Development of second mode instability in a mach 6 flat plate boundary layer with two dimensional roughness

Development of second mode instability in a Mach 6 flat plate boundary layer with two dimensional roughness Development of second mode instability in a Mach 6 flat plate boundary layer with two dimens[.]

(Received 24 August 2014; accepted 26 May 2015; published online 19 June 2015)

Particle image velocimetry, PCB pressure sensors, and planar Rayleigh scatteringare combined to study the development of second-mode instability in a Mach 6flow over a flat plate with two-dimensional roughness To the best of the au-thors’ knowledge, this is the first time that the instantaneous velocity fields andflow structures of the second-mode instability waves passing through the roughnessare shown experimentally A two-dimensional transverse wall blowing is used togenerate second-mode instability in the boundary layer and seeding tracer parti-cles The two-dimensional roughness is located upstream of the synchronizationpoint between mode S and mode F The experimental results showed that theamplitude of the second-mode instability will be greatly increased upstream ofthe roughness Then it damps and recovers quickly in the vicinity downstream ofthe roughness Further downstream, it acts as no-roughness case, which confirmsFong’s numerical results [K D Fong, X W Wang, and X L Zhong, “Numerical simu-lation of roughness effect on the stability of a hypersonic boundary layer,” Comput.Fluids 96, 350 (2014)] It also has been observed that the strength of the amplificationand damping effect depends on the height of the roughness.C 2015 Author(s) Allarticle content, except where otherwise noted, is licensed under a Creative CommonsAttribution 3.0 Unported License.[http://dx.doi.org/10.1063/1.4922389]

I INTRODUCTION

Hypersonic boundary layer transition remains a popular issue with the rapid development ofaeronautics and astronautics For hypersonic boundary layers, there has recently been a stronginterest in transition affected by surface roughness

Schneider1 mentioned that the mechanism of roughness-induced hypersonic boundary layertransition is very complex The transition process will be influenced by the roughness-inducedwake,2 4the crossflow,5Görtler instability,6transient growth7 , 8caused by streamwise vorticity, andthe interaction between the roughness and boundary layer instability waves or freestream acousticwaves Schneider’s review focused on the boundary layer transition caused by the roughness-induced unstable wake However, the interaction between the roughness and the boundary layerinstability waves, especially the second-mode instability waves, has not received much attention.Since Mack9 , 10defined second-mode instability in the hypersonic boundary layer, this kind ofinstability was believed to be one of the dominant instabilities in the hypersonic boundary layerand discovered experimentally by Kendall,11Demetriades,12Stetson and Kimmel,13 – 15and Casper

et al.16 , 17 The second-mode instability has a large amplification rate in the hypersonic ary layer Its interaction with roughness should not be ignored in roughness-induced hypersonicboundary layer transition.18

bound-Fedorov19 studied the receptivity of the hypersonic boundary layer to acoustic disturbancescattered by two-dimensional roughness theoretically and found that the second mode excitation

a) Electronic mail: cblee@mech.pku.edu.cn

leading to increased amplification or damping of the modal wave depending on its frequency range.Most recently, Fong22 , 23numerically studied the two-dimensional roughness effect on the sec-ond mode instability waves He mentioned that if a roughness element is placed downstream of thesynchronization point, the perturbations that have higher frequencies would be damped It has alsobeen found that if the roughness height is less than the local boundary layer thickness, large roughnessheight results in stronger amplification or stronger damping, depending on the roughness location.Heitmann and Radespiel24also simulated the evolution of a wave packet on a cone with roughness.However, there is still a lack of experimental results about the development of the frequencyand amplitude of the second-mode instability waves upstream and downstream of the roughness.Fujii25studied the effects of wavy-wall roughness on hypersonic boundary layers on a five-degreehalf-angle sharp cone at Mach 7.1 He found that the wavy-wall roughness, located well upstream ofthe breakdown region, could delay the transition under some conditions However, he did not focus

on the roughness’ effect on the second-mode instability waves upstream and downstream

The present study is conducted in the 120 mm Mach 6 quiet tunnel at Peking University Atwo-dimensional transverse wall blowing is used to generate second-mode instability waves in the flatplate boundary layer A two-dimensional roughness element is installed at 125 mm from the leadingedge of the flat plate, upstream of the synchronization point between mode S and mode F PCB pres-sure sensors are utilized to measure the second-mode instability waves upstream and downstream ofthe roughness element Particle image velocimetry (PIV) is used to show the flow structures upstreamand downstream of the roughness, compared to the PCB results Planar Rayleigh scattering (PRS)flow visualization is also taken as a supplement to the PIV and PCB results

II EXPERIMENTAL FACILITIES

The experimental parameters are listed in TableI

A Wind tunnel

The wind tunnel operates in a pressure-vacuum blow down infrastructure with a typicalon-condition test time of 30 s To avoid air liquefaction, the flow is heated to a nominal stagna-tion temperature of T0=433 K The stagnation pressure is held constant, and the unit Reynoldsnumber Reunit= ρ∞U∞/µ changes less than 3% in a running time The tunnel operates at quietand noisy conditions with the bleed valve open and closed, respectively The freestream flow den-sity ρ∞=0.021 kg/m3and the viscosity coefficient µ = 0.34 × 10−5Ns/m2can be calculated by

TABLE I The experimental parameters of the tunnel at PKU.

FIG 1 The flat plate model with PCB pressure sensors mounted at 90 mm–180 mm downstream of the leading edge The two-dimensional transverse wall blowing and two-dimensional roughness are also shown.

Sutherland’s law in the form

The flat plate model is shown in Fig.1 A 350 mm long flat plate was installed in the test section,

5 mm off the axis of the nozzle The flat plate is 90 mm wide at the leading edge and 60 mm wide

at the trailing edge The leading edge was sharp and beveled with an angle of 15◦ The siding edgeswere also sharpened and beveled at an angle of 45◦

Wall blowing procedure is utilized to enhance the second-mode instability waves The blowing slot is two-dimensional (3 mm × 40 mm) and 50 mm downstream of the leading edge.The blowing rate is set at 2 L/min Since the wall blowing will disturb the boundary layer more

wall-or less, the experimental area should be chosen as far downstream as possible On the other hand,limited by the nozzle exit, the oblique shock wave induced by the leading edge of the flat plate isreflected by the boundary layer on the nozzle and hits on the flat plate at about 200 mm downstream

of the leading edge of the flat plate Therefore, our experimental zone is set from x = 90 mm to

x=180 mm on the flat plate model

C Roughness location

Limited by the experimental zone, three two-dimensional roughness elements with differentheights (0.5 mm, 1.0 mm, 1.5 mm) (H) × 1 mm (L) × 60 mm (W) are mounted at 125 mm fromthe leading edge on the flat plate, respectively Here, the development of the second mode instabilitywaves can easily be detected upstream and downstream of the roughness

Since the relationship between the roughness location and the synchronization point of mode

S and mode F plays an important role in the developments of mode S,22 we should first definethe synchronization point in our case The synchronization location in the x coordinate can becalculated by22

xs= (ωs/F)2

Reunit

The synchronization point has a constant value of non-dimensional circular frequency ωs

=0.114, which is calculated by Linear Stability Theory (LST) and shown in Fig.2 The dimensionless

FIG 2 Distributions of phase velocities a and the dimensionless circular frequency ω for boundary-layer waves The mode

S synchronizes with mode F at the point where ω s =0.114 and a s = 0.927.

is above 1 MHz, and the sensor output is high-pass filtered at 11 kHz and, hence, suitable to sure the high-frequency instabilities in the hypersonic boundary layer The output from the PCBpressure sensors passes through a PCB 482C01 signal conditioner A DH5939 data acquisition sys-tem is used for data acquisition It has a bandwidth of 600 kHz and a 14-bits vertical resolution.The sampling rate is 5 MHz The detailed parameters of the PCB pressure sensor are mentioned

mea-by Fujii.25

As a supplement to the PCB results, the PRS is used to visualize the flow structure of the sonic flat plate boundary layer Carbon dioxide is injected into the tunnel from upstream of the electricheater The mass injection rate of the carbon dioxide is no more than 5% of the freestream flow Owing

hyper-to the low static temperature in the test section of the tunnel (less than 70 K), the condensation processconverts it into dry cold particles Given that the diameters of the particles are much less than thewavelength of the laser, this is a kind of Rayleigh scattering On the other hand, the temperature nearthe wall is high enough that the solid-state carbon dioxide becomes a gas state The line separatingthe black and white parts in the photograph is the condensation line, as shown in Figs.19and20 Thedisturbance in the boundary layer develops, and the black and white parts mix together to visualizethe flow structure This technique had been used by Smits’ group26 – 28in many kinds of hypersonicboundary layers

PIV is used to measure the near-wall boundary layer velocity field on the flat plate In our iment, tracer particles could hardly get into the laminar and transitional hypersonic boundary layersbecause of the Saffman force29caused by the large shear stress near the wall The laminar and tran-sitional hypersonic boundary layers also do not have enough mass convection as fully developedturbulent boundary layer

exper-The transverse wall blowing used to inject tracer particles into the boundary layer could partlysolve this problem However, it still faces many other challenges in hypersonic boundary layermeasurement, such as large movement of the tracer particles, large velocity gradient in the thinboundary layer, and intense scattering near the roughness and the wall

FIG 3 Schematic diagram of the experiment.

The preprocessing and post-processing of the PIV images are critical to the final velocity fieldresults, since the experiment is in a high-speed and high shear flow condition A great deal of work hasbeen performed to improve the hypersonic boundary PIV results, such as the prior calculation of theinitial velocity field, wall mask, roughness mask, wall scattering mask, wall weight arrangement, andflow structure smoothing This improved PIV method had been successfully utilized to measure thevelocity profile of a Mach 3 fully developed turbulent boundary layer The RMS uncertainty is about0.02-0.05, and the mean bias of the PIV method is about 0.01-0.015, depending on the displacementgradient.30

The flow was seeded with particles of 90 nm in diameter with transverse wall blowing A Nd:Yagdual-head laser of 400 mJ provided the illumination and a 12 bits TSI imager intense recorded thescattered light intensities A 200 mm lens is used to take photographs at three different areas at stream-wise direction, each of which is time-independent and has an image size of 20 mm × 16 mm, with aconversion factor of 1 pixel per 1.5625 µm in the image plane The semantics of the PIV experimentare shown in Fig.3

III RESULTS AND DISCUSSION

A Effect of wall blowing

First, the effect of transverse wall blowing to the boundary layer is investigated Since the tude of the second-mode instability waves is not so large, a linear y-axis is used to show the amplitudedevelopment of the second-mode instability waves more clearly The total pressure is 0.5 MPa, andthe unit Reynolds number Reunit=5.40 × 1061/m

ampli-Fig.4is the power spectral density (PSD) of the wall pressure fluctuation, without wall blowingmeasured by PCB pressure sensors We can see that the typical frequency band of the pressure fluctu-ation is between 80 kHz and 120 kHz, which is in the frequency band of the second-mode instabilitywaves on the flat plate.11The fluctuation is also amplified with streamwise distance Hence, it can beconfirmed that this kind of fluctuation is caused by the second-mode instability waves and its peakfrequency is about 105 kHz

From Fig.5, we can see that the typical frequency band of the pressure fluctuation is between

60 kHz and 100 kHz, which is also in the frequency band of the second-mode instability waves onthe flat plate The typical frequency band of the fluctuation in wall blowing case is lower, since the

FIG 4 PSD of the surface pressure fluctuation, without wall blowing, measured by PCB pressure sensors.

boundary layer is thicker Its peak frequency is 95 kHz and the fluctuation amplitude in this frequencyband is about an order of magnitude larger than the fluctuation amplitude in the no-blowing case inFig.4 Hence, it can be confirmed that transverse wall blowing could enhance the amplitude of thesecond mode instability waves in hypersonic flat plate, which is also mentioned by Johnson.31

Ghaffari32made a simulation which agreed well with Johnson’s31result and considered that thewall blowing will bring extra mass flow and thicken the boundary layer, which will, in turn, decreasethe frequency of the second-mode instability waves and enhance its amplitude The separation caused

by wall blowing will also decrease the viscosity of the flow and make the disturbance unstable asmentioned by Pagella.33 , 34

Balakumar’s result35also confirms that the adverse pressure gradient will amplify the first andsecond mode disturbances

In this section, the wall blowing was proven to be able to enhance the amplitude of the secondmode instability waves by our experimental result This method was used to make the second modeinstability on the flat plate more clear to be measured

B Flat plate case

Fig.6is the average PIV velocity field of the hypersonic boundary layer The results of 40 pairs

of recordings were averaged to give the mean result The total pressure is 0.5 MPa, and the injection

FIG 5 PSD of the surface pressure fluctuation, with wall blowing, measured by PCB pressure sensors.

FIG 6 Average PIV velocity field of the hypersonic boundary layer at 90 mm–150 mm downstream of the leading edge of the flat plate.

rate of the wall blowing is 2 L/min The boundary layer thickness is δ ≈ 4 mm from about 90 mm

to 150 mm downstream of the leading edge of the flat plate

We extract the streamwise velocity in different x locations and compare them with the Blasiusvelocity profile, shown in Fig.7 Since the boundary layer is disturbed by wall blowing and is nolonger a naturally developed laminar boundary layer, an x = 150 mm shift has been done to fit thePIV results with the Blasius profile The velocity defects in the lower region and plumps in theupper region of the boundary layer, which is shown in Fig.7, may be caused by the transverse wallblowing The mean bias errors of the PIV results are less than 10% of the freestream velocity, which

is shown in Fig.10 For the two points, distance is 20 mm, the correlation time is 0.0276 ms, andthe speed of the second-mode instability waves is

u= x/t =20 mm/0.0276 ms ≈ 724 m/s (4)Since the wavelength of the second-mode instability is about twice the boundary layer thick-ness,11 , 13the frequency of the second-mode instability waves is

is reasonable since the amplitude of the second-mode instability waves in the boundary layer of theflat plate is not as large as the cone and the disturbances of other frequencies are also effective

FIG 7 Comparison of the streamwise velocity profile between the mean results of PIV and the Blasius equation The PIV result in 100 mm, 120 mm, and 140 mm has been shifted to 250 mm, 270 mm, and 290 mm, respectively.

FIG 8 The mean bias errors of the PIV results to the Blasius profile.

C Effect of two-dimensional roughness

Three kinds of two-dimensional roughness elements with different heights of 0.5 mm, 1.0 mm,and 1.5 mm are installed 125 mm downstream of the leading edge of the flat plate For the boundarylayer, thickness δ ≈ 4 mm, and the heights of the roughness that we chose are about 0.125δ, 0.25δ,and 0.375δ, respectively The pressure data are band-pass filtered from 60 kHz to 100 kHz

FIG 9 Surface pressure fluctuation measured by PCB pressure sensors mounted in the streamwise direction The signal is band-passed between 60 kHz and 100 kHz There is no roughness.

FIG 10 The two-point correlation of the surface pressure fluctuation between x = 110 mm and x = 130 mm.

Fig.13is the comparison of the normalized spatial evolution of the wall pressure fluctuationbetween experimental and numerical results As mentioned above, the roughness at x = 125 mm islocated upstream of the synchronization point between mode S and mode F The simulation resultused for comparison is provided by Fong.22 Although having different shapes of the roughness,boundary layer thickness, and initial disturbances, the numerical and experimental results fit well,after necessary normalization

It can be seen in Fig 13 that upstream of the roughness (x = 105 mm–110 mm at Fong’scomputational fluid dynamics (CFD) results and x = 120 mm in our results), the amplitudes of thesecond mode instability waves increase about 2.5-3 times as the no-roughness case

In the region behind and close to the roughness, the amplitude of the second mode instabilitywaves is found damped and recovered quickly at x = 115-122 mm in the numerical simulation.However, this phenomenon is not so clear at x = 130-140 mm in the experimental results, which iscaused by the band-pass filter of the result (the signal is band-passed between 60 kHz and 100 kHz,but the typical frequency of the second mode instability is changing upstream and downstream ofthe roughness) In fact, the damping and recovering of the second mode instability physically existand can be seen more clearly in Fig.24(high-pass filtered at 11 kHz)

Further downstream of the roughness, the amplitude of the second mode instability waves isfound to develop similarly to the no-roughness case in our experimental results This confirmsFong’s22numerical simulation result that when the roughness is located upstream the synchronizationpoint between mode S and mode F, the amplitude of the second mode instability waves downstream

of the roughness is amplified similarly to the no-roughness case

FIG 11 Instantaneous PIV velocity field of the hypersonic boundary layer at 90 mm–150 mm downstream of the leading edge of the flat plate The vectors here indicate the velocity directions.