PIV measurements of supersonic slot-film cooling with shock/cooling-film interaction

Transcription

1 PIV measurements of supersonic slot-film cooling with shock/cooling-film interaction Pascal Marquardt 1,*, Frank Michaux 2, Michael Klaas 1 1: Chair of Fluid Mechanics and Institute of Aerodynamics, RWTH Aachen University, Aachen, Germany 2: ILA_5150 GmbH, Aachen, Germany * Correspondent author: p.marquardt@aia.rwth-aachen.de Keywords: High-speed PIV, Slot-film cooling, Shock/cooling-film interaction, Supersonic flow ABSTRACT Supersonic slot-film cooling is a promising cooling concept for surface temperature reduction of engine components that experience high thermal loads. If shocks are present in these components, their interaction with the cooling film may change the fundamental structure of the flow field in the vicinity of the surfaces that require cooling, which in turn can reduce the cooling effectiveness. The scope of this study is to analyze the influence of the injection Mach number of the cooling film and the shock strength on the shock/cooling-film interaction. Two different cooling films with injection Mach numbers of Ma i = 1.2 and 1.8 are injected beneath a turbulent boundary layer through a twodimensional slot nozzle at a freestream Mach number of Ma = Flow deflections of either β = 5 or 8 generate shock waves with different strength which impinge upon the cooling film. The flow field of the shock/cooling-film interaction is investigated by means of high-speed particle-image velocimetry, and the timeaveraged velocity fields and the Reynolds stress distributions are analyzed for three flow configurations. A high injection Mach number in combination with a low shock intensity shows moderate influence of the shock impingement on the cooling film. Lowering the injection Mach number or increasing the shock intensity leads to a highly disturbed flow with large separation bubbles. In these cases, the turbulent transport of heat and momentum between the cooling film and the outer flow is greatly increased. The results of the low shock strength cases are compared with large-eddy simulations. There is a reasonable agreement between the present study and the simulations with respect to the flow structure in the vicinity of the shock impingement position, the shock-induced transition of the laminar slot boundary layer, and the increase in turbulent transport. 1. Introduction In supersonic applications with high thermal loads, e.g., scramjet combustors, supersonic film cooling through two-dimensional slots is a promising cooling concept for surface temperature reduction [6, 10, 11]. However, if shocks that interfere with the cooling film occur in these combustors, a locally reduced cooling effectiveness might be the consequence. Figure 1 shows the basic structure of the flow field of a tangential film-cooling configuration that is not influenced by an impinging shock wave [10]. According to Juhany [5] and Seban & Back [16], the flow field can be divided into three regions. The first region is the potential-core region

2 right downstream the injection, which is bounded by the mixing layer that emanates from the lip and the slot-flow boundary layer. In this region, the cooling effectiveness is unity. The potentialcore region ends where the mixing layer and the slot-flow boundary layer merge and form the so-called wall-jet region that is characterized by intense mixing. Further downstream, the flow relaxes to that of an undisturbed turbulent boundary layer such that this region is called boundary-layer region. Fig. 1 Flow schematic with velocity profiles indicating the three distinct flow regions [5, 16] in a tangential film cooling configuration (Konopka et al. [10]) As mentioned above, the wall heat flux and, thus, the cooling effectiveness might change dramatically in the event that a shock impinges on this film-cooling flow. However, early literature report contradictory results concerning the extend of this change of the wall heat flux in this case. Alzner & Zakkay [1] performed experimental investigations of a shock/cooling-film interaction in an axisymmetric flow at a freestream Mach number of Ma = 6 with sonic injection. The shock was generated by an axisymmetric wedge around an axisymmetric centerbody with a flow deflection of 10. The measurement of the heat transfer distribution showed a reduction of the peak heat flux due to the injected cooling film. Experimental and numerical studies of a helium injection into a turbulent boundary layer at a freestream Mach number of Ma = 6.4 were conducted by Kamath et al. [7]. The cooling film was injected with an injection Mach number of Ma i = 3. The shocks impinging on the cooling film were generated by flow deflections of 5.5, 8, and The Reynolds-averaged Navier Stokes simulation (RANS) and the measurements of the wall heat flux indicated a small reduction of heat flux by the cooling film. Holden et al. [4] performed experiments in a shock tunnel at a freestream Mach number of Ma = 6 and injection with an injection Mach number of Ma i = 3. Shocks generated by either a 10, 15 or a 20 flow deflection impinged upon the cooling film. They found that film cooling has little or no effect on the peak heat transfer. Olsen et al. [13] conducted experimental investigations of a helium injection with an injection Mach number of Ma i = 3 into a turbulent

3 boundary layer at a freestream Mach number of Ma = 6.4. They found that the shock impingement position has no effect on the peak heat flux, but it is unclear in which flow region the measurements were made. Juhany & Hunt [6] concluded that the differences in the results arise from the flow region where the shock impinges upon the cooling film. While Alzner & Zakkay [1] investigated an interaction directly downstream of the injection point, Holden et al. [4] analyzed a shock impingement nozzle heights downstream of the injection. Juhany & Hunt [6] investigated experimentally a shock/cooling-film interaction in the wall-jet region and in the boundary layer region with injection Mach numbers of Ma i = 1.2 and 2.2 at a freestream Mach number of Ma = They found a weak impact of the shock interaction on the temperature at the wall as long as no separation occurs. Kanda et al. [8, 9] performed experiments with sonic injection into a boundary layer at a freestream Mach number of Ma = The shocks possessed a pressure ratio of either p 2 p 1 = 1.21 or They concluded their measurements by stating that mixing between the cooling flow and the freestream was not significantly increased by shock interaction. Konopka et al. [10, 12] performed large-eddy simulations (LES) of shock/cooling-film interaction in the potential-core region and the boundary layer region for injection Mach numbers of Ma i = 1.2 and 1.8. They found a shock induced decrease of the cooling effectiveness in all examined cases, however, the amount of the reduction in cooling effectiveness depends of the Mach number and the impingement position. The low Mach number case shows a stronger decrease with shock impingement in the boundary layer region, whereas the high Mach number case exhibits more cooling effectiveness decrease with shock interaction in the potential-core region. As shown above, the key parameters which determine the basic characteristics of this shock/cooling-film interaction are the freestream Mach number Ma, the injection Mach number of the cooling film Ma i, and the shock strength. The goal of this study is to analyze the influence of the injection Mach number Ma i and the shock strength on the shock/cooling-film interaction of a supersonic, laminar injection into a turbulent boundary layer by means of highspeed particle-image velocimetry (PIV). The cooling film is injected tangentially at injection Mach numbers of Ma i = 1.2 and 1.8 through a two-dimensional slot nozzle into a supersonic turbulent boundary layer with a freestream Mach number of Ma = An oblique shock generated by a flow deflection of either β = 5 or 8 impinges upon the cooling film approx nozzle heights downstream of the injection. This parameter configuration corresponds to the parameters investigated by Konopka et al [10, 12]. First, the boundary layer upstream of the cooling film injection is examined and compared against available data of a direct numerical simulation (DNS) of Pirozzoli & Bernardini [2, 3, 14, 15] to ensure a fully turbulent inflow

4 boundary layer. Then, the flow field is investigated in detail by high-speed PIV measurements. The mean flow field as well as turbulence statistics are analyzed and compared with regard to injection Mach number and shock strength to work out the influence of these parameters on the shock/cooling-film interaction. Finally, the results for a flow deflection of β = 5 are compared with the findings of the LES studies performed by Konopka et al. [10, 12]. 2. Experimental Setup 2.1 Wind tunnel and model All experiments have been conducted in the trisonic wind tunnel which is an intermittent working vacuum storage tunnel that is able to provide flows at Mach numbers reaching from 0.3 to 4.0 which are stable up to 3 seconds. The unit Reynolds number varies between and m 1 depending on the Mach number and the ambient conditions. The freestream Mach number Ma in the test section is calculated from the pressure ratio p/p 0. The static pressure p is measured via pressure taps in the test section side walls during the operation of the wind tunnel. The total pressure p 0 is measured with the same transducer just before each test run. The measurement error of the pressure transducer introduces an uncertainty in the Mach number determination of ±1.3% for the current setup. Fig. 2 Dimensions of the wind tunnel model and its location in the test section. The model, mainly made of aluminum, spans across the entire 400 mm x 400 mm test section of the wind tunnel, has an overall length of 960 mm, and possesses a thickness of 20 mm. The dimensions of the model and its position in the test section are sketched in figure 2. The incoming flow is tripped by a 0.2 mm thick zigzag tape 10 mm downstream of the wedgeshaped leading edge of the model to ensure a uniform turbulent boundary layer at the position of injection. The cooling flow is injected 560 mm downstream of the leading edge through a 200

5 mm wide, centered slot nozzle and develops along a 400 mm long flat plate. The oblique shock is generated by a wedge with an angle of either β = 5 or 8 that spans the entire test section width. The expansion fan emanating from the shock generator reaches the model 120 mm, resp. 87 mm for the 8 wedge, downstream of the shock impingement location. An interchangeable nozzle insert allows to change the injection Mach number without dismounting the model from the test section. The injection flow enters the nozzle insert symmetrically from both sides through rectangular ducts. Corner vanes inside the plenum chamber deflect the cooling flow by 90 to the main flow direction and smoothly adapt the crosssection areas between the inlets and the outlet to avoid flow separation inside the plenum. Before the flow is accelerated to the injection Mach number, it is guided through a honeycomb flow straightener with a cell size of 1.6 mm and a length of 28 mm. The static pressure and temperature are monitored via a pressure tap and a thermocouple downstream of the flow straightener. Upstream of the flow straightener, two struts are installed to avoid a deformation of the nozzle insert due to the increased pressure inside the plenum chamber. A spanwise cross section of the nozzle insert with the plenum chamber is depicted in figure 3. Fig. 3 Spanwise cross section of the nozzle insert with plenum. Figure 4 shows a close-up view of the cross section of the injection nozzles for both injection Mach numbers of Ma i = 1.2 and 1.8. The flow straightener upstream of the nozzle is inclined by an angle of 5 to reduce the amount of tracer particles impacting on the bottom part of the nozzle. The supersonic part of the Laval nozzle for the Ma i = 1.8 case is designed as a symmetric, bell-shaped nozzle with an exit height of S = 4 mm, whereas the nozzle for the

6 injection Mach number Ma i = 1.2 is the upper half of a symmetric nozzle to reduce the influence of manufacturing imperfections on the area ratio of the nozzle. The lip thickness of both nozzles is 1 mm. Fig. 4 Cross section of the slot nozzles for injection Mach number Ma i = 1.2 (left) and Ma i = 1.8 (right) To generate a steady cooling-film flow, the plenum chamber is fed with a controlled mass flow such that the static pressure at the nozzle outlet equals the static pressure of the freestream flow in the wind tunnel test section. This controlled mass flow is generated by a choked Venturi nozzle. A heat exchanger upstream of the Venturi nozzle controls the total temperature of the cooling fluid. Downstream of the Venturi nozzle, the flow passes through two DEHS seeding generators with 6 Laskin nozzles each. A bypass enables to control the seeding density without changing the overall mass flow rate of the cooling-film flow. With this setup, the mass flow rate settles within 1 s to steady state with a standard deviation of 0.5% of the set mass flow rate during a test run. The standard deviation of the static pressure inside the plenum is below 0.7% and the temperature is kept constant within ±0.2 K during each measurement. 2.2 PIV setup and data evaluation The PIV setup consists of a Quantronix Darwin Duo M laser and a Photron Fastcam SA5 high-speed PIV camera which are synchronized by an ILA synchronizer. The light sheet enters the test section through a window in the ceiling of the test section and is oriented vertically and parallel to the flow on the centerline of the model, see figure 2. The camera is mounted at a small angle ( 2 ) to the normal of the light sheet under Scheimpflug condition to reduce aero-optical aberrations. It is equipped with a 180 mm Tamron tele macro lens to realize a field of view of 20 mm x 20 mm in the measurement plane. In the current setup, the PIV system records 1000 samples per second with a resolution of 1024 px x 1024 px. To reduce the amount of laser light scattered from the model surface into the camera, the surface is highly polished. In addition to the seeding of the cooling flow, the main flow is also seeded with DEHS. The seeding in the main flow is filtered using a cyclone particle separator that reduces the mean particle diameter. With this setup, the particle response time measured across an oblique shock is τ p = 2.6 μs and

7 the corresponding effective mean particle diameter is d p = 0.7 μm. The resulting relaxation length of the particles in the freestream flow for small velocity changes is l p = 1.5 mm. The particle response time of the seeding in the cooling flow was measured by using the same type of particle generator without the cyclone separator to seed the flow across an oblique shock and was determined to be τ p,i = 7.1 μs and d p,i = 1.2 μm, respectively. Accordingly, the relaxation lengths of the particles in the cooling-film flow for the injection Mach numbers Ma i = 1.2 and 1.8 are l p = 1.8 mm and 2.9 mm. Each measurement consists of 1000 snapshots recorded over a measurement time of 1 s. After subtraction of a background image, the particle images are preprocessed using a non-linear Gaussian blur to reduce camera noise. The image evaluation uses an iterative correlation scheme with subpixel accurate image deformation. The window size used for PIV evaluation is 48 x 48 pixel with 75% overlap corresponding to a physical size of 1 mm x 1 mm. This leads to a final vector resolution of 0.25 mm. Since the surface reflections were masked in the recorded images, the first point used for PIV interrogation is at Δy = 0.25 mm off the wall. Outliers in the vector field are determined using a normalized median test [17], resulting in a validation rate over 90% in the final dataset. Since the field of view is approx. 20 mm x 20 mm in the current setup and the cooling-film flow evolves over a considerably greater length, the results for each set of flow parameters is composed of up to nine separate measurements along the centerplane of the model. The bounds of each measurement are indicated by thin black lines in the final vector fields. The small field of view and the high velocities of up to 600 m/s require pulse distances of 1000 ns or less. Hence, the relatively long laser pulse width of 210 ns introduces a significant amount of particle blur in the recorded particle images. Additionally, due to slight differences in the temporal pulse shape of both laser cavities, the effective pulse distance differs up to ±40 ns from the set pulse distance. This systematic error, which can be as high as 4% in the current measurements, has to be accounted for. To reduce this error, each measurement is conducted twice, where the cavities are triggered in reverse order between the measurements. With this approach, the systematic error occurs with inversed sign in both measurements such that it vanishes. The measured velocities U 12 for the cavity sequence 1-2 and U 21 for the cavity sequence 2-1 can be expressed as U 12 = Δs = U (Δt+dt 2 dt 1) = U (Δt+dt) Δt Δt Δt U 21 = Δs = U (Δt+dt 1 dt 2) = U (Δt dt) Δt Δt Δt with dt = dt 2 dt 1.

8 The quantity U denotes the velocity of the flow, dt 1 and dt 2 are the effective delays of laser cavities 1 and 2, and Δt represents the set pulse distance between the triggers of the two cavities. Since the velocity U is supposed to be the same in both cases, the pulse distance error dt can be determined when U 12 and U 21 are known by minimizing U dt Δt U 21 1 dt Δt In theory, a constant relative pulse distance error dt Δt over the measured field of view should correct a pure timing error. In practice, the corrected velocities from both cavity sequences show systematic differences towards the edge of the field of view. This could be explained by a slightly misaligned laser beam overlap in spanwise direction, where particles closer to or further away from the camera are illuminated, depending on the laser cavity. To compensate this, a twodimensional polynomial of third degree is used for dt Δt, whose coefficients are optimized in a non-linear least squares fit over the entire field of view. The uncertainty of the pulse distance correction is estimated as the root mean square difference between the local fit for each data point and the global optimization. To compute a conservative estimation of this uncertainty, a constant relative pulse distance error dt Δt is calculated in the global optimization instead of using the polynomial function in this procedure. A typical value of the uncertainty in the pulse distance error is in the range of 2 4 ns Results In this study, three cases of shock/cooling-film interaction with injection Mach numbers of Ma i = 1.2 and Ma i = 1.8 and two shock strengths based on deflection angles β = 5 and β = 8 are investigated. The reference case with an injection Mach number of Ma i = 1.8 and a flow deflection of β = 5 is denoted as case II. Here, the shock wave impinges upon the bottom wall at x imp S = 15. The shock angle σ, which equals the impingement angle, is σ = 28 in the reference case II with a static pressure ratio over the shock of p 2 p 1 = The Reynolds number of the injection based on the slot height S is Re i = u i S ν i = To analyze the influence of the injection Mach number on the shock/cooling-film interaction, the injection Mach number is reduced to Ma i = 1.2. In this case, in the following referred to as case I, the injection Reynolds number is Re i = The impact of the shock intensity on the flow is investigated by increasing the shock strength of the shock that impinges upon the cooling film downstream the injection point. This is accomplished by increasing the flow deflection to an angle of β = 8 leading to a shock angle of σ = 30.6 and a pressure ratio of p 2 p 1 = This case, called case III, can be divided into parts a and b, since there exist two stable flow configurations for this

9 parameter set. In all cases, the freestream Mach number is Ma = 2.45 ± 0.03 and the Reynolds number based on the slot height is Re = u 0 S ν 0 = ± 2.9%, with a total temperature ratio between the cooling flow and the main flow of T 0,i T 0 = 1.00 ± 0.8%. The parameters of the three flow configurations that are analyzed in this study are summarized in table 1. Case Ma x imp S Table 1 Flow parameters Shock strength Injection flow Blowing rate p 2 β [ ] σ [ ] Ma p i Re i M = ρ iu i 1 ρ u I II III (a/b) The results are normalized with the freestream velocity u 0, which is calculated from the wind tunnel Mach number and the total temperature. Depending on the ambient conditions, the freestream velocity is in the range of u 0 = m s with an uncertainty of ±0.6%. The error bars given in the results include random and bias errors. The estimation of the bias error includes the uncertainty in the pulse distance, the uncertainty of the freestream velocity for normalized values, and an estimated PIV noise of 0.1 px for the velocity fluctuations. The random error consists of the statistical uncertainties at a 95% confidence level. A typical value for the total error of the mean velocity is approx. 0.7% of the freestream velocity; however, the error increases in regions near the separation bubble and reaches values of approx. 2% of the freestream velocity. To ensure a fully developed turbulent boundary layer, the boundary layer developing on the flat plate is analyzed 0.5 S upstream of the injection point. It possesses a boundary layer thickness of δ 99 S = 2.0 and a Reynolds number based on δ 99 of Re δ99 = For comparison, DNS data of a turbulent boundary layer at Ma = 2 with Re δ99 = from Pirozzoli & Bernardini [2, 3, 14, 15], are superimposed with the current PIV measurements in figure 5. The minimum wall distance achieved in the PIV measurements is y = 0.25 mm. The wall normal profiles of the mean streamwise velocity u /u 0 (figure 5a) are in very good agreement over the entire measurement range down to y δ 99 = 0.03 (y = 0.25 mm). The measured velocity fluctuations u rms u 0 and v rms u 0 (figure 5b), however, show combined PIV inherent noise and wind tunnel freestream turbulence of about 1% at y > δ 99. The PIV and DNS data of u rms /u 0 match within the measurement uncertainty in the range 0.2 < y δ 99 < 1 and show a reasonable agreement

10 (a) Mean velocity u u 0 (b) velocity fluctuations u rms and v rms u 0 u 0 (c) Reynolds stress u v 2 u0 Fig. 5 Comparison of current boundary layer at x S = 0.5 with DNS data of Pirozzoli and Bernardini [2, 3, 14, 15]. closer to the wall, whereas the wall normal velocity fluctuations v rms /u 0 are in good qualitative agreement. The profiles of the Reynolds stress u v 2 u 0 (figure 5c) coincide well in the range y δ 99 > 0.2 and deviate closer to the wall. Overall, although the Mach numbers and Reynolds numbers of both cases differ, there is a satisfactory agreement between the measured boundary layer upstream of the injection point and the DNS data, and the inflow boundary layer can be considered fully turbulent. In figure 6, the normalized mean streamwise velocity u u 0 is shown for cases I and II. The isoline of Ma = 1, calculated under the assumption that the flow is adiabatic, is superimposed. Additionally, the incident shock, the reflected shock, and the expected start of the expansion fan are sketched. The positions of the shocks are found by analyzing the wall normal velocity component, where the flow deflection is clearly visible. For case I (Ma i = 1.2, β = 5 flow deflection), the shock wave imposes a deceleration of the flow at x S = 6, forming a large subsonic region reaching its maximum wall-normal extent at x s = 10 with a thickness of 2S. Case I u u 0 Ma = 1 Case II u u 0 expansion fan Fig. 6 Contours of mean streamwise velocity u u 0 for cases I and II (Ma i = , β = 5 flow deflection)

11 Although backflow occurs at up to 57% of the instantaneous samples at x S = 10, there is no backflow in the mean velocity field. The incident shock wave is reflected at the upper edge of the incoming shear layer at a height of y S = 2. When the injection Mach number is increased to Ma i = 1.8 (case II), the cooling film remains supersonic along the centerline of the injection nozzle. Only a small subsonic region with a thickness of y S = 0.25 develops at x S = 12. Compared to case I, the incident shock penetrates deeper into the shear layer and is reflected in the mixing layer at about y S = 0. (a) Normalized mean velocity u u 0 (b) Normalized velocity fluctuations u rms Fig. 7 Profiles of normalized mean velocity and velocity fluctuations along the centerline of the nozzle (y S = 0.75) for cases I and II (Ma i = , β = 5 flow deflection). u 0 The normalized mean velocity and velocity fluctuation profiles along the slot nozzle centerline at y S = 0.75 are shown in figure 7. The mean streamwise velocity for case I decreases by an amount of Δ u u 0 = 0.5 at x S = 10, whereas in case II, the impinging shock extends down to the cooling film, generating an abrupt velocity drop of Δ u u 0 = 0.1 at x S = 12. The profile of the velocity fluctuation u rms /u 0 along the centerline for case I in figure 7b indicates a highly turbulent flow with a peak turbulence intensity u rms u = 55% at x S = 10. For case II, the shock triggers a gradual increase of the turbulent fluctuations downstream of the velocity drop, leading to an approximately constant turbulence intensity of u rms u = 7% in the range x S > 25. The peaks in the velocity fluctuation profile of case II at x S = 32, 37, and 42 arise from the PIV measurement noise that increases towards the edge of each measurement area due to inhomogeneous particle image quality. In figure 8, the Reynolds stress u v 2 u0 is plotted for cases I and II. The reference case II shows an increase in Reynolds stress magnitude where the incident shock is reflected in the mixing layer at x s = 13. The increased Reynolds stress magnitude persists further downstream while moving slightly away from the wall and decreases starting from x s = 35. Additionally, the Reynolds stress near the wall shows negative values, hence indicating a shock induced transition

12 Case I Reynolds stress u v 2 u0 Case II Reynolds stress u v 2 u0 Fig. 8 Contours of Reynolds stress 2 u v u0 for cases I and II (Ma i = , β = 5 flow deflection). of the boundary layer on the wall. For case I, a strong increase in the magnitude of the Reynolds stress occurs in the shear layer where the flow is deflected upwards and the reflected shock is generated. Downstream of the direct shock interaction, a region with increasing Reynolds stress magnitude is formed in the range 0.75 < y S < 1.4, which implies a significantly increased turbulent transport of heat and momentum in the low Mach number case I compared to the high Mach number case II. For the parameter configuration of a high injection Mach number and an increased shock intensity, i.e., case III, two basic stable flow fields were found during the experiments. The distinctive feature between these flow fields is a significant change of the separation position of the cooling film. Moreover, this change in the separation position occurred randomly between individual measurements, whereby the case with the separation of the cooling film further downstream occurred much more frequently, or, to be more precise, in approx. 90% of all Case IIIa u u 0 Case IIIb u u 0 Fig. 9 Contours of mean streamwise velocity u u 0 for cases IIIa and IIIb (Ma i = 1.8, β = 8 flow deflection).

13 measurements. Hence, case III is divided into cases IIIa and IIIb with case IIIa as the case with the separation point of the cooling film further downstream. Because of the low probability of case IIIb, there is only data available up to x S = 27. The normalized mean streamwise velocity u /u 0 along the centerplane of the nozzle is shown in figure 9 for cases IIIa and IIIb. In both cases, a pronounced shock induced separation of the cooling film is present in the flow field. However, the separation occurs at different streamwise positions. While the flow separates in the vicinity of the shock foot at x S = 9.5 in case IIIa, the separation is shifted upstream to x S = 2.2 in case IIIb. The different locations of separation consequently lead to different deflection angles of the cooling film. In case IIIa, the cooling film is deflected upwards by 15.4 causing a strong deceleration of the flow with subsonic velocities downstream of x S = 15. The weaker deflection in case IIIb enables the deflected cooling film to remain supersonic over a longer distance. Both cases have their reattachment point at approx. x S = 18 and show a similar flow structure further downstream with a large subsonic region below y S = 1.5. The Reynolds stress u v 2 u0 for cases IIIa and IIIb is shown in figure 10. In both cases, a strong negative Reynolds stress can be found at the point where the separation shock emanates from the shear layer. Downstream of x S = 15, both cases show a similar qualitative structure of the Reynolds stress, although in case IIIb the magnitude of the Reynolds stress is around 40% higher. Compared to the reference case II, there is a significantly stronger turbulent transport in the mixing region in the range 13 < x s < 25 and in the shear layer further downstream. Case IIIa Reynolds stress u v 2 u0 Case IIIb Reynolds stress u v 2 u0 Fig. 10 Contours of Reynolds stress u v 2 u0 for cases IIIa and IIIb (Ma i = 1.8, β = 8 flow deflection). The results for case I and case II can be compared to the findings of Konopka et al. [10, 12] who performed large-eddy simulations (LES) of shock/cooling-film interaction with a freestream Mach number of Ma = 2.44 and injection Mach numbers of Ma i = 1.2 and 1.8. In the numerical

14 simulations, the shock generated by a flow deflection of 5 impinges upon the cooling film approx at x imp S = 17. The freestream Reynolds number based on the slot height Re in the investigations of Konopka et al. [10, 12] is Re = Thus, the Reynolds number is lower by a factor of approx. 3 compared to the present study. Additionally, there is a difference in the total temperature ratio. For injection with an injection Mach number of Ma i = 1.2 the total temperature ratio is T 0,i T 0 = 0.8 and for injection with an injection Mach number of Ma i = 1.8 it is T 0,i T 0 = Therefore, the blowing rate M of the LES is higher by approx. 6% (Ma i = 1.2) and 16% (Ma i = 1.8). For the low Mach number case, the general flow structure found in the present study (case I) is in good agreement with the data of Konopka et al. [10], although there are some minor differences. First of all, the LES and the PIV measurements show a great impact of the shock impingement on the cooling-film flow with a pronounced subsonic region downstream the shock impingement, which extends into the mixing layer and is characterized by increased turbulent transport. The LES shows an unsteady laminar separation bubble undergoing transition. This separation bubble is not captured by the time-averaged PIV results. This might be caused by insufficient resolution near the wall or the particle lag. However, backflow that occurs in the instantaneous velocity fields gives strong evidence of the existence of the separation. Additionally, the transition process triggered by the separation bubble is observed in the PIV measurements in form of negative values of the Reynolds stress near the wall downstream of the shock impingement position. Compared to the present study, the incident shock in the LES penetrates deeper into the shear layer and is reflected at approx. y S = 1, whereas the PIV measurements shows a shock reflection on top of the shear layer at approx. y S = 2. The present study shows a stronger influence of the incident shock on the cooling-film flow with a decrease in blowing rate. Therefore, the lower blowing rate of the present study compared to the LES can lead to a more pronounced upward deflection of the cooling-film flow, which pushes the shock reflection off the wall. As in the case of the low injection Mach number, Konopka et al. [12] also found a separated region at an injection Mach number of Ma i = 1.8 that is not captured in the PIV measurement of the present study (case II). The LES predicts a transition of the laminar slot boundary layer at the end of the separation bubble which is also found in the PIV measurements. However, there is a distinctive difference in the flow structure between the LES and the PIV measurements. In the LES, the reflected shock is formed by the compression waves that are created where the flow reattaches downstream the separation bubble. The compression waves that are generated by the upward flow deflection upstream the separation bubble do not unify. Hence, the incident shock is reflected on the bottom wall. In the present study, the shock is reflected at approx. y S = 0, thus in the mixing layer. Therefore, the shock must be formed by compression waves that

15 originate further upstream. This indicates a stronger impact of the shock impingement on the cooling-film flow in the experiments compared to the LES. An explanation can be found in the higher blowing rate of the LES, which is 16% higher than the blowing rate in the present study. A higher blowing rate tends to decrease the influence of the shock on the cooling-film flow leading to a smaller flow deflection upstream of the separation bubble. Overall, the results of the present study show a good agreement with the LES performed by Konopka et al. [10, 12]. Differences apparent in the flow structure can be explained with the differing blowing rates. 4. Conclusion In the present study, supersonic slot-film cooling with shock/cooling-film interaction has been investigated using high-speed PIV measurements. A laminar cooling film is injected tangentially with injection Mach numbers of Ma i = 1.2 and 1.8 beneath a turbulent boundary layer with a freestream Mach number of Ma = The inflow boundary layer has a thickness of 2.0 nozzle heights at the point of injection. A shock wave, generated by a wedge with either β = 5 or 8, impinges upon the cooling film nozzle heights downstream the injection point. For the supersonic turbulent boundary layer, the profiles of the mean streamwise velocity, the streamwise and the wall-normal velocity fluctuations, and the Reynolds stress are in good agreement with DNS data by Pirozzoli & Bernardini [2, 3, 14, 15]. Thus, the inflow boundary layer is confirmed to be fully turbulent at the point of injection. The flow structure in the shock/cooling-film interaction region is highly dependent on the injection Mach number and the shock strength. For a low shock intensity in combination with a high injection Mach number, the cooling film has sufficient momentum to prevent separation at the point of shock/cooling-film interaction. In this case, shock induced transition is visible on the boundary layer forming beneath the cooling film. The incident shock is reflected in the mixing layer between the shear layer and the cooling film, leading to an increased turbulent transport of heat and momentum in the shear layer. A reduced injection Mach number greatly increases the impact of the shock wave on the cooling film. Although no separation is apparent in the mean velocity field, backflow occurs in the instantaneous velocity fields and the cooling film is deflected off the wall. The incident shock is reflected on the edge of the shear layer and a large subsonic region with a thickness of 2 S is formed at the shock foot. Further downstream, the turbulent transport is greatly increased in the cooling film, the mixing layer, and the shear layer. Increasing the shock intensity at the high injection Mach number case leads to a pronounced shock induced separation. The separation bubble exhibits a height of approximately 1 S and a

16 length of 9 S 16 S. Two stable flow structures can be observed in the experiments. The separation point is either 9 S downstream the injection nozzle or further upstream at x S = 2.2. The latter case occurs about every tenth wind tunnel run, and no parameter was found that can force either of the two cases. The separation causes an extensive turbulent transport in the mixing region downstream the shock interaction. In the case where the separation is shifted upstream towards the injection point, the turbulent mixing is even more intense, with an overall increase of the Reynolds stress magnitude of about 40% compared to the more frequently occurring case with separation at the shock foot. The results with a low shock strength are compared to numerical studies of Konopka et al. [10, 12] who performed large-eddy simulations of a shock/cooling-film interaction with flow parameters similar to those in the present study, with exception of the Reynolds number, which is lower by a factor of three in the simulations. For both injection Mach numbers Ma i = 1.2 and 1.8, the simulations and the measurements consistently show a transition of the laminar slot boundary layer. The laminar separation bubble found in the simulations which triggers the transition is not apparent in the PIV measurements. The general flow structure shows differences according to the position where the incident shock is reflected. At both injection Mach numbers, the incident shock in the present study is reflected further off the wall due to differences in the total temperature ratio, and hence in the blowing rate. However, the simulations and the measurements of the current study agree in an increase of the turbulent transport caused by the shock/cooling-film interaction. 5. Acknowledgments This research is funded by the Deutsche Forschungsgemeinschaft within the research project Experimental Investigation of Turbulent Supersonic Film-Cooling Flows. 6. References [1] Alzner, E., Zakkay, V. (1971) Turbulent Boundary-Layer Shock Interaction with and without Injection. AIAA J 9(9): [2] Bernardini, M., Pirozzoli, S. (2001) Inner/outer layer interactions in turbulent boundary layers: A refined measure for the large-scale amplitude modulation mechanism. Phys Fluids 23: [3] Bernardini, M., Pirozzoli, S. (2001) Wall pressure fluctuations beneath supersonic turbulent boundary layers. Phys Fluids 23:085102

17 [4] Holden, M., Nowak, R., Olsen, G. & Rodriguez, K. (1990) Experimental Studies of Shock Wave/Wall Jet Interaction in Hypersonic Flow. In: 28 th Aerospace Science Meeting, Reno, AIAA Paper [5] Juhany, K. (1994) Supersonic Film Cooling Including the Effect of Shock Wave Interaction. Ph D Thesis, California Institute of Technology Pasadena, California [6] Juhany, K., Hunt, M. (1994) Flowfield Measurements in Supersonic Film Cooling Including the Effect of Shock-Wave Interaction. AIAA J 32(3): [7] Kamath, P., Holden, M. & McClinton, C. (1990) Experimental and Computational Study of the Effect of Shocks on Film Cooling Effectiveness in Scramjet Combustors. In: AIAA/ASME 5 th Joint Thermophysics and Heat Transfer Conference, Seattle, AIAA Paper [8] Kanda, T., Ono, F., Saito, T., Takahashi, M. & Wakamatsu, Y. (1996) Experimental Studies of Supersonic Film Cooling with Shock Wave Interaction. AIAA J 34(2): [9] Kanda, T. & Ono, F. (1997) Experimental Studies of Supersonic Film Cooling with Shock Wave Interaction (II). J Thermophys Heat Transfer 11(4): [10] Konopka, M., Meinke, M. & Schröder, W. (2012) Large-eddy simulation of shock-coolingfilm interaction. AIAA J 50(10): [11] Konopka, M., Meinke, M. & Schröder, W. (2013) Large-eddy simulation of shock-coolingfilm interaction at helium and hydrogen injection. Phys Fluids 25: [12] Konopka, M., Meinke, M. & Schröder, W. (2013) Large-eddy simulation of high Mach number film cooling with shock-wave interaction. Progress in Flight Physics 5: doi: /eucass/ [13] Olsen, G., Nowak, R., Holden, M. & Baker, N. R. (1990) Experimental Results for Film Cooling in 2-d Supersonic Flow Including Coolant Delivery Pressure, Geometry, and Incident Shock Effects. In: 28 th Aerospace Science Meeting, Reno, AIAA Paper [14] Pirozzoli, S., Bernardini, M. (2011) Turbulence in supersonic boundary layers at moderate Reynolds number. J Fluid Mech 688: [15] Pirozzoli, S., Bernardini, M. (2013) Probing high-reynolds-number effects in numerical boundary layers. Phys Fluids 25: [16] Seban, R. A., Back, L. H. (1962) Velocity and Temperature Profiles in Turbulent Boundary Layers with Tangential Injection. J Heat Transfer 84:45-54 [17] Westerweel, J. & Scarano, F. (2005) Universal outlier detection for PIV data. Exp Fluids 39: