Characterisation of a 3D l/h=5 Rectangular Cavity Flowfield using Experimental and Numerical Techniques

S.A.Ritchie*, K. Knowles †

Department of Aerospace, Power and Sensors Cranfield University, RMCS, Shrivenham,

Swindon, Wiltshire, SN6 8LA

s.a.ritchie@cranfield.ac.uk k.knowles@cranfield.ac.uk

N.J.Lawson‡

Department of Aerospace Sciences School of Engineering, Cranfield University, Bedfordshire, MK43 OAL

n.lawson@cranfield.ac.uk

Abstract

The application of particle image velocimetry (PIV) and surface pressure measurement to transonic cavity flow are presented. Data is recorded from a 3D l/h=5 rectangular cavity at a freestream Mach number of M∞=0.85. The PIV data is acquired using a commercially available digital PIV acquisition system and window deformation processing software. Time averaged 2D PIV results at three spanwise planes (z/w=0.5, 0.667 and 0.833) are compared with time averaged 3D URANS CFD simulations on the same planes. Time-averaged and unsteady cavity floor static pressure data on the three planes are compared for both the experimental and numerical data. The time-averaged floor pressure distributions and velocity vector maps for the experimental data shows the cavity to be exhibiting transitional-open flow behaviour with a strong oscillation feedback mechanism which excites the first three Rossiter oscillation modes. The numerical simulation predicts a flow behaviour which is typical of open flow behaviour with a strong feedback mechanism exciting the first and third Rossiter modes. The numerical simulation reveals one of the key limitations of the URANS method for predicting separated oscillating flows with the unsteady pressure spectra containing no broadband flow unsteadiness.

Keywords: Cavity Flow, Transonic Flow, Aero-acoustics, CFD, PIV, Unsteady Pressure, Stores Release.

1 Introduction Recently, the phenomenon of flow within a rectangular cavity submersed in freestream flow has become the focus of much research interest due to design drivers like stealth and aerodynamic efficiency in future aircraft projects such as the F-35 Joint Strike Fighter (JSF). These aircraft are designed such that the internal carriage of weapons is necessary to keep radar cross-section as low as possible in order to increase the aircraft’s survivability. However, when the weapons bay doors are opened, flow over the exposed weapons cavity results in a number of undesirable flow effects. These include self-sustaining acoustic resonances and high intensity tones which can lead to structural fatigue in ‘open’ cavities [1] and adverse longitudinal pressure distributions

*PhD Research Student, Aeromechanical Systems Group † Head, Aeromechanical Systems Group ‡ Senior Lecturer, Department of Aerospace Sciences, Cranfield School of Engineering

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leading to nose-in pitching moments on stores released from ‘closed’ cavities [2]. The two different cavity flow regimes, ‘open’ and ‘closed’ are primarily dependent on the length to depth ratio (l/h) of the cavity. Figure 1 and

Figure 2 show the mean flow features of ‘open’ and ‘closed’ cavity flows respectively for subsonic and supersonic flow speeds.

Many previous studies on rectangular cavity flows have focussed solely on the time-averaged and transient measurement of the flow pressures at the cavity surfaces using high frequency scanning transducers and qualitative visualisation techniques such as Schlieren imagery and oil flow visualisation [3-5]. Recently, the application of advanced optical techniques such as particle image velocimetry (PIV) [6] and laser Doppler anemometry (LDA) [7] has allowed detailed quantitative flow velocity data to be acquired with no physical intrusion into the flow.

PIV is now a fully established technique for the measurement of instantaneous two-dimensional velocity fields [6, 8]. The technique involves illuminating a two-dimensional plane within the flow using a double-pulsed laser light sheet. Homogeneous seeding is introduced into the flow and a pair of images of the illuminated plane are captured using a CCD camera, one during each laser pulse. Local seeding displacement is correlated between the frames of the image pair using spatial correlation techniques which results in an instantaneous two-dimensional vector map of the illuminated plane [9]. The instantaneous and non-intrusive nature of PIV means it is particularly suited to the measurement of high-speed flows with complex structures [10-13] and flows which, may otherwise, prove difficult to measure using traditional intrusive instruments [6, 14]. The technique is well suited to experimental conditions where flow times are short such as blow down or intermittent tunnel facilities where data acquisition times may be limited to as little as 10 seconds per run.

This paper presents two-dimensional PIV and surface static pressure results from a three-dimensional rectangular cavity with a length-to-depth ratio of l/h=5 and a width-to-depth ratio of w/h=2.5 at a freestream Mach number of M∞=0.85 (V∞=270ms-1) and a constant unit Reynolds number of 13.14x106 m-1. The cavity is l=160mm in length, h=32mm in depth and w=80mm in width. The time-averaged PIV and static pressure results acquired at three spanwise planes (z/w=0.5, 0.667 and 0.833) are compared with data from a URANS CFD simulation. The paper also highlights the inherent difficulties involved in acquiring successful PIV data from the transonic flow regime and the steps being taken to overcome these. To the authors’ knowledge these are the first published non-intrusive measurements of flow at spanwise planes other than the centreline plane within a rectangular cavity in the transonic flow regime.

2 Methodology All tests were conducted using the Department of Aerospace, Power and Sensors (DAPS) transonic wind tunnel (TWT) at Cranfield University’s Shrivenham campus, a schematic of which can be seen in Figure 4. The tunnel has a working section of 206mm (height) by 229mm (width) and is approximately 500mm in length. The facility is a closed circuit ejector driven tunnel supplied with air from two Howden screw-type compressors. The compressors supply air at up to 7 bar(g), which is dried and stored in a 34m³ reservoir. The stored air is sufficient to run the tunnel at a test section Mach number of M∞=0.85 for 10 seconds.

The x, y and z axes are orthogonal and aligned with the principal axes of the cavity in accordance with a right-handed system. The origin of the system is located as in Figure 3 at the junction between the upstream wall and the left side wall in the mouth plane of the cavity. The flow velocity components u, v and w are aligned with the principal x, y and z axes respectively

2.1 Particle Image Velocimetry (PIV)

The PIV measurements were performed using a clear cavity mounted in a modified tunnel sidewall. The clear cavity was constructed from polycarbonate and was attached to the underside of a raised flat plate which also acts as a splitter for the tunnel wall boundary layer. Data cannot be acquired in the first 2mm of the cavity depth due to the presence of the splitter plate. Similarly, the wind tunnel design does not allow the freestream flow to be measured using PIV, due to a lack of optical access. A detailed view of the cavity PIV rig can be seen in Figure 5.

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A custom-built flow seeding system injected water particles with a mass median diameter of 10µm into the windtunnel in order to seed the flow. The seeder supplied a rake of three Bete® PJ atomiser nozzles equi-spaced across the wind tunnel contraction section with high pressure water at 2000psi.

PIV data acquisition was performed using a Dantec FlowMap 500 processor box, a Kodak ES1.0 megapixel CCD camera and a New Wave Gemini Nd:YAG double pulsed laser. The Kodak ES1.0 camera frame rate and laser repetition rate allowed data to be recorded at up to 15Hz. The light sheet was projected into the cavity through the clear floor and was oriented parallel to the freestream direction. The spanwise position of the light sheet could be varied by moving the traverse on which the camera and laser were mounted in the y-axis in order to illuminate the three different measurement planes. From this point onwards, the z/w=0.5, 0.667 and 0.833 planes will be referred to as the CL, OC1 and OC2 respectively. The seeded light sheet was viewed via a surface coated mirror angled at 45° to the cavity right side wall which provided a field of view normal to the light sheet orientation. A detailed top view of the set up can be seen in Figure 6 and a detailed plan view in Figure 7. PIV data processing was performed using LaVision® DaVis software which is an FFT-based code that includes a window deformation algorithm.

The DaVis software employs an iterative image deformation algorithm, similar to those reviewed by Scarano [15], which more effectively extracts vectors from complex rotating flows with high velocity gradients. Whilst standard cross-correlation techniques use square interrogation regions in the first and second frame of an image pair, the window deformation technique deforms the interrogation region in the second frame according to the velocity gradient preset within that region. This leads to identical displacements for all seeding particles within a region which results in improved signal-to-noise ratio and thus higher vector field accuracy.

The details of the processing scheme used to extract flow data from the image pairs can be seen in Table 1 below.

Table 1 DaVis PIV Processing Details

Cavity Geometry l/h=5 Primary Correlation

Window Size (pixels) 32x32

Secondary Correlation Window Size (pixels) 16x16

Number of Iterations per Image Pair 4

Maximum Search Length

25% of window

size Vectors per Image 15876

2.2 Surface Static Pressure

The surface static pressure measurements were acquired using a modification to the rig compared to that seen in Figure 5. The clear cavity was replaced with an all aluminium cavity which was tapped with static taps along the CL, OC1 and OC2 planes. Each of the spanwise planes had 9 tappings equi-spaced between the streamwise positions x/l=0.1-0.9. The pressure data at each tapping was acquired using a Scanivalve® ZOC block electronic scanning pressure (ESP) module which captured data at 10kHz sampling rate. The time-averaged pressure results were constructed from the mean of 65536 samples acquired over 4 wind tunnel runs. The unsteady pressure spectra were constructed by averaging 4 spectra generated from 16384 samples each i.e. 1 wind tunnel run.

2.3 Numerical Simulation

The numerical simulation of the l/h=5 cavity presented in this paper was performed using the commercially available CFD code Fluent® and the mesh generation package GAMBIT®. The cavity flow was simulated as a half-domain case with a plane of symmetry constraint applied along the cavity centreline.

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The simulation was performed with the boundary layer approaching the cavity grown to the required thickness in separate domain over a distance of 1.2245m. The velocity profile of the boundary layer was patched to the inlet face of the computational domain with a user defined function (UDF) and was then allowed to grow naturally over the same 167.5mm as in the first simulation. This resulted in a boundary layer thickness of δ0.99=18.2mm at the reference point 30m upstream of the cavity leading-edge.

The domains for the cavities were sized at 500mm long to correspond to the size of the test rig flat plate and 320mm high to corresponding to the TWT test section width. Table 2 lists the details of the grids and flow solver variables for the two different cavity geometries.

Table 2 Numerical Simulation Details

Cavity Geometry l/h=5 Mesh Type Hexahedral

Total Number of Cells 952000

Cell Refinement in Cavity (length x depth x width)

160 x 64x40

Flow Solver Type Segregated-Implicit

Turbulence Model Realizable k-ε

Time Step Size (s) 1.76e-5 Total Number of

Time Steps 10000

Solution Flow Time (s) 0.1

The predictions were made using the segregated implicit solver with the realizable k-ε turbulence model. This particular turbulence model was chosen as it has been previously used in a number of studies involving flows with high shear and regions of recirculation and has been shown to be more effective for flows with regions of flow impingement and recirculation than the standard k-ε model [16]. The segregated-implicit solver was chosen over the coupled-implicit solver as it is less memory-intensive allowing solutions to be attained more quickly. The segregated solver also offers better convergence performance than the coupled solver for the cases considered. The solution time-step was defined such that each cycle of the 2nd Rossiter mode oscillation (1131Hz) was defined by 50 time-steps. This approach to time-step definition is based on the technique used by Soemarwoto and Kok [17] during the simulation of supersonic three-dimensional rectangular cavity flows.

The simulation was performed using 8 processors on the Cranfield University/Cambridge University High Performance Computing (HPC) Facility. With the available resources a single time step (30 iterations) was computed in approximately 6 minutes. Figure 7 shows the computational mesh and the mesh refinement at the cavity leading edge for the l/h=5 case.

3 Results and discussion

3.1 Pressure Data

3.1.1 Time-averaged Pressure Data

The time-averaged pressure coefficient data acquired along the floor of the l/h=5 cavity is shown in Figure 9. The three spanwise distributions show close agreement in trend along the entire cavity length. The Cp values between x/l=0.1-0.6 are very similar for the three planes suggesting that the pressure field along the first 60% is relatively uniform across the span. In the downstream 40% of the cavity, the spanwise positions show similar trends, however, there are slight variations in the peak Cp values. The peak Cp value is found on the CL plane of the cavity with reducing values seen on the OC1 and OC2 planes respectively. The Cp along the first 60% of the

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cavity floor shows a slight decrease moving downstream which reaches a minimum at approximately x/l=0.5 with a marginally negative Cp value. There is a rapid increase in Cp over the downstream 40% of the cavity length reaching a maximum value at x/l=0.9 which is the final pressure tapping along the cavity length. The measured Cp distributions show a variation from the typical open flow Cp profile suggested by Charwat et al. [18] which shows a pressure profile which is uniform over the first 80-85% of the cavity length with a rapid increase in Cp values in the final 15-20% where the flow within the cavity turns to flow vertically down the downstream wall. The measured pressure profiles suggest that the flow within the cavity is has a much larger vertical component driving flow towards the cavity floor and increasing the Cp values from an earlier streamwise position which is typical of a flow where the shear layer path is deflected into the cavity towards the floor. Stallings and Wilcox [19] define flow which exhibits a relatively uniform pressure distribution over the first 50-60% of the cavity length followed by an increase in Cp over the final 40-50% of the cavity length as transitional-open cavity flow where the shear layer is deflected into the cavity before reaching the downstream wall and then depending on the level of deflection, which is defined by the l/h ratio of the cavity, either i) deflects back out of the cavity as it approaches the downstream wall or ii) impinges on the downstream wall and turns to flow upstream within the cavity.

The peak Cp value in the CL and OC1 planes is Cp=0.1 which is seen at the x/l=0.9 streamwise tapping. The close agreement in the trends and peak Cp values in the CL and OC1 planes suggest very similar flow behaviour in the two planes. Further investigation of this will be made during the presentation of the PIV flow structure which follows. The peak Cp value at x/l=0.9 on the OC2 plane is smaller than compared with the CL and OC1 planes suggesting that the shear layer deflection into the cavity is reduced closer to the sidewalls and hence the shear layer impingement on the downstream wall. The peak Cp value in the OC2 plane is Cp=0.065 which is a 35% reduction on the values seen in the CL and OC1 planes. The PIV flow structure vector maps presented below will be used to further investigate the reasons for the reduction in peak Cp on the OC2 plane compared with the CL and OC1 planes as further comment cannot be made based on the surface pressure profiles alone.

3.1.2 Unsteady Pressure Data

Figure 10 shows the unsteady pressure spectra for the x/l=0.9 pressure tapping on the CL, OC1 and OC2 planes. The spectra show the presence of high intensity peaks within the signal, the frequencies of which are compared with the theoretical Rossiter frequencies calculated using the ‘modified-Rossiter’ equation [20] in Table 3.

Table 3 Comparison of l/h=5 Theoretical and Experimental Rossiter Mode Frequencies

Rossiter Mode

Number

Theoretical Oscillation

Frequency (Hz)

Experimental Oscillation

Frequency (Hz) 1 461.88 CL - 463.65 2 1131.29 CL – 1074.97 3 1800.70 CL – 1795.93 1 461.88 OC1 -463.65 2 1131.29 OC1 – 1084.94 3 1800.70 OC1 – 1795.94 1 461.88 OC2 -463.65 2 1131.29 OC2 – 1104.51 3 1800.70 OC2 – 1792.96

The correlation between theoretical and experimental oscillation characteristics is excellent for the 1st and 3rd Rossiter modes with the experimental data showing less than 0.5% variation with the theoretical data in both modes. The 2nd mode data shows a 2.4% variation on the CL plane rising to a 5.3% variation on the OC2 plane compared with the theoretical values. The cavity is shown to be oscillating with a 1st mode dominance and a peak sound pressure level (SPL) of 161dB. The 2nd and 3rd modes of oscillation are less intense than the 1st mode with peaks of 140dB and 129dB respectively. The 3rd mode of oscillation is the highest discernable mode of oscillation before the high level of broadband background noise envelops the pressure peaks. The attenuation of higher modes within the cavity is thought to be a result of the reduction in strength of the feedback mechanism within the cavity for transitional-open type flow compared with open type flow.

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3.1.3 Oscillation Mode Shapes

The experimentally measured mode shape which corresponds to the first Rossiter peak in the pressure spectra can be seen in Figure 11. This is the mode shape which corresponds to a modal number of m=1 in the modified Rossiter equation [20]. The mode shape has a distinctive ‘V’ profile which is typical of a Mode II oscillation based on the definitions given by Rossiter [20]. The peak SPL in this mode is located at x/l=0.9 and has a value of approximately 161dB on the three measurement planes. The minimum SPL value is located at x/l=0.5 is between 140-143dB on the three planes. The SPL values near the upstream wall (x/l=0.1) are lower than the SPL at the downstream end of the cavity (x/l=0.9) which can be explained by the motion of the shear layer. When the shear layer separates from leading edge of the cavity and begins to flap, the motion near the upstream wall is restricted compared to the downstream end of the cavity as would be expected for a free shear layer in which the amplitude of the oscillation increases with distance from the separation point. The minimum SPL trough in the profile is due to a pressure node caused by a π phase change in pressure seen in Mode II oscillation [20].

3.2 PIV Data

PIV image sets of 70 pairs were acquired per run at a 15Hz sampling rate and processed into instantaneous then time-averaged vector maps and using the DaVis code. Given a sample size of N=70 per run, statistically the time-averaged results will have a 12% uncertainty (1/√N) [21]. This was improved, however, to 3.7% by combining data from10 runs (700 image pairs) in each spanwise measurement plane. The data presented is under-sampled 3 times in order to aid the clarity of the flow structures.

On the centreline plane (CL), the flow structure extracted from the images contains a large recirculation (‘A’) which is centred at x/l=0.5, y/h=-0.5 and a second smaller recirculation (‘B’) centred at x/l=0.75, y/h=-0.87. The processing algorithm is unable to fully extract the details of the two flow features at the junction between the two recirculations as the flow directions are directly opposed which leads to difficulty in estimating the particle shift between the first and second frames in the pair. As a result, the upstream extents of recirculation ‘B’ and the downstream extents of recirculation ‘A’ are not well defined. The second recirculation is formed due to the deflection of the shear layer into the cavity at the downstream wall which is caused by the thick shear layer approaching the cavity. As the deflected shear layer approaches the downstream wall of the cavity, its path appears to flow out of the cavity over the trailing-edge but cannot change rapidly enough to fully reverse the deep flow deflection and impinges on the downstream wall. This causes the flow to travel towards the cavity floor and out in the spanwise direction towards the sidewalls. The slight change in shear layer path is, however, sufficient to cause the formation of a small recirculation region (‘B’) under the shear layer between the downstream extents of recirculation ‘A’ and the downstream wall. The peak velocity magnitude in the centreline plane is approximately V=140ms-1 (52% of freestream value) which is seen in the deflected shear layer near the downstream wall. The peak vertical velocity in the CL plane is v=80ms-1and occurs directly adjacent to the downstream wall.

The OC1 plane mean flow field shows close similarity in terms of flow structure to the CL plane with the large recirculation ‘A’ centred at x/l=0.5, y/h=-0.5 and the second recirculation ‘B’ centred at x/l=0.75, y/h=-0.87. As in the CL plane, recirculation ‘B’ is not well-defined at its upstream extents. However, the downstream extent of recirculation ‘A’ is more clearly defined than for the CL plane. The peak velocity magnitude in the plane is approximately V=140ms-1 (52% of freestream value) which as for the CL plane occurs in the deflected shear layer. The peak vertical velocity is also very similar to the CL plane value at v=80ms-1 which is seen in the flow adjacent to the downstream wall below the level of the shear layer impingement.

The OC2 plane shows a very different flow structure to those measured in the CL and OC1 planes. The downstream recirculation ‘B’ which is situated at approximately y/h=-0.8 in the CL and OC1 planes has moved vertically towards the mouth plane of the cavity and is centred at y/h=-0.6. The extents of the structure is also more clearly defined. The streamwise centre of the recirculation has also moved from x/l=0.75 in the CL and OC1 planes to x/l=0.93 in the OC2 plane. The size of recirculation ‘B’ is increased within the cavity due to the change in shear layer behaviour close to the cavity sidewall compared with the CL and OC1 planes. As the shear layer flows into the cavity on the OC2 plane it is prevented from deflecting as deeply as on the CL and OC1 planes because of the proximity of the sidewall which radically reduces the spanwise diversion of the flow in the OC2 plane at the downstream wall compared with that seen in the CL and OC1 planes. The shear layer path is thus deflected up towards the cavity mouth plane at a streamwise position of x/l=0.92, y/h=-0.65 to allow it to flow over the trailing-edge since it cannot spread out along the downstream wall. This causes the formation

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of a much larger downstream recirculation (‘B’) compared with the one seen in the CL and OC1 planes. The increase in the size of recirculation ‘B’ is accompanied by a reduction in the size of recirculation ‘A’ whose downstream extents is now seen at x/l=0.65 compared with x/l=0.5 in the CL and OC1 planes. The peak velocity magnitude within the cavity at the OC2 plane is approximately V=90ms-1 (33% of freestream value). The peak velocity in the OC2 plane is significantly lower than in the CL and OC1 planes as the shear layer is no longer deflected into the cavity which causes the flow acceleration over recirculation ‘A’ but instead is elevated above the level of the mouth plane by the proximity to the sidewall. The peak vertical velocity in the OC2 plane is approximately v=-60ms-1 which occurs in the vertical flow region adjacent to the downstream wall as in the CL and OC1 planes. The change in flow structure in the OC2 plane also explains the reduced peak Cp value in the pressure distribution (Figure 9) since the amount of flow impingement occurring at the downstream wall is reduced compared with the CL and OC1 planes.

The data between x/l=0-0.15 in each of the three planes shows very low speed and unstructured flow which is a direct consequence of the flow behaviour identified in oil flow visualisation studies conducted by Ritchie [22]. A pair of vertically oriented ‘tornado-like’ vortex structures are located in the cavity between x/l=0-0.15 which result in flow that is largely out-of-plane with respect to the two-dimensional PIV vector maps in the OC1 and OC2 planes. Figure 13 shows a graphical representation of the surface stream traces on the cavity surfaces based on the data acquired during the oil flow visualisation studies.

The flow data extracted from the raw image pairs shows the l/h=5 cavity to exhibit transitional-open flow behaviour which is in agreement with the findings from the surface pressure data. The transitional-open flow behaviour is thought to be caused by the thick oncoming boundary layer which results in a thick shear layer with a deep mean deflection into the cavity at the downstream wall.

3.3 Numerical Data

3.3.1 Time-averaged Pressure Data

The numerical Cp profiles seen in Figure 9 show differences in trend compared with the experimentally measured data. The profiles vary from slightly positive to negative along the first 85% of the cavity length before a rapid pressure increase to a maximum close to the downstream wall due to flow stagnation. The Cp trends and magnitudes of the numerical profiles across the three planes show close agreement which is consistent with the observations made in the experiments. The peak Cp within the cavity is seen on the CL plane with the OC1 and OC2 planes showing the second and third highest Cp values respectively. This is also consistent with the observations in the experimental and modelling approach 1 numerical data. At the final streamwise tapping in the experimental data (x/l=0.9), the Cp values on the CL and OC1 planes are higher than the corresponding numerical values which can be attributed to a difference in the flow type being exhibited within the cavities. The Cp profiles for numerical data are typical of those seen in a cavity exhibiting open flow behaviour compared with the transitional-open flow behaviour seen in the experimental study. At x/l=0.9, the numerical Cp values on the CL and OC1 planes are 0.03 counts lower than the experimentally measured values on the same planes.

3.3.2 Unsteady Pressure Data

The unsteady pressure spectra at the x/l=0.9 floor pressure monitor shows the existence of two distinct modes of oscillation within the cavity, with the 1st mode being the dominant which is in agreement with the experimental results. The 2nd oscillation mode is attenuated in the spectra to such a level that it is not visible above the baseline SPL level. The Rossiter mode frequencies from the simulation can be compared with the experimentally measured frequencies in Table 4 below.

The data shows that the simulated mode frequencies are approximately 50-80Hz higher than the theoretical oscillation frequencies calculated using the ‘modified-Rossiter’ equation. The difference in the frequencies are equivalent to a 9.5% variation in the 1st oscillation mode and a 3.8% variation on the 3rd oscillation mode. The simulation, however, has modelled successfully the feedback mechanism which causes the Rossiter modes and the results suggest that the increase in boundary layer thickness has caused the dominant mode of oscillation to switch from the 2nd mode to the 1st mode. The SPL values in the dominant oscillation mode show close agreement with the experimentally measured dominant mode SPL values.

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The spectra contain no broadband noise content which is a well-documented limitation of URANS in the simulation of separated fluctuating flows and is one of the drivers in the development of LES- and DES-based methods for the simulation of unsteady cavity flows [23, 24].

Table 4 Comparison of l/h=5 Experimental and Numerical Rossiter Mode Frequencies

Rossiter Mode

Number

Numerical Oscillation

Frequency (Hz)

Experimental Oscillation

Frequency (Hz) 1 CL - 510.54 CL - 463.65 2 CL - No Peak CL – 1074.97 3 CL - 1873.56 CL – 1795.93 1 OC1 - 510.54 OC1 -463.65 2 OC1 - No Peak OC1 – 1084.94 3 OC1 - 1873.56 OC1 – 1795.94 1 OC2 - 510.54 OC2 -463.65 2 OC2 - No Peak OC2 – 1104.51 3 OC2 - 1873.56 OC2 - 1800.70

3.3.3 Oscillation Mode Shapes

The unsteady pressure spectra show the presence of Rossiter oscillation modes within the flow with 1st mode dominance. The 1st mode shape based on the peak SPL value at each of the streamwise tapping locations can be seen in Figure 1 with a comparison to the experimentally measured 1st mode shape. The mode shows the distinct ‘V’ profile which is consistent with the experimental mode shape and is representative of a Mode II oscillation based on the definitions given by Rossiter [20]. The SPL minima within the mode shape are seen at x/l=0.5 which shows close agreement with the experimental data. This result is seen as further evidence that the simulation has successfully modelled the feedback mechanism within the cavity. The simulated SPL values are 5-8dB lower than the corresponding experimental values along the cavity length which can be attributed to the lower freestream unsteadiness seen in the numerical simulation. The peak SPL values in the numerical mode shapes are seen at x/l=0.9 which is consistent with the experimental mode shapes.

3.3.4 Time-averaged Flow Velocity Vector Fields

The time-averaged flow fields at each of the three spanwise planes for the numerical simulation can be seen in Figure 14 as velocity magnitude vector maps. The velocity magnitude vector maps show that the CL plane contains a large single recirculation extending from x/l=0.32 to x/l=1. The recirculation is centred at x/l=0.57, y/h=-0.5. A streamwise movement of the recirculation centre is clear when comparing the data in the CL, OC1 and OC2 planes. In the upstream end of the CL plane between x/l=0-0.30 the flow appears entirely streamwise due to the effect of the two ‘tornado-like’ structures convecting flow towards the centreline of the cavity and then forcing it downstream. The peak velocity in the CL plane in the area of the flow visible during the experimental PIV study is V=113ms-1 (41.85% freestream value) and is seen in the maximum shear layer deflection at x/l=0.85. This peak velocity is 23ms-1 lower than the peak value measured experimentally. However, the variation can be attributed to the difference in the shear layer deflections in the two different cases. In the experimental study, the shear layer was seen to have a large deflection into the cavity at the downstream wall which causes an acceleration of the flow over the deflected shear layer into the cavity near the downstream wall giving a peak velocity of V=140ms-1. Although the current simulation has the same boundary layer thickness as the experimental study, it is thought that the simulation results in a shear layer which does not show the same level of vertical flexibility as that seen experimentally. The peak vertical velocity within the cavity is v=77ms-1 which shows close agreement with corresponding velocity measured in the PIV study. In both cases, the peak velocity is seen directly adjacent to the downstream wall where the internal flow recirculates within the cavity.

The time-averaged velocity magnitude vector map on the OC1 plane shows that the flow structure in the cavity between x/l=0.32-1 is similar to that seen in the CL plane. This is consistent with the experimental PIV data which showed similar flow structures on the two planes. The large flow recirculation is centred at x/l=0.79,

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y/h=-0.51 shows that the centre of recirculation has moved downstream which was also seen in the PIV experimental data. The recirculation retains an unchanged size compared with the CL plane data. Between x/l=0-0.25 the flow also shows a vertical component which is caused by the ‘tornado-like’ vortices travelling up towards the mouth plane of the cavity. The peak velocity in the OC1 plane in the area of the flow visible in the PIV study is V=113ms-1 in the small region of the shear layer which is deflected in to the cavity at x/l=0.84. This is in close agreement with the data from the CL plane. The peak value is 27ms-1 lower than the values measured in the experimental study. The peak vertical velocity in the OC1 plane is v=76ms-1 which is seen in the flow travelling along the downstream wall towards the cavity floor. This value also is in good agreement with the v=80ms-1 peak vertical velocity measured at the same place in the PIV data.

The flow structure in the OC2 plane is in close agreement with the flow structure seen in the CL and OC1 planes. This is in contrast to the experimental data which shows twin recirculations in the OC2 plane caused by the deflection of the shear layer into and then out of the cavity. The change in flow structure is caused by the smaller shear layer deflection seen in the numerical simulation. The flow recirculation is centred at x/l=0.85, y/h=-0.49. The upstream extent of the recirculation becomes part of the ‘tornado-like’ vortex at approximately x/l=0.25 and the vertical flow component between x/l=0-0.25 is increased compared with the OC1 plane. The peak velocity in the OC2 plane is V=95ms-1 which is seen at x/l=0.85 where the maximum shear layer deflection into the cavity occurs. The peak value shows close agreement with the experimental data although this is thought to be coincidental since the flow structures in the two data sets are very different. The peak velocity is 18ms-1 lower than the peak velocities seen in the CL and OC1 planes. The peak vertical velocity in the OC2 plane is v=75ms-1 which is seen in the flow travelling along the downstream wall of the cavity towards the floor. This peak velocity is consistent with the values measured in the CL and OC1 planes.

Overall, the mean flow structure within the cavity is highly uniform across the span with a single large recirculation present downstream, of the ‘tornado-like’ vortices. The uniform flow structure across the span is different to the structure seen in the experimental study which showed a twin recirculation structure in the OC2 plane. The shear layer deflection into the cavity is small and the shear layer passes over the trailing-edge of the cavity with no impingement on the downstream wall. In the experimental case, the shear layer deflection was such that impingement occurred on the face of the downstream wall. The flow structure remains constant across the cavity span because the shear layer deflection is low and so does not change path to leave the cavity at the downstream wall. This is the reason for the twin flow structure in the experimental study. The flow structures are typical of open cavity flow behaviour and suggests that the increased boundary layer thickness in the simulation results in a change in flow behaviour which could be achieved by holding the boundary layer thickness constant and reducing the l/h value of the cavity.

The peak flow velocities within the cavity are similar across the three spanwise planes since the flow structure is uniform across the cavity. The peak velocities are lower than the corresponding values in the experimental study which is suggested is because as the shear layer deflection is less, given the velocity profile through the shear layer, the corresponding velocity magnitude within the cavity will also be lower.

3.4 General Remarks

Each of the experimental measurement techniques used to investigate different aspects of the flow i.e. pressure, structure, etc. provide data which draw the same conclusions about the type of flow which the cavity is exhibiting. Based on the definitions of flow types provided by Charwat et al. [18] and later by Stallings and Wilcox [19], the l/h=5 cavity geometry is shown to exhibit transitional-open flow behaviour with 2 flow recirculation regions in the cavity over which the shear layer passes.

The centreline plane internal flow structure compares well with the typical internal flow structure suggested by ESDU [25] for transitional-open flow. The centreline flow structure measured in the current experimental study shows that the shear layer over the cavity is deflected towards the cavity floor and impinges on the downstream wall of the cavity instead of fully passing out of the cavity. As the deflected shear layer changes path to flow out over the trailing-edge, a second recirculation region is formed between the upstream recirculation and the downstream wall. This compares with a single internal recirculation within the cavity which is typical of open type flow behaviour.

The difference between the type of flow exhibited by the experimental measurements and the numerical simulation can be attributed to the way in which the modelling of the shear layer bridging the cavity in the CFD. The numerical data suggests that the spreading rate of the shear layer is not modelled accurately when compared with the experimental study. This results in a thinner shear layer at the cavity downstream wall when compared

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with the experimental data. The thinner shear layer in the simulation has a much reduced mean shear layer deflection into the cavity which means that as the flow approaches the downstream wall it passes over the trailing-edge without showing a large change in flow path. This means that the internal flow structure shows only a single recirculation compared to that seen in the experimental data where the shear layer path changes rapidly at the downstream wall. The findings from the experimental and numerical studies suggest that increasing the thickness of the shear passing over a fixed geometry cavity causes the flow type to change to that which is representative of a higher l/h value i.e. from open to transitional-open.

Generally, light sheet and optical access in transonic facilities can be poor as the tunnels were not designed with PIV data acquisition in mind. In this case, the PIV rig design was limited to the attachment a fully clear cavity to the outside of the tunnel wall. A custom build facility would allow more detailed analysis of the flow fields in the freestream and in the cavity mouth plane which would allow a more complete description of the flow over the l/h=5 geometry.

Seeding response to changes in flow path and velocity could be improved with reduction in the size of the seed particles (see Dring [26]). For example, given the current seeding size of 10µm diameter, a particle density of 1000kgm-3 and an exponential deceleration from 150-20ms-1 in 20mm (which is representative of the flow velocity decrease near the downstream wall of the l/h=5 cavity), the particle Stokes number will vary from 0.036 to 0.009 which corresponds to a predicted error of 6 to 10%. Using seeding particles with sub-micron diameters would eliminate this error but would then require greater laser power to scatter an equivalent amount of light to keep the signal strength constant.

The unsteady nature of the cavity flow, particularly the large scale unsteady flow structures within the cavity, have proved difficult to capture using the Kodak ES1.0 CCD. The current acquisition rate of the CCD camera and Nd:YAG laser used for image acquisition is limited to 15Hz and as such is too low to fully resolve the flow structures associated with dominant frequencies of oscillation. The unsteady surface pressure data showed the first 3 Rossiter modes of oscillation to be present at 463, 1074 and 1795Hz. A time-resolved or cinematic PIV system with laser and camera repetition rates in the order of at least 2kHz would therefore needed to fully resolve the flow structures associated with even the first of the three modes of oscillation.

4 Conclusions Time-averaged PIV, surface pressure and numerical results have been presented for a 3D l/h=5 rectangular cavity. The comparison of time averaged PIV data with URANS CFD predictions has shown that the measured and simulated flows show different flow types. The experimental data shows transitional-open flow behaviour whilst the numerical data shows open flow behaviour. Both the experimental and numerical data show the existence of a strong feedback mechanism which results in Rossiter oscillation modes within the flow. The difference in the flow types between the experimental and numerical data is thought to be caused by the way in which the shear layer over the cavity is modelled; particularly the spreading rate.

Simulation of cavity flow using URANS based software has been shown to model successfully the internal flow structures and the feedback mechanism within the cavity which is the source of the Rossiter oscillation modes. However, the use of URANS for further investigation of cavity aeroacoustics is seen to be limited due to the inability of the technique to model broadband unsteadiness.

The experimental and numerical studies show that further development of both techniques is required before it will be possible to fully integrate the use of PIV and CFD for the detailed analysis of transonic cavity flows.

Acknowledgements The authors would like to thank the EPSRC and MBDA UK Ltd for their support of the project under the CASE award scheme. Thanks also go to John Boaler and Christof Surmann from LaVision GmbH for invaluable assistance with the DaVis software.

References 1. East, L., Aerodynamically induced resonance in rectangular cavities. Journal of Sound and Vibration,

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1966. 3(3): p. 277-287. 2. Stallings, R.L., et al., Measurements of Store Forces and Moments and Cavity Pressures for a Generic

Store in and Near a Box Cavity at Subsonic and Transonic Speeds. 1995, NASA-TM-4611. 3. Taborda, N., D. Bray, and K. Knowles. Passive control of cavity resonances in tandem configurations

AIAA 2001-2770. in 31st AIAA Fluid Dynamics Conference. 2001. Anaheim, CA. 4. Taborda, N., D. Bray, and K. Knowles. Visualisation of three dimensional cavity flows. in 5th World

Conference on experimental heat transfer, fluid mechanics and thermodynamics. 2001. Thessaloniki, Greece.

5. Garg, S. and L.N. Cattafesta III, Quantitative schlieren measurements of coherent structures in a cavity shear layer. Experiments in fluids, 2001(30): p. 123-134.

6. Adrian, R.J., Particle imaging techniques for experimental fluid mechanics. Annual Review of Fluid Mechanics, 1991(23): p. 261-304.

7. Durao, D., J. Pereira, and J. Sousa. LDV measurements of turbulent separated flow over a cavity. in 6th International Symposium on the Applications of Laser techniques to Fluid Mechanics. 1992. Lisbon, Portugal.

8. Pickering, C. and N. Halliwell. Particle Image Velocimetry: A New Field Measurement Technique. in Optical Measurements in Fluid Dynamics. 1985. Bristol: Institute of Physics.

9. Keane, R. and R.J. Adrian, Theory of cross-correlation analysis of PIV images. Applied Sci. Res., 1992(49): p. 191-215.

10. Sousa, J., C. Freek, and J. Pereira. PIV measurements of turbulence statistics in the three-dimensional flow over a surface mounted obstacle. in International Symposium on Applications of Laser Techniques to Fluid Mechanics. 1998. Lisbon, Portugal.

11. Gustavsson, J., Experiments on Turbulent Flow Separation, Masters Thesis, in Department of Mechanics. 1998, Royal Institute of Technology: Stockholm.

12. Cater, J. and J. Soria. PIV measurements of turbulent jets. in 4th International Symposium on Particle Image Velocimetry. 2001. Gottingen, Germany.

13. Grosjean, N., et al., Combining LDA and PIV for turbulence measurements in swirling flows. Measurement Science Technology, 1997. 8: p. 1523-1532.

14. Durst, F., A. Melling, and J. Whitelaw, Principles and Practice of Laser Doppler Anemometry. 2nd ed. 1981, London, New York: Academic Press.

15. Scarano, F., Iterative Image Deformation Methods in PIV. Measurement Science Technology, 2002(13): p. 1-19.

16. Prepared, et al., Best Practice Guidelines for Marine Applications of Computational Fluid Dynamics. 2002.

17. Soemarwoto, B.I. and J.C. Kok, Computations of Three-Dimensional Unsteady Supersonic Cavity Cavity Flow to Study the Effect of Different Downstream Geometries. 2001, National Aerospace Laboratory (NLR): Amsterdam, The Netherlands. p. 15.

18. Charwat, A.F., et al., An Investigation of Separated Flows - Part 1 : The Pressure Field. Journal of Aerospace Sciences, 1961a. 28(6): p. 457-470.

19. Stallings, R.L. and F.J. Wilcox, Experimental Cavity Pressure Distributions at Supersonic Speeds. 1987, NASA-TP-2683.

20. Rossiter, J.E., Wind Tunnel Experiments on the Flow Over Rectangular Cavities at Subsonic and Transonic Speeds. 1964, Royal Aircraft Establishment, Farnborough, UK.

21. Coleman, H. and W. Steele, Experimentation and uncertainty analysis for engineers. 1999, New York: John Wiley and Sons, Inc.

22. Ritchie, S.A., Doctoral Thesis (Under Preparation), in DAPS. 2005, Cranfield University: Swindon. 23. Spalart, P.R., Strategies for Turbulence Modelling and Simulations. International Journal of Heat and

Fluid Flow, 2000. 21(3): p. 252-263. 24. Sinha, N., et al. A Perspective on the Simulation of Cavity Aeroacoustics. in 36th Aerospace Sciences

Meeting and Exhibition. 1998. Reno, NV. 25. ESDU, Aerodynamics and aero-acoustics of rectangular planform cavities. Part I: Time-averaged

flow. 2004, ESDU 02008. 26. Dring, R., Sizing criteria for laser anemometry particles. Journal of Fluids Engineering, 1982. 104: p.

15-17. 27. ESDU, Drag of a rectangular planform cavity in a flat plate with a turbulent boundary layer for Mach

numbers up to 3. Part II : Open and transitional flows. 2002, ESDU.

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Figure 1 Time-averaged Flow Features of Open Cavity Flow [27]

Figure 2 Time-averaged Flow Features of Closed Cavity Flow [27]

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w

l

hFlow Direction

y

x

z

Figure 3 Right-Handed Axes Orientation System

Air Inlet from Main Control Valve

Atmospheric Blow-off Box

Quadrant HousingsTunnel Ejector Housing

Removable Tunnel Side Wall

Flow Direction

Figure 4 Layout of Shrivenham Transonic Wind Tunnel

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Figure 5 Cavity Rig Detail

Windtunnel Control

Data Acqusition Control

Main Control Valve Inlet

Water Supply

Seeder Unit

New Wave Gemini Double Pulsed PIV

Laser Kodak ES1.0 CCD Camera

Light Sheet Optics

Seeder Rake

Flow Direction

Cavity Rig

Figure 6 PIV Experimental Set up - Top View

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Surface Coated Mirror for Viewing Light Sheet Kodak ES1.0 CCD

Camera

New Wave Gemini Double Pulsed Laser

Light Sheet Optics

Data Acquisition ControllerCavity Rig

Transonic Wind Tunnel

Figure 7 PIV Experimental Set up - End View

Flow DirectionFlow Direction

Figure 8 Detail of Cavity Leading-Edge Cell Distribution – CL plane

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Streamwise Position (x/l)

Pre

ssur

eC

oeffi

cien

t(C

p)

0 0.2 0.4 0.6 0.8 1-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5 Centreline Plane - (z/w=0.5) - ExperimentalOffcentre 1 Plane - (z/w=0.667) - ExperimentalOffcentre 2 Plane - (z/w=0.833) - ExperimentalCentreline Plane - (z/w=0.5) - 3D CFD Experimental Boundary LayerOffcentre 1 Plane - (z/w=0.667) - 3D CFD Experimental Boundary LayerOffcentre 2 Plane - (z/w=0.833) - 3D CFD Experimental Boundary Layer

Figure 9 Time-averaged Cp Distribution along Cavity Floor on CL, OC1 and OC2 Planes - Experimental and Numerical Data

Frequency (Hz)

SP

L(d

B)

0 500 1000 1500 2000 2500

100

120

140

160

180

Centreline Plane - (z/w=0.5) - 3D CFD Experimental Boundary LayerOffcentre 1 Plane - (z/w=0.667) - 3D CFD Experimentnal Boundary LayerOffcentre 2 Plane - (z/w=0.833) - 3D CFD Experimental Boundary LayerCentreline Plane - (z/w=0.5) - ExperimentalOffcentre 1 Plane - (z/w=0.667) - ExperimentalOffcentre 2 Plane - (z/w=0.833) - Experimental

Figure 10 Unsteady Pressure Spectra at x/l=0.9 Tapping on CL, OC1 and OC2 Planes - Experimental and Numerical Data

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Streamwise Position (x/l)

SP

L(d

B)

0 0.2 0.4 0.6 0.8 1130

135

140

145

150

155

160

165

170Centreline Plane - (z/w=0.5) - 3D CFD Experimental Boundary LayerOffcentre 1 Plane - (z/w=0.667) - 3D CFD Experimental Boundary LayerOffcentre 2 Plane - (z/w=0.833) - 3D CFD Experimental Boundary LayerCentreline Plane - (z/w=0.5) - 3D CFD ExperimentalOffcentre 1 Plane - (z/w=0.667) - 3D CFD ExperimentalOffcentre 2 Plane - (z/w=0.833) - 3D CFD Experimental

Figure 11 First Rossiter Mode Shape on CL, OC1 and OC2 planes - Experimental and Numerical Data

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Streamwise Position (x/l)0 40 80 120 160

Velocity Magnitude (m/s): 0 75 150 225 300

Flow Direction (M=0.85)Centreline Plane - (z/w=0.5)

Offcentre1 Plane - (z/w=0.667)

Offcentre 2 Plane - (z/w=0.833)

0 0.25 0.5 0.75 1Streamwise Position (x/l)

0 40 80 120 160

Velocity Magnitude (m/s): 0 75 150 225 300

Flow Direction (M=0.85)Centreline Plane - (z/w=0.5)

Offcentre1 Plane - (z/w=0.667)

Offcentre 2 Plane - (z/w=0.833)

0 0.25 0.5 0.75 1

Figure 12 Time-averaged PIV Vector Maps on CL, OC1 and OC2 Planes - Coloured by Velocity Magnitude (m/s)

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Stre

amw

ise

Posi

tion

x/l

0.5

l/h =

5 ‘C

lean

’ Cav

ity G

eom

etry

0.0

1.0

A

B

C

DD

Figure 13 Graphical Representation of Surface Stream Traces from Oil Flow Visualisation Studies

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Velocity Magnitude (m/s): 0 75 150 225 300

Centreline Plane(z/w=0.5)

Streamwise Position (x/l)0 0.25 0.5 0.75 1

Offcentre Plane 2(z/w=0.833)

Offcentre 1 Plane(z/w=0.667)

Velocity Magnitude (m/s): 0 75 150 225 300

Centreline Plane(z/w=0.5)

Streamwise Position (x/l)0 0.25 0.5 0.75 1

Offcentre Plane 2(z/w=0.833)

Offcentre 1 Plane(z/w=0.667)

Figure 14 Time-averaged CFD Vector Maps on CL, OC1 and OC2 Planes - Coloured by Velocity Magnitude (m/s)

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