Mean Skin Friction Coefficient Research Articles

Evolution of Air Plastron Thickness and Slip Length over Superhydrophobic Surfaces in Taylor Couette Flows

Drag reduction (DR) using superhydrophobic surfaces (SHSs) has received intensive interest due to the emergence of SH coating technology. The air layer (plastron “δ”) trapped between the SHS and the water controls the flow slip over the SHSs. We demonstrate slippage over three fabricated SHSs in laminar and low turbulent Taylor–Couette flows. We experimentally investigate how the slip length increases with a higher Reynolds number (Re) over the tested SHSs; simultaneously, the air plastron thickness investigates using a viscous model. The mean skin friction coefficient (Cf) can be fitted to a modified semi-empirical logarithmic law expressed in the Prandtl–von Kármán coordinate. An effective slip length is estimated in the 35–41 µm range with an achieved 7–11% DR for the tested surfaces. Statistical analysis is used to develop a regression model from the experimental data. The model shows an R2 of 0.87 and good agreement with the experimental data. This shows the relation between the dimensionless slip length (b+), the dimensionless plastron thickness (δ+), and the Reynolds number, which is directly proportional. The regression model shows that b+ and Reynolds numbers have a higher impact on the δ+ than the surface wettability, which attribute to the small difference in the wetting degree between the three tested surfaces. The practical importance of the work lies in its ability to provide a deep understanding of the reduction in viscous drag in numerous industrial applications. Furthermore, this research serves as a groundwork for future studies on hydrophobic applications in internal flows.

Comparison of the mean skin friction with the heat transfer and the flow development in turbulent planar wall-attaching jet flows.

Measurements of the mean skin friction below turbulent planar wall-attaching offset jet flows were performed using oil-film interferometry for jets initially offset (Hs) 0.2 to 1 times the jet height (Hj) from the wall. The results were compared with turbulent flow field measurements and with previous heat transfer measurements. The profiles of the mean skin friction coefficient below the offset or preattachment region were similar when compared relative to the distance to the reattachment location (Xr). The initial recovery length of the mean skin friction downstream of the reattachment location was proportional to the reattachment length similar to the decrease in the wall pressure fluctuations in this region. The longer recovery and initial decay of the mean skin friction coefficient appeared to collapse in terms of (x-Xr)/Hj; as did the initial change in the mean static pressure, the measures of the mean flow development, and the Stanton number downstream of the reattachment point. The decay in the maximum of the turbulent stresses associated with the attached shear layer also collapsed in terms of (x-Xr)/Hj, unlike the fluctuating pressure and initial recovery of the mean skin friction. The change in the location of the minimum and zero in the turbulent shear stress as the flows transitioned to the wall jet region collapse in terms of x-Xr/Hj similar to the longer recovery and initial decay of the mean skin friction. The mean skin friction for flows with Hs of Hj and jet Reynolds numbers (Rej) of 21800 to 54500, varied as Rej-0.2 below the attaching jet, in the reattachment region, and in the downstream wall jet region.

Analysis of the Contribution of Large Scale Motions to the Skin Friction of a Zero-Pressure-Gradient Turbulent Boundary Layer Using the Renard-Deck Decomposition

Coherent flow structures in turbulent boundary layers have been an active field of research for many decades, as they might be the key to reveal the mechanics of turbulence production and transport in turbulent shear flows. Renard and Deck (2016) proposed a theoretical decomposition for the mean skin-friction coefficient based on the mean kinetic energy budget in the streamwise direction. This decomposition, referred to as the Renard-Deck (RD) decomposition, decomposes the mean skin friction generation into three physical mechanisms in an absolute reference frame, namely, direct viscous dissipation, turbulent kinetic energy production, and spatial growth. In this study, the large scale motions (LSMs) are extracted using a proper orthogonal decomposition (POD) of the velocity field based on high-spatial-resolution two-dimensional – two-component particle image velocimetry (HSR 2C-2D PIV) of a zero-pressure-gradient turbulent boundary layer (ZPG-TBL), and their effect on the skin friction via RD decomposition.

Time-Dependent Nonlinear Finite Difference Analysis of Buoyancy-Driven Convective Flow over an Oscillating Porous Moving Vertical Cylinder

The thermal and mass boundary layer flow of a time-dependent isochoric viscous fluid over an oscillating cylinder entrenched in a porous medium is investigated numerically. The governing problem contains a set of coupled nonlinear partial differential equations with significant initial and boundary conditions and are solved using an implicit finite difference scheme, namely Crank–Nicholson method. The importance of physical parameters on velocity profiles, temperature profiles, concentration profiles, local skin-friction coefficient, mean skin-friction coefficient, local Nusselt number, mean Nusselt number, local Sherwood number and mean Sherwood number is explained in detail and is depicted graphically. The validation of these results is verified with the existing results, and it is correlated well.

Nonlinearly most dangerous disturbance for high-speed boundary-layer transition

Laminar-to-turbulent transition in a zero-pressure-gradient boundary layer at Mach 4.5 is studied using direct numerical simulations. For a given level of total disturbance energy, the inflow spectrum was designed to correspond to the nonlinearly most dangerous condition that leads to the earliest possible transition Reynolds number. The synthesis of the inlet disturbance is formulated as a constrained optimization, where the control vector is comprised of the amplitudes and relative phases of the inlet modes; the constraints are the prescribed total energy and that the flow evolution satisfies the full nonlinear compressible Navier–Stokes equations; the cost function is defined in terms of the mean skin-friction coefficient and, once maximized, ensures the earliest possible transition location. An ensemble-variational (EnVar) technique is developed to solve the optimization problem. Starting from an initial guess, here a broadband disturbance, EnVar updates the estimate of the control vector at the end of each iteration using the gradient of the cost function, which is evaluated from the outcomes of an ensemble of possible solutions. Two inflow conditions are computed, each corresponding to a different level of energy, and their spectra are contrasted: the lower-energy case includes two normal acoustic waves and one oblique vorticity perturbation, whereas the higher-energy condition consists of oblique acoustic and vorticity waves. The focus is placed on the former case because it cannot be categorized as any of the classical breakdown scenarios (fundamental, subharmonic or oblique), while the higher-energy condition undergoes a second-mode oblique transition. At the lower energy level, the instability wave that initiates the rapid breakdown to turbulence is not present at the inlet plane. Instead, it appears at a downstream location after a series of nonlinear interactions that spur the fastest onset of turbulence. The results from the nonlinearly most potent inflow condition are also compared to other inlet disturbances that are selected solely based on linear theory, and which all yield relatively delayed transition onset.

Drag enhancement and turbulence attenuation by small solid particles in an unstably stratified turbulent boundary layer

Point-particle direct numerical simulations of particle-laden flows have been conducted to investigate the complex coupling between inertial particles, buoyancy force, and strong shear flows in an unstably stratified turbulent boundary layer over a flat plate. Two-way coupling and particle-particle collisions, i.e., four-way coupling, are considered in the dilute gas-solid flows. The simulation results indicate that the presence of inertial particles with diameter smaller than the Kolmogorov length scale tends to reduce the thermal displacement thickness and enthalpy thickness, while increasing the mean skin-friction coefficient and Nusselt number. The feedback force exerted by the particles on the fluid is found to contribute largely to the drag enhancement. The turbulence intensities and temperature fluctuations are significantly attenuated in the particle-laden flows with respect to the unladen flow. The budgets of the turbulent kinetic energy show that the particles have direct and indirect effects on the modulation of turbulence. On the one hand, the production and the viscous dissipation rate are suppressed by the particles in most regions of the boundary layer. On the other hand, the particle-turbulence interactions produce an extra energy source in the inner layer, while causing an additional energy sink in the outer layer of the boundary layer. These combined effects lead to the pronounced turbulence attenuation observed in this study.

THERMAL AND MASS DIFFUSIVE STUDIES ON A MOVING CYLINDER ENTRENCHED IN A POROUS MEDIUM

A numerical investigation is accomplished for an unsteady laminar free convective flow of a viscous incompressible fluid over an impulsively started semi-infinite vertical cylinder embedded in a porous medium. The level of temperature and concentration at the surface area of the cylinder are assumed to vary as functions of power law type, in the axial coordinate. The problem is governed by a system of coupled nonlinear boundary layer equations with appropriate variable surface boundary conditions and the numerical results are obtained using an implicit finite difference scheme of Crank-Nicholson type. The effects of physical parameters on velocity, temperature and concentration profiles and also on local and mean skin-friction coefficient, Nusselt number and Sherwood number are interpreted graphically. It is observed that the variable temperature and concentration exists in the boundary of cylinder relegates the rate of heat and mass transfer.

Investigation of turbulence and skin friction modification in particle-laden channel flow using lattice Boltzmann method

Interaction between turbulence and particles is investigated in a channel flow. The fluid motion is calculated using direct numerical simulation (DNS) with a lattice Boltzmann (LB) method, and particles are tracked in a Lagrangian framework through the action of force imposed by the fluid. The particle diameter is smaller than the Kolmogorov length scale, and the point force is used to represent the feedback force of particles on the turbulence. The effects of particles on the turbulence and skin friction coefficient are examined with different particle inertias and mass loadings. Inertial particles suppress intensities of the spanwise and wall-normal components of velocity, and the Reynolds shear stress. It is also found that, relative to the reference particle-free flow, the overall mean skin-friction coefficient is reduced by particles. Changes of near wall turbulent structures such as longer and more regular streamwise low-speed streaks and less ejections and sweeps are the manifestation of drag reduction.

Use of a rotating cylinder to induce laminar and turbulent separation over a flat plate

An innovative and easy technique using a rotating cylinder system has been implemented in a water tunnel experiment to generate an adverse pressure gradient (APG). The strength of the APG was varied through adjustment in the rotation speed and location of the cylinder. Then the technique was used for inducing a laminar separation bubble (LSB) and turbulent boundary layer (TBL) separation over a flat plate. A theoretical model to predict the pressure variation induced on the plate consists of an inviscid flow over a reverse doublet-like configuration of two counter rotating cylinders. This model quantified the pressure distribution with changes of cylinder speed and location. The dimensionless velocity ratio (VR) of the cylinder rotation rate to the mainstream velocity and gap to diameter ratio were chosen as the two main ways of varying the strength of the APG, which affects the nature and extent of the LSB as well as TBL separation. The experimental parametric study, using time-resolved digital particle image velocimetry, was then conducted in a water tunnel. The variation in height (h), length (l), and the separation point (S) of the LSB was documented due to the variation in the APG. The similar type of experimental parametric study was used to explore the unsteady, turbulent separation bubble in a 2D plane aligned with the flow and perpendicular to the plate. The mean detachment locations of TBL separation are determined by two different definitions: (i) back-flow coefficient (χ) = 50%, and (ii) location of start of negative mean skin friction coefficient (Cf). They are in good agreement and separation bubble characteristics agreed well with results obtained using different methods thus proving the validity of the technique.

Experimental investigation of influence of Reynolds number on synthetic jet vortex rings impinging onto a solid wall

Time-resolved particle image velocimetry was employed to study the effect of Reynolds number (Re sj) on synthetic jet vortex rings impinging onto a solid wall. Four Reynolds numbers ranging from 166 to 664 were investigated for comparison while other parameters were kept constant. It is found that the Reynolds number has a significant impact on the spatial evolution of near-wall vortical structures of the impinging synthetic jet. Velocity triple decomposition reveals that periodic Reynolds shear stresses produced by both impinging and secondary vortex rings agree well with a four-quadrant-type distribution rule, and the random velocity fluctuations are strengthened as Re sj increases. For radial wall jet, radial velocity profiles exhibit a self-similar behavior for all Re sj, and this self-similar profile gradually deviates from the laminar solution as Re sj is increased. In particular, the self-similar profile for low Re sj (166) coincides with the laminar solution indicating that periodic velocity fluctuations produced by vortex rings have little effect on the velocity profile of the laminar wall jet. This also provides evidence that the impinging synthetic jet is more effective in mixing than the continuous jet for the laminar flow. For the high Re sj, the mean skin friction coefficient has a slower decay rate after reaching peak, and the radial momentum flux has a higher value at locations far away from the impingement region, both of these can be attributed to the enhanced random fluctuations.

Air Blowing Into Boundary Layer Of A Flat Plate With Length-Dependent Permeability

A generalized analysis of the results of numerical and experimental studies of air blowing into a turbulent boundary layer through finely perforated surface consisting of alternating permeable and impermeable sections of varying length providing a sudden change in the flow conditions at the boundaries of these sections is presented. The air blowing coefficient Cb determined by the mass flow rate per unit area of the active perforated sample varied in the range from 0 to 0.008. It is shown that as Cb grows, the maximum reduction in the mean surface skin-friction coefficient CF, which is the value through the permeable area of perforated sample, reaches about 65 %. When keeping the equal mass flow rate Q for all tested combinations, the mean skin-friction coefficient remains constant, independent of geometrical parameters of permeable and impermeable sections. Increasing the length of the last permeable section leads to the growth of relaxation region which is characterized by the reduced skin friction values on the impermeable part of the flat plate.

Particle statistics in a two-way coupled turbulent boundary layer flow over a flat plate

In the present study, we investigate heavy solid particle statistics in a spatially developing turbulent boundary layer over a flat plate using the two-way coupled Eulerian-Lagrangian point-particle approach. The particles are much smaller than the Kolmogorov length scale in the dilute gas-solid flow. The simulation results show that the particle streamwise fluctuating velocity exceeds the fluid streamwise fluctuating velocity across the entire boundary layer. In the wall-normal and spanwise directions, however, the velocity fluctuations of the particles generally tend to be lower than those of the fluid. Moreover, the particle wall-normal and spanwise fluctuating velocities decrease monotonically with particle Stokes number and mass loading. In addition, it is found that the spatial evolution of the particle wall concentration along the streamwise direction is similar to that of the mean skin-friction coefficient. These new findings are of great importance in the industrial and environmental applications.

Vortex dynamics and wall shear stress behaviour associated with an elliptic jet impinging upon a flat plate

Vortical structures and dynamics of a Re h = 2100 elliptic jet impinging upon a flat plate were studied at H/d h = 1, 2 and 4 jet-to-plate separation distances. Flow investigations were conducted along both its major and minor planes using laser-induced fluorescence and digital particle image velocimetry techniques. Results show that the impingement process along the major plane largely consists of primary jet ring-vortex and wall-separated secondary vortex formations, where they subsequently separate from the flat plate at smaller H/d h = 1 and 2 separation distances. Key vortex formation locations occur closer to the impingement point as the separation distance increases. Interestingly, braid vortices and rib structures begin to take part in the impingement process at H/d h = 4 and wave instabilities dominate the flow field. In contrast, significantly more coherent primary and secondary vortices with physically larger vortex core sizes and higher vortex strengths are observed along the minor plane, with no signs of braid vortices and rib structures. Lastly, influences of these different flow dynamics on the major and minor plane instantaneous and mean skin friction coefficient levels are investigated to shed light on the effects of separation distance on the wall shear stress distributions.

Large-scale motions in a turbulent channel flow with the slip boundary condition

Direct numerical simulation (DNS) of a turbulent channel flow with the slip boundary condition was performed to investigate the spatial characteristics of large-scale motions (LSMs) in a drag-reducing flow and the influence of LSMs on drag reduction. The slip boundary condition was applied in the streamwise direction. DNS of a channel flow with the no-slip boundary condition was also conducted for comparison. The overall mean skin-friction coefficient of the flow with the slip boundary condition was reduced by 35% relative to the flow with the no-slip condition at the same bulk Reynolds number of 10,333. The streamwise and spanwise length scales of the LSMs in the outer region are larger with the slip boundary condition than with the no-slip condition due to a large population of long LSMs. These LSMs influence the near-wall region via roll-cell motions and footprints. Although the number of total streaks decreases, a portion of the footprints increases due to the influence of the outer LSMs. The streamwise vorticities around the low-speed footprints are attenuated more than those around the high-speed footprints. The LSMs and the near-wall footprints contribute 45% of the total reduction in the skin friction coefficient, with 25% of this contribution due to low-speed LSMs.

A theoretical decomposition of mean skin friction generation into physical phenomena across the boundary layer

A theoretical decomposition of mean skin friction generation into physical phenomena across the whole profile of the incompressible zero-pressure-gradient smooth-flat-plate boundary layer is derived from a mean streamwise kinetic-energy budget in an absolute reference frame (in which the undisturbed fluid is not moving). The Reynolds-number dependences in the laminar and turbulent cases are investigated from direct numerical simulation datasets and Reynolds-averaged Navier–Stokes simulations, and the asymptotic trends are consistently predicted by theory. The generation of the difference between the mean friction in the turbulent and laminar cases is identified with the total production of turbulent kinetic energy (TKE) in the boundary layer, represented by the second term of the proposed decomposition of the mean skin friction coefficient. In contrast, the analysis introduced by Fukagataet al.(Phys. Fluids, vol. 14 (11), 2002, pp. 73–76), based on a streamwise momentum budget in the wall reference frame, relates the turbulence-induced excess friction to the Reynolds shear stress weighted by a linear function of the wall distance. The wall-normal distribution of the linearly-weighted Reynolds shear stress differs from the distribution of TKE production involved in the present discussion, which consequently draws different conclusions on the contribution of each layer to the mean skin friction coefficient. At low Reynolds numbers, the importance of the buffer-layer dynamics is confirmed. At high Reynolds numbers, the present decomposition quantitatively shows for the first time that the generation of the turbulence-induced excess friction is dominated by the logarithmic layer. This is caused by the well-known decay of the relative contributions of the buffer layer and wake region to TKE production with increasing Reynolds numbers. This result on mean skin friction, with a physical interpretation relying on an energy budget, is consistent with the well-established general importance of the logarithmic layer at high Reynolds numbers, contrary to the friction breakdown obtained from the approach of Fukagataet al.(Phys. Fluids, vol. 14 (11), 2002, pp. 73–76), essentially based on a momentum budget. The new decomposition suggests that it may be worth investigating new drag reduction strategies focusing on TKE production and on the nature of the logarithmic layer dynamics. The decomposition is finally extended to the pressure-gradient case and to channel and pipe flows.

A Comparative Study of Fluid Flow and Mass Transfer in a Trumpet-Shaped Ladle Shroud Using Large Eddy Simulation

The advantages of trumpet-shaped ladle shrouds (TLS) have been frequently demonstrated over conventional straight-bore ladle shrouds (CLS) with respect to production efficiency and molten steel quality in continuous casting practices. The present study is to shed some lights on why the TLS are better than the CLS design by examining the fluid dynamics and mass transfer using large eddy simulation. The obtained numerical results were validated with particle imaging velocimetry experiments. Flow velocity, deformation, turbulent energy dissipation, and mixing kinetics of tracer were discussed. The results showed that the entering jet of the CLS flowed straight down into the tundish with a relatively high speed (average at 0.710 to 0.815 m/s) and turbulent kinetic energy. However, the trumpet section of a TLS intensified velocity differences, strain rates, and vortices, and promoted an increase on turbulence dissipation rate in the interior of the ladle shroud. The average speed of the entering jet to the tundish was decreased to 0.270 to 0.410 m/s from the 0.708 m/s of the inlet speed. The entering jet from the TLS swung, twisted and well mixed with surrounding fluid in the tundish, and dissipated its kinetic energy. Consequently, the turbulence of the whole flow field as well as the mean skin friction coefficient of tundish wall and the velocity of free liquid surface were reduced. A tracer experiment was carried out to study mass transfer and flow mixing behavior, and the results demonstrated that the use of the TLS increased the plug volume and decreased the dead zone, thereby enhancing inclusion flotation.

Sustainable drag reduction in turbulent Taylor-Couette flows by depositing sprayable superhydrophobic surfaces.

We demonstrate a reduction in the measured inner wall shear stress in moderately turbulent Taylor-Couette flows by depositing sprayable superhydrophobic microstructures on the inner rotor surface. The magnitude of reduction becomes progressively larger as the Reynolds number increases up to a value of 22% at Re=8.0×10(4). We show that the mean skin friction coefficient C(f) in the presence of the superhydrophobic coating can be fitted to a modified Prandtl-von Kármán-type relationship of the form (C(f)/2)(-1/2)=Mln (Re(C(f)/2)(1/2))+N+(b/Δr)Re(C(f)/2)(1/2) from which we extract an effective slip length of b≈19 μm. The dimensionless effective slip length b(+)=b/δ(ν), where δ(ν) is the viscous length scale, is the key parameter that governs the drag reduction and is shown to scale as b(+)∼Re(1/2) in the limit of high Re.

Turbulence and skin friction modification in channel flow with streamwise-aligned superhydrophobic surface texture

Direct numerical simulations of turbulent flow in a channel with superhydrophobic surfaces (SHS) were performed, and the effects of the surface texture on the turbulence and skin-friction coefficient were examined. The SHS is modeled as a planar boundary comprised of spanwise-alternating regions of no-slip and free-slip boundary conditions. Relative to the reference no-slip channel flow at the same bulk Reynolds number, the overall mean skin-friction coefficient is reduced by 21.6%. A detailed analysis of the turbulence kinetic energy budget demonstrates a reduction in production over the no-slip phases, which is explained by aid of quadrant analysis of the Reynolds shear stresses and statistical analysis of the turbulence structures. The results demonstrate a significant reduction in the strength of streamwise vortical structures in the presence of the SHS texture and a decrease in the Reynolds shear-stress component ⟨R12⟩ which has a favorable influence on drag over the no-slip phases. A secondary flow which is set up at the edges of the texture also effects a beneficial change in drag. Nonetheless, the skin-friction coefficient on the no-slip features is higher than the reference levels in a simple no-slip channel flow. The increase in the skin-friction coefficient is attributed to two factors. First, spanwise diffusion of the mean momentum from free-slip to no-slip regions increases the local skin-friction coefficient on the edges of the no-slip features. Second, the drag-reducing capacity of the SHS is further reduced due to additional Reynolds stresses, ⟨R13⟩.

Large eddy simulation of unsteady transitional flow on the low-pressure turbine blade

The aim of this paper is to predict the phenomenon of laminar separation, transition and reattachment in a low-pressure turbine (LPT). Self-developed large eddy simulation program of compressible N-S equations was used to describe the flow structures of T106A LPT blade profile at Reynolds number of 1.1×105 based on the exit isentropic velocity and chord length. The computational results show the distributions of time-averaged wall-static pressure coefficient and mean skin-friction coefficient on the blade surface. The locations of laminar separation and reattachment points occur around 87% and 98% axial chord, which agree well with experiment data. The two-dimensional shear layer is gradually unstable along the downstream half of the suction side as a result of the spanwise fluctuation and the roll up of shear layer via Kelvin-Helmholtz (KH) instability. Three-dimensional motions appear near 84% axial chord which later triggers spanwise vortexes and streamwise vortexes, leading to transition to turbulence in the separation bubble. Through introducing the concept of dissipation function, the high loss mainly comes from the places where strong shear layer and intense fluctuation exist. Furthermore, the separation region is only an accumulation center of the low-energy fluid rather than an area of loss source.

A211 円管内オリフィス板下流域の流れ場と壁面せん断応力 : レイノルズ数による影響(OS2 保全設備診断技術(3))

In the present study, the distributions of time-average and fluctuated wall shear stresses were measured using a flow vector sensor of MEMS and velocity downstream from an orifice using laser Doppler velocimetry. The air flow was supplied to a circular pipe from a blow-down wind tunnel. The diameter of the pipe were D = 51 mm, 100 mm and 194 mm. The diameter ratio were β (= d/D; d, diameter of orifice) = 0.41, 0.50 and 0.62. Near the wall in the recirculating region downstream from the orifice, the minimum mean skin friction coefficient was located at approximately x/h = 5, and the maximum RMS intensity skin friction coefficient at approximately x/h = 7. The absolute value of the minimum mean skin friction coefficient and the maximum RMS intensity skin friction coefficient decreased with increasing in Reynolds number. The similarity between skin friction coefficients of RMS and the FAC rate was confirmed.