Combined-Hole Film Cooling Designs Based on the Construction of Antikidney Vortex Structure: A Review

Film cooling is one of the most efficient and widely used cooling methods for high-temperature components. The interaction between the film cooling jet and main flow creates the counter-rotating vortex pair (CRVP), which enhances the mixing between coolant and hot stream and lifts the coolant film off the protected surface. The desire to overcome the unfavorable effects of CRVP and thus efficiently improve cooling effectiveness promotes various new combined-hole designs for film cooling. In this review paper, a summary of previous progress on film cooling and a special focus on recent literature related to the combined-hole film cooling designs with less difficulty in machining are provided. The underlying mechanisms of the enhancement in cooling effectiveness and film coverage due to antikidney vortex structure by combined holes are analyzed. Some perspectives on future prospects are finally addressed.

Characteristics of helicopter engine exhaust through scaled experiments using stereoscopic particle image velocimetry

Helicopter engines are often mounted atop the fuselage to keep the aircraft footprint small and optimal for operations. As a result, hot gases produced by the engines may inadvertently impinge upon the tail boom or dissipate inefficiently that compromises on operation safety. In this study, a scaled fuselage model with a hot air blower was used to simulate hot exhaust gases. The velocity field immediately outside the exhaust port was measured through stereoscopic particle image velocimetry to capture the trajectory and flow behaviour of the gases. Two cases were considered: freestream to exhaust velocity ratios of 0 (no freestream velocity) and 0.46 (co-flowing free stream), respectively. The formation of a counter-rotating vortex pair was detected for both cases but were opposite in the rotational sense. For the case without freestream, the plume formed into a small “kidney” shape, before expanding and dissipating downstream. For the case with freestream, the plume formed into a slenderer and more elongated “reversed-C” shape as compared to the case without freestream. It also retained its shape further downstream and maintained its relative position. These observations on the trajectory and shape of plume provide basis to understanding the nature and interaction of the plume with its surroundings.

Effect of velocity ratio on the interaction between plasma synthetic jets and turbulent cross-flow

Plasma synthetic jet actuators (PSJAs) are particularly suited for high-Reynolds-number, high-speed flow control due to their unique capability of generating supersonic pulsed jets at high frequency (${>}5$ kHz). Different from conventional synthetic jets driven by oscillating piezoelectric diaphragms, the exit-velocity variation of plasma synthetic jets (PSJs) within one period is significantly asymmetric, with ingestion being relatively weaker (less than $20~\text{m}~\text{s}^{-1}$) and longer than ejection. In this study, high-speed phase-locked particle image velocimetry is employed to investigate the interaction between PSJAs (round exit orifice, diameter 2 mm) and a turbulent boundary layer at constant Strouhal number (0.02) and increasing mean velocity ratio ($r$, defined as the ratio of the time-mean velocity over the ejection phase to the free-stream velocity). Two distinct operational regimes are identified for all the tested cases, separated by a transition velocity ratio, lying between $r=0.7$ and $r=1.0$. At large velocity and stroke ratios (first regime, representative case $r=1.6$), vortex rings are followed by a trailing jet column and tilt downstream initially. This downstream tilting is transformed into upstream tilting after the pinch-off of the trailing jet column. The moment of this transformation relative to the discharge advances with decreasing velocity ratio. Shear-layer vortices (SVs) and a hanging vortex pair (HVP) are identified in the windward and leeward sides of the jet body, respectively. The HVP is initially erect and evolves into an inclined primary counter-rotating vortex pair ($p$-CVP) which branches from the middle of the front vortex ring and extends to the near-wall region. The two legs of the $p$-CVP are bridged by SVs, and a secondary counter-rotating vortex pair ($s$-CVP) is induced underneath these two legs. At low velocity and stroke ratios (second regime, representative case $r=0.7$), the trailing jet column and $p$-CVP are absent. Vortex rings always tilt upstream, and the pitching angle increases monotonically with time. An $s$-CVP in the near-wall region is induced directly by the two longitudinal edges of the ring. Inspection of spanwise planes ($yz$-plane) reveals that boundary-layer energization is realized by the downwash effect of either vortex rings or $p$-CVP. In addition, in the streamwise symmetry plane, the increasing wall shear stress is attributed to the removal of low-energy flow by ingestion. The downwash effect of the $s$-CVP does not benefit boundary-layer energization, as the flow swept to the wall is of low energy.

Optimal perturbation for two-dimensional vortex systems: route to non-axisymmetric state

We investigate perturbations that maximize the gain of disturbance energy in a two-dimensional isolated vortex and a counter-rotating vortex pair. The optimization is carried out using the method of Lagrange multipliers. For low initial energy of the perturbation ( $E(0)$ ), the nonlinear optimal perturbation/gain is found to be the same as the linear optimal perturbation/gain. Beyond a certain threshold $E(0)$ , the optimal perturbation/gain obtained from linear and nonlinear computations are different. There exists a range of $E(0)$ for which the nonlinear optimal gain is higher than the linear optimal gain. For an isolated vortex, the higher value of nonlinear optimal gain is attributed to interaction among different azimuthal components, which is otherwise absent in a linearized system. Spiral dislocations are found in the nonlinear optimal perturbation at the radial location where the most dominant wavenumber changes. Long-time nonlinear evolution of linear and nonlinear optimal perturbations is studied. The evolution shows that, after the initial increment of perturbation energy, the vortex attains a quasi-steady state where the mean perturbation energy decreases on a slow time scale. The quasi-steady vortex state is non-axisymmetric and its shape depends on the initial perturbation. It is observed that the lifetime of a quasi-steady vortex state obtained using the nonlinear optimal perturbation is longer than that obtained using the linear optimal perturbation. For a counter-rotating vortex pair, the mechanism that maximizes the energy gain is found to be similar to that of the isolated vortex. Within the linear framework, the optimal perturbation for a vortex pair can be either symmetric or antisymmetric, whereas the structure of the nonlinear optimal perturbation, beyond the threshold $E(0)$ , is always asymmetric. No quasi-steady state for a counter-rotating vortex pair is observed.

Formation of surface trailing counter-rotating vortex pairs downstream of a sonic jet in a supersonic cross-flow

Direct numerical simulations were conducted to uncover physical aspects of a transverse sonic jet injected into a supersonic cross-flow at a Mach number of 2.7. Simulations were carried out for two different jet-to-cross-flow momentum flux ratios ($J$) of 2.3 and 5.5. It is identified that collision shock waves behind the jet induce a herringbone separation bubble in the near-wall jet wake and a reattachment valley is formed and embayed by the herringbone recirculation zone. The recirculating flow in the jet leeward separation bubble forms a primary trailing counter-rotating vortex pair (TCVP) close to the wall surface. Analysis on streamlines passing the separation region shows that the wing of the herringbone separation bubble serves as a micro-ramp vortex generator and streamlines acquire angular momentum downstream to form a secondary surface TCVP in the reattachment valley. Herringbone separation wings disappear in the far field due to the cross-interaction of lateral supersonic flow and the expansion flow in the reattachment valley, which also leads to the vanishing of the secondary TCVP. A three-dimensional schematic of surface trailing wakes is presented and explains the formation mechanisms of the surface TCVPs.