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Tunnel Background Noise on Compressible Convex-Corner Flows ARTICLE in JOURNAL OF AIRCRAFT · JULY 2013 Impact Factor: 0.56 · DOI: 10.2514/1.C031792
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JOURNAL OF AIRCRAFT Vol. 50, No. 4, July–August 2013
Tunnel Background Noise on Compressible Convex-Corner Flows Kung-Ming Chung,∗ Po-Hsiung Chang,† and Keh-Chin Chang‡ National Cheng-Kung University, Tainan 711, Taiwan, Republic of China DOI: 10.2514/1.C031792
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The perforated test section walls of a transonic wind tunnel are responsible for generating edgetones, thus contributing significantly to the overall noise level and possibly invalidating the measurements of surface pressure fluctuations. In the present study, the wind tunnel was assembled with perforated top/bottom walls, solid side walls, and four perforated walls. The focus was to investigate the effects of tunnel background noise on compressible convexcorner flows, which correspond to the upper control surface of an aircraft wing. External acoustic disturbance has a minor effect on the mean surface pressure distributions, including flow expansion and recompression near the corner. Higher peak pressure fluctuations, which are associated with shock excursion phenomena, are observed with more intense tunnel background noise, particularly for the flow with initial separated boundary layers.
convex corners at high subsonic Mach numbers, which corresponds to a simplified configuration of an upper deflected control surface. In general, there would be a mild initial expansion, followed by a strong expansion near the corner apex, and then there would be downstream recompression. An inviscid parameter M2 η was proposed to scale the flow properties. At M 0.64 and 0.83, the transition from subsonic to transonic expansion-corner flow was observed at M2 η 6.14 [6]. With an increasing freestream Mach number and convex-corner angle, a small separation bubble might be borne at the formation of a normal shock wave [8], and the boundary layer was separated at M2 η ≥ 8.95 [7]. The shock-induced separation resulted in a substantially increased energy level at lower frequencies, and the unsteadiness of the interaction was characterized by an intermittent region and a local peak pressure fluctuation. Further, Chung [6] also indicated that M2 η cannot be used as a similarity parameter at lower subsonic flows (M 0.34). Because the viscous sublayer is relatively unimportant when the Reynolds number is sufficiently large, p another scaling parameter (β M2 η∕ 1 − M2 ), which derived from the hodograph equation for compressible-corner flows [9], was proposed by Chung et al. [10] to scale the flow properties of compressible convex-corner flows. With the Mach number ranging from 0.34 to 0.89, compressible convex-corner flows can be categorized into three flow categories. For subsonic expansion flows and initial transonic expansion flows, the flow expansion near the corner apex and peak pressure fluctuations in the recompression process could be scaled linearly with β (less than 13). The flow expansion was less significant when the local Mach number exceeded the critical Mach number (or β ≈ 13–20). As β is greater than 20, the flow expansion near the corner apex (or the local peak Mach number) and peak pressure fluctuations appeared to be independent from β for an extensive shock-induced separated boundary layer, possibly indicating free interaction [11]. It is well known that acoustic excitation could be used as separatedflow control [12]. In a transonic flow, the aerodynamic loads induced by the acoustic wave might be only a weak flow perturbation, but they could be large enough to be employed as effective control forces. Lu et al. [13] indicated transonic flutter suppression using active acoustic excitations. The control parameters would be the excitation frequency, phase, and location. Furthermore, perforated test section walls in a transonic wind tunnel would generate discrete edgetones. High-level acoustic waves might invalidate fluctuating pressure measurements, and the proper interpretation of the Reynolds number effects in the transonic Mach number range may also be obscured [14]. For the present study, the test section was assembled with perforated top/bottom walls, solid side walls, and four perforated walls. Note that the same model was used in both test section configurations. Surface pressure measurements and oil-flow visualization were conducted to investigate the effects of tunnel background noise on the flow properties of compressible convex-corner flows. Before discussing the results of the present study, brief details of the experiment are outlined next.
Nomenclature Cp Cσ p M M1 p∞ , pw q Xi x x β δ η σp
= = = = = = = = = = = = =
pressure coefficient, pw − p∞ ∕q fluctuating pressure coefficient, σ p − σ p∞ ∕q freestream Mach number local Mach number upstream of shock mean surface static pressure freestream dynamic pressure region of separated boundary layer coordinate along the surface of the corner, cm normalized streamwise distance, x∕δ p similarity parameter, M2 η∕ 1 − M2 incoming boundary-layer thickness, mm convex-corner angle, deg fluctuating surface pressure
I.
Introduction
T
HE active modification of control surfaces, such as flaps and ailerons, could potentially play a role in performance optimization for an aircraft. At cruise speeds, the benefits of variable camber using a simple trailing-edge control surface could approach more than 10% for maximizing the lift-to-drag ratio, especially for nonstandard flight conditions [1]. However, the critical Mach number, onset of boundary-layer separation, and drag are strongly related to the deflection of control surfaces (or camber) [2]. A simplified model of deflected surface was studied by Chung [3]. The increment of lift coefficient appears to be a quadratic function of Mη, and a substantial increase in the lift-induced drag coefficient is observed in transonic separated flows. Further, a study by Mason [4] indicated that the critical Mach number is associated with the transition from subsonic to transonic speed regime, whereas the Reynolds number is important for the onset of boundary-layer separation. Studies on flow properties near the convex corner at the transonic flow regime are scarce. Ruban et al. [5] highlighted the contribution of viscous–inviscid interactions. The displacement thickness near the corner is affected by the overlapping region that lies between the viscous sublayer and the main part of the boundary layer. Further, Chung [6–8] examined a turbulent boundary layer that is past the
Received 19 December 2011; revision received 9 January 2013; accepted for publication 27 January 2013; published online 6 June 2013. Copyright © 2013 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 1542-3868/13 and $10.00 in correspondence with the CCC. *Research Fellow, Aerospace Science and Technology Research Center, Guiren District;
[email protected]. Senior Member AIAA. † Graduate Research Associate, Institute of Aeronautics and Astronautics, Guiren District;
[email protected]. ‡ Professor, Institute of Aeronautics and Astronautics, Guiren District;
[email protected]. 1011
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II.
Experiment
Downloaded by National Cheng Kung University on July 30, 2013 | http://arc.aiaa.org | DOI: 10.2514/1.C031792
A. Transonic Wind Tunnel
The experiments were conducted in the transonic wind tunnel (blowdown type) at the Aerospace Science and Technology Research Center (ASTRC) at the National Cheng-Kung University [15]. The operating Mach number ranges from 0.2 to 1.4, and the simulated Reynolds number is up to 3.5 × 107 ∕m. The major components of the facility include compressors, air dryers, a cooling water system, storage tanks, and a tunnel. The dew point of high-pressure air through the air dryers is maintained at −40 °C under normal operation conditions. The air storage volume for three storage tanks is up to 180 m3 at 5.15 MPa. The 600 mm2 test section is 1500 mm long. In the present study, the test section was assembled with perforated top/ bottom walls, solid side walls, (case A), and four perforated walls (case B). The freestream Mach numbers, M, were 0.64, 0.70, 0.83, and 0.89 0.01. Moreover, for all of the tests, stagnation pressure po was 172 0.5 kPa (25 psi), and the stagnation temperature, T o , was room temperature. The unit Reynolds number ranged from 20.1 to 24.1 × 106 ∕m. It is well known that the perforated test section walls of a transonic wind tunnel would induce strong acoustic wave or tunnel background noise. For the flat plate cases, the spectra show the existence of highlevel discrete peaks, which are discrete tones at frequencies ranging from 4 to 5 kHz. Examples of pressure spectra at M 0.64 are shown in Fig. 1. It is broadband for case B. Further, the normalized surface pressure fluctuations, σ p ∕q at 39 mm upstream of the convex corner, are summarized in Fig. 1. At M 0.64 and 0.70, the levels of σ p ∕q for cases A and B are roughly the same and increases with the
freestream Mach number. In particular, σ p at M 0.89 is 5.61 and 6.74% of the freestream dynamic pressure q for cases A and B, respectively. To acquire data, a NEFF 620 instruments system and a LeCroy data acquisition system were employed. The test conditions were recorded by the NEFF system, whereas the LeCroy 6810 waveform recorders were used for surface pressure measurements. A host computer using CATALYST software controlled the setup of the LeCroy waveform recorders through a LeCroy 8901A interface. The output range of each waveform recorder was adjusted for optimum resolution, and the sampling period is 5 μs (200 kHz). All input channels were triggered simultaneously using an input channel as the trigger source. B. Test Model
The test model comprised a flat plate and an interchangeable instrumentation plate shown in Fig. 2. The flat plate is 150 × 450 mm and is supported by a single sting mounted on the bottom wall of the tunnel. Six instrumentation plates (150 × 150 mm) with η (convexcorner angle) that equaled 0, 5, 10, 13, 15, and 17 deg were fabricated. The convex corner was located at 500 mm from the leading edge of the flat plate for a naturally developed turbulent boundary layer, and the boundary-layer thickness at 25 mm upstream of the convex corner was estimated to be about 7 mm. Note that the transition of the boundary layer under the present test conditions was close to the leading edge of the flat plate [16]. A total of 19 pressure taps, which were 6 mm apart and 2.5 mm in diameter, were drilled along the centerline of each instrumentation plate perpendicularly to the test surface for flush-mounted pressure transducers. Two side fences of 13.5 cmlength × 4.5 cmheight × 0.5 cm (thickness) were installed at both sides of the instrumentation plate to prevent crossflow. Further, the oil-flow visualization technique was employed to check the two-dimensionality of the flow and to visualize the surface flow pattern. A thin film of the mixture (titanium dioxide, oil, oleic acid, and kerosene) was applied on the surface of the instrumentation plate. The surface streamlines over the whole span were straight and parallel to the incoming flow direction for the flat plate cases or the attached expansion flows. Further, the accumulation line at the shock foot did not show any well-defined three-dimensional deformation of the shock surface, except near the lateral side-fence regions. In the separated region, the surface flowfield was not strictly twodimensional. C. Experimental Techniques
The dynamic pressure transducers (Kulite model XCS-093-25A, B screen), powered by a Topward electronic system (model 6102) with a power supply of 15.0 V, were employed for the surface pressure measurements. The transducer’s outer diameter is 2.36 mm, and its sensing element is 0.97 mm in diameter. The natural frequency is 200 kHz as quoted by the manufacturer. All pressure transducers were fixed using silicone rubber sealant, and the flushness was checked by a machinist’s block to minimize interference with the flow. External amplifiers (Ecreon model E713) were also employed to improve the signal-to-noise ratio. With a gain of 20, the rolloff frequency is about 140 kHz. Each test record contained 131,072 data points for statistical analysis. The data were divided into 32 blocks. The mean values of each block (4096 data points) were calculated.
Fig. 1
Tunnel background noise.
Fig. 2
Test configuration.
CHUNG, CHANG, AND CHANG
The uncertainty of the experimental data of the flat plate case was estimated to be 2.5 and 0.1% for the static pressure coefficient Cp and surface pressure fluctuation coefficient σ p ∕pw , respectively.
III.
Results and Discussion
Downloaded by National Cheng Kung University on July 30, 2013 | http://arc.aiaa.org | DOI: 10.2514/1.C031792
A. Surface Pressure Distributions
For subsonic expansion flow, examples of the normalized mean pressure distributions Cp (M 0.64 and 0.83) at η 5 deg (β 2.67 and 6.18) are shown in Fig. 3. The origin of the x coordinate is set at the corner. In general, the tunnel background noise has a minor effect on the expansion and recompression process near the corner. At further-downstream locations, the level of Cp in case B is lower than that of case A. Ruban and Turkyilmaz [17] indicated that the viscous sublayer exhibits very high sensitivity to pressure variations. A small pressure rise would lead to the thickening of the flow filaments, implying that the streamline at further-downstream locations from a convex corner is displaced from the wall with higher external acoustic disturbance. For the initial expansion flows, Cp distributions at M 0.70 (β 8.92 − 11.66) are shown in Fig. 4. The sonic condition is also shown for reference. Under both cases A and B, the flows expand to supersonic speed immediately downstream of the corner and then recompress to subsonic speed at x 1 − 2. Stronger expansion near the corner and a longer downstream pressure recovery process are associated with increasing η or β. However, there is only a slight difference in flow development between cases A and B. For the extensive separated flows, Cp distributions at M 0.89 (β 22.58 − 29.53) are shown in Fig. 5. It can be seen that there is a delay in the recompression process at further-downstream locations (x is greater than 3). The flows remain supersonic downstream of the corner and approach new equilibrium conditions for all test cases. With increasing η, there is strong expansion near the corner and lower level of Cp in downstream locations. The effect of external acoustic disturbance (cases A and B) is minimal.
Fig. 3 Distributions of mean pressure coefficient, η 5 deg, and subsonic expansion flows.
Fig. 4 Distributions of mean pressure coefficient and initial transonic expansion flows.
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B. Surface Pressure Fluctuations
The distributions of the fluctuating pressure coefficient Cσ p of subsonic expansion flows (M 0.64 − 0.83 at η 5 deg or β 2.67 − 6.18) are shown in Fig. 6. Under both cases A and B, the amplitude of peak Cσp downstream of the corner increases with the freestream Mach number, particularly for case B at M 0.83 (Cσ p;max 2.67%). Because the local peak Mach number and adverse pressure gradient for both test cases are roughly the same, the increment in peak Cσ p is considered due to the tunnel background noise. Further, Cσ p distributions for the cases of initial expansion flows (M 0.70) are shown in Fig. 7. Similar to the observation on the mean surface pressure distributions, as in Fig. 4, the effect of external acoustic disturbance is minimal. For the cases of a separated boundary layer (M 0.83, at η 13 15 deg or β 16.1 and 18.5), Chung [7] indicated that Cσ p increases downstream of the corner and reaches the maximum ahead of the separation point shown in Fig. 8 for case A. At further-downstream locations, the plateau level of pressure fluctuations increases slightly
Fig. 5 Distributions of mean pressure coefficient and extensive separated flows.
Fig. 6 Distributions of fluctuating pressure coefficient and subsonic expansion flows.
Fig. 7 Distributions of fluctuating pressure coefficient and initial transonic expansion flows.
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Fig. 8 Distributions of fluctuating pressure coefficient and transonic expansion flows.
with increasing η. For case B, sufficiently higher peak pressure fluctuations are observed downstream of the corner. A study on supersonic ramp flow by Dolling and Or [18] indicated that the maximum surface pressure fluctuations are essentially related to the oscillation of a shock wave, implying that higher tunnel background noise at M 0.83 would enhance the shock excursion phenomenon. At further-downstream locations, the distributions of Cσ p show a slower recovery process for case B. For M 0.89 at η 13–15 deg (or β 22.6–29.5), as shown in Fig. 9, these test cases correspond to an extensive separated boundary layer. In general, the amplitude of surface pressure fluctuations upstream of the corner, which is lower than that of flat plate cases, decreases gradually and reaches the minima at x 1.27 for all test cases. However, it is not clear why there is a lower level of Cσp for case B. Further studies are required. Moreover, there is a delay in the recompression process shown in Fig. 5. Therefore, the peak pressure fluctuations are observed at x 4.5–5.3 for all test cases, and then the amplitude of Cσ p decreases rapidly downstream to become a new equilibrium level. Note that the increment in peak pressure fluctuations ranges from 1.5 ∼ 3.3% with higher tunnel background noise at M 0.89.
Fig. 10 Expansion of convex-corner flows.
Fig. 11 Peak Mach number of convex-corner flows.
Viscous–inviscid interactions result in the flow expansion near the corner [5], and the local minimum mean surface pressure or the peak Mach number Mpeak would affect downstream flow properties, for example an attached/separated boundary layer. The minimum surface pressure coefficient (pw ∕p0 min is plotted against β for all test cases shown in Fig. 10. Note that the sonic condition corresponds to pw ∕p0 0.5283 for isentropic flow. In general, there is stronger expansion with higher β. Only a slight difference in pw ∕p0 min can be seen between cases A and B. Further, for a transonic expansion flow, the wall pressure signals could be the superposition of very large amplitude fluctuations on the undisturbed pressure signal. Thus, only the undisturbed pressure signals upstream of a shock wave were employed to calculate the local Mpeak . As shown in Fig. 11, Mpeak increases with β and approaches asymptotic values for both
cases A and B. External acoustic disturbance appears to have a minor effect on viscous–inviscid interactions near the corner. For the flow with a shock-induced boundary-layer separation, Chung [8] indicated that the increased Mpeak would result in a considerable growth of the separation length Xi . However, based on oil-flow visualization, there is less increment in Xi with Mpeak for case B shown in Fig. 12. A study by Tran and Bogdonoff [19] found that peak pressure fluctuations were governed by the overall inviscid shock strength and spatial extent of the intermittency. For case A, Chung et al. [11] discovered that the amplitude of (σ p ∕pw max increased with β for the attached and incipient separated flows. A big jump in the level of (σ p ∕pw max was observed at β is greater than 20, and is also shown in Fig. 13. For case B, the effect of tunnel background noise on the amplitude of (σ p ∕pw max is not significant for the subsonic expansion flow. Once the local Mpeak exceeds the critical Mach number (≈1.3), the amplitude of (σ p ∕pw max at M 0.83 and 0.89 is higher than that of case A, particularly for the test cases of the initial separated boundary layer. Further, Rubin and Turkyilmaz [17] indicated that the interaction region of the transonic expansion flow has a conventional triple-deck structure. Therefore, external acoustic disturbance (or pressure perturbation) might
Fig. 9 Distributions of fluctuating pressure coefficient and extensive separated flows.
Fig. 12 Separation length.
C. Effects of Tunnel Background Noise on Flow Properties
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References
Downloaded by National Cheng Kung University on July 30, 2013 | http://arc.aiaa.org | DOI: 10.2514/1.C031792
Fig. 13 Peak pressure fluctuations.
transmit from the upper deck to the lower deck, resulting in streamlines being displaced from the wall. It is considered that the decreased Xi for case B, shown in Fig. 12, is due to the thickening of the viscous sublayer (or an increment in Cp near the reattachment location). Further, Chung [8] proposed that shock excursion could be associated with the motion of a separation bubble (expansion and contraction). At a given test condition (the freestream Mach number and convex-corner angle), the decreased Xi , as a characteristic length, might imply higher frequency motion of the separation bubble. Subsequently, this would enhance shock excursion phenomenon and induce higher peak pressure fluctuations for the compressible convex-corner flow with a separated boundary layer shown in Fig. 13.
IV.
Conclusions
The perforated test section walls would generate discrete edgetones in a transonic wind tunnel, which would affect the flow development (expansion and recompression process), boundarylayer separation, and shock excursion on compressible convexcorner flows. In the present study, the amplitude of surface pressure fluctuations for the test cases of four perforated test section walls (case B) is considerably higher than those of solid side walls and perforated top/bottom walls (case A) at M 0.83 and 0.89. From the mean surface pressure distributions, it is found that the tunnel background noise has a minor effect on the transition from subsonic to transonic expansion flow and the local peak Mach number. However, the decreased separated-flow region is associated with the enhanced shock excursion phenomenon (or higher peak surface pressure fluctuations) for the test cases of four perforated test section walls. Such association implies that intense discrete edgetones would affect the viscous–inviscid interactions (or displacement of a viscous sublayer) downstream of the shock location and motion of the separation bubble. Therefore, care must be taken when interpreting the data of peak fluctuating loads obtained experimentally in a transonic wind tunnel with intense tunnel background noise.
Acknowledgments This research was supported by the National Science Council (NSC 99-2923-E-006-007-MY3). The authors are also thankful for the technical support of the Aerospace Science and Technology Research Center technical staff with the experiments. The authors are thankful to the Associate Editor and to the reviewers who clearly helped to make this paper better than it was initially.
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