Supersonic inlet buzz detection using pressure measurement on wind tunnel wall

Aerospace Science and Technology 86 (2019) 782–793

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Aerospace Science and Technology www.elsevier.com/locate/aescte

Supersonic inlet buzz detection using pressure measurement on wind tunnel wall Mohammad Farahani a,∗,1 , Abbas Daliri b,2 , Javad Sepahi Younsi b,2 a b

Sharif University of Technology, 145888, Tehran, Iran Ferdowsi University of Mashhad, 91779, Mashhad, Iran

a r t i c l e

i n f o

Article history: Received 25 October 2018 Received in revised form 30 January 2019 Accepted 1 February 2019 Available online 6 February 2019

a b s t r a c t Feasibility of an innovative buzz detection technique through measuring the static pressure outside a mixed-compression supersonic inlet is studied. The buzz is an instability phenomenon that occurs almost in all supersonic inlets. During the buzz, shock oscillation along with pressure and mass flow fluctuations affects the performance characteristics of the inlet. The main objective of this paper is to introduce a simple and easy-to-implement method for investigation of the buzz phenomenon in a supersonic inlet. The experimental data for far field-based are compared with those of the model-based one at free stream Mach numbers of 1.8, 2.0, and 2.2 and at zero degrees angle of attack for a mixed-compression inlet. The results show that this technique can measure exact value of buzz frequency as well as its onset. The present method uses pressure data obtained from the wind-tunnel wall instead of measuring the pressure inside or on the model surfaces which in most cases is very hard. However, to sense flow oscillations, caused by the buzz onset the sensors on the wind-tunnel wall must be located downstream of the point where the oblique shock from the spike impinges on the tunnel wall. The location of the measurement point as well as the distance between the sensor and the origin of the shock wave system are very important. © 2019 Elsevier Masson SAS. All rights reserved.

1. Introduction Supersonic inlets play an important role in the overall propulsion system operation, efficiency and aircraft maneuverability. In all flight conditions, the inlet should provide the required air flow with an appropriate quality at special velocity and pressure needed for the combustion unit of the engine with the lowest possible drag and irreversibility. Thus acceptable performance should be obtained at different flight regimes and angles of attack. Stability is one of the most important aspects of the flow quality [1]. At supersonic speeds a phenomenon called buzz, for both external and mixed compression inlets, which is associated with the instability of shock structure occur and has significant effects on the performance and other characteristics of the propulsion system. Buzz is known as self-sustained shock oscillations that occurs in supersonic inlets when the mass flow becomes lower than a cer-

*

Corresponding author. E-mail addresses: [email protected] (M. Farahani), [email protected] (A. Daliri), [email protected] (J.S. Younsi). 1 Department of Aerospace Engineering, P.O. Box 11365-8639. 2 Department of Mechanical Engineering, P.O. Box 91775-1111. https://doi.org/10.1016/j.ast.2019.02.002 1270-9638/© 2019 Elsevier Masson SAS. All rights reserved.

tain value. This unstable phenomenon is commonly due to several reasons such as complex shock-boundary layer and/or shock-shock interactions [2]. Large amplitude oscillations of shock structure results in pressure fluctuations and total pressure recovery reduction. In addition, this undesirable phenomenon leads to engine surge, combustion instability, thrust loss, and even structural damages [1]. For the case of mixed compression inlet, inlet unstart and the resulting combustion flameout might occur too [1,2]. Numerous experimental investigations were performed on the supersonic inlet buzz during the past 75 years. Among the earlier studies, are the experiments of Ferri and Nucci in 1951 [3] and Dailey in 1954 [4] that lead to important findings on the buzz initiation criteria. Ferri and Nucci concluded that buzz instability initiates when a velocity discontinuity across a vortex sheet that originates at a shock-shock interaction point (triple point) moves across the internal surface of the cowl lip. If this velocity difference becomes large enough, flow separation on the inner surface of the cowl with a consequent choking in the subsonic diffuser will occur. Such a description of the buzz is known as Ferri criterion or little buzz in the literature [3]. Dailey pointed out that the mass flow entering the diffuser suddenly is cut off by a strong interaction between the expelled normal shock and the boundary layer on the external compression surface. As the extent of this sepa-

M. Farahani et al. / Aerospace Science and Technology 86 (2019) 782–793

783

Nomenclature A d db D I L M P r Re T

amplitude of oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pa maximum body diameter or diameter of the inlet at the exit plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . mm diameter of the body blocked by the plug at the exit plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . mm hydraulic diameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m sound wave intensity . . . . . . . . . . . . . . . . . . . . . . . . . . W m−2 duct length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . mm Mach number pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N m−2 distance from the acoustic wave source . . . . . . . . . . . . m unit Reynolds number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1/m temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K

ration increases, it may obstruct the inlet and triggers the buzz. This explanation is called Dailey criterion or big buzz and entails high amplitude and low frequency oscillations [4]. Combination of the above two phenomena was also reported by Soltani et al. [5]. Other experimental studies were performed on the buzz cycle description for different supersonic inlets [5–18]. Effects of various parameters such as the Mach number [5], angle of attack [11,12] and bleed parameters [13–15] were also studied experimentally. Buzz studies in almost all experimental investigations were performed by measurement of pressure fluctuations on the internal and/or external surfaces of the inlet through high-frequency pressure transducers. In addition, some researchers used other tools such as Schlieren or shadowgraph image processing for measurement of buzz specifications [16–18]. Comparison of the visualization results with pressure measurements were done in these investigations, and good agreements are reported for several special cases where the large amplitude oscillations occur. The aforementioned buzz measurement technique that uses pressure data on the body surface has some difficulties. Buzz is an unsteady phenomenon with different oscillation frequencies depending on its mechanism and inlet type. Therefore, pressure transducers should be installed near the pressure taps to avoid time lag in the tubes (tube length should be short, 0.3 m, for a tube diameter of 3 mm with a pressure difference of 1 kPa to achieve negligible time lag [19]). On the other hand, common supersonic wind tunnels have small test sections in comparison with the low-speed tunnels and because of blockage limitations, models should be small. Consequently, installation of miniature fast-response high-resolution pressure transducers and their cables inside small wind tunnel models is very difficult, time-consuming and expensive. This problem is more profound for axisymmetric inlets because they could not be installed on the wind-tunnel side wall similar to the twodimensional inlets. Difficulties increase when it comes to troubleshooting or repairing a transducer or connection. In the cases, where bleed is applied, the internal space of the spike is used as the bleed duct and the risk of malfunctioning of transducers, tubes and wiring increases. The case of optical visualization has its own adversities too. Accurate Schlieren setup is hard to achieve. Meanwhile, there is no compiled optical buzz measurement method and current methodologies are case-dependent. In addition, this technique is useful only to find a single high-amplitude frequency, whereas the buzz may have multi frequencies. For most industrial and research studies regarding buzz measurement, these expenses are not affordable and may not be economical. In addition, as mentioned above, extracting quantitative results is not applicable for all cases. This paper introduces an innovative easy-to-implement, lowcost technique to detect and measure buzz characteristics. The

time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . s velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m s−1 freestream velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m s−1 axial coordinate from the nose of the inlet . . . . . . . mm Acoustic attenuation coefficient . . . . . . . . . . . . . . . . . . m−1 Shock angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . deg. Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kg m−3

t u U x

α β

ρ

Subscripts

∞ swi

free stream conditions point of impingement collision of shock wave with the wind tunnel wall

method uses a few common fast-response pressure transducers installed on the wind-tunnel wall and governs conventional signal processing methodologies to study buzz characters. This method greatly reduces the cost of model manufacturing in regard to drilling pressure taps, wiring, etc. and wind-tunnel testing. Using novel manufacturing methods such as 3D printing or rapid prototyping, this buzz measurement technique reduces the distance between computational inlet design analysis and wind-tunnel testing. This methodology could be governed for fast and low-cost evaluation of the effectiveness of different flow control means such as plasma and ZNMF actuators to control the buzz in small supersonic wind tunnels. The method may also be applicable to other problems concerning with the shock oscillation phenomenon such as buffeting. This paper describes the techniques used for the experiments and compares the results for both far field and near field buzz measurements using transducers installed in the model (model-based) at free stream Mach numbers of 1.8, 2.0, and 2.2 and at zero degrees angle of attack for a mixed-compression inlet. As it will be shown, the results are in good agreements for all cases examined in this investigation. 2. Experimental setup and procedure 2.1. Wind tunnel and flow condition The experiments were carried out in a continuous suction-type wind tunnel with a rectangular test section of 60 × 60 cm2 . The turbulence intensity of the flow in the test section ranges from 0.4% to 1.4%, depending on the free stream Mach number [11]. There exist, bleed holes on the upper and lower walls of the test section to stabilize and control wind tunnel shock and other reflected waves. Side wall windows of the test section have been made up of accurately manufactured optical glasses to allow the flow and shock pattern observation by Schlieren and shadowgraph flow-visualization techniques. The tunnel is indraft, so the totalpressure and temperature in the test section are constant, atmospheric. All tests were conducted at zero degrees angle of attack and at three different freestream Mach numbers of 1.8, 2.0 and 2.2 corresponding to Reynolds numbers of 1.1 × 107 , 1.0 × 107 , and 0.9 × 107 per meter, respectively with freestream total conditions of P 0 = 84 kPa and T 0 = 302 K. Measurement inaccuracies of the free stream parameters are listed in Table 1 [20]. Table 1 Free stream flow measurement Inaccuracies (%).

 M ∞ /M ∞

 T 0∞ /T 0∞

 P 0∞ /P 0∞

Re/Re

1.458

0.033

0.012

1.982

784

M. Farahani et al. / Aerospace Science and Technology 86 (2019) 782–793

Fig. 1. a) Inlet model in the wind tunnel, b) wind tunnel wall transducers configuration.

Fig. 2. Schematic of intake model and wind tunnel wall.

2.2. Model Fig. 1a, shows the wind-tunnel model used for the experiments. It is an axisymmetric mixed-compression inlet with a design Mach number of 2.0 and has an L/d ratio of 3.4. A conical plug is located at the end of the model to change the exit area that leads to the mass flow variations of the inlet during the tests. The plug translates along the body centerline through a DC motor and a ball screw (Fig. 2). The inlet mass flow rate and back-pressure ratio are controlled via changing the exit area. Note that the back-pressure determines the normal shock position and consequently design and off-design conditions of the inlet can be obtained. 2.3. Pressure transducers and test procedure Fast-response pressure transducers were used to measure pressure fluctuations on the model and on the wind-tunnel walls. Locations of pressure transducers on the wind-tunnel wall are shown in Fig. 1b and in the schematic drawing of Fig. 2. Several pressure taps have been located at different positions on the spike surface of the model to measure the static pressure distribution. As seen from Fig. 2, five high resolution pressure transducers are located on the wind-tunnel wall. The locations of these transducers are listed in Table 2. All sensors have an accuracy of ±0.1% of full scale and have natural frequency response of 150 KHz. An accurate

Table 2 Position of pressure transducers on the wind tunnel wall. Sensor name

x/d

W1 W2 W3 W4 W5

−0.2 1.3 5.3 7.0 7.6

data-acquisition board was used. The measurement frequencies of all tests were set to 2.7 kHz. Tests were conducted at free stream Mach numbers of 1.8, 2.0, and 2.2 and at zero degrees angle of attack. At the beginning of each test, the plug was in the rear position (fully open). Then, the plug was moved forward to reduce the exit area for every freestream Mach number. A set of eight exit areas were adjusted during the tests, and wall pressures were measured for each case. A parameter known as the exit blockage ratio (EBR) is introduced and will be used through the paper that identifies the position of plug. This parameter is defined as the ratio of the exit duct height blocked by the plug to the total height of the duct at the exit (EBR = db /d). Measurement inaccuracies of pressure ( P / P ) measured by the transducers used in the tests are 0.929 [20].

M. Farahani et al. / Aerospace Science and Technology 86 (2019) 782–793



2.4. Flow visualization setup

D2 Dt 2

In this experiment both Schlieren and shadowgraph optical techniques were used to visualize both shock pattern and flow structure on the external region of the inlet spike. Mirrors and light source were arranged in the Z-type configuration [22] and an accurate table with two degrees of freedom was used to locate the knife-edge at the focal of the receiving part. A high speed camera with recording speed of up to 1000 frames per second (fps) was used to record shock wave oscillations. 3. Theoretical background 3.1. Propagation of acoustic perturbation in a supersonic wind tunnel Shock wave oscillations in a supersonic flow can be considered as a source of acoustic perturbation. To investigate the problem, it is essential to explore the propagation of acoustic perturbations in supersonic flow. In order to calculate the local value of acoustic wave propagation parameters such as pressure (p) and velocity (u) in a more realistic case of wind tunnel tests, one must apply the physical principles using conservation of mass, momentum and energy for a viscous adiabatic flow. In a supersonic wind tunnel, wave propagates in three dimensions but for the sake of simplicity propagation of one-dimensional plane wave in a duct with a supersonic mean flow velocity is considered here. For an acoustic perturbation, one can write: 



ρ =ρ +ρ ,

p=p+p,

u = U∞ + u



(1)

− a2

785

 ∂2 D + 2 ( C U + a α ) p=0 f Dt ∂ x2

(5)

The above partial differential equation has a solution of [23]:

  α + C f M + jk p (x, t ) = C 1 exp − x 1+M   α + C f M + jk exp( j ωt ) + C 2 exp x 1−M 

(6)

where ω is the angular frequency and k is the angular wave number and is equal to ω/a. This solution shows that the total aeroacoustic attenuation in a moving medium (α + C f M) is sum of the contributions of the viscothermal effects and turbulent flow friction and the factors 1 ± M that represents the convective effect of the mean flow applies to the attenuation constants as well as to the wave numbers. In a supersonic flow, perturbations propagate only downstream so the solution for the left running waves do not really exist. It can be shown that in the case of supersonic flow (M > 1) both terms of Eq. (6) exist and give physical solutions. Equation (6) can be rewritten as,







p (x, t ) = C 1 exp −α + x · exp j



ωt − k+ x

   

+ C 2 exp −α − x exp j ωt − k− x

(7)

where:

α± =

α+CfM |1 ± M |

k± =

,

k

(8)

|1 ± M |

where U is the wind-tunnel freestream velocity. Assuming that perturbations of pressure and velocity in comparison with mean flow properties is small, i.e.

Eq. (7) show that the pressure wave in each location has a phase lag with the initial pressure wave emitted from the source and is equal to (k± x.) Considering the real or imaginary part of Eq. (7) and taking the root mean square, one can write:



RMS Re p (x, t ) = RMS Im p (x, t ) = P RMS (x)

ρ ρ

2

  1,

p p

2

  1,

u U

2 1

Du

∂p + 2αρ au + C f ρ u 2 = 0 (3) ∂x where 2αρ au is the pressure drop per unit length due to the viscothermal friction and C f ρ u 2 is the pressure drop per unit length due to the boundary-layer friction or wall friction. α is the attenDt

+

uation coefficient due to viscosity and for flows with rigid walls and thick boundary-layers, it can be calculated from the following equation [24]:



α=

2 aD

·

πμ f ρ

(4)

where D is the hydraulic diameter of the duct, a is the average speed of sound, μ is the dynamic viscosity, f is the wave frequency and ρ is the bulk density. C f in Eq. (3) is the duct frictioncoefficient ratio (C f = F /2D). In this study, the flow is assumed to be adiabatic so attenuation due to the heat conduction is not considered. For a small amplitude wave propagation in a moving medium with no transverse gradient, the thermodynamic process could be assumed to will remain almost isentropic and with further simplifications of Eq. (3), the wave equation for the pressure yields [23],





(2)

Thus terms involving quadratic parts in the acoustic perturbation variables p, ρ , and u can be neglected. According to reference [23], one-dimensional equation for dynamical equilibrium with viscothermal dissipation and turbulent friction loss can be written as:

ρ





   

1 = √ · C 1 exp −α + x + C 2 exp −α − x 2

(9)

Root mean square is a measure of the amplitude of a harmonic wave [25]. Therefore, Eq. (9) shows that the amplitude of the pressure wave decreases exponentially with the temporal location with an attenuation coefficient of α ± . For an adiabatic flow (i.e. T 0 (x) = T 0∞ ) inside a wind-tunnel assuming that at each point the isentropic relations are valid and using the Sutherland’s law for the viscosity of ideal gas [26], the attenuation coefficient can be rewritten as a function of the Mach number as: 3

T 04∞ f

α=A·

1 2

1 2

·

P0 where:

A=

1 D

 ·

4π C ∗

S = 110.4 K,

γ

γ +1

1

( T 0∞ + S · B ( M ))

1 2

 B (M ) = 1 +

, ∗

C = 1.458 × 10

· B ( M ) 4(γ −1)

γ −1 2

(10)

 M2 ,

−6

Fig. 3 shows variations of the total aeroacoustic attenuation versus Mach number for different friction coefficients, using equations (7) and (10) for T 0∞ = 302 K and P 0 = 80 kPa. This figure shows that values of α − is approximately one order of magnitude greater than the values α + as it is expected from Eq. (8) for Mach numbers between 1 and 2. In other words the second term of Eq. (9) has a greater influence in attenuating the pressure wave as it approaches downstream. It further implies that viscosity does not have considerable contribution in the attenuation coefficient

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M. Farahani et al. / Aerospace Science and Technology 86 (2019) 782–793

Fig. 3. Total aeroacoustic attenuation versus Mach number: T 0∞ = 302 K and P 0 = 70 kPa.

and the assumption of inviscid flow for a supersonic wind tunnel would be reasonable. The above simplified theory is relevant for a wind-tunnel duct with an empty test section considering no sound reflection and absorption effects. Attenuation coefficients of Fig. 3 take the effects of viscosity and friction into account. In the next section, other mechanisms of sound attenuation that exist in the wind-tunnel will be discussed. 3.2. Mechanisms of acoustic attenuation in a wind tunnel Generally, an acoustic wave loss’s energy as it propagates in a media, and acoustic attenuation is a measurement of this energy loss. There are different mechanisms for an acoustic attenuation such as sound scattering due to the local non-uniformities, viscothermal and friction losses, sound absorption, etc. Viscothermal and friction losses are discussed in the previous section. Another important mechanism of acoustic attenuation in the wind-tunnel is the acoustic absorption. Acoustic absorption refers to the process by which a material, structure, or object absorb the sound energy when the sound waves are encountered, in contrast to reflecting the energy. Part of the absorbed energy is transformed into heat, and part is transmitted through the absorbing body. In the windtunnel, the energy of sound is absorbed by the material of walls and model. There are many different ways by which this can happen: 1. Through viscous losses as the pressure wave pumps air in and out of the cavities in the absorbers, 2. By the thermal elastic damping, 3. By Helmholtz type resonators, 4. Through vortex shedding from sharp edges, 5. Through the direct mechanical damping in the material itself. Porous walls, upper and lower, of the test section, model, flow structure behind the model, and alpha mechanism to name a few are various means of acoustic absorption in wind tunnels. When a plane acoustic wave is encountered an acoustic absorber, the energy will be both absorbed and reflected. According to the previous definition of k and ω , the pressure of the incident wave, p, is described by:

p (x, t ) = A · exp(ωt )

(11)

The reflected wave, p r , is:

p r (x, t ) = B · exp(ωt − kx)

(12)

The proportion of sound absorbed by the surface is called the sound absorption coefficient and is defined as:

α∗ = 1 −

 2 B

A

(13)

The coefficient can be viewed as a percentage of the sound being absorbed, where 1.00 is an indication of a complete absorption (100%) while 0.01 indicates minimal absorption (1%). According to the aforementioned theories, it can be concluded that if the acoustic perturbation emitted inside the wind tunnel is considered as a plane wave, the amplitude of this wave decreases with an exponential function and with an attenuation coefficient of α . If A 0 is considered as the amplitude of the acoustic perturbation at a distance x downstream of an oscillating shock wave then:

A (x) = A 0 e −α x

(14)

4. Results and discussions 4.1. Inlet buzz measurement For the present inlet, at free stream Mach numbers of 2.0 and 2.2, the big buzz mechanism is active for all exit blockage ratios [21]. Moreover, for a freestream Mach number of 1.8 and at moderate exit blockage ratios, the big buzz is detected. However, for very small mass flow ratios the little buzz or Ferri mechanism becomes dominant. Table 3 shows the measured values of the buzz frequency for different freestream Mach numbers and for different mass flow ratios [21,27]. Fig. 4 shows schematic of three chronological sequences of the buzz for the present inlet and are compared with the related schlieren images for a freestream Mach number of 2.0. As seen, from Fig. 4a, the separation zone acts like a viscous wedge and a separated conical shock forms. This shock impinges with the normal shock at a point, known as “triple point” and a slip surface

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Fig. 4. Schematic of shock system during buzz for mixed-compression inlet together with the Schlieren sequences for the present inlet at design Mach number. Table 3 Model-based measured buzz frequencies for different mass flow rates and Mach numbers [21,27]. M∞

EBR (%) 65.0

67.5

70.0

75.0

80.0

1.8

Buzz frequency (Hz) Mass flow ratio ε

NBa 0.754

NB 0.673

96.0 0.600

119/485 0.491

493.8 0.377

2.0

Buzz frequency (Hz) Mass flow ratio ε

NB 0.832

91.5 0.736

96.3 0.662

113.2 0.539

127.5 0.430

2.2

Buzz frequency (Hz) Mass flow ratio ε

NB 0.920

80.0 0.807

84.0 0.710

104.0 0.577

120.0 0.460

a

NB = No Buzz.

emits from this point across which the flow velocity changes discontinuously. The corresponding shock foot becomes curved near the separation zone and creates a lambda-shock structure (Fig. 4a). As the exit-blockage-ratio increases (reduction of the inlet exit area by the plug mechanism), the aforementioned separation zone grows inside the duct (Fig. 4b, c). At this instance, the separation region blocks the flow direction and consequently, the incoming mass flow decreases (thus increasing the flow spillage). At the same time with the growth of separation, the normal shock moves upstream. At this point, reflection of the compression wave emitted from the exit plane of the inlet, returns towards the exit plane and is swallowed the separation region and normal shock wave. This mechanism, known as Dailey criterion, usually results during the high-amplitude oscillations of the normal shock and affects the inlet flow stability. For the present inlet at its design Mach number (i.e. M ∞ = 2.0) and for the mentioned mass flow ratio (see Table 3), this buzz initiation mechanism is dominant. Comprehensive discussions on the buzz characteristics of the present inlet can be found in reference [21]. In addition, details of the buzz initiation and its mechanism could be found in references [1–11]. In this study, the main objective is to examine the feasibility of the far-field buzz measurement method, using the wind-tunnel wall pressure taps. Therefore, explanation of the buzz mechanisms and the related phenomena will not be covered explicitly. In this study the propagation of shock wave oscillation far from the model has been investigated. A control volume outside the inlet duct (between cowl and wind-tunnel wall) is considered and the shock oscillation characteristic using the wind-tunnel wall pressure is investigated (the control volume is shown in Fig. 4c). Note that the effect of buzz on the region between the most up-

stream (point A) and the most downstream (point B) movement of the shock wave formed at the nose of the inlet is of interest. The experimental data show that the shock wave never reaches these points (points A & B). These points are located on the wind-tunnel wall downstream and upstream of the inlet model, W1 and W2 shown in Fig. 2. According to the Schlieren images and schematics of Fig. 4, as the normal shock moves upstream, the strength of the shock wave and its geometry changes. This means that the value of the static pressure at a point downstream of the shock wave varies as a function of time even if the shock wave never reaches that point. Moreover, the curved shock emitted from the triple point becomes weaker as it is propagated downstream due to increasing the distance from the shock formation foundation. Far away from the body, the required deviation of the streamlines decreases. Consequently, the weak curved shock changes to a Mach wave, hence the fluctuating pressures sensed by the wall pressure transducers are weaker than those measured by the transducers located on the body surface. This fact will be verified later from the experimental data. Therefore, it is expected that the amplitude of pressure oscillation downstream at a point near the wind-tunnel wall would be low and can be assumed as perturbation. As a result, the static pressure at point B can be assumed to be of the form:

p B = p B + p  (x, t )

(15)

In wind-tunnel testing, the model size is such that the flow in the vicinity of the wind-tunnel wall is almost uniform with low turbulence intensity. Therefore, there is no other physical mechanism to change the shock oscillation frequency. Consequently, influence of the buzz at points downstream of the oscillating shock wave can be treated as an acoustic perturbation that has the same frequency as the buzz according to Eq. (15). Furthermore, referring to the theory of wave propagation discussed in section 3, it is indicated that the amplitude of the perturbation term depends on both time and space. To verify the above, results of the pressure measurement on the wind-tunnel wall are compared with the data obtained from the surface of the inlet model, at the same conditions. 4.2. Wind tunnel wall pressure measurement 4.2.1. Frequency analysis Fig. 5 shows the pressure history together with the power spectral density of the wind-tunnel wall sensors (W1–W6) and

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Fig. 5. Measured pressure history and spectral density of wall sensors and Sensor S1 on model: M ∞ = 2.0 & EBR = 65.0%.

a sensor on the compression cone (S1), for an exit blockage ratio of 65.0% at a free stream Mach number of 2.0. For this exit blockage ratio, the experimental data and the Schlieren images do not show buzz phenomenon. Power spectrum of wind-tunnel wall transducers does not show significant pressure variations, and no buzz frequency can be detected from the pressure history. This further verifies that there are no other sources of pressure oscillations or sound emission other than the buzz in this windtunnel. The pressure history together with the power spectral density of the model and the wind-tunnel wall pressure transducers signals for a case with buzz for M ∞ = 2.0 are depicted in Fig. 6. This figure clearly shows that sensors W3, W4 and W5 have encountered the buzz frequency and its harmonics which are exactly equal to those values measured by the sensors located on the model, the data are shown in Table 3. However, the amplitudes of pressure signals from the wall transducers are smaller than those measured from the surface of the model. Note the pressure range for all points on the wall are scaled the same in Fig. 6 for a better judgment. As previously mentioned, the shock wave strength at positions far from the inlet, near the wall, is much less than the strength of the

shock wave near the compression cone. On the other hand, it was shown that pressure oscillations on points downstream of the shock (point B in Fig. 4c) depends strongly on the strength of the shock wave. Fig. 7 shows ratio of measured pressure values for sensors W2 and S7 behind the shock for various EBRs. From Fig. 7, it is clearly seen that the value of pressure near the wall is much less than its corresponding value on the model for all Mach numbers tested in this investigation. It verifies that the strength of the shock wave near the wall is reduced significantly. One of the reasons for this situation is the presence of back-pressure at the end of the model that leads to a high pressure zone inside the inlet and consequently, strengthens the shock wave. However, the flow downstream of the shock wave over the model does not encounter this applied back-pressure and the streamlines in this zone experience a weaker pressure jump with a very small deviation. Another interesting finding in the results is that sensor W1 located slightly ahead of the model, cannot measure buzz and there is no significant buzz frequency in its signal frequency spectrum. Shadowgraph images and schematics of the shock structure show that W1 is located beyond the region where the shock is oscillating. Sensor W1 is located upstream of the shock and it is not

M. Farahani et al. / Aerospace Science and Technology 86 (2019) 782–793

789

Fig. 6. Measured pressure history and spectral density of wall sensors and Sensor S1 on model: M ∞ = 2.0 & EBR = 80.0%.

expected to measure acoustic wave generated by the buzz since the incoming flow is supersonic. Although a frequency equal to the buzz frequency can be detected in the spectrum of the transducer W2, the amplitude of measured frequency is almost negligible. Fig. 8 shows shadowgraph images of the first and the last instances of a buzz cycle for an EBR = 80.0% for a free stream Mach number of 2.0. In this figure, the orientation of shock wave and shock angle is clearly demonstrated. If the shock waves are considered to be approximately straight until they impinge on the wind-tunnel wall, the following formula could be used to calculate horizontal coordinate of the shock impingement point to the wind-tunnel wall.

  x

d

= swi

yw d. tan β

(16)

where y w is the semi test section height and β is the shock angle at the inlet cone tip. From the visualization pictures the shock angles for the most downstream shock position (MDP) and for the most upstream shock position (MUP) during the buzz are measured to be 35.1◦ and 59.0◦ respectively. Then using Eq. (16), x/dswi is calculated

to be equal to 2.85 and 1.2 respectively (d = 150 mm). Table 2 shows that sensor W2 is located at x/d = 1.3. Considering the fact that shock wave angle reduces, to some extent, as the shock approaches the tunnel wall, it could be concluded that in this case, the point of impingement of the shock wave with the wind-tunnel wall remains downstream of W2 during all instances of the buzz cycle. The amplitude of the shock wave oscillation for EBR = 80% is greater than other lower exit blockage ratios. Thus, it could be implied that for a freestream Mach number of 2.0, the impingement point remains downstream of W2. The power spectral density shown in Fig. 6 for sensor W2 shows a fundamental frequency of buzz, about 127 Hz. However, as seen from Fig. 6c, a low amplitude signal is also shown by this sensor. Note that W2 is located upstream of the shock impingement point, however, it senses the buzz oscillations to some extent, Fig. 6c. The perturbations in this case is obviously propagated in the wind-tunnel wall via the boundary-layer. Inside the boundary-layer the flow velocity is subsonic and perturbations travel in both upstream and downstream directions [28]. Since sensor W2 is located near the shock foot, it senses the perturbations. In addition, one may expect wave propagation via wall boundary-layer toward W1 similar to a case of a body surface reported by Heidary et al. [29]. However, as seen

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Fig. 7. Ratio of measured wall pressure W2 and model pressure S7 behind the shock.

Fig. 8. Shock angle in downstream and upstream shock wave locations in a buzz cycle, M ∞ = 2.0 & EBR = 80.0%.

from the present data of sensor W1, Fig. 6b, there exists no dominant frequency in the PSD data for this sensor. Thus, it could be concluded that upstream perturbation through the subsonic layer of the wall for a free stream Mach number greater than unity, cannot extend far from its source. Furthermore, the wind-tunnel wall temperature is low and flow speed is high in this case of study,

thus, the boundary-layer is not very thick. Therefore, strong perturbations cannot be transferred by the boundary-layer far upstream of the shock foot and for this reason, W1 cannot sense the pressure fluctuations, caused by the buzz phenomenon. Similar results can be seen for Mach numbers of 1.8 and 2.2. Figs. 9, and 10, show the measured pressure history together with power spectral density of the wind-tunnel wall sensors as well as the output of a sensor located on the compression cone (S1) for an exit blockage ratio of 80.0% and for freestream Mach numbers of 1.8 and 2.0, respectively. For these Mach numbers the wind-tunnel wall transducers measure buzz frequency exactly equal to the one measured by the transducers located on the model similar to the case of M ∞ = 2.0, Fig. 6. In these cases, again, sensor W1 has not measured any pressure fluctuations, but for M ∞ = 1.8 the amplitude of the buzz measured by transducer W2 is higher in comparison with those of M ∞ = 2.0 and M ∞ = 2.2. As it is schematically shown in Fig. 9, the normal shock stands out of the inlet duct in its most downstream position for a free stream Mach number of 1.8 in the buzz cycle. Further, for this Mach number, even for the supercritical operating case, the normal shock does not enter the inlet duct. Hence, the orientation of the shock at MDP near the wind-tunnel wall has higher angle, and for some instances of the buzz cycle transducer W2 senses the pressure downstream of the shock system. Therefore, the spectrum of this sensor shows that the amplitude of the buzz oscillation in this case is higher and W2 can measure buzz oscillations more effectively. Similar discussions are applicable for the case of M ∞ = 2.2 and these cases are nearly similar, Fig. 10. For the lower exit blockage ratios, the results of the windtunnel wall measurements for the buzz frequency are exact, and the amplitude of pressure reduces as the measurement taps approach downstream. Table 4 summarizes the measured buzz frequency from the transducers located on the wind-tunnel wall for three freestream Mach numbers and for various exit blockage ratios. All trends in the case of EBR = 80.0% can be found for the lower EBRs too. Table 4 in comparison with Table 3 implies that this measurement method can exactly predict the buzz frequencies for various Mach numbers and different exit blockage ratios (or mass flow ratios).

4.2.2. Amplitude A parameter to investigate the amplitude of the pressure signals is the root mean square [25]. Fig. 11 shows the RMS values for the wall sensors W3–W5. The signals for each case are band-pass filtered near the measured buzz frequencies before taking their root mean square to isolate buzz oscillations. It is seen that the oscillation amplitude decreases as x/d increases i.e. getting further away from the shock foot. The mechanism of acoustic attenuation has been showed in section 3. This figure also confirms the exponential trend of amplitude reduction as explained in detail previously, section 3. Fig. 12 shows the exponential interpolation for different Mach numbers. In all cases, an exponential function with the form of Eq. (14) can be fitted to the data with a minimum R-squared value of 0.997. The corresponding coefficient in each case is tabulated in Table 5. Values of A 0 and α are not predicted exactly by theories because various effects are not taken into account using the simplified model explained in section 3. However, the measured values somehow confirm the acoustic attenuation mechanism in the wind-tunnel previously mentioned in Section 3.

M. Farahani et al. / Aerospace Science and Technology 86 (2019) 782–793

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Fig. 9. Measured pressure history and spectral density of wall sensors and Sensor S1 on model: M ∞ = 1.8 & EBR = 80.0%.

5. Conclusion

The feasibility of an inlet buzz-detection-scheme using pressure measurement on the wind-tunnel wall is studied experimentally for an axisymmetric mixed-compression inlet. The tests were conducted at free stream Mach numbers of 1.8, 2.0 (design Mach number), and 2.2 for different mass flow ratios. The measured pressure signals on the tunnel wall are compared with the measured pressure on the inlet cone surface. The value of buzz frequencies measured by the wind-tunnel wall sensors, for different exit blockage ratios, are exactly the same as those measured by the sensors located inside the model. However, it is seen that the amplitude of the measured buzz is lower in comparison with the value measured by the sensor on the model. The reason was shown to be due to the reduction of the inlet shock wave strength near the wall and acoustic attenuation along the tunnel test section. In addition, the appropriate position of the wall sensors to measure the shock wave instability was studied. If the sensor is

located upstream of the most forward position of the shock wave oscillation interval, it will not sense the measure buzz because the perturbations in the supersonic compressible flow propagates only downstream. It is better to locate the sensor near the mean shock-wall impingement point in order to measure the buzz more effectively. Moreover, theoretical prediction showed that the amplitude of the acoustic perturbation reduces exponentially. A simple mathematical model was presented that can be used to predict a rough estimation of the amplitude reduction along the tunnel wall. This methodology can be easily implemented to perform a rapid as well as a low-cost inlet stability measurement. It further can be used to investigate the effect of different flow control methods or geometry changes on the inlet stability, rapidly. Conflict of interest statement It is declared that there is no conflict of interest.

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Fig. 10. Measured pressure history and spectral density of wall sensors and Sensor S1 on model: M ∞ = 2.2 & EBR = 80.0%. Table 4 Measured buzz frequencies measured from pressure on wind tunnel wall. M∞ 1.8 2.0 2.2 a

EBR (%) 67.5

70.0

75.0

80.0

NBa 91.5 80.0

96.0 96.3 84.0

485.0 113.2 104.0

493.8 127.5 120.0

NB = No Buzz.

Fig. 11. Root mean square of pressure signal for the wall sensors W3–W5 at different Mach numbers.

M. Farahani et al. / Aerospace Science and Technology 86 (2019) 782–793

793

Fig. 12. Exponential interpolation of RMS value for different Mach numbers. Table 5 Interpolation coefficients for cases of Fig. 12. M∞

EBR

A0

α

R2

1.8 2.0 2.2

75.0 80.0 80.0

13.56 128.6 48.92

0.40 0.94 1.42

0.998 0.997 0.999

∗ NB

= No Buzz.

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