Wave-riding and wave-passing by ducklings in formation swimming

It has been commonly observed on open waters that ducklings/goslings follow their mothers in a highly organized formation. The questions arise: (1) why are they swimming in formation? (2) what is the best swimming formation? (3) how much energy can be preserved by each individual in formation swimming? To address these questions, we established a simplified mathematical and numerical model and calculated the wave drag on a group of waterfowl in a swimming formation. We observed two new and interesting findings: wave-riding and wave-passing. By riding the waves generated by a mother duck, a trailing duckling can obtain a significant wave-drag reduction. When a duckling swims at the ‘sweet point’ behind its mother, a destructive wave interference phenomenon occurs and the wave drag of the duckling turns positive, pushing the duckling forward. More interestingly, this wave-riding benefit could be sustained by the rest of the ducklings in a single-file line formation. Starting from the third one in a queue, the wave drag of individuals gradually tended towards zero, and a delicate dynamic equilibrium was achieved. Each individual under that equilibrium acted as a wave passer, passing the waves’ energy to its trailing one without any energy losses. Wave-riding and wave-passing are probably the principal reasons for the evolution of swimming formation by waterfowl. This study is the first to reveal the reasons why the formation movement of waterfowl can preserve individuals’ energy expenditure. Our calculations provide new insights into the mechanisms of formation swimming.

Effects of Heat Addition on Wave Drag Reduction of a Spiked Blunt Body

Drag reduction technology plays a significant role in extending the flight range for a high-speed vehicle. A wave drag reduction strategy via heat addition to a blunt body with a spike was proposed and numerically validated. The heat addition is simulated with continuous heating in a confined area upstream of the blunt body. The effects of heat addition on drag reduction in three flow conditions ( M = 3.98 , 5 , 6 ) were compared, and the influence of power density q h ( q 1 = 2.0 × 10 8 W / m 3 , q 2 = 5.0 × 10 8 W / m 3 , and q 3 = 1.0 × 10 9 W / m 3 ) of heating was evaluated. Results show that the heat addition has a positive way to reduce the drag of the body with a spike alone, and more satisfactory drag reduction effectiveness can be achieved at a higher Mach number. The drag reduction coefficient increases with q h in the same flow condition, with a maximum of 38.9% ( M = 6 ) as q 3 = 1.0 × 10 9 W / m 3 . The wave drag reduction principle was discussed by a transient calculation, which indicates that the separation region has entrainment of the heated air and expanded with its sonic line away from the blunt cone, which results in an alleviation of the pressure load caused by shock/shock interaction.

A numerical study on the single pulsed energy addition based unsteady wave drag reduction at varied hypersonic flow regimes

In this study, unsteady wave drag reduction in hypersonic flowfield using pulsed energy addition is numerically investigated. A single energy pulse is considered to analyze the time-averaged drag reduction/pulse. The blast wave creation, translation and its interaction with shock layer are studied. As the wave drag depends only on the inviscid aspects of the flowfield, Euler part of a well-established compressible flow Navier-Stokes solver USHAS (Unstructured Solver for Hypersonic Aerothermodynamics) is employed for the present study. To explore the feasibility of pulsed energy addition in reducing the wave drag at different flight conditions, flight Mach numbers of 5.75, 6.9 and 8.0 are chosen for the study. An [Formula: see text] apex angle blunt cone model is considered to be placed in such hypersonic streams, and steady-state drag and unsteady drag reductions are computed. The simulation results indicate that drag of the blunt-body can be reduced below the steady-state drag for a significant period of energy bubble-shock layer interaction, and the corresponding propulsive energy savings can be up to 9%. For energy pulse of magnitude 100mJ deposited to a spherical region of 2 mm radius, located 50 mm upstream of the blunt-body offered a maximum percentage of wave drag reduction in the case of Mach 8.0 flowfield. Two different flow features are found to be responsible for the drag reduction, one is the low-density core of the blast wave and the second one is the baroclinic vortex created due to the plasma energy bubble-shock layer interaction. For the same freestream stagnation conditions, these two flow features are noted to be very predominant in the case of high Mach number flow in comparison to Mach 5.75 and 6.9 cases. However, the ratio of energy saved to the energy consumed is noted as a maximum for the lower Mach number case.