by mechanical remote control system.The experimental model’s AOA can be adjusted between-6°and 6°.The throttling cone can be moved from 80 mm(fully open)to 110 mm(fully throttled).

4.Results and discussion

4.1.OICWI’s mass flow capture ability

Fig.4 Schematic diagram of experimental system in SITWT wind tunnel.

Fig.5 Geometrical sizes of experimental model and distributions of static taps/pitot probes.

Fig.6 Photograph of experimental model in SITWT.

Formulations accounting for the non-uniform pressure distributions in flow meter are used to calculate mass flow rate for the experimental model.They are shown below and flow in the flow meter is assumed to be throttled to subsonic conditions.φ is mass flux ratio.In the present formulations,the number of pitot probes is 16(n=16),and A0is the captured area.Pjand Ptjare static pressure and pitot pressure respectively.sjis the corresponding control area governed by pitot/static pressure probe j,and the cumulated sum of sjequals to flow meter’s cross section area.Pt∞is total pressure of incoming flow.γ is heat specific ratio of air. λjand q(λj)are flux functions of Eq.(2).

Fig.7 is schlieren maps of the experimental model at Ma∞=4.0 and 3.5 at different AOAs during the measuring procedures of mass flow rates.The throttling positions are xc=90 mm for Ma∞=4.0 and xc=89 mm for Ma∞=3.5,which will keep the flow in the mass flow meter fully throttled,but at the same time,the inlet is still fully started.xcis the throttling cone position.

Fig.8(a)is the measured mass flow rate at different throttling cone positions corresponding to different incoming flow conditions.Except non-fully throttled and unstart conditions,the measured values for each condition at different throttling cone positions are identical.Mean squared errors of the measured data corresponding to each free stream condition are less than 2%.Fig.8(b)presents the measured mass flow rates at different free stream Mach numbers and angles of attack.From those results,when the OICWI is fully started,its mass flow rate is probably proportional to the angle of attack.Mass flow rate is quite low at Ma∞=3.0 because of the unstart inlet.

4.2.OICWI’s anti-backpressure ability

Fig.9 shows mean static pressure distribution on body side’s symmetric plane when the throttling cone moves forward and back.When the throttling cone moves forward from 85 mm to 100 mm,mean static pressure in isolator increases gradually until xc=95 mm.At xc=100 mm,pressure rise has moved forward to the forebody areas and the inlet is unstarted.Comparing Fig.9(a)with(b),we can see that beginning position of pressure rise at body side is slightly ahead of that at cowl side at the same throttling cone position.This means that flow boundary layer of body side is thicker than that of cowl side.This phenomenon causes flow separation and it makes back pressure move forward more easily on body side than on cowl side.When the throttling cone moves forward and then moves backward to the same position,such as at xc=95 mm and xc=85 mm,pressure distributions on symmetric plane are almost identical with each other.This means that flow delay phenomena during the inlet’s restart process in present experimental conditions are weak.P is static pressure on static pressure taps of the experimental model.

Fig.7 Schlieren map of OICWI experimental model at Ma∞=4.0 and 3.5 during mass flow measurement procedures.

Fig.8 Mass flow rates of OICWI.

Fig.9 Mean static pressure distribution on symmetric plane at Ma∞ =4.0 and AOA=4°.

Fig.10 presents the filtered dynamic pressure distribution on D3 and D13 at Ma∞=4.0 and AOA=0°during the inlet’s unstart process.Keeping on moving throttling cone forward beyond xc=98 mm,back pressure at D13 will rise until buzz occurs and inlet is unstarted.The maximum back pressure is obtained by using mean static pressure at D13 just before buzz occurs.Table 2 isthe maximum antibackpressure at different Ma∞and AOAs.The maximum anti-backpressure increases with increasing Ma∞and AOA.Their values are about 40 and 26 times P∞for Ma∞=4.0 and 3.5 respectively.Pdis the dynamic pressure value on dynamic pressure sensors D3 and D13.Pbmaxis the maximum anti-back pressure of the experimental model.

Fig.10 Filtered dynamic pressure distribution at D3 and D13 at Ma∞ =4.0 and AOA=0°during inlet’s unstart period.

Table 2 Maximum anti-backpressure at different Ma∞and AOAs.

4.3.OICWI’s start and restart ability

Fig.11(a)presents the start,unstart and restart schlieren maps of the OICWI at Ma∞=4 and AOA=0°.The inlet is fully started as wind tunnel sets up.When the throttling cone moves forward to 100 mm,back pressure increases and the inlet is fully unstarted.When the throttling cone moves back to 92 mm,the inlet is restarted again.Fig.11(b)shows the dynamic pressure distribution on D3 and D13 during the inlet’s restart process.During the inlet’s unstart process,the inlet’s flow field is buzzing and the dynamic pressure on D3 and D13 has high-amplitude and low-frequency vibrations.As the throttle cone moves backward,buzz vanishes and shock train is swallowed into the isolator.Back pressure is still high during this period,and the low-amplitude but high-frequency vibration signals appear on D13.

Fig.12(a)presents the start,unstart and restart schlieren mapsatMa∞=3.5andAOA=0°.Fig.12(b)shows dynamic pressure distribution during the inlet restart period.Phenomenon and conclusions are similar with the above case.The difference is that when the throttling cone comes to xc=95 mm,the inlet has already been fully unstarted.This phenomenon shows that the inlet can only withstand a lower maximum back pressureatMa∞=3.5than thatat Ma∞=4.0.As the throttling cone keeps moving backward,the inlet is fully restarted.The low-amplitude and highfrequency static pressure vibrations on D13 vanish as the back pressure keeps on decreasing.

Fig.11 Restart phenomenon at Ma∞ =4.0 and AOA=0°.

Fig.12 Restart phenomenon at Ma∞ =3.5 and AOA=0°.

Fig.13 Unstart phenomenon at Ma∞ =3.0 and AOA=-4°,0°and 4°.

Fig.13(a)shows that the OICWI cannot fully establish start flow patterns from AOA=-4°to AOA=4°at Ma∞=3.0.There are strong separation shocks at body side in front of cowl lip.Reflected oblique shocks on cowl side are still visible.This means that flow field is supersonic at cowl side and flow separation occurs mainly at the body side.Fig.13(b)presents the dynamic pressure signal on D3 and D13 at AOA=0°.Pressure vibrations can be seen obviously.Vibrations on D3 are stronger than those on D13 since flow separation occurs mainly at the entrance of the inlet’s inner compression part.

5.Conclusions

The design method of osculating inward turning cone waverider forebody inlet has been introduced in this paper.The waverider forebody and inlet are integrally designed with no artificial modifications of their compression surface.An OICWI experimental model is designed under geometrical constraints.Wind tunnel experiments are conducted to test the performance of the designed OICWI from Ma∞=3.0 to 4.0.The OICWI’s mass flow capture ratio is relatively high and it is 0.73 at Ma∞=4.0 and AOA=0°.The forebody inlet’s maximum anti-backpressure values are around 40 times P∞at Ma∞=4.0 and about 26 times P∞at Ma∞=3.5(AOA is0°).TheOICWIcan startand restartat Ma∞=3.5 and 4.0 but cannot fully start at Ma∞=3.0.The promotional results obtained from the present studies suggest that OICWI will be a good option for airbreathing hypersonic vehicle’s forebody inlet compression system.Present novel approach will promote the use of OICWI in the studies on hypersonic airbreathing vehicles and it is an important way to improve the propulsion to drag performance of hypersonic airbreathing vehicles.

Acknowledgments

This study was supported by the National Natural Science Foundation of China(Nos.51376192 and 91216303).

Appendix A.Supplementary material

Supplementary data associated with this article can be found,in the online version,at http://dx.doi.org/10.1016/j.cja.2016.09.007.

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He Xuzhao received the Ph.D.degree in aerodynamics from CARDC in 2007,and now he is an associate professor there.His main research interests are hypersonic shape design and integration study of airbreathing hypersonic vehicles.

Zhou Zheng received the Ph.D.degree in aerodynamics from CARDC in 2016.His main research interest is hypersonic inlet study.

Qin Si is currently an engineer in CARDC.His main research interests include CFD and hypersonic inner outer flow interaction.

Wei Feng is currently an engineer in CARDC.His main research interests include hypersonic inlet design and experimental study.

Le Jialing is a fellow of Chinese Academy of Engineering and his research focuses on airbreathing propulsion.

29 December 2015;revised 8 April 2016;accepted 17 July 2016

Available online 21 October 2016

Inlet;

Integration design;

Inward turning cone;

Waverider;

Wind tunnel experiment

Ⓒ2016 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.This is anopenaccessarticleundertheCCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).

*Corresponding author.

E-mail address:hexuzhao@sina.com(X.He).

Peer review under responsibility of Editorial Committee of CJA.

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http://dx.doi.org/10.1016/j.cja.2016.09.007

1000-9361Ⓒ2016 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.

This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).