9.3 Transonic Flows

Contributed by:

M. Raffel, J. Kompenhans

Common problems appearing in the application of PIV at high flow velocitiesin wind tunnels are limited optical access and problems of focusing the imagesof the tracer particles due to vibrations and density gradients in the flow [60].Nevertheless, the instantaneous flow fields above a helicopter blade profile andin the wake of a model of a cascade blade have been investigated successfully attransonic flow velocities by means of the photographic PIV technique alreadya decade ago [310].

Today, PIV can be applied to transonic flows in industrial wind tunnels,such as the DNW-TWG with a cross-section of 1 × 1m2, even on a routinebasis. Modern model deformation measurement techniques allow for the deter-mination of the exact model location and deformation under load in parallelwith the measurement of the instantaneous flow fields. Furthermore, the si-multaneous application of Pressure Sensitive Paints (PSP) and PIV improvesour understanding of the complex flow field, for example over delta wings inthe transonic regime. Thus, PIV – in combination with PSP or deformationmeasurements – provides high quality data for the validation of numericalcodes (see section 9.8).

272 9 Examples of Application

Table 9.7. PIV recording parameters for cascade flow.

Flow geometry Ma = 1.27 parallel to light sheetMaximum in-plane velocity Umax ≈ 400m/sField of view 150× 100mm2

Interrogation volume 2.8× 2.8× 1mm3 (H ×W ×D)Dynamic spatial range DSR ≈ 57 : 1Dynamic velocity range DVR ≈ 100 : 1Observation distance z0 ≈ 1mRecording method single frame/double exposureAmbiguity removal image shifting/rotating mirrorRecording medium 35mm film, ASA 3200, 100 lps/mmRecording lens f = 100mm, f# = 2.8Illumination Nd:YAG lasera 70mJ/pulsePulse delay ∆t = 2− 4µsSeeding material oil droplets (dp ≈ 1µm)

a frequency doubled

The first two experiments were carried out in the DLR high-speed blow-down wind tunnel (HKG). Transonic flow velocities are obtained by suckingair from an atmospheric intake into a large vacuum tank. A quick-actingvalve, located downstream of the test section, is rapidly opened to start theflow. Ambient air, which is dried before entering the test chamber, flows fora maximum of 20 s through a test section with 725mm spanwise extension.Grids in the settling chamber and a high contraction ratio lead to a lowturbulence level in the test section.

9.3.1 Cascade Blade with Cooling Air Ejection

The aim of this investigation was to study the effect of the ejection of coolingair on the wake behind a model of a cascade blade. Due to a specially adaptedwind tunnel wall above and below the model and an adjustable tailboard abovethe model, the flow field of a real turbine blade could be simulated in a re-alistic manner. The PIV recordings were taken with the photo-graphical PIVrecording system utilizing the high-speed rotating mirror for image shifting ata time delay between the two laser pulses of 2−4µs. The PIV parameters usedfor this investigation are listed in table 9.7. Figure 9.12 presents the instanta-neous flow velocity field at the trailing edge of the plate (thickness 2 cm) for acooling mass flow rate of 1.4% at a free stream Mach number of Ma = 1.27.Expansion waves and terminating shocks can be easily seen. No data wereobtained in the area above the model as the laser light was blocked off by themodel. Data drop-out was also found in the area directly downstream of themodel. The reason is mainly that the size of the interrogation area could notbe further decreased at evaluation. This would have been necessary in orderto satisfactorily resolve the strong velocity gradients close to the trailing edge

9.3 Transonic Flows 273

−2 −1 0 1 2 3 4 5 6 7

−2

−1

0

1

2

3

Reference Vector: 200 m/s

X/d

Y/d

(u −365m/s, v +0m/s)

−2 −1 0 1 2 3 4 5 6 7

−2

−1

0

1

2

3

X/d

Y/d

Fig. 9.12. Flow velocity (top) and vorticity field (bottom) behind a cascade bladeat Ma = 1.27 and a cooling mass flow rate of 1.4%.

of the model. In addition, strong density gradients in this part of the flow fieldcaused much broader particle images. Without ejection of cooling air, the wakebehind the plate can be characterized as a vortex street [310]. With ejectionof air this is no longer true: two separate thin shear layers can be detected inthe presentation of the instantaneous vorticity shown in figure 9.12.

9.3.2 Transonic Flow Above an Airfoil

The application of PIV in high-speed flows yields two additional problems: theresulting behavior of the tracer particles and the presence of strong velocitygradients.

For the proper understanding of the velocity maps it is important to knowhow far behind a shock will the tracer particles again move with the velocityof the surrounding fluid. Experience shows that a good compromise between

274 9 Examples of Application

Table 9.8. PIV recording parameters for transonic flow above a NACA0012 airfoil.

Flow geometry Ma = 0.75 parallel to light sheetMaximum in-plane velocity Umax ≈ 520m/sField of view 300× 200mm2

Interrogation volume 5.6× 5.6× 1mm3 (H ×W ×D)Dynamic spatial range DSR ≈ 57 : 1Dynamic velocity range DVR ≈ 150 : 1Observation distance z0 ≈ 1mRecording method single frame/double exposureAmbiguity removal image shifting/rotating mirrorRecording medium 35mm film, ASA 3200, 100 lps/mmRecording lens f = 100mm, f# = 2.8Illumination Nd:YAG lasera 70mJ/pulsePulse delay ∆t = 3µsSeeding material oil droplets (dp ≈ 1µm)

a frequency doubled

particle behavior and light scattering can be found if this distance is allowedto be of the order of one or two interrogation areas.

Strong velocity gradients in the flow will lead to a variation of the displace-ment of the images of the tracer particles within the interrogation area. Thisinfluence can be reduced by application of image shifting, that is by decreasingthe temporal separation between the two illumination pulses and increasingthe displacement between the images of the tracer particles by image shiftingto the optimum for evaluation. This is especially important if autocorrelationand optical evaluation methods are applied as in this case it is required to beable to adjust the displacement of the tracer particles to the range for optimalevaluation (i.e. ≈ 200µm). The PIV parameters used for this investigation arelisted in table 9.8.

In the case of optical evaluation methods image shifting helps also to solvethe problem of large variations of the displacements of the tracer particle im-ages within the PIV recording. A successful evaluation is achieved for a rangeof particle image displacements of 150µm ≤ dopt ≤ 250µm. The upper andlower limits for this optimal particle image displacement is determined bythe flow to be investigated and can be adapted to the optimal range of dis-placement on the recording medium by applying the image shifting technique,and adding an additional shift in the direction of the mean flow. Less datadrop-out can be expected by this means.

Strong velocity gradients are present in flow fields containing shocks as arepresent in transonic wind tunnels. Figure 9.13 shows such an instantaneousflow field – again above a NACA 0012 airfoil with a chord length of Cl = 20 cm– at Ma∞ = 0.75 [103]. By subtracting the speed of sound from all velocityvectors the supersonic flow regime and the shock are clearly detectable. Due

9.3 Transonic Flows 275

Naca 0012 airfoil

Fig. 9.13. Instantaneous flow field over a NACA 0012 airfoil at α = 5◦ andMa∞ =0.75, Ushift = 174m/s, Cl = 20 cm.

to the application of image shifting (Ushift = 174m/s) the requirement forthe fluctuations to be less or equal to the particle image diameter could befulfilled with an optimum interrogation spot diameter of 0.7mm even at thelocation of the shock. No data drop-out is found even in interrogation spotslocated in front and behind the shock (flow velocities from U = 280m/s to520m/s). The associated parameters for the PIV recording are presented intable 9.9.

The previous two examples should demonstrate, that already a decade agothe physical problems associated with the application of PIV in transonic flowscould be tackled with some experimental effort even for photographic record-ing. To date, many of these problems have been solved in a more general way,for example using frame straddling enabling pulse delays of the laser of muchless than 1µs (optimal displacement of particle images). Furthermore, sophis-ticated evaluation algorithms providing high local resolution even in presenceof strong displacement gradients and much stronger pulse lasers providingmuch higher intensities allow for either larger observation areas or a smaller

Table 9.9. Image recording parameters associated with the instantaneous flowfield of figure 9.13.

M = 1 : 6.7 N ≈ 15

Umin Umax ∆t Ushift ∆Xshift ∆Xmin ∆Xmax

[m/s] [m/s] [µs] [m/s] [µm] [µm] [µm]without I.S. 200 520 5 0 0 149 388with I.S. 3 174 78 167 311

276 9 Examples of Application

aperture leading to sharp particle images even in case of strong vibrations ofthe wind tunnel and the PIV setup.

9.3.3 Shock Wave/Turbulent Boundary Layer Interaction

Contributed by:

F. Scarano, R.A. Humble, B.W. van Oudheusden

The interaction between an oblique shock wave and a turbulent bound-ary layer (SWTBLI) creates a series of complicated flow phenomena, suchas unsteady flow separation and shock/turbulence interaction that presentunique experimental challenges [307], [313] and [314]. The application of PIVin the supersonic flow regime presents the specific challenges of describing thehigh-speed flow in the presence of shock waves with sufficient accuracy, neces-sitating the quantitative evaluation of the tracer particle’s dynamic behavior[312]. The SWTBLI problem additionally requires the large velocity gradientclose to the wall and the high-frequency turbulent fluctuations to be resolved.The PIV parameters used for this investigation are listed in table 9.10.

The particle tracer relaxation time/length is a crucial parameter dictat-ing the spatio-temporal resolution of the measurement. It is directly evalu-ated by measuring the particle velocity profile across a planar steady shockwave. Figure 9.14 shows the normal velocity profile against the shock-normalabscissa s, and returns a particle relaxation time of τp = 2.1µs. The

Table 9.10. PIV recording parameters for shock wave/turbulent boundary layerinteraction on a flat plate (second set denotes parameters for boundary layer study.)

Flow geometry parallel to light sheetMaximum in-plane velocity Umax ≈ 500m/s (Ma = 2.1)Field of view 124× 39mm2 (16× 5mm2) (W ×H)Interrogation volume 1.9× 1.9× 1.5mm3 (0.7× 0.08× 1.5mm3)Dynamic spatial range DSR ≈ 136 : 1Dynamic velocity range DVR ≈ 400 : 1Observation distance z0 ≈ 600mm (z0 ≈ 150mm)Recording method dual frame/single exposureAmbiguity removal frame separation (frame-straddling)Recording medium full frame interline transfer CCD

1376× 1040 (432 active) pixelsRecording lens f = 60mm, f# = 8 (f = 105mm, f# = 8)Illumination Freq. doubled Nd:YAG laser,

400mJ/pulse at 532 nmPulse delay ∆t = 2µs (0.6µs)Seeding material TiO2 (dp ≈ 400 nm)

9.3 Transonic Flows 277

Fig. 9.14. Normal velocityprofile against shock-normalabscissa s.

corresponding frequency response is fp ≈ 0.5MHz. The Stokes numberSt = τp/τflow (τflow = δ/U∞) expresses the fidelity of particle tracers in thespecific flow experiment [311]. For the present case St = 0.06, yielding anRMS tracking error below 1%.

The flow statistical properties are evaluated on the basis of 500 PIV record-ings acquired at 10Hz in a supersonic wind tunnel of 270(H)× 280(W )mm2

test section. The upstream mean boundary layer profile (δ99 = 20mm,Reθ = 3.36× 104) scaled with inner variables is shown in figure 9.15. The ex-perimental data agree with the composite formula down to y+ ≈ 200. Whenthe evaluation is carried out using high-aspect ratio interrogation windows(61 × 7 pixels) the wall-normal spatial resolution is improved extending theagreement to the overlap region (y+ ≈ 80, y < 0.2mm).

Fig. 9.15. Upstream meanboundary layer velocity profile.

278 9 Examples of Application

Fig. 9.16. Single PIV recording with mean velocity profile.

The instantaneous recording depicted in figure 9.16 shows a non-uniformseeding particle concentration due to the density variation in the flow. Theincident and reflected shock waves can be visualized by the increase in tracerparticle density, whilst the boundary layer is highlighted by a comparativelylower seeding level. Laser light reflections from the wall were minimized duringthe experiment by illuminating almost tangent to the wall.

An instantaneous stream-wise velocity distribution is shown in figure 9.17(top). The incoming boundary layer has a clear intermittent nature. Theglobal structure of the interaction is formed by the impinging shock penetrat-ing the boundary layer, turning and weakening until it vanishes at the sonicline. The adverse pressure gradient generated by the shock causes a dilationof the subsonic layer, which causes a second compression wave system to em-anate upstream of the impinging shock. The irregular shape of the separatedregion exhibits turbulent coherent structures, mostly originating from the sep-arated shear layer instability. Downstream of the interaction these structuresenhance the momentum mixing, which drives the boundary layer recovery.

The mean flow behavior is described by the averaged velocity field infigure 9.17 (middle). The incident and reflected shock waves are visible asa sharp flow deceleration and change of direction for the first, whereas thereflected shock exhibits a smoother spatial variation of the velocity due toits unsteady nature and the averaging effect. An inflection point prior toseparation is visible in the boundary layer profile. However, from the meanvelocity vector profiles no reverse flow can be inferred. After reattachment,the distorted boundary layer has approximately doubled its thickness anddevelops downstream with a relatively low rate of recovery.

The spatial distribution of the turbulence intensity magnitude(u′2 + v′2)1/2/U∞ is depicted in figure 9.17 (bottom) and shows the turbu-lent properties of the incoming boundary layer, the increased level of fluctu-ations throughout the interaction region and its redevelopment downstream.The higher level of fluctuations associated to the impinging shock (approxi-mately 4%) is typically encountered in these experimental conditions and isascribed to the combined effect of the decreased measurement precision and

9.3 Transonic Flows 279

Fig. 9.17. Instantaneous stream-wise velocity distribution (top), mean velocityvector field (middle) and turbulence intensity magnitude (bottom).

280 9 Examples of Application

to small fluctuations of the shock position. The increased level of fluctuationsassociated with the impinging shock penetrating the boundary layer is dueto its interaction with turbulent coherent structures convected in this region.The reflected shock exhibits a clear unsteady behavior and relatively highlevels of fluctuation, which in this case should not be regarded as turbulence.Two weak features downstream of the reflected shock (one parallel and theother roughly perpendicular to it) are due to optical aberration effects in-troduced by the inhomogeneous index of refraction field of this compressibleflow [308].