Pressure Drag Reduction Research Articles

Experimental investigation on heated spheres entering water vertically at different temperatures

Our investigation of spheres entering water at high-temperature reveals that elevated temperatures modify traditional cavitation patterns and trigger novel fluid dynamic phenomena. Experimental analysis of the high-temperature sphere’s water entry process has identified four distinct cavitation morphologies: small cavities, complete cavities, dual cavities, and unstable cavities. These phenomena result from the sphere’s thermal effects altering the local flow dynamics around it, consequently impacting the hydrodynamic coefficients. Notably, thermal conditions cause the contact line from the sphere’s midpoint to transition to its tail, leading to transformations in cavity types. Furthermore, simulations employing the lattice Boltzmann method elucidate how unstable steam films formed on hot surfaces induce boundary slip, reducing pressure drag. This observation provides further insight into established mechanisms of fluid drag reduction. Our study deepens the understanding of how temperature influences water entry dynamics and offers new perspectives on reducing drag during the water entry process of objects.

Study on characteristics and prediction of the pressure drag of the swept strut under supersonic wide-range conditions

In this paper, the numerical simulation of the swept strut ramjet combustor was carried out under wide-range conditions (Ma3 = 1.8 ∼ 5.0), and the pressure drag characteristics of the swept strut were discussed. The results show that the pressure drag characteristics of the swept strut are related to the Mach number of the combustor inlet and the swept angle of the strut. The decreased boundary of the strut pressure drag coefficient gradually advances with the decrease of the Mach number of the combustor inlet. When Ma3 = 1.8 ∼ 2.0, the pressure drag reduction boundary is α = 15°. When Ma3 = 2.2 ∼ 2.8, the pressure drag reduction boundary is α = 45°. When Ma3 = 3.0 ∼ 4.0, the pressure drag reduction boundary is α = 60°. When Ma3 = 5.0, the pressure drag reduction boundary is α = 65°. In addition, with the decrease of the Mach number of the combustor inlet, the pressure drag reduction performance benefit brought by increasing the swept angle of the strut will gradually increase. Furthermore, a pressure drag coefficient prediction model suitable for wide-range conditions and multiple configurations of swept struts was proposed based on deep learning. The prediction model consists of two parts in series, which includes the prediction model of the surface pressure coefficient of the swept strut based on multilayer perceptron (MLP) and the prediction model of the pressure drag coefficient of the swept strut based on convolutional neural network (CNN). To improve the prediction accuracy of the MLP model, new training samples were added based on the ensemble-based uncertainty quantification, and the improved MLP model was obtained by retraining. The results show that both the two prediction models have high prediction accuracy under the effect of multiple complex flow characteristics on the strut. The results of this study are helpful to provide a reference for the aerodynamic drag reduction design of the strut in the wide-speed supersonic combustor.

Hypersonic Flow past LD-Haack Series, Parabolic Series, Power Series Nose Cone: A Comparative Study

This research paper presents a detailed aerodynamic analysis of three rocket nose cone designs—LD-Haack, Parabolic, and Power Series—under hypersonic conditions ranging from Mach 5 to Mach 12. Using advanced Computational Fluid Dynamics (CFD) simulations in ANSYS Fluent, the study focuses on key aerodynamic parameters, including drag force, drag coefficient, velocity, pressure, and temperature distributions. The results indicate that the Parabolic Nose Cone offers the most favorable aerodynamic performance, with the lowest drag force and drag coefficient across all Mach numbers. This superior performance can be attributed to its ability to streamline airflow and minimize boundary layer separation, effectively reducing pressure drag and limiting the onset of turbulent wake regions. In contrast, the LD-Haack Series Nose Cone, though designed to minimize wave drag at supersonic speeds, shows moderate drag at hypersonic velocities due to its less optimal control of boundary layer behavior. The Power Series Nose Cone, despite its highly tapered shape, experiences the highest drag. This is largely caused by increased flow separation and turbulent wake generation, which exacerbate pressure drag, particularly at higher Mach numbers. These findings highlight the critical influence of nose cone geometry on aerodynamic efficiency and emphasize the importance of optimizing designs for hypersonic applications. This study provides valuable insights for aerospace engineers seeking to reduce drag and improve performance in high-speed flight scenarios.

Unraveling hydrodynamic interactions in fish schools: A three-dimensional computational study of in-line and side-by-side configurations

We numerically investigate the hydrodynamic interactions between a pair of three-dimensional (3D) fish-like bodies arranged in both in-line and side-by-side configurations. The morphology and kinematics of these fish-like bodies are modeled on a live rainbow trout (Oncorhynchus mykiss) observed during steady swimming in the laboratory. An immersed-boundary-method-based incompressible Navier–Stokes flow solver is employed to capture the flow dynamics around the fish-like bodies accurately. Our findings indicate that hydrodynamic performance of individual fish in both arrangements is influenced by their spatial separation when in close proximity as well as by the relative phase difference between the two fish. In the case of in-phase in-line schools, the leading fish experiences up to 5.3% increase in propulsive efficiency, attributed to the water blockage effect caused by the following fish. In comparison, the following fish experiences an increase in drag and power consumption along its body. Detailed analysis reveals that this rise in drag primarily results from an increase in friction drag (89%), driven by the amplified velocity field around the fish's body. Furthermore, altering the phase difference between the fish can help reduce pressure drag on the following fish by affecting the interaction between incoming vortex rings and its trunk. In side-by-side schools with in-phase swimming, a reduction of 6.8% in power consumption on the caudal fin is achieved for each fish when the transverse distance is maintained at 0.25 body lengths. Flow analysis reveals that the decrease in power usage is attributed to a diminished velocity field between the caudal fins, facilitating flow separation and subsequently reducing energy expenditure required for generating comparative thrust. For the out-of-phase swimming, the side-by-side school system experiences enhanced thrust production, owing to a wake energy recapture mechanism. The degree of enhancement varies for each fish and is determined by the specific phase difference. These insights obtained from our study hold the potential to inform the design and navigation strategies of underwater robotic swarms.

On the fluid drag reduction in scallop surface.

In the field of biomimetics, the tiny riblet structures inspired by shark skin have been extensively studied for their drag reduction properties in turbulent flows. Here, we show that the ridged surface texture of another swimming creature in the ocean, i.e., the scallops, also has some friction drag reduction effect. In this study, we investigated the potential drag reduction effects of scallop shell textures using computational fluid dynamics simulations. Specifically, we constructed a conceptual model featuring an undulating surface pattern on a conical shell geometry that mimics scallop. Simulations modeled turbulent fluid flows over the model inserted at different orientations relative to the flow direction. The results demonstrate appreciable friction drag reduction generated by the ribbed hierarchical structures encasing the scallop, while partial pressure drag reduction exhibits dependence on alignment of scallop to the predominant flow direction. Theoretical mechanisms based on classic drag reduction theory in turbulence was established to explain the drag reduction phenomena. Given the analogous working environments of scallops and seafaring vessels, these findings may shed light on the biomimetic design of surface textures to enhance maritime engineering applications. Besides, this work elucidates an additional evolutionary example of fluid drag reduction, expanding the biological repertoire of swimming species.

Pressure drag reduction via imposition of spanwise wall oscillations on a rough wall

The present study tests the efficacy of the well-known viscous drag reduction strategy of imposing spanwise wall oscillations to reduce pressure drag contributions in transitional and fully rough turbulent wall flow. This is achieved by conducting a series of direct numerical simulations of a turbulent flow over two-dimensional (spanwise-aligned) semi-cylindrical rods, placed periodically along the streamwise direction with varying streamwise spacing. Surface oscillations, imposed at fixed viscous-scaled actuation parameters optimum for smooth wall drag reduction, are found to yield substantial drag reduction ( $\gtrsim$ 25 %) for all the rough wall cases, maintained at matched roughness Reynolds numbers. While the total drag reduction is due to a drop in both viscous and pressure drag in the case of transitionally rough flow (i.e. with large inter-rod spacing), it is associated solely with pressure drag reduction for the fully rough cases (i.e. with small inter-rod spacing), with the latter being reported for the first time. The study finds that pressure drag reduction in all cases is caused by the attenuation of the vortex shedding activity in the roughness wake, in response to wall oscillation frequencies that are of the same order as the vortex shedding frequencies. Contrary to speculations in the literature, this study confirms that the mechanism behind pressure drag reduction, achieved via imposition of spanwise oscillations, is independent of the viscous drag reduction. This mechanism is responsible for weakening of the Reynolds stresses and increase in base pressure in the roughness wake, explaining the pressure drag reduction observed by past studies, across varying roughness heights and geometries.

Hydrodynamic drag reduction in ribbed microchannel with infused non-Newtonian lubricants

Liquid-infused surfaces have recently gained prominence in engineering applications owing to their versatile characteristics such as self-cleaning, anti-fogging, drag reduction, and enhanced heat transfer. In this article, a numerical analysis of pressure-driven flow past a periodic array of rectangular transverse grooves infused with non-Newtonian immiscible lubricants is performed. The volume of fluid method is employed to capture the interface between primary and secondary fluids, and the power-law model is deployed to mimic the non-Newtonian lubricant. The drag reduction capability of the microchannel is examined for various parameters such as Reynolds number, liquid fraction, viscosity ratio, viscosity index, and contact angle. It is observed that the introduction of a non-Newtonian fluid (shear-thickening or shear-thinning) drastically modifies the interface velocity and hydrodynamic resistance. In particular, a shear-thinning lubricant enhances the slip length as the viscosity index (n) is reduced owing to the reduced viscosity at the interface. Note that, for a lubricant having n = 0.7, the percentage improvement in the slip length is 382% in comparison with a Newtonian counterpart having the same viscosity ratio, N = 0.1. Importantly, the introduction of a shear-thinning lubricant with a viscosity ratio N = 5, a liquid fraction of 0.8, and a behavior index n = 0.7 yielded a pressure drag reduction of 63.6% with respect to a classical no-slip channel and of 23% with reference to a microchannel with the Newtonian lubricant. Moreover, at high Reynolds numbers, Re→50, the drag mitigation is slightly lowered due to the primary vortex shift in the cavity. Furthermore, the effect of the interface contact angle (θc) is investigated, as θc drops from 90° (flat) to 45° (convex); the meniscus curvature is enhanced, and the effective slip length is reduced. These observations suggest that a shear-thinning lubricant-infused microchannel is a promising candidate for drag reduction in lab-on-chip applications.

Effectives of Different Shaped Dimples on a NACA Airfoil

This research addresses changes in the aerodynamic properties of the airfoil caused by modifying the surface in the form of dimples. The first surface changes mentioned here the wing model has dimples that face inside and outward. Airfoil models that have been modified to illustrate variation lifting and dragging at varying angles of attack (AOA). Surface adjustments are made here by taking into account the various types and forms of dimples. When an airfoil reaches a certain angle of attack, dimples serve to reduce pressure drag because wake production begins owing to boundary layer separation. Dimples on an aeroplane wing function similarly to vortex producers. They cause turbulence, which slows down boundary layer splitting, decrease wake, and reduces pressure drag. It has helped to improve the lift and raise the AOA of the stall. Dimples on the surface of an aircraft wing do not considerably increase pressure drag due to the wing already has an aerodynamic form, but they may impact its aerodynamic properties when the airfoil is at AOA, which is one of the issues raised in this research. The outcomes legitimize the increment in the general lift and decrease in drag by the airfoil

Study on Aerodynamic Drag Reduction at Tail of 400 km/h EMU with Air Suction-Blowing Combination

In order to further reduce the aerodynamic drag of High-speed Electric Multiple Units (EMU), an active flow control drag reduction method combining air suction and blowing is proposed at the rear of the EMU train. A numerical calculation method based on realizable k-ε is used to investigate the aerodynamic drag characteristics of a three-car EMU with a speed of 400 km/h. The influence of different suction-blowing mass flow rates, the position and number of suction and blowing ports on the aerodynamic drag and surface pressure of the EMU tail are analyzed. The results demonstrate that suction and blowing at the tail reduce the pressure drag of EMU. And with the growth of air suction-blowing mass flow rate, the aerodynamic drag reduction rate of the tail car gradually increases, but the increment of drag reduction rate gradually decreases. Under the same mass flow rate of the suction and blowing, the closer the ports are to the upper and lower edges of the windscreen, the lower the pressure drag of the tail car is. At the same flow flux of air suction and blowing, the more the number of ports, the better the pressure drag reduction effect of the tail car. This study provides a reference for the next generation of EMU aerodynamic drag reduction and is of great significance for breaking through the limitations of traditional aerodynamic drag reduction.

Experimental Investigation and Intelligent Optimization of Airfoil Zero-Lift Drag Reduction with Plasma Actuators

Micro aerial vehicles flying at low speeds are becoming increasingly popular in military and daily life. Nevertheless, the short cruise time related to the poor aerodynamic efficiency of the wing at low Reynolds numbers is still a key issue. To deal with this, a spanwise plasma actuator array is used to reduce the zero-lift drag of a low-Reynolds-number airfoil, and experimental optimization of the electrical parameters is performed with intelligent algorithms. Results show that for efficient drag reduction, an unsteady unidirectional jet working mode should be preferred by the plasma actuator. In this mode, the drag reduction maps are mostly flat, and the drag reduction magnitude is insensitive to the variation of input voltage amplitude. There exists a threshold particle-observed Strouhal number (0.2) below which the drag reduction effectiveness drops sharply. As a comparison, the map of the power saving ratio shows a steep gradient, and its maximum always resides on the lower bound of duty cycle. With increasing freestream velocity, the mean drag reduction decreases monotonically. A genetic algorithm shows superior performance over surrogate-based optimization by reaching a maximum drag reduction of 40% and a peak power saving ratio of 0.7. Particle image velocimetry results reveal that there exists a laminar separation bubble on the airfoil. With plasma actuation, the transition location is shifted upstream, and the separation region is eliminated significantly. At low speeds, this pressure drag reduction exceeds the friction drag increase, resulting in a net drag decrease. However, transition-induced drag variation can only explain part of the total drag reduction, and the rest is inferred to be turbulent friction drag reduction.

Minimizing airfoil drag at low angles of attack with DBD-based turbulent drag reduction methods

Dielectric Barrier Discharge (DBD) based turbulent drag reduction methods are used to reduce the total drag on a NACA 0012 airfoil at low angels of attack. The interaction of DBD with turbulent boundary layer was investigated, based on which the drag reduction experiments were conducted. The results show that unidirectional steady discharge is more effective than oscillating discharge in terms of drag reduction, while steady impinging discharge fails to finish the mission (i.e. drag increase). In the best scenario, a maximum relative drag reduction as high as 64 % is achieved at the freestream velocity of 5 m/s, and a drag reduction of 13.7 % keeps existing at the freestream velocity of 20 m/s. For unidirectional discharge, the jet velocity ratio and the dimensionless actuator spacing are the two key parameters affecting the effectiveness. The drag reduction magnitude varies inversely with the dimensionless spacing, and a threshold value of the dimensionless actuator spacing of 540 (approximately five times of the low-speed streak spacing) exists, above which the drag increases. When the jet velocity ratio smaller than 0.05, marginal drag variation is observed. In contrast, when the jet velocity ratio larger than 0.05, the experimental data bifurcates, one into the drag increase zone and the other into the drag reduction zone, depending on the value of dimensionless actuator spacing. In both zones, the drag variation magnitude increases with the jet velocity ratio. The total drag reduction can be divided into the reduction in pressure drag and turbulent friction drag, as well as the increase in friction drag brought by transition promotion. The reduction in turbulent friction drag plays an important role in the total drag reduction.

Heat transfer augmentation in solar heat exchanger duct with louver-punched V-baffles

A vortex generator's ability to create secondary flow and accelerate rapid fluid mixing allows it to effectively improve thermal performance in a solar heat exchanger duct. A newly created louver-punched V-baffle (LPVB) vortex generator was tested experimentally in the current study and the flow and thermal patterns were also investigated using a three-dimensional CFD simulation. The Realizable k–ε turbulence model was utilized in the simulation and the predictions were verified using experimental data and correlations. By directing the impinging air onto the duct's heated surface, the square louver on the baffle served the primary function of reducing pressure drag. Air was used as the test fluid, flowing at Reynolds numbers (Re) from 5300 to 23,000 into the constant heat-fluxed duct. On the heated wall that was set up by letting the V-apex direct upstream, the LPVBs with a 45° attack angle (α) were repeatedly positioned. There were two aspects to the current investigation. First, the optimal relative baffle pitches (PR) and louver angles (β) conditions were determined by looking at the LPVB characteristics, which included four β and three PR at a fixed relative louver size (LR = 0.5) and baffle height (BR = 0.4). Second, three relative louver sizes (LR = 0.3–0.9) were investigated at the optimal PR and β. According to the results, the solid-baffle friction loss is significantly reduced by the LPVB with β > 0° while the heat transfer is slightly lower. In the first part, the LPVB with PR = 1.5, β = 45° has the optimal performance while in the second part, the one with LR = 0.9 yields the greatest performance. A numerical flow model was computed to understand the flow and thermal patterns. The findings were verified using the available measurements, and there is close agreement between the experimental and numerical results.

Experimental and numerical investigation of squat submarines hydrodynamic performances

This paper empirically examines the hydrodynamic performances of squat submarines under the resistance and wave tests beside numerical investigation of pressure drag reduction techniques. Despite vast information about the operation of the streamlined fluid vessels, there is not much information about the geometries and hydrodynamic behaviors of squat vessels with L/D ratios below four. This study experimentally investigates the impacts of various relative depths and flow inclinations, intending to find drag, heave, and sway forces at the velocities of 0.5, 1.0, 1.5, 2.0, and 2.5-m/s. A one-tenth scaled model of a squat submarine is examined under the resistance and wave train scenarios as the captive model in the towing tank experiments via 110 unique testing scenarios. Then, different pressure drag reduction techniques on the full-scale submarine are evaluated numerically at one-phase fluid by developing stern geometric optimization, nose rod devices, water corridors, and surface patterns at the bow and stern. Results present drag forces increase up to 150% at the 0.5D level for the resistance and wave tests due to the influences of the free surface water. The drag coefficients at the fully submerged depth of 6D differ by up to 13.3% between the numerical and experimental evaluations.

Effect of wall slip on laminar flow past a circular cylinder

A numerical study of two-dimensional flow past a confined circular cylinder with slip wall is performed. A dimensionless number, Knudsen number ($Kn$) is used to describe the slip length of cylinder wall. The Reynolds number ($Re$) and Knudsen number ($Kn$) ranges considered are $Re = [1, 180]$ and $Kn = [0, \infty)$, respectively. Time-averaged flow separation angle ($\bar{\theta_s}$), dimensionless recirculation length ($\bar{L_s}$) and the tangential velocity ($\bar{u_{\tau}}$) distributed on the cylinder's wall, drag coefficient ($\bar{C_d}$) and drag reduction ($DR$) are investigated. The time-averaged tangential velocity distribution on the cylinder's wall fit well with the formula $\bar{u_{\tau}} = [\frac{\alpha}{1+{\beta}e^{-{\gamma}({\pi}-{\theta})}}+{\delta}]sin(\theta) $, where the coefficients ($\alpha$, $\beta$, $\gamma$, $\delta$) are related with $Re$ and $Kn$. Several scaling-laws are found, $log(\bar{u_{{\tau}max}})\sim{log(Re)}$ and $\bar{u_{{\tau}max}}\sim{Kn}$ for low $Kn$, ($\bar{u_{{\tau}max}}$ is the maximum tangential velocity on the cylinder's wall), $log(DR)\sim{log(Re)}$ ($Re\leq45$ and $Kn\leq0.1$), $log(DR)\sim{log(Kn)}$ ($Kn\leq0.05$). At low $Re$, $DR_v$ (the friction drag reduction) is the main source of $DR$. However, $DR_p$ (the differential pressure drag reduction) contributes the most to $DR$ at high $Re$ ($Re>\sim60$) and $Kn$ over a critical number. $DR_v$ is found almost independent to $Re$.

THE IMPACT OF DIFFERENT OUTWARD AND INWARD PROTRUSION POSITIONS ON THE NACA 1410 AIRFOIL SECTION AT VARIOUS ANGLES OF ATTACK

The current work aims to increase the NACA 1410 airfoil's aerodynamic efficiency by altering its surface qualities for various angles of attack. The NACA 1410 airfoil's lower surface has semicircular outward and inward protrusions for a more advantageous profile. The lift and drag coefficients were calculated using CFD, at various attack angles, from -2º to 18º. An ANSYS Fluent Workbench model of the NACA 1410 airfoil was used to investigate flow characteristics at 3 x 105 Reynolds numbers. The semicircular protrusions caused turbulence, reducing pressure drag and increasing lift, delaying flow separation. The NACA1410 profile has protrusions facing outward, increasing the pitch moment coefficient. The inward protrusion was found to be more advantageous in the study of the effects of surface alterations on airfoils at various angles of attack.

The pressure drag reduction effect of tandem swimming by Caranx sexfasciatus and Rhincodon typus

The pressure drag reduction effect of tandem swimming by Caranx sexfasciatus and Rhincodon typus

Adjoint-Based Sensitivity Analysis for Airfoil Flow Control Aiming at Lift-to-Drag Ratio Improvement

Sensitivities of drag and lift to body force and blowing/suction are investigated based on a continuous adjoint method through Reynolds-averaged Navier–Stokes simulation (RANS). For a Clark-Y airfoil, changes in the drag, the lift, and the lift-to-drag ratio are found to be caused by different mechanisms depending on the type and locations of control input. Improvement in the lift-to-drag ratio by body forces is achieved by both pressure drag reduction and pressure lift enhancement. The effective angle for blowing/suction is nearly normal to the surface, and blowing around the leading edge and blowing/suction on the lower/upper surface near the trailing edge improve the lift-to-drag ratio effectively. Investigation on the control amplitude reveals that the present sensitivity analysis is valid when the blowing/suction velocity is less than 1% of the freestream velocity. The sensitivities are observed to be slightly weakened by decreasing the Reynolds number due to the difference in the baseline drag and lift coefficients, whereas the higher angle of attack is found to raise the sensitivities. Finally, the similar sensitivity analysis is performed also for NACA4412 and NACA0012, and it is found that slight differences in the shape result in substantial differences in the sensitivities.

An Investigation of Aerodynamic Characteristics of Three Bluff Bodies in Close Longitudinal Proximity - Part 2

<div class="section abstract"><div class="htmlview paragraph">The work described in this paper is a continuation of an investigation into the effects of systematic changes in upper-body geometry on the aerodynamic drag of passenger-car-like bluff-body models in close longitudinal proximity and operating in platoon formations. The original work, presented in SAE paper 2019-01-0659, showed measurements of the aerodynamic drag of individual models within three-model platoons and for which each model was tested in three different upper-body configurations This provided a data-set of 27 platoon configurations to compare with the three baseline conditions of the isolated models. The work contrasted with other published platooning research in which the spacing, between homogeneous models in the platoons, was the only variable to be considered.</div><div class="htmlview paragraph">In this publication the results of further wind tunnel tests, using the same models as before but in two-model platoons, providing a further 9 test configurations are compared with the original data. In addition, the results of CFD analyses for both the two and three-model platoon configurations are reported to help provide a more detailed and illustrated explanation of the modification of flow regimes and subsequent forces due to close-proximity.</div><div class="htmlview paragraph">The most significant influence on drag of the proximity tests was shown to be the interference on upstream wakes due to the presence of a following model. The shielding effect provided to trailing models also resulted in a drag reduction by reducing pressure drag on upright nose surfaces. But shielding also resulted in a drag penalty by reducing flow velocity over the radiused leading edges, particularly of the A-pillars thereby reducing a low pressure zone which, in unobstructed flow, yields a drag reduction for the Windsor model.</div></div>

Passive Control of Vortex Shedding and Drag Reduction in Laminar Flow across Circular Cylinder Using Wavy Wall Channel

Numerical simulations of incompressible laminar flow past a circular cylinder using wavy wall confinement are performed in order to study drag reduction and vortex shedding suppression for Reynolds numbers (50 ≤ Re ≤ 280) and blockage ratios (0.5 ≤ D/H ≤ 0.9), where D is the cylinder diameter and H is the channel height. The optimum configuration of wavy wall confinement is identified to have an amplitude of 0.2D and wavelength of 4D which manifests the minimum drag coefficient and complete vortex shedding suppression (zero lift coefficient). The flow over the cylinder with optimized wavy wall confinement produces a stable vortex pair in the wake of the cylinder. The length of vortex pair in the wake increases by increasing the Reynolds number and decreasing the blockage ratio. The drag on the cylinder reduces when the length of vortex pair increases due to early flow separation and reduction in pressure drag. The drag coefficient decreases by 36% in comparison to the plane wall confinement at D/H = 0.5. The drag coefficient decreases for wavy wall configuration by about 67% for D/H = 0.7 and 94% for D/H = 0.9. The lift coefficient remains zero at all Reynolds numbers and blockage ratios which indicates complete suppression of vortex shedding.

Separation drag reduction through a spanwise oscillating pressure gradient

Abstract