Skin Friction Drag Reduction Research Articles

Experimental investigation of a spanwise plasma jet array in a turbulent boundary layer for skin-friction drag reduction

Three different types of particle imaging velocimetry (PIV) measurements, namely planar-PIV, micro-PIV, and stereo-PIV, are integrated to provide a full picture of the interaction between a spanwise plasma jet array and a turbulent boundary layer (TBL) at Reθ = 1208. Quiescent-flow characterization reveals that the plasma actuator array induces a wavy jet. With increasing duty cycle (DC), the peak jet velocity grows yet the height of the jet body decreases. When the TBL is actuated by such a plasma jet array, the spanwise distribution of the relative drag variation exhibits two regions with opposite signs, and the formation of these two regions can be attributed to the upwash and the downwash effects of the plasma-induced vortex, respectively. After spatial-averaging in the plasma actuation zone, net drag reduction (DR = 3.2%) is only achieved at the lowest DC of 10%. Although, by increasing the duty cycle, more drag reduction can be obtained in the upwash zone, the accompanying drag increase in the downwash zone is even prominent.

Experimental Study on the Effect of Skin Friction Drag and Convective Heat Transfer for Viscoelastic and Pseudoplastic Fluid Flow

Drag Reducing Agents (DRAs) have a huge impact and major concern in engineering and industrial applications. It makes the fluid flow turbulent to laminar, dampens eddy reduces head loss by up to a certain limit, and saves pumping energy costs. Viscosity is the property that dampens eddy due to the viscous effect, which increases the fluidity up to a certain limit. Pseudoplasticity is the shear thinning effect that decreases viscosity when the flow rate increases. So, for the viscoelastic effect, we can increase the concentration up to a certain limit to reduce head loss. Still, during flow due to the pseudoplastic effect, the viscosity will start decreasing which is a negative effect. So, these combined effects are studied to reduce skin friction drag in the pipeline and save energy costs which will be convenient for the food industry, chemical, and medicine industries. In this investigation, investigation is carried out for 0.3 g/L, 0.2 g/L, and 0.15 g/L of xanthan gum in turbulent flow to observe the pressure drop and heat transfer rate. The study reveals that after increasing viscosity the pressure drop reduced significantly. Conversely, the heat transfer rate was also reduced due to the poor mixing effect. A higher performance and less vibration of the pump was also observed. It was concluded that the frictional pressure drop was reduced up to 85 % and the heat transfer rate was reduced by up to 90% by increasing the concentration of the DRA up to 0.3 g/L at 10 LPM than the pure water or base fluid as a working substance on the double pipe heat exchanger. As the heat transfer rate reduced up to 90% with reducing pressure drop another aim of the study was to establish a concentration and flowrate for which the heat transfer rate is maximum and it was found at a concentration of 0.15 g/L of DRAs (drag reducing agents) at 22 LPM (maximum flowrate at this setup).

Direct numerical simulation of skin friction drag reduction on supersonic turbulent boundary layers with micro-blowing

The flow control mechanism and skin friction drag reduction characteristics of micro-blowing on a Ma2.25 supersonic turbulent boundary layers are investigated through direct numerical simulations, and the effects of blowing intensity and micro-hole arrangement on turbulent structure and skin friction drag in the local control region and downstream region are considered. The results show that the skin friction drag decreases remarkably in the control region under the influence of micro-blowing, and a certain drag reduction can still be maintained in the downstream region. The drag reduction performance in the control region is jointly determined by blowing intensity and micro-hole arrangement. The drag reduction performance of the staggered arrangement is 5.7% and 11.1% higher than that of the inline arrangement at blowing intensities of 0.2% and 0.5%, respectively. However, it is found that the drag reduction in the downstream region is only determined by the blowing intensity and almost independent of the micro-hole arrangement. The effect of micro-blowing on turbulent structures is quantitatively characterized by energy spectrum analysis, and it shows that the streamwise scales of the near-wall streaks are significantly reduced under the influence of micro-blowing. In addition, the compressibility of fluids and the local reverse transfer in the strong expansion region are significantly improved under the influence of micro-blowing. These effects should be considered when performing Large Eddy Simulation modeling of supersonic turbulent boundary layers with micro-blowing.

Opposition flow control for reducing skin-friction drag of a turbulent boundary layer

This work explores the dynamic response of a turbulent boundary layer to large-scale reactive opposition control, at a friction Reynolds number of Reτ≈2240. A surface-mounted hot-film is employed as the input sensor, capturing large-scale fluctuations in the wall-shear stress, and actuation is performed with a single on/off wall-normal blowing jet positioned 2.4δ downstream of the input sensor, operating with an exit velocity of vj=0.4U∞. Our study builds upon the work of Abbassi [] and includes a control-calibration experiment and a performance assessment using PIV- and PTV-based flow field analyses. With the control-off calibration-experiment conducted , a transfer kernel is identified so that the velocity fluctuations that are to-be-controlled can be estimated. The controller targets large-scale high-speed zones in an “opposing” mode and low-speed zones in a “reinforcing” mode. A desynchronized mode was tested for reference and consisted of a statistically similar control mode, but without synchronization to the incoming velocity fluctuations. An energy-attenuation of about 40 % is observed for the opposing control mode in the frequency band corresponding to the passage of large-scale motions. This proves the effectiveness of the control in targeting large-scale motions: an energy-intensification of roughly 45% occurs for the reinforcing control mode instead, while no change in energy, within the wall-normal range targeted, appears with the desynchronized control mode. Moreover, direct measures of the skin-friction drag are inferred from PTV data. Results indicate that the opposing control logic yields the lowest wall-shear stress (3% lower than the desynchronized control, and 10% lower than the uncontrolled flow). Finally, a FIK-decomposition of the skin-friction coefficient revealed that the off-the-wall turbulence follows a consistent trend with the PTV-based wall-shear stress measurements, although biased by an increased shear in the wake of the boundary layer given the formation of a plume due to the jet-in-crossflow actuation. Published by the American Physical Society 2024

Turbulent drag reduction using dolphin-inspired near-wall ultrasonic microvibrations

The skin-friction drag generated by wall-bounded turbulent flows can potentially be reduced by a wall-parallel oscillatory motion. Inspired by microvibrations and the high sensitivity of dolphin skin, we examine whether wall-normal undulating motion actuated by longitudinal micro-ultrasonic waves (LMUWs) with ultrasonic-frequency oscillations and micro-size amplitudes significantly alters the multi-eddy motion on the surface, thereby reducing skin-friction drag. Simulations of the LMUW-induced turbulent flows are performed in an open channel at a Reynolds number of 1.24 × 106 for three motion modes, i.e., two traveling waves (downstream and upstream) in the streamwise direction and a standing wave. It is verified that the wall-normal turbulent fluctuations are remarkedly altered within the viscous sublayer of the turbulent boundary layer, resulting in a reduced velocity gradient. This leads to lower or even extinguished friction drag, which is strongly associated with the LMUW-excitation mode. Informed and validated by numerical results, we further derived a theoretical model for the dynamic boundary layer. This model is based on Fourier series expressions of the velocities and is used to elucidate the underlying mechanisms in association with the LMUW-excited turbulent flow and active friction drag reduction. The results indicate that upstream traveling waves enable 100% friction drag reduction, while downstream traveling waves are capable of overcoming the trade-off between friction and pressure drag, accomplishing 100% total drag reduction. This study thus provides a novel active and controllable method for turbulent drag reduction.

Turbulent drag reduction in compressible flows using streamwise traveling waves

Skin-friction drag reduction (DR) in supersonic turbulent channel flows using streamwise traveling waves of spanwise velocity (STWSV) has been studied using direct numerical simulations. In the present study, simulations are carried out for different phase speeds of the upstream and downstream traveling waves for a bulk Mach number Mab=1.5 and bulk Reynolds number Reb = 3000. The efficacy of the control has been investigated for other bulk Reynolds numbers as well. The Stokes layer generated by the control affects the near-wall statistics primarily by modifying the coherent structures, thereby either reducing or aggravating the skin-friction drag. For Reb = 3000 and Mab=1.5, a maximum drag reduction (DRmax) of 49% is achieved, primarily due to suppression of sweeps and ejections on application of control. The efficacy of skin-friction drag reduction varies in a small range when Reb is varied from 3000 to 6000; however, the maximum drag reduction is observed for Reb = 4000, owing to a drastic decrease in sweep events. Quadrant analysis reveals that for drag reduction (DR) cases, STWSV reduce magnitude of streamwise u′ and wall-normal w′ velocity fluctuations magnitude and stacks them around zero. In contrast, w′ is increased for drag increase (DI) cases. Skin-friction decomposition using Fukagata, Iwamoto and Kasagi (FIK) identity suggests that the control alters the turbulent component significantly. The behavior of the control is also studied at Mab = 0.3 and 2.5, and it is observed that the maximum drag reduction obtained decreases for high bulk Mach numbers.

Design and characterization of a virtual-dimple plasma actuator for turbulent skin-friction drag reduction

Design and characterization of a virtual-dimple plasma actuator for turbulent skin-friction drag reduction

Numerical Investigations of Outer-Layer Turbulent Boundary Layer Control for Drag Reduction Through Micro Fluidic-Jet Actuators

Drag reduction through turbulent boundary layer control (TBLC) is an essential way to develop green aviation technologies. Compared with traditional approaches for drag reduction, turbulence drag reduction is a relatively new technology, particularly for skin friction drag reduction, and it is becoming a hotspot problem worldwide. This paper focuses on the research of micro fluidic-jet actuators used for outer-layer boundary layer control with high-performance computing (HPC). This study aims to reduce turbulent drag by reshaping the flow structure within the turbulent boundary layer. To ensure the calculation accuracy of the core region and reduce the consumption of computing resources, a zonal LES/RANS strategy and WMLES method are proposed to simulate the effects of fluidic-actuators for outer-layer boundary control, in which high-performance computing has to be involved. The studies are performed on the classical zero-gradient turbulent flat plate cases, in which three different control strategies named “W-control,” “V-control,” and “VW-control” are used and compared to study the effects of drag reduction under a low Reynolds number at Reτ = 470 and a higher Reynolds number at Reτ = 4700. The mechanism for drag reduction is analysed via a pre-multiplied spectral method and a parallel dynamic mode decomposition (DMD) method. The results show that the present approach can effectively simulate the outer-layer turbulent boundary control where the “V-control” with the fluidic-jet actuator array behaves well to achieve an average drag reduction (DR) rate of more than 5% for the high Reynolds number case of the flat plate boundary layer. The high Reynolds shear stress and turbulent kinetic energy distribution in the boundary layer region show an obvious uplift under the effects of actuators, which is the main mechanism for drag reduction.

Experimental investigation of a grid plasma jet array in a turbulent boundary layer for skin-friction drag reduction

Toward turbulent skin-friction drag reduction, a novel layout of plasma actuator with a grid anode is devised (grid edge length: L), capable of producing an array of wall-normal plasma jets. The characteristics of this plasma jet array and its interaction with a turbulent boundary layer are investigated experimentally with a particle imaging velocimetry. Results show that the quiescent flow field of the plasma actuator is dominated by a standing vortex ring attached at the inner sides of the square grid, a wall-normal jet flow issued from the grid center, and a downwash flow between adjacent grids. When a tandem array of 11 plasma jets are issued into the cross flow, an equilibrium stage is reached after the third jet. In this stage, the main body of the wall-normal jet bends noticeably to the cross flow, and its leeward side hosts a reverse flow zone, extending downstream to form a slender low-speed wedge (LSW). Two vortical structures are prominent: the streamwise counter-rotating vortex pair residing in the two sides of the jet body, and the arch-shape negative spanwise vortex situated on the LSW root. In the grid-middle plane, the production of turbulence is enhanced across the entire boundary layer, and a second production peak is identified at y+=26. Reduction of the spanwise-averaged wall shear stress is achieved downstream of plasma actuation at x/L≥19.4, and part of the drag reduction fruit earned by ejection is offset by the spanwise transportation of high-velocity fluids toward the middle plane.

Simulation of flow over a fixed and oscillating circular cylinder with different surface roughness patterns using a multi-block-multi-mesh framework immersed boundary method

The effect of surface roughness on forces over a cylinder and the resulting vortex patterns at low Reynolds numbers are not well reported in the literature. This paper investigates flow over fixed and transversely oscillating two-dimensional rough cylinders with different roughness heights and spacing. A novel multi-block-multi-mesh framework-based immersed boundary method is developed to resolve the roughness elements over the cylinder surface, using a relatively coarser mesh at the outer domain. Small re-circulation zones trapped inside the roughness elements are captured. A drastic reduction in skin-friction drag is observed due to these vortices for both fixed and oscillating cylinders. Higher roughness height resulted in better lock-in phenomena at lower oscillation frequencies. However, the vortex shedding modes did not show much sensitivity to surface roughness.

On the relationship between manipulated inter-scale phase and energy-efficient turbulent drag reduction

We investigate the role of inter-scale interactions in the high-Reynolds-number skin-friction drag reduction strategy reported by Marusic et al. (Nat. Commun., vol. 12, 2021). The strategy involves imposing relatively low-frequency streamwise travelling waves of spanwise velocity at the wall to actuate the drag generating outer scales. This approach has proven to be more energy efficient than the conventional method of directly targeting the drag producing inner scales, which typically requires actuation at higher frequencies. Notably, it is observed that actuating the outer scales at low frequencies leads to a substantial attenuation of the major drag producing inner scales, suggesting that the actuations affect the nonlinear inner–outer coupling inherently existing in wall-bounded flows. In the present study, we find that increased drag reduction, through imposition of spanwise wall oscillations, is always associated with an increased coupling between the inner and outer scales. This enhanced coupling emerges through manipulation of the phase relationships between these triadically linked scales, with the actuation forcing the entire range of energy-containing scales, from the inner (viscous) to the outer (inertial) scales, to be more in phase. We also find that a similar enhancement of this nonlinear coupling, via manipulation of the inter-scale phase relationships, occurs with increasing Reynolds number for canonical turbulent boundary layers. This indicates improved efficacy of the energy-efficient drag reduction strategy at very high Reynolds numbers, where the energised outer scales are known to more strongly superimpose and modulate the inner scales. Leveraging the inter-scale interactions, therefore, offers a plausible mechanism for achieving energy-efficient drag reduction at high Reynolds numbers.

Airfoil Friction Drag Reduction with Net Power Savings Using Pulsed-Direct-Current Plasma Actuation

This paper reports the results of experiments in which flush-mounted pulsed-direct-current plasma actuator arrays were used to achieve skin-friction drag reduction on a NACA 63012A airfoil at a zero attack angle over the Mach number range of corresponding to a chord Reynolds number range of . The objective of the experiments was to document both the level of drag reduction and the net power savings achievable over this Mach number range. The arrays were designed to produce a spanwise array of opposed wall jets confined to the turbulent boundary-layer buffer region. These served to intervene in the autonomous near-wall mechanism that produces buffer-layer streamwise vorticity and is largely responsible for high levels of friction drag. It was demonstrated that the actuator array produces unprecedented levels of friction drag reduction with significant net power savings. Perhaps most interesting was the observation that the actuator authority has to be reduced for increased Mach numbers in order to keep the wall jets confined to the turbulent boundary-layer buffer region. This gave rise to a net power savings that scaled as . Unlike many previous experiments with plasma actuators, these results show that this form of flow control would not be authority limited in actual flight applications.

Bio-inspired Surface Texture Fluid Drag Reduction using Large Eddy Simulation

Skin friction drag can be reduced through the application of bio-inspired riblet surfaces. Numerical simulations were performed using Large Eddy Simulation (LES) to investigate the effect of using riblets on reducing skin friction drag. In this study, three different riblet configurations were used; scalloped, sawtooth and a new design, hybrid, riblet. To validate the effect of using the proposed hybrid riblet design compared with other riblets used in the literature; before applying to complex geometries, they were initially applied to a flat plate in parallel arrangement. Results showed skin friction coefficient reduction of 14% using the proposed hybrid riblet. This reduction was 9.2 times and 1.2 times more compared to sawtooth and scalloped configurations, respectively. The hybrid riblet was then applied partially and fully to NACA 0012 airfoil. Skin friction coefficient reduction of 34.5% was obtained when the hybrid riblet fully applied on the airfoil surface. Furthermore, the Convergent-Divergent (C-D) arrangement was studied, where the riblets were placed fully on the NACA 0012 and aligned with a yaw angle with respect to the flow direction. The convergent lines are inspired by the sensory part of the shark skin, whereas the divergent lines or herringbone are found on the bird feather. The two different riblet configurations, sawtooth and hybrid were modeled with the C-D arrangement and the hybrid riblet with C-D arrangement contributed to higher skin friction coefficient reduction, 34.5%, than the sawtooth riblet shape, 26.75%. Moreover, the C-D arrangement was compared to the parallel arrangement and shown that the C-D arrangement increased the lift coefficient (cl) of the airfoil, the flow separation was delayed and the overall performance of the airfoil was enhanced.

Phononic-subsurface flow stabilization by subwavelength locally resonant metamaterials

The interactions between a solid surface and a fluid flow underlie dynamical processes relevant to air, sea, and land vehicle performance and numerous other technologies. Key among these processes are unstable flow disturbances that contribute to fundamental transformations in the flow field. Precise control of these disturbances is possible by introducing a phononic subsurface (PSub). This comprises locally attaching a finite phononic structure nominally perpendicular to an elastic surface exposed to the flowing fluid. This structure experiences ongoing excitation by an unstable flow mode, or more than one mode, traveling in conjunction with the mean flow. The excitation generates small deformations at the surface that trigger elastic wave propagation within the structure, traveling away from the flow and reflecting at the end of the structure to return to the fluid-structure interface and back into the flow. By targeted tuning of the unit-cell and finite-structure characteristics of the PSub, the returning waves may be devised to resonate and reenter the flow out of phase, leading to significant destructive interference of the continuously incoming flow waves near the surface and subsequently to their attenuation over the spatial extent of the control region. This entire mechanism is passive, responsive, and engineered offline without needing coupled fluid-structure simulations; only the flow instability’s frequency, wavelength, and overall modal characteristics must be known. Disturbance stabilization in a wall-bounded transitional flow leads to delay in laminar-to-turbulent transition and reduction in skin-friction drag. Destabilization is also possible by alternatively designing the PSub to induce constructive interference, which is beneficial for delaying flow separation and enhancing chemical mixing and combustion. In this paper, we present a PSub in the form of a locally resonant elastic metamaterial, designed to operate in the elastic subwavelength regime and hence being significantly shorter in length compared to a phononic-crystal-based PSub. This is enabled by utilizing a sub-hybridization resonance. Using direct numerical simulations of channel flows, both types of PSubs are investigated, and their controlled spatial and energetic influence on the wall-bounded flow behavior is demonstrated and analyzed. We show that the PSub’s effect is spatially localized as intended, with a rapidly diminishing streamwise influence away from its location in the subsurface.

Drag reduction by means of an array of staggered circular cavities at moderate Reynolds numbers

Further insight into the physics of boundary layers developing over an array of circular cavities at moderate Reynolds numbers (Reθ up to 3400) is gained from hot wire boundary layer surveys on a range of parameters. The findings are consistent with literature as to the possibility of reducing skin friction drag with circular perforations. The results evidence a modification of the mean velocity profile, an increase of the wake parameter and the shape factor associated to a decrease of the skin friction. The modifications of the boundary layer as well as the skin friction reduction are more pronounced when the open area ratio is increased, which is achieved by increasing the cavity diameter or equivalently by decreasing the inter-cavity spacing. The turbulent activity is shifted in the upward direction, the burst intensity decreases in the buffer layer (10<Y+<35) and increases in the upper part of the logarithmic region/beginning of outer layer (80<Y+<200) with the formation of an outer peak in the turbulence intensity profile. The premultiplied spectra and the streamwise shear stress profiles evidence an energy surplus in the same part of the boundary layer and for the highest open area ratios a “bi-hump” behaviour. The formation of outer quasi-streamwise rollers is believed to be the cause of this energy hump in the spectrum. The turbulence statistics show a striking similarity with the turbulent boundary layer in presence of wall-normal blowing. It is believed that the cavities promote a vertical velocity component that displaces the turbulent activity towards the outer region. Different hypotheses to explain the modification of the flow statistics are detailed in the paper.

Reinforcement learning of control strategies for reducing skin friction drag in a fully developed turbulent channel flow

Reinforcement learning is applied to the development of control strategies in order to reduce skin friction drag in a fully developed turbulent channel flow at a low Reynolds number. Motivated by the so-called opposition control (Choi et al., J. Fluid Mech., vol. 253, 1993, pp. 509–543), in which a control input is applied so as to cancel the wall-normal velocity fluctuation on a detection plane at a certain distance from the wall, we consider wall blowing and suction as a control input, and its spatial distribution is determined by the instantaneous streamwise and wall-normal velocity fluctuations at distance 15 wall units above the wall. A deep neural network is used to express the nonlinear relationship between the sensing information and the control input, and it is trained so as to maximize the expected long-term reward, i.e. drag reduction. When only the wall-normal velocity fluctuation is measured and a linear network is used, the present framework reproduces successfully the optimal linear weight for the opposition control reported in a previous study (Chung &amp; Talha, Phys. Fluids, vol. 23, 2011, 025102). In contrast, when a nonlinear network is used, more complex control strategies based on the instantaneous streamwise and wall-normal velocity fluctuations are obtained. Specifically, the obtained control strategies switch abruptly between strong wall blowing and suction for downwelling of a high-speed fluid towards the wall and upwelling of a low-speed fluid away from the wall, respectively. Extracting key features from the obtained policies allows us to develop novel control strategies leading to drag reduction rates as high as 37 %, which is higher than the 23 % achieved by the conventional opposition control at the same Reynolds number. Finding such an effective and nonlinear control policy is quite difficult by relying solely on human insights. The present results indicate that reinforcement learning can be a novel framework for the development of effective control strategies through systematic learning based on a large number of trials.

Turbulent Drag Reduction by Travelling Waves of Spanwise Lorentz Force

Travelling waves induced by spanwise Lorentz force for skin-friction drag reduction are studied in the present work using direct numerical simulations, with particular focus on the streamwise and spanwise travelling waves. The overall picture of drag reduction in the frequency-wavenumber parameter space, omega -kappa _x-kappa _z is uncovered. It is found that both drag reduction maps for the streamwise and spanwise travelling waves are featured with a drag reduction (mathcal{D}mathcal{R}) region and a drag increase (mathcal{D}mathcal{I}) region. For the streamwise travelling wave of spanwise Lorentz force, the mathcal{D}mathcal{R} and mathcal{D}mathcal{I} regions are located in the same parameter regime compared to that of the streamwise travelling wave of spanwise wall velocity, while for the spanwise travelling wave, the mathcal{D}mathcal{R} variation at any fixed kappa _z is similar to that of spanwise oscillating Lorentz force. An exploration of the oblique travelling wave with an angle to the mean flow shows that the optimal drag reduction appears when the wave travels backward relative to the flow direction, and the "ribbon" structure is a general phenomenon appearing in all oblique travelling wave cases. The ensemble averaged positive and negative quasi-streamwise vortices become asymmetric when the travelling wave is imposed, and the near-wall high- and low-speed streaks are significantly tilted in the spanwise direction. Spanwise oscillation, streamwise and spanwise travelling waves share strong similarity in the statistics, energy spectra as well as turbulent structure modulation.

Skin-friction drag reduction by axial oscillations of the inner cylinder in turbulent Taylor–Couette flows

Skin-friction drag reduction by axial oscillations of an inner cylinder is numerically investigated at radius ratio (η = 0.5) using direct numerical simulation. In the present study, at fixed optimal oscillating period, the effect of oscillating amplitude on skin-friction drag reduction is investigated in detail. Furthermore, the effect of Reynolds number (ranging from 1000 to 5000) is also investigated. Our results show that as we keep increasing the oscillating amplitude, the drag reduction first increases and then decreases after a critical threshold dependent on the considered Reynolds number. Crossing the threshold value leads to re-organization of flow into a patchy turbulent state with large presence of small-scale structures. With increasing oscillating amplitude, the near-wall high and low-speed streaks get skewed in the θ–z plane followed by break down of high-speed streaks. Spatial density of the vortical structure decreases till threshold amplitude while the quadrant analysis shows that the movement of high-speed fluid away from walls plays an important role in the attenuation of Reynolds shear stresses.

Time-Series-Data Interpolation Applied to Boundary-Layer Profiles Measured on Different Flights

Turbulent boundary-layer profiles on an aircraft surface were measured during flight by pitot rakes in an experiment at subsonic speeds. Because separate flights have different flight sequences in terms of time, it is not easy to compare boundary-layer profiles measured on different flights with the corresponding premised conditions directly. Using one flight as a reference, this paper proposes a method to find the closest flight condition for each time instance from data from other flights by calculating a residual norm in combinations of flight variables. The results show that the proposed method successfully finds the best matches of the time instances from the second flight with those of the first flight. In addition, applying the interpolation method using response surface methodology further improves the accuracy of evaluation in the flight range of Mach 0.4 to Mach 0.8. The total uncertainty level of the proposed interpolation method was found to be 5.7%. Although this level of uncertainty is expected to be reduced, the effectiveness of the proposed interpolation method was presented in conjunction with an evaluation of its applicability to determine the riblet effect in reducing skin-friction drag qualitatively.

Optimisation and Analysis of Streamwise-Varying Wall-Normal Blowing in a Turbulent Boundary Layer

Skin-friction drag is a major engineering concern, with wide-ranging consequences across many industries. Active flow-control techniques targeted at minimising skin friction have the potential to significantly enhance aerodynamic efficiency, reduce operating costs, and assist in meeting emission targets. However, they are difficult to design and optimise. Furthermore, any performance benefits must be balanced against the input power required to drive the control. Bayesian optimisation is a technique that is ideally suited to problems with a moderate number of input dimensions and where the objective function is expensive to evaluate, such as with high-fidelity computational fluid dynamics simulations. In light of this, this work investigates the potential of low-intensity wall-normal blowing as a skin-friction drag reduction strategy for turbulent boundary layers by combining a high-order flow solver (Incompact3d) with a Bayesian optimisation framework. The optimisation campaign focuses on streamwise-varying wall-normal blowing, parameterised by a cubic spline. The inputs to be optimised are the amplitudes of the spline control points, whereas the objective function is the net-energy saving (NES), which accounts for both the skin-friction drag reduction and the input power required to drive the control (with the input power estimated from real-world data). The results of the optimisation campaign are mixed, with significant drag reduction reported but no improvement over the canonical case in terms of NES. Selected cases are chosen for further analysis and the drag reduction mechanisms and flow physics are highlighted. The results demonstrate that low-intensity wall-normal blowing is an effective strategy for skin-friction drag reduction and that Bayesian optimisation is an effective tool for optimising such strategies. Furthermore, the results show that even a minor improvement in the blowing efficiency of the device used in the present work will lead to meaningful NES.