E ects of shock wave/boundary-layer interaction on ...scientiairanica.sharif.edu/article_3928_d66dd76159725aebb70fa5c7… · performance and stability of a mixed-compression inlet

Scientia Iranica B (2016) 23(4), 1811{1825

Sharif University of TechnologyScientia Iranica

Transactions B: Mechanical Engineeringwww.scientiairanica.com

E�ects of shock wave/boundary-layer interaction onperformance and stability of a mixed-compression inlet

M.R. Soltania;�, A. Daliria and J. Sepahi Younsib

a. Department of Aerospace Engineering, Sharif University of Technology, Tehran, P.O. Box 1458889694, Iran.b. Faculty of Mechanical & Aerospace Engineering, Ferdowsi University of Mashhad, Mashhad, Iran.

Received 24 January 2015; received in revised form 8 May 2015; accepted 26 October 2015

KEYWORDSSupersonic inlet;Shockwave/Boundary-LayerInteraction (SBLI);Pseudo-shock;Shock train;Buzz.

Abstract. Experiments were conducted to study various kinds of Shock wave/BoundaryLayer Interaction (SBLI) in an axisymmetric mixed-compression inlet. Experimental�ndings were compared and veri�ed by numerical solutions where possible. Di�erent typesof SBLI relevant to the mixed-compression inlets are classi�ed. Interactions of normal shockwave/boundary-layer at subcritical condition and in buzz condition are investigated usingSchlieren and shadowgraph ow visualization as well as unsteady pressure recordings. Thedata is compared with the CFD predictions. Interactions of cowl lip re ected obliqueshock and the terminal normal shock with the spike boundary-layer at both criticaland supercritical operations, which lead to pseudo-shock phenomena, are also studied.Experimental pressure recordings are used for validation and discussion. For near-criticalthrottling values, interaction of internal compression oblique shocks with boundary-layerand pseudo-shock phenomenon is dominant. Formation of lambda shock due to interactionof separated boundary-layer with normal shock wave is investigated. Each type of owinteraction phenomena has di�erent e�ects on the stability and performance of the inlet.Interaction of terminal normal shock with internal duct boundary-layer causes pseudo-shock phenomenon that increases ow distortion and reduces total pressure recovery.Interaction of normal shock with cone boundary-layer causes buzz instability and degradesinlet performance.© 2016 Sharif University of Technology. All rights reserved.

1. Introduction

For supersonic vehicles, the inlet must decelerate theincoming ow to subsonic speeds before delivering itto the combustion chamber. The compression couldbe done by a normal shock or by a series of obliqueshocks. The latter case produces lower entropy changesand is frequently used. Depending on whether theoblique shock waves are generated inside or outsidethe inlet duct, such designs are referred to as internaland external compression inlets, respectively. Bothexternal and internal types of compression are also used

*. Corresponding author.E-mail address: [email protected] (M.R. Soltani)

in appropriate degrees to reduce their de�ciencies in an-other design known as mixed compression. In all cases,interaction of shock wave with inlet surface boundary-layer is inevitable. Oblique shock waves interact withboundary-layer and cause adverse pressure gradientthat makes the boundary-layer ready for separation.A �nal near-normal shock wave (or an oblique shockwave of strong-shock solution) turns the ow fromsupersonic to subsonic through a strong transonic SBLIand will usually separate the ow. Flow separationgreatly impacts the inlet performance by means ofreducing the total pressure recovery and by adding ow distortion. As the ow is typically separatedat the entrance of subsonic di�user, it becomes non-uniform at the engine face [1]. This ow distortion

1812 M.R. Soltani et al./Scientia Iranica, Transactions B: Mechanical Engineering 23 (2016) 1811{1825

disturbs inlet performance and harms the engine. Theterminal normal shock can be expelled out of theinlet duct by reducing the inlet mass ow ratio (atsubcritical operating condition); however, the progresswill result in the shock interaction with the boundary-layer of the external compression surface that will leadto sudden high-amplitude ow oscillations called buzz.In addition to degrading the inlet performance, buzzcan lead to trust loss, engine surge, or even aircraftstructural damages [2].

Numerous studies have been carried out on su-personic inlet performance and stability since 1940.Much information could be found in the literature ondi�erent aspects of various types of supersonic inletmodels [3-14]. Performance characteristics of inlet incases of extensive maneuvering range [3,4], unstart [5],buzz phenomenon, and application of boundary-layerbleed [6-14] have recently been investigated. Inaddition to these experiments, many computationalstudies have been accomplished on the supersonic inlet ow and buzz phenomenon as well as ow controlmethods [15-19].

Shock wave boundary-layer interaction as a fun-damental gas dynamics phenomenon can be foundin many practical aerospace related problems rangingfrom transonic aircraft wings to hypersonic vehiclesand engines. A comprehensive survey of the interac-tion of shock wave and turbulent boundary layer waspublished by Viswanath in 1988 [20]. In his paper,an overview of some developments in understanding,prediction, and control of two-dimensional SBLI athigh speeds was presented. A general review ofdi�erent aspects of SBLI along the wall surface ofinternal compressible ows was presented by Matsuoet al. [21]. In this study, the fundamental featureof shock train and pseudo-shock, several predictionmethods, and control methods of pseudo-shock weredescribed. Also, understandings related to self-excitedoscillations of pseudo-shock were reviewed. A summaryof the Computational Fluid Dynamics (CFD) simu-lations of SBLI was also presented in a review paperand methods of DNS, LES, and RANS were comparedwith experiments and the capabilities and limitationsof each turbulent model were described [22]. Also,application of LES method for simulation of shock waveinteractions in nozzles was performed [23,24]. Recently,comprehensive study on the advances of SBLI withemphasis on ow unsteadiness, heat transfer predic-tion, multi-shock boundary-layer interaction, and owcontrol techniques has been performed [25]. Otherrecent studies have been carried out on unsteadiness ofSBLI [26,27] and control methods such as bleed, vortexgenerator, and micro actuators [28-30]. Also, somerecent experiments and theoretical e�orts have beenmade to investigate the e�ect of ow control methodssuch as bleed on SBLI for supersonic and hypersonic

inlets [31-35]. The main idea of these notable papersis to discuss the most general aspects of shock waveboundary-layer interactions relevant to supersonic airinlets.

Studying the physics of complicated ow cor-responding to SBLI in order to employ the resultsfor designing inlets and related ow control devicesis useful. Although several studies have been per-formed on SBLI and its control means, some of thecomplicated aspects of SBLI are not discovered yetand it is needed to perform more experiments andsimulations to perceive the physics of ow interactions.On the other hand, generalization and application ofthe fundamental SBLI ows for practical ow devicessuch as inlets are very useful and could hardly befounded in the literature. Along with classi�cationof SBLI ows relevant to mixed-compression inlets,this paper aims to present a novel analysis to relateSBLI phenomena to inlet performance and stabilitythrough evaluation of experimental and numerical evi-dences.

2. Experimental setup

2.1. Wind tunnelThe experiments are conducted in a continuoussuction-type wind tunnel with a rectangular test sec-tion of 60 � 60 cm2. The tunnel is equipped witha exible nozzle that can be adjusted during thetests. The turbulence intensity of the ow in the testsection ranges from 0.4% to 1.4%, depending on thefree-stream Mach number [12]. There exist porousbleed holes on the upper and lower walls of the testsection which can stabilize and control wind tunnelshock and other re ected waves. Side wall windowsof the test section have been made up of optical glasseswhich allow the ow and shock pattern observation bymeans of Schlieren and shadowgraph ow visualizationsystems. The tunnel is indraft; thus, total pressure andtotal temperature in the test section are constant andatmospheric.

2.2. ModelFigure 1(a) shows the inlet model used in the ex-periments. It is an axisymmetric mixed-compression

Figure 1. (a) Inlet model in wind tunnel. (b) Tip coneand pressure taps.

M.R. Soltani et al./Scientia Iranica, Transactions B: Mechanical Engineering 23 (2016) 1811{1825 1813

Figure 2. Schematic of the intake model and its instruments.

Table 1. Measurement inaccuracies (%).

�M1=M1 �P01=P1 �Re=Re �P=P �"=" ��=�

1.458 0.012 1.982 0.929, 1.421 2.418 1.421

inlet with design Mach number of 2.0 and L=d = 3:4.Bleed could be added or removed by replacing tip cones(Figure 1(b)). However, in this study, no bleed isapplied. A conical plug is located at the end of themodel to change the exit area of the inlet during thetests. The plug translates along the intake centerbodyvia a DC motor and a ball screw (Figure 2(b)).The inlet mass ow rate and back pressure ratio arecontrolled through changing the exit area. Note thatthe back pressure determines the normal shock positionand consequently design and o�-design conditions ofthe intake can be obtained.

2.3. Pressure transducers and test procedureSixty two sensitive pressure transducers have beenused to measure static and total pressures on themodel and wind tunnel walls. Several pressure tapshave been located on di�erent positions of the spikesurface to measure the static pressure distribution.Two multi-probe rakes, TR (Throat Rake) and MR(Main Rake) as shown schematically in Figure 2, havebeen located at the throat (x=d = 0:8 and � =270�) and at the exit (x=d = 2:4 and � = 90�)sections of the intake with blockage ratios of 2% and4.3%, respectively. Rake TR has 12 probes and isused to measure the boundary-layer pro�le and owbehavior at the throat section. Rake MR has 17probes and is used to measure the boundary-layerpro�le, inlet total pressure recovery, mass ow rate,and ow distortion at the exit face of the model. Twosingle-probe rakes (PR1 and PR2) are also locatedat x=d = 1:4 � � = 0� and at x=d = 1:8 � � =180�, respectively, for total pressure losses measure-ment. All sensors have accuracy of �0:1% of fullscale and a corresponding natural frequency responseof 150 KHz. An accurate industrial data acquisition

board is used. The frequency of measurement is2800 Hz.

The intake has been tested at a free-stream Machnumber of 2.0 without implementation of the bleed. Alltests were conducted at zero-degree angle of attack.At the beginning of each test, the plug was in therear position (fully open exit). Then, the plug wastranslated forward to reduce the exit area. For everyfree-stream Mach number, a similar set of eight exitareas was adjusted during the tests and pressures atsixty two points were obtained.

Measurement inaccuracies of some important val-ues are listed in Table 1. Two values have beenreported for static pressure since two di�erent typesof pressure transducers have been used in this work.

2.4. Flow visualization setupIn this experiment, both Schlieren and shadowgraphoptical techniques were used to visualize shock patternand ow structure on the external region of the inlet.Mirrors and light source were arranged in a Z-typecon�guration [36] and an accurate table with twodegrees of freedom was used to locate the knife-edge(razor blade in this case) at the focal of the receivingpart. A CCD camera with a recording speed of 1000frames per second (fps) was also used for taking thepictures.

3. Numerical method

A Computational Fluid Dynamics (CFD) solver devel-oped by authors was used to simulate the ow inside theinlet at its design free-stream Mach number, M1 = 2:0,in all operating conditions. In this code, Reynolds-Averaged Navier-Stocks (RANS) equations are solvednumerically. Neglecting body forces, these equations,


in two-dimensional conservative forms, are:

@Q@t

+@T@x

+@U@y

+ �V =@T�@x

+@U�@y

+ �V� + S;(1)

Q =

26666664��u��E�k�!

37777775 ; T =

26666664�u

P + �u2

�u��uH�uk�u!

37777775 ;

U =

26666664�v�uv

P + ��2

�vH�vk�v!

37777775 ; V =1y

26666664�v�uv��2

�vH�vk�v!

37777775 ;

Tv =

266666640�xx�xy

u�xx + v�xy � qx(�L + �k�t)@k@x(�L + �!�t)@!@x

37777775 ;

Tv =

266666640�xx�xy

u�xy + v�yy � qy(�L + �k�t)@k@x(�L + �!�t)@!@x

37777775 ;

Tv =

266666640�xr

�rr � ��u�xy + v�yy � qy(�L + �k�t)@k@x(�L + �!�t)@!@x

37777775 ; (2)

where Q denotes the conservative variable vector, Tand U are inviscid ux vectors, Tv and Uv are theviscous ux vectors in each spatial direction, V and Vvare the source terms associated with the asymmetry,and S is the source term due to the turbulence modelequations.

For a 2D axisymmetric problem, let � = 1. Usingexplicit �nite volume discretization, Eq. (1) becomes:

Qn+1i;j =Qni;j � �ti;j

Ai;j

"4Xk=1

(Fc)k�sk

#� ��ti;jVi;j

+�ti;jAi;j

"4Xk=1

(Fv)k�sk

#+ ��ti;jVvi;j ;

(3)

where:

Fc =

2664 �q�uq + nxP�vq + nyP�uH

3775 ; Fv =

2664 0nx�xx + ny�xynx�xy + ny�yynx�x + ny�y

3775 ;�x = u�xx + v�xy + k

@T@x

;

�x = u�xy + v�yy + k@T@y

: (4)

In the above equations, H is the total enthalpy, A is thearea of the cell, �s is the length of the cell face, and qis the velocity component normal to the cell face. Theconvective uxes are computed by the second-orderaccurate Roe scheme. Also, a �nite volume method,consistent with the overall discretization method, isused to calculate viscous uxes. Further descriptionsof the governing equations and the numerical consider-ations could be found in [37,38].

Viscosity coe�cient is calculated using the lin-ear interpolation of laminar and turbulent viscositycoe�cients. Laminar viscosity coe�cient is molecularviscosity and it has been calculated using Sutherlandrelation. The turbulent viscosity coe�cient, however,has been calculated by the Menter's two-equation eddyviscosity k � ! SST turbulence model [38]. The eddyviscosity of SST model is de�ned by [39]:

�T = (a1k)=max(a1!; F2): (5)

With a1 being a constant, equals the term @u=@y andF2 is a function that is one for boundary-layer ows andzero for free shear layers [39].

The grid used for the simulations is shown inFigure 3. This grid was generated by an elliptic gridgenerator and could be re�ned or stretched in all orpart of the physical domain. This structured grid isre�ned at the cowl lip and at the internal walls in orderto capture physics of the boundary layer ow.

An intensive grid resolution study was performedto ensure the independence of the numerical solutionfrom the grid size. Finally, a �ne grid with about 90000

Figure 3. Elliptic grid around the inlet of study andboundary conditions.


Figure 4. Comparison of the present numerical prediction with experimental pressure recordings, M1 = 2:0, � = 0, andEBR = 60%: (a) Static pressure ratio distribution on the spike; and (b) radial distribution for total pressure ratio atx=d = 2:4.

cells was chosen as the most optimum one. Further,near the wall, turbulent ow behavior is considered andthe �rst node (or cell centroid) is chosen at y+ equalto unity.

Figure 4(a) compares the numerical and exper-imental static pressure distributions on the spike forExit Blockage Ratio (EBR) of 60% and at a free-streamMach number of 2.0 at zero-degree angle of attack. Itcould be seen that relatively good agreement betweennumerical prediction and experimental data exists.The error seen in the region of throat may be due tothe e�ect of rake TR and struts blockage that have notbeen taken into account in the numerical prediction.However, maximum error in this region does not exceed25%. Total pressure ratio at the subsonic di�useris measured by the rake MR at x=d = 2:4 and iscompared with the numerical prediction in Figure 4(b).Again, good agreement between the experimental andnumerical data is achieved. The pro�le of Figure 4(b)further ensures that the extent of ow separation hasbeen simulated with acceptable accuracy.

Figure 5 compares the axial density gradientcontour together with shadowgraph shock structurevisualization for a free-stream Mach number of 2.0 atzero-degree angle of attack for a supercritical conditionto be de�ned in the next section. It can be seen thatthe location and inclination of shock waves have beensimulated precisely. It also veri�es good performanceof the numerical solver.

4. Inlet operating regimes

This section will remind di�erent operating regimes ofmixed-compression inlet under study and the corre-sponding shock patterns. Characteristic curve of aninlet, as shown in Figure 6, demonstrates variation oftotal pressure recovery of inlet versus inlet mass owratio. Total pressure recovery of inlet, �, is de�ned as

Figure 5. Comparison of numerical axial density gradientcontour with experimental shadowgraph image, M1 = 2:0and � = 0.

the ratio of the mean total pressure at the end of theinlet duct to the free-stream total pressure. For thecurrent inlet, mean total pressure at the end of the inletduct is measured by the rake MR. Mass ow ratio, ",is the ratio of captured mass ow rate to the mass owrate in the case of full ow operation (no spillage) [2].It is also de�ned as the ratio of free-stream to full owcaptured streamtube area.

" =_m1_mc

=A1Ac

: (6)

Characteristic curve of the inlet under study at a free-stream Mach number of 2.0, achieved by experimentalpressure recordings, is shown in the left-hand side ofFigure 6. As shown in this curve, three main operating


Figure 6. Experimental characteristic curve and operating regimes of mixed-compression inlet of this study andcorresponding shock pattern at M1 = 2:0.

regimes can be found for the inlet. These regimeswere obtained through changing the inlet exit area bymeans of plug during the experiments. When the inletexit area (Ae) is open and the back pressure is lowenough, the inlet operates at supercritical condition.Mass ow ratio is almost constant while back pressureratio increases in this operating condition. The verticalregion in the characteristic curve and the schematic (I)corresponds to this condition. According to schematic(I), normal shock is located in the divergent part of thedi�user for this operating region.

The terminal shock location is forced by applyingthe backpressure to the inlet (by combustion chamberin the real engine). In this case, increase in the surfacepressure in the divergent part together with the adversepressure gradient due to the shock makes the ow proneto separation and, consequently, low pressure recovery;also, high ow distortion occurs. As the exit area isfurther decreased, normal shock wave moves towardthe throat until it stands in the throat and the criticaloperating regime happens. The best operating pointof the inlet is the critical point as maximum MFRand TPR are achievable. Schematic (II) in Figure 6shows the shock pattern relevant to this case. Thenearly horizontal part in the curve, Figure 6(a), showsthe critical operating condition. As seen in the curve,maximum amounts for both mass ow ratio and totalpressure recovery are obtained in this case. By closingthe inlet exit area further beyond the critical point, nor-mal shock expels out of the inlet duct and ow spillagewould happen; as a result, the inlet mass ow ratiodeteriorates. In this case, interaction of the obliqueand the normal shock is inevitable (schematic (III),Figure 6(b). The ow would become unstable if theexit area is further decreased and the buzz phenomenonwould be triggered. In this case, inlet performancedecreases as it can be seen in characteristic curve ofthe inlet, Figure 6(a).

In all operating conditions of the inlet, interaction

of shock with boundary-layer would greatly a�ect the ow �eld as well as the inlet performance. Physicalaspects of SBLI in each operating region highly dependon the location of shock waves. According to this fact,types of ow separation in a mixed-compression inletcan be categorized. This task will be accomplished inthe following section and the ow �eld corresponding toeach category will be studied in the proceeding sections.

5. Classi�cation of SBLI formixed-compression inlets

For the mixed-compression inlets, compression is ac-complished by a series of oblique shocks and a ter-minal normal shock. When operating in supercriticalcondition, a portion of supersonic compression occursinside the inlet duct via an oblique shock train anda near-normal shock while in subcritical condition, allcontraction takes place out of the inlet duct via one orseveral oblique shocks (depending on the ramp design)and terminates with a normal shock. There existdi�erent types of ow interactions relevant to thesedi�erent shock structures.

Figure 7 shows the grey-scale contour of axialderivative of density for the Exit Blockage Ratio (EBR)of 61% at a free-stream Mach number of 2.0 and atzero-degree angle of attack. It could be consideredas the numerical Schlieren image of ow that is usefulfor understanding the shock structures inside the ductwhere experimental visualization of the ow is impos-sible. Comparing with schematics of Figure 6, it couldbe found that this �gure is related to a supercriticaloperating condition. As Figure 7(a) demonstrates, the ow is compressed by an oblique shock before enteringthe duct. The external compression for the case studyis done by a single conical shock due to the single-coneramp. The external oblique shock in the case of full ow (critical and supercritical operating conditions atthe design Mach number) impinges with the cowl lip


Figure 7. Numerical grey-scale contour of axial density gradient, M1 = 2:0, � = 0, and EBR = 61%.

and is then re ected towards the spike surface. Thisincident shock separates the ow on the spike surface.Due to the formation of separated region, a separationshock forms and interacts with the re ected obliqueshock.

Figure 7(b) depicts the enlarged picture of thisoblique shock wave boundary-layer interaction zone.Separated ow reattaches downstream and a separationbubble is formed. An expansion fan and a reattachmentshock wave are also produced to change the owdirection and to expand it. The ow then passesthrough consecutive re ections of oblique shock fromboth upper and lower walls of the duct and forms anoblique shock train. In the present paper, interactionsof re ected oblique shocks with the boundary-layertogether with the interactions of oblique shocks witheach other are called oblique shock interactions. Detailson the physical phenomena related to these interactionswill be presented in the subsequent sections.

The ow passes terminal normal shock afterpassing the oblique shock train. If no boundary layerexists, the pressure would increase discontinuously by asingle normal shock. However, in the real ow, adversepressure gradient due to the shock separates the owat normal shock foot and the shock structure gets theshape of lambda. Figure 7(c) illustrates the enlargedimage of ow at the normal shock location. The owbecomes subsonic downstream of the normal shock, butthe extent of separation increases. Flow is retarded inthe separation region and the major part of the mass ow passes through the upper and lower separationzones (core region). As the e�ective ow area decreases,the ow accelerates again and becomes supersonic inthe core region. In this case, ow acts like passingthrough a supersonic di�user and a weaker normal

shock is generated. This process continues; however,the generated shocks become weaker and the distancebetween them decreases. Finally, the ow becomesfully subsonic. The region of successive normal shocks,which is caused by the interaction of normal shockwith boundary-layer, is called normal shock train inthe literature [20].

The subsonic ow then goes through a mixingregion where there is no shock; but pressure graduallyincreases to some extent. Static pressure in this regiondoes not change along the vertical axis. The detailsfor the ow in this region will be presented later inSection 7. The term pseudo-shock is used for thewhole region of normal shock train and mixing region.Depending on the location of normal shock, or bettersay the inlet backpressure, the length of pseudo-shockmay be di�erent.

For the subcritical operating condition where thenormal shock expels out of the inlet duct, interactionof normal shock with boundary-layer can be found aswell. This interaction may or may not cause owseparation. Figure 8 shows the ow visualization

Figure 8. (a) Shadowgraph ow visualization for:M1 = 2:0, � = 0, and EBR = 65%. (b) Schlieren owvisualization for: M1 = 2:0, � = 0, and EBR = 70%.


Figure 9. Classi�cation of di�erent SBLI ows related toa mixed-compression inlet.

images for 2 subcritical operation points. Figure 8(a)depicts the shock structure for the inlet at a free-stream Mach number of 2.0 and an exit blockageratio of 65%. As shown in the �gure, the normalshock is not strong enough to separate the ow, butthere exist weak interactions and normal shock footbifurcates. Yet, the ow in this case is stable. Byfurther increasing the EBR, shock becomes strongerand the scale of separation grows. This causes theself-induced oscillations of shock. The phenomenon iscalled Buzz. Figure 8(b) illustrates the shock structureof ow in this case using a Schlieren image. Dueto a greater ow separation, the angle of separation-shock and its strength increase; consequently, shockbifurcation increases and normal shock gets the shapeof lambda. Further study of ow physics in this case isconsidered in Section 8.

Therefore, interactions of shock with boundary-layers relevant to mixed-compression inlets can beclassi�ed into three major groups. Figure 9 indicatesthe classi�cation chart for a mixed-compression inletSBLI ow according to the operating conditions. Fur-ther discussion on each ow interaction phenomenonrelevant to mixed-compression inlet on the basis ofnumerical and experimental results will be brought inthe upcoming sections.

6. Oblique shock interactions

Figure 10 depicts variations of the wall static pressureratio along the interaction zone together with thecontour of Mach number for the present inlet at a free-stream Mach number of 2.0 and for an Exit Blockageratio of 60%. The level of ood contour is boundedin order that the region of subsonic and supersonic ow can be divided and the sonic line becomes rec-ognizable. As shown in this �gure, a separationbubble forms downstream of the separation point S. Adividing streamline between points S and R can be seenthat separates the recirculating bubble from the owstreaming from upstream to downstream. An energy

Figure 10. Wall pressure distribution in a shock-inducedseparated ow together with contour of Mach number forM1 = 2:0, � = 0, and EBR = 60%.

Figure 11. Sketch of ow induced by a shock re ectionwith separation.

transfer takes place from high-speed ow outside thebubble towards the separated inner region. This factcauses the ow velocity to increase as they approachdownstream and reattaches the streamline [1]. Due tothe strong interaction of shock with boundary-layer,this inner region is highly a�ected by the viscosity. Asit is illustrated in Figure 10, speci�c shock patterns areshaped by this interaction.

Figure 11 shows a schematic of the ow inducedby a shock re ection with separation. A separationshock is located upstream of point S and de ects the ow direction upward. This separation shock interactswith the incident shock. The slope of the separationbubble is smooth; hence, the compression near thesurface is performed by several compression waves. Inthe reattachment part, the direction of ow shouldbe changed downward; therefore, an expansion fan isformed. Downstream of the separation bubble, the ow


direction becomes parallel to the surface by means of areattachment shock. As seen in Figure 11, incidentshock penetrates the rotational inviscid part of theboundary-layer and bends due to the reduction of localMach number. The intensity of shock weakens andvanishes when it reaches the boundary-layer sonic line.

The wall pressure distribution of Figure 10 ini-tially exhibits a steep rise, associated with separation.Another more progressive pressure rise is seen to occurduring the reattachment. It is found from the pressuredistribution that there exists considerable deviationfrom sudden pressure jump of the pure inviscid solu-tion, Figure 10. The reason is that in the strong shockinteractions, the viscosity plays a key role in the owstructure. Subsequent oblique shocks, re ected fromupper and lower walls of the inlet duct, also interactwith boundary-layer when impinging with the oppositesurface; but the interactions become weaker and noseparation would occur.

However, the question is that how such an inter-action a�ects the inlet performance? Figure 12 showsnumerical results for the radial distribution of totalpressure ratio across the separation zone for EBR =61%. Shaded region indicates the total pressure lossesin comparison with the inviscid shock re ection. It isfound from this �gure that interaction of oblique shockwith spike boundary-layer creates a region of dead owand reduces the total pressure of the inlet. At theend of the �rst pressure rise zone, total pressure lossis maximum due to the extent of the ow separationin that position. Also, interactions of shock waveswith the boundary-layer of the internal surface of inletcowl result in some total pressure losses, Figure 12.Using some means of boundary-layer removal wouldhelp avoiding the total pressure losses.

7. Normal shock train and pseudo-shock

Figure 13 shows contour of the axial density derivativetogether with the static pressure distribution on the

Figure 12. Numerical results for radial distribution oftotal pressure ratio across the interaction zone,EBR = 61%.

Figure 13. Numerical wall pressure distribution andpressure distribution across a horizontal line together withthe corresponding contour of axial density derivative,M1 = 2:0, � = 0, and EBR = 60%.

wall and in the middle line of the duct for the presentmixed-compression inlet at a free-stream Mach numberof 2.0 and for Exit blockage ratio of 60%. A normalshock train inside the duct appears. Dark regionsbehind the shocks demonstrate subsonic region. Itcould be found that the ow behind the shock goesthrough subsonic to supersonic isentropically and againdecelerates to subsonic speed through a subsequentnormal shock. Pressure increases sharply through eachshock and then decreases behind the shock until itreaches the downstream normal shock. It is foundfrom either the pressure distribution or the contourthat the strength of shocks decreases as they approachdownstream. The region in which the shocks arelocated is called the shock train region. After thelast shock, the ow becomes subsonic, but there existsvelocity di�erence between the core ow and the near-wall region. As a result, a momentum exchange processbetween the core and the inner region ow takes placethat makes the ow fully developed at the end of theregion. The static pressure becomes constant along theradial direction, as seen in Figure 13, but the velocitypro�le changes continuously until the ow becomesuniform.

Figure 14 depicts axial density derivative forthe mixed-compression inlet at di�erent back pressureratios for a free-stream Mach number of 2.0. Forlow back pressure ratios, most of the compression isdone by oblique shock train and a single normal shockis seen. In this case, separated ow at the engineface highly a�ects the ow distortion. Increasing thebackpressure ratio pushes the terminal normal shockupstream and the normal shock train forms. Formoderate EBRs, the length of normal shock train and


Figure 14. E�ect of back pressure ratio on the numericalcontour of axial density derivative, M1 = 2:0.

the mixing region as well as the number of consecutiveshocks is large. As EBR further increases, the length ofpseudo-shock decreases. If the length of pseudo-shockbecomes smaller in comparison with the throat length,the amount of total pressure loss decreases.

Figures 15 demonstrates experimental measure-ments for total pressure recovery and ow distortion,respectively, at rake MR for di�erent exit blockageratios at free-stream Mach number of 2.0 and at zero-degree angle of attack. For cases with buzz, thetime average of pressure signal is used. For EBR =50%, variation of the total pressure across the radialdirection is high since the terminal shock is locatedaft and the separated ow region is thicker. As theblockage ratio increases, the terminal shock movesupstream and the separated region becomes thinnerand total pressure increases. For EBR = 62:5%, itis seen that a near-constant total pressure distributionis achieved, Figure 15(a). The ow distortion for thisblockage ratio is also lower; however, a small deviationfrom the uniform distribution near the upper wall

occurs. Having performance curve of Figure 6 andshadowgraph image of Figure 8(a) in mind, we knowthat at EBR = 65:0%, the present inlet performs inthe subcritical condition. Therefore, the separation dueto the terminal normal shock is completely eliminatedat the engine face and as a result, a more uniformstagnation pressure distribution is achieved as shownin Figure 15(a) for EBR = 65%. For the subsequentsubcritical operating conditions, the ow distortionremains rather low. Losses due to buzz phenomenonand ow separation on the compression surface causethe amount of stagnation pressure to reduce as the inletmass ow ratio decreases.

Figure 16 shows the pressure spectra at x=d =2:4 measured by rake MR for di�erent exit block-age ratios before buzz onset at a free-stream Machnumber of 2.0 and at zero-degree angle of attack.For EBRs equal to 55.0% and 60.0% at measuredpressure spectra, this �gure indicates high magnitudeat almost all frequencies, which is a typical behaviorof separated ow. An important point is that theamplitude of pressure signal at di�erent frequenciesfor EBR = 60:0% is lower than the one for EBR =55:0%. As the terminal normal shock moves upstreamthrough increasing the back pressure, the pseudo-shockapproaches upstream and its length decreases. As aresult, the momentum exchange between central core ow and low-speed dissipative ow starts earlier forgreater EBRs and because of this oscillations of ownear the wall, it decreases. For higher exit blockageratios, one cannot �nd any considerable magnitudesat high and at moderate frequencies. This is anotherreason for the trend of ow distortion that is illustratedin Figure 15(b).

Therefore, it is seen that the pseudo-shock highlya�ects inlet performance parameters, especially owdistortion, at the engine face. On the other hand,pseudo-shock has some dynamic distortion e�ects thatstem from the self-excited oscillations of shock-train.

Figure 15. (a) Experimental radial total pressure distributions at rake MR at di�erent EBRs, M1 = 2:0 and � = 0. (b)Experimental ow distortions at rake MR for di�erent EBRs at M1 = 2:0 and � = 0.


Figure 16. Spectra of measured wall pressure for di�erent exit blockage ratios at x=d = 2:4, M1 = 2:0, and � = 0.

Figure 17. Spectra of measured total pressure for two EBRs at r=d = 0:27, x=d = 2:4, M1 = 2:0, and � = 0.

When shock interacts with boundary-layer, the loca-tion of shock cannot be determined easily since it uctuates with time, even if boundary conditions areheld constant upstream and downstream of the shock.

Figure 17 shows spectra of total pressure mea-sured at x=d = 2:4 and in the centreline of inletduct (r=d = 0:27) for a free-stream Mach numberof 2.0. Wall pressure spectra for EBR = 62:5%and EBR = 65:0%, as shown in Figure 16, has noconsiderable oscillation frequencies. Furthermore, totalpressure distribution of Figure 15(a) con�rms that thewidth of retarded ow region is far less than the lowerexit blockage ratios. Therefore, the ow in the coreregion at these exit blockage ratios is expected to beuniform while the upstream and downstream bound-ary conditions are constant. However, as Figure 17illustrates, several active frequencies can be found in

the total pressure spectra of stagnation pressures. Thereason may be oscillations of the pseudo-shock thatcause the downstream total pressure to uctuate. Thestrength of normal shock trains may di�er as they moveupstream and downstream. In correlation with theshock strength, total pressure loss due to shock di�ersand makes the total pressure at the end of the inletduct change. Meanwhile, no distinct frequency can bedetected to assign for the pseudo-shock oscillations.

Total pressure tap of Figure 17 is located nearlyat the end of inlet duct. At EBR = 62:5% and 65.0%,pressure tap is located at the end of mixing regionof pseudo-shock and in the separated ow of spikesurface. Thus, oscillations of pseudo-shock structuredo not lead to an alternating total pressure change inthis region, but inject some oscillatory perturbationsinto the mixing region. This leads to a set of random


oscillations and in this way, a set of frequencies withconsiderable magnitude can be found in the pressurespectra. The spectra of EBR = 65:0% involve morefrequencies with considerable magnitude in comparisonwith the EBR = 62:5%, while the ow is expected tobe less oscillatory due to elimination of the pseudo-shock at EBR = 65:0%. The expelled normal shockfor EBR = 65:0% interacts with the boundary-layerof external compression cone that leads to little buzzoscillations. This ow phenomenon is discussed in thenext section.

8. Subcritical interactions

As the inlet back pressure increases, the upstreamnormal shock is pushed until it expels out of the inletduct. In this case, interaction of normal shock withboundary-layer occurs. For moderate back pressureratios, the interaction is weak (Figure 8(a)). Furtherreduction of exit area strengthens the normal shock andthe boundary-layer becomes prone to separation.

Figure 18 shows schematic of the normal SBLItogether with a Schlieren image of ow �eld for thepresent mixed-compression inlet. Separation zone actslike a viscous wedge and a separation shock forms. Thisshock interacts with normal shock in a point knownas triple point and a slip line emits from the pointof interaction across which the ow velocity changessharply. Shock foot declines near the separation zoneand creates a lambda-like structure. The separationzone grows inside the duct and results in ow spillage.In this way, separation blocks the ow direction andincreases the inlet back pressure. It is found to beone of the mechanisms of Buzz initiation known asDailey criterion [40]. This mechanism results in highamplitude oscillations of normal shock and a�ects theinlet ow stability.

Another buzz mechanism was found by Ferri andNucci in 1951 [41]. They concluded that buzz startswhen vortex sheet, which stems from interaction of

Figure 18. (a) Schlieren image of ow �eld. (b)Schematic of normal SBLI of mixed-compression inlet.

Figure 19. Power spectral density of sensor S7 atdi�erent EBR values, x=d = 0:374, M1 = 2:0, and � = 0.

shock waves, collides with the cowl inner surface.Velocity discontinuity across the vortex sheet causesthe ow on internal surfaces of the duct to separateand di�user chocking results. This mechanism leadsto low-amplitude high-frequency oscillations of normalshock wave.

For the present inlet, the dominant mechanism isDailey criterion. Figure 19 shows the power spectraldensity of pressure recording for a tap on the externalcompression cone surface. It is seen that signi�cantfrequencies are detectable in relation with buzz forvarious EBRs. The fundamental frequency of buzzincreases as the exit blockage ratio increases. Notethat as the mass ow ratio reduces the strength ofthe shock, interaction increases. To better realizethe behavior of boundary-layer during a buzz cycle,Schlieren images of the ow �eld are provided inFigure 20. This �gure shows four consecutive instantsin a big buzz cycle (high-amplitude oscillation). Thetime interval between each image is 1ms. It is seen thatas the time interval increases, the separation zone growsand pushes the upstream normal shock towards theincoming ow. Extent of the separation region is seen

Figure 20. Schlieren images of four consecutive instantsof buzz: M1 = 2:0, � = 0 and EBR = 75:0%.


to increase and when the normal shock is positionedin the most upstream location, t = 4 ms, the inletis completely blocked. This �gure shows the greatstrength of SBLI for the present inlet. Therefore, itcan be concluded that application of ow control by anymeans, such as the boundary-layer suction, is essentialfor this inlet.

9. Conclusion

This study reveals the existence of various shock waveboundary-layer interactions relevant to the supersonicinlets. Results show that these ow interaction phe-nomena have di�erent e�ects on the stability and onthe performance of the inlet. Interaction of terminalnormal shock with internal duct boundary-layer causespseudo-shock phenomenon that leads to increase in ow distortion and reduction of total pressure recovery.In addition, interaction of normal shock wave withexternal cone boundary-layer causes buzz instabilityand degrades inlet performance. The unsteady natureof ow due to shock boundary-layer interactions is alsodetected by means of experimental measurements. Insupercritical operating condition, pseudo-shock has anoscillatory nature that may cause dynamic distortionat the engine face. In subcritical operating conditionthat normal shock resides on the external compressioncone, normal shock interacts with boundary-layer inthat region. This interaction, if the back pressureratio is high enough, leads to ow separation andmay even chock the inlet. It causes self-excited owoscillations, called buzz, and speci�c frequencies can befound for oscillations in the measured pressure spectra.Flow stability of inlet highly depends on the buzzcharacteristics. In order to avoid harmful e�ects of suchinteractions, ow control devices such as boundary-layer bleed should be applied.

Consequently, behavior of SBLI ow phenomenashould be understood carefully in order to consider thecorresponding e�ects of interactions during the inletdesign process and for designing ow control devices.

Acknowledgement

The authors gratefully acknowledge the supports of theMesbah Research Institute.

Nomenclature

Latin letter

Ac Inlet capture area (m2)A1 Captured free stream area (m2)d Intake maximum outer diameter (m)L Intake length (m)

_m Mass ow rate through inlet (kg/s)M Mach numberP Pressure (Pa)

Greek letter

" Mass ow ratio, A1=Ac� Pressure recovery� Angle of attack (deg)� Rotational angle (deg)� Cone angle (deg)

Subscripts

0 Total conditions1 Free stream conditions

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Biographies

Mohammad Reza Soltani received his PhD degreein Aerodynamics from the University of Illinois atUrbana-Champaign, USA, and is now Professor in theAerospace Engineering Department at Sharif Univer-sity of Technology, Tehran. His research interestsinclude applied aerodynamics, unsteady aerodynamics,wind tunnel testing, wind tunnel design, and dataprocessing.

Abbas Daliri received his BS degree in MechanicalEngineering from Ferdowsi University of Mashhad,Mashhad, Iran. He has MS in Aerodynamics from theAerospace Engineering Department at Sharif Univer-sity of Technology, Tehran, Iran. He is now a PhDcandidate of Aerodynamics at Ferdowsi University ofMashhad, Mashhad, Iran. His �eld of interest isexperimental aerodynamics and uid mechanics andwind tunnel testing.

Javad Sepahi Younsi was born in 1985 in Younsi,Gonabad, Iran. He received his MS and PhD degreesin Aerodynamics from the Aerospace Engineering De-partment at Sharif University of Technology, Tehran,Iran. He is now Assistant Professor in the Mechanicaland Aerospace Engineering Department at FerdowsiUniversity of Mashhad, Mashhad, Iran. He works inthe �eld of numerical and experimental aerodynam-ics.

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