Wake of a DST Submarine Model captured by Stereoscopic Particle Image Velocimetry

This paper describes low-speed wind-tunnel testing of a new 2 m long Defence Science and Technology generic conventional submarine model by stereoscopic particle image velocimetry (SPIV). The aim is to capture three components of velocity for a model side-slip of 10 ◦ at model-length Reynolds numbers of 4×10 and 8×10 to allow study of the submarine wake. From ensemble averages of 3000 SPIV image pairs, the most striking flow feature is on the upper hull of the new model. It is a system of three co-rotating vortices produced by a cruciform appendage which consists of a vertical fin and two horizontal hydroplanes. Cross-sectional SPIV at 51.1%, 65.0% and 81.5% of the model length (L) indicates that vortex circulation is strongest from the fin, followed by the windward hydroplane then the leeward hydroplane. Increasing the Reynolds number from 4×10 to 8×10 increases circulation of the vortex system by ≃ 3% and shifts the fin wake leeward by up to 0.5%L. Introduction The Defence Science and Technology (DST) generic conventional submarine model tested here is based on a conceptual design by Joubert [5]. It was established by the DST Group Maritime Division to foster international cooperation on bench-marking and validation studies of submarine hydrodynamics. Work began in the early 2010s, which involved testing of a 1.35 m long Joubert model in the DST low-speed wind tunnel. The testing included 2-component particle image velocimetry [6], surface-pressure measurements [4] and flow visualisation [7] to provide experimental data to guide numerical modelling [1, 2]. It primarily captured the wake at a model side-slip or yaw angle of 10 ◦ to assist interpretation of largescale flow separation in a submarine manoeuvre. A recent design study [9] offered some insights into the manoeuvring behaviour of the Joubert model, and this led to a few geometric modifications to improve the directional stability of the model. The modified geometry is known as ‘BB2’, after [9]. Given that key changes involved a new vertical fin and two horizontal fin hydroplanes on the upper hull, there is a need to characterise the wake produced by this cruciform appendage to assist on-going studies. This is the first SPIV investigation of the wake flow produced by the new DST submarine model (BB2), where the model is tested at a yaw angle (ψ) of 10 ◦ and at high Reynolds numbers. DST Generic Model (BB2) for Wind-Tunnel Testing Figure 1 shows the new geometry of the DST submarine model. The model used for this test has a fixed length (L) of 2 m and a length-to-diameter ratio of 7.3. It is axisymmetric for the first 7.0%L, where the nose shape is derived from a NACA-0018 forebody. On the casing, the fin shape is that of NACA-0022 with a height of 8.0%L and a chord length of 15.7%L. On the fin, there are two NACA-0015 horizontal hydroplanes with a combined span of 11.7%L and a root chord of 3.3%L. The leading edge of each hydroplane is swept at 9.3 ◦, where the ratio between the root chord and the tip chord is 0.77. The longitudinal distance is 28.3%L from the tip of the nose to the leading edge of the fin, and is 29.6%L from the tip of the nose to the leading edge of the hydroplanes. The hydroplanes are located at 5.6%L above the casing. For further details of the geometry, see [5, 9]. The model (see figure 1) is truncated at 95%L for sting-mounted testing in the DST low-speed wind tunnel. The tunnel is a closed-loop facility driven by a 660 kW, 3.96 m diameter, 8 blade fan, and the test section is 2.743 m wide, 2.134 m high and 6.553 m long. For this test, the freestream velocities (U∞) are ≃ 29 m/s and ≃ 61 m/s, which correspond to body-length Reynolds numbers (ReL = LU∞/ν, where ν is the kinematic viscosity of air) of 4×10 and 8×10. To trip the flow over the hull, a circumferential ring of trip dots (diameter of 1.27 mm and center-to-center spacing of 2.54 mm) is located on the model at 5%L. The height of the trip dots is 0.29 mm and 0.15 mm for the Reynolds numbers of 4×10 and 8×10, respectively. The fin and the hydroplanes are untripped. The method of sizing the trip dots is from [3]. SPIV Measurement Technique To perform SPIV, the flow is seeded with ≃ 1 μm diameter (di-ethyl-hexyl-sebacat) oil droplets at concentration of 20 to 30 mg/m and the seeding is illuminated by a dual-cavity Litron Nd:YAG laser (8 ns pulse at ≃ 425 mJ). To minimise stray reflections, the model and the test-section walls are painted black. By orientating the laser-sheet normal to the streamwise x direction, this allows the cross-sectional flow to be captured by a pair of LaVision digital cameras (6600 by 4400 pixels with CCD resolution of 5.5 μm/pixel). The cameras are located outside the test section and are fitted with a 200 mm lens set at f-stop=5.6 to provide an adequate depth-of-field. The reproduction ratio is ≃ 10 and the useful field-of-view is up to 280 mm by 180 mm (or 0.14L wide by 0.09L high). The cameras are arranged symmetrically about the laser-sheet at oblique angles of ≃ 45 ◦ (figure 1) and a tilt-and-shift technique is used to allow sharp corner-to-corner focusing and to reduce vignetting [8]. To ease alignment and targeting, the cameras, laser and lasersheet forming optics are mounted on a common optical bench. By traversing the bench in the vertical z direction, the field-ofview captures the flow over the upper hull, mid hull and the lower hull at a fixed streamwise location of the model. To capture the flow at different streamwise x locations, the model is translated forward or backward on a floor rail in the test section. The measurement locations are at 51.1%L, 65.0%L and 81.5%L; see figures 1 and 2. SPIV Data Processing To correlate successive SPIV images, the laser-sheet is set at a fixed thickness ∆x laser ≃ 3.5 mm, and the laser-pulse delay time (∆tpulse; typically in a few microseconds) is adjusted via a programmable timing unit (LaVision PTU X) such that ∆tpulse∼0.3∆x laser/U∞. The images are calibrated with a twosided (LaVision 309-15) target and the velocity field is computed by using the commercial DaVis 8.3 software.